3D modelling of sheet pile corner in difficult ground conditions

3D MODELLING OF SHEET PILE CORNER IN DIFFICULT GROUND CONDITIONS JOSÉ BENEDITO GONÇALVES ARÊDE CALEJO Dissertação submetida para satisfação parcial dos requisitos do grau de MESTRE EM ENGENHARIA CIVIL — ESPECIALIZAÇÃO EM GEOTECNIA Orientador: Professor Doutor António Milton Topa Gomes Coorientador: Professor Doutor Ole Hededal JULHO DE 2015 MESTRADO INTEGRADO EM ENGENHARIA CIVIL 2014/2015 DEPARTAMENTO DE ENGENHARIA CIVIL Tel. +351-22-508 1901 Fax +351-22-508 1446  [email protected] Editado por FACULDADE DE ENGENHARIA DA UNIVERSIDADE DO PORTO Rua Dr. Roberto Frias 4200-465 PORTO Portugal Tel. +351-22-508 1400 Fax +351-22-508 1440  [email protected].pt  http://www.fe.up.pt Reproduções parciais deste documento serão autorizadas na condição que seja mencionado o Autor e feita referência a Mestrado Integrado em Engenharia Civil - 2014/2015 - Departamento de Engenharia Civil, Faculdade de Engenharia da Universidade do Porto, Porto, Portugal, 2015. As opiniões e informações incluídas neste documento representam unicamente o ponto de vista do respetivo Autor, não podendo o Editor aceitar qualquer responsabilidade legal ou outra em relação a erros ou omissões que possam existir. Este documento foi produzido a partir de versão eletrónica fornecida pelo respetivo Autor. 3D modelling of sheet pile corner in difficult ground conditions Aos meus pais, irmãs, amigos e avô Life is not the number of days you live, is the number of days you remember Pasha 3D modelling of sheet pile corner in difficult ground conditions 3D modelling of sheet pile corner in difficult ground conditions i ACKNOWLEDGMENTS This project is the climax of an unforgettable phase of my life that defined me as a civil engineer and as a citizen of the world. During the five years of my degree, and especially in the last 4 months, I had the support from many people, to whom I would like to express my gratitude:  To my supervisor in Portugal, Professor António Topa Gomes, for all the recommendations, guidance, motivation and feedback;  To my supervisor at COWI, Professor Ole Hededal, for the theoretical support, recommendations and especially for providing me this amazing opportunity of developing my thesis in such a recognized company;  To all the staff of COWI, who provided me with the necessary knowledge to conclude my project successfully and also for the advice given to thrive in the engineering world;  To António Fonseca, for the companionship and laugh in every day we spent together at COWI, and for all the critics, suggestions and discussion of the problems I was facing day by day;  To Diana Abrunhosa, for being an awesome adventure partner, keeping me inspired and motivated to accomplish my objectives as an engineer and as a person;  To my dearest friend João Nogueira, for being my University companion and, for sure, a friend for life;  To all the people that shared with me these 5 years of knowledge gain, personal development and increase of life profit;  To my parents and sisters, regardless of the continent they are, the support never fades. 3D modelling of sheet pile corner in difficult ground conditions ii 3D modelling of sheet pile corner in difficult ground conditions iii ABSTRACT Anchored sheet piles are used as perimeter bunds for a reclamation area. Example of such use is the Värtahamnen Port, in Stockholm. In this case, soil conditions are relatively poor consisting of soft clay/sediments overlaying a thin layer of till and, under that, very competent bedrock. The soft sediments are improved by means of either lime-cement columns or rigid inclusions consisting of grout piles installed by high-pressure jetting. A key element in the design is the corner layout where the sheet piles are mutually supporting each other by ties instead of anchor plates. The backfilling construction method, the complex ground conditions and the kinematics of the retaining system are difficult to analyse analytically or by simple design methods. Hence, a three dimensional finite element method model is developed using PLAXIS 3D to investigate the performance of the corner in terms of global deformations and stability, earth pressure distribution as well as forces in structural elements. The author opted to focus on three scenarios related to different conditions of soil reinforcement (by jet grouting or lime-cement piles) to study changes in wall behaviour and global stability. Results obtained are according to expected. The application of soil reinforcement reduces earth pressures acting on the wall. Moreover, soil reinforcement reduces maximum deformations of the retaining wall and maximum structural forces. Jet grouting reveals to be a conservative and necessary solution for the stability of the sheet pile wall. Also, a sensitivity analysis to evaluate the influence of surface roughness of the sheet pile wall is provided. KEYWORDS: multi-anchored sheet pile wall, soil improvement, lime-cement piles, jet grouting, numerical analysis, finite element method, mutually supported corner, backfilling. 3D modelling of sheet pile corner in difficult ground conditions iv 3D modelling of sheet pile corner in difficult ground conditions v RESUMO Cortinas de estaca-prancha são usadas como paredes de retenção para efeitos de reclamação de terreno. Um caso tipo é o porto Värtahamnen, em Estocolmo. Nesta situação, as condições do solo são fracas consistindo numa camada de argila mole normalmente consolidada (sedimentos) sobre uma fina camada competente de till (depósitos glaciares), sob a qual está presente uma camada bastante competente de maciço rochoso. A camada de sedimentos é reforçada tanto por colunas de cal-cimento ou blocos rígidos constituídos por estacas instaladas via jet grouting a alta pressão. Um elemento chave no dimensionamento é a forma do canto onde as cortinas de estaca-prancha se suportam mutuamente por tirantes em vez de ancoragens de placa. O método construtivo por enchimento, as complexas condições do solo e a cinemática do sistema de retenção tornam-se de difícil análise pela via analítica ou métodos simples de dimensionamento. Assim, na presente dissertação é desenvolvido um modelo tri-dimensional pelo método dos elementos finitos usando o PLAXIS 3D para investigar a performance do canto em termos de deformações e estabilidade global, distribuição de pressões de terras assim como os esforços nos elementos estruturais. O autor optou por se focar em três cenários relacionados com diferentes condições de melhoramento do solo (jet grouting ou colunas de cal-cimento) de modo a estudar alterações no comportamento da estrutura e estabilidade global. Os resultados obtidos são de acordo com esperado. A aplicação de técnicas de reforço do solo reduz as pressões de terra a atuar na cortina. Além disso, o solo reforçado reduz as deformações máximas da cortina e os máximos esforços na estrutura. A aplicação de jet grouting revelou ser uma solução conservadora e necessária para a estabilidade da cortina. Na presente tese é também apresentada uma análise de sensibilidade para avaliar a influência da rugosidade da cortina metálica. PALAVRAS-CHAVE: cortinas estaca-prancha pluri-ancoradas, melhoramento de solo, colunas de calcimento, Jet Grouting, análise número, método elementos finitos, canto com suporte mútuo, enchimento. 3D modelling of sheet pile corner in difficult ground conditions xii 6.2. SUGGESTIONS FOR FUTURE RESEARCH ......................................................................... 117 3D modelling of sheet pile corner in difficult ground conditions xiii TABLE OF FIGURES Figure 2.1 - Värtahamnen port: a) Construction of pile deck (Stockholm Royal Seaport) and b) render of final shape of the port (Aarsleff 2014) ............................................................................................. 3 Figure 2.2 - Geometry of the port and phases of construction (Aarsleff 2014) ..................................... 4 Figure 2.3 - Lifting of a gravity L-wall for positioning on-site ................................................................ 5 Figure 2.4 - Location of the corner in Värtahamnen Port (Aarsleff 2014) ............................................. 5 Figure 2.5 - Plan of the Värtahamnen port with location of the corner (Aarsleff 2014) .......................... 6 Figure 2.6 - 3D representation of the sheet pile corner: anchors, sheet pile wall (dark blue), gravity wall (dark grey), filling material (light blue) and soil reinforcement (grey) .................................................... 6 Figure 2.7 - Variation of PSR with distance from the corner and aspect of the site (Ou et al. 1996) ..... 7 Figure 2.8 - Relation of vertical earth pressure with depth, revealing silo effect ................................... 9 Figure 2.9 - Detailed plan of sheet pile wall, anchors and corner tie rods (COWI 2015) ....................... 9 Figure 2.10 - Example of double wall tie cofferdam (left) and cellular cofferdams (right) (C.J. Mahan) 10 Figure 2.11 - Scheme of the anchors in the corner ............................................................................10 Figure 2.12 - Expected failure mechanisms in the corner: tilting around tip (left) and translation (right) .........................................................................................................................................................11 Figure 2.13 - Typical soil profile from Stockholm coastal area ............................................................12 Figure 2.14 - Disposal of the applied ground reinforcement ...............................................................12 Figure 2.15 - Soil profile on-site with layers' thickness .......................................................................13 Figure 2.16 - Samples of the Sprängsten material used as backfill.....................................................15 Figure 2.17 - Drainage system installed before applying top layer of filling material ............................15 Figure 2.18 - U (left) and Z (right) steel sheet pile sections and correspondent interlocks ...................16 Figure 2.19 - Hydraulic system used for pile driving pressing method (ThyssenKrupp 2010) ..............17 Figure 2.20 - Representations of impact (left) and vibration (right) pile driving methods (ThyssenKrupp 2010) ................................................................................................................................................18 Figure 2.21 - Example of connections of the tie rods to the sheet pile wall: normal bolting with plate (left) and MACALLOY type rods (right) ..............................................................................................19 Figure 2.22 - Example of different anchoring techniques (ThyssenKrupp 2010) .................................20 Figure 2.23 - Representation of a deadman anchor (side cut) ............................................................20 Figure 2.24 - Admissible location of anchor blocks (ThyssenKrupp 2010) ..........................................21 Figure 2.25 - Admissible location of anchor blocks in cohesive soils (ThyssenKrupp 2010) ................21 Figure 2.26 - Representation of waling beam (left) and concrete capping beam (right) .......................22 Figure 2.27 - Execution of dry mixing lime, lime-cement or cement pile (Moseley & Kirsch 2004) .......23 3D modelling of sheet pile corner in difficult ground conditions xiv Figure 2.28 - Representation of the failure modes assumed in a block of piles (Moseley & Kirsch 2004) ......................................................................................................................................................... 23 Figure 2.29 - Example sheet pile wall with lime-cement piles used as soil reinforcement (Moseley & Kirsch 2004) ..................................................................................................................................... 24 Figure 2.30 - Steps of application of jet grouting (ArchiExpo) ............................................................. 25 Figure 2.31 - Three techniques of jet grouting: single, double (or twin) and triple. Top (Solentanche Bachy) and bottom (Moseley & Kirsch 2004) ..................................................................................... 26 Figure 3.1 - Terzaghi and Peck Diagrams (Matos Fernandes 1990) .................................................. 30 Figure 3.2 - Free earth support method (Vieira & Matos Fernandes 2000) ......................................... 31 Figure 3.3 - Fixed earth support method (Vieira & Matos Fernandes 2000)........................................ 31 Figure 3.4 - Representation of ETM procedure (Carrubba & Colonna 2000) ...................................... 32 Figure 3.5 - Bilinear stress-displacement relationship (Carrubba & Colonna 2000) ............................ 33 Figure 3.6 - Representation of wall deformations associated with active and passive limit states ....... 35 Figure 3.7 - Soil masses generating earth pressures on retaining wall ............................................... 36 Figure 3.8 - Sketch of the retaining wall system (left) and adopted representative structural model (right) ................................................................................................................................................ 39 Figure 3.9 - Lateral earth pressures on the wall produced be the three scenarios .............................. 40 Figure 3.10 - Bending moments (kN.m/m) on the wall for the three case scenarios: T&P, K0 and Ka (from left to right) .............................................................................................................................. 41 Figure 3.11 - Shear forces (kN/m) on the wall for the three case scenarios: T&P, K0 and Ka (from left to right) ................................................................................................................................................. 42 Figure 3.12 - Wall deformation (mm) for the three case scenarios: T&P, K0 and Ka (from left to right) . 43 Figure 4.1 - Plane Strain conditions ................................................................................................... 45 Figure 4.2 - 10-node tetrahedral element used in PLAXIS 3D for soil discretisation (adapted from PLAXIS 2013a) ................................................................................................................................. 47 Figure 4.3 - 16-node element used for interfaces (left) and 6-node triangles used for plate elements (right) (adapted from PLAXIS 2013a) ................................................................................................ 47 Figure 4.4 - Soil layers in three dimensional display using PLAXIS 3D............................................... 48 Figure 4.5 - Borehole used to input soil layers in PLAXIS 3D (left) and soil-structure profile (right) ..... 48 Figure 4.6 - Detailed drawing of wall 2, showing variation of till level. ................................................. 49 Figure 4.7 - Plan of sheet pile wall and anchors distribution: upper level at -0.4m (left) and lower level at -9m (right) ..................................................................................................................................... 50 Figure 4.8 - Structural elements modelled in PLAXIS 3D: Sheet pile wall (blue), Gravity wall (grey), Waling (pink) and anchors (black), with highlighting of anchor on wall 2. ........................................... 50 Figure 4.9 - Scenario with no reinforcement: left - top view at depth -14m and right - general cross section .............................................................................................................................................. 51 Figure 4.10 - Scenario with KC Piles: left - top view at depth -14m and right - general cross section .. 52 3D modelling of sheet pile corner in difficult ground conditions xv Figure 4.11 - 3D representation of KC scenario, showing the KC Piles (brown)..................................52 Figure 4.12 - Top view of the scenario with KC Piles with Jet Grouting reinforcement (KC&JG) at depth -14m and general cross section .........................................................................................................53 Figure 4.13 - 3D representation of KC&JG scenario, showing the KC Piles (brown), jet grouting (dark grey) and spoil (light grey) .................................................................................................................54 Figure 4.14 - Horizontal plan describing the lengths of the model's borders .......................................55 Figure 4.15 - Detail of the surface with fixed displacements in Xand Y-directions, simulating L gravity wall ...................................................................................................................................................55 Figure 4.16 - Diagram representative of perfectly elastic-plastic model (PLAXIS 2013b) ....................56 Figure 4.17 - Concept of dilation angle ..............................................................................................57 Figure 4.18 - Critical State line ..........................................................................................................58 Figure 4.19 - Horizontal cross section of idealized sheet pile .............................................................60 Figure 4.20 - Loading phases 3 to 8 for the no reinforcement case (NR) ............................................62 Figure 5.1 - Location of selected cross sections ................................................................................64 Figure 5.2 - Horizontal effective earth pressures extracted in three different locations: at the interface, at 0.05 m and at 0.5 m from the wall ..................................................................................................65 Figure 5.4 - Wall deformation normalized to wall height, for NR (s/H) .................................................66 Figure 5.5 - Transverse displacement of capping beam (m) ...............................................................67 Figure 5.6 - Deformation of sheet pile wall in a 3D environment .........................................................67 Figure 5.7 - Effective vertical (left) and horizontal (right) earth pressures at CSB, PSD and "at rest" section, for NR ..................................................................................................................................68 Figure 5.8 - Ratio of effective horizontal and vertical stresses at CSB and PSD .................................69 Figure 5.9 - Horizontal (Y-direction) earth pressures at -9 m ..............................................................70 Figure 5.10 - Vertical effective stresses at depth -10m, revealing corner effect ..................................70 Figure 5.11 - Effective Vertical Stresses at vertical sections L1 (25.5;19.5) and L2 (25.5;-5) ..............71 Figure 5.12 - Normalized wall deformation (s/H) at CSB along loading phases, in percentage of wall height................................................................................................................................................72 Figure 5.13 - Normalized wall deformation (s/H) at PSD along loading phases, in percentage of wall height................................................................................................................................................73 Figure 5.14 - Lateral displacement of wall in Y-direction at depths -0.4 m and -9 m............................74 Figure 5.15 - Scheme of corner opening (left) and pulling of wall 2 (right) ..........................................74 Figure 5.16 - Wall displacement in Y-direction (Horizontal displacement) ...........................................75 Figure 5.17 - Wall displacement in Z-direction (Vertical displacement) ...............................................75 Figure 5.18 - Displacement in Y-direction at CSC, showing outwards wall rotation .............................76 Figure 5.19 - Horizontal wall displacement at depth -0.4 m (left) and -9 m (right) ...............................76 3D modelling of sheet pile corner in difficult ground conditions xvi Figure 5.20 - Wall deformation at CSC, along loading phases ........................................................... 77 Figure 5.21 - Axial forces (kN) in anchors and ties at upper (0.4 m) and lower (-9 m) levels ............... 78 Figure 5.22 - Axial force in waling at -9 m (kN) .................................................................................. 79 Figure 5.23 - Axial force in capping beam (kN) .................................................................................. 79 Figure 5.24 - Bending moments in waling beam at -9m (kN.m) .......................................................... 80 Figure 5.25 - Bending moments in capping beam (kN.m) .................................................................. 80 Figure 5.26 - Bending moment diagram at PSD, CSB and CSC (kN.m) ............................................. 81 Figure 5.27 - Vertical axial force in sheet pile wall (kN/m) .................................................................. 82 Figure 5.28 - Vertical axial force in sheet pile wall at CSB (kN) .......................................................... 82 Figure 5.29 - Detail of the soil layer 1m thick, between sheet pile and monolith ................................. 83 Figure 5.30 - Effective horizontal (left) and vertical (right) stresses at CSB and PSD.......................... 84 Figure 5.31 - Coefficient of Reduction of lateral earth pressures ........................................................ 85 Figure 5.32 - Effective vertical stresses in cross section at x=19 ........................................................ 86 Figure 5.33 - Effective vertical stresses at depth -11m, in a cross section at x=19 ............................. 86 Figure 5.34 - Principal directions in a cross section at x=19 ............................................................... 87 Figure 5.35 - Normalized wall deformation (s/H) at CSB along loading phase for KC, in percentage of wall height ........................................................................................................................................ 88 Figure 5.36 - Lateral displacement of wall in Y-direction at depth -0.4 m and -9 m, for KC ................. 88 Figure 5.37 - Wall displacement in Y-direction (Horizontal displacement) for KC ................................ 89 Figure 5.38 - Wall displacement in Z-direction (Vertical displacement) for KC .................................... 89 Figure 5.39 - Horizontal wall displacement at depth -0.4 m (left) and -9 m (right) for KC..................... 90 Figure 5.40 - Normalized wall deformation (s/H) at CSC along loading phases for KC, in percentage of wall height ........................................................................................................................................ 90 Figure 5.41 - Axial forces in anchors and ties at upper (-0.4 m) and lower (-9 m) levels, for KC (kN) .. 91 Figure 5.42 - Axial force in waling at -9m, for KC (kN) ....................................................................... 92 Figure 5.43 - Axial force in capping beam, for KC (kN) ...................................................................... 92 Figure 5.44 - Bending moments in waling beam at -9 m (kN.m) ......................................................... 93 Figure 5.45 - Bending moments in capping beam (kN.m) .................................................................. 93 Figure 5.46 - Bending moment diagram at CSB and CSC, for KC (kN.m) .......................................... 94 Figure 5.47 - Effective horizontal stresses in front and back of the sheet pile wall (kPa) ..................... 95 Figure 5.48 - Vertical axial force in sheet pile wall at CSB, for KC (kN) .............................................. 95 Figure 5.49 - Effective horizontal (left) and vertical (right) stresses at CSB and PSD, for KC&JG ....... 96 Figure 5.50 - Coefficient of lateral earth pressures ............................................................................ 97 Figure 5.51 - Effective vertical stresses in cross section at x=19 m .................................................... 98 3D modelling of sheet pile corner in difficult ground conditions xvii Figure 5.52 - Principal directions in a cross section at x=19 m ...........................................................98 Figure 5.53 - Displacement in Y-direction of monolith composed by Jet grouting and KC Piles ..........99 Figure 5.54 - Normalized wall deformation (s/H) at CSB along loading phases for KC&JG, in percentage of wall height ................................................................................................................100 Figure 5.55 - Lateral displacement of wall in Y-direction at depth -0.4 m and -9 m ...........................100 Figure 5.56 - Wall displacement in Y-direction (Horizontal displacement), for KC&JG ......................101 Figure 5.57 - Wall displacement in Z-direction (Vertical displacement), for KC&JG ..........................101 Figure 5.58 - Horizontal wall displacement at depth -0.4 m (left) and -9 m (right), for KC&JG ...........102 Figure 5.59 - Normalized wall deformation (s/H) at CSC along loading phases for KC&JG, in percentage of wall height ................................................................................................................102 Figure 5.60 - Axial forces in anchors and ties at upper (-0.4 m) and lower (-9 m) levels, for KC&JG (kN) ................................................................................................................................................103 Figure 5.61 - Axial force in waling at -9m, for KC&JG (kN) ...............................................................104 Figure 5.62 - Axial force in capping beam, for KC&JG (kN) ..............................................................104 Figure 5.63 - Bending moments in waling beam at -9 m (kN.m) .......................................................105 Figure 5.64 - Bending moments in capping beam (kN.m) .................................................................105 Figure 5.65 - Bending moment diagram at CSB and CSC, for KC&JG (kN.m) ..................................106 Figure 5.66 - Vertical axial force in sheet pile wall at CSB, for KC&JG (kN) ......................................107 Figure 5.67 - Coefficient of reduction of lateral earth pressures at CSB, for KC and KC&JG.............108 Figure 5.68 - Normalized wall deformation (s/H) at CSB in last loading phase for KC and KC&JG, in percentage of wall height ................................................................................................................109 Figure 5.69 - Lateral displacement of wall in Y-direction at depths -0.4 m and -9 m for KC and KC&JG .......................................................................................................................................................110 Figure 5.70 - Axial forces in anchors and ties at upper (-0.4 m) and lower (-9 m) levels, for KC and KC&JG ...........................................................................................................................................110 Figure 5.71 - Bending moment diagram at CSB for KC and KC&JG (kN.m) .....................................111 Figure 5.72 - Normalized wall deformation (s/H) at CSB in last loading phase for surface roughness 0.3, 0.5 and 2/3, in percentage of wall height ...................................................................................113 Figure 5.73 - Bending moment at CSB for surface roughness 0.3, 0.5 and 2/3 (kN.m) .....................113 Figure 5.74 - Vertical axial force in sheet pile wall at CSB for surface roughness 0.3, 0.5 and 2/3 (kN) .......................................................................................................................................................114 3D modelling of sheet pile corner in difficult ground conditions xviii 3D modelling of sheet pile corner in difficult ground conditions xix TABLE OF TABLES Table 3.1 - Soil parameters used for lateral earth pressure calculation ..............................................37 Table 3.2 - Properties of structural elements......................................................................................38 Table 3.3 - Reaction forces for the three case scenarios....................................................................42 Table 4.1 - Input soil parameters used initially in the model ...............................................................57 Table 4.2 - Input undrained soil parameters .......................................................................................57 Table 4.3 - Description of structural elements used in situ .................................................................59 Table 4.4 - Input structural element parameters used in the model ....................................................59 Table 4.5 - Adapted input parameters for sheet pile ...........................................................................59 Table 4.6 - Description of phases of construction for each study scenario ..........................................61 Table 5.1 - Three cases (NR, KC and KC&JG) analysed with PLAXIS 3D..........................................63 Table 5.2 - Comparative cases KC and KC&JG ...............................................................................107 Table 5.3 - Surface roughness chosen for the sensitivity analysis ....................................................112 3D modelling of sheet pile corner in difficult ground conditions xx 3D modelling of sheet pile corner in difficult ground conditions xxi SYMBOLS, ACRONYMS AND ABBREVIATONS E - elastic modulus [KPa] KC Piles - lime-cement piles PSR - plane strain ratio T&P - Terzaghi and Peck ETM - equivalent tie support method Rd - passive resistant force (kN) Ri - equivalent force in step i (kN) xi - distance of equivalent force in step i (m) Ti - force in anchor i (kN) yi - distance from the top of the wall to the anchor i (m) SRM - sub-grade reaction method J - moment of inertia Kh - horizontal sub-grade reaction modulus w - horizontal wall displacement (m) z - depth (m) k - spring stiffness in SRM; anchor axial stiffness (kN/m) a - non-dimensional coefficient L - length (m) A - area (m2) Fd - driving force (kN) mu - mass weight (kg) ru - distance to point of rotation (m) Ω - frequency of excitation D - diameter (m) σz - vertical earth pressure (kPa) K, K0 - at-rest earth pressure coefficient Ka - active earth pressure coefficient Kp - passive earth pressure coefficient φ' - friction angle (º) δ - wall roughness β - sloping of ground surface (º) 3D modelling of sheet pile corner in difficult ground conditions 6 Figure 2.5 - Plan of the Värtahamnen port with location of the corner (Aarsleff 2014) The corner is constituted by one main wall and a perpendicular smaller wall. The main wall develops parallel to the adjacent pile deck and is supported by two levels of anchors. On the other hand, the smaller wall is connected with tie rods to the main wall, supported in the top corner by an anchor and laterally prevented by neighbouring gravity L wall. Figure 2.6 shows a three dimensional model of the structure for better understanding the previous description. It is clear where the filling material (light blue) is deployed, the location of anchors, the layout of sheet pile wall (dark blue) and the gravity wall (grey). Figure 2.6 - 3D representation of the sheet pile corner: anchors, sheet pile wall (dark blue), gravity wall (dark grey), filling material (light blue) and soil reinforcement (grey) Anchors (lower level hidden by filling) Anchors Soil Reinforcement Backfilling Material Soft Clay Glacial Till Sheet pile wall Gravity Wall Corner Ties (lower level hidden by soil reinforcement) 3D modelling of sheet pile corner in difficult ground conditions 7 The description of the entire system and adopted structural model are explained in detail in the following chapters, depending on the type of analysis (analytical or numerical). Following, is presented a description of the particular aspects that make this special case an important subject of study, as well as some considerations that should be necessary to take into account when analysing and studying the present situation. 2.1.3.1. Corner Effects In excavations where corners exist it has been verified the occurrence of a phenomenon characterized by the restriction of wall deflection, which is here named as corner stiffening effect. In some situations, this corner effect has such influence on the behaviour of the retaining wall that can be taken into account to, for example, reduce costs in ground improvement (Ou et al. 2008). The corner stiffening effect is normally observed in the displacement at the centre of retaining walls far from the corners, where the movement is generally higher than the values observed in areas near the corner. Furthermore, calculated values using plane strain analysis result in much higher deformations than the observed in construction sites at the central section of the retaining wall (Lee et al. 1998). This fact, among others, lead to increasing research by many authors in order to obtain a relationship between the wall displacement and the plain strain analysis calculated displacement. One of the parameters used to develop such studies is the plain strain ratio (PSR), which relates the maximum displacement of a wall in a certain section with the maximum displacement of the same cross section calculated using plain strain analysis. The PSR varies between zero and the unity, when the section in study is in a plain strain condition. Ou et al. (1996) developed a relationship between the PSR and the shape of excavation area, as well as with distance to corners for specific cases, described in Figure 2.7. Figure 2.7 - Variation of PSR with distance from the corner and aspect of the site (Ou et al. 1996) As the referred stiffening effect is very sensible to different parameters, such as stiffness of strutting system, depth of excavation, location of rigid layer and even by the horizontal geometry of the 3D modelling of sheet pile corner in difficult ground conditions 8 excavation, it is not clearly evaluated using only two dimensional plain strain analysis. In fact, it has been verified by many authors that in excavation pits with corners the displacements in centre of excavation walls have higher values when calculated by plane strain finite element analysis than in three dimensional finite element analysis (Ou et al. 2008), (Finno et al. 2007). The case study in the present thesis, a sheet pile corner under backfilling conditions, is a typical situation that had not been thoroughly studied before and a small amount of information is available on the literature. Therefore, the previously described corner effect might not be the same for excavation and backfill type of loadings on retaining walls, which adds up to the difficulties in predicting the behaviour of the structure. Another possible consequence due to the existence of corners in the sheet pile system may be a similar effect to the known silo effect. This effect was described by Janssen in 1895 as a reduction of the earth pressure in the bottom of silos. Basically, in the top of the silos the vertical earth pressure develops similarly to the typical triangular distribution from Rankine's formulation, but tends to an asymptotic limit as it becomes deeper. Using the shear plane method, it is possible to analytically verify this fact, by simply calculating the static equilibrium of an infinitesimal horizontal layer, taking into account the weight of the soil mass and upwards friction from walls surface resultant of horizontal earth pressure (Widisinghe & Sivakugan 2012). According to the later confirmed Jáky's assumption (Pipatpongsa & Heng 2010), it is plausible to admit at rest pressure conditions and, therefore, K0 as the coefficient of earth pressure at rest using the horizontal and vertical stresses at centre of the section. By solving the static equilibrium, one obtains a function of vertical stress with the depth in equation (2.1), where D is the silo diameter, K the coefficient of earth pressure at rest,  the soil weight and  the surface roughness.            D zK exp K D z.tan.4 1 tan.4     ( 2.1 ) Plotting the equation (2.1) with the depth z, obtains the diagram in Figure 2.8. The parameters used were 2 m as the diameter D, unit weight γ of 21 kN/m3. The surface roughness angle δ corresponds to 2/3 of the friction angle, which was 40º. Earth pressure coefficient K was calculated using Jáky's formula and is dependent on the friction angle. The resultant graph clearly shows the asymptotic tendency of vertical stress as the depth increases. It is interesting to also note that the initial inclination is close to the unit weight of the soil, which indicates that close to the surface the arching effect and consequent silo effect is practically none. The similarity of the silo shape to the corner shape makes it possible to assume that an analogous effect may occur. Taking this fact into account, it is possible to expect some influence of the corner in the behaviour of the fill material, resulting in possible reduced earth pressures and increased vertical stresses in the sheet pile wall, among other consequences of this effect. 3D modelling of sheet pile corner in difficult ground conditions 9 Figure 2.8 - Relation of vertical earth pressure with depth, revealing silo effect 2.1.3.2. Corner Tie Rods Figure 2.9 shows a plan of the sheet pile wall and placement of anchors rods. On the right side, close to the corner, the walls are mutually supported by a group of 10 tie rods. These structural elements were used instead of anchors due to the difficulties that would be found in placing the anchor blocks of the smaller wall. Figure 2.9 - Detailed plan of sheet pile wall, anchors and corner tie rods (COWI 2015) Corner Tie Rods Anchors Anchored Wall Mutually supported corner σz ≈ γ*z 3D modelling of sheet pile corner in difficult ground conditions 10 In the back side of the wall, where the anchor blocks are located, the fill material will be placed. When the backfill material pushes the wall system outwards it is expected that in the mutually supported corner the group of tie rods work in tension as a response to the tendency of corner opening, resultant from the pushing of both walls. It is an intuitive prediction, but sill the behaviour and distribution of stresses in these structures under such conditions is not totally known and predictable. In fact, this situation has some similarities with double wall tied cofferdams, which are commonly used for waterfront structures and excavation enclosures (Figure 2.10). These structures consist in two parallel steel sheet pile walls connected by ties, creating a space in between that is filled with granular material, such as sand, gravel or even rock (Gui & Han 2009). Therefore, it is possible to admit that in both cases the wall, and consequently the tie rods are under the same backfill kind of loading. Figure 2.10 - Example of double wall tie cofferdam (left) and cellular cofferdams (right) (C.J. Mahan) However, in cofferdams the design is simply done by admitting a plane strain deformation analysis and calculation. In the assumed case of study this may not be correct and possibly is too conservative. Actually, the tie rods stiffness varies along the wall, due to different lengths, as represented in Figure 2.11. As the ties are connected to both walls, it appears to be difficult to calculate the correct stiffness to use in plane strain calculations. In reality, the most common situation where a similar corner tie rod disposition is used is on cellular cofferdams, normally utilized to retain water and soil out of the excavation pit. Though, these are subjected to external earth pressure, and not to internal backfill pressure. Figure 2.11 - Scheme of the anchors in the corner 3D modelling of sheet pile corner in difficult ground conditions 11 2.1.3.3. Failure Mechanisms As there is not enough knowledge on the behaviour of this specific structure, two main failure mechanisms were thought a priori when approaching any design of this detail. Translation of wall system and tilt around the longer wall are assumed to occur in the retaining system in the corner, as represented in Figure 2.12, and both are probable to occur simultaneously. The translation of the corner is expected to occur in the direction perpendicular to the main long wall, named here as wall 1, and may be accompanied by a circular failure of the soil mass in front of the wall. Therefore, the stability is assumed to be assured by the passive resistance of the soil in front of wall 1 and by the anchor system. The rotation of the structure occurs along the base of wall 1, pushing this wall outwards and the smaller wall, referred as wall 2, upwards. To assure the stability of the corner against rotation, it is thought to make use of the friction with the soil in the back of the wall 2, an anchor in the top of the same wall and passive resistance of soil in front of wall 1, Figure 2.12 - Expected failure mechanisms in the corner: tilting around tip (left) and translation (right) 2.1.3.4. Soil Reinforcement The ground in the construction area is mainly composed by a thick layer of soft sediment clay on top of glacial till and bedrock. This is the typical soil profile of the marine soil found in Scandinavia, detailed in Figure 2.13. The layer of till and bedrock prove normally to be competent structures capable of bearing high loads. However, the same cannot be said to the soft marine clay. In fact, the clay material in the region is resultant from the deposition of sediments that have been carried by the network of rivers that shore Stockholm. As the river flow keeps raking the seabed along the time, the clay does not suffer much consolidation. Therefore, it shows low strength parameters that rise up many concerns when building in such conditions. 3D modelling of sheet pile corner in difficult ground conditions 12 Figure 2.13 - Typical soil profile from Stockholm coastal area When such soil conditions are present on site and it is necessary to achieve the required level of strength, techniques of soil reinforcement ought to be used. Therefore, lime-cement piles (KC Piles) were applied to the clay seabed using a deep-mixing method all along the back of the sheet pile wall and jet grouting columns done in the critical areas next to the corner, as idealized in Figure 2.14. It is possible that this improved ground would behave similarly to a monolith, especially in the corner, where a concrete block is likely to be created. This way, the reinforced soil would transmit earth pressures directly to bearing stratum, in this case the glacial till. However, the reduction in earth pressure is not certain, as the behaviour of the KC Piles and jet grouting is not surely known. It should be examined if there is any shear deformation that may induce earth pressures into the sheet pile wall and what is the failure mode of these systems. Figure 2.14 - Disposal of the applied ground reinforcement 3D modelling of sheet pile corner in difficult ground conditions 13 2.2. GROUND CONDITIONS The ground on site assumed in the analysis of the current work is a typical Scandinavian marine soil structure, composed of natural sediments, over a thin layer of natural glacial till, below which lies a very competent bedrock, as outlined in Figure 2.13. At this point, only introductory and geological considerations are done regarding the soil. Though, for each type of analysis in the following chapters the assumed ground profiles and geotechnical properties are provided in detail. 2.2.1. CLAYEY SEABED The first particular aspect of the ground in situ is the seabed composed by soft clay. As detailed in Figure 2.15, it is a layer of clayey soil varying between 5 and 9 m of thickness, resultant from the deposition of river sediments in the coastal banks. It is a very fine and low permeable material, normally constituted by particles with less than 0.002 mm of diameter and with a plastic behaviour at the appropriate water content. Clay can be classified by the Atterberg limits which relates its behaviour with the water content and also by the plasticity index, liquidity index and activity level. Normally consolidated clay is generally a problematic soil when it comes to design of geotechnical structures. Due to low cohesion, typical undrained behaviour and, in some situations, thixotropy, it is not considerable to completely assure stability of structures such as foundations and sheet pile walls. In the region where the case study is placed, the appearing clay has relatively low values of undrained shear strength, down to 3 kPa. Figure 2.15 - Soil profile on-site with layers' thickness 2.2.2. GLACIAL TILL The glacial till is a mix of a wide variety of granular particles, with varying sizes and shapes, from clay to boulders. It was formed by the movements of existing glacial ice in Scandinavia, which transported, eroded and deposited the rock fragments during advance and retreat of the ice mass (Strahler & Strahler 1973). 3D modelling of sheet pile corner in difficult ground conditions 14 The granular composition goes from large boulders to fine clay. The smaller elements are formed due to erosion or abrasion between the elements of larger dimension and the bedrock underlying the glacier. Also, as it was deposited due to the melting of ice that contained the debris, it shows little stratification, thus has a less uniform arrangement of particles. In general, glacial till is a competent and resistant material. In this specific case, the 2 to 5 m layer of till (Figure 2.15) shows a high value of friction angle and therefore has an adequate bearing capacity. 2.3. BACKFILL CONDITIONS 2.3.1. CONSIDERATIONS IN BACKFILLING One of the peculiar aspects of the situation that is being investigated is the construction method and its design considerations. As it was stated before, backfilling and excavation are generally two possible construction methods to use with retaining walls. Although in the end of the construction stage the shape is the same, i.e. there is a mass of soil being retained, the loading conditions in the wall and in the soil are different. Therefore, the expected behaviour is dissimilar (Bilgin 2010). So, in order to calculate the earth pressures for the design of tied sheet pile walls under backfilling conditions some considerations that are taken into account in excavations cannot be assumed. For example, the Terzaghi-Peck diagrams, which are often used to design multi-tied excavations, were developed from results of many observations of excavations in constructions sites. In reality, some authors that performed the few existing studies regarding backfill conditions concluded that the backfilling method has considerably higher wall deformations compared with excavation. Also, the wall tip deformations are even more affected by the construction method. Moreover, bending moments are significantly higher in backfilling than in excavations (Bilgin 2010). These conclusions lead to uncertainty about the design methods that should be applied to multi-tied sheet pile walls under backfilling conditions. Regarding the procedures of construction, backfilling is done by layers that in the current situation, as the fill is submerged, will not be well compacted. In marine works, it is normally a dredge that spreads the material in layers. Though, the top layers, which will be used for infrastructure, are normally compacted and its application more controlled. 2.3.2. BACKFILL MATERIAL The fill material is described as a frictional material, with high values of friction angle. It is composed of gravel and large sharp boulders (see Figure 2.16), retrieved normally from other ground works, resultant from blasting and excavation. The large elements sizes give the soil high levels of permeability, providing it with a drained behaviour. The main function of the so called Sprängsten (translated to blasted) is to provide the base for the construction of infrastructures necessary for the port. While the lower layers serve solely as capable filling, the top layers will cover the underground service systems of the building, such as the drainage systems (Figure 2.17) and will be the contact layer with the structures above. Therefore, the material applied above water level has to be well compacted and its performance controlled. 3D modelling of sheet pile corner in difficult ground conditions 15 Figure 2.16 - Samples of the Sprängsten material used as backfill The interaction of the backfill material with the sheet pile wall is of main interest when analysing the behaviour of the structure. Actually, such interface characteristic should be studied to understand the effect of interface resistance (surface roughness) in lateral pressures on the wall and any disturbances in corner effects. Figure 2.17 - Drainage system installed before applying top layer of filling material 2.4. ELEMENTS OF ANCHORED SHEET PILE WALL 2.4.1. SHEET PILE WALL In order to retain the soil that will become the foundation ground for infrastructures of the port, sheet pile walls were used as the retaining system. These types of retaining structures, commonly known as LARSSEN sheet piles, are applied in different situations that include excavations, waterfront structures, bridge abutments, cuttings, landfill, 3D modelling of sheet pile corner in difficult ground conditions 22 2.4.4. WALING AND CAPPING BEAM The waling and capping beam are two elements of the sheet pile wall responsible for redistributing the reaction forces between the sheet pile wall and the anchors. Also, both provide higher stiffness to the wall, as well as connection between piles to prevent vertical shear and consequent relative vertical movement. However, typically the waling beam is made of steel and located in intermediate heights of the sheet pile wall, whereas the capping beam is built on top of the wall, working as a cap (Chu 2010). Figure 2.26 - Representation of waling beam (left) and concrete capping beam (right) When designing these structures, the structural model of the beams should be considered simple supported with point loads applied by the anchor loads. Still, beams can alternatively be considered continuous and thus with fixed supports. Yet, this procedure is less conservative than the first option. Also, during the design, the possible loss of a tie rod has to be checked and a waling length of two times the single length should be considered. The capping beam should in addition be designed to resist shear stresses due to relative vertical wall movement resultant of differential settlements or lateral bending. Besides, in the case of quays where the capping beam is the mooring zone, the stresses caused by the contact with mooring ships should be taken into account and additional safety measures should be considered. 2.5. SOIL IMPROVEMENT 2.5.1. KC PILES Lime-cement piles, or in Swedish, Kalkcementpelare (KC Piles), are result of a soil stabilization technique where quicklime or cement are mixed in situ with soft soil, which can be constituted by soft clay or silt as well as organic soils. In the application of this method, a mixing tool ("egg beater") rotates as it goes deeper in the ground, remoulding the soil. When the required depth is reached, the required mix of lime, lime-cement or cement is supplied and mixed with the stabilizing soil, as the mixing tool rotates and returns to the surface (see Figure 2.27). The use of lime-cement columns has been increasing since their development in the 1970's (Broms & Boman 1975). The method has been used in situations where soft marine deposits are existent, such as in ports and harbour areas, with the main purposes of increasing load bearing and reducing ground settlements. Application of such techniques has also extended to embankments, roadways and foundations in soft ground. 3D modelling of sheet pile corner in difficult ground conditions 23 Figure 2.27 - Execution of dry mixing lime, lime-cement or cement pile (Moseley & Kirsch 2004) Most commonly used at the present time in Japan and in Scandinavian countries, such as Sweden and Finland, KC Piles have turned out to be a competitive solution for soil improvement and stabilization. It actually became an alternative for ground improvement that, although may appear more costly due to use of finely ground quicklime, has a lower total cost as less lime than cement is required (Moseley & Kirsch 2004). The main idea of soil improvement when using blocks of KC Piles is increasing bearing resistance and shear strength. This is mainly achieved by the chemical reactions between lime, cement and soil particles. What can be observed is that the quicklime reacts with fine particles of clay, occurring flocculation, whereas the cement reacts and agglomerates granular particles. So, lime-cement mixes are recommended to use in organic soils when the desired shear strength cannot be obtained with other mixes. Figure 2.28 - Representation of the failure modes assumed in a block of piles (Moseley & Kirsch 2004) 3D modelling of sheet pile corner in difficult ground conditions 24 By increasing the resistance and shear strength, the stabilized soil, which works as a block, will have failure modes different from the previous not stabilized soil. Such failure modes are represented in Figure 2.28. The design of these structures have to take into account the assumed failure modes, which depends on the penetration depth into a stiff layer below the wall and in the bearing capacity of the columns themselves. In the situations where KC Piles are applied in the stability of deep excavations with sheet pile walls (Figure 2.29), such as the case of the Stockholm Port, these will have two functions, depending on where the columns are placed. If a block of piles is located behind the sheet pile wall, then they will reduce the active earth pressure, assuming they transfer the load to the bottom of the block without spreading. However, if located in front of the sheet pile wall, the columns will increase the passive earth pressure, reducing the risk of toe failure. KC Piles are characteristic for its ductility and high permeability, compared to unstabilized soil. Actually, lime-cement piles have been reported to have failure strain values around 2% for ultimate strength of 130 kPa, revealing to be less brittle than cement piles (Moseley & Kirsch 2004). Also, their undrained shear strength can rise up to 200 kPa and to have a modulus of deformability E50 of 200Cu. Figure 2.29 - Example sheet pile wall with lime-cement piles used as soil reinforcement (Moseley & Kirsch 2004) 3D modelling of sheet pile corner in difficult ground conditions 25 Single columns located below an embankment might suffer lateral displacement caused by high lateral earth pressure due to the fill. Such situation may be possible to occur in the present case study. However, these displacements are usually small and large values may only be expected when the stability of the embankment is low and the global factor of safety is lower than 1.5 (Moseley & Kirsch 2004). 2.5.2. JET GROUTING PILES Among the available solutions in the market, jet grouting is one of the most versatile forms of ground improvement. Although it is a technology with a high technical demand, with this technique it is possible to increase ground strength, prevent groundwater flow and provide structural stiffness with one single application. Jet grouting technique started being developed in the 1950s mainly in Japan, where it was first used to improve effectiveness of water tightness. In this situation, the untreated soil was eroded and then ejected to the surface, being afterwards replaced by cement-based slurry to provide imperviousness. Later, jet grouting was used to create thin cut-off walls as well as to seal gaps between sheet piles. In the 1970s, rotating jet grouting emerged in Japan to satisfy new demands and was later introduced in Europe, becoming worldwide popular since then. The principle idea of this technology is to physically erode the ground using a high-pressure water or grout, in order to improve the surrounding soil. Normally, the drill is first introduced to the required depth and only afterwards the pressured jet (water or grout) is applied while withdrawing the equipment, creating the desired jet grout column (see Figure 2.30). Figure 2.30 - Steps of application of jet grouting (ArchiExpo) 3D modelling of sheet pile corner in difficult ground conditions 26 After the globalization of the jet grouting, three main variants emerged, as shown in Figure 2.31. The single system is a simple form of jet grouting, with a single jet grout eroding and mixing the soil. It is a not so much controlled process as below ground water level (where often jet grouting occurs) the eroding distance can be reduced due to the absence of surrounding air, increasing the necessary energy to cut the desired diameter. The double system is similar to the single system with the addition of compressed air that shrouds the grout jet. This way, the eroding capacity is increased especially below the water table, due to the creation of an atmosphere around the grout. Still, this option is not so controlled and can produce more spoil that expected, this is, more residual grout than the eroded volume of soil. The triple system uses grout, water jet and compressed air surrounding the water. This method consists of a single grout jet that is located approximately half a metre below a composite jet of water shrouded by compressed air. This way, it is a method that is better controlled and the quality of the final product can be defined according to the necessary. In addition to these systems, later in the 1980s and 1990s the jet grouting technique evolved to a more complex system called "Crossjet grouting", allowing for a better control of eroding capability and therefore columns diameters. This basically consists in two non-horizontal jets that collide at a certain distance, limiting their eroding capacity. In some cases, it can be coupled with conventional deep mixing methods in order to enhance control of soil mixing. Figure 2.31 - Three techniques of jet grouting: single, double (or twin) and triple. Top (Solentanche Bachy) and bottom (Moseley & Kirsch 2004) 3D modelling of sheet pile corner in difficult ground conditions 27 In the present case study there are several reasons for the use of jet grouting in the area of the corner instead of the lime-cement piles used in the rest of the reinforced zone along the wall. Firstly, the ground in the corner zone presented boulders and rock fragments of large size mixed with the soft soil. Therefore, the equipment used in the execution of KC Piles, the rotating "egg beater", was not suitable for these ground conditions, as it could not fragment such large and strong particles to provide a good soil mix. As jet grouting only uses the water or grout jet pressure to erode the soil, the big boulders could be fragmented with high pressure jet if necessary. Secondly, the structural stability could not be assured with certainty due to many unpredictable three dimensional effects and deformations, as explained before. So, in order to maintain a conservative and safe approach, the jet grouting was a reasonable solution. As already mentioned, it is expected that the jet grouting piles would work as a monolith with high compressive strength, up to 1 MPa, and absorb earth pressures from the fill, reducing instability factors. 3D modelling of sheet pile corner in difficult ground conditions 28 3D modelling of sheet pile corner in difficult ground conditions 29 3 ANALYTICAL ANALYSIS 3.1. INTRODUCTION TO ANALYTICAL ANALYSIS In the analysis of deep excavation problems with multi-tied retaining walls, independently of the type of analysis, the first requirement is obtaining a correct distribution of earth pressure. When designing an earth retaining structure, the main point is determining the correct lateral earth pressures and the resultant response of the retaining structure. However, depending on the construction process, if it is an excavation or backfilling, the methods to calculate the earth pressure distribution along the wall may be different. This is related mainly to the deformation mode of the wall and mechanisms of load transfer through arch effects in each of the processes. In this chapter are presented different approaches to design retaining structures in multi-tied excavations, such as Terzaghi & Peck diagrams, the Equivalent Tie Support Method and the Subgrade Reaction Method. Besides, a simple analysis of the sheet pile wall in the case study presented in the previous chapter is provided, assuming three different cases of lateral earth pressure distribution. This serves as a reference for the three-dimensional analysis in chapter 4. 3.2. TERZAGHI & PECK DIAGRAMS Terzaghi & Peck diagrams were developed by Terzaghi and Peck in 1967 as a result of observations of strutted excavations (Figure 3.1). They were suggested based on empirical information of braced excavations, where compression forces in each strut were measured and afterwards the apparent diagrams could be derived, i.e. the pressure distribution on the wall based on the strut force per area of influence. Terzaghi & Peck (T&P) diagrams were then formulated both for cohesionless and cohesive materials. Although for cohesionless soils they are directly applicable and no further concerns exist, for cohesive soils the diagrams should be used taking into account stability numbers, based on stability of the excavation base. As T&P diagrams were developed from braced excavations, they are commonly accepted as a reliable method for calculating this type of retaining walls but may not be used for tie-back walls in some situations. However, they can be used to calculate initial pre-stresses in pre-stressed tie-back walls, as these may show as much stiffness as braced excavations. 3D modelling of sheet pile corner in difficult ground conditions 30 Figure 3.1 - Terzaghi and Peck Diagrams (Matos Fernandes 1990) Nevertheless, it is important to introduce the understanding of such diagrams as an accepted method for calculation of design earth pressures in excavations. 3.3. EQUIVALENT TIE SUPPORT METHOD The Equivalent Tie Support Method (ETM) is a tool that can be used to calculate multi-supported structures using simple equilibrium equations. In short, this method assumes an equivalent tie for each excavation stage, which represents the resultant force of the tie forces system. For using this method, it is necessary to resort to the classical design methods. Therefore, these have to be explained before fully understand this method. 3.3.1. CLASSICAL DESIGN METHODS The main two classical design methods are free and fixed earth support. They are based on the existence of limit equilibrium state (active and passive) in both sides of the wall, which is simply supported in the tie and in the tip and it is analysed as a beam subjected to lateral earth pressures. These methods differ from each other mainly in the type of support adopted in the tip of the wall (Vieira & Matos Fernandes 2000). The free earth support method admits the soil on the embedded part of the wall cannot produce negative bending moment, therefore admitting a simple support on the tip of the wall. By means of moment equilibrium to discover the necessary embedded length and horizontal force equilibrium it is possible to obtain the anchor forces (Figure 3.2). 3D modelling of sheet pile corner in difficult ground conditions 31 Figure 3.2 - Free earth support method (Vieira & Matos Fernandes 2000) The fixed earth support method considers that the soil embedding the wall produces negative bending moment, thus admitting a fixed support on the tip of the wall. In this case, it is necessary to have a resistant force Rd that represents passive force in front of the wall. Considering an "equivalent beam" it is necessary to identify the location of null bending moment where a hinge will be placed, splitting the wall in two statically determined beams. Afterwards, using static equilibrium equations it is possible to determinate the anchor forces, passive reaction Rd and embedded length of the wall (Figure 3.3). Figure 3.3 - Fixed earth support method (Vieira & Matos Fernandes 2000) 3.3.2. EQUIVALENT TIE SUPPORT METHOD PROCEDURES - - - Calculate - 3D modelling of sheet pile corner in difficult ground conditions 38 3.5.3. SHEET PILE WALL SYSTEM As it can be observed in the sketch in Figure 3.8, the structure analysed is a single 24.4 m height retaining wall supported by two levels of anchors and embedded on the soil in the bottom tip. However it is assumed that there will be rotational movement around the tip, without any restraint. Therefore, the structural model adopted is a vertical beam, simply supported on the bottom and with two elastic supports representing the anchors. The properties of the structural elements are similar to the ones used on site, described in Table 3.2. The stiffness of the elastic supports (i.e. springs) was calculated using the real parameters and based on Hooke's law in equation (3.8), where k is anchor axial stiffness, E its elastic modulus, A the cross section area and L the length of the anchor rod. ( 3.8 ) The two levels of anchors have different lengths and spacing. According to the provided plans, the upper rods are spaced 2.80 m have 50 m length, while lower rods are spaced 1.40 m and have 25 m length. Therefore, it is expected that anchors have different stiffness. An important aspect to notice is that soft clay present in situ does not provide enough reliable strength. This means that for conservative reasons the layer of clay in front of the sheet pile wall was not taken into account when calculating earth pressures. Thus, it is assumed it will not generate any passive earth pressure resistant to the rotation of the wall. Table 3.2 - Properties of structural elements Element Description Material Inertia y (m4/m) Stiffness, k (kN/m) Young Modulus, E (kN/m2) Sheet Pile AZ 46-700 2 Steel S430 1,154x10-3 N/A 200x106 Upper Anchor Rods SAS 670/800 3 (ϕ63,5) Steel 670/800 N/A 12668 200x106 Lower Anchor Rods SAS 670/800 (ϕ75) Steel 670/800 N/A 35344 200x106 2 AZ 46-700 are Z-section sheet piles of the AZ series marketed by Arcelor Profil Luxembourg. It is a Z-section with 4400 cm2/m section modulus and 700mm driving step. They are different of similar section piles from other companies. Therefore, specifications are retrieved from the commercial product detail, which can be found in Appendix. 3 SAS 670/800 are anchor rod systems marketed by Stahlwerk Annahütte. They are threaded bars with yielding stress (0,2% strain) and maximum stress of 670 and 800 N/mm2 respectively. Specifications are retrieved from the commercial product detail, which can be found in Appendix 3D modelling of sheet pile corner in difficult ground conditions 39 Figure 3.8 - Sketch of the retaining wall system (left) and adopted representative structural model (right) 3.5.3. ANALYSIS OF THE RESULTS The analytical analysis performed to the sheet pile wall is based on a simple adoption of the structural model presented before with lateral earth pressures applied on the wall, calculated using the three different approaches already discussed. The total lateral earth pressures applied on the wall for each of the approaches are shown in the graph on Figure 3.9 (calculations in Appendix). It is possible to observe that on top the wall the earth pressures are higher for the T&P, while below -3 and -9 m earth pressures are higher for K0 and Ka, respectively. In the layer where the monolith is located, only lateral pressure due to water differential is acting on the wall. As it was assumed in the beginning of this analysis, the monolith is supposed to absorb earth pressures from soil layers above and untreated soil behind the block. Hence, it explains the inexistence of lateral pressures besides the differential water pressure below -11 m. These diagrams shape were already expected, as lateral pressures calculated by earth pressure coefficients are increased with depth due to overburden. Furthermore, lateral earth pressures present higher values for the situation where at rest coefficient was used, which is valid since Ka is logically smaller than K0. As the two cases that use earth coefficients to calculate lateral earth pressures have higher values on the bottom of the sheet pile wall compared to the case using T&P diagrams, it can be expected higher forces in the lower anchor level for such situations. 3D modelling of sheet pile corner in difficult ground conditions 40 Figure 3.9 - Lateral earth pressures on the wall produced be the three scenarios For the structural analysis, the retaining wall is studied as a beam subjected to lateral earth pressures. It was then input in structural calculation software with the loads correspondent to the three study approaches. After running the structural analysis using calculation software (Robot Structural Analysis, by AutoDesk), the obtained bending moments, shear forces and reaction in the supports are shown below in Figure 3.10, Figure 3.11 and Table 3.3, respectively. By observing Figure 3.10 it is possible to conclude that using Terzaghi & Peck diagrams there is a higher distribution of bending moment along the structure. This is acceptable as T&P diagrams were empirically obtained after observation of strutted excavations, where arching effect and consequent bending moment redistribution are highly present. In the K0 case maximum values of bending moment are higher than the T&P. It can be noticed as well that bending moments are higher than the Ka scenario, which is obvious since earth pressures calculated using coefficient Ka are smaller than in K0. In all three cases, extreme bending moments occur in the lower anchors level and in the area between both anchor levels, approximately at same depth. 3D modelling of sheet pile corner in difficult ground conditions 41 Figure 3.10 - Bending moments (kN.m/m) on the wall for the three case scenarios: T&P, K0 and Ka (from left to right) By examining both Figure 3.11 and Table 3.3 it is possible to verify that again maximum shear force value is higher for K0 case. Also, reaction forces are approximately the same for both levels of anchorage in T&P case, while for the other situations they are approximately two times higher in lower anchors in comparison to upper anchors. This is expected and can actually be closer to the real forces distribution for situations of backfilling, where arching effects and consequently load distribution to anchors are not as influencing as in excavations. Another interesting aspect is the total lateral force applied in each case. T&P diagrams have a higher resultant than Ka and similar to K0. Actually, the resultant using T&P diagram is 45% higher than the resultant force from the active lateral earth pressures. This percentage is close to what is stated in Matos Fernandes (1990) that in cohesionless soils, T&P diagrams result in lateral force at least 30% higher than the resultant force due to active earth pressures. 3D modelling of sheet pile corner in difficult ground conditions 42 Figure 3.11 - Shear forces (kN/m) on the wall for the three case scenarios: T&P, K0 and Ka (from left to right) Table 3.3 - Reaction forces for the three case scenarios Reactions (kN/m) T&P Ko Ka Upper Anchor 362,00 227,91 143,87 Lower Anchor 341,79 491,09 329,59 Tip 16,72 18,90 21,77 Total 720,51 737,90 495,23 To calculate anchor forces in upper and lower level it is only necessary to multiply the obtained values with by rod spacing. Taking into account the characteristic yielding capacity of the rods specified in the commercial products (see note 3) and using the basic relation of stress, force and area, one can do simple ultimate capacity verification. The maximum yielding force (with no partial coefficients) of the upper and lower rods is 1845 kN and 2960 kN, respectively. In fact, observing the maximum reaction values of the three cases for both for upper and lower anchors and multiplying by rod spacing, one obtains 1014 kN and 687 kN, respectively. This is an indicator that the stresses are in a safe load field, yet it should be considered that no partial safety coefficients were used. The obtained wall deformation for three scenarios is represented in Figure 3.12. In all cases the main deformation mode is rotation along the bottom tip of the sheet pile. However, in T&P scenario the top of the wall has the higher deformation value because T&P diagrams consider a constant earth pressure distribution. So as the top is not restrained horizontally and has a higher load compared to the rest of the wall, it is expected that it will have higher lateral movement. On the contrary, for the cases K0 and 3D modelling of sheet pile corner in difficult ground conditions 43 Ka the top has lower deformation, while maximum values of lateral movement occur in the zone of positive bending of the sheet pile. Figure 3.12 - Wall deformation (mm) for the three case scenarios: T&P, K0 and Ka (from left to right) Another important aspect to note is the low deformation in the area right below the lower anchor. This reflects the inexistence of lateral earth pressures representing the absorbing behaviour of the monolith. Actually, in case the anchors' stiffness is higher than expected, it is possible that in this lower zone back bending (wall deforms backwards) may occur, which in extreme values could generate unexpected pressures on the back of the wall due to leaning of sheet pile wall against the monolith. Having the analytical study of the sheet pile wall, it is possible now to proceed to the three dimensional analysis with a base reference. 3D modelling of sheet pile corner in difficult ground conditions 44 3D modelling of sheet pile corner in difficult ground conditions 45 4 THREE-DIMENSIONAL MODELLING IN PLAXIS 3D 4.1. NUMERICAL ANALYSIS 4.1.1. 3D ANALYSIS The complex case of a mutually supported corner under backfilling conditions is not a common situation and, as it has already been referred, research around these problems is reduced and practically non-existent in the literature. Retaining structures have been studied mainly in the cases of enclosed excavations. However, the backfilling process is much different and retaining structures under such conditions require separate studies. The existence of the corner itself intuitively leads to the necessity of a 3D analysis. In these situations the distribution of earth pressures is relevant in all three Cartesian directions, in opposition to the supposed in a 2D plane strain analysis, that the third Cartesian stress perpendicular to the plan (i.e. direction of the infinite length - Figure 4.1) is constant and not used in calculations. Furthermore, the behaviour of the two mutually supported walls is dependent on the interaction between both. So, using two dimensional analysis, the corner (i.e. the two connected walls) mode of deformation is not predictable. Another relevant aspect that may require a third dimensional analysis is the significant 3D effects that may arise from lateral arching of retained soil and lateral flexure of the wall-waling system, as suggested by Lee et al. (1998). Actually, the simple 2D plane strain analysis does not replicate such lateral action. Therefore, deformations and stresses in the structure may differ from the results of the analytical analysis. Figure 4.1 - Plane Strain conditions 3D modelling of sheet pile corner in difficult ground conditions 46 As summary, 3D analysis is relevant as different levels of deformations, structural forces and earth pressures are expected along the sheet pile wall system. 4.1.2. FINITE ELEMENT METHOD Due to the already explained complexity of the presented case study a three-dimensional analysis is required, which is the central idea of this thesis. A finite element analysis in a third dimension environment is a complex method to analyse geotechnical problems that consume much time and resources. Therefore, it is normally used in cases where analysis using plain strain or axisymmetric conditions cannot represent accurately the real conditions and boundaries of the problem. The finite element method is a numerical method of analysis commonly used to solve highly undetermined and complex problems. In Geotechnics it is a usual situation to face this sort of problems that are not accurately solved with simple models. In fact, for the case of multi-propped walls, some authors concluded that simplified methods of analysis where an appropriate calibration of the geotechnical data is made could provide comparable values of bending moment and anchor forces with those of finite element analysis (Carrubba & Colonna 2000). However, simplified methods, such as the Equivalent Tie Support Method (ETM) or the Sub-grade Reaction Method (SRM), do not take into account interactions between soil, wall and anchors, as they assume only the final limit equilibrium condition. Therefore, these do not provide complete information about the variations of soil displacement through all the phases and certainties about global stability, that is worsened for a three dimensional situation. Although the finite element analysis gives results close to the reality, it is a very sensible method that encloses a correct modelling of boundaries and geometry, an efficient and good quality mesh, the adequate choice on the constitutive models of the soil as well as of the soil parameters. 4.1.3. PLAXIS 3D The software chosen to perform the required computations was PLAXIS 3D. It is a common and very popular finite element analysis program, specialized in geotechnical applications and with three dimensional capacities. The fact that it provides wide information regarding displacements, stresses and strain in soil and structural elements with a considerable level of accuracy makes PLAXIS 3D an acceptable and desired program in the geotechnical field. Three types of calculations are possible to perform, namely Plastic, Consolidation and Safety Analysis. For the presented case, plastic calculations are necessary as it is required information regarding movements of soil and stress-strain conditions. PLAXIS 3D is based in the finite element method with basic equations of static equilibrium and kinematic relations. By associating constitutive relations representative of the soils, it provides a realistic representation of soil behaviour. The soil is discretised into 10-node tetrahedral element (Figure 4.2). However, structural elements have different types of element. As shown in Figure 4.3, plates have 6-node triangles, while interfaces have 16-node element with pair nodes (two nodes in the same coordinates); beams and node-to-node anchors have 3-node line elements. These differences in element types have to be considered when analysing outputs, because shape functions are different and therefore interpolated results may have different meanings. 3D modelling of sheet pile corner in difficult ground conditions 47 Figure 4.2 - 10-node tetrahedral element used in PLAXIS 3D for soil discretisation (adapted from PLAXIS 2013a) Figure 4.3 - 16-node element used for interfaces (left) and 6-node triangles used for plate elements (right) (adapted from PLAXIS 2013a) 4.2. INPUT INFORMATION 4.2.1. SOIL LAYERS The soil volume is composed by three soil layers, shown in Figure 4.4, which are input in the model via representative boreholes, represented in Figure 4.5. The soil profiles used in the boreholes were based on Figure 2.15, after simplifications of layers' thickness. To avoid unnecessary density of images, all boreholes can be found in the Appendix. The lower layer represents glacial till and develops from the bottom of the model at -25 metres, which represents bedrock, up to a depth varying between -20.5 and -16 metres, depending on the location. The medium layer is the soft clay, from the top of glacial till up to -11 metres. The material of this layer may change to a material simulating KC Piles or Jet Grouting, depending on the study scenarios that are presented afterwards. The top layer consists of the fill material, which is deposited in layers and is only existent in the back of the retaining wall. Actually, on site this top layer is constituted by the same material (Sprängsten) in three different conditions and therefore these are soil layers with different properties. These layers were detailed in the previous chapter for the analytical analysis, where they were all considered. However, as the named compact fill is only 0.40 metres thick and has the same unit weight as the "uncompact" fill, the layer from surface to depth of -11.0 metres was assumed for the modellation as "uncompact" fill. The material placed on the top deck, over 0.0 metres is replaced by a surface load. 3D modelling of sheet pile corner in difficult ground conditions 54 Figure 4.13 - 3D representation of KC&JG scenario, showing the KC Piles (brown), jet grouting (dark grey) and spoil (light grey) 4.2.4. BOUNDARY CONDITIONS The boundary conditions in the limits of the model are set by default to the following configuration:  Vertical boundary planes are fixed in the perpendicular direction, but free in plane vertical and horizontal directions, i.e. boundaries with their normal in X-direction have ux = 0 and boundaries with their normal in Y-direction have uy = 0;  Bottom boundary plane is fixed in all direction (ux = uy = uz = 0);  Ground surface is free in all directions. The limits of the model were defined to xmin = -5; xmax = 40; ymin = -30 and ymax = 70, as schemed in Figure 4.14. Such values were obtained after trials so that a plane strain deformation state at all vertical model boundaries was achieved and boundaries conditions would have low influence on the results. The boundaries perpendicular to Y-direction and the boundary at x = -5 should be carefully chosen and understood. First, the boundaries at ymin = -30 and ymax = 70 were chosen so that there would exist enough space to model the anchors as well as to provide place for the occurrence of a passive failure slip in the till. The necessary distance D for these failure curves to happen can be approximately determined a priori using the equation (4.1), where H is the high of soil layer with failure and φ is the friction angle. ( 4.1 ) The boundary at x = -5 is crucial as this must represent plane strain deformation conditions. Otherwise, the results will come highly influenced by the movement restriction provided by the default boundary settings. However, it should be reduced to a minimum amount of structural elements, in order to decrease computation time. The necessary conditions are achieved at the plane strain deformation cross section (PSD), which is demonstrated in Chapter 5. 3D modelling of sheet pile corner in difficult ground conditions 55 An important aspect not yet described is the connection between the sheet pile wall and the existent gravity wall. Actually, wall 2 is assumed as being simply supported by the gravity wall and its movement in the backend prevented in X-direction. However, as it is not of interest studying the gravity wall and taking into account that its movements will not affect largely the structure's behaviour, L walls were modelled as surfaces with both movements in Xand Y-direction fixed. Only settlement in Z-direction is allowed (see Figure 4.15). Figure 4.14 - Horizontal plan describing the lengths of the model's borders Figure 4.15 - Detail of the surface with fixed displacements in Xand Y-directions, simulating L gravity wall 3D modelling of sheet pile corner in difficult ground conditions 56 4.2.5. SOIL MODELS AND PARAMETERS In order to obtain an acceptable output from any computation it is necessary to have selected adequate constitutive laws that represent accurately the soils' behaviour in the model. Among the available soil models, the simple elastic-plastic model with Mohr-Coulomb (MC) failure criteria was chosen for all types of soil. This model is a constitutive soil model that provides a simple representation with need for few and easily obtained parameters, such as friction angle (φ), dilation angle (ψ), cohesion (c), poisson coefficient (υ) and elastic modulus (E). Due to its simplicity based on perfectly elastic-plastic behaviour, it is normally used to perform faster initial approximate calculations before opting for more complex soil models (see Figure 4.16). However, it may not provide accurate and so realistic behaviour in some kinds of soil such as in normal consolidated clays, where some hardening may occur. In this case, other models such Soil Hardening or Soft Soil Creep could be used to obtain a closer behaviour to reality, yet in detriment of computation speed (PLAXIS 2013b). Besides, such models require advanced parameters that need to be determined with more soil tests and afterwards calibrated to the model. Despite the fact that these models should be used for representing the clay layer, the author still opted to use Mohr-Coulomb because it was intended an initial approach to the problem. Figure 4.16 - Diagram representative of perfectly elastic-plastic model (PLAXIS 2013b) For the soil mass representing soil improvement with lime-cement piles (KC Piles) was also used MC model. However, for modelling jet grouting and the grout spoil a linear elastic model was chosen. This choice was based on the assumption that the monolith will not plastify and there will be no internal rupture. In reality this assumption is not correct, but as the yielding of the grouting occurs much later than the soil and the objective is to study soil behaviour, it is an acceptable option. In Table 4.1 are described all soil parameters that were used in the input of PLAXIS 3D. Most of the values were based on provided information by COWI, regarding soil in situ. However, Poisson ratio values were obtained from average observed values in the literature. As no information regarding the coefficient of earth pressure K0 was provided, it was set to Auto in PLAXIS 3D, which means that the program automatically computes this value based on Jaky's formula, in equation (3.3). Fill and glacial till are described as having a drained behaviour, whereas clay and improved clay (KC Piles) appear to show undrained conditions, due to low permeability. Therefore, in these materials undrained properties should be used, as described in Table 4.2, instead of the initially presented drained parameters in Table 4.1. 3D modelling of sheet pile corner in difficult ground conditions 57 Table 4.1 - Input soil parameters used initially in the model Soil Unit Weight, γ (kN/m3) Poisson ratio, υ Friction Angle, φ (º) Cohesion, c (kPa) Oedometric modulus, Eoed (MPa) Clay 12,82 0,4 27,6 0,85 310 Fill 21 0,2 38 0,001 10 Glacial Till 21 0,3 40 0,001 100 Jet Grouting 24 0,1 N/A N/A 3,17x107 JG Spoil 22 0,1 N/A N/A 2,56x107 KC Piles 14 0,15 36,8 46 16500 The friction angle and cohesion, resultant of interpretation of geotechnical tests, are used without application of specific partial factors and thus are characteristic values. For purely frictional soils cohesion value is 0,001 because PLAXIS shows numerical issues if the cohesion is null. Table 4.2 - Input undrained soil parameters Soil Undrained shear strength, cu (kPa) Clay 8,68 KC Piles 104,1 Another parameter that needs to be introduced in the material information for granular materials is the dilation angle ψ (Figure 4.17). This characteristic is particularly important in plastic analysis using Mohr-Coulomb model as it is associated with volume deformations in plastic domain. The dilation angle indicates how the soil volume changes with shearing, which means that positive dilation angle will result in volume increase in a pure shearing condition. Figure 4.17 - Concept of dilation angle The granular fill is simply deposited (i.e. no compaction) thus initial void ratio is smaller than the critical, typically close to the unity. After loading resultant from the weight of soil layers placed above, void ratio will reduce until it reaches (if it really does) critical state (see Figure 4.18). Therefore, the dilation parameter, which in Figure 4.18 is represented by Ψ (e-ecrit), is positive, so the 3D modelling of sheet pile corner in difficult ground conditions 58 soil is contractive. Consequently dilation angle will be negative, which means reduction of volume. So, dilation is assumed to be zero in the granular materials as the settlement is not relevant for the studies in the present thesis. Figure 4.18 - Critical State line Regarding the Poisson ratio, it is relevant to refer that clayey soil show a higher value than granular soil. As glacial till can be assumed as a mixture of both types of soil and based on commonly used values, an average ratio was chosen. Concerning more rigid structures like the jet grouting and the KC Piles, typical values of concrete were input. It is important to denote that Oedometric (or Constrained) Modulus, Eoed, is obtained after in situ geotechnical tests. The Young Modulus, E, is then derived from the equation (4.2). ( 4.2 ) 4.2.6. STRUCTURES AND INTERFACES The elements in PLAXIS 3D used to represent the retaining wall and the anchors were plate elements and node-to-node anchors, respectively. To simulate no-displacement deadman anchors, fixed displacement nodes were used, as anchors displacement are not under study. For the capping and waling beams, beam elements were chosen. In Table 4.3 are presented the real element description. The sizes and type of the elements were based on information about the construction site used as example, which was provided in an internal document of COWI. It was decided to use similar sheet pile walls, beams and anchors profiles so the analysis could provide an acceptable representation of the real structure, in order to the results to be useful. Plates and beams were modelled using purely elastic models. However, anchors were modelled with elastic-plastic models, with yielding tensile strength of 1877 kN and 1312 kN for lower and upper anchors, respectively. To simulate failure to buckling, yielding compressive strength was set to 1 kN, because PLAXIS does not accept 0 kN. 3D modelling of sheet pile corner in difficult ground conditions 59 Table 4.3 - Description of structural elements used in situ Element Description Material Waling 2x UNP 400 Steel S355 Sheet Pile AZ 46-700 Steel S430 Upper Anchor Rods SAS 670/800 (ϕ63,5) Steel 670/800 Lower Anchor Rods SAS 670/800 (ϕ75) Steel 670/800 Capping Beam (1,00x1,00) Concrete The input parameters for the structural elements are shown in Table 4.4. The required parameters are unit weight, Poisson ratio, elastic modulus, area and inertia x and y, I2 and I3 in PLAXIS, respectively. Table 4.4 - Input structural element parameters used in the model Element Unit Weight, γ (kN/m3) Poisson ratio, υ Elastic Modulus, E (kPa) Area, A (m2) Inertia y, I2 (m4) Inertia x, I3 (m4) Waling 77 0,3 2,10x108 1,82x10-2 3,00x10-5 4,07x10-4 Sheet Pile 3,15 0,3 2,00x108 2,87x10-2 N/A N/A Upper Anchor 78 0,3 2,00x108 3,17x10-3 7,98x10-7 7,98x10-7 Lower Anchor 78 0,3 2,00x108 4,42x10-3 2,00x10-6 2,00x10-6 Capping 25 0,1 3,00x107 1,0 8,33x10-2 8,33x10-2 When doing the input of the structure parameters, some adaptations had to be made, such as in the plate elements representing the sheet pile wall. In Table 4.5 are described specific input parameters of plates. Table 4.5 - Adapted input parameters for sheet pile Element E1 (kN/m2) E2 (kN/m2) G12 (kN/m2) G13 (kN/m2) G23 (kN/m2) E'A (kN) Sheet Pile 2,20x107 1,10x106 1,10x106 1,47x106 4,41x105 N/A To obtain the equivalent properties of the sheet pile AZ 46-700, the true values of the sheet pile were input in a transformation spreadsheet provided by the developer of PLAXIS. The calculations occurring in this transformation are based in the equations (4.3) to (4.7), where Esteel is the elastic modulus of steel, E1, E2, G12, G13 and G23 are calculation parameters, I1 is inertia and d the section height, equivalent to h in Figure 4.19. ( 4.3 ) ( 4.4 ) 3D modelling of sheet pile corner in difficult ground conditions 60 ( 4.5 ) ( 4.6 ) ( 4.7 ) Figure 4.19 - Horizontal cross section of idealized sheet pile The correct interaction between soil and sheet pile wall has to be modelled using an interface. This interface, characterized for having pair nodes in the area elements, will provide a better simulation of the thin layer between the sheet pile wall and the soil. Interfaces use similar soil models to reproduce its real behaviour. For the case of Mohr-Coulomb model, the interface friction angle input represents in reality the skin friction of the sheet pile wall, i.e. the roughness of steel. For this model, the model and parameters of interfaces are set to be the same as the adjacent soil. However, the skin friction angle representing roughness between the sheet pile wall and soil mass will be 2/3 of the soil friction angle, which is set when describing interface strength properties for each soil. In equation (4.8), Rinter symbolizes the variation factor of the strength parameters represented by the friction angle, φ. Therefore, using the suggested value will result in the reduction of resistance in the interface elements. This value was initially chosen based on reviewed literature (PLAXIS 2013a) and experience of the author. Although it is a high value, as roughness between sand and steel plate may vary from 0 to 0.5, it was suggested as a first approach taking into account corrosion of steel plate and Z shape of the sheet pile wall. However, the roughness value should be subject of a parametric study, to understand its influence in the behaviour of the wall and load distribution. ( 4.8 ) For the situation of rigid structures such as the Jet Grouting monolith and the KC Piles, Rinter is the unitary value because it is assumed that both types of material do not have reduced strength in interfaces. 4.2.7. LOADING AND STAGES OF CONSTRUCTION As the structure behaviour is highly dependent on the construction process, it was necessary to apply different loading phases to simulate initial conditions, implementation of anchors and sheet piles, jet 3D modelling of sheet pile corner in difficult ground conditions 61 grouting, application of KC Piles and backfilling by layers. So, seven stages of construction were configured in the model for the three study scenarios. In Table 4.6 is a description of the different phases of loading and in Figure 4.20 a 3D representation. It is important to note that lime-cement columns are applied before driving the sheet pile walls in place and jet grouting is done afterwards, as described on site. The backfilling material is deposited on layers of two metres, although first layer is three metres thick. Also, the capping beam is only activated before filling the last two metres. In reality, the capping beam uses the last layer of filling material as base for the concrete deployment, so it should simulated similarly. Table 4.6 - Description of phases of construction for each study scenario Phase NR KC KC&JG Initial Phase Initial Stress State Initial Stress State Initial Stress State P1 Sheet Pile Wall, Waling Beam and Corner Ties KC Piles KC Piles P2 Anchors Sheet Pile Wall, Waling Beam and Anchors/Ties Sheet Pile Wall, Waling Beam, Jet Grouting (w/ spoil) and Anchors/Ties P3 Fill 3 m (to -8m) Fill 3 m (to -8m) Fill 3 m (to -8m) P4 Fill 5 m (to -6m) Fill 5 m (to -6m) Fill 5 m (to -6m) P5 Fill 7 m (to -4m) Fill 7 m (to -4m) Fill 7 m (to -4m) P6 Fill 9 m (to -2m) Fill 9 m (to -2m) Fill 9 m (to -2m) P7 Fill 11 m (to 0m) and capping beam Fill 11 m (to 0m) and capping beam Fill 11 m (to 0m) and capping beam P8 Surface loading 90kPa Surface loading 90kPa Surface loading 90kPa Over the top layer is applied a surface loading which represents the application of the 2,4 m layer of fill material above deck in combination with an equivalent load representative of differential water load and traffic loads. In total, the final surface loading applied is 90 kPa, providing a conservative load case scenario. 3D modelling of sheet pile corner in difficult ground conditions 62 Figure 4.20 - Loading phases 3 to 8 for the no reinforcement case (NR) P2 P4 P3 P5 P6 P7 P8 3D modelling of sheet pile corner in difficult ground conditions 63 5 ANALYSIS OF RESULTS 5.1. METHODOLOGY To fully understand and comprehend the case study, it is necessary to choose the relevant information to extract from the output of computations provided by PLAXIS 3D. These must provide a clear and simple view of the wall behaviour and soil-structure interaction. Therefore, an important aspect to examine is the deformation mode of wall system (i.e. wall 1 and wall 2). The wall movements can then be related to the distribution of stresses in the structural system, which is significant information to this study. Also, information of high relevance is the reduction of lateral earth pressures that is expected to occur on the sheet pile wall. One of the first assumptions made before studying this case was the transfer of loads from the soil mass above and behind the monolith to the bearing stratum (glacial till and bedrock), for the situation KC and KC&JG. This load transfer mechanism should be verified by studying the stress distribution inside the block. Table 5.1 shows a summary of the cases explained in Chapter 4, which are throughout this chapter analysed and compared. Firstly, the base situation with no soil reinforcement (NR) is deeply scrutinized, followed by a less detailed study of the cases with soil reinforcement, KC and KC&JG. Table 5.1 - Three cases (NR, KC and KC&JG) analysed with PLAXIS 3D Case Abbreviation Description No soil Reinforcement NR Model with no soil reinforcement KC Piles Reinforcement KC Model with lime-cement piles (KC Piles) reinforcement KC Piles and Jet Grouting Reinforcement KC&JG Model with lime-cement piles reinforcement and jet grouting near the corner 5.1.1. CROSS SECTIONS In order to obtain a clear visualization of the results and progress along the wall development, several key cross sections were selected. These cross sections, with the location as in Figure 5.1, are distributed along the wall and are expected to represent all the relevant aspects introduced before. 3D modelling of sheet pile corner in difficult ground conditions 70 Figure 5.8 - Horizontal (Y-direction) earth pressures at -9 m As introduced in the Chapter 2, another consequence of corner effects may be the reduction of vertical stresses, similarly to what happens in a silo. This is probable to occur in areas closer to the connection between both walls. Figure 5.9 shows the effective vertical stresses at depth -10 m, located in the fill layer. It is clear the reduction of vertical earth pressures closer to the wall. However, such reduction is more remarkable near the corner, in the proximity of the walls connection. In Figure 5.10 are represented the effective vertical stresses in two line vertical sections, L1 and L2. Vertical line section L1 (25.5;19.5) is located close to the corner and is compared with line section L2 (25.5;-5) in a region far from the wall's influence and in plane strain state. What can be observed is that there is a significant reduction in the effective vertical stresses, reaching 50% at some depths. This means that part of the vertical stresses may have been transferred to the sheet pile wall, where consequently an increase of axial forces is expected. Figure 5.9 - Vertical effective stresses at depth -10m, revealing corner effect L1 ▪ L2 ▪ 3D modelling of sheet pile corner in difficult ground conditions 71 Figure 5.10 - Effective Vertical Stresses at vertical sections L1 (25.5;19.5) and L2 (25.5;-5) 5.3.2. WALL DEFORMATION MODE The following aspect to analyse is the deformation mode of the wall along the loading phases. This is the first indicator of how the wall responds to the lateral earth pressures generated by the soil mass. Figure 5.11 shows the wall deformation at cross section B (CSB) in the zone of mutually supported wall, represented by normalized deformation to wall height. It is possible to observe that during the initial loading stages the wall rotates along the top, which according to Terzaghi (1941) is theoretically typical of excavated multi-strutted walls, accompanied by small translation and bending. However, the wall immediately shows rotation around the wall tip in the following phases. The described change of behaviour may be related to the fact that during the initial filling level (up to - 6m), the resultant of earth pressures is located at a lower part of the wall, in comparison with the last loading stages. This aspect combined with high corner ties stiffness and reduced tip wall embedment results in a higher movement of the wall in the tip than in the top. Yet, this shape changes as the filling takes place and the location of total soil impulse ascends on the wall. As the last loading phase is reached, it is clear the rotation around the tip with higher deformation in the upper tie in comparison with the lower tie, similar to deformation of non pre-stressed multi-tied walls in excavations (Matos Fernandes 1990). L1 L2 3D modelling of sheet pile corner in difficult ground conditions 72 Figure 5.11 - Normalized wall deformation (s/H) at CSB along loading phases, in percentage of wall height In respect to the displacement values, the maximum observed value was 0.15% of total wall height, corresponding to absolute displacement of 3.3 cm and occurs in the bending zone of the wall, between the two levels of ties, due to flexibility of the sheet pile. On the top half of the wall, the normalized deformation is higher than 0.1% which can be, according to data collected by Matos Fernandes (1990), enough to mobilize active pressures (see Figure 3.8). Thus, in Figure 5.7 it was verified that earth pressure ratio was close to active coefficient, so it is possible that the soil is reaching the active limit state. In Figure 5.12 it is shown the wall displacement in PSD section, which represents multi-anchored section. It is notable a significant difference in the deformed shape of the wall from the mutually tied section. In fact, the tendency for a rotation around the top of the wall during initial loadings maintains, but the final shape is different. There is still a rotation around the tip of the wall, but deformation in top and lower anchors is approximately the same, revealing a higher curvature in the lower part of the wall. This distinction can be explained by the fact that in the mutually supported corner the wall behaves as a rigid structure, due to both higher ties' stiffness and to the perpendicular connection with wall 2, leading to a deformed shape with less arching. Deformation values in the PSD sections do not exceed 0.08% of wall height, revealing that the region where the wall is anchored is stiffer (i.e. less deformation) than mutually supported walls, which Global wall shape - - - 3D modelling of sheet pile corner in difficult ground conditions 73 corroborates what was suggested by Figure 5.7 . As briefly explained in section 5.2, this may result from the fact that the small wall 2 is simply anchored on top and does not provide the same stiffness to wall 1 as an enclosed retaining system or a continuous anchored wall would. Figure 5.12 - Normalized wall deformation (s/H) at PSD along loading phases, in percentage of wall height Another relevant elucidation that can be taken from observation of Figure 5.11 and Figure 5.12 is that the surcharge application of 90kPa is responsible for almost 70% of wall deformation at the top. Actually, the value of surcharge is equivalent to a loading of approximately 8 m of filling material, which corresponds to almost 40% of total filling (i.e. filling in the back of the wall and equivalent "surcharge" filling). So, it is possible to conclude that the surcharge is an important factor that should be carefully considered. Still regarding the wall movement, Figure 5.13 shows the displacement of the wall in Y-direction at depth of -0.4 m and -9 m, where the waling beams and anchors (or ties) are placed. Once again, it can be verified that the displacement on top is higher than displacement in the middle, which describes a rotation of the wall around the bottom. However, this figure shows a better perspective of the relative displacements in the various cross sections. In fact, it can be observed that the wall stiffness in the mutually supported area is not constant, appearing to be more rigid in the connection of both walls (at cross section D) and more flexible in the first ties (near cross section A). This may be related to the fact that the first ties have considerable more length that the ties closer to the walls' connection, thus less rigid. Global wall shape - - - 3D modelling of sheet pile corner in difficult ground conditions 74 Similarly to what was introduced in section 5.2, the retaining wall displacement is opposite of the expected and stated in reviewed literature (section 2.1.3.1). The fact that this situation deals with a not enclosed retaining structure, as wall 2 is simply supported by a top anchor, it is reasonable that the corner has a global reduced stiffness compared with the mutually supported zone. Figure 5.13 - Lateral displacement of wall in Y-direction at depths -0.4 m and -9 m Also, Figure 5.13 reveals that earth pressure redistribution verified in Figure 5.8 can occur due to arching effects. Observing both figures side by side it is possible to conclude that the zones with less deformation have higher earth pressures, in opposition to zones with larger deformations. Another interesting detail that can still be observed in Figure 5.13 is the deformation in the transition zone, from anchored to mutually supported wall. It can be seen that at the upper level (-0.4 m) there is a smooth variation of the displacement, whereas this variation is more abrupt at the lower level (-9 m). Such variations can be explained by the reduced anchor spacing and higher stiffness at lower level, which will not allow for a smooth bending of the wall. 5.3.3. DEFORMATION OF CORNER To analyse the deformation of the mutually supported corner it is necessary to observe the cross section C (CSC), located in the middle section of wall 2. In combination with information in cross section B (CSB) and D (CSD), it is expected to provide a satisfactory view of the internal deformation of the corner regarding rotation around wall 1, as well as pulling of wall 2 and opening of the wall system. The pulling of wall 2 is an effect characterized by the outwards movement of wall 1 and inwards movement of wall 2. The opening of corner is a consequence of movement of walls 1 and 2 outwards, revealing the shape similar to the one of an opening book (see Figure 5.14). Figure 5.14 - Scheme of corner opening (left) and pulling of wall 2 (right) 3D modelling of sheet pile corner in difficult ground conditions 75 The outwards rotation that is expected for the wall system, as described in Chapter 2, is visible by observation of wall displacements in Yand Zdirection, i.e. in horizontal and vertical directions, schemed in Figure 5.15 and Figure 5.16. The movements are represented by a colour scale and simplified by the arrows indicating intensity and direction at different depths. The rotation around the tip of the wall results from the combination of settlement in vertical direction higher in the proximity of walls' connection and larger horizontal displacements on the top of the wall. Figure 5.15 - Wall displacement in Y-direction (Horizontal displacement) Figure 5.16 - Wall displacement in Z-direction (Vertical displacement) The observed rotation movement is a result of two main characteristics of the wall. Firstly, wall 2 is only supported by an anchor on top, which is responsible for preventing rotation and providing stabilization, as referred before. Secondly, the existent ground slope does not provide sufficient embedment of wall 2 and contributes for a sliding (i.e. translation with settlement) of the wall in Ydirection. After observation of displacements at CSC throughout loading phases displayed in Figure 5.17 it becomes clear that the rotation of the wall is practically the same in all depths, i.e. no lateral bending 3D modelling of sheet pile corner in difficult ground conditions 76 occurs. Also, as the deformation is similar to CSD, disregarding minimal elastic deformation of the material, it can be concluded that the main movement in the corner is rotation along the tip combined with translation. However, it is interesting to notice that in the initial loading phases the rotation movement is in the opposite direction. This is possibly due to the anchor placed on top of wall 2 and lower location of earth pressure global force. Figure 5.17 - Displacement in Y-direction at CSC, showing outwards wall rotation The effect of opening of the wall system can be analysed by observation Figure 5.18. It shows the horizontal displacement of sheet pile wall at the two levels of anchorage (or tie). What can be concluded is that it is not a relevant effect at the top of the wall but becomes clearer in the lower level. At depth -9 m there is a lateral wall bending outwards, which reveals a situation of small opening of the corner. Figure 5.18 - Horizontal wall displacement at depth -0.4 m (left) and -9 m (right) 3D modelling of sheet pile corner in difficult ground conditions 77 In Figure 5.19 is presented the wall displacement at CSC for different loading phases. It is possible to verify a large influence of the ties in restricting movement. In the initial filling phases, the top of the wall shows negative deformation which means the wall is moving inwards. Analysing Figure 5.19 side by side with in Figure 5.11, for the same initial loading stages it is possible to verify positive deformation (in Y-direction) in wall 1, leading to the idea that initially wall 1 is pulling the top of wall 2 inwards (X-direction), by activation of the corner ties. This reveals the pulling effect that was described Figure 5.14. However, in the following loading stages this effect is inexistent, probably because earth pressure is high enough to sufficiently stretch the corner ties. Figure 5.19 - Wall deformation at CSC, along loading phases 5.3.4. STRUCTURAL FORCES 5.3.4.1 Anchors and Ties The variation axial forces in the anchors and ties are an important factor to observe and understand. This is associated with different wall deformation and rods stiffness. In Figure 5.20 are displayed the forces in anchors and corner ties for both upper and lower levels, at - 0.4 m and -9 m respectively. At first, it is possible to verify that globally, axial forces are higher in lower level than in upper level, with a maximum of 750 kN and 300 kN respectively. In the PSD section are observed the lower forces values that increase along the rods in the anchored wall, reaching the maximum in the transition zone to the mutually supported wall, which is normal taking into account this is the area with more displacement. 3D modelling of sheet pile corner in difficult ground conditions 78 In the corner ties, the development of the forces reveals a different shape. It is observable a minimum at the longest and shortest tie, and the maximum values in the middles ties. This is associated with the various levels of displacement at this part of the wall (Figure 5.12), as well as with the varying stiffness of the ties. An interesting aspect is the high drop of the forces from the anchors to the ties. This may signify that a higher amount of forces due to earth pressures is supported by the anchored wall than by the mutually supported wall. There might be some relations with lateral arching effects, which are a consequence of different stiffness along the wall. Figure 5.20 - Axial forces (kN) in anchors and ties at upper (0.4 m) and lower (-9 m) levels The anti-rotation anchor on top of wall 2 reaches yielding, at 1312 kN. This is the critical structural element, responsible for maintaining stability of the corner and of the wall system. Therefore, any soil reinforcement is expected to change the force in this element. 5.3.4.2 Waling and Capping Beam The waling and capping beams are responsible for providing higher lateral stiffness to the wall and prevent relative settlement of the sheet piles. Figure 5.21 shows the axial force in the waling located at -9 m. The axial force is 550 kN at PSD section and increases to 1000 kN, when starts the mutually supported wall. At the mutually supported zone, the axial force reduces until it reaches the corner, after which rises up again to 200 kN. The reduction of axial force in the beam as it gets closer to the corner is result of the distribution of forces to the corner ties and to the sheet pile wall. Similar behaviour is observed for the capping beam, in Figure 5.22. Though, in capping beam maximum values reach 2500 kN in wall 1 and 1000 kN in wall 2. 3D modelling of sheet pile corner in difficult ground conditions 79 Figure 5.21 - Axial force in waling at -9 m (kN) The existence of peaks in the axial force distribution for the waling beam, in opposition to the capping beam, is because of the interaction with the ties. In fact, it is expected a practically constant diagram of axial force between the ties support, with point drops at the ties connection. However, numerical calculations suffer much interference in such sensible areas. Consequently, peaks similar to what is observed in Figure 5.21 are probable to occur. Figure 5.22 - Axial force in capping beam (kN) Figure 5.23 and Figure 5.24 show the diagram of bending moments at waling beam and capping beam, respectively. The maximum positive and negative bending moments in the capping beam are 372.8 kN.m and -481.1 kN.m, respectively. These are much higher compared to the values in the waling beam, 147.6 kN.m and -119.8 kN.m for positive and negative bending moments, respectively. This is mainly explained by the fact that the introduction of anchors and ties reduces the maximum curvature of the beam, even introducing in extreme situations an opposite curvature. Consequently, bending moment is also reduced as to linear proportion with curvature. 3D modelling of sheet pile corner in difficult ground conditions 86 Another interesting effect is the reduction of vertical stresses in the soil layer between the monolith and the sheet pile wall due to the so called silo effect. This is observable in Figure 5.31. The vertical stresses can be drastically reduced up to levels close to 0 kPa. However, in general reductions are up to 50% of at rest pressures, as it can be derived from Figure 5.32. Relevant consequences of this effect are the increase of vertical forces in the sheet pile wall and increase of stresses in the monolith, which can be noticed by the increase of vertical stresses in the borders of the monolith in comparison with the values in the middle section. Figure 5.31 - Effective vertical stresses in cross section at x=19 Figure 5.32 - Effective vertical stresses at depth -11m, in a cross section at x=19 5.4.1.2 Transfer of Loads through the Monolith To verify the assumption that the earth pressures are absorbed by the monolith, it is necessary to observe the development and change of principal directions throughout the block of KC Piles. Figure 5.33 shows the distribution of principal directions in a vertical plane cross section at x=19. In the back side of the monolith, horizontal earth pressures are taken by the monolith and transferred to the till layer. This is concluded by observing the paths illustrated by the directions of the principal stresses. Monolith 3D modelling of sheet pile corner in difficult ground conditions 87 However, in the front side of the monolith, the vertical stresses that were relieved from the spacing layer are not transferred to the bottom layer. In fact, these are transmitted back to the soil layer at a lower depth, which can also contribute for the increase of lateral earth pressures observed in Figure 5.30 for CSB section around depth -19 m. Figure 5.33 - Principal directions in a cross section at x=19 5.4.2. WALL DEFORMATION MODE In Figure 5.34 is displayed the shape of the wall along the loading phases. There is the tendency for a rotation along the tip of the wall, similarly to what was observed in the NR case. However, the wall shape is different along the depth. It is possible to observe that below depth -15 m, the wall is in a sub-vertical position, different from NR case (dashed line). This is resultant of the presence of the KC Piles behind the wall. Although these are present up to depth -11 m, the effect of earth pressures above the monolith is obviously observed some meters below the top of the monolith. However, above -9 m, the depth of the lower level of ties, the bending shape of the wall is similar to the case NR, though with less deformation. Moreover, comparing wall deformation in the NR case with KC case, it is possible to conclude that the presence of KC Piles reduces displacement on top almost 30%. 3D modelling of sheet pile corner in difficult ground conditions 88 Figure 5.34 - Normalized wall deformation (s/H) at CSB along loading phase for KC, in percentage of wall height In Figure 5.35 it is observable the lower deformation in comparison with NR case. Yet, the shape of the wall at depths -0.4 m and -9 m is similar to those in Figure 5.13, though at -9 m the variation of displacement in the transition zone (i.e. between anchored wall and mutually supported wall) is less abrupt for the KC case. Figure 5.35 - Lateral displacement of wall in Y-direction at depth -0.4 m and -9 m, for KC 3D modelling of sheet pile corner in difficult ground conditions 89 Another interesting aspect is the wall displacement at -0.4 m. In fact, it is higher for the KC case than for the NC case, described in Figure 5.13, in the area where the wall is multi-anchored. It is a rather strange situation, as the application of KC Piles is expected to reduce deformations. However, it is possible that the more rigid KC Piles mitigate the difference of stiffness along the wall, leading it to have a more uniform displacement. 5.4.3. DEFORMATION OF CORNER In Figure 5.36 and Figure 5.37 is possible to observe the deformation of wall 2 in Yand Zdirection. As explained in section 5.3.3, rotation of the wall results from the combination of movement in these two directions, simplified by the black arrows. Similarly to the NR case, wall system rotates outwards, though with lower values, as it can be seen by the colour scale. This is an obvious consequence of the application of KC Piles. Still in Figure 5.36 is possible to observe the maximum horizontal displacement due to bending, occurring in the area between upper and lower tie levels. Figure 5.36 - Wall displacement in Y-direction (Horizontal displacement) for KC Figure 5.37 - Wall displacement in Z-direction (Vertical displacement) for KC 3D modelling of sheet pile corner in difficult ground conditions 90 Similar to the observed for the NR case, the opening of wall system is not prevented with soil reinforcement using KC Piles, as it can be verified in Figure 5.38. In fact, displacement in wall 2 is not effectively reduced by the application of KC Piles, even having at some depths displacements higher than in the case with no reinforcement. This can be noticed in Figure 5.39, where wall shape at CSC for last loading stage in NR case is represented by a dashed line. Figure 5.38 - Horizontal wall displacement at depth -0.4 m (left) and -9 m (right) for KC Though maximum displacement is higher than in NR case, at depths below lower ties level is noticeable the influence of KC Piles. Another interesting aspect, also visible in Figure 5.34, is a slight increase of deformation at depth -20 m. This can be related with a rotation-translation movement of the monolith that pushes the soil and consequently the wall at the bottom. Figure 5.39 - Normalized wall deformation (s/H) at CSC along loading phases for KC, in percentage of wall height 3D modelling of sheet pile corner in difficult ground conditions 91 5.4.4. STRUCTURAL FORCES 5.4.4.1 Anchors and Ties The forces in anchors and ties are shown in Figure 5.40. It is possible to note the reduction in the value of maximum force to 510 kN and 290 kN in lower and upper levels of support, respectively. Similar tendency that was observed in the NR case is verified in this situation, though with lower values. However, it is relevant to note the following differences:  Forces in upper level remain practically the same, while force in lower levels decrease up to 30%;  Differences of forces from anchors to ties are less pronounced. Such observations lead to the conclusion that KC Piles have high influence in the lower support levels, but few influence in the upper levels. Furthermore, it is possible that the reduced difference of forces from anchors to ties is associated with lower lateral earth pressure redistribution due to arching effect, as relative displacements are smaller (Figure 5.35). Figure 5.40 - Axial forces in anchors and ties at upper (-0.4 m) and lower (-9 m) levels, for KC (kN) The anti-rotation anchor, located at the top of wall 2, shows, as expected, a reduced axial force of 1227 kN. However, it is still a high value in comparison with the other anchors and is close to the yielding value of 1312 kN. 5.4.4.2 Waling and Capping Beam The axial forces in the waling beam for KC are shown in Figure 5.41. It is possible to notice a reduction of approximately 25% at PSD section and 35% of the maximum axial force. However, in wall 2, the force at the waling can drop 50%. The tendency of reduction of axial forces in the area of mutually supported wall and closer to the corner, as observed for the NR case, is clear. This variation of axial force might represent relevant information for the design of the waling, as it could be helpful to optimize the beam's dimensions, thus reducing costs in material. In the capping beam, however, the reduction of axial force is almost none. In Figure 5.42 is verified that the existent reduction of axial forces is mainly in the anchored part of the wall, which is 3D modelling of sheet pile corner in difficult ground conditions 92 practically insignificant. So, it can be concluded that the distribution of axial forces in the capping beam remains the same, thus leading again to the idea that soil reinforcement does not affect structural elements closer to the top. Figure 5.41 - Axial force in waling at -9m, for KC (kN) Figure 5.42 - Axial force in capping beam, for KC (kN) The bending moment in the waling beam, shown in Figure 5.43, has a similar shape and distribution in comparison with NR case. However, maximum and minimum bending moment values are (as expected) lower, associated with reduction of earth pressures and consequent lower acting forces. In capping beam, maximum value of bending moment is close to obtained in NR, but minimum value is much lower. Actually, these take place in the connection between wall 1 and 2. Therefore, the connecting system of the sheet piles in this location is critical and should be subject of detailed study. NR --- NR --- KC __ KC __ 3D modelling of sheet pile corner in difficult ground conditions 93 Also, bending moment diagram does not follow the same shape as in NR case, as visible in Figure 5.44. In fact, in the multi-anchored part of the wall the positive bending moments (in blue) show a triangular shape, in opposition to the same diagram in the NR situation. Again, as in other parameters evaluated, the application of KC Piles has not much influence in forces of upper structural elements. Figure 5.43 - Bending moments in waling beam at -9 m (kN.m) Figure 5.44 - Bending moments in capping beam (kN.m) 5.4.4.3 Sheet Pile Wall Bending moments in the sheet pile wall are represented in Figure 5.45 for section CSB and CSC. In comparison with the diagram obtained for NR case, represented by dashed line, it is possible to note that the maximum bending moment is in fact higher for the KC scenario. This can be due to the slight increase of earth pressures that can be seen above -11 m in Figure 5.30, but also associated with a reduced arching effect. 3D modelling of sheet pile corner in difficult ground conditions 94 An interesting result is the inversion of bending moments that is verified below the monolith depth (-11 m). This is a rather strange effect but can be in part explained by observation of lateral earth pressures in the back and in the front of the wall. The presence of higher earth pressures in front of the wall than in the back at depth -15 m, as highlighted in Figure 5.46, are probably responsible for generating negative bending moments. In the tip of the wall, however, exist positive bending moments, revealing the embedment of the wall in the till layer. Figure 5.45 - Bending moment diagram at CSB and CSC, for KC (kN.m) In Figure 5.47 is shown the vertical axial force in the sheet pile at cross section CSB. As expected, it is possible to see that there is a reduction of axial force at the depths of the monolith. Also, above -11 m the axial load is lower than in NR case, in dashed line. It is not an expected result as supposedly above the monolith there are no relevant changes in vertical earth pressures. Therefore, it is not explainable such reduction of axial force in the sheet pile, though this aspect is not significant. 3D modelling of sheet pile corner in difficult ground conditions 95 At the till layer the axial force is again taken by mobilizing shear strength of the soil, but in this case no load is observed at the tip, as axial force is 0 kN. This is consistent with the fact that it is required more displacement to mobilize tip resistance than shear resistance, therefore the non existence of axial force at the wall tip. Besides, it is normal to obtain no tip resistance as the cross section area of the sheet pile wall is low. Figure 5.46 - Effective horizontal stresses in front and back of the sheet pile wall (kPa) Figure 5.47 - Vertical axial force in sheet pile wall at CSB, for KC (kN) 3D modelling of sheet pile corner in difficult ground conditions 102 Figure 5.57 - Horizontal wall displacement at depth -0.4 m (left) and -9 m (right), for KC&JG In Figure 5.58 the wall deformation at CSC shows the less evident of pulling of top of wall 2. Displacement is reduced at lower depths, due to jet grouting monolith. However, maximum displacement, located between upper and lower support levels, is in fact higher than the case with no soil reinforcement, in dashed line. Figure 5.58 - Normalized wall deformation (s/H) at CSC along loading phases for KC&JG, in percentage of wall height 3D modelling of sheet pile corner in difficult ground conditions 103 5.5.4. STRUCTURAL FORCES 5.5.4.1 Anchors and Ties In Figure 5.59 are displayed the axial forces in the anchors and ties. It is possible to observe a general decrease of forces, with a reduction to 430 kN and 280 kN in lower and upper anchors respectively. The anchor/tie forces in lower levels approximate to the forces in upper levels, while these last maintain close to initial case. Again here is verified the fact that the application of soil reinforcement has low influence in structures in the upper part of the wall. Axial forces in the lower level reduce in all supports, resulting from the reduction of horizontal earth pressures especially in the location of the lower corner ties, that are covered by spoil from jet grouting. However, in the upper level there is an increase in the corner ties. There is a tendency to achieve a more uniform distribution of forces along the supports. This is associated with the fact that the deformation of the wall in the top also has a more uniform shape. Figure 5.59 - Axial forces in anchors and ties at upper (-0.4 m) and lower (-9 m) levels, for KC&JG (kN) These results show similar tendency with what was obtained in the analytical analysis, in section 3.5.3, for the Ka and K0 case scenario (see Table 3.3). The anchor forces are higher for lower supports and lower in the upper supports. In comparison with Ka, the case K0 shows more conservative values of anchors forces for the lower level (491 kN), even though in the upper level anchors forces are slightly lower than what was obtained with 3D analysis (228 kN). On the other hand, T&P diagrams provide much different results. In fact, the anchors forces are higher in upper level than in the lower level, in opposition to what was observed in this analysis. This means that T&P diagrams may not be applicable for calculation of support forces when performing 2D plane strain analysis of this situation. The anti-rotation anchor, in the top of wall 2, gives much lower forces of 990 kN. This is below the yielding limit as expected, though it is a still high value for such critical element. It is suggested by the author that an extra anchor, in similarity to the anchored wall, would provide enough safety levels. 3D modelling of sheet pile corner in difficult ground conditions 104 5.5.4.2 Waling and Capping Beam In Figure 5.60 and Figure 5.61 are presented the axial forces in waling and capping beam, respectively. Axial forces in waling reduce up to 50%, to a maximum of 500 kN. However, in the capping beam the reduction is minimal. As in NR case, represented by a dashed line, there is a tendency of decrease of axial force in the beams close to the connection between wall 1 and wall 2. In the waling, in the anchored part of the wall axial forces distribution tends to a uniform shape. Figure 5.60 - Axial force in waling at -9m, for KC&JG (kN) Figure 5.61 - Axial force in capping beam, for KC&JG (kN) In Figure 5.62, the maximum and minimum bending moments in the waling beam show much variation, comparing with Figure 5.23. Maximum bending moment reduces almost 30% and minimum reduces up to 50%, which are rather relevant values. The distribution shape is similar and extreme values appear in the same sections. NR --- NR --- KC&JG __ KC&JG __ 3D modelling of sheet pile corner in difficult ground conditions 105 In Figure 5.63 are represented the bending moments in capping beam. The maximum bending moment has insignificant reduction while minimum moment reduces up to 20%. However, the bending moments show a different shape in comparison with NR scenario. In fact, in the anchored part of the wall capping beam is subject to more negative bending moments. Moreover, the shape of positive bending moments close to PSD section shows a triangular form, in opposition to the uniform shape in NR case. The higher bending moment and the triangular shape at this section are expected, as deformation tends to be lower and more uniform, in comparison with the other sections of the wall closer to the corner, where a change of curvature is observed. Figure 5.62 - Bending moments in waling beam at -9 m (kN.m) Figure 5.63 - Bending moments in capping beam (kN.m) 3D modelling of sheet pile corner in difficult ground conditions 106 5.5.4.3 Sheet Pile Wall Bending moments at CSB and CSC are displayed in Figure 5.64. It is clear the increase of bending moment at both section in the part of the wall above the lower anchor level (-9 m) up to 235 kN.m. However, similar to what happens in KC case, the bending moments have an inversion below the anchor level due to the almost inexistence of earth pressures on the wall. In Figure 5.65 is represented the vertical axial force in the sheet pile wall at CSB. Again, is clear the reduction of axial force, especially through all the depth of the monolith. Like in the NR case, the axial force is then taken by the glacial till through mobilization of shear force. Figure 5.64 - Bending moment diagram at CSB and CSC, for KC&JG (kN.m) 3D modelling of sheet pile corner in difficult ground conditions 107 Figure 5.65 - Vertical axial force in sheet pile wall at CSB, for KC&JG (kN) 5.6. COMPARISON BETWEEN KC AND KC&JG In order to evaluate the performance of the two different scenarios of soil improvement KC and KC&JG, a comparison study should be performed. In reality, the soil reinforcement with jet grouting reveals to be more expensive than application of KC Piles. Also, the block of jet grouting created may result in a too conservative solution. Therefore, it is important to observe and compare the effects of such soil improvement techniques in the earth pressures distribution, wall displacements and variation of forces in structural elements. If such differences are relevant, especially in structural forces, it may result in the possibility of downgrading and consequent saving of costs. Table 5.2 - Comparative cases KC and KC&JG Case Abbreviation Description KC Piles Reinforcement KC Model with lime-cement piles (KC Piles) reinforcement KC Piles and Jet Grouting Reinforcement KC&JG Model with lime-cement piles reinforcement and jet grouting near the corner 5.6.1. COEFFICIENT OF EARTH PRESSURE The first parameter to observe is the efficiency of the soil reinforcement technique in reducing the lateral earth pressures on the wall. In fact, the main objective of the ground improvement is to absorb the earth pressures and transfer them directly to the bearing till layer. This may be verified by 3D modelling of sheet pile corner in difficult ground conditions 108 admitting a coefficient of earth pressures, which relates horizontal earth pressures after application of soil reinforcement with the horizontal earth pressures in the scenario with no reinforcement. Figure 5.66 shows the coefficient of lateral earth pressures for scenario KC and KC&JG at section CSB. It is interesting to observe that as expected earth pressures are reduced up to 80% for the KC&JG case below depth -8 m, associated with the beginning of the jet grouting spoil. This reduction is constant down to -13 m, when it slowly increases reaching a "gain" of earth pressures, probably due to concentration of stresses in this area, as explained in the previous chapter. In KC scenario is possible to observe a similar behaviour to KC&JG. However, reduction of earth pressures begins at a lower depth (-11 m), where the reinforced layer is located. At depth -19m earth pressures increase up to a peak "gain", as in KC&JG. Figure 5.66 - Coefficient of reduction of lateral earth pressures at CSB, for KC and KC&JG Spoil 3D modelling of sheet pile corner in difficult ground conditions 109 In both scenarios two interesting aspects can be observed:  Reduction of lateral earth pressures is noticed before the depth of the reinforced soil layer, probably associated with soil arching effects;  Above the depth of beginning of earth pressure reduction there is a slight gain of earth pressures. In general, the reinforcement with jet grouting appears to cause a higher reduction of lateral earth pressures. However, the consequences of such effect are better visible in changes in deformation levels and structural forces. 5.6.2. WALL DEFORMATION MODE A result of reduction of earth pressures is variation in wall deformation. In Figure 5.67 are displayed wall shapes at CSB for KC and KC&JG cases. Maximum displacement is, as expected, lower in soil reinforcement with jet grouting. Though, such reduction from KC&JG to KC scenario is up to 12%, which in absolute values corresponds to a reduction of 3 mm. Such variation may not be significant. Although the wall shape is similar in both cases, it is interesting to note that below depth -15 m, displacements are slightly higher in KC&JG scenario. This is probably associated with higher weight of jet grouting, which combined with the ground slope, has a higher transversal displacement. Figure 5.67 - Normalized wall deformation (s/H) at CSB in last loading phase for KC and KC&JG, in percentage of wall height Figure 5.68 shows the lateral displacement of the wall at depths -0.4 m and -9 m. It is clear the lower wall displacement for the KC&JG scenario close to the corner, where in fact the jet grouting reinforcement is applied. However, this reduction is mitigated closer to the PSD section. These results are not surprising as the jet grouting is only applied in the area closer to the corner, while in the zone 3D modelling of sheet pile corner in difficult ground conditions 110 where the wall is multi-anchored the soil reinforcement is only executed using KC Piles. Besides, this tendency shows that the application of jet grouting in the corner practically only has local effects, which are not felt in farther areas like at PSD. The maximum horizontal displacement is observed at both levels to be located where the longer tie is connected, i.e. close to the transition zone from anchored wall to mutually supported wall. This leads to the idea that such area should be stiffer to allow uniform wall displacement, which could be achieved by either enlarging jet grouted area or upgrading the longer anchors. Figure 5.68 - Lateral displacement of wall in Y-direction at depths -0.4 m and -9 m for KC and KC&JG 5.6.3. STRUCTURAL FORCES In Figure 5.69 are presented the axial forces in anchors and ties for both compared scenarios. It is observable a significant reduction of stresses (up to 30%) in lower corner ties. Such effect is caused by the presence of jet grouting spoil at -8 m above the depth of the lower support level, at -9 m. As a benefit, downgrading in the middle ties at lower level could be considered and further studied. In the other elements, it is possible to observe a small reduction in anchors close to the transition zone from anchored to mutually supported wall. This variation is associated with lower deformations in this area, as observed in Figure 5.68. Closer to PSD section structural forces remain the same in both cases. Figure 5.69 - Axial forces in anchors and ties at upper (-0.4 m) and lower (-9 m) levels, for KC and KC&JG 3D modelling of sheet pile corner in difficult ground conditions 111 The anti-rotation anchor on top of wall 2 which is a critical element for the stability of the corner has significant variations. For KC anchor force is 1227 kN, while for KC&JG it is reduced to 990 kN. This represents a reduction of almost 20% in the axial stresses, locating the anchor in 75% of yielding stress. The bending moment in the wall at CSB is presented in Figure 5.70. In general, maximum and minimum bending moment is higher for the scenario KC&JG. This is may be associated with the fact that reducing earth pressures in the back of the wall, increases the effect of generated passive earth pressures in front of the wall. This will lead to higher extreme bending moments. Therefore, this is another effect that traduces the higher reduction of earth pressures for the KC&JG scenario. Figure 5.70 - Bending moment diagram at CSB for KC and KC&JG (kN.m) Globally, it is noticed that the application of jet grouting reduces deformation, although not in a significant amount, and has a relevant reduction of axial stresses in the corner ties at lower level. However, the maximum and minimum bending moments can actually be slightly increased, though not significantly to justify a change of the sheet pile grade. 3D modelling of sheet pile corner in difficult ground conditions 118  Improve modelling of jet grouting and KC Piles, by creating realistic pile groups, instead of a soil unit and application of interfaces to simulate interaction with surrounding soil layers;  Provide a study on minimum capacity of KC Piles that assures acceptable deformation and safety levels;  Develop a sensitivity study on anchors' stiffness, to understand influence of this parameter;  More realistic modelling of the materials. 3D modelling of sheet pile corner in difficult ground conditions 119 BIBLIOGRAPHY Aarsleff (2014). Presentation about Värtahamnen Arcelor Mittal (2014). Brochure: Extension of existing quay in Cadiz, Spain. Bilgin, Ö. (2010). Numerical studies of anchored sheet pile wall behavior constructed in cut and fill conditions. 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Mahan (http://www.cjmahan.com) - access date: 23rd April Soletanche Bachy (http://www.soletanche-bachy.com) - access date 23rd April Stockholm Royal Seaport (http://www.stockholmroyalseaport.com/en/) - access date: 23rd April 3D modelling of sheet pile corner in difficult ground conditions 121 APPENDIX COMMERCIAL BROCHURE SAS 670/800 Ø 18 - 75 mm Adapted from Stahlwerk Annahütte 3D modelling of sheet pile corner in difficult ground conditions 122 COMMERCIAL BROCHURE AZ 46-700n Adapted from Arcelor Mittal 3D modelling of sheet pile corner in difficult ground conditions 123 LOCATION OF BOREHOLES 3D modelling of sheet pile corner in difficult ground conditions 124 CALCULATIONS OF EARTH PRESSURES IN ANALYTICAL ANALYSIS T&P K0 Ka Water in front of wall Water behind wall Strata Depth [m] Soil pressure Surcharges Water Pressure [KPa] Soil Pressure Surcharges Pressure [KPa] Soil Pressure Surcharges Pressure [KPa] 2,4 56,18 5,58 0,00 61,76 0,00 7,32 7,32 0,00 4,29 4,29 156,18 5,58 0,00 61,76 9,02 7,32 16,34 5,28 4,29 9,57 150,35 5,58 0,00 55,93 9,02 7,32 16,34 5,28 4,29 9,57 -0,36 50,35 5,58 0,00 55,93 17,39 7,32 24,71 10,18 4,29 14,47 -0,36 34,85 7,73 0,00 42,58 22,81 9,61 32,42 14,12 5,95 20,07 -0,4 34,85 7,73 0,39 42,97 22,99 9,61 32,99 14,23 5,95 20,57 -0,86 34,85 7,73 4,91 47,48 24,96 9,61 39,48 15,45 5,95 26,30 -8 34,85 7,73 4,91 47,48 55,67 9,61 70,19 34,46 5,95 45,31 -9 34,85 7,73 4,91 47,48 59,97 9,61 74,49 37,12 5,95 47,97 -11 34,85 7,73 4,91 47,48 68,57 9,61 83,09 42,44 5,95 53,30 -11 0,00 0,00 4,91 4,91 0,00 0,00 4,91 0,00 0,00 4,91 -11 0,00 0,00 4,91 4,91 0,00 0,00 4,91 0,00 0,00 4,91 -11 0,00 0,00 4,91 4,91 0,00 0,00 4,91 0,00 0,00 4,91 -20,5 0,00 0,00 4,91 4,91 0,00 0,00 4,91 0,00 0,00 4,91 -20,5 0,00 0,00 4,91 4,91 0,00 0,00 4,91 0,00 0,00 4,91 -22 0,00 0,00 4,91 4,91 0,00 0,00 4,91 0,00 0,00 4,91 Rock Till -25 Top Fill Compact Fill Uncompact Fill JG Spoil JG 3D modelling of sheet pile corner in difficult ground conditions 125 PARAMETERS USED IN ANALYTICAL ANALYSIS Unit Weight [kN/m³] Friction Angle [°] K0 Ka Uncompacted Fill 21 38 0,38 0,24 Compacted Fill 21 45 0,29 0,17 Top Fill (above deck) 22 45 0,29 0,17 Till 21 40 0,36 0,22 Load [kN/m²] Unit Weight [kN/m³] Water difference 4,905 9,81 Traffic Load 25 Earth Pressure Surcharges