A Finite Element‑Based Methodology for the Thermo‑mechanical Analysis of Early Age Behavior in Concrete Structures

Cifuentesetal. Int J Concr Struct Mater (2019) 13:41 https://doi.org/10.1186/s40069-019-0353-0 RESEARCH A Finite Element-Based Methodology fortheThermo-mechanical Analysis ofEarly Age Behavior inConcrete Structures H. Cifuentes1* , F. Montero‑Chacón2, J. Galán3, J. Cabezas4 and A. Martínez‑De la Concha1 Abstract This paper presents a general procedure based on fracture mechanics models in order to analyze the level of crack‑ ing and structural safety in reinforced concrete elements at early ages, depending on the stripping time. Our proce‑ dure involves the development of a thermo‑mechanical numerical model based on the finite element method that accounts for the change in the mechanical properties of concrete with time. Moreover, fracture mechanisms are analyzed by means of a material damage model, which is characterized via specific experimental results obtained for standard specimens and notched beams under three‑point bending testing. The loading conditions are both thermal and mechanical, and are obtained from the hydration process for a given concrete dosage. The presented methodol‑ ogy allows for the determination of the optimal stripping time, whereas it helps assessing the analysis of the cracking and the stress states of the elements under consideration. A practical application, namely the analysis of a retaining wall, is used to validate our methodology, showing its suitability in engineering practice. Keywords: heat of hydration, early age cracking, thermo‑mechanical model, fracture mechanics of concrete © The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creat iveco mmons .org/licen ses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. 1 Introduction Concrete mechanical behavior at early age is characterized by the development of low mechanical properties and the appearance of thermal stresses generated by temperature gradients from the heating process during the cement hydration (Wang and Luan 2018). Moreover, along with the exothermal reaction, material shrinkage takes place. This phenomenon can generate the so-called early-age cracking in concrete, which can be extremely harmful if a premature application of the load is performed (Mihashi and Leite 2004). On the other hand, the correct choice of the stripping time of an on-site cast in place concrete structure results in significant savings in the implementation of the structure (i.e., cost and time), with the structural safety factors depending on the chosen time and the lack of excessive cracking level in the material. For a proper analysis of concrete at early ages, the evolution of the thermal, mechanical, and fracture properties of the material must be known (Bergström and Byfors 1980; Lee etal. 2016), as well as the relationship between them. This issue, then, promotes having a complete picture of the behavior of concrete in a period of time close to the pouring age (Faria etal. 2006). In this work a numerical model has been developed in order to estimate the optimal time for removing the formwork without damaging the structure. In addition, the model also provides the maximum load that a structure of concrete can support at a certain age. This fact is very important during the on-site execution, where time plays a crucial role and should be diminished as much as possible (Wu etal. 2011). Traditionally, structural health monitoring (SHM) systems have focused on monitoring the conditions of the concrete using external techniques based on accelerometers or displacement transducers, among others (Park and Yim 2017). Moreover, monitoring the internal properties of concrete requires the development of Open Access International Journal of Concrete Structures and Materials *Correspondence: [email protected] 1 Dpto. Mecánica de Medios Continuos y Teoría de Estructuras, ETS de Ingeniería, Universidad de Sevilla, Seville, Spain Full list of author information is available at the end of the article Journal information: ISSN 1976‑0485 / eISSN 2234‑1315 Page 2 of 20 Cifuentesetal. Int J Concr Struct Mater (2019) 13:41 embedded sensors so as to gather data during the curing stage (Newell and Goggins 2018). In this sense, in order to measure the temperature in the concrete and characterize the curing process from the first pour, an embedded sensor was designed. The monitoring framework addresses aspects related to sensing, local wired transmission, data storage, and visualization. Furthermore, a numerical model has been developed in order to assess the cracking level and stress states in terms of the stripping time. More precisely, the model takes into account the thermal processes taking place during the cement hydration and has been characterized and verified experimentally with laboratory specimens (e.g., standard specimens and notched beams) and large structures, respectively. The model also accounts for the evolution of mechanical properties with time, as well as the fracture mechanisms via cohesive elements. Service loading conditions are based on the heat of hydration for a given concrete dosage. Although other reliable numerical models can be found in the literature (Kwan and Ma 2017; Lee and Kim 2009), the most of them are mainly focused on the behavior of the material and the methodology described in this work presents an eminently practical purpose but considering the different advanced approaches involved in the early age behavior of concrete structures, from the chemical reactions produced during the evolution of the hydration of the cement to the macroscopic analysis of the concrete structure, with insitu measurements, by using fracture mechanics models based on bi-linear cohesive laws of concrete in tension at early ages. The methodology herein described is very complete and different from other similar methodologies that can be found in the bibliography since it integrates all the different analyzes carried out in this work in the design process of a concrete structure, from the set-up of the numerical models, the experimental verification and validation in laboratory and the application in a real structure. This methodology considers the analysis of the experimental evolution of the mechanical properties of concrete at early age and its relationship with the developed temperature, which can be easily measured in situ, through thermo-chemical–mechanical models (Schindler and Folliard 2005). Likewise, the mechanical behavior of concrete structures was analyzed by numerical models based on the fracture mechanics of concrete, using cohesive laws for its tensile behavior that evolve with the age of the material. However, the procedure is of a very simple work application, requiring only the measurement of the temperature as the control parameter to be compared with the numerical predictions and to check whether the hydration of cement is taking place correctly. The methodology presented in this work has been applied in a real case such as a slender retaining wall in Loja (Granada, Spain), allowing the determination of the optimal stripping time and providing an assessment of the cracking and stress states of these elements during the construction process, proving its validity. It must be remarked that, as pointed out by Mihashi and Leite, the potential damage generated during the hydration processes in large concrete structures can be harmful for their durability; thus, new methodologies for the control of early age cracking are essential to ensure the sustainability of these types of structures (Mihashi and Leite 2004). 2 Methodology The main objective of the model is to analyze the thermomechanical behavior of concrete structures at early ages in order to determine the optimal stripping time while providing a proper security level in compliance to the serviceability limit state (SLS). Therefore, the numerical model presented herein takes into account the evolution of material properties with age, the hydration process, the thermally-induced stresses, the evolutionary construction phases, and the total elapsed loading time. In this section, we present the thermal model that is used to analyze the hydration process and the mechanical model that is used to analyze the thermo-mechanical stresses resulting from the former phenomenon. 2.1 Analysis oftheHeat ofHydration The starting point of the thermo-mechanical model is the analysis of the cement hydration process (Ulm and Coussy 1995). Thus, in order to include this into the methodology, it is necessary to account for the heat flux that evolves with the curing period. Although there are several models available in the literature (Bernard etal. 2003; Hattel and Thorborg 2003; Wang and Lee 2010), the model used to predict the flow of the heat of hydration is that from Schindler and Folliard (Schindler and Folliard 2005) because of its simplicity and dependence on the type of cement and concrete composition. Schindler and Folliard proposed a novel method in order to quantify the heat flux transferred to the concrete mix and originated by the hydration of the cement. According to this method, the total heat of hydration of a Portland cement class is a function of the heat of hydration provided by its components, which is given by: where Hcem is the total heat of hydration of the Portland cement (J/g) considering fully-hydrated cement and pi is (1) H cem = 500p C3S+ 260p C2S+ 866p C3A+ 420p C4AF +624 pSO3 +1186 pFreeCaO +850 pMgO Page 3 of 20 Cifuentesetal. Int J Concr Struct Mater (2019) 13:41 the mass of the i-th component to the total cement ratio. Table1 shows the components of cement classes I and II (Poole 2007). The progress of the hydration of Portland cement can be quantified by the so-called degree of hydration, δ , which varies from 0 to 1 (with 1 indicating a complete hydration). This degree of hydration is defined as the ratio of the heat transferred at a given time t, H(t) in J/g, to the total amount of heat in the reaction (van Breugel 1998): with Hu the total heat available for the hydration reaction, Hu=Hcem . The degree of hydration is usually modelled using an exponential curve with the following mathematical expression: where δu is the total degree of hydration, β is the hydration shape parameter, τ is the hydration time parameter (in hours), and te is the equivalent age (in hours) at the reference temperature, Tr (K), which is given by: where t is the time interval (in hours), T is the average temperature of the concrete mix (in K), R is the universal gas constant (8.314J/mol/K), and Ea is the activation energy (J/mol) defined as proposed in (Schindler and Folliard 2005) which is in accordance to Arrhenius theory. Once these parameters are calculated, the rate of the heat generation due to the hydration process, Qh , can be obtained as: where Wc is the cement content (kg/m3). A detailed description of the model can be found in (Schindler and Folliard 2005; van Breugel 1998). (2) δ (t)= H(t) Hu (3) δ(te) = δue −  τ te β (4) t e(t)= t  0 e− Ea R1 Tr − 1 T� t (5) Q h(t)=HuWc  τ te  β  β te  δ(te)  e−Ea R1 Tr − 1 T . The heat equation, which can be solved by means of the finite element method (FEM), is then used to determine the evolution of the temperature in the concrete mix at any instant t by: where ρ is the density, cp is the specific heat, k is the thermal conductivity, and the source term is the volumetric heat flux as defined in Eq.(5). As mentioned above, Eq.(6) is solved by means of the FEM in order to determine the temperature of the concrete mix at any point of the domain and at any instant within the curing period. This temperature field is consequently used by the thermo-mechanical model in order to evaluate the mechanical properties and determine the thermal stresses that may induce early age cracking. Convective and radiative boundary conditions are considered by accounting for their corresponding heat fluxes, qcv and qrd , respe ctively, as: where h is the film coefficient between concrete and air, Tcv is the temperature of the convective boundary, Tr is the radiant room temperature, σ is the Stefan-Boltzmann constant, ∈ is the emissivity, and Trd is the temperature of the radiative boundary. 2.2 Thermo‑mechanical Model Since the numerical model has to provide the stress and cracking states in the material produced by the hydration process, along with other mechanical loads, a thermomechanical model has to be defined (Cifuentes and Karihaloo 2018). Consequently, the model should also consider the evolution of material properties with age. Thus, the socalled concrete damage plasticity (CDP) model, developed by Lubliner etal. (1989), and with modifications by Lee and Fenves (1998), is used in this work. The CDP model has proven capabilities for the analysis of fracture in concrete specimens and structures (Cifuentes and Karihaloo 2018; Montero-Chacón etal. 2015, 2017). (6) ρ cp ∂T ∂t −∇ (k∇T)=Q h (7) qcv =h ( Tcv −Tr) (8) q rd =σ∈  T4 rd −T4 r  Table 1 Weight fractions ofthecomponents ofcement classes I andII tothetotal cement ratio. Class C3S C2S C3A C4AF FreeCaO SO3MgO I 0.565 0.140 0.100 0.080 0.029 0.035 0.013 II 0.51 0.24 0.053 0.166 0.004 0.025 0.009 Page 4 of 20 Cifuentesetal. Int J Concr Struct Mater (2019) 13:41 The continuum damage model formulation in elasticity (Kachanov 1980; “Continuum damage mechanics: Part I-General concepts” 1988) reads as follows: where σ is the Cauchy stress tensor, d is the damage variable, Del 0 is the original (i.e., undamaged) elastic stiffness tensor, and εel is the elastic strain. The total strain tensor in concrete, ε , can be split into the instantaneous reversible elastic strain, εel , the irreversible inelastic strain, εin , the creep strain, εc , the shrinkage strain, εs , and the thermal expansion strain, εth (Bazant 1988): The creep strain at the instant t > t0 for those cases where concrete is loading at t0, can be considered as a reduction of the Young’s modulus through the creep coefficient as follows (Neville 1995): The creep coefficient, ϕ(t,t0) , can be calculated in different ways. In this paper, it was determined according to the Model Code formulations (fib CEB-FIP 2012), considering the specific type of cement employed in the concrete fabrication, the geometry of the structure and the relative humidity of the ambient environment. In the CDP model, the inelastic strain tensor, εin , takes into account the irreversible inelastic strains, as those arose from concrete cracking. In the case of uniaxial tension, for instance, the equivalent inelastic strain, ˜εin , is defined in terms of the damage variable as: where ˜εck is the cracking strain (which is irreversible), ft is the tensile strength, and E0 is the initial undamaged elastic modulus. The damage variable, d , is a scalar defined in terms of the effective stress tensor and hardening or softening variables, which can be independently defined for either compression or tension, respectively. These values control the evolution of the yield surface and the degradation of the elastic stiffness, Del . Along with the yield surface function, a flow potential function is required to define the plastic flow. In the present CDP model, a Drucker- Prager hyperbolic function is used for the flow potential (Lubliner etal. 1989; Lee and Fenves 1998). The thermal expansion strain takes into account the effect of the temperature change in the concrete mix with respect to the room temperature promoted mainly by the hydration process, especially at early ages: (9) σ =(1−d)D el 0 :ε el (10) ε=εel +εin +εc+εs+εth (11) ε c = σ c (t 0 ) Eci ·ϕ(t,t0) . (12) ˜ ε in =˜εck − d 1−d · f t E0 where α is the thermal expansion coefficient, T is the temperature field obtained from solving Eq.(6), and I the identity tensor. In order to characterize the material response with the use of the CDP model, it is therefore necessary to provide the material elastic constants (i.e., Young’s modulus, E , and Poisson’s ratio, ν ), coefficient of thermal expansion ( α ), uniaxial tensile behavior in terms of stress-opening (e.g., a linear function defined by the tensile strength, ft , and fracture energy in mode I, GF ) and damage-opening laws, uniaxial compressive behavior in terms of stressinelastic crushing strain and damage-inelastic crushing strain laws, and the Drucker–Prager associated parameters (i.e., dilation angle, eccentricity, surface shape parameter, and compressive biaxial to uniaxial strength ratio). This model is available in the commercial software Abaqus (SIMULIA Corp 2016) and more details on its implementation can be found in (Montero-Chacón etal. 2015, 2017). As explained in the next section, the previous CDP parameters can be defined in terms of the temperature, which is obtained in the thermal analysis, and the curing time. Although early age cracking is a coupled thermo-mechanical problem, the thermal and mechanical problems can be solved in a sequential process as the mechanical dependency of the thermal properties has been assumed negligible. In the cases presented herein, however, the influence of the curing age in the material properties is stronger than that of the temperature as gradients below 30°C are expected. 2.3 Summary oftheMethodology The model described above allows the estimation of the optimal stripping time for concrete structures considering the cement hydration process and potential early age cracking. We present a methodology for the analysis of early age cracking in large concrete structures by implementing the aforementioned models with the FEM. The procedure consists of the following steps: • Step 1: Determination of the volumetric heat flux [use Eq.(5)]. • Step 2: Identification of the mechanical properties of the concrete in terms of its age. • Step 3: Solving of the thermal problem (using the volumetric heat flux from step 2). • Step 4: Solving of mechanical problem (using T obtained in step 3). • Step 5: Determination of the stress fields and crack widths (based on equivalent plastic strains). (13) εth = α(T − Tr)I Page 5 of 20 Cifuentesetal. Int J Concr Struct Mater (2019) 13:41 • Step 6: On-site monitoring (optional) and standard checks. Step 5 can be implemented within a specific objective function in order to optimize the stripping time, which is already accounted for in the numerical model. This becomes very relevant in the case of large structures where time plays an important role in the cost of the structure and, as is already known, its execution is somehow limited by the curing time. 3 Material Characterization The two first steps of the methodology require both the determination of the volumetric heat flux and the identification of the mechanical properties of the concrete in terms of its age. Therefore, it is mandatory to characterize the input material parameters used in the present methodology so as to complete the analysis. In this section, we present an experimental approach to the characterization of such properties. 3.1 Measurement oftheHeat ofHydration One of the main aims of the numerical model is to consider the heat of hydration of the cement during the curing process of the concrete. This issue has been analyzed by concreting a 1m side cube with embedded temperature sensors as described below. Although the heat of hydration of the cement is usually measured under adiabatic or semi-adiabatic conditions (Krauß and Hariri 2006; Schindler and Folliard 2005; Ulm and Coussy 1998), in this case the cube was not isolated, making possible the calibration of the numerical model in a massive element in which the heat of hydration is very high (especially at the center of the cube) and with thermal interaction with the environment in realistic conditions. The classical method used in curing monitoring are based on the analysis of the temperature profile (Azenha etal. 2009). A non-destructive sensing system has been implemented with a low-cost and compact design, especially suited to be embedded into concrete. Wired sensors have been chosen for the sake of simplicity and in order to gather the information required by the numerical model. Concrete is an extremely aggressive material at early stages (Neville 1995). Thus, the sensor layer exposed to the surrounding concrete must ensure an accurate measure of the temperature but also be protected from the direct contact. Then, the sensors are placed within freshly poured reinforced concrete and the first signals are checked to ensure that the system can be used from the first pour. The sensors were tested so as to evaluate the suitability of the protection. The results showed no effects on the response and accuracy of the sensor. The digital temperature sensor DS18B20 (Maxim Integrated, Inc.) has been used. This 1-wire sensor is fairly accurate and can give up to 12 bits of precision. It can work with any microcontroller using a single digital pin, and multiple sensors can be directly connected to the same pin since each one has a unique 64-bit identifier. The sensor covers the range of temperatures for the target application. 3.1.1 Calibration andSealing Tests Preliminary tests were carried out for the characterization and verification of the sensors before placing them into the concrete. The linearity and accuracy of the sensors were compared with two thermocouples. The tests were performed by immersing the sensors in a container with water, as shown in Fig.1a. It must be noted that water has two main advantages over air: it requires an easier control of the temperature and it shows higher stability. Moreover, it allows checking the proper sealing of the sensors. To protect the sensors and ensure the sealing, they were coated with a special lacquer and resin. The sensor was found to work accurately when compared to the temperature readings of the thermocouples. It must be remarked that the sensor follows a similar evolution to that of the references with an offset of only 0.29 ± 0.5 °C. Figure 1b shows the results of the sealing test performed for 80 sensors. The maximum deviation of the temperature was 0.47°C and no problems in data communication were detected. 3.1.2 Construction Site Conditions A second test was performed on the sensors which replicates, as closely as possible, on site conditions in order to determine the effects of concrete. Thus, the sensors were deployed inside the pour, and the gathered data was transmitted to the 3PB0012 data acquisition board (Sure- Electronics) governed by a PIC24FJ256GB106 microcontroller located outside the mix. A 1m3 mold was designed using steel backed formwork. The mold was filled with reinforced concrete. This test determines if it is possible to use the sensors inside concrete and check the data transmission. A total amount of 80 sensors were deployed covering the entire volume of the mold as depicted in Fig.2a, and a total of 4 sensors were placed on each steel bar. Figure2b shows the final distribution of the sensors tied to the reinforcement bars. For the placement of the sensors a specific part was designed and fabricated using 3D printing. The data acquisition board includes multiplexors and drivers to read the data from the sensors individually. Figure 3a shows the cast concrete cube without the mold, and some internal and external temperature measurements are shown in Fig.3b. The temperature profiles Page 6 of 20 Cifuentesetal. Int J Concr Struct Mater (2019) 13:41 presented in this figure correspond to sensors embedded in the concrete cube at different locations and the room temperature, following the procedure proposed by Azenha etal. (2009). As can be seen in the figure, the temperature increases in the first hours as the cement and water react aggressively, reaching a peak during this time. It must be remarked that some internal sensors reach a temperature lower than others. This is mainly due to the fact that these sensors are located close to the surface, where the heat is dissipated out of the concrete cube. After the first 24h, the temperature drops, following the fluctuations of the room temperature, as observed in Fig.3b. It must also be noted that the cube has not been isolated with the purpose of calibrating the numerical model when considering all sorts of external influences. Therefore, the heat dissipation by convective mechanisms through the outer surface can be accounted for. Fig. 1 a Calibration process of the sensor DS18B20: sensor and thermocouples used as reference immersed in water, and b temperature measurement during the sealing tests. Fig. 2 Arrangement of the temperature sensors on the rebars: a assembly scheme, and b final setup. Page 7 of 20 Cifuentesetal. Int J Concr Struct Mater (2019) 13:41 3.2 Evolution oftheMechanical Properties ofConcrete withAge 3.2.1 Elastic Modulus, Compressive Strength, andTensile Splitting Strength As pointed out in Sect.2.2, the mechanical properties required by the CDP model are mostly defined by the uniaxial tension and compression tests, while the biaxial and triaxial tests are required for the definition of the evolution of the yield surface potential. In this study, we have carried out laboratory tests in order to characterize the uniaxial compressive and tensile behavior of the concrete at different ages. Specifically, we have measured the compressive strength, the Young’s modulus, the split tensile strength and the specific fracture energy of the concrete at the ages of 1, 2, 3, 4, 5, 6, 7, 14, 21, and 28days. In this sense, all the specimens have been made with ready-mix concrete from the same batch. The concrete type used in this study was the one usually employed in construction, with the following weight content ratio of cement/water/sand/gravel/ superplasticizer = 1/0.43/2.31/3.07/2.57/0.009. The sand and gravel used in the mix were siliceous aggregates with a maximum size of 16mm mixed following Fuller’s sieve curve. The cement type used for the paste was CEM-II/ A-L/42.5R, according to UNE EN197-1:2011, in a 325kg/ m3 dosage. A strict control of the specimen-making process was carried out so as to minimize the scatter in test results. Since the proposed methodology is intended for actual concrete structures, the concrete mix has been supplied by the construction supplier, being the same material as the one employed on the actual construction site. The characteristic compressive strength ( fc ) was determined by means of crushing tests on 100mm cubes in accordance with UNE EN12930-3:2009. The indirect tensile strength ( fst ) was obtained through cylinder splitting tests according to UNE EN12930-6:2010. The splitting tests were carried out on 100mm diameter by 200mm long cylindrical specimens. The CDP model requires the value of the direct tensile strength ( ft ). Since the approach presented herein is for engineering practice purposes, the Model Code approximation (fib CEB-FIP 2012) is used: The Young’s modulus of the concrete ( Ec ) was obtained according to UNE EN12390-13:2014 by gradually loading a cylindrical specimen in compression to approximately one-third of its failure load and measuring the corresponding strain. Strain values were measured using two linear variable differential transformer (LVDT) sensors mounted on two concentric steel rings fixed to the concrete specimen and separated 2/3 of the length of the specimen. The mean values of the measured mechanical properties of the concrete and their deviations are given in Fig.4, for different ages. It must be remarked that the maximum deviation was of 12% and the results are in agreement with those obtained by other authors (Dao etal. 2009; De Schutter and Taerwe 1997; Kim etal. 2004; Ojdrovic etal. 1987). As shown in Fig. 4, the experimental results can be accurately fitted by a trilinear curve using the measurements at the ages of 1, 7, and 28days. This approximation (14) ft=0.9fst Fig. 3 a Cast concrete cube used in the calibration process and b experimental measurements in some temperature sensors inside the concrete cube, and the room temperature. Page 8 of 20 Cifuentesetal. Int J Concr Struct Mater (2019) 13:41 a b c Fig. 4 Evolution of the mechanical properties with age: a compressive strength, b indirect tensile strength, and c Young’s modulus. Page 9 of 20 Cifuentesetal. Int J Concr Struct Mater (2019) 13:41 allows to reduce the number of tests needed to determine the evolution of fc , fst , and Ec with age. In the case of the Young’s modulus (Fig.4c), the real trend and the trilinear approximation are practically coincident. Finally, the determination of the parameters describing the flow potential surface (e.g., the Drucker–Prager model) requires bi- and tri-axial tests which are difficult to implement in a structural laboratory (Jankowiak and Łodygowski 2005). However, a global range for the aforementioned parameters, in the case of normal strength concrete, can be found in (SIMULIA Corp 2016). Moreover, a sensitivity analysis of these parameters was carried out and the main conclusion is that the fracture behavior, in the present application, is strongly influenced by the uniaxial behavior. 3.2.2 Fracture Properties In order to determine a size-independent value of the specific fracture energy of the concrete the simplified boundary effect method proposed by Abadalla and Karihaloo (2003), Karihaloo etal. (2003) has been used. On the basis of this method, the size-independent fracture energy of the concrete is obtained by testing, according to the RILEM three-point bending test (3PBT), two different single size specimens with two different notch-to-depth ratios, provided they are well separated ( a/D = 0.05 and 0.50). According to this procedure, the size-dependent fracture energy of the concrete ( Gf ) is obtained for every notch. Then, the boundary effect equations demonstrated by Hu and Wittmann (Cifuentes etal. 2017; Hu and Wittmann 1992) must be applied to each specimen with different notch depth, obtaining a system of two equations and two unknowns, being one of these unknowns the size-independent fracture energy of the concrete, GF , and the other one the transition length, al .Prismatic notched specimens were subjected to 3PBT according to the experimental requirements of the work- of-fracture method described in the RILEM recommendation (RILEM 1985). The geometric dimensions of the specimens were 100 mm in width, 100 mm in depth, 400mm of span, and 440mm in length, with two wellseparated relative notch depths of 0.05 and 0.5. Four samples were tested for each notch to depth ratio and age of concrete. The tests were conducted in a ± 25 kN dynamic machine with a closed-loop servo control. The very low rate of loading was controlled by a crack mouth opening displacement (CMOD) gauge so that the fracture occurred in a stable manner. A reference frame with an LVDT displacement transducer was used to measure the vertical displacement at the midpoint of the specimen as seen in Fig.5. Thus, the load-CMOD (P-CMOD) and load–displacement (P–δ) curves for all specimens were recorded. The supports were of antitorque design, so that any parasitic torque affecting the test specimen was eliminated. As observed in Fig. 6, the maximum value of the specific fracture energy of the concrete is reached at the age of 2days. After that, the values of GF start to decrease slightly. The explanation to this effect is similar to that concerning the fracture behavior of high-strength concrete: when the age of the concrete increases, its compressive strength and Young’s modulus also increase. Thus, this means that the older the concrete is, the more effect the cement paste has on its fracture behavior and its stiffness reduces the frictional part originated by the coarse aggregates, which on the other hand provide higher fracture energy values (Cifuentes and Karihaloo 2013). At the age of 1day, the strength of the concrete is still very low, and this is reflected on its fracture energy. This effect is related with the evolution of the brittle behavior of concrete with age, when the stiffness of the cement paste increases due to the increase of the degree of hydration of the cement. Figure7 shows the characteristic length, lch , obtained as follows: The characteristic length is an important fracture parameter as it establishes a relationship between the three main fracture properties of concrete (Hillerborg etal. 1976). Since lch is related to the brittleness (15) l ch = E c G F f2 st Fig. 5 Three‑point bending test of a notched specimen according to the RILEM work‑of‑fracture method. Page 16 of 20 Cifuentesetal. Int J Concr Struct Mater (2019) 13:41 Fig. 15 Retaining wall construction in Loja (Granada, Spain): a main dimensions of the wall in meters, location of the temperature sensors S1 to S8 and indication of the construction stages and, b in situ construction of the wall. Fig. 16 Finite element model of the retaining wall: a C3D8T elements for concrete, and b T3D2 elements for the steel rebars. Page 17 of 20 Cifuentesetal. Int J Concr Struct Mater (2019) 13:41 be directly measured (SIMULIA Corp 2016). For this reason, the authors suggest the used of inelastic strains (i.e., the equivalent plastic strains, ˜εpl t ) combined with the element size ( hel ), so as to estimate the crack width through the following expression: Finally, since the ULS and SLS states have been successfully checked, we can remark that the work plan, especially the stripping time allocation, was appropriate. This was also confirmed by the experimental observations. 6 Conclusions One of the main problems in the construction of large concrete structures is early age cracking, a phenomenon promoted by the exothermic reaction resulting from cement hydration, which rises the temperature in the mix producing temperature gradients that eventually generate thermal stresses. Moreover, this problem becomes of utmost importance in staged constructions and the (16) w ∼ hel ˜ε pl t. Table 2 Thermophysical parameters considered in the thermal analysis. Parameter Value Density, ρ (kg/m3) 2240 Coefficient of thermal expansion, α (1/K) 10−5 Thermal conductivity, k (W/mK) 2.5 Specific heat, cp (J/kgK) 922 Film coefficient, concrete‑air, hc (W/m2K) 9 Film coefficient, concrete‑formwork, hcs (W/m2K) 1 Room temperature, Tr (°C) 27 Fig. 17 Evolution of the temperature measured by S1, S2, S4, and S5 sensors and its corresponding numerical prediction. Page 18 of 20 Cifuentesetal. Int J Concr Struct Mater (2019) 13:41 determination of stripping times. Thus, it is evident that a methodology for the determination of the stress and cracking states, so as to check its compliance with respect to the standards, is a demand for civil engineers. In this work, a finite element-based methodology for the analysis of early age behavior is presented. It consists of two sequentially-coupled models, namely, a heat transfer finite element model used first in order to determine the evolution of the temperature within the concrete mix due to the hydration process, and a subsequent thermo-mechanical finite element model, based on the continuum damage theory, so as to evaluate the stress and cracking states of the structure. In order to determine the material properties required by these models, an experimental campaign has been carried out. In the first place, the mechanical properties (i.e., elastic and fracture properties) have been obtained through several tests, showing that trilinear time-dependent functions fit well the mechanical evolution. On the other hand, a new experimental setup was defined in order to monitor the hydration process within the concrete mix in terms of the temperature at different Fig. 18 Thermo‑mechanical response of the retaining wall: Temperature distribution (in °C) at a 3 days; b 11 days; and c 28 days; and vertical stresses (in N/cm2) at d 3 days; e 11 days; and f 28 days. Page 19 of 20 Cifuentesetal. Int J Concr Struct Mater (2019) 13:41 locations. These experimental results have been used in the validation of the model, and the numerical thermal and mechanical predictions are in agreement with the experimental results and observation. Finally, the presented methodology has been used for the determination of the optimum stripping time and the thermo-mechanical characterization of evolutionary constructions, namely, a retaining wall site in Loja (Granada, Spain). In this sense, the ULS and SLS states have been properly checked, and the numerical predictions, again, are in agreement with the experimental observations, demonstrating the suitability of our methodology for the analysis of early age assessment in large structures. This methodology is very simple and requires the control of the evolution of the temperature inside the concrete, during the hydration of the cement, as the only verification parameter, resulting in a simple but reliable procedure to be carried out on site and that allows to determine the optimum stripping time of a concrete structure. Future work will be devoted to the optimization of construction times, while reducing the operation and maintenance costs. Acknowledgements The authors acknowledge all the funding provided for the development of the research reported in this study. Authors’ contributions HC planned the experimental and numerical studies. JG and JC designed the sensors and carried out the experimental measurements of temperature. FM and AM developed the numerical modeling and performed the numerical analysis. All authors contributed to write the paper. All authors read and approved the final manuscript. Funding This work has been developed within the framework of activities of the Research and Development project: “T3CI: Technology for curing control infra‑ structure construction” funded by the CDTI and sponsored by AZVI Inc., Aertec Ingeniería y Desarrollo Inc. and Geolen Ingeniería Inc. A partial financial sup‑ port was also provided for this research by the Spanish Ministry of Economy and Competitiveness under Project BIA2016‑75431‑R. Availability of data and materials All data generated or analysed during this study are included in this published article. Competing interests The authors declare that they have no competing interests. Author details 1 Dpto. Mecánica de Medios Continuos y Teoría de Estructuras, ETS de Ing‑ eniería, Universidad de Sevilla, Seville, Spain. 2 Dpto. Ingeniería, Universidad Loyola Andalucía, Calle Energía Solar 1, 41014 Seville, Spain. 3 Dpto. Ingeniería Electrónica, Sistemas Informáticos y Automática, Universidad de Huelva, Huelva, Spain. 4 Dpto. Ingeniería Electrónica, ETS de Ingeniería, Universidad de Sevilla, Sevilla, Spain. Received: 30 November 2018 Accepted: 10 June 2019 References Abdalla, H. M., & Karihaloo, B. L. (2003). Determination of size‑independent specific fracture energy of concrete from three‑point bend and wedge splitting tests. Magazine of Concrete Research, 55(2), 133–141. Azenha, M., Faria, R., & Ferreira, D. (2009). Identification of early‑age concrete temperatures and strains: Monitoring and numerical simulation. Cement & Concrete Composites, 31(6), 369–378. https ://doi.org/10.1016/j.cemco ncomp .2009.03.004. 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