Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique

Universidade do Minho Escola de Engenharia Antonio Romanazzi Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique December 2021 UMinho | 2021 Antonio Romanazzi Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique Antonio Romanazzi Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique Doctoral Thesis Civil Engineering Work concluded under the supervision of Professor Daniel V. Oliveira Doctor Rui A. Silva Universidade do Minho Escola de Engenharia December 2021 To my sister and my brother Umuntu, ngumuntu, ngabantu Despacho RT - 31 /2019 - Anexo 3 Declaração a incluir na Tese de Doutoramento (ou equivalente) ou no trabalho de Mestrado DIREITOS DE AUTOR E CONDIÇÕES DE UTILIZAÇÃO DO TRABALHO POR TERCEIROS Este é um trabalho académico que pode ser utilizado por terceiros desde que respeitadas as regras e boas práticas internacionalmente aceites, no que concerne aos direitos de autor e direitos conexos. Assim, o presente trabalho pode ser utilizado nos termos previstos na licença abaixo indicada. Caso o utilizador necessite de permissão para poder fazer um uso do trabalho em condições não previstas no licenciamento indicado, deverá contactar o autor, através do RepositóriUM da Universidade do Minho. Licença concedida aos utilizadores deste trabalho Atribuição-NãoComercial-CompartilhaIgual CC BY-NC-SA https://creativecommons.org/licenses/by-nc-sa/4.0/ IV Acknowledgements During this long experience, several persons contributed to make this thesis possible and to make me enjoy the work, and I would like to express my gratitude to all of them. At first, I want to express my gratitude to my supervisors Professor Daniel Oliveira and Dr. Rui Silva, for their fundamental support, suggestions, discussions, enthusiasm and encouragement. Thanks to them, I was able to further evolve beyond the professional level. Thanks to the entire staff of the Laboratory of Structures: Marco for his infinite patience, Mr. Gonçalves for teaching me all the secrets of the geotechnical analyses, Mr. Matos for teaching me whatever is possible to do in the lab for making the experiments to work (from welding to calibration of instruments), Cesar, Luciano and Carlos for their friendship and availability. I would like to thank the entire staff of the NESDE for their support during my period at the LNEC: Dr. Alfredo Campos Costa, Dr. Paulo Candeias, Dr. Alexandra Carvalho, Artur, Aurélio, Susana and Maria. I would like to thank all the Master students I had the opportunity to follow: Aidarbek, Michiel, Reza, and in particular Eduarda for her interesting discussions. A profound thanks to João Bernardino Lda. Construções Ecológicas for building the rammed earth mockups. Thanks to the Portuguese Science and Technology Foundation (FCT) for the scholarship with reference SFRH/BD/131006/2017 and for the funding provided through the project SafEarth - PTDC/ECMEST/2777/2014 (POCI-01-0145-FEDER-016737). I would like to thank all my friends from capoeira for their friendship and good times together: Morango, Cayma, Suri, Carpinta, Maracuja and Burití. I want to thank all my vimaranenses friends – Bea and Fra, Ali and Sepideh, Giorgos, Giogiò, Carla, Jacopo, Rafael, Maria Pia, Gianpaolo, Lidia – and my Italian supporters: Nicola, Tamara, Giorgio, Marco, Piero, Marco and Marco. I would like to thank the “earth team” with who I had the opportunity to have fun building whatever was possible to build with earth, between a beer and another: Carlo and Claudio. I want to thank those persons who became my second family and were there to support, discuss, smile, cheer and toast from the very first moment of this journey: Xinyu, Meera, Telma, Alberto, Rafael, Leslie, Elesban, Pilar, Fabio and Nicoletta. To them is all my gratitude. Thank you and never lose the fun! Thanks to my family, my father and my mother, my sisters and my brothers, and my niece. Without their support, this research would not have been the same. Thanks to all the persons who have been part, even for a short time, of this experience. Thanks to all the persons who will be there after this experience. Thanks to me for believing in this experience. Saravá! Despacho RT - 31 /2019 - Anexo 4 Declaração a incluir na Tese de Doutoramento (ou equivalente) ou no trabalho de Mestrado STATEMENT OF INTEGRITY I hereby declare having conducted this academic work with integrity. I confirm that I have not used plagiarism or any form of undue use of information or falsification of results along the process leading to its elaboration. I further declare that I have fully acknowledged the Code of Ethical Conduct of the University of Minho. VI Resumo A taipa é uma técnica construtiva difundida mundialmente, não só pelo património arquitectónico mas também pelos novos edifícios. Além disso, estima-se que cerca de um quarto da população mundial viva em habitações de terra crua. Contudo, as estruturas de taipa são caracterizadas por elevada vulnerabilidade sísmica, que combinada com o elevado risco sísmico das zonas em que se situam e a elevada exposição sísmica, resulta num risco sísmico associado bastante elevado. Apesar da crescente preocupação com o risco sísmico das construções de taipa, o seu comportamento sísmico requer ainda investigação, enquanto que se torna necessário o desenvolvimento de soluções de reforço adequadas para reduzir o risco de colapso e a consequente perda de vidas e de património cultural. Entre as várias técnicas de reforço, os rebocos armados (TRM) são amplamente utilizados em edifícios de alvenaria devido à sua eficácia. Apesar do reforço TRM em património construído em adobe ter demonstrado uma melhoria significativa da capacidade sísmica, pouca investigação foi ainda realizada sobre a utilização desta técnica no reforço de construções de taipa. Neste contexto, a presente tese pretende contribuir para o conhecimento da resposta sísmica de estruturas de taipa e avaliar a eficácia de várias soluções de reforço TRM, tendo em consideração a compatibilidade dos materiais. O extenso programa experimental executado incluiu primeiramente a análise geotécnica dos solos, usada posteriormente para definir as misturas de taipa e das argamassas à base de terra. Seguidamente, os diferentes materiais foram caracterizados, nomeadamente a taipa e os componentes dos reforços TRM (matriz e malha). Assim, as interações entre o TRM e a taipa foram investigadas por meio de ensaios de tração direta em cupons de TRM, ensaios de arranque ( pull-out ), ensaios de corte ( single-lap shear ) e ensaios de compressão diagonal em muretes de taipa. Com base nos resultados dos ensaios de arranque, foi deduzido um modelo analítico de tensão-escorregamento que inclui um novo parâmetro de dano. Para conhecer melhor a resposta ao corte das estruturas em taipa, foi realizado um ensaio de corte cíclico quási-estático numa parede de taipa, a qual foi posteriormente reforçada com a solução de TRM proposta e testada novamente. Finalmente, a resposta para fora do plano de paredes de taipa foi analisada por meio de um ensaio em mesa sísmica, realizado num modelo de taipa que foi posteriormente reforçado com TRM e testado novamente. De uma forma geral, os resultados demonstram que a solução proposta de reforço TRM melhorou a capacidade sísmica dos modelos de taipa em termos de deslocamentos e ductilidade, embora o dano e a resistência da estrutura não tivessem sido completamente recuperados. Palavras-chave: argamassa reforçada compatível, ensaio cíclico no plano, ensaio dínamico fora do plano, modelo analítico. VII Abstract Rammed earth construction is spread worldwide, not only as in architectural heritage but also as in new buildings. In addition, around one fourth of the global population is estimated to live in earth dwellings. However, rammed earth structures are characterised by high seismic vulnerability, which combined with the high seismic hazard of the areas where these buildings are located and high seismic exposure, turns into an associated high seismic risk. Despite the increasing concern for the seismic risk associated to rammed earth structures, the knowledge on their seismic response still requires further investigation, while adequate strengthening solutions are needed to reduce their risk of collapse and consequent loss of life and cultural heritage. Among the various seismic strengthening techniques, textile reinforced mortars (TRM) are widely accepted for masonry buildings because of their effectiveness. Although research on the use of TRM for adobe heritage demonstrated significant improvement of the seismic capacity, very few investigations have been conducted so far on TRM as a strengthening solution for rammed earth buildings. In this framework, the present thesis intends to cover the gap in knowledge on the seismic response of rammed earth structures and to assess the effectiveness of various TRMstrengthening solutions, while considering the compatibility of the materials. The extended experimental program conducted included at first the geotechnical analysis of the raw soils, which was later used to design the mixtures for rammed earth and earth-based mortars. Afterwards, the rammed earth material and each component (matrix and mesh) of the TRM-strengthening were characterised. Thus, the interactions between the TRM and the rammed earth were investigated by means of direct tensile tests on TRM coupons, pull-out tests, single-lap shear tests and diagonal compression tests of rammed earth wallets. Based on the pull-out observations, an analytical bond stress-slip law was inferred, while including a novel damage parameter. In order to gain further insight on the shear response of rammed earth structures, a quasi-static in-plane cyclic test was conducted on a rammed earth sub-assemblage, which subsequently was strengthened with the proposed TRM solution and tested again. Finally, the out-of-plane response of rammed earth walls was investigated by means of a shake table test of an un-strengthened mockup, which was also subsequently strengthened with TRM and tested again. The overall results demonstrate that the proposed TRM-strengthening solution effectively improved the seismic capacity of the rammed earth mockups in terms of displacements and ductility, despite the previous damage state and the resistance of the structure could not be completely recovered. Keywords: analytical model, compatible textile reinforced mortar, in-plane cyclic test, out-of-plane shake table test. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique XIV • 𝑝 Perimeter yarn • 𝑄 Relative axial stiffness between the matrix and fibre • RE_I Rammed earth mixture 1 • RE_II Rammed earth mixture 2 • ROI Region of interest • RS_I Raw soil 1 • RS_II Raw soil 2 • SL Atterberg Limit - Shrinkage limit • SLGM Single lap-shear test with glass fibre mesh • SLNM Single lap-shear test with nylon mesh • 𝑠(𝑥) Slip distribution along the interface • 𝑠 = 𝑢f− 𝑢m Slip at the interface matrix-fibre • 𝑠el Elastic slip • 𝑠ult Sliding at failure • TCGeoM Tensile test on coupon with geomesh • TCGM Tensile test on coupon with glass fibre mesh • TCNM Tensile test on coupon with nylon mesh • TEX Linear density • TRM Textile Reinforced Mortar • 𝑡 Thickness of the specimen • 𝑢el Displacement at end of elastic phase • 𝑢f Fibre deformation • 𝑢LEult Ultimate displacement at the loaded end • 𝑢m Matrix deformation • W/S Water content to dry weight ratio • 𝑤 Width of the specimen • 𝛾 Shear deformation • 𝛾ult Ultimate shear strain • 𝛾𝜏max Shear strain at shear strength • 𝜌 Density • ∆𝐻 Horizontal displacements Index of Symbols XV • ∆𝑉 Vertical displacements • 𝜅 Interface stiffness • 𝜉(𝑢) Damage function of sliding • 𝜀peak Elongation at peak • 𝜏 Shear stress • 𝜏(𝑥) Shear distribution along the interface • 𝜏(𝑠) Interface constitutive law • 𝜏fri Frictional stress • 𝜏max Interfacial shear strength • 𝜑 Friction angle • 𝜓 Dilatation angle Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique XVI Index of Figures Figure 2.1. Examples of UNESCO World Heritage sites built with earth (photos: internet): a) Çatal Hüyük, b) Jericho, c) Great wall of China, d) ziggurat of Chogha Zanbil, e) Mohenjo Daro, f) Chan Chan, g) Ait Benhaddou, h) Shibam…………………….……………….…………………………………..7 Figure 2.2. Rammed earth building technique: a) modern and traditional formworks (HB 195, 2009), b) external formwork (Doat et al., 1989), c) manual rammers (Doat et al., 1989), and d) pneumatic rammer (photo: Antonio Romanazzi)………………………….………………………………9 Figure 2.3. Rammed earth examples: a) construction in Leon (photo: Antonio Romanazzi), and b) constructive details (LNEC, 1953)…………………………………………..……………………………..10 Figure 2.4. Geographical distribution of: a) seismic hazard (source: United Nations/ Global Seismic Hazard Assessment Program), b) earthen buildings and UNESCO World Earthen Heritage (source: CRATerre ENSAG), and c) population density, 2015 (source: United Nations. DESA/ Population Division)………………………………………………………………..…………………………..10 Figure 2.5. Main directions of the building to assess the simplified indexes……………………………………..22 Figure 2.6. Scheme of the kinematic approach assuming a rigid rotating mechanism……………………….24 Figure 2.7. Location of the analysed buildings and comparison with the Portuguese seismic hazard zonation for far-field earthquakes……………………………….……………………..……………………25 Figure 2.8. In-plane analysis of the buildings by index: a) 𝛾1,𝑋, b) 𝛾1,Y, c) 𝛾2,𝑋, d) 𝛾2,Y, e) 𝛾3,𝑋, f) 𝛾3,Y…………………………………………………………………………………………………………………26 Figure 2.9. Out-of-plane analysis of the buildings: a) 𝛾𝜆,𝑋, b) 𝛾𝜆,𝑌, c) kinematic approach in direction X, d) kinematic approach in direction Y………………………………………………..…………………..…27 Figure 2.10. Traditional strengthening solutions for rammed earth structures…………………………………29 Figure 2.11. Textile Reinforced Mortar (TRM)……………………………………………………………………………31 Figure 2.12. A proposed approach to design an appropriate solution for the protection of built heritage..33 Index of Figures XVII Figure 3.1. Particle size distribution analysis: a) soil retained at sieve #10, b) sedimentation, and c) soil passing the sieve #10 and retained at sieve #200………………………..………….…………………38 Figure 3.2. Particle size distribution curves of RS_I and RS_II compared with Fuller distribution and recommended envelop by (Houben & Guillaud, 1994)………………….…………..………………..38 Figure 3.3. Limits of consistency: a) liquid limit (𝐿𝐿), and b) plastic limit (𝑃𝐿)….……………………………..40 Figure 3.4. Casagrande chart of the limits of consistency of RS_I and RS_II compared with the envelope recommended for rammed earth in (Houben & Guillaud, 1994)……………………...……………40 Figure 3.5. Standard Proctor test…………………………………………………………………………………………..41 Figure 3.6. Results of standard Proctor test for RS_I and RS_II…………………………………………………….41 Figure 3.7. Comparison of the particle size distribution between the original soils and the corrected soils……….………………………………………………………………………………………..………………42 Figure 3.8. Comparison of the standard Proctor curves between the original soils and the corrected soils……….…………………………………………………………………………………………..……………42 Figure 3.9. Control of water content of a mixture through the drop ball test: a) mixture excessively dry, b) mixture excessively wet, and c) mixture with adequate water content for compaction….…..…43 Figure 3.10. Compression tests of the rammed earth cylinders: a) test set-up, and b) failure mode………44 Figure 3.11. Stress-strain curves resulting from the compression test of the cylinders: a) RE_I, and b) RE_II…………………………………………………………………………………………………………..…..45 Figure 3.12. Analysis of Young's modulus as a function of the compression level for: a) RE_I, and b) RE_II………………..……………………………………………………………………………………………..45 Figure 3.13. Characterization of earth-based mortars: a) flow table test, b) Alcock’s test (linear shrinkage), c) three-point bending test, and d) compression test………………………………………………..…47 Figure 3.14. Correlation between the clay content and: a) W/S and linear shrinkage, and b) flexural and compressive strength……………………………………………………………………………………….....48 Figure 3.15. Axial compression tests of the earth-based mortars: a) test setup, and b) failure mode……..49 Figure 3.16. Stress-strain curves resulting from the compression test of the cylinders: a) EM_I, and b) EM_II………………………………………………………………………………………………………..........49 Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique XVIII Figure 3.17. Analysis of Young's modulus as a function of the compression level for: a) EM_I, and b) EM_II……………………………………………………………………………………………………………….49 Figure 3.18. Meshes selected for the experimental program: a) Glass fibre mesh (GM), b) Nylon mesh (NM), c) geomesh (GeoM), d) intersection GM, e) intersection NM, f) intersection GeoM, g) detail section GM, h) detail section NM, i) detail section GeoM, j) cross section GM, k) cross section NM, and l) cross section GeoM…………………………………………………………………….51 Figure 3.19. Setup of the tensile tests on mesh specimens………………………………………………………….52 Figure 3.20. Linear force-strain curves of the meshes tested in tension: a) GM (X direction), b) NM (Y direction), and c) GeoM (X direction)…………………………..……………………………………….....54 Figure 4.1. Manufacturing of TRM coupon specimens: a) first layer of earth mortar, b) setting of the mesh, and c) second layer of earth-based mortar............................…………………….………………...59 Figure 4.2. Setup of the direct tensile tests conducted on TRM-coupon specimens…………………………..59 Figure 4.3. Linear force-axial strain curves of the direct tensile tests on coupon specimens: a) TCGM, b) TCNM, c) TCGeoM, d) comparison between GM and TCGM, e) comparison between NM and TCNM, and f) comparison between GeoM and TCGeoM……………………..……………………….61 Figure 4.4. Failure mode of the TRM coupons tested in tension: a) side-view of TCGM, b) front-view of TCNM, and c) front-view of TCGeoM………………………………………………………………………..62 Figure 4.5. Manufacturing of the specimens for the pull-out tests: a) drilled moulds, and b) casting of the mortar……………………………………………………………………………………………………….…….63 Figure 4.6. Setup of the pull-out tests. ……………………………………………………………………………………63 Figure 4.7. Failure modes (FM) observed in the pull-out tests. ……………………………………………..………64 Figure 4.8. Pull-out response curves of the POGM specimens: a) displacement at the loaded end, and b) displacement at the free end. ………………………………………………………………………..……..65 Figure 4.9. Results of the pull-out tests conducted on the PONM specimens: a) response curve considering the displacement at the loaded end, and b) boxplot of the maximum linear force as function of the bonded length. ……………………………………………………………………..……66 Index of Figures XIX Figure 4.10. Statistical analysis of POGM results considering the bonded length and: a) maximum linear force, b) linear force at sliding onset, c) ultimate displacement at the loaded end, d) ultimate displacement at the free end, e) displacement at the loaded end for the maximum linear force, and f) linear force at the end of the elastic phase………………………………………………………..68 Figure 4.11. Setup of the single lap-shear tests…………………………………………………………………………70 Figure 4.12. Failure modes (FM) observed in the single lap-shear tests………………………………………….70 Figure 4.13. Response curves obtained from the single lap-shear tests conducted on the SLGM specimens: a) displacement at the loaded end, and b) displacement at the free end……….…71 Figure 4.14. Response curves obtained from the single lap-shear tests conducted on the SLNM: a) displacement at the loaded end, and b) displacement at the free end……………………………..72 Figure 4.15. Statistical analysis of SLGM results considering the bonded length and: a) maximum linear force, b) linear force to onset sliding, c) displacement at the loaded end for the maximum linear force, and f) ultimate sliding………………………………………………………………………….73 Figure 4.16. Comparison of the results from the different tests conducted on GM specimens in terms of: a) average maximum linear force, and b) average linear force to onset sliding………………….74 Figure 5.1. Response curves obtained from the pull-out tests on POGM specimens: a) loaded-end (𝐿b 150 mm), b) free-end (𝐿b 150 mm), c) loaded-end (𝐿b 90 mm), and d) free-end (𝐿b 90 mm)………………………………………………………………………………………………………………..80 Figure 5.2. Adhesion-friction bond stress-slip relationship assumed to simulate the results of the pull-out tests………………………………………………………………………………………………………………..80 Figure 5.3. Scheme of the interface static interaction during a pull-out test……………………………………..81 Figure 5.4. Shear stress distribution along the interface during the elastic response…………………………82 Figure 5.5. Shear stress distribution along the interface during the nonlinear response……………………..83 Figure 5.6. Damage curve of the section of the yarn due to friction………………………………………………..85 Figure 5.7. Sensitivity analysis of the BSR parameters………………………………………………………………..88 Figure 5.8. Simulation of the pull-out tests and comparison with the experimental curves, considering the slip at the: a) loaded-end, and b) free-end…………………………………………………………………89 Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique XX Figure 6.1. Manufacturing of RE wallets: a) manual compaction within the formwork, and b) demoulding……………………………………………………………………………………………………….93 Figure 6.2. Application of the TRM strengthening: a) scraping and wetting of the surface, b) application of the first layer of the earth-based mortar and mesh, and c) application of the second layer of the earth-based mortar……………………………………………………………………………………..93 Figure 6.3. Diagonal compression test setup: a) scheme, b) disposition of the LVDTs, and c) DIC apparatus…………………………………………………………………………………………………………96 Figure 6.4. Scheme of the loading-unloading profile of the cyclic diagonal compression tests……………..96 Figure 6.5. Comparison of shear stress-strain curves obtained from the diagonal compression tests for different: a) rammed earth mixtures, b) TRM-strengthening solution for RE_II, c) TRMstrengthening solution for monotonic test of RE_II, d) TRM-strengthening solution for cyclic test of RE_II, e) loading condition for un-strengthened RE_II, and f) loading condition for TRMstrengthened RE_II……………………………………………………………………………………………..99 Figure 6.6. Analysis of shear modulus as a function of the shear stress level for: a) DG-Mono-URE_I, b) DG-Mono-GRE_I, and c) DG-Mono-NRE_I……………………………………………………………….102 Figure 6.7. Analysis of shear modulus as a function of the shear stress level for: a) DG-Mono-URE_II, and b) DG-Mono-GeoRE_II………………………………………………………………………………………..102 Figure 6.8. Principal tensile strains contour plot at the peak shear stress (𝛾𝜏max) of: a) DG-Mono-URE_I_2, b) DG-Mono-GRE_I_3, c) DG-Mono-NRE_I_2, and at the ultimate shear strain (𝛾ult) of: d) DGMono-URE_I_2, e) DG-Mono-GRE_I_3 and f) DG-Mono-NRE_I_2……………………..…………105 Figure 6.9. Principal tensile strains contour plot at the peak shear stress (𝛾𝜏max) of: a) DG-MonoURE_II_2, b) DG-Mono-GeoRE_II_1, and at the ultimate shear strain (𝛾ult) of: c) DG-MonoURE_II_2, and d) DG-Mono-GeoRE_II_1……………………………………………………..…………105 Figure 6.10. Principal tensile strains contours plot at the end of loading and unloading of each cycle for the wallets Cyclic_URE_II_1 and Cyclic_GeoRE_II_2……………………………………………….107 Figure 7.1. Setup of the in-plane cyclic tests: a) elevation, b) plan, c) foundation, d) construction, and e) holes for the tie rods………………………………………………………………………………………….112 Figure 7.2. Details of the steel profiles…………………………………………………………………………………..113 Index of Figures XXI Figure 7.3. Overview of the loading system of the URE-IP sub-assemblage……………………………………115 Figure 7.4. Loading profile of the un-strengthened model URE-IP………………………………………………..115 Figure 7.5. Position of the sensors used to monitor accelerations and deformation during the cyclic inplane tests: a) accelerometers, and b) LVDTs………………………………………………………….117 Figure 7.6. Cracking pattern of the URE-IP model……………………………………………………………………118 Figure 7.7. Natural vibration modes of the un-strengthened mockup obtained from the DI-URE-IP-01 test: a) Mode 1, b) Mode 2, and c) Mode 3…………………………………………………………………….119 Figure 7.8. Change in vibration modes of the un-strengthened model after the cyclic loading tests (DIURE-IP-03): a) Mode 1, b) Mode 2, and c) Mode 3...........................……………………………120 Figure 7.9. Comparison of mode first shapes obtained from DI-URE-IP-01 and DI-URE-IP-03 tests……..122 Figure 7.10. Envelope profiles obtained for the un-strengthened model URE-IP: a) positive displacement the left wing-wall, b) positive displacement of the right wing-wall, c) negative displacement of the left wing-wall, and c) negative displacement of the right wing-wall……………………………123 Figure 7.11. Relative displacements of the envelop profiles of the un-strengthened model URE-IP for the: a) positive loading direction, and b) negative loading direction…………………………………….124 Figure 7.12. Response curve of the un-strengthened model URE-IP: a) cycles, and b) overall envelope…………………………………………………………………………………………………………125 Figure 7.13. Envelopes of the response curve of the un-strengthened model URE-IP for each loading loop: a) overall curve, and b) comparison between the negative and positive loading directions………………………………………………………………………………………………………..126 Figure 7.14. Scheme to evaluate the strength decay consequent to cyclic loading………………………….127 Figure 7.15. Force decay observed in the cyclic test of the un-strengthened model URE-IP: a) first repetition, and b) second repetition……………………………………………………………………….127 Figure 7.16. Evaluation of the loading and unloading stiffness from the response curve of each cycle: a) positive loading, b) positive unloading, c) negative loading, and d) negative unloading……..129 Figure 7.17. Stiffness degradation of the un-strengthened model URE-IP: a) loading stiffness, and b) unloading stiffness…………………………………………………………………………………………….130 Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique XXII Figure 7.18. Energy calculation for each cycle of the in-plane test: a) dissipated by the structure, and b) input into the system. ………………………………………………………………………………………..131 Figure 7.19. Dissipated and input energy of the un-strengthened model URE-IP considering: a) loops, b) cycles, and c) cumulative energy. ………………………………………………………………………..132 Figure 7.20. Equivalent damping coefficient of the un-strengthened model URE-IP…………………………133 Figure 7.21. Scheme of the equivalent bi-linear and linear structure according to (BS EN 1998-1, 2004) and (Consiglio Superirore dei Lavori Pubblici, 2008)…………………………………………………134 Figure 7.22. Comparison of the non-linear experimental response with the equivalent elastic-perfectly plastic and elastic systems of the URE-IP model: a) loading in the positive direction, and b) loading in the negative direction……………………………………………………………………………135 Figure 7.23. Scheme of TRM-strengthening and fixing system……………………………………………………137 Figure 7.24. TRM strengthening of the GeoRE-IP model: a) web-wall, and b) wing-wall……………………..137 Figure 7.25. Loading profile of the strengthened model GeoRE-IP……………………………………………….138 Figure 7.26. Cracking pattern of the GeoRE-IP model……………………………………………………………….139 Figure 7.27. Natural vibration modes of the strengthened model obtained from the DI-GeoRE-IP-01 test: a) Mode 1, b) Mode 2, c) Mode 3, d) Mode 4, and e) Mode 5………………………………………140 Figure 7.28. 𝑀𝐴𝐶 between tests DI-URE-IP-03 and DI-GeoRE-IP-01…………………………………….……..141 Figure 7.29. Change in frequency values of the strengthened model GeoRE-IP………………………………142 Figure 7.30. Comparison of the mode shapes of the strengthened model GeoRE-IP through the dynamic identification tests…………………………………………………………………………………………….143 Figure 7.31.Evolution of the damage indexes of the strengthened model GeoRE-IP: a) 𝑑, and b) 𝑑2……144 Figure 7.32. Deformation profiles obtained for the strengthened model GeoRE-IP: a) positive horizontal displacement of the left wing, b) positive horizontal displacement of the right wing, c) negative horizontal displacement of the left wing, and c) negative horizontal displacement of the right wing……………………………………………………………………………………………………………….145 Figure 7.33. Asymmetric loading profile of the strengthened model GeoRE-IP……………………………….145 Index of Figures XXIII Figure 7.34. Relative displacements of the deformation profiles of the strengthened model GeoRE-IP for the: a) positive loading direction, and b) negative loading direction……………………………….146 Figure 7.35. Response curve of the strengthened model GeoRE-IP: a) for each cycle, and b) overall envelope…………………………………………………………………………………………………………147 Figure 7.36. Envelopes of the response curve of the strengthened model GeoRE-IP for each loading loop: a) overall curve, and b) comparison between the negative and positive loading directions…148 Figure 7.37. Comparison between the envelopes of the response curves of the un-strengthened and strengthened models: a) overall curves, and b) envelope of the cycles………………………….148 Figure 7.38. Force decay observed in the cyclic test of the strengthened model GeoRE-IP: a) first repetition, and b) second repetition……………………………………………………………………….149 Figure 7.39. Stiffness degradation of the strengthened model GeoRE-IP and comparison with that of the un-strengthened one: a) loading stiffness, and b) unloading stiffness……………………..…….150 Figure 7.40. Dissipated and input energy of the strengthened model GeoRE-IP and comparison with that of the un-strengthened one: a) loops, b) cycles, and c) cumulative energy……………………..151 Figure 7.41. GeoRE-IP equivalent damping coefficient for each loop……………………………………………152 Figure 7.42. Comparison of the non-linear experimental response with the equivalent elastic-perfectly plastic and elastic systems of the GeoRE-IP model: a) loading in the positive direction, and b) loading in the negative direction……………………………………………………………………………153 Figure 7.43. Comparison of the equivalent elastic-perfectly plastic and elastic systems of the URE-IP and GeoRE-IP models: a) loading in the positive direction, and b) loading in the negative direction………………………………………………………………………………………………………….154 Figure 8.1. Geometry of the un-strengthened rammed earth mockup URE-ST tested on the shaking table………………………………………………………………………………………………………………159 Figure 8.2. Construction of the rammed earth mockup tested on the shaking table: a) foundation, b) preparation of the earth-mixture, c) and d) mechanical compaction……………………………..160 Figure 8.3. Seismogenic faults considered for generating the seismic signals (MF - Messejana Fault; HF - Horseshoe Fault) and the location assumed for the structural sub-assemblage (Odemira)……………………………………………………………………………………………………….163 Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique XXX Table 5.1. Properties of the earth-based mortar and glass fibre mesh used in the specimens of the pullout tests……………………………………………………………………………………………………………78 Table 5.2. Results of the pull-out tests conducted on POGM specimens with bonded lengths of 150 mm and 90 mm……………………………………………………………………………………………………….79 Table 5.3. Bond stress-slip parameters obtained by implementation of the direct problem approach……87 Table 5.4. Optimized bond stress-slip parameters resulting from the sensitivity analysis……………………88 Table 5.5. Comparison of the parameters obtained from the experimental curves with those obtained from the analytical curves (CoV in between brackets)………………………………………………….89 Table 5.6. Errors of the simulated parameters with respect to the experimental ones………………………..89 Table 6.1. Material properties of the rammed earth mixtures (RE_I and RE_II) used in the experimental program……………………………………………………………………………………………………………92 Table 6.2. Material properties of the earth-based mortar mixtures (EM_I, and EM_II) used in the strengthening of the wallets…………………………………………………………………………………..94 Table 6.3. Material properties of the meshes (NM, GM, and GeoM) used in the strengthening of the wallets……………………………………………………………………………………………………………..94 Table 6.4. Outline of the experimental program on diagonal compression tests……………………………….95 Table 6.5. Parameters of the loading-unloading profile of the cyclic diagonal compression tests………….96 Table 6.6. Results of the average values of the entire diagonal compression tests program………………101 Table 7.1. Material properties of rammed earth used to build the structural sub-assembly tested to inplane shear…………………………..…………………………………………………………………………111 Table 7.2. Parameters according to Cauchy and Froude similitude laws for a scale factor λ= 0.8……….114 Table 7.3. Testing protocol of the un-strengthened model URE-IP………………………………………………116 Table 7.4. Natural frequencies obtained in each dynamic identification DI-URE-IP test…………………….120 Table 7.5. Main results of the cyclic test on the un-strengthened model URE-IP……………………………..125 Table 7.8. Parameters of the equivalent elastic-perfectly plastic and elastic systems for the unstrengthened model URE-IP………………………………………………………………………………..135 Index of Tables XXXI Table 7.9. Materials used for TRM-strengthening of the model GeoRE-IP………………………………………136 Table 7.10. Testing protocol of the strengthened model GeoRE-IP………………………………………………138 Table 7.11. Comparison of results of natural frequencies between tests DI-URE-IP-03 and DI-GeoRE-IP01…………………………………………………………………………………………………………………141 Table 7.12. Natural frequencies detected for each dynamic identification DI-GeoRE-IP…………………….142 Table 7.13. Main results of the cyclic test on the strengthened model GeoRE-IP……………………………..147 Table 7.14. Comparison of the main results of the un-strengthened and strengthened models………….149 Table 7.17. Parameters of the equivalent elastic-perfectly plastic and elastic systems for the strengthened model GeoRE-IP……………………………………………………………………………………………….152 Table 7.18. Comparison of parameters of the equivalent elastic-perfectly plastic and elastic systems for the un-strengthened model URE-IP and the strengthened model GeoRE-IP…………………….153 Table 8.1. Material properties of rammed earth used to build the mockup tested on the shaking table………………………………………………………………………………………………………………160 Table 8.2. Characteristics of the LNEC 3D shaking table (LNEC, 2010)………………………………………..161 Table 8.3. Characteristics of the actuators of the shaking table (LNEC, 2010)……………………………….162 Table 8.4. Shake table testing protocol of the un-strengthened mockup URE-ST…………………………….166 Table 8.5. Ground motion parameters of the inputs of the URE-ST mockup that achieved the target response spectra………………………………………………………………………………………………169 Table 8.6. Damage detection of the un-strengthenened mockup URE-ST according to (Muin & Mosalam, 2017)…………………………………………………………………………………………………………….177 Table 8.7. 𝐵𝑆𝐹, 𝐵𝑆𝐶 and 𝑒BSC values obtained for each seismic input applied to the URE-ST mockup………………………………………………………………………………………………………….187 Table 8.8. Material used for the TRM-strengthening of the rammed earth mockup………………………….193 Table 8.9. Shaking table testing protocol of the strengthened mockup NRE-ST………………………………196 Table 8.10. Ground motion parameters of the inputs of the NRE-ST mockup that achieved the target response spectra………………………………………………………………………………………………198 Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique XXXII Table 8.11. Comparison of the values of the natural frequencies obtained from the DI-URE-ST-09 and DINRE-ST-01 tests……………………………………………………………………………………………….203 Table 8.12. Damage detection of the TRM-strengthenened mockup nRE-ST according to (Muin & Mosalam, 2017)……………………………………………………………………………………………….206 Table 8.13. 𝐵𝑆𝐹, 𝐵𝑆𝐶 and 𝑒BSC values obtained for each seismic input applied to the NRE-ST mockup………………………………………………………………………………………………………….214 Chapter 1. Introduction 1 Chapter 1 INTRODUCTION 1.1 General framework and motivation Earthen materials have been extensively recognized in the development of human civilizations through time, as part of their architectural heritage. In fact, more than 150 of the World Heritage sites were built with raw earth (UNESCO World Heritage Centre, 2017), which include houses, religious and civil monuments, and entire historic towns and archaeological sites. Furthermore, about one fourth of the global population is estimated to live in earthen buildings (Romanazzi et al., 2019; Silva et al., 2013). The popularity of earthen materials can be attributed to the local availability of the raw material, sustainability of the process, ease of building, adequate thermal and acoustic isolation, and low cost. Several building techniques based on the use of soil are reported in the literature, yet adobe, compressed earth blocks and rammed earth are among the most used nowadays. On the other hand, earth architecture is affected by high seismic vulnerability, which results from low to moderate strength of the material, poor structural maintenance and lack of engineering approach in design and building practices. As a consequence of the high seismic vulnerability, earthen structures are unable to sustain large inertial forces associated to moderate and strong ground motion. In 2012, UNESCO reported that about one fourth of the in-danger World Heritage sites are built with earthen materials (UNESCO, 2012). Apart from that, another main concern is the threat of major injures and loss of life related to the potential collapse of such structures. In this context, the need to protect cultural heritage while saving lives remarks the importance of finding appropriate strengthening solutions to reduce the seismic vulnerability of earthen structures (Michiels, 2015; Tolles et al., 2002). Various interventions conducted on existing rammed earth dwellings in the last decades highlight the empirical strategies adopted in designing the solution and the lack of knowledge on their seismic response. In this context, the research on strengthening systems for rammed earth is rather recent and the solutions so far proposed might result not compatible with this heritage. On the other hand, the strengthening with textile reinforced mortar (TRM), which is widely accepted for masonry buildings because of its effectiveness and compatibility, has been mainly investigated for adobe structures, while its application for rammed earth buildings counts only few studies and needs further research. In addition, the response of un-strengthened rammed earth structures is still not well known, in particular with regard to the mechanical properties, and the in-plane and out-of-plane behaviour of the walls under cyclic and Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 2 dynamic excitation. It should be clear that such research must be conducted following an interdisciplinary approach, which should consider the geotechnical analysis of the raw material, the characterisation of each component (rammed earth, textile and mortar) and their interaction, and finally the investigation of un-strengthened and TRM-strengthened subassemblies. 1.2 Objectives Given the above framework, the main objective of this research is to develop a newly compatible and low-cost textile reinforced mortar-based technique for the seismic protection of rammed earth heritage. Given the broad field of this topic, the research is limited to the use of unstabilised rammed earth and earth-based mortar. However and in order to assess the effectiveness of the proposed strengthening solution, each of the experimental characterisation was conducted on both un-strengthened and TRM-strengthened specimens. Furthermore, the vernacular rammed earth heritage from Alentejo (Southern Portual) was considered as case study to individuate features for the design of specific tests and methodology. In this way, a contribution on the knowledge of rammed earth properties is provided as well. The main objective will be achieved by fulfilling the following specific objectives: - To characterise the physical and mechanical properties of each component, namely soil, rammed earth, earth-based mortar and mesh; - To characterise the interaction between the components, particularly at mesh-mortar and support-mesh-mortar levels; - To define an analytical bond stress-slip law for describing the response of the TRMstrengthening system; - To evaluate the performance of the un-strengthened rammed earth structure and the effectiveness of the TRM-strengthening solution under in-plane and out-of-plane static and dynamic conditions. 1.3 Outline of the thesis In order to fulfil the aforementioned objectives, the present thesis is organised in nine Chapters, as follows: In Chapter 2, the topic of earth architecture, the importance of the protection of its heritage and the seismic vulnerability of rammed earth structures is introduced. The literature review is focused on the Chapter 1. Introduction 3 main achievements regarding the mechanical properties of rammed earth, its overall structural behaviour and numerical modelling strategies. Afterwards, a simple tool for a first screening of rammed earth seismic vulnerability is proposed. Subsequently, a further overview on the strengthening approaches to reduce the seismic vulnerability of rammed earth is reported. The literature review continues with the analysis of the principal systems adopted so far, differentiating the traditional strengthening solutions from the textile reinforced mortar. Finally, a specific section is dedicated to the theory supporting the compatibility of the intervention. Chapter 3 addresses the experimental characterisation of the materials used in the experimental programme. The geotechnical analysis is presented at first, which was the base to design the entire programme of this research. Subsequently, the investigation is focused on the definition of the mechanical and physical properties of the rammed earth mixtures, earth-based mortar mixtures and different meshes (glass fibre mesh, nylon mesh and geomesh). The results are discussed in terms of optimal water content, dry density, shrinkage, compressive strength, tensile strength and Young’s modulus. Therefore, correlations between composition of the earth materials and their mechanical and physical properties are inferred. Furthermore, to investigate the non-linear response of rammed earth and earth-based mortars, a specific stepwise analysis considering the compressive level and the Young’s modulus is presented. In Chapter 4, the experimental definition of the interaction at micro-scale level between the TRM component is described. Different experimental setups were considered. In particular, the interaction mortar-mesh was investigated by means of direct tensile test on TRM coupon specimens, which was complemented with pull-out tests. Single lap-shear tests were performed to analyse the local response of substrate-matrix-mesh. For each data set, descriptive analyses were performed to correlate the bond length with the experimental observation in terms of failure modes and performance. Chapter 5 presents the definition of an analytical model to describe the pull-out response of the TRM-strengthening solution proposed. At first, a brief review of the different analytical approaches is discussed, and the pull-out curves obtained from the experimental programme are analysed. Accordingly, the assumptions of the constitutive law are stated, and the analytical solution is inferred. In addition, a new damage model is implemented, which consider the reduction of the fibre cross section due to the friction between the materials. Consequently, the algorithm to simulate the pull-out response is implemented and calibrated on the experimental observations. Chapter 6 reports the experimental programme focused on the investigation of the shear behaviour of rammed earth wallets and the effectiveness of the proposed TRM-strengthening solutions. The Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 4 manufacturing process of the specimens is also analysed with the intent to verify the traditional procedure of building with rammed earth. The experimental results are discussed with respect to the shear behaviour, shear strength and effectiveness of the TRM-strengthening. Furthermore, a stepwise analysis is conducted to correlate the shear modulus with the different stress levels. Finally, the results of digital image correlation are presented in terms of full field strain configurations and crack patterns. Chapter 7 reports the results of an extended experimental program on the in-plane cyclic behaviour of a rammed earth structural sub-assemblage. The construction of the rammed earth model and the test setup are illustrated at first. The results of the in-plane cyclic test on the un-strengthened wall are presented and discussed in terms of cracking pattern, dynamic characterisation, displacement capacity, base shear forces and strength decay. In addition, the stiffness degradation and energy dissipation are analysed to calculate the equivalent damping coefficient. Therefore, equivalent elastic and elastic-perfectly plastic systems are proposed. Afterwards, the application of the TRM-strengthening solution is described, focusing on the materials and the fixing system. Subsequently, as for the un-strengthened model, the results of the in-plane cyclic test of the TRM-strengthened wall are reported and discussed. Finally, the effectiveness of the TRM solution is evaluated with regard to the performance of the previous unstrengthened case. In Chapter 8, an extended shaking table experimental programme is presented. At first, the building of the mockup and the setup of the test is illustrated. Emphasis is given to the characterisation of the seismic signals. The results are reported and discussed with regard to the cracking pattern damage identification, displacements, based shear coefficient and dissipated energy. In particular, with the aim at covering the gap in the correlation between the performance of the mockup and seismic event, statistical analysis on the structural response as function of the properties of the ground motion are discussed. Finally, to assess the effectiveness of the strengthening solution, the outcomes of the TRMstrengthened mockup are compared with the ones of the un-strengthened structure. Finally, Chapter 9 summarises the main conclusions of the thesis and presents proposals for future research. In addition, recommendations for the production and application of compatible TRMstrengthening solutions for rammed earth heritage are presented with basis on the performed experimental work. Chapter 2. Rammed earth heritage 5 Chapter 2 RAMMED EARTH HERITAGE: SEISMIC VULNERABILITY AND STRENGTHENING SOLUTIONS The present chapter aims at introducing the topic of earth architecture, the relevance of the protection of its heritage and the seismic vulnerability of rammed earth structures. In particular, a general overview is provided on the main literature results with regard to the mechanical properties of rammed earth, overall structural behaviour and numerical modelling approaches. Accordingly, a simple tool for a first screening of rammed earth vulnerability is proposed. Subsequently, a further overview on the strengthening strategies for reducing the seismic vulnerability of rammed earth is reported. The literature review presented the principal systems adopted so far, differentiating the traditional strengthening solutions from the textile reinforced mortar. A specific section is dedicated to the theory of the compatibility of the intervention. Finally, the main gaps are summarised in the conclusions. 2.1 Chronological and geographical distribution of earth architecture Archaeological sites prove that soil for building was among the first material used by humans and that earthen construction accompanied urban progress during various stages of civilization (Jaquin et al., 2008; Pacheco-Torgal & Jalali, 2012). The fact that similar building techniques were developed in an unrelated way and in different cultural regions represents a particular aspect of earthen architecture. Earthen permanent dwellings are found in the nowadays Anatolia region (Çatal Hüyük, Turkey) (Figure 2.1a) and in Jericho (Palestine) (Figure 2.1b), which are dated back to around 6000 B.C. Earth was used as well in China during the Ming Dynasty (XIV-XVII century) and Quin Dynasty (III century B.C.), as rammed earth sections of the Great Wall of China are still present in Gansu Province (Figure 2.1c); while in Japan, an example of rammed earth wall can be observed in the Horyuji Temple built 13 centuries ago (Jaquin, 2008). In the Egyptian culture, the production of earth blocks was related to the annual floods of the Nile River, as described in the Old Testament [Exodus 5:7f.; 16:18f]. Here, the use of sun-dried bricks can be traced back to XIV-XV century BC, as evidenced by the Nubian vault in the storage room of the tomb of Ramses II (around 1300 BC) and by paintings illustrating all phases of production and use of earth blocks (around 1500 BC) (Fathy, 1973; Niroumand et al., 2013). The use of earth blocks was widespread also in the Mesopotamia and neighbouring regions with the purpose of building both dwellings and religious Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 6 constructions, such as the ziggurat of Chogha Zanbil in Iran (Figure 2.1d) (Pollock, 1999). The first written rules for building with the earth appeared in fired clay tablets of the time of Hammurabi (around 1800 b.C.), constituting a remarkable milestone in the development of earthen architecture. Earth has been used for more than 5 millennia as well in nowadays regions of Turkmenistan, Uzbekistan, and Kazakhstan (Minke, 2013), as demonstrated by the ruins of the ancient city of Afrasiab (Northern Samarkand) or by the cities of Bukhara and Chiwa, which have more than 2500-year-old history. In turn, the city of Mohenjo Daro (Figure 2.1e) in Pakistan constitutes a proof that earthen techniques were known in this region since the third millennium BC at least (Jansen, 2003). Moving to the American continent, a high level of knowledge on different earth building techniques was achieved in the Pre-Columbian age. Several archaeological sites, as the Huaca del Sol pyramid in Moche Valley (200-500 A.D.) or the Chan Chan city (Figure 2.1f), were entirely made with earth (Pollock, 1999). Nevertheless, rammed earth was introduced as building techniques likely after 1549 with the European colonisation. Different religious and civil architectures were built in Brazil; however, following a flooding in 1850, the use of rammed earth was reduced while several rammed earth architecture were demolished (Jaquin et al., 2008). Also in North America, e.g. Arizona or New Mexico, examples of houses built with earth are similar to the dwellings found in Anatolia (Bardou et al., 1986). In Europe, earthen constructions have been commonly used in different countries (Akermann, 2011), as for instance in France (Guillaud, 2008), Portugal (Correia, 2007; Fonseca, 2007), Czech Republic and Italy (Conti et al., 1999). Regarding the rammed earth technique, although it is difficult to establish exactly place and time of its origin, there is evidence that this technique was already developed in Mediterranean basin in the era of Phoenicians and Greeks, as found in Natural History of Plinio, “the walls made of compacted earth that can be seen in Barbaria (Cartago) and in Spain, where they are called ‘molded walls’, the soil is set between two wooden boards […] there is no cement or mortar that is harder than soil […] the watching towers built by Anibal in Spain […] are made of compacted earth” . The further archaeological survey confirmed that rammed earth was used to build dwellings, sometimes finished with lime or marble (Houben & Guillaud, 1994). In the last centuries and in various regions, the knowledge of traditional earth building techniques were displaced by "modern" techniques (mostly steel and concrete), which are thought to stand for wealth in contrast to poverty. However, it is evident that traditional earthen architecture represents the cultural identity of many countries and their inclusion in UNESCO World Heritage list (Schroeder, 2016) (e.g. the impressive rammed earth houses in Ait Benhaddou in Morocco (Figure 2.1g) or the city of Shibam in Chapter 2. Rammed earth heritage 7 Yemen (Figure 2.1h) is changing the concept of the earthen buildings from poverty to a matter of pride. A further consequence of the change of building practices is the loss of the knowledge on how to build with earth. Indeed, building with earth was an activity mainly conducted by the extended families or local communities, whose know how was handed down through generations, fulfilling also an important social and cultural role. On the other hand, "modern" building techniques are based on industrial business models, which endanger the protection of the tangible and intangible heritage values of earth architecture. Consequently, the protection of earthen heritage not only means the protection of tangible goods, but as well of local identities and knowledges developed along the history of human communities. (a) (b) (c) (d) (e) (f) (g) (h) Figure 2.1. Examples of UNESCO World Heritage sites built with earth (photos: internet): a) Çatal Hüyük, b) Jericho, c) Great wall of China, d) ziggurat of Chogha Zanbil, e) Mohenjo Daro, f) Chan Chan, g) Ait Benhaddou, h) Shibam. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 14 Table 2.3. Composition in terms of content of clay, silt, sand and gravel of rammed earth mixtures found in literature. Reference Clay [%] Silt [%] Sand [%] Gravel [%] (Bui & Morel, 2009) 4 31 48 17 (Toufigh & Kianfar, 2019) 5 0 40 55 (Bui et al., 2014) 8 34 8 50 (Nowamooz & Chazallon, 2011) 8 4 60 28 (Jaquin, 2012) 10 - - - (Miccoli et al., 2014) (Silva et al., 2014) 11 25 65 (Maniatidis & Walker, 2008) 12 13 45 30 (Silva et al., 2014) 14 16 32 38 (Arrigoni et al., 2017) 20 8 59 13 (El-Nabouch, 2017) 20 65 15 0 The water content of a mixture made with soil is another important aspect to be considered for the compaction. Such characteristic is related to the mixture composition (Bui et al., 2009) and affects the dry density (𝜌) of a rammed earth element and its mechanical properties (Walker et al., 2005). For a given compaction energy and mixture, the optimal water content can be identified as the amount of water to attain the maximum dry density of the material. As water content values approximate such value, the soil attains almost its maximum dry density, which in turn is an indicator of the compressive strength of the earth material (Attom, 1997; El-Nabouch, 2017; Kouakou & Morel, 2009; Mesbah et al., 1999; Morel et al., 2007). The optimum water content is usually calculated by means of standard Proctor test in laboratory or estimated by the drop ball test in-situ. An optimal water content in the range 8% and 12% by dry weight of material was found in literature (Arrigoni et al., 2017; Bui et al., 2009; Bui & Morel, 2009; Bui et al., 2014; Corbin & Augarde, 2015; El-Nabouch et al., 2018; El-Nabouch et al., 2017; Kennedy, 2009; Maniatidis & Walker, 2008; Mellaikhafi et al., 2021; Miccoli et al., 2014; Nowamooz & Chazallon, 2011; Silva et al., 2014; Toufigh & Kianfar, 2019), while a wide range of dry density (𝜌) is observed which varies from 1.750 g/cm3 to 2.200 g/cm3 (Houben & Guillaud, 1994; Mellaikhafi et al., 2021; Rodríguez-Mariscal et al., 2021). Such variation in optimal water content and dry density can be ascribed to the intrinsic non-homogeneity of the mixture and to the different compaction and size of the specimens. Chapter 2. Rammed earth heritage 15 With regard to the mechanical properties of rammed earth, compressive strength is one of the most important parameters to assess the load-bearing capacity of rammed earth structures (Ciancio et al., 2013; Jaquin et al., 2009a; Piattoni et al., 2011). Several studies have been carried out on the compressive strength (𝑓c) of rammed earth specimens with different size and shapes (Bui et al., 2016; Maniatidis & Walker, 2008; Wangmo et al., 2021; Yamin et al., 2004). The results reported in literature show large scattering of the values, which can be partially due to the inherent heterogeneity of the material, and to the unavailability of standardised test procedure. In fact, since there are no standards specifically for testing the compressive strength of rammed earth materials, the investigations followed the ASTMD1633 standard (ASTM D1633-17, 2007) for compressive strength of soil-cement cylinders (Erdogmus & Garcia, 2015), or proposed procedures from ASTM standards for cement mortars and from masonry design rules (Maniatidis & Walker, 2008). Furthermore, since the mechanical properties of rammed earth are influenced by the manufacturing conditions (e.g. moisture content, compaction energy, sample size and stabilization), the absence of standardised protocols for preparing the specimens does not permit a comparison between the results obtained by diverse studies (Allahvirdizadeh et al., 2019; El-Nabouch, 2017). In fact, the size of the specimen affects the material grading (Hall & Djerbib, 2004a), which in turn influences its moisture content. Apart from the size of the specimen, also the shape affects the compressive strength of the rammed earth. As found in literature, substantial differences are found between prismatic and cylindrical specimens (Bui et al., 2009; El-Nabouch et al., 2017; Maniatidis & Walker, 2008). One of the reasons can be that the friction between the mixture and the formwork during manufacturing is greater in the prismatic specimens, so the cylindrical specimens can be compacted better and consequently perform better mechanical properties. As well as the different confining effect that can occur with the testing plates might implicate such variances in the results. An additional side effect related to the compressive test on rammed earth is the large dispersion in evaluating the Young’s modulus (𝐸). Such property is sensitive to the range of the compressive stress range considered in the regression analysis (Bui et al., 2014; El-Nabouch, 2017; Maniatidis & Walker, 2008), besides being related to factors associated with specimens manufacturing (e.g. materials, moisture content, specimens size and stabilization) and to testing procedures. Despite observing a direct relationship between the Young’s modulus and the compressive strength (El-Nabouch et al., 2017; Jaquin, 2012; Maniatidis & Walker, 2008), a precise correlation between these two mechanical properties was not possible to be defined. The values of dry density, optimal water content, compressive strength and Young’s modulus found in literature are summarised in Table 2.4 along with the size of the tested specimens. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 16 With regard to the Poisson’s ratio, only few experimental results were found, which values vary in the range 0.22 – 0.30 (Bui et al., 2014; El-Nabouch, 2017; Miccoli et al., 2014). Table 2.4. Dry density, optimal water content, compressive strength and Young's modulus found in literature. Reference Specimen size [𝐜𝐦] 𝝆 [𝐠/𝐜𝐦𝟑] 𝑶𝑾𝑪 [%] 𝒇𝐜 [𝐌𝐏𝐚] 𝑬 [𝐌𝐏𝐚] (Walker et al., 2016) 30X30X60 1.920 13 0.81 65 (Bui et al., 2014) 40X40X70 1.920 11 1.90 500 (Liu & Tong, 2017) ∅4 h= 8 1.649 21 1.04 103 (El-Nabouch, 2017) 25X25X50 1.878 12 1.15 365 (Silva et al., 2014) 55X55X20 2.100 10 1.26 1034 (Bui et al., 2016) 100X100X30 2.000 - 1.30 500 (Arrigoni et al., 2017) ∅10 h= 20 2.080 8 1.40 - (Pakand & Toufigh, 2017) ∅7.5 h= 15 2.043 12 1.77 - (Kosarimovahhed & Toufigh, 2020) ∅7.5 h= 15 2.143 7 1.85 34 (Walker et al., 2016) ∅30 h= 60 1.850 13 1.90 - (Lilley & Robinson, 1995) 15X15x15 2.020 - 1.90 - (El-Nabouch, 2017) ∅10 h= 20 1.790 12 2.00 763 (Toufigh & Kianfar, 2019) ∅7.5 h= 15 1.946 12 2.23 143 (Maniatidis & Walker, 2008) ∅10 h= 20 1.850 13 2.46 160 (Hallal et al., 2018) ∅10 h= 20 1.76 18 1.30 40 (Reyes et al., 2019) 32X28X14 1.78 15 1.11 - (Toufigh & Kianfar, 2019) ∅7.5 h= 15 1.946 12 2.23 143 (Miccoli et al., 2015) 50X50X11 2.190 9 3.73 4207 The tensile strength (𝑓t) is another relevant parameter in the analysis of rammed earth structures under cyclic loads (Bui et al., 2014; Miccoli et al., 2015). Nevertheless, due to the fragility of the material, few experimental investigations were carried out by means of Brazilian tests (Bui et al., 2014; Hallal et al., 2018; Namikawa & Koseki, 2007; Toufigh & Kianfar, 2019), direct tensile test (Araki et al., 2016) or pull-off tests (Miccoli et al., 2014). The outcomes resulted in tensile strength values between 0.10 MPa and 0.35 MPa, which suggest that such property can be assumed as 10% of the compressive strength of rammed earth (Bui et al., 2019; Bui et al., 2014; Hallal et al., 2018; Minke, 2013; Nabouch et al., 2015; Silva et al., 2014; Toufigh & Kianfar, 2019; Yamin et al., 2004). The shear strength of rammed earth (𝑓s) is also very limited, as demonstrated by few investigations of which results are in the range Chapter 2. Rammed earth heritage 17 0.15 MPa – 0.85 MPa. In general, two different test procedures are used to assess the shear behaviour of rammed earth, namely direct shear test (El-Nabouch, 2017; Miccoli et al., 2014) and diagonal compression test (El-Nabouch, 2017; Silva et al., 2014; Yamin et al., 2004) following the standard ASTM E519 (ASTM E519-02, 2002). As found in (Silva et al., 2014), the shear strain-stress curves showed an early peak shear stress, related to the cohesion provided by the binder effect of the clay. When the cohesion is damaged, a significant reduction of the stiffness is observed, and the shear behaviour is promoted by friction and interlocking. Due to the different levels of porosity of the material, and to the clay content which increases the affinity with water (Murad et al., 1995), earthen materials are characterised by good to excellent hygroscopic behaviour. Such capacity from one side evidences the ability to buffer moisture and improve indoor air quality, but it also significantly affects the mechanical behaviour of the material in relation with its moisture content (Bernat-Maso et al., 2017; Bui et al., 2014; El-Nabouch, 2017; Gerard et al., 2015; Jaquin et al., 2009b; Maniatidis & Walker, 2003; Narayanaswamy, 2016). In fact, a decrease of the shear strength, compressive strength and cohesion was observed with the increase of the material moisture content (Bui et al., 2014; Champiré et al., 2016; Jaquin et al., 2009b; Narayanaswamy, 2016; Wu et al., 2012). Another peculiarity of rammed earth is a hardening behaviour similar to the consolidation in soil mechanics, where if a preload is applied, the material behaviour is nearly elastic till such value and the more the preload increases, the more the Young’s modulus increases (Bui et al., 2011; Miccoli et al., 2014). In order to obtain reliable simulation of the seismic performance of a rammed earth structure, the shear characteristics of the material should be appropriately determined. Being the rammed earth a result of compaction of different layers, these shear characteristics include the cohesion and the friction angle of the layers (intralayers) and of the interface between layers (interlayers). Following the Mohr-Coulomb theory, the cohesion (𝑐) and friction angle (𝜑) were experimentally determined from the relationship between the shear and normal stresses obtained by the shear box test (El-Nabouch, 2017; El-Nabouch et al., 2018), a triaxial compression test (Nowamooz & Chazallon, 2011), or direct shear tests (El-Nabouch et al., 2018). In particular, in (ElNabouch et al., 2018) direct shear tests were performed both for intralayers and interlayers. The results showed that the shear strength at the interlayers is between 78-91% of that at the intralayers, while the interlayer friction angle was 35° which resulted slightly lower that that at the intralayer (37°). Such result suggest that the friction angle is related to the roughness of the components at the microscopic scale, and therefore to the particle size distribution of the mixture. As for the cohesion, its value at the interlayers was obtained of about 80% of the intralayer (respectively 24 kPa and 30 kPa), which may indicate that the intralayers are more compacted than the interlayer. Another way to obtain such parameters is by Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 18 calibration of numerical models (Bui et al., 2014, 2016; Miccoli et al., 2014; Silva et al., 2014; Wangmo et al., 2021). Some authors suggest a direct relation of the cohesion with compressive strength of the form 𝑐 =0.10÷0.14𝑓c (Bui et al., 2014), or with tensile strength of the form 𝑐 =1.5𝑓t (Miccoli et al., 2015; Silva et al., 2014). However, significant dispersion is observed in the literature on the values of cohesion, varying from 30 kPa to 560 kPa, while friction angle (𝜑) was in the range 35°– 45°. The values of dry density, shear strength, cohesion and friction angle found in literature are summarised in Table 2.5 along with the size of the tested specimens. The shear behaviour of rammed earth is also affected by the dilatation angle (𝜓); nevertheless, the investigation of this parameter has not been addressed in depth. Recently, (Bui et al., 2019), analysed the influence of the dilation angle on the behaviour of rammed earth walls by means of finite element models observing that such parameter only influences the ultimate displacements. However, large dispersion was found in the literature with values of the dilatation angle varying from 𝜓 =0° (Miccoli et al., 2015), 𝜓=12° (Silva et al., 2014) and 𝜓= 30° (Bui et al., 2019). Table 2.5. Dry density, shear strength, cohesion and friction angle found in literature. Reference Specimen size [𝐜𝐦] 𝝆 [𝐠/𝐜𝐦𝟑] 𝒇𝐬 [𝐌𝐏𝐚] 𝒄 [𝐤𝐏𝐚] 𝝋 [°] (Silva et al., 2014) 55X55X20 2.100 0.15 189 37 (Bui et al., 2014) 40X40X70 1.920 0.18 170 51 (Yamin et al., 2004) 250X250X50 1.920 0.37 - - (Miccoli et al., 2014) 50X50X11 2.190 0.65-0.85 - 39 (Nowamooz & Chazallon, 2011) ∅7.1 h= 14.7 2.00 - 13 41 (El-Nabouch, 2017) 49X49X36 - - 30 35 (Kosarimovahhed & Toufigh, 2020) 15X15X18 2.143 - 50 65 (Corbin & Augarde, 2015) 6X6X2 2.131 - 68 44 (Bui et al., 2016) 100X100X30 2.000 - 130 45 (El-Nabouch, 2017) 10X10X3.5 - - 135-260 45 (Silva et al., 2014) 50X50X12 2.190 - 561 37 (El-Nabouch et al., 2018) 25X25X50 - - 30 37 (Reyes et al., 2019) 32X28X14 1.78 0.03 - - The tensile fracture energy (𝐺f) and compressive fracture energy (𝐺c) are other fundamental parameters in the non-linear analysis of rammed earth structure under shear loads (Corbin & Augarde, 2014; Miccoli et al., 2015; Silva et al., 2014), nevertheless few studies focused on the determination of Chapter 2. Rammed earth heritage 19 such parameters, of which results present relevant scattering (see Table 2.6). (Silva et al., 2014) proposed a relation between the fracture energy and the strength of the rammed earth material, estimating the mode-I tensile fracture energy as 𝐺f=0.029𝑓t and the compressive fracture energy as 𝐺c=1.6𝑓c. Table 2.6. Tensile fracture energy and compressive fracture energy values found in literature. Reference 𝑮𝐟 [𝐍/𝐦𝐦] 𝑮𝐜 [𝐍/𝐦𝐦] (Corbin & Augarde, 2014) 0.002 - (Silva et al., 2014) 0.004 - (Miccoli et al., 2015) 0.011 6 (Bui et al., 2019) 0.12 10-25 (Hussaini & Toufigh, 2019) 0.020 - Although material characterisation is required for the implementation of a structural model, experimental tests on rammed earth sub-assemblies are fundamental to investigate their overall out-ofplane and in-plane performance. In (Reyes et al., 2019), a full-scale wall was tested under cyclic in-plane loads. The results showed that the earthen walls are very brittle and their lateral load capacity decreases for low drift demands. In (Shrestha et al., 2020), pull-down tests on un-strengthened rammed earth walls showed the high vulnerability of the structure against the out-of-plane loads and the separation of the main façade at the corner joints. In (Reyes et al., 2018) and (Reyes et al., 2019), the results of cyclic test and dynamic tests on full-scale rammed earth walls show that failure mechanisms are dominated by the presence of diagonal cracks and that the shear capacity is controlled by the wall axial load and aspect ratio. In addition, rammed earth exhibits high energy dissipation capacity, while the lateral stiffness decreases rapidly at early stage of lateral displacements. As can be noted, only few studies have been conducted on full-scale rammed earth walls due to the complexity of such tests, while very few analyses have been focused on the dissipative capacity and stiffness degradation. Therefore, further experimental investigations on the in-plane and out-of-plane response of rammed earth walls are required. Despite the performances of earthen materials are estimated through their unconfined compressive strength and apparent stiffness, different studies underline the complexity of the mechanical response of such materials, which cannot be described by only compressive strength and Young’s Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 20 modulus (Bui et al., 2014; Champiré et al., 2016; Nowamooz & Chazallon, 2011). With this regard and to investigate the high variability of mechanical properties, different material models have been developed, while the calibration considered microand macro-modelling strategies for both Finite Element Method (FEM) and Discrete Element Method (DEM) (Bui & Bui, 2020; Bui et al., 2016; Miccoli et al., 2015; Silva et al., 2014). (Riyono et al., 2018) proposed a hierarchical constitutive model based on the elasto-plastic theory which was validate with experimental results (Araldi et al., 2018). In this model, the elasticity is assumed isotropic, as demonstrated by experiments in which the Young’s modulus resulted similar between the parallel and perpendicular direction of compaction (Bui & Morel, 2009; Bui et al., 2016). Two plastic failure surfaces are supposed to limit the stress state along different modes of failure due to the excessive shearing and due to tensile stress. In (Reyes et al., 2019), a concrete damage plasticity model was adopted to reproduce the non-linear behaviour of rammed earth and its different response under tension and compression state. In damage plasticity theory, a material constitutive model is defined by a yielding criterion and a law of plastic flow. The yielding criterion refers to all possible combination of stresses at which the material attains the plastic response range, while the law of plastic flow refers to the kinematic relations that regulate the plastic excursion. The criterion is also based on the assumption that failure can be represented by uniaxial tension and compression plasticity parameters (Lubliner et al., 1989). The results demonstrate that such model represents adequately the hysteretic response and damage concentration detected during the experimental tests. In (Bui et al., 2019; Bui et al., 2018; Bui & Bui, 2020; Bui et al., 2016), following the discrete element method, a rammed earth structure was modelled as an assemblage of discrete blocks (intralayers) connected with interfaces (interlayers). The rammed earth layers were assumed homogeneous and isotropic, with Mohr-Coulomb failure criterion with a tension cu-toff behaviour. As for the interlayers, the Mohr-Coulomb interface model with a tension cut-off was used which considered both shear and tensile failure, and interface dilatation was included. The results are consistent with the experimental outcomes. In (Gomes et al., 2011), finite element method with macro-modelling approach was adopted. However, the performed static analysis is not able to detect the real capacity of a rammed earth structure. In addition, the model was not calibrated on experimental evidence. In (Miccoli et al., 2016), finite element method with micro-modelling approach was followed to simulate the in-plane behaviour of rammed earth under cyclic shear-compression. The material of the layer was assumed isotropic, as demonstrated in (Jaquin, 2008) and in (Bui & Morel, 2009), and it was simulated with a Chapter 2. Rammed earth heritage 21 total strain rotating crack model (TSRCM), wile Mohr-Coulomb failure criterion was used as material model for the interface between layers. The constitutive law based on the total strain rotating crack model is able to reproduce the non-linear behaviour of the rammed earth layer in tension and compression, although it is not able to simulate the damage and plasticity of the material. The compressive behaviour is described by a multi-linear curve, while the tensile response is reproduced by an exponential softening curve. Then, the numerical model was calibrated on experimental tests and a sensitivity analysis was conducted. The results demonstrated that failure is influenced by the tensile strength and friction angle of the interface material, while cohesion and the layer thickness showed limited effect on the shear behaviour. As for the seismic assessment of rammed earth buildings, few non-linear analyses, as pushover analyses (Barros et al., 2015; Ortega et al., 2015) and non-linear dynamic analyses (Allahvirdizadeh et al., 2019, 2021) were performed. Therefore, various numerical investigations on rammed earth performance have been conducted with satisfactory results; nevertheless, only in few cases the simulation was calibrated on experimental observation, particularly for the out-of-plane dynamic response. In addition, despite different material models were considered, a constitutive law able to describe the damage and plasticity of rammed earth still requires further investigation. 2.2.2 Simple tools for rammed earth vulnerability assessment As previously discussed, advanced numerical models provide reliable information on the seismic vulnerability assessment of rammed earth structures; nevertheless, an aspect that must be considered for such analyses is their high computational and time demand. Consequently, they are not applicable to all the cases, while the protection of vernacular rammed earth buildings and the safety of modern constructions require a quick response. Therefore, in such a context, a simplified method was presented by (Silva et al., 2018) and (Silva et al., 2018) as a supporting tool for the first screening of large samples of constructions, which in any case cannot substitute advanced analysis for the seismic assessment at decision-making. This method followed the approach presented by (Lourenço & Roque, 2006) and (Lourenço et al., 2013), which suggests indexes based on geometrical characteristics and local seismic hazard. It should be noted that simplified methods for seismic assessment are valid in the case of masonry structures with “box-behaviour” (Lourenço et al., 2011); in the case of rammed earth buildings, the “box-behaviour” is not guaranteed as previously explained; in spite of this, the simplified method can be a qualitative indicator of the seismic performance of rammed earth buildings, rather than a quantitative safety assessment. Hence, four indexes were proposed for each main direction (longitudinal 𝑋 and Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 22 transversal 𝑌, as showed in Figure 2.5), in particular, three indexes to investigate the in-plane failure (𝛾1, 𝛾2, and 𝛾3) and one for the out-of-plane collapse (𝛾λ). Figure 2.5. Main directions of the building to assess the simplified indexes. Index 𝛾1 represents the in-plane area ratio and it is the ratio between the area of the shear resistant wall (𝐴w) and the total in-plane area of the building (𝐴t), as in Eq. 2.1: 𝛾1i=𝐴wi 𝐴t Eq. 2.1 where 𝑖 is the considered direction. It should be noted that the index 𝛾1 disregards the slenderness of the wall and the mass of the buildings. Here, the suggested values by (Lourenço et al., 2013), which considers the peak ground acceleration, are proposed as a threshold, since any further indications for rammed earth were not found in the literature. Index 𝛾2 is the area of the resistant wall (𝐴w) to the deadweight ratio (𝐺), as in Eq. 2.2: 𝛾2i=𝐴wi 𝐺 Eq. 2.2 which unit of measure is defined as m2/MN. To calculate the weight of the rammed earth wall, the value of 1900 kg/m3 was assumed for the density of the material (Lacoutre et al., 2007). The threshold proposed by (Lourenço et al., 2013) is also here considered, as values for rammed earth were absent in the literature. Index 𝛾3 represents the ratio between the total shear for seismic loads (𝐹E) and the shear resistant of the structure (𝐹Rdi). The seismic loads are evaluated from a horizontal static load analysis equivalent to the seismic action (𝐹E=𝛽𝐺), where 𝛽 is an equivalent seismic coefficient related to the designed Chapter 2. Rammed earth heritage 23 ground acceleration. As for the shear resistant, it can be assessed as the contribution of all earthquakeresistant walls 𝐹Rdi=∑𝐴wi𝑓vk, where the shear strength 𝑓vk is calculated according to Eurocode 6 (BS EN 1996-1-1, 2005) 𝑓vk =𝑓vk0 +0.4𝜎d. Here, 𝑓vk0 is the cohesion, which is assumed equal to zero in absence of further information, while 0.4 results from the tangent of the friction angle (𝑡𝑎𝑛Φ). Therefore, index 𝛾3 is (Eq. 2.3): 𝛾3i=𝐴wi 𝐴w∙𝑡𝑎𝑛𝛷 𝛽 Eq. 2.3 here 𝛽 is assumed equal to the 𝑃𝐺𝐴, as recommended by (Lourenço et al., 2013), while the value of 𝑡𝑎𝑛Φ equal to 0.70 (Φ=35°) was adopted as it is the minimum value reported (Jaquin, 2008). Index 𝛾3 assumes the meaning of a traditional safety verification approach used for structural design, therefore its threshold value is 1. Regarding the out-of-plane failure, index 𝛾λ is the slenderness as the ratio between the height (ℎwi) and the thickness (𝑡w) of the resistant wall, as in Eq. 2.4: 𝛾λi=ℎwi 𝑡w Eq. 2.4 For this index, the considered threshold values were of 10 according to (NZS 4297, 1998), of 8 as suggested by (Arya et al., 2013), (IS 13827, 1998), (NBC 204, 1994) and (NMAC 14.7.4. 2009, 2011) and the most restrictive of 6 as indicated in (ASTM E2392M, 2010). In addition, the out-of-plane performance of the traditional rammed earth wall was assessed through a kinematic approach assuming a rigid rotating mechanism (Consiglio Superirore dei Lavori Pubblici, 2008; Mendes, 2014). In this method, the capacity curve of a multi-degree of freedom (MDOF) system in terms of displacement 𝑑 and multiplier 𝛼 is obtained resorting the virtual work principle of a system of horizontal forces proportional to the mass. The verification is led with the comparison of the seismic demand that activates the mechanism with the spectral acceleration of a single degree of freedom (SDOF) system equivalent to the MDOF system. In such a scheme (Figure 2.6), the centre of rotation was calculated assuming no tensile strength and compressive strength (𝑓t) of 1.0 MPa, that was defined as a safety low value from the literature (Correia, 2007; Miccoli et al., 2014; Silva et al., 2016). While the seismic demand is (Consiglio Superirore dei Lavori Pubblici, 2008) (Eq. 2.5): Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 30 embedded in adobe walls was proved to increase the seismic performance of the structure; however, such solution is suitable to reinforce new buildings rather than strengthen existing ones. In (Shrestha et al., 2020), the strengthening strategy used reinforced concrete dowels and wedges inserted between rammed earth blocks, while an anchorage system between floor beams and rammed earth façade was also proposed. The system controlled the failure mechanism with limited failure of the walls, nevertheless such solution is not applicable to existing buildings. With respect to strengthening solutions for existing structures, mock-ups strengthened with an externally embracing timber system were tested in (Bui et al., 2011; Lacoutre et al., 2007; Yamin et al., 2004). In this way, the formation of out-of-plane collapse mechanisms was limited and the in-plane structural ductility was increased. (Reyes et al., 2020) proposed a strengthening system consisting of steel strips applied on both faces of the walls and connected with steel connectors through the thickness. The results showed an improvement of the in-plane and out-of-plane response of walls. The solution resulted to increase the in-plane and out-of-plane stiffness, strength, ductility and stability of the specimen. In (Reyes et al., 2019) the use of timber straps and post-tensioned vertical tensors was investigated to strengthen damaged rammed earth wall. The intervention proved to be adequate as the initial lateral stiffness was restored, while an enhancement of the lateral load capacity, displacement capacity and energy dissipation capacity was attained. Although a general improvement of the in-plane and put-of-plane capacity of the rammed earth walls was obtained with the above-described systems, such solutions might be invasive for the existing buildings. For this reason, an externally applied strengthening technique based on the use of mesh embedded in earth-based mortar is proposed. 2.3.2 Textile Reinforced Mortar (TRM) The strengthening technique based on textile reinforced mortar (TRM) has been developed in the last decades, in particular for masonry buildings. This solution was demonstrated to be efficient to mitigate the vulnerability of masonry structures thanks to its tensile strength and reduced self-weight (De Felice et al., 2014; Ghiassi et al., 2012). The TRM is a composite system in which an inorganic matrix confers compressive strength, bonds an embedded mesh to the substrate (i.e. existing wall) and grants geometrical stability to the strengthening, while the embedded mesh improves the tensile strength of the system (i.e. matrix-mesh-structure) and the capacity to further distribute the stresses through adhesion and friction (Blondet et al., 2005; De Felice et al., 2014; Righetti et al., 2016) (Figure 2.11). Chapter 2. Rammed earth heritage 31 Figure 2.11. Textile Reinforced Mortar (TRM) The investigation of TRM as a strengthening solution for earthen buildings was initiated and widely addressed by PUCP, in response to high the seismic risk associated with the Peruvian adobe housing (Vargas, 1983; Vargas et al., 1986, 2005, 2007). The extended experimental program on the TRM technique was conducted on adobe structural elements and mock-ups, which were strengthened by means of synthetic meshes externally applied with earth-based mortar (Blondet et al., 2006, 2005; Lacoutre et al., 2007; Michiels, 2015; Noguez & Navarro, 2005; Vargas et al., 2005; Zavala & Igarashi, 2005). The outcomes demonstrate an improvement of the in-plane resistance and overall structural ductility; while, although evident damaged occurred, the out-of-plane overturning of the walls was prevented (Figueiredo et al., 2013; Noguez & Navarro, 2005; Torrealva, 2016; Torrealva & Acero, 2005). In (Blondet et al., 2006, 2005; Bossio et al., 2013; Reyes et al., 2019; Zavala & Igarashi, 2005), different types of meshes (geosynthetic, plastic or metallic meshes) embedded in TRM for adobe houses were tested and showed an improvement of the seismic capacity of the structure, in particular when geosynthetic meshes are applied. Similar results were achieved in (Noguez & Navarro, 2005) using synthetic mesh. In (Figueiredo et al., 2013), cyclic in-plane tests were conducted on an un-strengthened adobe wall, which was repaired and then strengthened with plastic mesh. It was proven that the stiffness of the wall could be recovered with a significant improvement of the ductility, energy dissipation, and shear capacity; in addition, the fragile failure was avoided. On the other hand, the investigation of externally bonded fibres to increase the lateral load capacity and ductility of a rammed earth walls is rather recent. Nonetheless, the first outcomes report an improvement of the overall seismic capacity similar to that attained for adobe masonry (Fagone et al., 2017, 2019; Liu et al., 2015; Wang et al., 2017). In fact, the use of geosynthetic meshes demonstrated to enhance the in-plane and out-of-plane performance of rammed earth walls, improving the ductility and reducing the risk of collapse (Lacoutre Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 32 et al., 2007). In (Reyes et al., 2019), it was found that steel welded meshes can improve the in-plane shear strength and the out-of-plane capacity of rammed earth wall by preventing premature local failures and by providing confinement after cracking. The lateral stiffness was not significantly affected, while deformation and energy dissipation capacity of walls was enhanced. The effect of the mesh on the outof-plane dynamic response of the wall was found negligible for low intensity motions, but it increased with the increase of the base excitation. In (Miccoli et al., 2017), near surface mounted polyester fabric strips applied with cement mortar on rammed earth walls increased the in-plane energy dissipation and the ductility. Satisfactory improvement of the in-plane capacity of rammed earth walls strengthened with tarpaulin strips bonded externally with an inorganic compound is reported in (Wang et al., 2019). Although several experimental and numerical investigation were conducted on rammed earth structure strengthened with TRM, research on the local response of the solution is still lacking. In addition, very few analysis were performed on the experimental data in terms of influence of the strengthening on the dynamic properties of the existing building, hysteretic energy dissipation and decay of the structural stiffness and strength; while the numerical simulations of rammed earth structure under cyclic and dynamic load were not verified with real observations. Finally, the compatibility of the solutions so far investigated should require further discussion. 2.3.3 Compatibility To preserve the authenticity of architectural heritage, any intervention must meet functional, technical, and conceptual requirements (Figure 2.12). The functional requirements are referred to as the objectives to be pursued (e.g. to improve the ductility of the structure). The technical requirements deal with the features of single materials and their interaction, representing so the practical interface to achieve the goal of the intervention (e.g. mechanical properties of mortar and composite materials to improve the seismic performance of the structure). The conceptual requirements concern the approach to design the intervention. In this regard, the concept of “reversibility”, meant as the possibility to turn a step back into original conditions after the intervention, was the base in architectural heritage, yet often difficult to fulfil. Therefore, a more realistic approach based on “repairability” and “compatibility” has been adopted recently. The “repairability” stands for not precluding or impeding future treatments to improve the previous conditions along with the development of knowledge and technologies. The “compatibility” ensures that introduced treatment materials will not induce negative consequences, guaranteeing the long-term effectiveness of the intervention (van Balen et al., 2005). Chapter 2. Rammed earth heritage 33 In this framework, beside the merely engineering performance of the strengthening systems so far investigated, a key aspect that has not been adequately addressed is the compatibility of the solution. To this purpose, the compatibility of the intervention must consider physical properties (e.g. thermal dilatation), mechanical properties (e.g. stiffness), chemical properties (e.g. reaction with water), mineralogical properties and aesthetic properties (e.g. colour). Therefore, it is evident that compatibility is a fundamental requirement to be met to reduce the vulnerability of rammed earth heritage, which can be achieved only with a multi-disciplinary approach to the problem. Given the above, to guarantee the aesthetic, mineralogical, chemical and physical compatibility, the proposed TRM-strengthening considers the use of the same source materials, which in this case is the raw soil to manufacture the rammed earth and the earth-based mortar, while the mechanical properties of each component (rammed earth, mortar and mesh) are experimentally determined to ensure the mechanical compatibility of the solution. Figure 2.12. A proposed approach to design an appropriate solution for the protection of built heritage. 2.4 Conclusions In the present chapter a general overview of the earthen constructions is provided particularly focusing on the distribution and relevance of earthen architectural heritage, the seismic vulnerability of rammed earth structures, the available strengthening solutions, and their compatibility with existing buildings. The importance of earthen heritage is enclosed in the tangible values of the architecture, but as well in the intangible values of the local identities and knowledges developed by each community, for which a prompt and effective protection is needed. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 34 In this context, to propose suitable interventions aiming at reducing the seismic vulnerability of existing structures, the characterisation of the rammed earth is fundamental. Therefore, the geotechnical properties of soil (particle size distribution, optimal water content and dry density) should be defined at first to guarantee adequate mechanical characteristics of the material. However, although different standards, normative and guidelines are available, the harmonisation of such documents is required to make the different studies comparable. As for the mechanical properties of rammed earth, in general high scattering of the results was found, which is due to the non-homogeneity of the material, to the absence of standard protocols for manufacturing and testing of specimens and to the lack of indication for data analysis (e.g. regression analysis for calculating the Young’s modulus). However, rammed earth materials are characterised by low to moderate compressive strength, low tensile strength and shear strength. Experimental characterisation of the tensile strength is not easy to perform due to the natural fragility of the material; nevertheless, numerical investigation found a relationship between the tensile strength and the compression strength as 𝑓t=0.10𝑓c. The shear response of rammed earth was found influenced by the cohesion and friction angle of the material, which can be assumed as 𝑐 =0.10÷0.14𝑓c and 𝜑 = 35°, respectively. The tensile fracture energy and compressive fracture energy were observed to affect the shear behaviour as well, however very few studies were focused on these parameters which were defined as 𝐺f=0.029𝑓t and as 𝐺c=1.6𝑓c, respectively. Consequently, the overall scattering of results and lack of data of mechanical properties of rammed earth indicate that further studies are needed. Beside the characterisation of rammed earth material, experimental investigation on the overall inplane and out-of-plane response of sub-assemblies is fundamental. Nevertheless, due to the complexity of such tests, only few studies were conducted on full-scale rammed earth walls, while very few analyses were focused on the dissipative capacity and stiffness degradation. Therefore, further experimental investigations on the in-plane and out-of-plane response of rammed earth walls are required. With regard to the numerical analysis of rammed earth structures, several researches were conducted with satisfactory results. Nevertheless, only in few cases the simulation was calibrated on experimental observation, particularly for the out-of-plane dynamic response. Moreover, despite the use of different material models, a constitutive law able to describe the damage and plasticity of rammed earth still requires investigation. Although advanced numerical models provide reliable information on the seismic vulnerability assessment of rammed earth structures, a limitation due to the high computational and time demand Chapter 2. Rammed earth heritage 35 must be regarded. In this context, a simplified method was proposed as a supporting tool for the first screening of large samples of constructions, which in any case cannot substitute advanced analysis for the seismic assessment at decision-making phase. Based on the analysis of local seismic culture, a concern for the seismic risk was already developed through the past generations, from which solutions to reduce the seismic vulnerability were empirically elaborated. Subsequently, different strengthening and reinforcement systems have been proposed in the last decades with the support of scientific evidence. The aim of such solutions is to improve the in-plane performance of the walls, enhance the ductility, confer the overall box-behaviour of the structure, and contain the out-of-plane collapse mechanism of the external walls. As a result, a general improvement of the seismic capacity of the rammed earth was attained; however, such solutions might be invasive for the existing buildings. For this reason, the application of textile reinforced mortar (TRM) for rammed earth heritage is proposed. An extended experimental program was conducted on the use of synthetic meshes externally applied with earth-based mortar, which demonstrated an overall improvement of the lateral load capacity and ductility. Nevertheless, such investigation considered adobe structures, while experimental and numerical research on TRM for rammed earth heritage is rather recent. In general, lack of knowledge on the local response of the TRM components is observed, while very few experimental analyses were focused on the influence of the TRM on the dynamic properties of existing structures, the hysteretic energy dissipation and decay of the structural stiffness and strength. In addition, the numerical simulations of rammed earth structure under cyclic and dynamic loads were not validated with real observations. Finally, the compatibility of the solutions so far investigated should require further discussion. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 36 Chapter 3 TRM COMPONENTS As presented in the Chapter 2, the textile reinforced mortar (TRM) is a composite material, in which each component (rammed earth, mesh and earth-based mortar) has a specific role. In particular, the matrix transfers the stress (or deformation) from the substrate to the embedded mesh by adhesion and friction, while providing stability to the TRM and protecting the mesh from environmental actions. On the other hand, the mesh distributes stresses and cracking, while enhancing the ductility of the structure. Therefore, the definition of the mechanical and physical properties of each component is fundamental to evaluate the performance of the TRM, and allows to design the most compatible solution, also guaranteeing the durability of the intervention. This chapter presents the experimental characterisation of the components later used in the TRM and is organized in sections, in which each material and its related framework are addressed. At first, geotechnical analyses were conducted on two different soils, on the base of which different mixture designs of rammed earth and earth-based mortars were defined. Then, the dry density, compressive strength, and Young’s modulus of the two designed mixtures of rammed earth were evaluated. With regard to the earth-based mortars designed with each supplied raw soil, the experimental investigation addressed the correlation between the clay content and the flexural and compressive strength, dry density, and linear shrinkage. Consequently, the most suitable earth-based mortar for each type of soil was selected and the Young’s modulus was assessed subsequently. As for the meshes, three different types of mesh were selected with basis on a previous survey on the local market. The tensile behaviour was investigated and the physical and geometrical properties were determined to evaluate whether the meshes meet the requirements for composite materials. Finally, the main outcomes of the characterisation of the component materials are summarized. 3.1 Geotechnical analysis e correction of the soils In natural state, a soil is defined as a ternary system containing solid, liquid, and gaseous phases. The solid phase is composed of organic and inorganic materials, being the later formed from residual rock and minerals, such as silicates, feldspar, lime, gypsum, clay minerals, water-soluble salts, oxides of aluminium and iron. The inorganic material can be also described considering its composition in terms of size of grain, as gravel, sand, silt, and clay. Therefore, given the fact that the clay acts as a binder, while gravel, sand and silt constitute the skeleton, in general any earthen compound can be potentially Chapter 3. TRM components 37 used as building material. However, the amount of clay fraction and its large specific surface area is the cause of water sorption, which confers plasticity to the mixture but induces as well swelling and shrinkage, affecting so the structural behaviour of an earthen building. For this reason, to establish whether a soil is suitable for a specific earthen technique, geotechnical analyses to obtain quantitative data in terms of particle size distribution, the type of clay and dry density, are conducted. In this framework it is already reported that, since the material supplying could not cover the large amount of soil required from the entire experimental program of this research, two different raw soils from Alentejo region, hereinafter referred as RS_I and RS_II, were firstly characterised for being used as raw materials. The particle size distribution (PSD) of a soil represents the percentage of weight content of the different sizes of grain and it is typically obtained from two analysis processes, namely sieving and sedimentation (LNEC E196, 1966). Since the soil is a highly non-homogeneous material, the quartering method is led at first to obtain a representative sample. Afterwards, the sample, previously dried in the oven at 100°C for 24h, is sieved through sieve #10 (2 mm aperture). The retained soil is then washed using an appropriate sieve, while being careful to avoid loss of coarse material. This step intends to clean likely fine particles stuck to coarse grains. After drying for 24h at 100°C, the material is sieved through a series of sieves with decreasing aperture size (Figure 3.1a), hence the percentage of passing material for each sieve is calculated as: 𝑃i=𝑃S−∑𝑃T 𝑃S Eq. 3.1 Where 𝑃 s is the weight of the dry sample and 𝑃T is the weight of the retained material in all the sieves with an aperture equal or larger than the one considered. The passing material through sieve #10 is used for sedimentation analysis that is based on Stoke’s law, for which it is possible to relate the velocity of sedimentation of a particle with its diameter (hypothesized as a sphere) and the viscosity of the liquid in which the particle is in suspension. Therefore, a sample of the fine fraction is dispersed in an antiflocculating solution of sodium hexametaphosphate and sodium carbonate. Afterwards, the sample is washed with distilled water through sieve #200 (0.074 mm) and the passing material is collected in a beaker. Then the beaker is shaken vigorously to put all particles in suspension and the density is recorded along a logarithmic time interval (Figure 3.1b); while the material retained at sieve #200 is dried and sieved with a set of sieves from #40 to #200 (from 0.425 mm to 0.074 mm of aperture size) (Figure 3.1c). Figure 3.2 and Table 3.1 report the PSD curve of RS_I and RS_II together with the envelope curve recommended by (Houben & Guillaud, 1994) and the Fuller curve for rammed earth, which intend to Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 38 guarantee adequate dry density and reduced shrinkage of rammed earth elements. As result, both RS_I and RS_II did not fit the suggested distribution, presenting high clay content and low sand and gravel fractions; consequently, high shrinkage and low values of dry density are expected if RS_I and RS_II are directly used for manufacturing rammed earth. However, the high clay content allowed to optimize the raw soils by mixing with local coarse materials. Thereby, the supplying of raw soils and the related transportation were minimized in response to the large quantity of materials required by the experimental program. (a) (b) (c) Figure 3.1. Particle size distribution analysis: a) soil retained at sieve #10, b) sedimentation, and c) soil passing the sieve #10 and retained at sieve #200. Table 3.1. Particle ranges content of raw soils. Soil Clay [%] Silt [%] Sand [%] Gravel [%] RS_I 29 32 20 19 RS_II 17 23 30 31 Clay < 0.002 mm < silt < 0.06 mm < sand < 2 mm < gravel Figure 3.2. Particle size distribution curves of RS_I and RS_II compared with Fuller distribution and recommended envelop by (Houben & Guillaud, 1994). The mechanical and physical properties of the earthen materials are defined by several factors, including the content and type of the clay fraction. The type of clay, and therefore its behaviour, is determined by the characteristics and proportions of the constituent minerals; but to identify such Chapter 3. TRM components 39 features, specific equipment and complex process are needed. Yet, simpler tests can be carried out to evaluate qualitatively the behaviour of the clay fraction; with this regard, the determination of the Atterberg’s limits is among the most used, which include the liquid limit (𝐿𝐿), plastic limit (𝑃𝐿), and shrinkage limit (𝑆𝐿). The Atterberg’s limits are defined by the water content values that bound the transition of the possible states (liquid, plastic, semi-solid and solid) of a sample of soil sieved through 0.425 mm. In the present investigation, the limits of consistency were determined with basis on the Portuguese standard (NP 143, 1969). The liquid limit (𝐿𝐿) is experimentally determined by the Standard Casagrande device, which consists of a cup where a soil paste is placed into and a groove is cut at the centre. The cup is then lifted and dropped onto the base by a cam from a height of 10 mm counting the blows until the groove is closed for a length of 12.7 mm (Figure 3.3a). The water content in percentage to close the groove with 25 blows is defined as the liquid limit. Four tests are led varying the water content to achieve closure in a range of 15-35 blows; therefore, a linear regression is performed and the water content corresponding to 25 blows is interpolated. As for the plastic limit (𝑃𝐿), it represents the water content at which the fine soil changes from plastic to semi-solid state. The plastic limit is determined by rolling a thread of a paste of fine soil on a non-porous surface (e.g. glass); when the thread of 3.2 mm diameter crumbles, it means that the plastic behaviour is lost and therefore the plastic limit is achieved (Figure 3.3b). The plasticity index (𝑃𝐼) is another important parameter, which results from the difference between the liquid limit and the plastic limit (𝑃𝐼 = 𝑃𝐿 − 𝐿𝐿) and represents the range of water content for which the soil exhibits plastic properties. On this regard, soils are so classified as non-plastic (𝑃𝐼 = 0), slightly plastic (0 < 𝑃𝐼 < 7), medium plastic (7 < 𝑃𝐼 < 17) and highly plastic (𝑃𝐼 > 17). The index of activity (𝐴𝐼) provides a broader compression on the influence of the clay fraction on the behaviour of the full soil, as it results from the ratio between the 𝑃𝐼 and the percentage of clay fraction (below 0.002 mm) (Skempton, 1953), and represents the aptitude of the soil to swell due to adsorption of water. Therefore, 𝐴𝐼 can be used as an indicator of the shrinkage of earth-based material. Furthermore, a direct positive correlation was found between 𝐴𝐼 and the contribution of the cohesion to the shear strength (Skempton, 1953). As for the classification based on the 𝐴𝐼, a soil can be identified as non-active (𝐴𝐼 < 0.75), medium active (0.75 <𝐴𝐼 < 1.25) and active (𝐴𝐼 > 1.25). The limits of consistency of soils RS_I and RS_II are reported in Table 3.2 and the respective points are plotted in the chart of Casagrande with the envelope recommended by (Houben & Guillaud, 1994) for rammed earth in Figure 3.4. Both soils can be classified as lean clay with low to medium plasticity and no or low dilatancy (Casagrande, 1948); while, considering the 𝐴𝐼, both RS_I and RS_II are classified Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 46 Table 3.6. Compositions of analysed mortars EM_I and EM_II. Mortar Clay [%] Silt [%] Sand [%] EM_I-c09 9 10 70 EM_I-c11 11 12 67 EM_I-c12 12 14 64 EM_II-c06 6 8 86 EM_II-c08 8 11 81 EM_II-c10 10 13 77 At first, the water content (𝑊/𝑆) for the optimal workability of the mortar was iteratively defined according to the flow table test (BS EN 1015-3, 1993), by setting a value of 170 mm, as suggested by (Gomes et al., 2019) (Figure 3.13a). Afterwards, for each composition of mortar, three specimens with dimensions 30X30 300 mm3 were cast to measure the shrinkage by means of the Alcock’s test (HB 195, 2009) (Figure 3.13b), and three specimens with dimensions 40X40X160 mm3 were cast for the mechanical characterisation according to EN 1015-11 (BS EN 1015-11, 1993). After a drying period of 28 days in constant hygrothermal conditions (𝑇 = 20 ±2°C and 𝑅𝐻 =57.5 ± 5%), the mechanical tests were performed under three-point bending loading with monotonic displacement control at speed 1.5 μm/s (Figure 3.13c). Then, the remaining parts of the specimens were tested under compression at a constant speed of 25 μm/s (Figure 3.13d). These test speeds were defined to achieve failure within a period of 30 s and 90 s (HB 195, 2009). A sample of material was collected after each test to obtain its equilibrium water content, as the latter might affect the mechanical properties of the rammed earth. The equilibrium water content resulted in range 0.20 – 0.80 %. For each mortar composition, the average values and the coefficient of variation of density (𝜌), linear shrinkage (𝐿s), flexural strength (𝑓 b), and compressive strength (𝑓 c) are summarized in Table 3.7 with the water content for the optimal workability (𝑊/𝑆), while the corresponding graphs in relation with the clay content are illustrated in Figure 3.14. In general, larger 𝑊/𝑆 and linear shrinkage (𝐿𝑠) were observed with the increasing of clay content; nonetheless the trend was not continuous along the two mortars (Figure 3.14a). Such results can be due to the different mineralogical composition between the clay of RS_I and RS_II. In fact, the plastic limit of clay of RS_I resulted lower compared to the clay of RS_II (see Section 3.1), meaning that, to achieve a plastic consistency, the clay of RS_I required less water than the clay of RS_II. However, a continuous trend can be noted when the mechanical properties are analysed (Figure 3.14b); therefore, the flexural and compressive strength of an earth-based mortar can be assumed mostly related to the percentage of Chapter 3. TRM components 47 clay rather than its typology. Afterwards, to select the most suitable mortar for the proposed TRM, the maximum value of linear shrinkage of 2% was set as recommended by (Gomes, 2013); accordingly, the mixture EM_I-c09 was chosen as EM_I. With regard the EM_II, the mixture EM_II-c06 was selected despite not meeting the recommended 𝐿s threshold, since reducing further the clay content would produce a mortar with insufficient mechanical strength. In conclusion, the compressive strength of mortars EM_I and EM_II was, respectively, 0.66 MPa and 0.49 MPa, while the flexural strength was 0.29 MPa and 0.21 MPa, which are found to be consistent with the values found in literature (Gomes, 2013; Gomes et al., 2019). (a) (b) (c) (d) Figure 3.13. Characterisation of earth-based mortars: a) flow table test, b) Alcock’s test (linear shrinkage), c) three-point bending test, and d) compression test. Table 3.7. Properties of the analysed earth-based mortars. Mortar 𝑾/𝑺 [%] 𝝆 [𝐠/𝐜𝐦𝟑] 𝑳𝐬 [%] 𝒇𝐜 [𝐌𝐏𝐚] 𝒇𝐛 [𝐌𝐩𝐚] EM_I-c09 18 1.81 (1%) 1.33 0.66 (15%) 0.29 (4%) EM_I-c11 19 1.82 (1%) 2.00 0.87 (7%) 0.49 (22%) EM_I-c12 20 1.81 (2%) 3.00 1.25 (7%) 0.53 (13%) EM_II-c06 20 1.86 (1%) 2.11 0.49 (3%) 0.21 (5%) EM_II-c08 22 1.86 (1%) 3.00 0.51 (8%) 0.22 (15%) EM_II-c10 27 * * * * * Because of the elevate W/S required by EM_II60-40_c10, unsuitable values of linear shrinkage were expected, therefore these tests were not performed. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 48 (a) (b) Figure 3.14. Correlation between the clay content and: a) W/S and linear shrinkage, and b) flexural and compressive strength. Subsequently, the Young’s modulus of the selected mortars was evaluated by means of axial compression tests on three cylindrical specimens with 90 mm of diameter and 175 mm of height, casted and dried in the same conditions of the prismatic specimens. Prior to testing, a thin layer of gypsum was applied on the top and bottom surfaces of the specimens to guarantee the correct distribution of the load. The tests were conducted under displacement control at a constant speed of 1.5 μm/s, while the load was monitored with a load cell and the axial deformations at the middle third section of the specimens were recorded with three LVDTs disposed radially (Figure 3.15a). A characteristic diagonal fracture observed for earth-based mortar is shown in Figure 3.15b, while the curves of the compression tests on cylinders are illustrated in Figure 3.16a and Figure 3.16b for EM_I and EM_II, respectively. Since any recommendations or standards to calculate the Young’s modulus were found for earth-based mortar, the change of stiffness related to the microstructural damage level was investigated by means of stepwise linear regressions of the stress-stain curves, considering ranges of 10% 𝑓 c with increments of 2% between each step. The Young’s modulus values of the different ranges are reported in Figure 3.17 as function of the average stress level of the respective range normalised by 𝑓 c. The coefficient of determination 𝑅2 is also reported. The fact that the Young’s modulus is not constant with increasing stress values highlights the high nonlinear behaviour of EM_I and EM_II, even for low rate of compression load. In addition, the Young’s modulus evaluated in range 0% - 30% of 𝑓 c is reported in Figure 3.17, which is the common range considered in material characterisation. The average values refer as 𝐸m were 2729 MPa (CoV = 23%) and 1232 MPa (CoV = 14%) for EM_I and EM_II, respectively; which resulted overestimated in comparison with the stepwise analysis, however in line with values found by other authors (Gomes, 2013; Gomes et al., 2019). Chapter 3. TRM components 49 (a) (b) Figure 3.15. Axial compression tests of the earth-based mortars: a) test setup, and b) failure mode. (a) (b) Figure 3.16. Stress-strain curves resulting from the compression test of the cylinders: a) EM_I, and b) EM_II. (a) (b) Figure 3.17. Analysis of Young's modulus as a function of the compression level for: a) EM_I, and b) EM_II. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 50 It is here reported that a further earth-based mortar labelled as EM_0 was also used. The EM_0 was characterised in a previous investigation (Oliveira et al., 2017), however additional mechanical tests were conducted to assess the flexural strength 𝑓 b and the compressive strength 𝑓 c, which resulted 0.5 MPa (CoV=14%) and 1.2 MPa (CoV=12%), respectively. The average Young’s modulus 𝐸m, computed by linear fitting of the stress-strain curves in the range 0-30% of 𝑓 c, was of about 4915 MPa. 3.4 Characterisation of reinforcing meshes Regarding the fibres to integrate the TRM strengthening solution, locally available low-cost meshes were individuated considering their sufficient flexibility and adequate aperture size (4–22 mm) to permit satisfactory embedding of the mortar and adhesion to the support. Therefore, a glass fibre mesh (GM), a nylon mesh (NM) and a geomesh (GeoM) were selected. The meshes exhibited different weft or geometrical characteristics; in particular, GM presented a net aperture of 8X9 mm2 (Figure 3.18a) while the intersection between the orthogonal threads was woven (Figure 3.18d); conversely, the NM had a net aperture of 16X21 mm2 (Figure 3.18b) and welded intersection connecting the threads. While the GeoM showed a net aperture of 22X25 mm2 (Figure 3.18c) and woven union between the yarns (Figure 3.18f). In addition, the manufacturing process of a single yarn and its cross section are different among the meshes; in fact, as can be observed through a microscopic zoom, yarns of GM are made of a bundle of glass fibre filament (Figure 3.18g) and presented a cross section of 0.29 mm2 (Figure 3.18j), while the yarns of NM are made of a single extruded nylon thread (Figure 3.18h) with a cross section of 0.97 mm2 (Figure 3.18k). Contrary, the yarns of the GeoM are composed of bonded filament (Figure 3.18i) and a cross section of 3.09 mm2 (Figure 3.18l). Consequently, being the features different along the orthogonal orientations, the linear density (𝑇𝐸𝑋) (Vasconcelos, 1993) was calculated for both the longitudinal (𝑋) and transversal (𝑌) separately; while grammage (𝐺𝑆𝑀) (ISO 3374, 2000) and density (𝜌) referred to the entire mesh. The physical and geometrical characterisation of the meshes are reported in Table 3.8. Chapter 3. TRM components 51 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) Figure 3.18. Meshes selected for the experimental program: a) Glass fibre mesh (GM), b) Nylon mesh (NM), c) geomesh (GeoM), d) intersection GM, e) intersection NM, f) intersection GeoM, g) detail section GM, h) detail section NM, i) detail section GeoM, j) cross section GM, k) cross section NM, and l) cross section GeoM. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 52 Table 3.8. Physical properties of GM, NM and GeoM. Mesh Price [€/𝐦𝟐] Mesh size [𝐦𝐦𝐗𝐦𝐦] 𝑻𝑬𝑿𝐗 [𝐠/𝐤𝐦] 𝑻𝑬𝑿𝐘 [𝐠/𝐤𝐦] 𝑮𝑺𝑴 [𝐠/𝐦𝟐] 𝝆 [𝐠/𝐜𝐦𝟑] 𝑨𝐲 [𝐦𝐦𝟐] GM 0.85 8X9 471 424 93 1.610 0.29 NM 0.63 16X21 765 874 63 0.897 0.97 GeoM 0.78 22X25 4210 2820 215 3.09 According to (NATIONAL RESEARCH COUNCIL, 2004), all the selected meshes meet the grammage (GSM) requirement for fabrics integrating composites materials, whose value should be lower than 600 g/m2. The tensile behaviour of the dry meshes was evaluated according to the procedure prescribed by (ASTM D6637, 2010) and (de Felice et al., 2018). Five specimens were prepared per mesh type with a width of about 50 mm. The free length of the specimens depended on the mesh type, namely 300 mm for GM and GeoM, while 200 mm for NM, as different magnitudes of elongation were expected. To avoid sliding of the specimen through the clamps during the test, steel plates were fixed at the extremities of each specimen in an additional bonded length of 50 mm using an epoxy compound. The tests were conducted under displacement control with different testing speeds according to the mesh type, namely 10 μm/s for GM, 50 μm/s for GeoM and 100 μm/s for NM, while the axial deformation was monitored with a single LVDT between clamps (Figure 3.19). Figure 3.19. Setup of the tensile tests on mesh specimens. The resulting tensile curves in terms of force per width of specimen (𝐹 w) against axial strain are shown in Figure 3.20. It should be noted that the only direction along which the mesh showed highest Chapter 3. TRM components 53 tensile resistance is below discussed in terms of maximum linear force (𝐹 wpeak), tensile strength (𝑓 t), elongation at peak load (𝜀peak) and Young’s modulus (𝐸y). GM was characterised by a linear response up to the maximum force, which attained an average value of 18.42 kN/m (CoV = 11%) for a corresponding elongation of 0.021 mm/mm (CoV = 10%); afterwards, the resistance dropped with the consecutive breaking of fibres and the complete failure of the yarns (Figure 3.20a). Contrary, NM response was nonlinear since early load level and the failure was achieved with the maximum linear force, which resulted in average 3.18 kN/m (CoV = 4%) (Figure 3.20b) and with the related elongation of 0.340 mm/mm (CoV = 16%). Finally, the behaviour of the GeoM was initially nonlinear, followed by a short plateau and then hardening with linear response up to the peak load, which attained an average value of 42.08 kN/m (CoV = 3%) and elongation of 0.097 mm/mm (CoV = 3%). The failure occurred with breaking of the fibres and yarns (Figure 3.20c). Thus, the tensile strength (𝑓 t) could be assessed considering the maximum force evenly distributed through the number of the effective yarns and the cross section of the threads. The resulting average 𝑓 t was 625.80 MPa (CoV = 11%), 54.37 MPa (CoV = 4%) and 340.46 MPa (CoV = 3%), for GM, NM and GeoM, respectively. Therefore, the Young’s modulus (𝐸y) was calculated through a linear regression of the stress-strain values in the range 0-30% of 𝑓 t obtaining 31981 MPa (CoV = 6%) for GM, 361 MPa (CoV = 4%) for NM, and 2626 MPa (CoV = 6%) for GeoM. The results of the mechanical characterisation of the meshes are reported in Table 3.9. As observed, the three meshes presented different features; in fact, despite GeoM showed the highest maximum linear force, the highest tensile strength was attained by GM. While NM exhibited the largest elongation. Yet, the main difference was found in the Young’s modulus which resulted in different magnitude between the meshes. Nonetheless, all the meshes are deemed appropriate for the proposed TRM-strengthening. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 54 (a) (b) (c) Figure 3.20. Linear force-strain curves of the meshes tested in tension: a) GM (X direction), b) NM (Y direction), and c) GeoM (X direction). Table 3.9. Mechanical properties of the tested meshes. Mesh 𝑭𝐰𝐩𝐞𝐚𝐤 [𝐤𝐍/𝐦] 𝒇𝐭 [𝐌𝐏𝐚] 𝛆𝐩𝐞𝐚𝐤 [𝐦𝐦/𝐦𝐦] 𝑬𝐲 [𝐌𝐏𝐚] GM 18.42 (11%) 625.80 (11%) 0.021 (10%) 31981 (6%) NM 3.18 (4%) 54.37 (4%) 0.340 (16%) 361 (4%) GeoM 42.08 (3%) 340.46 (3%) 0.097 (3%) 2626 (6%) 3.5 Conclusions The present chapter reports the characterisation of the component materials of the TRMstrengthening, namely rammed earth, earth-based mortars and meshes. At first, geotechnical analyses were performed on two different raw soils from Alentejo region (RS_I and RS_II). According to the literature and basing on the geotechnical results, both RS_I and RS_II were considered not appropriate for rammed earth technique because of the high clay content and the low dry Chapter 3. TRM components 55 density after compaction for the required high OWC. Thus, low mechanical strength was expected for rammed earth manufactured with RS_I or RS_II. Nonetheless, the high clay content was favourable in view of optimizing the materials while reducing the transportation of raw soils for the subsequent experimental programme. Therefore, to obtain soils appropriate for rammed earth, coarse material was added in percentage of 30% of coarse sand and 30% of gravel to 40% of raw soil, resulting in corrected mixtures CS_I and CS_II. Afterwards, geotechnical analyses on CS_I and CS_II confirmed their suitability for rammed earth technique, as the clay content reduced to 12% and 6%, while the dry density increased to 2.13 g/cm3 and 2.02 g/cm3 for a OWC of 9% and 12%, for CS_I and CS_II, respectively. Subsequently, the mechanical characterisation of rammed earth manufactured with CS_I and CS_II, labelled RE_I and RE_II, aimed at defining the compressive strength (𝑓 c) and the Young’s modulus, while verifying the reliability of the drop ball test for the manufacturing process. As result, the average density of the RE_I and RE_II cylinders was 2.14 g/cm3 (CoV = 3%) and 1.87 g/cm3 (CoV = 8%) for a water addition of 9% and 11%, respectively, which were consistent with the Proctor test result. While the average compressive strength (𝑓 c) achieved a value of 1.5 MPa (CoV = 10%) for RE_I and 0.56 MPa (CoV = 13%) for RE_II, which were within the range of values presented in literature. As for the Young’s modulus, the stepwise analysis based on the level of compressive stress demonstrated the nonlinear behaviour of rammed earth even for low rates of compression. However, the Young’s modulus (𝐸r) in the range 0-30% of 𝑓 c commonly considered for materials investigation resulted in average 506 MPa (CoV = 20%) for RE_I and 213 MPa (CoV = 33%) for RE_II. To define the earth-based mortars used in the subsequent experimental program, different mixtures with the base on RS_I and RS_II were tested by varying their clay content. Therefore, for each composition, the 𝑊/𝑆 ratio for optimal workability was established at first. Afterwards, the average linear shrinkage (𝐿s), flexural strength (𝑓 b) and compressive strength (𝑓 c) were evaluated. To establish the most suitable mixture, the threshold of 2% of linear shrinkage was set as suggested in literature. Consequently, the earth-based mortars EM_I and EM_II were individuated and their compressive strength was, respectively, 0.66 MPa and 0.49 MPa, while the flexural strength was 0.29 MPa and 0.21 MPa. With regard the Young’s modulus, a stepwise analysis was conducted on stress-strain curves of compression tests on cylinders. The results of the analysis showed the nonlinear response of the earth-based mortars in spite of the low stress values. Yet, the Young’s modulus (𝐸m) calculated in the range 0-30% of 𝑓 c resulted in average 2729 MPa (CoV = 23%) and 1232 MPa (CoV = 14%) for EM_I and EM_II, respectively, which were found consistent with the literature. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 62 behaviour might be due to the small aperture size of the GM. While in case of TCNM and TCGeoM, cracks were widespread and more uniformly distributed, as a consequence of the higher deformability of the meshes and the larger aperture size, which promoted a better embedding of the mesh and prevented the detachment of the mortar during the last stage (Figure 4.4b and Figure 4.4c). (a) (b) (c) Figure 4.4. Failure mode of the TRM coupons tested in tension: a) side-view of TCGM, b) front-view of TCNM, and c) front-view of TCGeoM. 4.2 Characterisation of the matrix-fibre bond behaviour The pull-out test intends to complement the investigation on the matrix-fibre interaction. The setup considers a yarn or a mesh band embedded for a specific bonded length in a cylinder of mortar, of which the diameter is to avoid damage in the matrix. As a result, the geometry of the pull-out specimen allows analysing the tangential stress-strain distribution along the interface of the two materials. It is specified that the pull-out program was only conducted on the only GM and NM (see Section 3.4.) embedded in EM_I (see Section 3.3.). In this regard, the width of the embedded mesh was fixed to 50 mm, while different bonded lengths were tested depending on the mesh type. In the GM case, the bonded lengths considered were 30 mm, 50 mm, 90 mm, and 150 mm, while the embedded lengths adopted for NM were 15 mm, 20 mm, 30 mm, 50 mm and 70 mm. The pull-out specimens consisted of cylinders of EM_I mortar with ±150 mm diameter and height corresponding to the bonded length. Specific molds were previously drilled to promote the drying of the mortar while inside and oiled to facilitate the removal of the specimens (Figure 4.5a). For each bonded length, five specimens were casted ensuring the correct filling of the mold and perfect alignment of a single mesh band, while the unbonded part of the mesh was kept vertically to avoid any damage due to bending (Figure 4.5b). The specimens, hereinafter labelled according to the nomenclature PO#type of mesh#bonded Chapter 4. TRM composite 63 length#_number of specimen (e.g. POGM150_1), were demolded after 7 days while the overall drying took place for a period of 28 days under constant hygrothermal conditions (𝑇 = 20 ± 2 °C and 𝑅𝐻 = 60 ± 5 %). Prior testing steel plates were fixed with epoxy compound at both extremities of the mesh for a bonded length of 50 mm to guarantee the grip in the testing machine. The pull-out tests were conducted under different displacement-controlled speeds according to the expected elongation, in particular 10 μm/s was adopted for POGM and 50 μm/s was adopted for PONM. To monitor likely sliding of the yarns within the mortar, the displacements of the mesh were recorded by means of one LVDT set at the free end and two LVDTs set at the loaded end close to the mortar surface, while the load was recorded by a load cell, as illustrated in Figure 4.6. (a) (b) Figure 4.5. Manufacturing of the specimens for the pull-out tests: a) drilled moulds, and b) casting of the mortar. Figure 4.6. Setup of the pull-out tests. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 64 The failure modes are here presented, although they are later throughout discussed with respect to the different type of specimens in terms of mesh and bonded length. As illustrated in Figure 4.7, three types of failure mode were observed during the tests, which correspond to tensile failure at the unbonded part of the mesh (𝐹𝑀1), tensile failure in an embedded section of mesh (𝐹𝑀2) and mesh slipping within the mortar (𝐹𝑀3). However, it is reported that, the failure of the mortar occurred in some specimens due to damaging during the preparation of the respective test. 𝐹𝑀1 𝐹𝑀2 𝐹𝑀3 Figure 4.7. Failure modes (FM) observed in the pull-out tests. The response curves of the POGM specimens are reported in terms of linear force (𝐹 w), which considered the width of the mesh, against the displacement recorded at the loaded end (𝑑LE) (Figure 4.8a) and displacement at the free end (𝑑FE) (Figure 4.8b). In general, the POGM specimens exhibited an initial elastic response, in which the load is transferred from the yarns to the matrix by adhesion until attaining the bond strength. Subsequently, micro-cracks developed on the interface mortar-mesh and the response became nonlinear. During the nonlinear stage, both mechanism of adhesion and friction coexisted until the bond strength was attained in the section corresponding to the free end. Afterwards, sliding of the mesh occurred at this section and friction controlled the load transfer from the mesh to the matrix. Finally, one of the failure modes above described was achieved. Such behaviour is consistent with findings on TRM composite system used in masonry buildings (Banholzer, 2006; Banholzer et al., 2005; Dalalbashi et al., 2018; Donnini et al., 2018; Ferreira et al., 2016; Zhang et al., 2013). Table 4.1 summarises the results of the maximum linear force (𝐹 wpeak) and failure mode (𝐹𝑀) in relation to the bonded length (𝐿b). It is observed that failure due the mesh slipping within the mortar (𝐹𝑀3) occurred only for POGM30, while tensile failure in an embedded section of mesh (𝐹𝑀2) was found in the remaining cases. In addition, increasing values of maximum linear force up to a constant value of 12.8 kN/m were obtained. Nonetheless, the POGM maximum capacity resulted lower than that of the GM (18.42 kN/m, see Section 3.4.). Chapter 4. TRM composite 65 (a) (b) Figure 4.8. Pull-out response curves of the POGM specimens: a) displacement at the loaded end, and b) displacement at the free end. Table 4.1. Results of the pull-out tests conducted on the POGM specimens Spec. 𝑭𝐰𝐩𝐞𝐚𝐤 [𝐤𝐍/𝐦] 𝑭𝑴 Spec. 𝑭𝐰𝐩𝐞𝐚𝐤 [𝐤𝐍/𝐦] 𝑭𝑴 Spec. 𝑭𝐰𝐩𝐞𝐚𝐤 [𝐤𝐍/𝐦] 𝑭𝑴 Spec. 𝑭𝐰𝐩𝐞𝐚𝐤 [𝐤𝐍/𝐦] 𝑭𝑴 30_1 4.6 3 50_1 6.9 2 90_1 13.2 2 150_1 14.4 2 30_2 * * 50_2 5.2 2 90_2 12.5 2 150_2 13.7 2 30_3 3.7 3 50_3 * * 90_3 9.9 2 150_3 12.7 2 30_4 3.8 3 50_4 5.4 2 90_4 13.4 2 150_4 14.0 2 30_5 4.2 3 50_5 8.8 2 90_5 14.8 2 150_5 9.2 2 Av. (CoV) 4.1 (10%) Av. (CoV) 6.6 (25%) Av. (CoV) 12.8 (14%) Av. (CoV) 12.8 (17%) * Failure of the mortar. With regard to the PONM specimens, no displacements were observed at the free end section. For this reason, only the curves in terms of linear force (𝐹 w) and displacement at the loaded end are represented in Figure 4.9a; while the boxplots illustrated in Figure 4.9b describe the results of the maximum linear force (𝐹 wpeak) as function of the bonded length (𝐿b). Table 4.2 reports the maximum linear force (𝐹 wpeak) and failure mode (𝐹𝑀) for each bonded length (𝐿b). As demonstrated in Figure 4.9a, the pullout response of the specimens was similar despite the different bonded length of the mesh. Such result is further confirmed by the boxplots in Figure 4.9b, for which the bonded length did not influence the maximum linear force. In addition, as reported in Table 4.2, the force capacity was found similar to the tensile capacity of the NM that was 3.2 kN/m (see Section 3.4), while the failure of any PONM occurred with the rupture of the mesh at an unbonded section (𝐹𝑀1). Furthermore, based on the fact that a single Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 66 transversal yarn embedded in the mortar was found to be sufficient to achieve the full tensile capacity of the mesh, as in case of PONM15 and PONM20, the bond in POGM was assumed to be granted by mechanical anchoring of the welded orthogonal yarns. Therefore, the behaviour response of PONM was concluded to not be representative of a typical matrix-fibre interface response. (a) (b) Figure 4.9. Results of the pull-out tests conducted on the PONM specimens: a) response curve considering the displacement at the loaded end, and b) boxplot of the maximum linear force as function of the bonded length. Table 4.2. Results of pull-out tests on the PONM specimens. Spec. 𝑭𝐰𝐩𝐞𝐚𝐤 [𝐤𝐍/𝐦] 𝑭𝑴 Spec. 𝑭𝐰𝐩𝐞𝐚𝐤 [𝐤𝐍/𝐦] 𝑭𝑴 Spec. 𝑭𝐰𝐩𝐞𝐚𝐤 [𝐤𝐍/𝐦] 𝑭𝑴 Spec. 𝑭𝐰𝐩𝐞𝐚𝐤 [𝐤𝐍/𝐦] 𝑭𝑴 Spec. 𝑭𝐰𝐩𝐞𝐚𝐤 [𝐤𝐍/𝐦] 𝑭𝑴 15_1 2.8 1 20_1 3.9 1 30_1 3.9 1 50_1 4.0 1 70_1 3.7 1 15_2 * * 20_2 * * 30_2 3.6 1 50_2 3.8 1 70_2 3.7 1 15_3 3.9 1 20_3 3.6 1 30_3 3.0 1 50_3 3.4 1 70_3 3.2 1 15_4 * * 20_4 * * 50_4 3.9 1 70_4 3.7 1 20_5 3.5 1 50_5 3.8 1 Av. (CoV) 3.4 (-) Av. (CoV) 3.7 (5%) Av. (CoV) 3.5 (14%) Av. (CoV) 3.8 (6%) Av. (CoV) 3.6 (9%) * Failure of the mortar. 4.2.1 Descriptive statistical analysis of pull-out test results Based on the above discussed findings of pull-out tests, a descriptive statistical analysis was performed only on the POGM results. The analysis considered the bonded length (𝐿b) in relation to the maximum linear force (𝐹 wpeak) (Figure 4.10a), linear force at the sliding onset (𝐹 ws) (Figure 4.10b), ultimate displacement at the loaded end (𝑑LEult) (Figure 4.10c), ultimate displacement at the free end Chapter 4. TRM composite 67 (𝑑FEult) (Figure 4.10d), displacement at the loaded end for the maximum linear force (𝑑LE,Fwpeak ) (Figure 4.10e) and linear force at the end of the elastic phase (𝐹el) (Figure 4.10f). It is specified that 𝑑LEult and 𝑑FEult were defined as the displacement at failure or when the linear force decreased to 80% of 𝐹 wpeak, particularly for POGM30. The boxplots in Figure 4.10 represent the median, the 25th and 75th percentiles, while the whiskers are the maximum and the minimum of the data set. A bilinear relationship between the bonded length (𝐿b) and the maximum linear force (𝐹 wpeak) was found in Figure 4.10a. Indeed, the average maximum linear force increased as a function of the bonded length up to 90 mm, after which 𝐹 wpeak seems to attain a constant value. Therefore, the minimum bonded length to fully develop the anchoring of the mesh is deemed of about 90 mm. For the bonded length of 30 mm, failure occurred due to sliding of the mesh inside the mortar (𝐹𝑀3); while, for larger bonded lengths, failure was achieved with the rupture of an embedded mesh section (𝐹𝑀2), yet the full exploitation of the GM tensile capacity was not achieved in any case. The failure for tensile load lower than the GM capacity can be ascribed to damage of fibres due to friction with mortar and to telescopic effect of the yarns, for which the progressive breaking down of filaments from the sleeve to the core (see Section 3.4.) prevented to attain the mesh tensile strength (Banholzer, 2006; De Felice et al., 2018). Figure 4.10b shows that the linear force when the sliding onset (𝐹 ws) increased linearly with the bonded length, yet with values substantially lower than the maximum linear force (𝐹 wpeak), meaning that sliding activates a friction configuration that contributes to the bond mechanism. Nevertheless, the friction generated at each yarn is not expected to assume an uniform distribution along the bonded length as a consequence of the damage levels of the yarns; in addition, uneven stress levels are also expected along the width of the mesh band, leading to premature failure of the GM. Figure 4.10c, Figure 4.10d and Figure 4.10e suggest that the slipping level is correlated to the failure of an embedded section of the mesh. In fact, for bonded length larger than 30 mm, the observed failure mode was 𝐹𝑀2 (see Section 4.2.), while the ultimate displacement at the loaded end (𝑑LEult ) was found constant and similar to ultimate displacement at the free end (𝑑FEult) and to the displacement at the loaded end for the maximum linear force (𝑑LE,Fwpeak ). Therefore, the wearing caused by such level of displacement might contribute to the failure. In Figure 4.10d, lower values of ultimate displacement at the free end (𝑑FEult) are observed for larger bonded length, meaning that larger anchorage provides higher restraint to the sliding of the mesh. Finally, two groups of bonded lengths (30−50 mm and 90−150 mm) within which the linear force at the end of the elastic phase (𝐹el) is comparable are identified in Figure 4.10f. The groups Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 68 show considerably different values, indicating that the elastic load capacity of the mesh-mortar interface was not fully developed for bonded lengths shorter than 90 mm. (a) (b) (c) (d) (e) (f) Figure 4.10. Statistical analysis of POGM results considering the bonded length and: a) maximum linear force, b) linear force at sliding onset, c) ultimate displacement at the loaded end, d) ultimate displacement at the free end, e) displacement at the loaded end for the maximum linear force, and f) linear force at the end of the elastic phase. Chapter 4. TRM composite 69 4.3 Characterisation of the substrate-matrix-fibre bond behaviour The single lap-shear test intends to investigate the local fibre-matrix-substrate interaction. The test configuration is composed of a portion of TRM-strengthening applied on a substrate and subjected to shear loads. Thereby, the stress transmission at matrix-fibre interface and thence at substrate-matrix interface is analysed. To this purpose, the tests were conducted according to a RILEM recommendation of TC 250-CSM (de Felice et al., 2018). The applied TRM considered GM and NM meshes (see Section3.4.) and different bonded lengths, while the width of the strengthening surface was fixed in 80 mm. The support used to prepare the specimens consisted of rammed earth blocks with dimensions of 150X100X200 mm3. The blocks were compacted in three layers using the composition RE_I while the addition of water was controlled by means of the drop ball test, whose OWC resulted similar to the water content assessed in the Proctor test (see Section 3.1. and Section 3.2.). The drying of the blocks occurred for a period of 28 days, after which the TRM strengthening was applied on one of the largest surfaces. To promote adherence and prevent early water reduction of the mortar, the substrate surface was first scraped and wet; afterwards, a layer of earth mortar EM_I (see Section 3.3.) with 5 mm thickness, 80 mm width and length equal to the bonded length was applied. Then, a single mesh band with 80 mm width, which corresponded to 8 yarns for GM and 5 yarns for NM, was placed on the mortar parallel to the surface of the support and covered with a second layer of mortar with 5 mm of thickness. In the NM case, just a single bonded length of 30 mm was considered since no sliding was expected, as observed for PONM; while for GM 30 mm, 60 mm, 90 mm and 120 mm bonded lengths were considered. Five specimens were prepared for each type of mesh and bonded length, which afterwards were labelled according to the nomenclature SL#type of mesh#bonded length#number of specimen (e.g. SLNM30_1). The single-lap shear tests were conducted after drying the TRM mortar for 28 days in laboratory conditions. As illustrated in the test setup (Figure 4.11), steel plates were bonded with an epoxy compound to the loaded end extremity to allow the gripping in the testing machine, while the rammed earth block was fixed to the steel frame guaranteeing the alignment of the mesh for shear loads. The test was conducted under monotonic displacement control with speed 10 μm/s, both for SLGM and SLNM specimens. The displacement of the mesh at the loaded end was monitored by means of two LVDTs set in the mesh immediately after the mortar, while one LVDT was used to monitor the displacements at the free end. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 70 Figure 4.11. Setup of the single lap-shear tests. It is reported that only three failure modes of those typically found in TRM strengthened masonry (Ascione et al., 2015; de Felice et al., 2014; Focacci et al., 2017) were observed (Figure 4.12); particularly, debonding at the support-mortar interface (𝐹𝑀1), sliding of the textile with detachment of the top mortar layer (𝐹𝑀2), and mixed failure at the support-mortar interface and detachment of the top mortar layer (𝐹𝑀3). 𝐹𝑀1 𝐹𝑀2 𝐹𝑀3 Figure 4.12. Failure modes (FM) observed in the single lap-shear tests. Figure 4.13a and Figure 4.13b present the SLGM response curves in terms of linear force (𝐹 w) against the displacement at the loaded end (𝑑LE) and displacement at the free end (𝑑FE), respectively. In general, SLGM specimens showed an initial elastic response, in which the load was transferred by adhesion from the yarn to the matrix and then from the matrix to the support. Once that the shear strength was attained either at the mortar-mesh or rammed earth-mortar interface, micro-cracks were developed. Consequently, the response at this stage became nonlinear resulting from the combination of adhesion and friction mechanisms. Finally, failure occurred when either the cohesion was destroyed at the rammed earth-mortar interface (𝐹𝑀1) or when the interfacial shear stresses at the mortar-mesh interface achieved the strength of the mortar (𝐹𝑀2). Chapter 4. TRM composite 71 The results of SLGM specimens in terms of maximum linear force (𝐹 wpeak) and failure mode (𝐹𝑀) in respect to the bonded length (𝐿b) are summarized in Table 4.3. Failure for sliding of the textile and consequent detachment of the top mortar layer (𝐹𝑀2) was observed in most of the specimens; contrarily, debonding at the support-mortar interface (𝐹𝑀1) was found for SLGM30 and SLGM60, while mixed failure (𝐹𝑀3) was only for SLGM120. Finally, the shear resistance of the TRM portion increased with the bondend length (𝐿b). (a) (b) Figure 4.13. Response curves obtained from the single lap-shear tests conducted on the SLGM specimens: a) displacement at the loaded end, and b) displacement at the free end Table 4.3. Results of single-lap shear tests conducted on the SLGM specimens. Spec. 𝑭𝐰𝐩𝐞𝐚𝐤 [𝐤𝐍/𝐦] 𝑭𝑴 Spec. 𝑭𝐰𝐩𝐞𝐚𝐤 [𝐤𝐍/𝐦] 𝑭𝑴 Spec. 𝑭𝐰𝐩𝐞𝐚𝐤 [𝐤𝐍/𝐦] 𝑭𝑴 Spec. 𝑭𝐰𝐩𝐞𝐚𝐤 [𝐤𝐍/𝐦] 𝑭𝑴 30_1 2.45 1 60_1 2.54 1 90_1 4.99 2 120_1 7.01 2 30_2 2.95 2 60_2 3.86 2 90_2 5.54 2 120_2 5.85 3 30_3 2.58 2 60_3 5.21 2 90_3 5.41 2 120_3 6.70 3 30_4 2.43 1 60_4 3.94 2 90_4 4.68 2 120_4 6.63 3 30_5 2.50 2 60_5 3.93 1 90_5 5.58 2 120_5 7.26 2 Av. (CoV) 2.58 (8%) Av. (CoV) 3.90 (24%) Av. (CoV) 5.24 (7%) Av. (CoV) 6.69 (8%) With regard to the SLNM specimens, the results in terms of linear force (𝐹 w) against the displacement at the loaded end (𝑑LE) and displacement at the free end (𝑑FE) are shown in Figure 4.14a and Figure 4.14b, respectively. In this case, the response was nonlinear since early stage of loading and Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 78 5.2 Experimental data and assumption of the model The material properties of the earth-based mortar and glass fibre mesh, presented in Section 3.3. and Section 3.4. respectively, are here briefly reported for convenience. Regarding the earth-based mortar EM_0, the average flexural strength 𝑓b was 0.5 MPa (CoV=14%), while the average compressive strength 𝑓c was 1.2 MPa (CoV=12%). The average Young’s modulus 𝐸m, computed by linear fitting of the stressstrain curves in the range 0-30% of 𝑓c, was of about 4195 MPa (CoV=20%). With regard to GM, the average maximum linear force 𝐹wpeak attained in the tensile test was 18.4 kN/m (CoV=11%), while the average tensile strength of a single yarn 𝑓t and the peak axial strain 𝜀peak were 626 MPa (CoV 11%) and 0.021 mm/mm (CoV=10%), respectively. In addition, an average Young’s modulus 𝐸y of 31981 MPa (CoV 6%) was obtained by linear fitting of the tensile stress-strain curve in the range 0-30% of 𝑓t (Table 5.1). Table 5.1. Properties of the earth-based mortar and glass fibre mesh used in the specimens of the pull-out tests. Material 𝑭𝐰𝐩𝐞𝐚𝐤 [𝐤𝐍/𝐦] 𝜺𝐩𝐞𝐚𝐤 [𝐦𝐦/𝐦𝐦] 𝒇𝐭 [𝐌𝐏𝐚] 𝑬𝐲 [𝐌𝐏𝐚] 𝑨𝐲 [𝐦𝐦𝟐] 𝒇𝐜 [𝐌𝐏𝐚] 𝒇𝐛 [𝐌𝐏𝐚] 𝑬𝐦 [𝐌𝐏𝐚] GM 18.42 0.021 625.8 31981 0.294 - - - EM_0 - - - - - 1.17 0.50 4915 It is here reported that the calibration of the analytical model was performed only on the specimens belonging to POGM90 and POGM150 series. In addition, for sake of clarity, the displacements are hereinafter referred to as 𝑢. The experimental curves of POGM90 and POGM150 are reported in Figure 5.1 in terms of linear force (𝐹w) against displacement at the loaded end (𝑢LE) and displacement at the free end (𝑢FE), while Table 5.2 summarizes the pull-out results of the average maximum elastic force per width 𝐹el and the corresponding elastic displacement at the loaded end 𝑢el, maximum force per width 𝐹wpeak and ultimate displacement at the loaded end 𝑢LEult, which are later on considered in the algorithm to define the 𝐵𝑆𝑅. Based on the literature (Carozzi et al., 2016; D’Antino et al., 2014; Focacci et al., 2017; Sueki et al., 2007; Zhang et al., 2013; D’Antino et al., 2018) and the observations presented in Section 4.2., the experimental pull-out curves can be divided into two zones, to which correspond different shear stress distributions along the interface mesh-mortar. A linear response was observed while the load was transmitted from the yarns to the matrix by adhesion and the shear strength was not Chapter 5. Analytical bond stress-slip model for pull-out test 79 achieved. When the elastic force 𝐹el was attained, micro-cracks developed at the interface and the response became nonlinear. During the nonlinear stage, adhesion was still at the interface of the bonded fibres (𝐿b), while friction between the fibre and the matrix was the resistant mechanism in the detached length (𝐿d). As the debonding propagated along the yarns, the stiffness of the load-slip curve decreased, until the shear strength was attained at the free-end. Afterwards, only friction controlled the load transfer from the mesh to the matrix. Table 5.2. Results of the pull-out tests conducted on POGM specimens with bonded lengths of 150 mm and 90 mm. Specimen 𝑳𝐛 [𝐦𝐦] 𝑭𝐞𝐥 [𝐤𝐍/𝐦] 𝒖𝐞𝐥 [𝐦𝐦] 𝑭𝐰𝐩𝐞𝐚𝐤 [𝐤𝐍/𝐦] 𝒖𝐋𝐄𝐮𝐥𝐭 [𝐦𝐦] POGM150_1 150 2.64 0.170 14.34 2.320 POGM150_2 150 2.48 0.230 13.66 1.960 POGM150_3 150 2.92 0.156 12.66 2.540 POGM150_4 150 2.38 0.100 13.98 2.630 Average (CoV %) 2.61 (9) 0.164 (33) 13.66 (5) 2.362 (13) POGM90_1 90 3.13 0.201 13.22 3.840 POGM90_2 90 2.99 0.170 12.51 3.270 POGM90_3 90 2.83 0.122 13.44 2.670 POGM90_4 90 2.67 0.086 14.78 3.380 Average (CoV %) 2.91 (7) 0.145 (35) 13.49 (7) 3.290 (15) (a) (b) Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 80 (c) (d) Figure 5.1. Response curves obtained from the pull-out tests on POGM specimens: a) loaded-end ( 𝐿𝑏 150 mm), b) free-end ( 𝐿𝑏 150 mm), c) loaded-end ( 𝐿𝑏 90 mm), and d) free-end ( 𝐿𝑏 90 mm). 5.3 Analytical model Given the above experimental observations, an adhesion-friction constitutive law was assumed for the 𝐷𝐵𝑃 approach. The constitutive law consists in a linear response with stiffness 𝜅 up to the shear strength 𝜏max and corresponding elastic slip 𝑠el. Subsequently, the strength decreases to a constant shear friction resistance 𝜏fri until failure occurrs (see Figure 5.2). Figure 5.2. Adhesion-friction bond stress-slip relationship assumed to simulate the results of the pull-out tests. Considering the pull-out scheme, the tensile force in the yarn 𝐹 is transferred to the matrix 𝑀 through the interface and then spread through the matrix to the reaction plate by compressive stress. Thereby, given the static equilibrium along the embedded length (see Figure 5.3) and considering the infinitesimal interface 𝑑𝑥, the equilibrium can be expressed as: 𝑑𝐹 𝑑𝑥 =−𝑑𝑀 𝑑𝑥 =𝑝𝜏(𝑥) Eq. 5.1 Chapter 5. Analytical bond stress-slip model for pull-out test 81 where 𝑝 is the perimeter of the yarn and 𝜏 is the shear stress at the yarn-matrix interface. Figure 5.3. Scheme of the interface static interaction during a pull-out test. Since the slip in the section 𝑥 represents the difference between the axial deformation of the fibre and the matrix as 𝑠(𝑥)=𝑑𝑢 𝑑𝑥 =𝜀y−𝜀m, which can be defined, respectively, as 𝜀y=𝐹 𝐴y𝐸y and 𝜀m= −𝐹 𝐴m𝐸m, the slip can be also expressed as: 𝑑𝑢 𝑑𝑥 =𝐹(𝑥) 𝐴y𝐸y+𝐹(𝑥) 𝐴m𝐸m Eq. 5.2 where 𝐴m, 𝐴y, 𝐸m and 𝐸y are the cross-sections and the Young’s modulus of the matrix and fibre, respectively. It is specified that since a direct measurement of the section of influence of the mortar was not possible, the value of 𝐴m was assessed through a sensitivity analysis. Thereby, substituting the Eq. 5.2 into Eq. 5.1, one obtains: 𝑑𝐹 𝑑𝑥 =𝑑2𝑢 𝑑𝑥2=Q𝑝𝜏 Eq. 5.3 where 𝑄= 1 𝐴y𝐸y+1 𝐴m𝐸m represents the relative axial stiffness between the two components. Therefore, Eq. 5.3 expresses the analytical problem statement of the pull-out test that must be solved in accordance with the stage in which the section is found, namely linear stage and nonlinear stage, as it is following addressed. 5.3.1 Linear stage During the linear stage, the load was transferred by means of adhesion and the assumed interface 𝐵𝑆𝑅 is 𝜏=𝜅𝑢 (Figure 5.2), which substituted in Eq. 5.3 leads to: 𝑢′′ −𝜆2𝑢=0 Eq. 5.4 with 𝜆=√𝑝𝜅𝑄. The general solution of this second differential equation is: 𝑢(𝑥)=𝐶1𝑒𝜆𝑥 +𝐶2𝑒−𝜆𝑥 Eq. 5.5 Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 82 which derived and substituted in Eq. 5.2 leads to: 𝐹(𝑥)=𝑑𝑢 𝑑𝑥1 𝑄=1 𝑄(𝐶1𝜆𝑒𝜆𝑥 −𝐶2𝜆𝑒−𝜆𝑥) Eq. 5.6 To obtain the constants C 1 and C 2, a system of Eq. 5.6 is solved considering as boundary conditions the force in the fibre at the free-end, which is null 𝐹(0)=0, and the force in the fibre at the loaded-end, which is equal to the pull-out force, namely 𝐹(𝐿b)=𝑃. From here, 𝐶1=𝐶2= 𝑃𝑄 𝜆(𝑒𝜆𝐿−𝑒−𝜆𝐿), which substituted in Eq. 5.6 result in the force distribution along the fibre 𝐹(𝑥) as: 𝐹(𝑥)=𝑃 (𝑒𝜆𝑥 −𝑒−𝜆𝑥) (𝑒𝜆𝐿𝑏−𝑒−𝜆𝐿𝑏)=𝑃 𝑠𝑖𝑛ℎ(𝜆𝑥) 𝑠𝑖𝑛ℎ(𝜆𝐿b) Eq. 5.7 while the shear 𝜏(𝑥) and slip 𝑠(𝑥) distribution along the interface are, respectively: 𝜏(𝑥)=𝑑𝐹 𝑑𝑥1 𝑝=𝑃𝜆 𝑝𝑐𝑜𝑠ℎ(𝜆𝑥) 𝑠𝑖𝑛ℎ(𝜆𝐿b) Eq. 5.8 and: 𝑢(𝑥)=∫ 𝐹(𝑥)𝑄𝑑𝑥 𝑥 0=𝑃𝑄 1 𝑠𝑖𝑛ℎ(𝜆𝐿b)∫𝑠𝑖𝑛ℎ(𝜆𝑥)𝑑𝑥 𝑥 0 Eq. 5.9 For pull-out forces lower than the elastic limit load 𝐹(𝐿b)=𝑃<𝐹el, the shear stress at the interface is less than the shear strength 𝜏max and the yarn and the matrix are full bonded. Once that the pull-out force achieves the elastic load 𝐹(𝐿b)=𝑃=𝐹el, the shear strength 𝜏max is attained at the loaded end 𝑥=𝐿b and the debonding occurs at that section. Hence, the shear stress distribution of such configuration is illustrated in Figure 5.4 and Eq. 5.8 becomes Eq. 5.10. Figure 5.4. Shear stress distribution along the interface during the elastic response. 𝜏(𝐿b)=𝜏max =𝑃el 𝜆 𝑝𝑐𝑜𝑠ℎ(𝜆𝐿) 𝑠𝑖𝑛ℎ(𝜆𝐿) Eq. 5.10 While the slip at the loaded-end results: 𝑠(𝐿b)=𝑢el = =∫ 𝐹(𝑥)𝑄𝑑𝑥 𝐿b 0=𝑃𝑄 1 𝑠𝑖𝑛ℎ(𝜆𝐿b)∫𝑠𝑖𝑛ℎ(𝜆𝑥)𝑑𝑥= 𝐿b 0 =𝑃el𝑄1 𝑠𝑖𝑛ℎ(𝜆𝐿b)1 𝜆[𝑐𝑜𝑠ℎ(𝜆𝐿b)−1] Eq. 5.11 Chapter 5. Analytical bond stress-slip model for pull-out test 83 Therefore, when the experimental elastic pull-out load and displacement are attained (𝐹el and 𝑢el, respectively), the shear strength 𝜏max and the shear stiffness of the interface 𝜅 can be calculated by solving the system of equations composed of Eq. 5.10 and Eq. 5.11 at the coordinate of the loaded end (𝑥=𝐿b). 5.3.2 Nonlinear stage For pull-out loads going beyond the elastic limit 𝐹(𝐿b)=𝑃>𝐹el, micro-cracks develop at the interface and propagate in the further sections towards the free end. This implicates that the fibre and mortar are debonded in the length 𝐿d, while they are still adhered in the remaining length 𝐿b–𝐿d. In such configuration, the shear stress distribution is composed of constant frictional stress 𝜏fri in the debonded length 𝐿d<𝑥<𝐿b and adhesion 𝜏=𝜅𝑢 along the bonded length 𝐿−(Lel −Ld)<𝑥< 𝐿b−𝐿d, while the shear strength 𝜏max is achieved at the coordinate 𝑥=𝐿b–𝐿d (see Figure 5.5). Figure 5.5. Shear stress distribution along the interface during the nonlinear response. Consequently, the pull-out force is the sum of the forces resulting from adhesion and friction in the respective length, obtained as: 𝐹(𝐿b)=𝑃=𝐹Imax +𝐹II = 𝜏max 𝑝 𝜆𝑡𝑎𝑛ℎ[𝜆(𝐿b−𝐿d)]+𝜏fri𝑝𝐿d Eq. 5.12 In this case, the boundary conditions are represented by the force in the fibre at the free end, which is null 𝐹(0)=0, the force in the fibre at the loaded end, which is equal to the pull-out force 𝐹(𝐿b)= 𝑃, and the force at the coordinate between bonded and debonded length, which corresponds to 𝐹(𝐿b−𝐿d)=𝜏max 𝑝 𝜆𝑡𝑎𝑛ℎ[𝜆(𝐿b−𝐿d)] Eq. 5.13 Introducing these boundary conditions to solve Eq. 5.3, the force distribution 𝐹(𝑥) along the elastic length can be expressed as: 𝐹I(𝑥)=𝜏max 𝑝 𝜆𝑡𝑎𝑛ℎ[𝜆(𝐿b−𝐿d)] 𝑠𝑖𝑛ℎ(𝜆𝑥) 𝑠𝑖𝑛ℎ[𝜆(𝐿b−𝐿d)] [𝐿−(𝐿el −𝐿d)<𝑥<𝐿b−𝐿d] Eq. 5.14 While the force distribution 𝐹(𝑥) along the debonded length can be calculated as: 𝐹(𝑥)=𝐹Imax +𝐹II = 𝜏max 𝑝 𝜆𝑡𝑎𝑛ℎ[𝜆(𝐿b−𝐿d)]+𝜏fri𝑝(𝑥−𝐿b+𝐿d) [𝐿b−𝐿d<𝑥<𝐿𝑏] Eq. 5.15 Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 84 Consequently, the slip along the yarn 𝑠(𝑥) can be evaluated according to the stage in which the considered section is found, in particular, the elastic slip at the end of the bonded length is: 𝑠el(𝐿b−𝐿d)= =∫ 𝐹Imax(𝑥)𝑄𝑑𝑥 𝐿b−𝐿d 0= =∫ 𝜏max𝜆𝑄 𝑝𝑡𝑎𝑛ℎ[𝜆(𝐿b−𝐿d)] 𝑠𝑖𝑛ℎ(𝜆𝑥) 𝑠𝑖𝑛ℎ[𝜆(𝐿b−𝐿d)]𝑑𝑥 𝐿b−𝐿d 0= =𝐹Imax𝜆1 𝑠𝑖𝑛ℎ[𝜆(𝐿b−𝐿d)][𝑐𝑜𝑠ℎ[𝜆(𝐿b−𝐿d)]−1] Eq. 5.16 [𝐿−(𝐿el −𝐿d)<𝑥<𝐿b−𝐿d] And the frictional slip at the end of the debonded section is: 𝑠fri(𝐿b)=∫ 𝐹(𝑥) 𝐸𝐴 𝑑𝑥 𝐿b 𝐿b−𝐿d= =∫ 𝐹Imax +𝜏fri𝑝(𝑥−𝐿b+𝐿d)𝑄𝑑𝑥= 𝐿b 𝐿b−𝐿d =𝐿d𝑄(𝐹Imax +𝜏fri𝑝𝐿d 2) [𝐿b−𝐿d<𝑥 <𝐿b] Eq. 5.17 Therefore, the total slip is the sum of the slip along the bondend length and the debonded length, and it is equal to: 𝑠(𝐿b)=𝑢=𝑠el +𝑠fri = =𝐹Imax𝜆𝑄 1 𝑠𝑖𝑛ℎ[𝜆(𝐿b−𝐿d)][𝑐𝑜𝑠ℎ[𝜆(𝐿b−𝐿d)]−1]+𝐿d𝑄(𝐹Imax +𝜏fri𝑝𝐿d 2) Eq. 5.18 In this configuration, the unknowns are the debonded length 𝐿d and the shear friction 𝜏fri, which can be obtained by solving the system of equations composed of Eq. 5.12 and Eq. 5.18 and considering the experimental pull-out force 𝑃 and slip 𝑢 in the nonlinear branch of the curve as input. 5.3.3 Damage model As previously discussed in Section 4.2. and further reported in (Romanazzi et al., 2019), the failure of the pull-out tests with bonded lengths of 50 mm, 90 mm and 150 mm occurred in an embedded section of the yarns for tensile forces lower than the strength capacity of the dry mesh. This premature failure of the mesh was ascribed to damage accumulation in the yarns, as a consequence of the friction between the components as slipping progressed. In view of that, a damage model which considers the reduction of the effective cross section of the yarn as a function of the sliding was implemented. The damage function was defined as: 𝜉(𝑢)=𝐴y−𝐴yd 𝐴y𝑥100 Eq. 5.19 Chapter 5. Analytical bond stress-slip model for pull-out test 85 where 𝐴y and 𝐴yd represented the initial cross section of the yarn, hence undamaged state, and the reduced cross section of the yarn due to friction, respectively. Since 𝐴yd(𝑢) is function of the sliding to which the yarn was subjected in the nonlinear stage, to deduce the correlation between friction and damage, the damage that led to the failure was calculated at first. Therefore, for the ultimate load of the POGM50, POGM90 and POGM150, the reduced cross section at failure was evaluated as: 𝐴yd=𝑃ult 𝑛°𝑓t Eq. 5.20 where 𝑓t is the tensile strength of the dry mesh and 𝑛 is the number of yarns, to which corresponds the ultimate slip evaluated as 𝑠ult =𝑢LEult–𝑢el. Afterwards, a regression analyses was performed within the range of slip in the nonlinear stage and the corresponding damage. In addition, the constraint 𝜉(0)=0 was introduced, meaning that the damage is null at the end of the elastic stage (𝑢=𝑢el), resulting (see Figure 5.6): 𝜉 =(1.541𝑒1.294(𝑢−𝑢el)−1.541)𝑋 1 100 Eq. 5.21 Figure 5.6. Damage curve of the section of the yarn due to friction. Therefore, the value of 𝜉(𝑢) (Eq. 5.21) is introduced as a factor to reduce the effective area of the yarn in the evaluation of the friction forces as: 𝜏fri𝑝(𝜉(𝑢))𝐿d Eq. 5.22 which is then considered in the system of equations of the nonlinear stage composed of Eq. 5.12 and Eq. 5.18. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 86 5.4 Implementation of the algorithm and results The algorithm to solve the problem stated above begins with the identification of the end of the linear stage; thereby, the corresponding pull-out force 𝐹el and displacement 𝑢el are introduced as known in the system of equations Eq. 5.10 and Eq. 5.11. In that way, the maximum shear stress 𝜏max and the shear stiffness 𝜅 can be obtained. To verify the reliability of the elastic values, a linear regression of the pull-out records up to 𝐹el and 𝑢el can be performed and the 𝑅2 value checked. To solve the nonlinear stage, several pairs of pull-out force-displacement 𝑃−𝑢 can be adopted in the system of equations constituted by Eq. 5.12 and Eq. 5.18, obtaining so the debonded length 𝐿d and the shear friction 𝜏fri. For this reason, the experimental curves are discretized by load points in increments of 10% of 𝐹wpeak and considering the corresponding displacement 𝑢. For each step, the damage function 𝜉(𝑢) is calculated according to Eq. 5.21 and it is introduced through Eq. 5.22 in the system of equations constituted by Eq. 5.12 and Eq. 5.18. Since different values of shear friction 𝜏fri might result from each step, the average value of 𝜏fri is calculated as to be lower than or equal to the shear strength 𝜏max. In the cases of such restriction being unverified, the shear friction is considered equal to the shear strength. Finally, once obtained the 𝐵𝑆𝑅, it is verified through the simulation of the pull-out experiments, which is performed by increasing the value of the displacement at the loaded end 𝑢(𝐿b), while the corresponding value of pull-out force is evaluated from Eq. 5.10. When the displacement at the loaded end is equal to the elastic slip 𝑢(𝐿b)=𝑠el, the end of the linear behaviour is achieved. Further increasing the displacement induces the response to the nonlinear stage. Therefore, the corresponding pull-out force in the nonlinear stage is calculated by solving the system of equations constituted by Eq. 5.12 and Eq. 5.18, where the unknowns are the pull-out force 𝑃 and the debonding length 𝐿d. At this stage, the damage model is introduced by Eq. 5.21 in Eq. 5.12, while, the failure of the mesh is controlled for each step of pull-out force by checking whether the corresponding tensile stress in the yarn is lower than the tensile strength of the dry mesh through: 𝜎y(𝑃(𝑢))= 𝑃 𝐴y(1−𝜉(𝑢)) Eq. 5.23 When this last condition is not verified, the tensile failure of the mesh is achieved, and the simulation stops. Thereby, the simulated pull-out force-slip curve 𝑃(𝑢) is obtained and compared with the experimental curve to verify the accuracy. Afterwards, a sensitivity analysis is performed by varying the values of 𝜏max and 𝑠el in a range of −10% and +10%, leading to a set of 9 constitutive laws for each sample, which are further checked by the simulation of the pull-out response as previously described. Chapter 5. Analytical bond stress-slip model for pull-out test 87 Finally, since the bond stress-slip law is independent from the geometry of the specimen, the optimum values of 𝜏max–𝑠el are selected among all the 9 possibilities and are used to verify the simulations for the different bonded lengths. The methodology described above was implemented considering the experimental values reported in Table 5.2. The obtained 𝐵𝑆𝑅s of each specimen are illustrated in Table 5.3. As mentioned above, 𝜏fri must not exceed the shear strength 𝜏max, differently the value of the shear friction must be assumed as the shear strength. Nonetheless, such condition was not satisfied in all the cases. It can be also noted that the results show scattering in particular with regard to the interface stiffness 𝜅, which presents a coefficient of variation of 61%. Such dispersion can be explained by the large variance of the considered experimental elastic displacement uel, which affects the solution of the equations Eq. 5.10 and Eq. 5.11. Table 5.3. Bond stress-slip parameters obtained by implementation of the direct problem approach. Simulation 𝝉𝐦𝐚𝐱 [𝐌𝐏𝐚] 𝒔𝐞𝐥 [𝐦𝐦] 𝜿 [𝐌𝐏𝐚/𝐦𝐦] 𝝉𝐟𝐫𝐢 [𝐌𝐏𝐚] 𝒔𝐮𝐥𝐭 [𝐦𝐦] POGM_150_1 0.40 0.170 2.336 0.40 2.610 POGM_150_2 0.24 0.230 1.022 0.24 3.080 POGM_150_3 0.57 0.132 4.305 0.57 2.200 POGM_150_4 0.59 0.091 6.540 0.59 2.140 POGM_90_1 0.39 0.201 1.951 0.39 2.680 POGM_90_2 0.46 0.170 2.697 0.46 2.480 POGM_90_3 0.67 0.307 2.191 0.67 2.100 POGM_90_4* 1.22 0.221 5.527 1.22 3.650 Average (CoV %) 0.47 (31%) 0.186 (38%) 3.006 (61%) 0.47 (31%) 2.470 (14%) * The results obtained from POGM_90_4 are considered outliers according to ASTM E178 (ASTM E178-02, 2000) . Subsequently, the sensitivity analysis was performed for each specimen, which led to a set of 9 combinations of (𝜏max–𝑠el). However, among all the combinations, only the pairs (𝜏max–𝑠el) that provided a simulated pull-out curve consistent with the experimental response were considered to formulate the definitive 𝐵𝑆𝑅, as illustrated in Figure 5.7. Thereby, the final bond stress-slip relationship parameters are reported in Table 5.4. It should be noted that the shear strength 𝜏max, the elastic slip 𝑠el, the elastic stiffness 𝜅 and the shear friction 𝜏fri are equal for both bonded lengths (90 mm and 150 mm). In fact, those parameters characterise the elastic stage, which does not differ among POGM90 and POGM150 specimens, while the ultimate slip 𝑠ult may vary, since it is affected by the damage of the yarn. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 94 Three different TRM solutions were applied on the wallets, resulting from the combination of the different meshes and mortars. In particular, the mortars EM_I and EM_II were used for the wallets built with RE_I and RE_II mixtures, respectively. In this way, the mineralogical compatibility was guaranteed, since the mortar was composed with the same soil of the corresponding rammed earth material. While, the used meshes were GM and NM for the RE_I wallets, and GeoM for the RE_II wallets. The properties of the materials used for the different TRM solutions are summarised in Table 6.2 and Table 6.3, although a throughout discussion is reported in Section 3.3 and Section 3.4. However, it is specified that a stepwise analysis was performed to investigate the evolution of the Young’s modulus of EM_I and EM_II; nevertheless, the classical value 𝐸m is here considered as Young’s modulus (see Section 3.3). Subsequently, the strengthened specimens dried during one month in laboratory conditions. The wallets were weighted before testing to evaluate the bulk density of the rammed earth, which resulted in an average value of 2.14 g/cm3 (CoV = 3%) and 2.07 g/cm3 (CoV = 2%) for RE_I and RE_II, respectively. These values of bulk density are consistent with the dry density values obtained from the standard Proctor test, being the latter 2.13 g/cm3 and 2.02 g/cm3 for RE_I and RE_II, respectively. Table 6.2. Material properties of the earth-based mortar mixtures (EM_I, and EM_II) used in the strengthening of the wallets. Mixture Clay [%] Silt [%] Sand [%] Gravel [%] 𝝆 [𝐠/𝐜𝐦𝟑] 𝒇𝐜 [𝐌𝐏𝐚] 𝒇𝐭 [𝐌𝐏𝐚] 𝑬𝐦 [𝐌𝐏𝐚] EM_I 9 10 70 - 1.81 0.66 0.29 1978 EM_II 6 8 86 - 1.86 0.49 0.21 1221 Table 6.3. Material properties of the meshes (NM, GM, and GeoM) used in the strengthening of the wallets. Type of mesh Mesh size [𝐦𝐦𝐗𝐦𝐦] 𝑨𝐲 [𝐦𝐦𝟐] 𝑭𝐰𝐩𝐞𝐚𝐤 [𝐤𝐍/𝐦] 𝒇𝐭 [𝐌𝐏𝐚] 𝜺𝐩𝐞𝐚𝐤 [𝐦𝐦/𝐦𝐦] 𝑬𝐲 [𝐌𝐏𝐚] GM 8X9 0.29 18.42 625.80 0.021 31981 NM 16X21 0.97 3.18 54.37 0.340 361 GeoM 22X25 3.09 42.08 340.46 0.097 2626 With the aim at investigating the change of shear properties due to repeated actions, the experimental program considered monotonic loads and cyclic loads. In particular, the specimens manufactured with RE_I mixture were subjected to monotonic displacement until failure; wile the walletts made with RE_II were tested under monotonic and cyclic loads. Accordingly, the specimens were labelled Chapter 6. Diagonal compression tests on rammed earth panels 95 as DG-#type of load-#type of mesh#rammed earth mixture-#number of specimen (e.g. DG-MonoGRE_I_1) as summarised in Table 6.4. Table 6.4. Outline of the experimental program on diagonal compression tests. Label Rammed earth TRM components Number of specimens Type of loading DG-Mono-URE_I RE_I - 3 Monotonic DG-Mono-GRE_I EM_I + GM 3 DG-Mono-NRE_I EM_I + NM 3 DG-Mono-URE_II RE_II - 2 DG-Mono-GeoRE_II EM_II + GeoM 2 DG-Cyc-URE_II - 2 Cyclic DG-Cyc-GeoRE_II EM_II + GeoM 2 To guarantee the application of the load along the diagonal of the wallet and avoid any bending and punching, angular steel supports with length of 100 mm were used to set the specimen with a rotation of 45°. Afterwards, a set of two LVDTs were fixed in the middle third of the two diagonals of one side of the wallets, here referred as LVDT_V and LVDT_H, to measure the vertical and horizontal displacements, respectively (Figure 6.3a). Since local detachment of the TRM was likely to occur after cracking, the LVDTs were screwed directly into the rammed earth (Figure 6.3b). In addition, the other side of wallets was monitored with digital image correlation technique (DIC) to observe the surface full field strain (Figure 6.3c). Regarding the testing protocol, the monotonic displacement-controlled tests were performed with a rate 2 μm/s, while the cyclic displacement-controlled tests were conducted by varying the rate and amplitude of the established displacement. It should be noted that, for stability reasons, the unloading was conducted until attaining a residual force of 2 kN (inversion condition), as illustrated in Figure 6.4 and Table 6.5. It is specified also that the cyclic protocol was defined with basis on the results of the monotonic tests; in this framework, the first cycle aimed to investigate the loadingunloading response in the elastic domain, whereas the remaining cycles intended to investigate the shear degradation in the plastic domain. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 96 (a) (b) (c) Figure 6.3. Diagonal compression test setup: a) scheme, b) disposition of the LVDTs, and c) DIC apparatus. Figure 6.4. Scheme of the loading-unloading profile of the cyclic diagonal compression tests. Table 6.5. Parameters of the loading-unloading profile of the cyclic diagonal compression tests. Cycle Ramp Speed Displacement Amplitude Inversion condition 1 Loading 2 μm/s 0.7 mm Unloading − 10 μm/s 2 kN 2 Loading 2 μm/s 0.7 mm Unloading − 10 μm/s 2 kN 3 Loading 2 μm/s 0.7 mm Unloading − 10 μm/s 2 kN 4 Loading 4 μm/s 1.5 mm Unloading − 20 μm/s 2 kN 5 Loading 4 μm/s 1.5 mm Unloading − 20 μm/s 2 kN Chapter 6. Diagonal compression tests on rammed earth panels 97 6 Loading 4 μm/s 1.5 mm Unloading − 20 μm/s 2 kN 7 Loading 4 μm/s 1.5 mm Unloading − 20 𝜇𝑚/𝑠 2 𝑘𝑁 8 Loading 4 𝜇𝑚/𝑠 Failure 6.2 Results and discussion The results of the diagonal compression tests in terms of shear stress (𝜏), shear strain (𝛾) and shear modulus (𝐺) are discussed in the present section. The shear stress (𝜏) and the shear strain (𝛾) were calculated according to ASTM E519 (ASTM E519-02, 2002), namely (Eq. 6.1): 𝜏 =0.707∙𝑃 𝐴n Eq. 6.1 where 𝑃 is the applied load and 𝐴n represents the net area of the specimen calculated as follows (Eq. 6.2): 𝐴n=(𝑤+ℎ 2)∙𝑡∙𝑛 Eq. 6.2 where 𝑤, ℎ and 𝑡 are the width, height, and thickness of the specimen, respectively, while 𝑛 represents the percent of the gross area of the specimen that is solid, which can be considered equal to 1 in the case of the tested wallets. As for the shear strain, it was calculated as follows (Eq. 6.3): 𝛾 =∆𝑉+∆𝐻 𝑔 Eq. 6.3 where ∆𝑉 and ∆𝐻 are, respectively, the vertical and horizontal displacements recorded by the LVDTs, while 𝑔 is the gage length. In order to analyse the influence of the rammed earth mixture, the type of strengthening solution and the load conditions, the graphs present a comparison between DG-Mono-URE_I and DG-Mono-URE_II (Figure 6.5a), DG-Mono-NRE_I, DG-Mono-GRE_I and DG-Mono-URE_I (Figure 6.5b), DG-Mono-URE_II and DG-Mono-GeoRE_II (Figure 6.5c), DG-Cyc-URE_II and DG-Cyc-GeoRE_II (Figure 6.5d), DG-Cyc-URE_II and DG-Mono-URE_II (Figure 6.5e), and DG-Cyc-GeoRE_II and DG-Mono-GeoRE_II (Figure 6.5f). In Figure 6.5a, it can be noted that the shear response of un-strengthened rammed earth wallets is initially linear elastic, during which particularly the cohesion provided by the clay fraction contributes to the shear stiffness of the wallet. When the first crack occurs, the rammed earth begins to lose cohesion, Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 98 while interlocking and friction between the surfaces of the main cracks continue to develop, leading to a non-linear response. Subsequent to the full propagation of the diagonal crack, the friction and interlocking promoted by the aggregates are the main resisting mechanisms up to the peak load, which is followed by a plateau until the failure. In addition, despite the different mixture used to compact the specimens DG-Mono-URE_I and DG-Mono-URE_II, the response was found similar (Figure 6.5a). A comparison of the response of different TRM-strengthening solutions for the specimens built with RE_I demonstrates an increased plateau after peak, in particular in case of DG-Mono-URE_I (Figure 6.5b). Similarly, the use of GeoM embedded in EM_II enhanced the shear deformation capacity of the respective wallets (Figure 6.5c and Figure 6.5d). A response similar to the monotonic test on un-strengthened wallets is observed for un-strengthened specimens subjected to cyclic diagonal compression loading (Figure 6.5d). In fact, the behaviour is linear elastic until losing cohesion; afterwards, the main crack occurs and the response becomes non-linear consequently to the development of friction and interlocking mechanisms. However, a softening branch follows the peak load in cyclic tests, suggesting that the loading-unloading further degrades the friction and interlocking phenomena (Figure 6.5d, Figure 6.5e and Figure 6.5f). In addition, the unloading occurs at a constant deformation and the consecutive loading follows the same path at constant strain (Figure 6.5d), meaning a total absence of residual elasticity. (a) (b) Chapter 6. Diagonal compression tests on rammed earth panels 99 (c) (d) (e) (f) Figure 6.5. Comparison of shear stress-strain curves obtained from the diagonal compression tests for different: a) rammed earth mixtures, b) TRMstrengthening solution for RE_II, c) TRM-strengthening solution for monotonic test of RE_II, d) TRM-strengthening solution for cyclic test of RE_II, e) loading condition for un-strengthened RE_II, and f) loading condition for TRM-strengthened RE_II. The results of the entire diagonal compression tests program are reported in Table 6.6 in terms of average values of shear strength (𝜏max), corresponding shear strain (𝛾𝜏max), and ultimate shear strain (𝛾ult). Despite the different compressive strength between RE_I and RE_II (see Table 6.1), the shear strength average values (𝜏max) obtained for the un-strengthened specimens DG-Mono-URE_I, DG-MonoURE_II and DG-Cyc-URE_II are similar, namely 0.08 MPa (Table 6.6). Such result evidences a low contribution of the cohesion to the shear strength of the rammed earth (Skempton, 1953), which therefore is essentially provided by friction and interlocking mechanisms in both types of rammed earth. When the average shear strength values of the TRM-strengthened DG-Mono-GRE_I and DG-Mono-NRE_I wallets are compared with the reference series DG-Mono-URE_I, an enhancement of up to 25% can be observed. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 100 However, such values of 𝜏max in the strengthened wallets are within the variance of the results of DGMono-URE_I. Consequently, it is not possible to assert absolutely that the TRM improved the shear strength of the rammed earth wallets. Such observation is more evident comparing DG-Mono-GeoRE_II and DG-Cyc-GeoRE_II specimens with the corresponding un-strengthened wallets DG-Mono-URE_II and DG-Cyc -URE_II, respectively. Nevertheless, the improvement of the shear capacity provided by the TRMstrengthening is visible by analysing the shear deformations of DG-Mono-GRE_I, DG-Mono-NRE_I, and DG-Mono-GeoRE_II, against the respective un-strengthened wallets. In fact, in the case of DG-MonoURE_I, the average shear deformation in correspondence to the shear strength was 0.003 mm/mm, while average values of 𝛾𝜏max of 0.007 mm/mm and 0.031 mm/mm were achieved for DG-MonoGRE_I and DG-Mono-NRE_I, respectively (Table 6.6). Similar improvement was obtained for the wallets built with RE_II, where the average value of 𝛾𝜏max was 0.009 mm/mm for DG-Mono-URE_II, while the average 𝛾𝜏max of 0.017 mm/mm was attained for DG-Mono-GeoRE_II (Table 6.6). Such results indicate that the TRM was activated in the non-linear branch once that the cohesion at the main crack was lost. In fact, the peak stress was early reached for the un-strengthened cases, whereas in the TRMstrengthened wallets, the mesh was able to further support part of the deformation. Nonetheless, the influence of the TRM-strengthening is more evident at the ultimate stage. Indeed, the ultimate shear strain (𝛾ult) resulted 0.034 mm/mm for DG-Mono-URE_I, while values of 0.024 mm/mm and 0.041 mm/mm were attained for DG-Mono-GRE_I and DG-Mono-NRE_I, respectively (Table 6.6). However, for the DG-Mono-GRE_I case, it should be considered that detachment of the TRM across the crack occurred after the peak load, which might have affected the confining effectiveness of the strengthening. Contrarily, in the case of DG-Mono-NRE_I, the nylon mesh withstood large deformation which reduced the friction or interlocking along the crack with the consequent drop of shear stress. Similar improvements were obtained for specimens built with RE_II. In such case, the 𝛾ult values were 0.032 mm/mm and 0.037 mm/mm for DG-Mono-URE_II and DG-Mono-GeoRE_II, respectively; which are further confirmed by the results of cyclic tests, being the ultimate shear strain equal to 0.042 mm/mm for DG-Cyc-URE_II and 0.058 mm/mm for DG-Cyc-GeoRE_II. In addition, for the TRM-strengthened DGMono-GeoRE_II and DG-Cyc-GeoRE_II cases, the effectiveness of the GeoTRM is recognised in further preventing the collapse of the halves of the wallets in the ultimate stage. Chapter 6. Diagonal compression tests on rammed earth panels 101 Table 6.6. Results of the average values of the entire diagonal compression tests program. Test 𝝉𝐦𝐚𝐱 [𝐌𝐏𝐚] 𝜸𝛕𝐦𝐚𝐱 [𝐦𝐦/𝐦𝐦] 𝜸𝐮𝐥𝐭 [𝐦𝐦/𝐦𝐦] DG-Mono-URE_I 0.08 (19%) 0.003 0.034 DG-Mono-GRE_I 0.10 (10%) 0.007 0.024 DG-Mono-NRE_I 0.10 (20%) 0.031 0.041 DG-Mono-URE_II 0.08 0.009 ** 0.032 ** DG-Mono-GeoRE_II 0.07 0.017 0.037 DG-Cyc-URE_II 0.08 0.015 0.042 DG-Cyc-GeoRE_II 0.08 0.010 0.058 ** One of the LVDTs moved after cracking, therefore the post-elastic records are not reliable. Subsequently, the change of shear stiffness related to the microstructural damage level was investigated by means of stepwise linear regressions of the stress-stain curves, considering ranges of 10% 𝜏max with increments of 2% between each steps up to 90 % of 𝜏max. Accordingly, the shear modulus values (𝐺) as function of the normalised average stress level of the respective range as 𝜏/𝜏max are reported in Figure 6.6 and Figure 6.7 for the specimen built with RE_I and RE_II, respectively. The coefficient of determination 𝑅2 is also reported. In general, the shear modulus of the DG-Mono-URE_I specimens presents a constant initial trend. Afterwards, the shear modulus decreases with increasing values of 𝜏/𝜏max, which is consistent with the loss of cohesion which reduces the stiffness of rammed earth (Figure 6.6a). Similar results were obtained for DG-Mono-GRE_I (Figure 6.6b), whereas specimens DG-Mono-NRE_I presented negative shear modulus or low correlation coefficient (Figure 6.6c), which can be ascribed to unreliable measurements of LVDTs due to fault of the fixing system. Negative values of shear modulus or low values of coefficient of correlation were obtained as well for DG-Mono-URE_II (Figure 6.7a) and DG-Mono-GeoRE_II tests (Figure 6.7b), therefore defining a reliable range of shear modulus was not feasible. However, the classical value of shear modulus (𝐺) was evaluated in range 0% - 30% of 𝜏max, which is the common range considered in material characterisation. Nevertheless, reliable shear modulus was obtained for the only DG-Mono-URE_I, DG-Mono-GRE_I and DG-Mono-NRE_I specimens, which resulted 357 MPa, 794 MPa and 2045 MPa, respectively. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 102 (a) (b) (c) Figure 6.6. Analysis of shear modulus as a function of the shear stress level for: a) DG-Mono-URE_I, b) DG-Mono-GRE_I, and c) DG-Mono-NRE_I. (d) (e) Figure 6.7. Analysis of shear modulus as a function of the shear stress level for: a) DG-Mono-URE_II, and b) DG-Mono-GeoRE_II. Chapter 6. Diagonal compression tests on rammed earth panels 103 6.3 Digital Image Correlation (DIC) analyses In addition to the physical monitoring of displacements by means of LVDTs, Digital Image Correlation (DIC) was used to obtain further information. Digital Image Correlation (DIC) is an opticallybased technique used to measure the 2D or 3D full-field evolution of surface coordinates of a specimen throughout a test. The measured coordinate fields are later used to calculate derived fields, such as displacements, strains, strain rates, velocities, and curvatures. Furthermore, DIC is a non-contact technique that can be applied to several materials, despite the scale and type of test. In practical terms, DIC consists in tracking a pattern, so-called speckle pattern, of a defined region-of-interest (ROI) within the images of a sequence. The first frame of the sequence (before motion) is set as the reference image against which the other images (during motion) are compared. The ROI contains a series of subset that designate the interrogation points, and which are typically defined at some regular spacing (step size) in a way that the neighbouring subsets may or not overlap. Therefore, the subsets are numerically correlated from the reference image to each subsequent image by approximating the pattern through an interpolant function that can be shaped on each image of the sequence. Afterwards, a matching criterion is used to couple each subset between the reference image and the deformed images of the sequence, which, once it is satisfied, provides the measured coordinates of the centre of each subset as result. Digital Image Correlation has been already used in experimental research providing reliable results (Miccoli et al., 2014; Torres et al., 2020). To perform DIC on the available face of the wallets, a speckle pattern was created with black spots on a white background and the pictures were captured in a time frame of 10s with a SONY α6000 24.7 megapixel, with 16−50 mm (24−75 mm) – 3.5 lens and setting 𝑓/11− 1/10𝑠 (Figure 6.3c). Subsequently, the DIC analyses were performed using GOM Correlate software (GOM Correlate, 2019) and MatLab software (MATLAB, 2018) where the facet size and step size values were set as 20 and 15, respectively. The contours of the Cauchy principal tensile strains are illustrated in Figure 6.8 for DG-Mono-URE_I2, DG-Mono-GRE_I-3 and DG-Mono-NRE_I-2, while Figure 6.9 reports the DIC results of DG-Mono-URE_II2 and DG-Mono-GeoRE_II-1. It is specified that the frames refer to the peak load (𝛾𝜏max) and the ultimate load (𝛾ult). In all specimens built with RE_I, when the shear strength was achieved (𝜏max), a main crack was formed along the diagonal and passing through the layers of the rammed earth (Figure 6.8a-b-c); afterwards delamination along the layers interface occurred (Figure 6.8d-e-f). Such result indicates that the rammed earth responds as a monolithic material up to the shear strength. In addition, DIC results validate the assumption of a pure shear strain field in the centre of the wall, as only tensile strains orthogonal to the vertical crack were detected. A different behaviour is observed for specimens built with Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 110 Chapter 7 IN-PLANE CYCLIC RESPONSE OF A RAMMED EARTH SUB-ASSEMBLAGE The experimental work presented in the previous chapters allowed characterising mechanical properties of the rammed earth as a building material, such as Young’s modulus, shear modulus, compressive and shear strength, among others. Such properties are fundamental for the numerical modelling of rammed earth structures using simplified methods and assumptions, such as the linear elastic analysis while considering homogeneous and isotropic material. However, the structural response of a rammed earth wall may implicate phenomena that cannot be described through simplified analyses and which implicate considering damage mechanisms and hysteretic behaviour. Whereas reliable mechanical properties can be assessed by means of relatively simple tests as those previously presented, parameters to describe the hysteretic response, as stiffness and strength degradation or energy dissipation, can only be determined by simulating cyclic loads. The importance of such parameters lies on the fact that an accurate seismic vulnerability assessment of a structure is the basis for the implementation of appropriate strengthening solutions. In addition, reliable values of hysteretic properties allow defining simplified models for designing, yet including the actual structural dissipative capacity, which otherwise would be only possible with sophisticated models, which are unpractical. Within the framework described above, an experimental program was conducted to investigate the in-plane cyclic performance of a rammed earth structural sub-assemblage in the form of an I-shaped wall. The purpose was to characterise the response and to evaluate the hysteretic properties of the wall under shear loads. Afterwards, the wall was strengthened with TRM and subjected to further in-plane cyclic loading. The chapter presents at first the test setup, describing the materials used to build the wall and the testing protocol. The subsequent section reports and discusses the experimental results in terms of cracking pattern, dynamic characterisation, displacement capacity, base shear forces and strength decay. Further discussion is focused on the stiffness degradation and energy dissipation, which allowed determining the equivalent damping coefficient. Hence, equivalent elastic and elastic-perfectly plastic systems were calculated based on the experimental curves, according to simplified models for masonry structures (BS EN 1998-1, 2004; Consiglio Superirore dei Lavori Pubblici, 2008; Tomaževič, 1997; Tomaževič, 2006). Chapter 7. In-plane cyclic response of a rammed earth sub-assemblage 111 Afterwards, a section is dedicated to the TRM-strengthening solution applied; in particular, the material used, the strengthening scheme and the fixing system are illustrated. Subsequently, as for the previous un-strengthened case, the results of the TRM-strengthened wall are reported and discussed. Furthermore, the effectiveness of the TRM solution is evaluated with basis on the results of the previous un-strengthened test. Finally, the main findings are summarised. 7.1 Materials and testing setup of the un-strengthened model (URE-IP) With the aim at investigating the in-plane response of rammed earth walls of traditional singlestorey buildings with timber roof, a reduced scale 1:1.25 sub-assemblage was built with an I-shape geometry plan. The geometry was defined based on a preliminary numerical investigation (Allahvirdizadeh et al., 2019). Buttresses were included in the sub-assemblage as representation of the walls found in this type of buildings at providing stability to the web wall during the in-plane cyclic loading. Hence, the model consisted of two wing walls with 120 cm length and a web wall with 280 cm length, while the thickness of the wall was 40 cm and the height was 180 cm. The foundation of the model consisted of limestones embedded in a concrete layer of 10 cm thick cast on a steel plate (Figure 7.1a and Figure 7.1b). The plate included welded vertical connectors to avoid sliding of the concrete layer and was adequately fixed to the lab strong-floor with tie rods (Figure 7.1c). Afterwards, the rammed earth wall was built by mechanical compaction of the moistened mixture in layers of about 10 cm thick using a complete timber mould (Figure 7.1d). The soil mixture used to build the structural sub-assembly was RE_II (see Section 3.2), which was also used to build a set of wallets tested under diagonal compression (see Section 6.1) and the mock-up tested on the shaking table (see Section 8.1). It should be noted that the structural subassembly was demoulded immediately after achieving the full height of the walls, while the drying occurred for a period of about 4 months in laboratory conditions. The properties of RE_II material are briefly reported in Table 7.1, although they are throughout discussed in Chapter 3. It is specified that, although a stepwise analysis was performed to investigate the Young’s modulus value as a function of the stress level, 𝐸re value is here considered as the Young’s modulus of the material (see Section 3.2). Table 7.1. Material properties of rammed earth used to build the structural sub-assembly tested to in-plane shear. Soil Clay [%] Silt [%] Sand [%] Gravel [%] 𝛒 [𝐠/𝐜𝐦𝟑] 𝒇𝐜 [𝐌𝐏𝐚] 𝐄𝐫𝐞 [𝐌𝐏𝐚] RE_II 6 9 38 47 2.02 0.56 213 Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 112 The test setup was designed to allow the application of cyclic horizontal displacements at the top. Thus, two U-steel profiles were placed on the wing walls and were connected by two tie rods crossing them through holes created during the construction (Figure 7.1e). The stiffness and contact surface of the steel profiles were designed to provide even distribution of the loads during the test and to avoid punching on the wing walls (Figure 7.2). (a) (b) (c) (d) (e) Figure 7.1. Setup of the in-plane cyclic tests: a) elevation, b) plan, c) foundation, d) construction, and e) holes for the tie rods. Chapter 7. In-plane cyclic response of a rammed earth sub-assemblage 113 Figure 7.2. Details of the steel profiles. As referred previously, the sub-assembly was built with a geometric scale factor of 𝜆=0.80, which was a limitation imposed by the laboratorial facilities. Thus, the design of the in-plane cyclic tests considered the compliance with Cauchy’s or Cauchy-Froude’s similitude laws on the scaled geometry, stress-strain relationships of materials, mass and gravity forces, and boundary conditions (Carvalho, 1998). Theoretically, a similitude scale law between the model and the real prototype structure allows to assume the structural response of a scaled model, including the damage patterns and failure mechanisms, to be similar to the behaviour observed in a real structure. The similitude is obtained according to Cauchy and Froude similitude laws, as given in Eq. 7.1 and Eq. 7.2: 𝐶𝑎𝑢𝑐ℎ𝑦 𝑛𝑢𝑚𝑏𝑒𝑟= 𝜌𝐿3𝜐2 𝐿 𝐸𝐿2=𝜌𝜈2 𝐸 Eq. 7.1 𝐹𝑟𝑜𝑢𝑑𝑒 𝑛𝑢𝑚𝑏𝑒𝑟= 𝜌𝐿3𝜐2 𝐿 𝜌𝐿3𝑔=𝜈2 𝐿𝑔 Eq. 7.2 Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 114 where 𝜌 is the density, 𝐿 is the length, 𝑣 is the velocity, 𝐸 is the Young’s modulus and 𝑔 is the gravity acceleration. Considering the equations, the Cauchy number represents the ratio between inertial forces and restoring forces, while the Froude number corresponds to the ratio between the inertial forces and gravity forces. The correlation between the main geometrical and physical properties of the full-scale and the reduced model is reported in Table 7.2. Accordingly, to simulate the scaled vertical load of a traditional timber roof, the wall was loaded with bags for a total weight of 11.77 kN after a drying period of four months. The in-plane cyclic displacements were applied by an actuator with 300 kN capacity, which was connected with a cylindrical hinge to the mock-up and with a spherical hinge to the reaction wall; in addition, a compressed air system was set to support the actuator. In this way, the transmission of bending moment and the influence of the weight of the actuator were prevented (Figure 7.3). Table 7.2. Parameters according to Cauchy and Froude similitude laws for a scale factor λ = 0.8. Parameter Symbol Unit Cauchy Froude Length 𝐿 [m] 𝜆 𝜆 Young’s modulus 𝐸 [MPa] 1 1 Specific mass 𝜌 [kg/m3] 1 𝜆−1 Area 𝐴 [m2] 𝜆2 𝜆2 Volume 𝑉 [m3] 𝜆3 𝜆3 Mass 𝑚 [kg] 𝜆3 𝜆2 Displacement 𝑑 [m] 𝜆 𝜆 Velocity 𝑣 [m/s] 1 𝜆0.5 Acceleration 𝑎 [m/s2] 1 𝜆−1 Weight 𝑊 [N] 𝜆3 𝜆2 Force 𝐹 [N] 𝜆2 𝜆2 Moment 𝑀 [Nm] 𝜆3 𝜆3 Stress 𝜎 [MPA] 1 1 Strain 𝜀 [m/m] 1 1 Time 𝑡 [s] 𝜆 𝜆0.5 Frequency 𝑓 [Hz] 𝜆−1 𝜆−0.5 Chapter 7. In-plane cyclic response of a rammed earth sub-assemblage 115 Figure 7.3. Overview of the loading system of the URE-IP sub-assemblage. The test was conducted by controlling the displacement in the loading direction of a point at the top of the left wing (control point). The cyclic testing protocol considered increasing target displacements in both directions (positive and negative), and one repetitions for each positive and negative cycle, as indicated in Figure 7.4 and Table 7.3. In addition, operational modal analyses (OMA) were performed to check the changes in values of the natural frequencies and modal shapes along the tests, which were named as DI-URE-IP-#number of test . Figure 7.4. Loading profile of the un-strengthened model URE-IP. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 116 Table 7.3. Testing protocol of the un-strengthened model URE-IP. Cycle Rate [𝛍𝐦/𝐬] ∆𝒅 [𝐦𝐦] Drift [%] DI-URE-IP-01_WVL DI-URE-IP-01 1 2 ± 0.2 0.01 2 5 ± 0.4 0.02 3 5 ± 0.8 0.04 4 15 ± 1.2 0.07 5 30 ± 2.4 0.13 DI-URE-IP-02 6 60 ± 3.6 0.19 7 60 ± 4.8 0.27 DI-URE-IP-03 With regard to the dynamic identification tests, the model was discretized in a grid of accelerometers with 4x5 points, as showed presented in Figure 7.5a. The disposition and orientation of the accelerometers was defined in order to monitor the in-plane and out-of-plane vibrations. As for monitoring deformations, a set of 4 LVDTs were placed at each wing-wall, measuring displacements in the direction of the loading along a vertical profile (LVDT-1A to LVDT-1D, and LVDT-5A to LVDT-5D); additional 4 LVDTs were placed horizontally at each inner corner to measure relative displacements between the wing-walls and the web-wall (LVDT-2A to LVDT-2D, and LVDT-4A to LVDT-4D). Further 3 LVDTs were set along the base of the wall to monitor the possible sliding at the foundation interface (LVDT-2D, LVDT-3D and LVDT-4D). The deformations at the middle-third zone of the web-wall were also monitored using 6 LVDTs placed in horizontal, vertical, and diagonal alignments. The position of the LVDTs is illustrated in Figure 7.5b. Chapter 7. In-plane cyclic response of a rammed earth sub-assemblage 117 (a) (b) Figure 7.5. Position of the sensors used to monitor accelerations and deformation during the cyclic in-plane tests: a) accelerometers, and b) LVDTs. 7.2 Results of the un-strengthened model URE-IP and discussion The results of the in-plane cyclic test for the un-strengthened rammed earth model (URE-IP) are presented in the subsequent sections in terms of cracking pattern, dynamic properties, displacements, base shear coefficient, stiffness decay, energy-based analysis and proposal of bi-linear and linear equivalent systems. 7.2.1 Cracking pattern The cracking pattern of the un-strengthened rammed earth model was monitored during the cyclic tests. Minor cracks were first observed on wing-walls close to the loading surface during the 5th cycle, however a main horizontal crack formed in the web-wall along one of the interfaces between layers at an early stage of the 6th cycle. Afterwards, further two diagonal cracks opened at the lower inner corner of the web-wall, connecting with the previous horizontal crack, as showed in Figure 7.6. It should be noted that three types of failure modes are encountered when a general structural masonry wall is subjected to in-plane seismic loads, which depend on the geometry of the structural element, slenderness, quality of materials, boundary restraints and acting loads (Tomaževič, 2006). In the case of low vertical loads, in-plane actions usually cause shearing and then sliding of two superimposed blocks. Whereas shear failure might occur when the principal tensile stress, developed under a combination of vertical and horizontal loads, exceeds the tensile strength of the material and results into a characteristic diagonal crack in the wall. Finally, in the case of high shear strength and high moment to shear ratio, flexural failure might be achieved with the typical crushing of the compressed zones at the end of the wall. Thus, considering the observed cracking pattern, the URE-IP wall subjected Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 118 to in-plane loads responded as a non-homogeneous material as consequence of the low tensile and shear strength of the interface between layers and low vertical loads. Figure 7.6. Cracking pattern of the URE-IP model. 7.2.2 Dynamic properties Identifying the dynamic properties of a structure, such as natural frequencies and mode shapes, is experimentally possible; nonetheless, imposing an initial condition to a system, as initial acceleration, velocity or displacement, might be not feasible for actual cases or might induce further damage to the building. Therefore, methods based on the responding vibration of a structure under natural excitation were implemented, known as Operation Modal Analysis (OMA) or output-only analysis. In OMA methods, the input is assumed to be stochastic, defined as white noise, smooth and broadband and it is considered uniformly distributed (Ghalishooyan & Shooshtari, 2015; Zhang et al., 2004). Complying with such assumption allows the recorded signal on the structure to be analysed in frequency domain, usually through a Fourier transform function known as frequency response function (𝐹𝑅𝐹), and to obtain the power spectral density (𝑃𝑆𝐷) of the signal, which identifies the eigenvalues of the structure. In addition, determining the dynamic properties of a structure along its lifetime allows to detect whether or not damage occurs. In fact, the change of frequencies or mode shapes is related to the evolution of the structural stiffness, which in turn is associated with the concept of degradation of materials or structural elements, such as variation of geometry, aging cracking or change in boundary conditions. Furthermore, dynamic identification of a structure allows to calibrate representative numerical models, which can be used as basis for parametrical and sensitivity studies of materials properties. In the following analysis, the Enhanced Frequency Domain Decomposition (𝐸𝐹𝐷𝐷) method was applied to the results obtained from the dynamic identification tests, which allows to estimate with accuracy the modal frequencies (𝑓) and mode shapes (Φ). It should be noted that to guarantee the basic assumption Chapter 7. In-plane cyclic response of a rammed earth sub-assemblage 119 of white noise and obtain accurate data resolution, the duration of each dynamic identification record was of 20 minutes and sampling frequency was of 200 Hz. ARTeMIS Modal software (ARTeMIS, 2013) was used to analyse the obtained signals. The OMA performed on the wall before applying the vertical load was identified as DI-URE-IP-01_WVL, while the dynamic identification after application of the vertical load and before testing the wall was labelled as DI-URE-IP-01. Further, two dynamic identification tests were performed, namely after the 5th cycle and at the end of the cyclic test protocol, which were named as DIURE-IP-02 and DI-URE-IP-03, respectively. For the sake of brevity, only the results of DI-URE-IP-01 test are presented with detail in this section, while Annex A.1 presents the detailed results of the remaining dynamic identification tests. As a result, three natural frequencies and corresponding modal shapes were distinguished. The first frequency was 𝑓1=18.12 Hz and corresponded to an out-out-plane bending of the web-wall (Figure 7.7a); the second frequency was 𝑓2=24.46 Hz and involved the out-of-plane bending in reversed-phase of the boundaries of the wall (Figure 7.7b); finally the third frequency was 𝑓3=32.04 Hz which entailed the out-of-plane of the boundaries in reversed-phase with the bending of the middle-section of the wall (Figure 7.7c). 𝑓1=18.12 Hz 𝑓2=24.46 Hz 𝑓3=32.04 Hz (a) (b) (c) Figure 7.7. Natural vibration modes of the un-strengthened model obtained from the DI-URE-IP-01 test: a) Mode 1, b) Mode 2, and c) Mode 3. The results of the entire dynamic identifications test sequence on the URE-IP wall model are reported in Table 7.4. It should be noted that no difference in the values of the frequencies was detected between the condition before applying the vertical load (DI-URE-IP-01_WVL) and that after (DI-URE-IP-01). This indicates that the additional mass of the vertical loading (15% of the rammed earth mass) did not affect the dynamic properties of the system. No difference in natural frequency was observed at the dynamic identification DI-URE-IP-02. The last dynamic identification (DI-URE-IP-03) was performed after the main crack occurred, resulting in a decrease of the first natural frequency to 17.08 Hz and the Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 222 Considering the vertical profiles of the relative displacements, an initial out-of-plane rigid rotation and subsequent bending of the web-wall due to the formation of the cracks was observed, being the maximum displacements in the web-wall of about 12 mm. Subsequently, linear and quadratic relationships with high coefficient of determination were found for the maximum out-of-plane displacement of the control point (𝑑max CP ) as function of the various parameters characterising the seismic inputs; meaning that the response in terms of maximum out-of-plane displacement of the mockup could be predicted on the basis of the ground motion. Subsequently, the effectiveness in terms of displacement capacity of the TRM solution was evaluated by analysing the maximum displacement of the control point (𝑑max CP ) attained by the URE-ST and NRE-ST mockups. The comparison reported an improvement of the NRE-ST displacement capacity of about 130% with respect to the maximum displacement of the un-strengthened mockup. Similarly to the URE-ST mockup, the base shear force was estimated assuming that the damping contribution is null for each local maximum or minimum relative displacement of the structure. Afterwards, the error (𝑒BSC) due to neglecting the damping forces was assessed, which resulted to be reduced for most of the seismic inputs. Nevertheless, it attained a maximum overestimation of the base shear coefficient of 205 %. However, the precautionary consideration of 𝐵𝑆𝐶 at damping force equal to zero resulted in a 𝐵𝑆𝐶max of the NRE-ST mockup of 0.65. Subsequently, linear and quadratic relationships with high coefficient of determination were found to describe the absolute maximum base shear coefficient 𝐵𝑆𝐶max as function of the ground motion parameters. Nevertheless, no correlation was found between the 𝑃𝐺𝐷 and the maximum absolute 𝐵𝑆𝐶max. Such result can be a consequence of the natural period of the structure with respect to the frequency content of the seismic input. Afterwards, the effectiveness of the TRM solution was evaluated by analysing the maximum base shear coefficient 𝐵𝑆𝐶max attained by the URE-ST and the NRE-ST mockups as function of the ground motion parameters. The results reported that the URE-ST mockup presented higher strength capacity, which suggested that the nylon mesh based TRM-strengthening could not provide further strength when applied on such massive structure subjected to dynamic loads. Finally, the energy-based investigation showed that the dissipative capacity of the NRE-ST mockup was almost constant throughout the 𝐼𝐷𝐴 program, while the performance index (𝑃I) was of 0.46. Afterwards, to further assess the effectiveness of the TRM-strengthening, the energy dissipated 𝐸i(𝑇) and the performance index (𝑃I) as function of the input energy (𝐼𝐸) of the URE-ST and NRE-ST mockups were compared. The results demonstrated that the URE-ST mockup dissipated higher energy compared Chapter 8. Out-of-plane shake table test of a rammed earth sub-assemblage 223 to NRE-ST, while the performance index, which was assumed as indicator of the effect of the strengthening, indicated that the use of nylon mesh could not provide further hysteretic or damping capacity to the sub-assemblage. In conclusion, the rammed earth sub-assemblage demonstrated sufficient shear capacity in terms of 𝐵𝑆𝐶 and energy dissipation. However, the TRM-strengthening with the use of nylon mesh did not provide further capacity to a massive structure under dynamic loads, for which a more resistant mesh, such as GeoM, is probably required. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 224 Chapter 9 CONCLUSIONS AND FUTURE WORKS 9.1 Main conclusions The investigation presented in this thesis addresses the seismic performance and strengthening of rammed earth structures by means of compatible externally bonded solutions. The aim was to cover a gap in the knowledge regarding TRM-strengthening techniques for rammed earth heritage and to contribute to the characterisation of rammed earth materials and structures. To fulfil the aforementioned objectives, a comprehensive experimental program was conducted at the department of Civil Engineering of the University of Minho and at the Earthquake Engineering and Structural Dynamic division of the National Laboratory of Civil Engineering (LNEC) in Lisbon. Firstly, geotechnical analyses were performed on two different raw soils collected from Alentejo region (RS_I and RS_II), which resulted as not being appropriate for rammed earth construction due to their high clay content and low dry density after compaction. Therefore, coarse sand and gravel materials were added, leading to the corrected mixtures CS_I and CS_II. The geotechnical analyses conducted subsequently evidenced their suitability for rammed earth. The characterisation of rammed earth manufactured with CS_I and CS_II, respectively referred to as RE_I and RE_II, aimed at defining the physical and mechanical properties of both materials. As result, the average density (𝜌) of the RE_I and RE_II cylinders was consistent with the Proctor test result, while the average compressive strength (𝑓 c) was within the range of values presented in literature. As for the Young’s modulus, a stepwise analysis based on the level of compressive stress was conducted, which demonstrated the nonlinear behaviour of rammed earth even for low compressive stresses. However, the Young’s modulus (𝐸r) in the range 0-30% of 𝑓 c, commonly considered for other materials, was also provided. In conclusion, RE_I and RE_II presented suitable mechanical properties for building, despite of the low compressive strength of the latter. Different mixtures of earth-based mortars composed with soil RS_I or RS_II were analysed by varying their clay content. Therefore, for each composition, the 𝑊/𝑆 ratio for optimal workability was firstly defined. Afterwards, the linear shrinkage (𝐿s), flexural strength (𝑓 b) and compressive strength (𝑓 c) were evaluated. To individuate the most suitable mixture, a threshold of 2% of linear shrinkage was set as suggested in literature. With regard to the Young’s modulus, a stepwise analysis was conducted on stress-strain curves of compression tests conducted on cylindrical specimens. The results of the analysis Chapter 9. Conclusions and future work 225 showed the early nonlinear response of the earth-based mortars for low stress values. However, the Young’s modulus (𝐸m) calculated in the range 0-30% of 𝑓 c was found consistent with the literature. Based on the characteristics of EM_I and EM_II, the earth-based mortars are assumed compatible with rammed earth, as the mineralogical composition is equal. Moreover, although the earth-based mortars presented higher Young’s modulus compared to rammed earth, the overall stiffness of the matrix layer and the rammed earth wall is deemed similar. As for the reinforcing meshes, a glass fibre mesh (GM), nylon mesh (NM) and geomesh (GeoM) were selected for integrating different strengthening solutions. All the meshes presented different weft or geometrical characteristics; however, their aperture size was considered adequate to permit their embedding in the mortar and their grammage (𝐺𝑆𝑀) met the requirement for composite materials (inferior to 600 g/m2). With regard to the tensile capacity, although GeoM achieved the highest linear strength (𝐹 wpeak), GM presented the material with the highest tensile strength (𝑓 𝑡). Substantial difference was found in the peak elongation (𝜀peak) and the Young’s modulus (𝐸𝑦) values. Finally, although the properties of GM, NM, and GeoM were found substantially different among them, their geometrical and mechanical characteristics were considered appropriate for the proposed TRM-strengthening solutions. Being the TRM a composite material, the interactions between the components of the proposed TRM solution were experimentally studied at different levels. In particular, the interaction between matrix and fibre was investigated by means of tensile tests on TRM coupons (TCNM, TCGM, and TCGeoM) and pull-out tests (PONM and POGM), while the mortar-fibre-substrate interaction was analysed through singlelap shear tests (SLNM and SLGM). The direct tensile tests on TRM coupons resulted in the typical 3stages behaviour found in literature, which corresponded to the enhanced initial stiffness due to the contribution of the mortar (stage I), the cracking of the matrix (stage II) and the pure tensile response of the mesh (stage III). However, different developments of the stage II and type of failure were observed with respect to the geometrical and mechanical properties of the embedded mesh. Furthermore, the average linear force achieved in TCGM was lower than the tensile capacity of GM, which suggests likely damage of the glass fibre yarns due to friction within the mortar. The pull-out tests showed distinct responses depending on the mesh type and embedded length. In general, POGM specimens were characterised by an elastic branch, which corresponded to a transmission of load by adhesion between matrix and yarns. Afterwards, the response became nonlinear, during which both adhesion and friction mechanisms defined the interface bond. Finally, sliding occurred and friction was the only bond mechanism, which likely caused damage to the fibres and the consequent reduction of the tensile Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 226 capacity. Contrarily, the bond of PONM specimens was found to be provided by the transversal yarns, which, being welded to the longitudinal ones, promoted mechanical anchoring of NM mesh to the mortar. As for the interaction substrate-matrix-mesh, the SLNM response was found nonlinear since an early stage, while detachment of the mortar from the substrate occurred for values of force lower than the tensile capacity of the nylon mesh. Therefore, the shear strength at the matrix-support interface is the weakness of NM-TRM solution. Whereas, SLGM specimens showed an elastic response with the transmission of load by adhesion from the yarn to the matrix and thence to the support. Once that the bond strength was achieved at the mortar-mesh interface, friction and the consequent nonlinear response was developed. The failure occurred when either the cohesion at the rammed earth-mortar interface or the adhesion at the mortar-mesh interface was destroyed. Finally, since the predominant failure of SLGM was due to detachment of the mortar for loads lower than those of POGM, the adhesion of the matrix was assumed as the weakness of the GM-TRM system. Subsequently, a novel bond stress-slip (𝐵𝑆𝑅) analytical model was developed on the basis of the pull-out observations. The assumed model was constituted of an adhesion-friction law with a linear elastic relation τ = κu up to the shear strength τmax, after which the shear stress becomes a constant shear friction strength τfri. In addition, a damage model was introduced to reproduce the wearing of the yarns caused by its friction within the matrix. Thus, the algorithm was implemented and the 𝐵𝑆𝑅 was calibrated on the experimental observations by means of a further sensitivity analysis. Although the 𝐵𝑆𝑅 was limited in three parameters, the calibrated analytical model predicted with accuracy the elastic and nonlinear responses of the pull-out test representing an effective tool that can be developed in further numerical applications. The monotonic diagonal compression tests on wallets demonstrated that the shear behaviour of un-strengthened rammed earth is initially linear elastic, during which the shear strength and stiffness are developed by the cohesion of the clay. Subsequent to the first crack, friction is developed with the consequent nonlinear response of the wallet. Thereafter, the friction and interlocking promoted by the aggregates provide strength up to the peak stress, which is followed by a plateau until the failure. Although the behaviour of un-strengthened wallets subjected to cyclic loads was similar to that of monotonic tests, a softening response followed the peak load, which suggested that the loading-unloading cycles further degraded the surface across the crack with the consequent reduction of the friction and interlocking mechanisms. Furthermore, the loading-unloading process followed the same path with a constant deformation, meaning that the residual elasticity is totally absent once that the elastic phase is exceeded. Chapter 9. Conclusions and future work 227 With regard the shear strength (𝑓 s), although the two mixtures RE_I and RE_II presented different compressive strength, the shear strength attained in the diagonal compression test was identical in any case; similar results were found for all the TRM-strengthened cases. Therefore, the shear strength of the rammed earth wallets was essentially provided by friction and interlocking of the coarse particles rather than by the TRM-strengthening solution. On the other hand, the effects of the various TRM solutions were observed in terms of improvement of the deformation capacity, suggesting that the TRM was activated once that the cohesion was destroyed and the first crack occurred. However, detachment of the GM-TRM across the main crack at the mortar-substrate interface was observed after the peak stress; consequently, the confining effect of the TRM was affected. Similarly, the large deformation sustained by NM-TRM reduced the friction along the crack surfaces with the consequent decrease of shear load. Contrarily, the effectiveness of the Geo-TRM was observed in preventing the collapse of the wallets while improving its hysteretic capacity. The shear modulus of the different rammed earth configurations was analysed as a function of the stress level. In general, the results presented a constant initial trend of the shear modulus, which progressively decreased with the increasing of the stress level, in consistency with the development and opening of micro-cracks. However, the classical value of shear modulus (𝐺) was evaluated in range 0% - 30% of τmax. The Cauchy principal tensile strains assessed with DIC validated the assumption of a pure shear strain field in the centre of the wallets and that the rammed earth under pure shear strain up to the shear strength can be assumed as a monolithic material. Afterwards, delamination between layers occurred. In addition, the DIC technique allowed to detect the different cracking patterns and capacity to redistribute the strains according to the TRM-strengthening solution. As a result, GM-TRM showed a wider main crack and local spreading of the deformations, whereas NM-TRM demonstrated a broad spread of strains and development of further cracks until the ultimate stage. In the case of the Geo-TRM solution, a single main crack with concentration of strains nearby the constrained areas was detected, suggesting that the geomesh was well embedded within the mortar. In conclusion, the TRM in general did not increase the shear strength of the rammed earth wallets; however, improvement of the deformation capacity of the rammed earth was observed, in particular for the TRM solution with the use of NM; whereas, the use of GeoM prevented the collapse of the specimens while enhancing the deformation capacity. The experimental program on a rammed earth sub-assemblage subjected to cyclic in-plane loading aimed at characterising the hysteretic behaviour and effectiveness of the Geo-TRM solution. The crack Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 228 pattern of the un-strengthened model (URE-IP) demonstrated that the rammed earth of a wall subjected to low vertical loads and in-plane loading cannot be assumed as a homogeneous material. The analysis of the lateral stiffness in the nonlinear branch indicated that a plastic-deformation state of the model could be modified only by exceeding the peak displacement of the previous step. An energy-based analysis of the URE-IP model showed that increasing the displacement demand beyond the elastic response leads the structure to a plastic domain, which cannot be recovered during the unloading path. Based on the energy analysis, the equivalent damping ratio was observed to slightly increase with large displacement demands, confirming the non-conservative phenomena that occurred in the inelastic domain. Hence, equivalent elastic and elastic-perfectly plastic systems were inferred to support the seismic design of rammed earth structures or assessment of existing ones. The crack pattern of the in-plane cyclic test on the model strengthened with Geo-TRM (GeoRE-IP) evidenced that, although the previous damage state of the model was not recovered, the TRMstrengthening was able to redistribute the loads involving the entire structure. Such result was confirmed by the dynamic characterisation tests and by analysing the degradation of the lateral stiffness of the GeoRE-IP model. Regarding the envelopes of the 𝐵𝑆𝐶–displacement curves, the GeoRE-IP model presented an early nonlinear response consequent to the former damage state of the model; nonetheless, the TRMstrengthening resulted effective, as it increased the 𝐵𝑆𝐶max and drift. The effectiveness of the TRMstrengthening was found in the higher dissipative capacity provided to the structure with respect to the demanded energy. Similar improvements were observed in the equivalent elastic and elastic-perfectly plastic systems of the GeoRE-IP model, in which the ductility and behaviour factor of the strengthened model were improved. In conclusion, the TRM-strengthening was effective in recovering the strength capacity of the original structure while providing further dissipative and ductility capacity. Nonetheless, the overall lateral stiffness was not recovered by the strengthening, for which other repairing interventions might be required. The shaking table investigation of a rammed earth sub-assemblage subjected to incremental dynamic analysis (𝐼𝐷𝐴) aimed at defining the out-of-plane dynamic response of rammed earth walls and at assessing the effectiveness of the applied N-TRM strengthening solution. The crack pattern of the un-strengthened mockup (URE-ST) confirmed the lower tensile strength of the interfaces between layers with respect to the tensile strength of the rammed earth layers. The overall structural damage of the URE-ST mockup was also detected by means of input-output modal analysis performed at each step of 𝐼𝐷𝐴. Nevertheless, Chapter 9. Conclusions and future work 229 a complementary method was adopted to define the occurrence of damage during the ground motion. The results identified the development of damage in the URE-ST mockup consistently with the observed cracking pattern. Analysing the relative displacement profiles of the URE-ST mockup, an out-of-plane rigid rotation was observed. Subsequently, linear and quadratic relationships with high coefficient of determination were found between the maximum out-of-plane displacement of the control point (𝑑max CP ) and the various parameters used to characterise the seismic inputs; meaning that the response in terms of maximum out-of-plane displacement of the mockup can be predicted on the basis of the ground motion. With regard to the base shear force, it was estimated assuming that the damping contribution was null for each stationary points of the relative displacement time series. Linear and power relationships with high coefficient of determination were found to describe the absolute maximum base shear coefficient 𝐵𝑆𝐶max as function of the ground motion parameters. Nevertheless, no correlation was found between the 𝑃𝐺𝐷 and the maximum absolute 𝐵𝑆𝐶max. Such result can be a consequence of the natural period of the structure with respect to the frequency content of the seismic input. To further assess the seismic capacity of the URE-ST mockup, the energy-based investigation was conducted considering the structure in the global reference system. The results showed that the dissipative capacity 𝐸i(𝑇) of the URE-ST mockup was almost constant throughout the seismic tests. In addition, the performance index (𝑃I) was introduced as a ratio between the energy provided by the ground motion and the energy dissipated and absorbed by the structure. After the shaking table tests of the URE-ST mockup, it was repaired by means of grout injection and strengthened with a NM-TRM solution (NRE-ST). The crack pattern of the NRE-ST mockup indicated that the repairing and TRM-strengthening could not fully recover the previous damage state. As for the URE-ST case, the results of the dynamic identification tests and the complementary method to detect local damage were in line with the observed crack pattern. Considering the vertical profiles of the relative displacements, an initial out-of-plane rigid rotation and subsequent bending of the web-wall due to the formation of the cracks was observed. Subsequently, linear and quadratic relationships with high coefficient of determination were found for the maximum out-of-plane displacement of the control point (𝑑max CP ) as function of the various parameters characterising the seismic inputs; meaning that the response in terms of maximum out-of-plane displacement of the mockup could be predicted on the basis of the ground motion. The effectiveness in terms of displacement capacity of the strengthened mockup was evaluated by comparison of the maximum displacement of the control point (𝑑max CP ) attained by the Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 230 URE-ST and NRE-ST mockups, which resulted in an improvement of the displacement capacity of the latter. Similarly to the URE-ST mockup, the base shear force was estimated assuming that the damping contribution is null for each local maximum or minimum relative displacement of the structure. On this regard, linear and quadratic relationships with high coefficient of determination were also found to describe the absolute maximum base shear coefficient 𝐵𝑆𝐶max as a function of the ground motion parameters. Nevertheless, no correlation was found between the 𝑃𝐺𝐷 and the maximum absolute 𝐵𝑆𝐶max. Such result can be a consequence of the natural period of the structure with respect to the frequency content of the seismic input. Afterwards, the effectiveness of the TRM solution was evaluated by analysing the maximum base shear coefficient 𝐵𝑆𝐶max attained by the URE-ST and the NRE-ST mockups as a function of the ground motion parameters. The results suggested that the nylon mesh based TRM-strengthening could not provide further strength when applied on such massive structure subjected to dynamic loads. Finally, the energy-based investigation showed that the dissipative capacity of the NRE-ST mockup was almost constant throughout the 𝐼𝐷𝐴 program. Afterwards, to further assess the effectiveness of the TRM-strengthening, the energy dissipated 𝐸i(𝑇) and the performance index (𝑃I) of the URE-ST and NREST mockups were compared as a function of the respective input energy (𝐼𝐸). The results showed that the URE-ST mockup dissipated higher energy compared to NRE-ST, while the performance index, which was assumed as indicator of the effect of the strengthening, indicated that the use of nylon mesh could not provide further hysteretic or damping capacity to the sub-assemblage. In conclusion, the rammed earth sub-assemblage demonstrated adequate shear capacity in terms of 𝐵𝑆𝐶 and energy dissipation. However, the TRM-strengthening with the use of nylon mesh did not provide further capacity to a massive structure under dynamic loads, for which a more resistant mesh, such as GeoM, is probably required. 9.2 Recommendations for rammed earth structures and TRM-strengthening techniques The experimental program presented in the thesis provided a better understanding of the behaviour of rammed earth and TRM-strengthening solutions for such structures. A further step is to render the findings in recommendations for further investigations and practitioners. It is reported that such recommendations are based on the experience acquired during the experimental work, and they should be regarded as indicative and not as requirements. Following, the main recommendations are listed Chapter 9. Conclusions and future work 231 regarding the manufacturing of rammed earth materials, the TRM components and the application of the strengthening solution: • The expeditious drop ball test was confirmed to be reliable in assessing the optimal water content of the earth mixture; • To manufacture rammed earth walls, a compaction of layers of about 10 cm is satisfactory to obtain appropriate value of dry density and thus compressive strength of the material; • To prepare earth-based mixtures, the same soil of the rammed earth structure should be used; in this way, mineralogical compatibility is guaranteed; • A maximum linear shrinkage (𝐿s) of 2% is suggested to design an earth-based mortar; • To avoid detachment of the matrix and provide adequate embedding of the mesh, the aperture size of the latter should be larger than 10 mm, while the thickness and the width of the yarn should not exceed 1 mm and 3 mm, respectively; • In order to promote confinement effect of walls in the case of cracking, the threshold of peak elongation of the reinforcing mesh should be lower than 0.10 mm/mm; • The maximum linear force of the embedded mesh should be higher than 20 kN/m, ideally in both directions; • For the sake of the representativeness of the onsite material, to evaluate the compressive strength and the Young’s modulus of rammed earth components and earth-based mortars, cylindrical specimens with ratio 𝐻/𝑑 = 2 is suggested. The rammed earth cylinder should be composed in 3 layers with the OWC assessed by means of the drop ball test. • Before applying the TRM technique, the surface of the rammed earth wall should be scratched and wet, to improve the adhesion between the support and the mortar, while reducing early water reduction from the matrix; • The mesh should be applied stretched to avoid any bedding of the yarns, which could likely damage its fibres; • To improve the transference of loads from the structure to the reinforcing mesh, connectors should be plugged in distance in the range 25 – 30 cm; Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 238 Bulletin 159. (1996). Smith E.W. and Austin G.S. Adobe, pressed-earth, and rammed-earth industries in New Mexico. New Mexico Bureau of Mines and Mineral Resources . https://books.google.pt/books?id=uM1QAQAAIAAJ Bulletin 5. (1987). G.F. Middleton, revised by L.M. Schneider. 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Construction and Building Materials , 203 , 567–578. https://doi.org/10.1016/j.conbuildmat.2019.01.070 Annex A.1. In-plane cyclic response of a rammed earth sub-assemblage 257 Annex A IN-PLANE CYCLIC RESPONSE OF A RAMMED EARTH SUB-ASSEMBLAGE In the present Annex A, the results of the experimental programme on the in-plane cyclic response of a rammed earth sub-assemblage are reported in detail. The annex reports the data of the modal analyses, the stiffness degradation and the energy-based analysis for both the cases of the unstrengthened rammed earth model and the TRM-strengthened rammed earth model. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 258 A.1 Un-strengthened rammed earth in-plane test: modal analyses 𝑓1=18.04 Hz 𝑓2=24.54 Hz 𝑓3=32.09 Hz Figure A.1.1. Modal shapes of the un-strengthened model obtained from the dynamic identification test DI-URE-IP-01_WL related to the natural frequency: a) Mode 1, b) Mode 2, and c) Mode 3. 𝑓1=18.12 Hz 𝑓2=24.46 Hz 𝑓3=32.04 Hz Figure A.1.2. Modal shapes of the un-strengthened model obtained from the dynamic identification test DI-URE-IP-01 related to the natural frequency: a) Mode 1, b) Mode 2, and c) Mode 3. 𝑓1=18.24 Hz 𝑓2=24.66 Hz 𝑓3=32.75 Hz Figure A.1.3. Modal shapes of the un-strengthened model obtained from the dynamic identification test DI-URE-IP-02 related to the natural frequency: a) Mode 1, b) Mode 2, and c) Mode 3.. Annex A.1. In-plane cyclic response of a rammed earth sub-assemblage 259 𝑓1=17.08 Hz 𝑓2=29.92 Hz 𝑓3=32.80 Hz Figure A.1.4. Modal shapes of the un-strengthened model obtained from the dynamic identification test DI-URE-IP-03 related to the natural frequency: a) Mode 1, b) Mode 2, and c) Mode 3.. A.2 Un-strengthened rammed earth in-plane test: stiffness degradation Table A.2.1. Loading and unloading stiffness of the un-strengthened model URE-IP for each cycle. Cycle Loop 𝑲𝐋𝐋𝐨𝐨𝐩 + [𝐤𝐍/𝐦𝐦] 𝑲𝐋𝐋𝐨𝐨𝐩 − [𝐤𝐍/𝐦𝐦] 𝑲𝐔𝐋𝐋𝐨𝐨𝐩 + [𝐤𝐍/𝐦𝐦] 𝑲𝐔𝐋𝐋𝐨𝐨𝐩 − [𝐤𝐍/𝐦𝐦] 1 1 189.23 157.61 221.27 201.80 2 187.61 158.75 219.25 190.42 2 1 169.89 112.74 160.55 150.60 2 123.22 106.88 158.64 144.29 3 1 118.80 127.50 119.61 130.67 2 78.33 97.61 111.07 122.27 4 1 74.76 95.00 81.82 107.57 2 53.19 68.74 73.50 99.11 5 1 51.39 53.87 38.82 50.24 2 21.25 30.08 33.98 42.29 6 1 19.59 18.14 16.70 36.79 2 9.58 16.81 16.12 31.16 7 1 8.37 19.14 15.87 18.05 2 6.78 9.20 14.71 15.85 Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 260 A.3 Un-strengthened rammed earth in-plane test: energy-based analysis Table A.3.1. Dissipated and input energy of the un-strengthened model URE-IP for each cycle. Cycle Loop 𝑬𝐝𝐢𝐬 𝐋𝐨𝐨𝐩 [𝐤𝐍𝐦𝐦] 𝑬𝐝𝐢𝐬 𝐜𝐲𝐜 [𝐤𝐍𝐦𝐦] 𝑬𝐝𝐢𝐬 𝐜𝐮𝐦 [𝐤𝐍𝐦𝐦] 𝑬𝐬𝐲𝐬 𝐋𝐨𝐨𝐩 [𝐤𝐍𝐦𝐦] 𝑬𝐬𝐲𝐬 𝐜𝐲𝐜 [𝐤𝐍𝐦𝐦] 𝑬𝐬𝐲𝐬 𝐜𝐮𝐦 [𝐤𝐍𝐦𝐦] 𝑬𝐝𝐢𝐬 𝐋𝐨𝐨𝐩 𝑬𝐬𝐲𝐬 𝐋𝐨𝐨𝐩 [%] 𝑬𝐝𝐢𝐬 𝐜𝐲𝐜 𝑬𝐬𝐲𝐬 𝐜𝐲𝐜 [%] 𝑬𝐝𝐢𝐬 𝐜𝐮𝐦 𝑬𝐬𝐲𝐬 𝐜𝐮𝐦 [%] 1 1 5.69 11.37 11.37 12.56 25.78 25.78 43 44 44 2 5.68 13.22 45 2 1 18.54 37.16 48.53 41.09 83.19 108.97 44 45 45 2 18.62 42.10 45 3 1 61.02 117.62 166.15 117.45 234.21 343.18 48 50 48 2 56.60 116.76 52 4 1 109.92 201.42 367.57 213.61 404.15 747.32 48 50 49 2 91.49 190.54 51 5 1 297.20 503.08 870.64 517.97 904.91 1652.23 53 56 53 2 205.87 386.94 57 6 1 350.86 613.05 1483.69 670.88 1166.96 2819.19 53 53 53 2 262.20 496.08 52 7 1 434.43 799.63 2283.32 676.48 1308.27 4127.47 58 61 55 2 365.19 631.79 64 Annex A.1. In-plane cyclic response of a rammed earth sub-assemblage 261 A.4 TRM-strengthened rammed earth In-plane test: modal analyses 𝑓1=17.06 Hz 𝑓2=24.68 Hz 𝑓3=29.86 Hz 𝑓4=33.20 Hz 𝑓5=34.30 Hz Figure A.4.1. Modal shapes of the strengthened model obtained from the dynamic identification test DI-GeoRE-IP-01 related to the natural frequency: a) Mode 1, b) Mode 2, c) Mode 3, d) Mode 4, and e) Mode 5. 𝑓1=17.07 Hz 𝑓2=23.66 Hz 𝑓3=29.87 Hz 𝑓4=31.91 Hz 𝑓5=33.23 Hz Figure A.4.2. Modal shapes of the strengthened model obtained from the dynamic identification test DI-GeoRE-IP-02 related to the natural frequency: a) Mode 1, b) Mode 2, c) Mode 3, d) Mode 4, and e) Mode 5. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 262 𝑓1=16.81 Hz 𝑓2=22.68 Hz 𝑓3=29.85 Hz 𝑓4=31.25 Hz 𝑓5=32.92 Hz Figure A.4.3. Modal shapes of the strengthened model obtained from the dynamic identification test DI-GeoRE-IP-03 related to the natural frequency: a) Mode 1, b) Mode 2, c) Mode 3, d) Mode 4, and e) Mode 5. 𝑓1=15.78 Hz 𝑓2=21.10 Hz 𝑓3=28.94 Hz 𝑓4=29.85 Hz 𝑓5=30.92 Hz Figure A.4.4. Modal shapes of the strengthened model obtained from the dynamic identification test DI-GeoRE-IP-04 related to the natural frequency: a) Mode 1, b) Mode 2, c) Mode 3, d) Mode 4, and e) Mode 5. Annex A.1. In-plane cyclic response of a rammed earth sub-assemblage 263 A.5 TRM-strengthened rammed earth In-plane test: stiffness degradation Table A.5.1. Loading and unloading stiffness of the strengthened model GeoRE-IP for each cycle. Cycle Loop 𝑲𝐋𝐋𝐨𝐨𝐩 + [𝐤𝐍/𝐦𝐦] 𝑲𝐋𝐋𝐨𝐨𝐩 − [𝐤𝐍/𝐦𝐦] 𝑲𝐔𝐋𝐋𝐨𝐨𝐩 + [𝐤𝐍/𝐦𝐦] 𝑲𝐔𝐋𝐋𝐨𝐨𝐩 − [𝐤𝐍/𝐦𝐦] 1 1 33.69 43.29 58.78 66.46 2 33.21 42.26 59.02 62.80 2 1 37.58 29.57 46.44 34.99 2 28.83 29.36 45.14 33.87 3 1 31.73 28.62 37.26 36.57 2 24.71 26.48 37.02 33.25 4 1 26.88 24.38 29.32 24.28 2 19.91 18.33 28.82 21.75 5 1 22.82 18.12 24.30 19.92 2 16.43 15.41 23.93 17.77 6 1 17.45 15.54 20.32 17.73 2 13.44 13.09 20.12 16.30 7 1 14.11 12.84 18.37 15.01 2 11.18 10.38 17.33 12.89 8 1 11.17 10.37 16.25 11.44 2 9.33 8.13 15.34 11.10 9 1 9.35 7.93 14.28 10.43 2 7.91 6.44 14.18 9.60 10 1 9.05 5.48 11.11 9.18 2 6.67 5.12 10.72 8.40 11 1 5.75 5.45 10.81 8.68 2 5.70 5.10 10.63 8.36 Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 270 Seismic input URE-ST-04 Duration [s] 9.96 PGA [m/s2] 0.247 PGV [m/s] 0.016 PGD [mm] 3.42 Arias intensity [m/s] 3.2824e-05 Cumulative Absolute Velocity [g∙s] 0.0231 Input Energy [kNm] 0.020 Specific Energy Density [m2/s] 1.3479e-04 Figure B.1.5. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input URE-ST-04. Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 271 Seismic input URE-ST-05 Duration [s] 9.96 PGA [m/s2] 0.595 PGV [m/s] 0.023 PGD [mm] 4.11 Arias intensity [m/s] 1.7846e-04 Cumulative Absolute Velocity [g∙s] 0.0497 Input Energy [kNm] 71.2578 Specific Energy Density [m2/s] 2.8389e-04 Figure B.1.6. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input URE-ST-05. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 272 Seismic input URE-ST-06 Duration [s] 9.96 PGA [m/s2] 0.613 PGV [m/s] 0.025 PGD [mm] 4.18 Arias intensity [m/s] 1.4397e-04 Cumulative Absolute Velocity [g∙s] 0.0456 Input Energy [kNm] 64.2956 Specific Energy Density [m2/s] 2.7435e-04 Figure B.1.7. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input URE-ST-06. Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 273 Seismic input URE-ST-07 Duration [s] 9.96 PGA [m/s2] 0.501 PGV [m/s] 0.023 PGD [mm] 4.00 Arias intensity [m/s] 1.4287e-04 Cumulative Absolute Velocity [g∙s] 0.0462 Input Energy [kNm] 0.063 Specific Energy Density [m2/s] 2.6801e-04 Figure B.1.8. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input URE-ST-07. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 274 Seismic input URE-ST-08 Duration [s] 9.96 PGA [m/s2] 0.554 PGV [m/s] 0.024 PGD [mm] 4.05 Arias intensity [m/s] 1.3912e-04 Cumulative Absolute Velocity [g∙s] 0.0455 Input Energy [kNm] 0.061 Specific Energy Density [m2/s] 2.5585e-04 Figure B.1.9. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input URE-ST-08. Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 275 Seismic input URE-ST-09 Duration [s] 19.96 PGA [m/s2] 0.164 PGV [m/s] 0.023 PGD [mm] 6.69 Arias intensity [m/s] 4.3261e-05 Cumulative Absolute Velocity [g∙s] 0.0475 Input Energy [kNm] 0.059 Specific Energy Density [m2/s] 8.1032e-04 Figure B.1.10. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input URE-ST-09. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 276 Seismic input URE-ST-10 Duration [s] 19.96 PGA [m/s2] 0.329 PGV [m/s] 0.029 PGD [mm] 8.27 Arias intensity [m/s] 1.0818e-04 Cumulative Absolute Velocity [g∙s] 0.0704 Input Energy [kNm] 0.116 Specific Energy Density [m2/s] 0.0011 Figure B.1.11. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input URE-ST-10. Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 277 Seismic input URE-ST-11 Duration [s] 19.96 PGA [m/s2] 0.306 PGV [m/s] 0.029 PGD [mm] 8.51 Arias intensity [m/s] 1.0119e-04 Cumulative Absolute Velocity [g∙s] 0.0685 Input Energy [kNm] 0.117 Specific Energy Density [m2/s] 0.0013 Figure B.1.12. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input URE-ST-11. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 278 Seismic input URE-ST-12 Duration [s] 19.96 PGA [m/s2] 0.327 PGV [m/s] 0.029 PGD [mm] 8.52 Arias intensity [m/s] 1.0512e-0 Cumulative Absolute Velocity [g∙s] 0.0705 Input Energy [kNm] 0.121 Specific Energy Density [m2/s] 0.0013 Figure B.1.13. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input URE-ST-12. Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 279 Seismic input URE-ST-13 Duration [s] 39.96 PGA [m/s2] 0.321 PGV [m/s] 0.052 PGD [mm] 19.05 Arias intensity [m/s] 3.2349e-04 Cumulative Absolute Velocity [g∙s] 0.1924 Input Energy [kNm] 0.471 Specific Energy Density [m2/s] 0.0064 Figure B.1.14. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input URE-ST-13. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 286 Seismic input URE-ST-20 Duration [s] 89.96 PGA [m/s2] 1.257 PGV [m/s] 0.130 PGD [mm] 88.08 Arias intensity [m/s] 0.0096 Cumulative Absolute Velocity [g∙s] 1.6669 Input Energy [kNm] 10.498 Specific Energy Density [m2/s] 0.1203 Figure B.1.21. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input URE-ST-20. Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 287 Seismic input URE-ST-21 Duration [s] 89.96 PGA [m/s2] 1.201 PGV [m/s] 0.132 PGD [mm] 87.94 Arias intensity [m/s] 0.0105 Cumulative Absolute Velocity [g∙s] 1.7754 Input Energy [kNm] 11.040 Specific Energy Density [m2/s] 0.1202 Figure B.1.22. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input URE-ST-21. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 288 Seismic input URE-ST-22 Duration [s] 89.96 PGA [m/s2] 1.109 PGV [m/s] 0.130 PGD [mm] 88.16 Arias intensity [m/s] 0.0098 Cumulative Absolute Velocity [g∙s] 1.7147 Input Energy [kNm] 10.681 Specific Energy Density [m2/s] 0.1203 Figure B.1.23. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input URE-ST-22. Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 289 Seismic input URE-ST-23 Duration [s] 89.96 PGA [m/s2] 1.132 PGV [m/s] 0.130 PGD [mm] 88.03 Arias intensity [m/s] 0.0093 Cumulative Absolute Velocity [g∙s] 1.6256 Input Energy [kNm] 10.365 Specific Energy Density [m2/s] 0.1202 Figure B.1.24. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input URE-ST-23. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 290 Seismic input URE-ST-24 Duration [s] 89.96 PGA [m/s2] 0.970 PGV [m/s] 0.090 PGD [mm] 14.06 Arias intensity [m/s] 0.0069 Cumulative Absolute Velocity [g∙s] 1.3929 Input Energy [kNm] 5.984 Specific Energy Density [m2/s] 0.0510 Figure B.1.25. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input URE-ST-24. Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 291 Seismic input URE-ST-25 Duration [s] 89.96 PGA [m/s2] 2.144 PGV [m/s] 0.126 PGD [mm] 18.53 Arias intensity [m/s] 0.0312 Cumulative Absolute Velocity [g∙s] 2.9463 Input Energy [kNm] 17.684 Specific Energy Density [m2/s] 0.1004 Figure B.1.26. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input URE-ST-25. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 292 Seismic input URE-ST-26 Duration [s] 89.96 PGA [m/s2] 2.393 PGV [m/s] 0.148 PGD [mm] 21.21 Arias intensity [m/s] 0.0375 Cumulative Absolute Velocity [g∙s] 3.2382 Input Energy [kNm] 22.161 Specific Energy Density [m2/s] 0.1305 Figure B.1.27. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input URE-ST-26. Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 293 Seismic input URE-ST-27 Duration [s] 89.96 PGA [m/s2] 4.115 PGV [m/s] 0.215 PGD [mm] 31.84 Arias intensity [m/s] 0.0867 Cumulative Absolute Velocity [g∙s] 4.8928 Input Energy [kNm] 50.088 Specific Energy Density [m2/s] 0.3047 Figure B.1.28. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input URE-ST-27. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 294 Seismic input URE-ST-28 Duration [s] 89.96 PGA [m/s2] 4.765 PGV [m/s] 0.265 PGD [mm] 40.91 Arias intensity [m/s] 0.1309 Cumulative Absolute Velocity [g∙s] 5.9838 Input Energy [kNm] 76.814 Specific Energy Density [m2/s] 0.4777 Figure B.1.29. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input URE-ST-28. Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 295 Seismic input URE-ST-29 Duration [s] 89.96 PGA [m/s2] 4.519 PGV [m/s] 0.290 PGD [mm] 42.60 Arias intensity [m/s] 0.1402 Cumulative Absolute Velocity [g∙s] 6.2296 Input Energy [kNm] 84.798 Specific Energy Density [m2/s] 0.5120 Figure B.1.30. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input URE-ST-29. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 302 𝑓1=14.19 Hz 𝑓2=22.37 Hz (a) (b) 𝑓3=23.83 Hz 𝑓4=25.80 Hz (c) (d) 𝑓5=31.80 Hz (e) (f) Figure B.2.1.4. Dynamic properties of the un-strengthened mockup obtained from the DI-URE-ST-04 test: a) Mode 1, b) Mode 2, c) Mode 3, d) Mode 4, e) Mode 5, and f) 𝑀𝐴𝐶 . Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 303 𝑓1=14.17 Hz 𝑓2=22.18 Hz (a) (b) 𝑓3=23.81 Hz 𝑓4=25.75 Hz (c) (d) 𝑓5=31.52 Hz (e) (f) Figure B.2.1.5. Dynamic properties of the un-strengthened mockup obtained from the DI-URE-ST-05 test: a) Mode 1, b) Mode 2, c) Mode 3, d) Mode 4, e) Mode 5, and f) 𝑀𝐴𝐶 . Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 304 𝑓1=13.92 Hz 𝑓2=22.08 Hz (a) (b) 𝑓3=23.80 Hz 𝑓4=25.65 Hz (c) (d) 𝑓5=31.19 Hz (e) (f) Figure B.2.1.6. Dynamic properties of the un-strengthened mockup obtained from the DI-URE-ST-06 test: a) Mode 1, b) Mode 2, c) Mode 3, d) Mode 4, e) Mode 5, and f) 𝑀𝐴𝐶 . Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 305 𝑓1=13.78 Hz 𝑓2=22.41 Hz (a) (b) 𝑓3=23.80 Hz 𝑓4=25.59 Hz (c) (d) 𝑓5=30.77 Hz (e) (f) Figure B.2.1.7. Dynamic properties of the un-strengthened mockup obtained from the DI-URE-ST-07 test: a) Mode 1, b) Mode 2, c) Mode 3, d) Mode 4, e) Mode 5, and f) 𝑀𝐴𝐶 . Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 306 𝑓1=13.60 Hz 𝑓2=22.05 Hz (a) (b) 𝑓3=23.75 Hz 𝑓4=25.43 Hz (c) (d) 𝑓5=30.19 Hz (e) (f) Figure B.2.1.8. Dynamic properties of the un-strengthened mockup obtained from the DI-URE-ST-08 test: a) Mode 1, b) Mode 2, c) Mode 3, d) Mode 4, e) Mode 5, and f) 𝑀𝐴𝐶 . Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 307 𝑓1=13.75 Hz 𝑓2=21.92 Hz (a) (b) 𝑓3=23.76 Hz 𝑓4=25.05 Hz (c) (d) 𝑓5=29.96 Hz (e) (f) Figure B.2.1.9. Dynamic properties of the un-strengthened mockup obtained from the DI-URE-ST-09 test: a) Mode 1, b) Mode 2, c) Mode 3, d) Mode 4, e) Mode 5, and f) 𝑀𝐴𝐶 . Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 308 B.2.2 Damage detection Table B.2.2. Damage indexes 𝑑 and 𝑑2 computed for each mode of the un-strengthened mock-up through the dynamic identification tests. Damage index DI-UREST-02 DI-UREST-03 DI-UREST-04 DI-UREST-05 DI-UREST-06 DI-UREST-07 DI-UREST-08 DI-UREST-09 𝑑𝑓1 [%] 0 1 1 2 3 4 6 5 𝑑𝑓1 2[%] 0 3 3 3 7 8 11 9 𝑑𝑓2[%] 0 0 0 1 1 0 1 2 𝑑𝑓2 2[%] 0 0 0 2 3 0 3 4 𝑑𝑓3[%] 0 0 0 0 0 0 0 0 𝑑𝑓3 2[%] 0 0 0 0 0 0 0 0 𝑑𝑓4[%] 0 0 0 0 1 1 1 3 𝑑𝑓4 2[%] 0 0 0 0 1 1 3 6 𝑑𝑓5[%] 0 1 0 1 2 3 5 6 𝑑𝑓5 2[%] 0 3 0 2 4 6 10 11 Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 309 B.3 Un-strengthened rammed earth shake table test: energy-based analysis Table B.3.1. Dissipated hysteretic energy, input hysteretic energy, and ratio between dissipated and input energy during the seismic test of the URE-ST mock-up. Seismic input 𝑬𝐢 [𝐤𝐍𝐦] 𝑰𝑬 [𝐤𝐍𝐦] 𝑷𝐈 [-] URE-ST-01 0.002 0.009 0.196 URE-ST-02 0.006 0.014 0.418 URE-ST-03 0.005 0.011 0.418 URE-ST-04 0.013 0.020 0.620 URE-ST-05 0.030 0.071 0.420 URE-ST-06 0.028 0.064 0.428 URE-ST-07 0.028 0.063 0.444 URE-ST-08 0.032 0.061 0.522 URE-ST-09 0.043 0.059 0.721 URE-ST-10 0.057 0.116 0.486 URE-ST-11 0.061 0.118 0.514 URE-ST-12 0.059 0.121 0.485 URE-ST-13 0.324 0.471 0.688 URE-ST-14 0.811 1.659 0.488 URE-ST-15 0.898 1.655 0.542 URE-ST-16 0.845 1.643 0.514 URE-ST-17 1.724 2.727 0.632 URE-ST-18 4.261 10.565 0.403 URE-ST-19 4.714 10.459 0.451 URE-ST-20 4.693 10.498 0.447 URE-ST-21 4.958 11.040 0.449 URE-ST-22 4.751 10.681 0.445 URE-ST-23 4.537 10.365 0.438 URE-ST-24 4.721 5.985 0.789 URE-ST-25 9.659 17.684 0.546 URE-ST-26 12.837 22.161 0.579 URE-ST-27 29.225 50.088 0.583 URE-ST-28 44.922 76.814 0.585 URE-ST-29 47.961 84.798 0.566 URE-ST-30 111.198 184.673 0.602 URE-ST-31 172.541 279.441 0.617 Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 310 B.4 TRM-strengthened rammed earth shake table tests: seismic inputs 𝑃𝐺𝐴=𝑚𝑎𝑥|𝑢󰇘g(𝑡)| 𝑃𝐺𝑉 =𝑚𝑎𝑥|𝑢󰇗g(𝑡)| 𝑃𝐺𝐷 =𝑚𝑎𝑥|𝑢g(𝑡)| (a) (b) (c) 𝐼𝐴=𝜋 2𝑔∫ (𝑢󰇘g(𝑡))2𝑑𝑡 𝑇d 0 𝐶𝐴𝑉=∫ |𝑢󰇘g(𝑡)|𝑑𝑡 𝑇d 0 𝐼𝐸 =𝑚∫ |𝑢󰇗g(𝑡)𝑢󰇘g(𝑡)|𝑑𝑡 𝑇d 0 (d) (e) (f) 𝑆𝐸𝐷=∫ |𝑢󰇗g(𝑡)|2𝑑𝑡 𝑇d 0 (g) Figure B.4.1. Ground motion parameters of the shake table tests on the NRE-ST mockup: a) 𝑃𝐺𝐴 , b) 𝑃𝐺𝑉 , c) 𝑃𝐺𝐷 , d) 𝐴𝐼 , e) 𝐶𝐴𝑉 , f) 𝐼𝐸 , and g) 𝑆𝐸𝐷 . Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 311 Seismic input NRE-ST-01 Duration [s] 9.96 PGA [m/s2] 0.428 PGV [m/s] 0.022 PGD [mm] 1.74 Arias intensity [m/s] 7.5408e-05 Cumulative Absolute Velocity [g∙s] 0.0277 Input Energy [kNm] 0.034 Specific Energy Density [m2/s] 1.2431e-04 Figure B.4.2. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input NRE-ST-01. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 318 Seismic input NRE-ST-08 Duration [s] 39.96 PGA [m/s2] 1.205 PGV [m/s] 0.095 PGD [mm] 30.18 Arias intensity [m/s] 0.4406 Cumulative Absolute Velocity [g∙s] 0.0455 Input Energy [kNm] 1.898 Specific Energy Density [m2/s] 0.0173 Figure B.4.9. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input NRE-ST-08. Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 319 Seismic input NRE-ST-09 Duration [s] 39.96 PGA [m/s2] 0.687 PGV [m/s] 0.059 PGD [mm] 18.96 Arias intensity [m/s] 7.1157e-04 Cumulative Absolute Velocity [g∙s] 0.2748 Input Energy [kNm] 0.748 Specific Energy Density [m2/s] 0.0069 Figure B.4.10. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input NRE-ST-09. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 320 Seismic input NRE-ST-10 Duration [s] 39.96 PGA [m/s2] 1.026 PGV [m/s] 0.081 PGD [mm] 32.90 Arias intensity [m/s] 0.0013 Cumulative Absolute Velocity [g∙s] 0.3714 Input Energy [kNm] 1.548 Specific Energy Density [m2/s] 0.0162 Figure B.4.11. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input NRE-ST-10. Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 321 Seismic input NRE-ST-11 Duration [s] 39.96 PGA [m/s2] 0.772 PGV [m/s] 0.075 PGD [mm] 29.36 Arias intensity [m/s] 8.4092e-04 Cumulative Absolute Velocity [g∙s] 0.3024 Input Energy [kNm] 1.139 Specific Energy Density [m2/s] 0.0132 Figure B.4.12. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input NRE-ST-11. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 322 Seismic input NRE-ST-12 Duration [s] 39.96 PGA [m/s2] 0.829 PGV [m/s] 0.083 PGD [mm] 34.93 Arias intensity [m/s] 0.0013 Cumulative Absolute Velocity [g∙s] 0.3763 Input Energy [kNm] 1.662 Specific Energy Density [m2/s] 0.0183 Figure B.4.13. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input NRE-ST-12. Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 323 Seismic input NRE-ST-13 Duration [s] 99.96 PGA [m/s2] 0.846 PGV [m/s] 0.083 PGD [mm] 44.60 Arias intensity [m/s] 0.0044 Cumulative Absolute Velocity [g∙s] 1.1089 Input Energy [kNm] 4.747 Specific Energy Density [m2/s] 0.0436 Figure B.4.14. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input NRE-ST-13. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 324 Seismic input NRE-ST-14 Duration [s] 99.96 PGA [m/s2] 0.944 PGV [m/s] 0.117 PGD [mm] 74.96 Arias intensity [m/s] 0.0061 Cumulative Absolute Velocity [g∙s] 1.3066 Input Energy [kNm] 7.908 Specific Energy Density [m2/s] 0.0933 Figure B.4.15. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input NRE-ST-14. Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 325 Seismic input NRE-ST-15 Duration [s] 99.96 PGA [m/s2] 1.096 PGV [m/s] 0.128 PGD [mm] 85.43 Arias intensity [m/s] 0.0091 Cumulative Absolute Velocity [g∙s] 1.6056 Input Energy [kNm] 10.842 Specific Energy Density [m2/s] 0.1194 Figure B.4.16. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input NRE-ST-15. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 326 Seismic input NRE-ST-16 Duration [s] 99.96 PGA [m/s2] 1.173 PGV [m/s] 0.136 PGD [mm] 88.23 Arias intensity [m/s] 0.0094 Cumulative Absolute Velocity [g∙s] 1.6324 Input Energy [kNm] 11.450 Specific Energy Density [m2/s] 0.1278 Figure B.4.17. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input NRE-ST-16. Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 327 Seismic input NRE-ST-17 Duration [s] 99.96 PGA [m/s2] 1.739 PGV [m/s] 0.127 PGD [mm] 14.04 Arias intensity [m/s] 0.0160 Cumulative Absolute Velocity [g∙s] 2.0696 Input Energy [kNm] 10.997 Specific Energy Density [m2/s] 0.0670 Figure B.4.18. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input NRE-ST-17. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 334 Seismic input NRE-ST-24 Duration [s] 99.96 PGA [m/s2] 4.272 PGV [m/s] 0.286 PGD [mm] 42.22 Arias intensity [m/s] 0.1324 Cumulative Absolute Velocity [g∙s] 6.0356 Input Energy [kNm] 87.167 Specific Energy Density [m2/s] 0.5063 Figure B.4.25. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input NRE-ST-24. Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 335 Seismic input NRE-ST-25 Duration [s] 99.96 PGA [m/s2] 7.116 PGV [m/s] 0.425 PGD [mm] 67.59 Arias intensity [m/s] 0.2799 Cumulative Absolute Velocity [g∙s] 8.6111 Input Energy [kNm] 182.740 Specific Energy Density [m2/s] 1.2240 Figure B.4.26. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input NRE-ST-25. Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 336 Seismic input NRE-ST-26 Duration [s] 99.96 PGA [m/s2] 9.112 PGV [m/s] 0.547 PGD [mm] 88.34 Arias intensity [m/s] 0.4571 Cumulative Absolute Velocity [g∙s] 11.0111 Input Energy [kNm] 302.340 Specific Energy Density [m2/s] 2.0482 Figure B.4.27. Time-history of acceleration, velocity and displacement, Fourier amplitude spectrum and spectrum of pseudo-acceleration, pseudo-velocity and displacement of seismic input NRE-ST-26. Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 337 B.5 TRM-strengthened rammed earth shake table tests: dynamic properties and damage identification B.5.1 Modal analysis Table B.5.1. Natural frequencies detected for each dynamic identification test of the un-strengthened mock-up URE-ST. Dynamic identification 𝒇𝟏 [𝐇𝐳] 𝒇𝟐 [𝐇𝐳] 𝒇𝟑 [𝐇𝐳] 𝒇𝟒 [𝐇𝐳] 𝒇𝟓 [𝐇𝐳] DI-NRE-ST-01 12.57 19.65 22.80 24.84 27.07 DI-NRE-ST-02 12.63 19.86 22.81 24.93 27.14 DI-NRE-ST-03 12.64 19.88 22.81 24.90 27.41 DI-NRE-ST-04 12.60 19.81 22.82 24.83 27.01 DI-NRE-ST-05 12.87 19.77 22.84 24.93 27.11 DI-NRE-ST-06 12.36 19.06 22.74 24.82 27.82 DI-NRE-ST-07 12.19 19.01 22.61 24.89 27.63 DI-NRE-ST-08 12.18 18.53 22.59 24.93 27.42 Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 338 𝑓1=12.57 Hz 𝑓2=19.65 Hz (a) (b) 𝑓3=22.80 Hz 𝑓4=24.84 Hz (c) (d) 𝑓5=27.07 Hz (e) (f) Figure B.5.1.1. Dynamic properties of the un-strengthened mockup obtained from the DI-NRE-ST-01 test: a) Mode 1, b) Mode 2, c) Mode 3, d) Mode 4, e) Mode 5, and f) 𝑀𝐴𝐶 . Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 339 𝑓1=12.63 Hz 𝑓2=19.65 Hz (a) (b) 𝑓3=22.81 Hz 𝑓4=24.93 Hz (c) (d) 𝑓5=27.14 Hz (e) (f) Figure B.5.1.2. Dynamic properties of the un-strengthened mockup obtained from the DI-NRE-ST-02 test: a) Mode 1, b) Mode 2, c) Mode 3, d) Mode 4, e) Mode 5, and f) 𝑀𝐴𝐶 . Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 340 𝑓1=12.64 Hz 𝑓2=19.88 Hz (a) (b) 𝑓3=22.81 Hz 𝑓4=24.90 Hz (c) (d) 𝑓5=27.41 Hz (e) (f) Figure B.5.1.3. Dynamic properties of the un-strengthened mockup obtained from the DI-NRE-ST-03 test: a) Mode 1, b) Mode 2, c) Mode 3, d) Mode 4, e) Mode 5, and f) 𝑀𝐴𝐶 . Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 341 𝑓1=12.60 Hz 𝑓2=19.81 Hz (a) (b) 𝑓3=22.82 Hz 𝑓4=24.83 Hz (c) (d) 𝑓5=27.01 Hz (e) (f) Figure B.5.1.4. Dynamic properties of the un-strengthened mockup obtained from the DI-NRE-ST-04 test: a) Mode 1, b) Mode 2, c) Mode 3, d) Mode 4, e) Mode 5, and f) 𝑀𝐴𝐶 . Seismic protection of rammed earth heritage based on a compatible externally applied strengthening technique 342 𝑓1=12.87 Hz 𝑓2=19.77 Hz (a) (b) 𝑓3=22.84 Hz 𝑓4=24.93 Hz (c) (d) 𝑓5=27.11 Hz (e) (f) Figure B.5.1.5. Dynamic properties of the un-strengthened mockup obtained from the DI-NRE-ST-05 test: a) Mode 1, b) Mode 2, c) Mode 3, d) Mode 4, e) Mode 5, and f) 𝑀𝐴𝐶 . Annex B.1.1. Un-strengthened rammed earth shake table test: seismic input 343 𝑓1=12.36 Hz 𝑓2=19.06 Hz (a) (b) 𝑓3=22.74 Hz 𝑓4=24.82 Hz (c) (d) 𝑓5=27.82 Hz (e) (f) Figure B.5.1.6. Dynamic properties of the un-strengthened mockup obtained from the DI-NRE-ST-06 test: a) Mode 1, b) Mode 2, c) Mode 3, d) Mode 4, e) Mode 5, and f) 𝑀𝐴𝐶 .