2023 | Book

# Numerical Modeling Strategies for Sustainable Concrete Structures

## SSCS 2022

Editors: Prof. Pierre Rossi, Prof. Jean-Louis Tailhan

Publisher: Springer International Publishing

Book Series : RILEM Bookseries

2023 | Book

Editors: Prof. Pierre Rossi, Prof. Jean-Louis Tailhan

Publisher: Springer International Publishing

Book Series : RILEM Bookseries

This volume highlights the latest advances, innovations, and applications in the field of sustainable concrete structures, as presented by scientists and engineers at the RILEM International Conference on Numerical Modeling Strategies for Sustainable Concrete Structures (SSCS), held in Marseille, France, on July 4-6, 2022. It demonstrates that numerical methods (finite elements, finite volumes, finite differences) are a relevant response to the challenge to optimize the utilization of cement in concrete constructions while checking that these constructions have a lifespan compatible with the stakes of sustainable development. They are indeed accurate tools for an optimized design of concrete constructions, and allow us to consider all types of complexities: for example, those linked to rheological, physicochemical and mechanical properties of concrete, those linked to the geometry of the structures or even to the environmental boundary conditions. This optimization must also respect constraints of time, money, security, energy, CO2 emissions, and, more generally, life cycle more reliably than the codes and analytical approaches currently used. Numerical methods are, undoubtedly, the best calculation tools at the service of concrete eco-construction. The contributions present traditional and new ideas that will open novel research directions and foster multidisciplinary collaboration between different specialists.

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Several constructions in earthquake-prone areas in developing countries do not meet current seismic codes, mainly because of the rampant informal construction. These circumstances require effective seismic retrofitting interventions through solutions of an acceptable cost that allow the most extensive application possible. This research focuses on developing a low-cost, low-carbon-footprint material with the required ductility parameters for seismic retrofitting applications. First, a plain UHPC is optimized under compressive strength, cost, and carbon footprint criteria. After that, the second stage of this study determines the binary combination of fibers, among those available in the Colombian market, that permit reaching the necessary ductility parameters for the desired application at a lower cost. The ductility parameters considered are the energy capacity absorption (g) and the strain capacity at maximum tensile strength (εpc) measured in the direct tensile test. Various statistical and computational tools such as Artificial Neural Networks, Design of Experiments, and Multi-Objective Optimization were utilized to lesser the experimental campaign. The mathematically optimized dosage was experimentally evaluated. Finally, the optimal fiber volume fraction for the necessary UHPFRC ductility parameters for seismic strengthening applications (g ≥ 50 kJ/m3 and εpc ≥ 0.3%) was selected at only 1.7%. This optimal fiber combination was composed of 0.34% of smooth high-strength steel (lf/df = 65) fibers, and 1.36% of normal strength hooked end steel fibers (lf/df = 80). It is relevant to highlight that this optimized UHPFRC outperforms the ductility parameters obtained by other authors with successful applications in the seismic strengthening field.

The prediction of the long-term behavior of prestressed concrete structures is important in order to assess and/or extend the service life of such structures. Here, a modelling of the delayed strains (creep and shrinkage of concrete and relaxation of steel), based on the relations of the next Eurocode 2 (EC2), is used to predict the behavior of the internal vessel of the VERCORS mock-up of a French NPP. This modelling considers the influence of the temperature and of the relative humidity (varying under service conditions). The predicted delayed strains are compared with the measurements and different hypotheses are tested to improve the prediction of the delayed strains.

Finite element approximations of phase-field models for fracture are often used to simulate cracking processes in solids and structures. However, non-linearity, the requirement of extremely fine meshing, and/or large-scale simulations make numerical crack prediction a tedious task with this family of models. Such problems demand enormous computational resources. Under a sequential computing framework, these lead to extremely slow computations with non-feasible computer processing times. As a remedy, domain decomposition approaches that facilitate parallel computing can subdue these issues and significantly decrease computational time and memory. This contribution discusses and compares two ways of setting up domain decomposition for phase-field models under a distributed computing framework. Notably, in the context of parallel computing, a monolithic strategy set up via the vectorial finite elements is compared to a staggered finite element strategy for a hybrid phase-field model. A detailed comparison of performance, scalability, and efficiency on thousands of parallel processors is established for a large-scale fracture mechanics problem with millions of unknowns.

The present work describes the analysis of a long and jointless concrete foundation reinforced with conventional steel meshes and discrete polypropylene fibers. A thermo-mechanical nonlinear transient simulation is performed to assess the cracking risk and magnitude of the fiber reinforced concrete (FRC) due to the heat development generated from the cement hydration in the early stages of the concrete hardening phase. The thermal and cracking material data considered in the constitutive model are calibrated from the experimental program conducted when casting the concrete foundation. The concrete shrinkage, viscoelasticity and maturity concepts are also considered in the analysis.The results of the numerical simulations revealed an adequate performance of the hybrid reinforcement to limit the crack opening of the concrete foundation since early ages, while significantly reducing the conventional steel reinforcement ratio.

This work aims to fill the gap between experimentation on laboratory specimens and structural diagnosis of mass concrete hydraulic structures affected by alkali-aggregate reaction (AAR) by conducting numerical and experimental investigations on an existing hydroelectric facility affected by AAR.A large experimental program was performed to characterize the mechanical properties and the kinetics of the AAR chemical reaction for the original mass concrete used in the construction of the facility (maximum aggregate size of 76 mm). The importance of considering mechanical and chemical size effects is discussed, on the basis of the asymptotic fracture energy and the free AAR expansion curve.The developed phenomenological hygro-chemo-mechanical approach for AAR modelling in mass concrete hydraulic structures is presented. The efficient and yet simple approach is based on three analyzes: transient thermal analysis, transient hygral analysis, and final multi-physical analysis that includes mechanical loading. The modelling approach was validated with existing benchmarks from the literature and provided very promising results, despite the simplifications made and the assumptions for some uncertain input parameters.Application of the numerical modelling approach to the existing hydraulic facility demonstrated its feasibility in an industrial context. It also provided fairly similar damage pattern if compared to the existing cracking pattern and improved the understanding of the complex structural behaviour of the facility. Comparison of displacement model predictions and available monitoring data allowed to assess an important size effect between laboratory and in-situ expansions.

Based on the lower bound static approach of the yield design (or limit analysis) theory, this paper proposes and develops a simple method for deriving the biaxial interaction diagrams of a reinforced concrete section at both ambient and elevated temperatures. Such a method is an extension of the work of Pham et al. [5] (A straightforward procedure for deriving the biaxial interaction diagrams of RC sections in fire) where the previous complex 3D failure surfaces are simplified here to a superposition of simple 2D interaction diagrams for different orientations of the resulting bending moment in the section. In addition to the proposed theoretical solutions, their validation is provided by their favourable comparison with some experimental results available in the literature.

This work follows studies conducted in the framework of the French research program MaCEnA (PIA), aiming to predict air leakage through a reinforced (and prestressed) concrete structure. As mentioned by the international Benchmark VeRCoRs, only very few teams were able to predict them and variations of at least one order of magnitude between participants were observed.Reinforced concrete tightness estimation is of the utmost importance for confinement vessels but also to assess concrete structures durability. One of the reasons for these difficulties lies in the fact that air leakage prediction is the last step of complex, multiphysics and coupled simulations. On the one hand, to predict concrete permeability, saturation evolution of the porous network needs to be correctly addressed. On the other hand, cracks predictions (numbers, openings, and appearance time) is essential but not sufficient since roughnesses, tortuosities and connectivities of these latter also strongly influence the leakage rate. After a first part showing the capacity of the used model to mimic the behavior of a structural representative volume, this contribution quantifies the effect of the use of autocorrelated random fields modelling the tensile strength on the concrete structural leakage prediction. The results highlight that the air leakage prediction can easily vary by one order of magnitude for the same random field parameters. Moreover, during mechanical loading, observation of the cracks evolutions (numbers, openings and positions) allows for quantifying the prevalence of material and structural heterogeneity and explains the sudden evolution of leakage rate.

The reinforcement corrosion due to chloride ingress is an important deterioration mechanism, which may compromise the service life of reinforced concrete structures. This study presents a bridge monitoring system coupled with an advanced chemo-mechanical computational method for an estimation of chloride ingress and reinforcement corrosion. Based on-site measurements, a digital replica of the bridge is calibrated and by applying the degradation models, the reduction of structural performance is simulated. Apart from the structural analysis, the data from the monitoring system can be used to deduce information about the daily traffic crossing the bridge. Pilot applications of the proposed coupled framework are shown for two concrete bridges, where a 150-years-long chloride attack was assumed for the assessment of the long-term structural performance. The structural resistance was evaluated by the methods based on fib MC 2010, namely the estimation of a coefficient of variation method (ECOV) and partial factor method (PFM).

Chloride induced corrosion has been an important issue for many reinforced concrete structures. Over the past decades, numerous transport models has been developed to simulate the process. Most existing transport models focused and are validated only on well-known traditional materials such as regular concrete and cement paste. New materials such as Ultra-High-Performance Concrete (UHPC) and High-Performance Fiber-Reinforced Concrete (UHPFRC), however, are less studied from the numerical perspective. The objective of this study is to propose a new transport model for UHPC and UHPFRC to simulate the water transport process in these less permeable materials. The model has been implemented in an in-house finite element method (FEM) software TransChlor2D and validated with experimental results from Dynamic Vapor Sorption (DVS) test on crushed UHPFRC samples subjected to dry-wet cycles. The research provides a 2D numerical model allowing to estimate durability of UHPC and UHPFRC structures under realistic boundary conditions.

Two methods are proposed to characterize the thermal fingerprint of a binder from an insulated mockup test realized on a jobsite, rather than using a classic quasi-adiabatic test in lab condition. The first part introduces the model used to compute the temperature evolution at early age, using a Finite Element solver. The second part presents the two methods. The first method is based on the estimation of the heat loss of the mockup. Then, a methodology similar to a standard quasi-adiabatic test is done, by computing (i) the total heat generated during hydration, (ii) the hydration rate and (iii) the chemical affinity. The second method is based on an imposed form of the hydration affinity function, with three parameters. A Finite Element model of the mockup is used, and a minimisation between the computed temperature evolution and the experimental one allow to identify the three parameters. The two methods are validated on a purely numerical study. Then, a real example is presented, and the relevance of the two methods are discussed.

The current effort towards the progressive switch from carbon-based to renewable energy production is leading to a relevant spreading of both on- and off-shore wind turbine towers. Regarding reinforced concrete shallow foundations of onshore wind turbine steel towers, possible reductions of reinforcement obtainable by employing steel fibre-reinforced concrete (SFRC) may increase their sustainability, speed of erection, and competitiveness. At the same time, there is a strong need to extend the life of foundations erected more than 15 years ago, originally designed for only 20 years. The paper presents a numerical investigation based on the results of a research programme in progress at Politecnico di Milano with ENEL, concerning the reinforcement with steel fibres of concrete shallow foundations embedded in a sandy soil subjected to both cyclic and monotonic loading. The approach takes advantage from a careful modelling of soil-structure interaction to highlight the safety margins correlated to conventional design and shows how the multi-directional resistance of SFRC allows a significant reduction of resources, preventing any brittle behaviour correlated to a reinforcement reduction.

This paper explores the possibilities of pumped storage hydropower (PSH), checking the possibilities of using new engineering tools such as 3D printing. The use of such technology for concrete has gained rapid development in recent years due to the advantages in structural optimization and economy with formwork in conventional construction. Practical engineering applications have proven the applicability of 3D printing in large-scale construction of building components, and compared to conventional manufacturing methods, this advanced technique has several advantages and offers almost unlimited potential for geometric complexities. We explore new design conceptions with the help of numerical modeling in two ways: (i) during the early ages considering the phenomena of hydration; (ii) after hardening of concrete verifying the integrity of the structure. The results indicated that numerical modeling can point to new solutions that will help address the challenges posed by greater sustainability in energy generation and storage in the 21st century.

After a rapid state of the art, an innovative numerical method dedicated to reinforced concrete is presented. Constructed upon a strong mathematical basis, this method gives qualitative results on real-life projects. It illustrates the contribution dual analysis can have to the civil engineering world, bringing together robustness, readable results, and error bracketing.

In the context of regulatory changes, EDF CIH has been conducting research on concrete pathologies for more than 25 years. This research has led to the development of a numerical model for assessing the behaviour of affected structures. This model, which is now used industrially, is an integral part of the sustainable and safe operation of a structure with swelling. It enables the structure to be re-qualified, but also to efficiently design the maintenance programs for EDF Hydro's facilities.

The physical origins of the properties controlling the thermal response of nanoporous materials are fundamentally related to atomic-scale processes. Therefore, the techniques that enable assessing the nanoscale are required to properly understand the thermal properties of cement-based materials. In this paper, we review the techniques of classical molecular simulations that can be used to link the structure of materials to their thermal properties. We focus on the heat capacity, thermal expansion, and thermal conductivity. Results on various phases present in cement systems (tricalcium silicate, C-(A)-S-H, Friedel’s salt, and ettringite) are presented. The fundamental property data provided on the thermal properties are valuable input for multiscale modeling and prediction of the thermal behavior of cement-based materials.

This paper investigates the explosive spalling of high-strength concrete and the shear capacity of high-strength reinforced concrete (RC) beams, taking into consideration the impact of carbonation during and after a fire. First, the spalling model of the multi-scale platform was upgraded. In this study, the limit state of spalling was upgraded in consideration of the strain threshold of concrete in the strain softening range. This upgraded spalling model was validated by experiments on ultra-high-strength concrete during high-temperature heating. Based on the simulation results, explosive spalling was computationally predicted by the proposed model. Second, shear failure of high-strength RC beams subjected to high-temperature fire heating was analytically investigated and the proposed model was found to be able to roughly reproduce shear capacity and ductility after high-temperature heating. High concentration of carbon dioxide (CO2) was found to have a large effect on the shear behavior of RC beams, increase their stiffness and shear capacity.

Rock-shotcrete interfaces are commonly encountered in mining and civil engineering infrastructures, which can trigger localised failure due to stress concentration. These interfaces are usually reinforced with support systems such as rock bolts and the behaviour of rock-shotcrete-bolt systems is often difficult to predict mechanically. In this study, we introduce a new technique to model rock-shotcrete interfaces embedding rock bolts using the finite element method. The proposed approach is implemented in the general purpose simulation package Abaqus via its user-defined element (UEL) subroutine. The proposed model takes into account the uneven interface roughness and the complex interaction between its components. The cohesive stiffness of the model degrades proportionally to the damage that occurs due to this interaction. The stiffness of the bolt connection and its location are also considered in the proposed mathematical formulation. The present bolted cohesive element has been validated experimentally; good agreement has been obtained between the measurement and numerical simulation under the conditions of direct shear test and bolt pull-out tests. Mesh independence has also been verified by examining the effect of mesh size on the overall force-displacement response of typical structures. With the model at hand, the effects of key installation parameters such as number of bolts, their inclinations and material properties have been investigated.

Concrete mix design is an important stage in the design of concrete structures, especially in the case of specific structures such as high-rise buildings, long bridges, and other massive structures, or when a specific type of concrete is used, such as green, recycled, high-strength, lightweight, etc. The proper design of the mix proportions assures that the concrete is as economical as possible, and that the successful construction and exploitation stages are provided. Concrete mix design methods include analytical, experimental, and statistical methods. Determination of the optimal mix proportions of concrete, according to the relevant concrete property is commonly obtained by using a hybrid of these methods, called the semi-experimental methods which usually include some statistical method combined with experimental testing. This paper determines the feasibility of application of ANSYS for the mix design of concrete reinforced with carbon nanotubes or carbon nanofibers. The work here explores the possibilities given by the program, examines the feasibility of numerical modeling in concrete mix design, and compares the results of the numerical simulations with the results of previous experimental testing of CNT/CNF reinforced concrete.

This paper employs computational simulation to investigate the seismic performance of a prototype 14-story building with core-walls, located in Downtown Los Angeles and designed in accordance with the pertinent minimum code requirements. The computational representation of the building employs the beam-truss model (BTM) for the walls and floor slabs. The BTM allows capturing the cyclic inelastic behavior of RC walls and slabs, while being conceptually simpler than, e.g., continuum finite element models. Nonlinear static and dynamic analyses are conducted. The latter consider a set of triaxial ground motions scaled at two intensity levels, namely, those of the design earthquake and the risk-targeted maximum considered earthquake (MCEr).The analyses provide insights into the evolution of structural system damage and lateral strength degradation, while also elucidating the complex interaction between the webs and flanges of the core wall and the system effects associated with coupling between the walls, beams, slabs, and columns. The potentially detrimental effect of the multidirectional nature of the seismic motion on the inelastic deformability of the wall components is also demonstrated. The implications of the obtained results, in the context of the currently employed performance-based seismic design procedures in the United States, are also discussed.

Refined physics-based models generally present a relevant number of parameters to calibrate against experimental data, which might be unavailable for the mixture or the service scenario of interest. This represents one of the most relevant issues in material modelling, especially when descriptive models are adapted to serve as predictive ones. Additionally, accurate small-scale models are particularly suitable for simulating laboratory tests. The up-scaling to structural members, or even entire structures, requires the identification of bridging parameters, responsible for bringing the small-scale models’ accuracy into the engineering models adopted for the long-term prediction at the structural level. This paper presents a methodological approach to deal with the uncertainty featuring the models calibration in case of limited experimental data. In addition, a strategy of up-scaling, relying on the fuzzy logical approach is presented. The activity performed is framed into the Horizon 2020 project ReSHEALience [1].

Stress evolution of restrained concrete is directly related to early-age cracking (EAC) potential of concrete, which is a tricky problem that often happens in engineering practice. Due to the global objective of carbon reduction, Ground granulated blast furnace slag (GGBFS) concrete has become a more promising binder comparing with Ordinary Port-land Cement (OPC). Although GGBFS concrete produces less hydration heat which further prevents thermal shrinkage, the addition of GGBFS highly increases the autogenous shrinkage and thus increases EAC risk. This study presents experiments and numerical modelling of the early-age stress evolution of GGBFS concrete, considering the development of autogenous deformation and creep. Temperature Stress Testing Machine (TSTM) tests were conducted to obtain the autogenous deformation and stress evolution of restrained GGBFS concrete. By a self-defined material sub-routine based on the Rate-type creep law, the FEM model for simulating the stress evolution in TSTM tests was established. By characterizing the creep compliance function with a 13-units continuous Kelvin chain, forward modelling was firstly conducted to predict the stress development. Then inverse modelling was conducted by Bayesian Optimization to efficiently modify the arbitrary assumption of the codes on the aging creep. The major findings of this study are as follows: 1) the high autogenous expansion of GGBFS induces compressive stress at first hours, but its value is low because of high relaxation and low elastic modulus; 2) The codes highly underestimated the early-age creep of GGBFS concrete. They performed well in prediction of stress after 200 h, but showed significant gaps in predictions of early-age stress evolution; 3) The proposed inverse modelling method with Bayesian Optimization can efficiently adjust the aging terms which produced best modelling results. The adjusted creep compliance function of GGBFS showed a much faster aging speed at early ages than the one proposed by original codes.

The behavior of confined water molecules in C-S-H has a great influence on various physical and chemical properties of C-S-H gel, which further determine the macroscale behavior of cement-based materials such as creep, shrinkage, and cracking. Here, using molecular simulations, we investigate the effect of relative humidity (RH) on the behavior of C-S-H at the molecular scale taking as reaction path the interlayer distance (spanning interlayer pores up to small gel pores). The confining pressures, desorption isotherm, the potential of mean force (PMF), stable basal spacings, meta-stable domains, elastic modulus perpendicular to the pore surface, and cavitation of nano-confined water are analyzed. We evaluate these properties as a function of interlayer distance at various RH, ranging from (liquid) saturated (RH = 100%) to completely dried (RH = 0%) conditions at ambient temperature (300 K). From the PMF profiles and pressure isotherms, we can identify equilibrium basal spacings and meta-stable domains. We observe that the stable basal spacing decreases when the RH decreases, therefore interlayer pore shrinkage contributes to drying shrinkage of cement-based materials. We also show that cavitation of water in small C-S-H interlayer spaces is pore size-dependent. Each of these properties can be useful to explain the physical origins of the thermo-hygro-mechanical behavior of cement-based materials and provide a methodology to improve the performance of these materials.

Using ultrahigh-performance fibre-reinforced concrete (UHPFRC) for reinforcement lap splice field connections simplifies construction details, reduces on site labour work and overall enhances connection performance and durability. Existing design equations for determining the required development length for normal concrete cannot be used for fibre-reinforced concrete. This paper presents the development of a refined nonlinear finite element model at rib-scale using the 3D concrete constitutive model EPM3D implemented in ABAQUS which enables explicitly expressing the bond performance of lap splices in UHPFRC according to the tensile properties of the concrete, the cover thickness and the bonded length. The numerical results show accurate simulation of the maximum strength, splitting failure mode, crack pattern, and steel stress distribution over the bonded length from different configurations of experimental bond tests. This methodology illustrates the value of nonlinear finite element analysis toward the harmonization of a bond test configuration and its contribution into the development of design guidelines for UHPFRC lap splice connections.

3D concrete printing technology (3DCP) have gained wide attention. They indicated their potential to become a serious supplement to conventional concrete casting in molds. The main reason for this is it directly addresses the challenges related to the sustainability and productivity of the construction industry. However, the current practice is based on the trial-and-error procedure, which makes the research of the 3DCP process expensive and time-consuming. One of the reasons is that there exist significant knowledge gaps regarding the relations between the design, material, and process parameters. Therefore, it is of vital importance to establish a relation between the process parameters and the printed product to avoid unreliability and failure. By implementing a numerical simulation of the 3DCP process, a more fundamental understanding of the relations between the printing process, the process parameters, and the properties of the printed product could be achieved.In this study, layer-wise Finite Element Method (FEM) combined with a pseudodensity approach, known from in topology optimization is applied. Along with the progressing printing process, all material parameters vary spatially and temporarily due to the time dependency of the curing process. The numerical simulations allow to reliably estimate the failure mechanisms that might occur during the 3D concrete printing of a wall structure.

The fracture process of concrete involves phenomena of considerable complexity, such as scale effect and softening behavior, which are directly linked to the heterogeneity of this material. These phenomena pose great challenges to the fracture modeling. Probabilistic models that deal directly with heterogeneity are a powerful tool to overcome these challenges, since they consider the natural variability of the mechanical responses. The present work refers to the simulation of concrete fracture by means of a 3D probabilistic finite element model in which interface elements are employed to represent the cracks explicitly. Friction between crack surfaces is also taken into account in the model. The three-dimensional modeling of cracks allows the fracture process to be analyzed in a more realistic way. Different sample sizes were considered to enable the assessment of the scale effect prediction, taking into account empirical reference data. The possibility of occurrence of different softening levels was also investigated.

During a 3D concrete printing process, the mechanical charactesitics of the material at hand are continuously evolving due to hydration. From the theoretical point of view, the constitutive relations must be defined in rate form. We think that this restriction is mandatory and must be taken into account. On another hand, to predict eventual instabilities, the finite strain range is a priori assumed within the formulation where the kinematics must be adapted in adequacy. Here use is made of a multiplicative decomposition of the actual deformation gradient into its known intermediate part at an earlier time and the relative deformation gradient with respect to the configuration at that time. The incremental constitutive relations and evolution equations can then be ideally defined on the above intermediate configuration prior to be transported back to the reference configuration within a Lagrangian formulation. The early age creep is here introduced through an internal variable approach that is motivated by the generalized Maxwell model. A set of finite element simulations is performed to illustrate the efficiency of the proposed framework. In particular, a slump-test-like example is given where a method can be highlighted to help identifying, in future works, the material parameters relative to the early-age creep.

Concrete is one of the most used materials worldwide with a high environmental impact. Over past years, numerous attempts to minimize the associated effects on the environment by using more sustainable materials or by improving the performance of the material (e.g. high strength concrete, fiber reinforcement) have been introduced. The increase in material performance must be accompanied by better models and design approaches to take full advantage of the potential benefits. In this contribution, a discrete fiber and a multi-level model for the analysis of SFRC structures are used to assess the influence of a chosen fiber type, content, and orientation on the structural response. Zero-thickness cohesive interface elements capture the post-cracking behavior. The discrete fibers are modeled using truss elements. The bond between fibers and concrete is modeled using an elastoplastic bond-slip law, and the effects of fiber bending, friction, and matrix spalling are accounted for using a sub-model at the level of the interface element. The predictive capabilities of both models are validated and compared with fiber pull-out experiments. Finally, the prospects of applying complex FE models in conjunction with methods of optimization to design an SFRC tunnel lining segment are discussed. The objective is to minimize the total segment thickness and the fiber content while a constraint ensures that the required failure probability is retained.

Chloride-induced corrosion of steel reinforcement in concrete, creep and shrinkage and freezing-thawing are some of the major causes responsible for deterioration of reinforced concrete (RC) structures. The repair of damaged structures results in relatively high direct and indirect costs. Therefore, to predict their durability it is important to have a numerical tool, which is able to account for the above mentioned processes and their consequences for the structural safety. In the paper a recently developed coupled Chemo-Hygro-Thermo-Mechanical model for concrete is briefly discussed. The model is implemented into a 3D finite element code and it is aimed to model processes related to corrosion of steel reinforcement, freezing-thawing and creep and shrinkage of concrete. The macro-cell corrosion of steel reinforcement accounts for all relevant processes before and after depassivation of reinforcement and it is coupled with the mechanical model for concrete, which is based on the microplane model. Loading due to freezing-thawing of concrete is formulated in the framework of poromechanics. Drying creep of concrete is simulated based on the hygro-mechanical model at the meso scale. Investigated is the influence of the interaction between non-elastic deformations of cement paste (basic creep and shrinkage), load induced damage and heterogeneity of concrete. The application of the model is illustrated on several numerical examples.

An important function of a reactor containment vessel is to provide sufficient leakage tightness during normal operation and severe accident condition. The purpose of this paper is to present a set of numerical models along with a study methodology to understand the mechanisms most responsible for aging and leakage tightness degradation of prestressed reinforced concrete containment vessels without liner. The solution proposed here is adapted to the study of full-size buildings while most research work dealing with this matter offers sophisticated modeling techniques mostly suitable for local studies.The methodology is applied to study the thermo-hydro-mechanical behavior of Vercors mock-up [1]. Vercors is an experimental mock-up of a reactor containment building at 1/3 scale (with diameter of 7.7 m, height of 20 m and thickness of 0.4 m) built at EDF Lab “Les Renardières” near Paris in 2015 to analyze the possibility of the life extensions of French Nuclear Power Plants. The mock-up is finely instrumented, and its behavior is monitored from the beginning of the construction. In the numerical application of our modelling methodology to Vercors mock-up, the thermo-hydro-mechanical models are all calibrated by considering first the material test specimen and then the in-situ measurements, to have a representative digital clone of the mock-up. All necessary models and resolution strategy are implemented in Code Aster® (EDF) finite elements program.

This paper presents the numerical modeling of plain concrete specimens subjected to uniaxial tensile stresses. The simulations are performed using a three-dimensional macroscopic probabilistic model for semi-explicit concrete cracking. As it is well known, concrete structures are largely sensible to the scale effects that can be attributed, among other reasons, to the heterogeneous nature of the material. The model used herein, which is developed in the framework of the finite element method, considers the material heterogeneity through the assumption that each finite element represents a volume of heterogeneous material, with mechanical properties of tensile strength and fracture energy being randomly distributed over the mesh according to the Weibull and lognormal distributions, respectively. The cracks are created with different energy dissipation according to an isotropic damage law. The results are obtained through Monte Carlo simulations using a parallelization strategy with OpenMp to allow feasible 3D simulations of real structures in a viable computational time. With the purpose of modeling the uniaxial tensile test and verifying the prediction of the scale effects, simulations of three prismatic plain concrete specimens with different sizes are performed.

This study presents a new numerical approach using tools developed to perform a molecular simulation to investigate the wall effect on aggregates and mortar distribution in concrete. Aggregates are represented by spheres interacting via a generalized truncated Lennard-Jones potential. This approach allows obtaining the particle profiles according to the reference frame of interest (e.g., the confined directions). Then the particle-based distributions are transformed into continuum profiles of volume fractions using a convolution. Based on volume fraction profiles, transport or mechanical properties are estimated by the Mori-Tanaka scheme from classical homogenization. Results are compared to experimental work. The numerical method could be generalized and used for other applications in different fields. In civil engineering, perspectives include using the aggregate distribution to conduct a finer analysis, and the results would be extremely relevant for the prediction of the water content profile and the evolution of pathologies such as carbonation, corrosion, ISR, etc..

The study aims to investigate the mechanism of early-age cracks in different massive concrete structures (i.e. tunnels, bridge foundations and underground parking garages), with the objective of answering the following three specific questions: 1) How does the parameters of concrete proportion mix (e.g. w/c ratio, cementitious materials, aggregates, etc.) influence the formation of autogenous shrinkage and creep, especially at early age with the focus on the first 24 h? 2) How to build theoretical and numerical model for the process of early-age crack formation and then quantify the damage status of concrete materials? 3) How to link the results derived from material scale to structural scale, and provide useful reference for practical engineering projects? To study the basic mechanism a research program is performed in which different mixes are tested in a Temperature and Stress Testing Machine (TSTM). Furthermore autogenous shrinkage is measured in different ways. Modeling with a FEM-tool is used to predict the risk of early age cracking. The results indicate that the combined shrinkage (or expansion and the relaxation (or creep) during the first hours of hydration have a huge influence on the stresses that develop later and with that are important to determine the risk of cracking in massive concrete structures. Since investigating the stresses that built up in the first hours after casting in such a TSTM is rather difficult, we designed a new version of the TSTM machine in which dog bone specimens are tested vertically in a Universal Testing Machine (Instron).

Despite the increase in computational power, the accurate modelling of crack openings in reinforced concrete remains an open problem for structural elements of complex shapes. Since the national CEOS.fr project dedicated to the control of cracking for large structures, it is accepted that the statistical scaling effect on the tensile strength of concrete and the realism of the concrete steel slip law are two essential ingredients to achieve a good level of accuracy in the prediction of crack spacing and openings. The implementation of these two aspects in finite element codes faces two problems: on the one hand, the statistical scaling effect depends on the dimension of the tensioned zone, which varies with cracking, and on the other hand, the steel-concrete slip is generally longer than the size of the finite elements. In this context, proposing homogenized reinforced concrete finite elements is problematic. The most common methods consist in using random mechanical property fields to integrate the statistical aspect of the tensile strength, and the slip is explicitly modelled by joint elements, preventing the use of homogenized elements. However, it is possible to avoid both random draws and explicit modelling of concrete-steel interfaces. The proposed method generalizes the notion of phase fields to address both problems simultaneously. A first phase field integrates the scale effect, and another one the steel-concrete slip. The FE code Castem (CEA) has been modified to allow such generalizations. After having given the theoretical bases of the methods used, we will comment two implementations.

Between 2007 and 2014, UGE, Alstom and other industrials partners developed a new concept of railways track called New Ballastless Track (NBT). The concept was validated under 10 million fatigue cycles on a real-size mock-up at UGE. A first numerical study using a non-linear model was performed to evaluate the possibility of replacing the original reinforced concrete layer of the track slab with Steel Fibre Reinforced Concrete. The objective is to simplify the NBT track’s construction and take advantage of the redistribution of mechanical stresses on a hyper-static structure. This study led to the conclusion that this replacement was very relevant.This paper is on optimizing this Fibre Reinforced Concrete (FRC) solution by using the same non-linear numerical model. It is shown that this optimization procedure leads to a significant reduction of CO2 emissions compared with the initial one.

Macro-cell corrosion, as one of the typical deterioration factors to structural concrete, has drawn enormous engineering interests in the past years. Steel corrosion accompanied with macro-cell circuit is related to both electric fields and chemical substances of polarized metals and electrolytes. The dynamically-equilibrated various substances in the pore solutions of concrete act an important role in terms of electron carrying as well as interaction with the porous skeleton of cementitious material. Therefore, it’s meaningful to investigate such multi-ion kinetics associated with macro-cell corrosion to further study the deterioration of reinforcement as well as concrete. This paper contains a numerical and experimental evaluation of the multi-ion kinetics with pseudo concrete electrolyte. As a key species of cementing material, the authors focus on the profiles of Ca2+ concentrations as a major cation of concrete around the positive and negative electrodes, which are significantly affected by the initial saturation of calcium hydroxide and the supply of carbon dioxide. Three predominant mechanisms are summarized depending on the Ca(OH)2 and CO2 condition. Experiments and numerical simulation applied to pseudo concrete show satisfactory correlation to reveal the governing mechanism based on polarization and the Nernst-Plank theory with multi-ion mass equation.

Discrete models, which are based on two-node elements or particle assemblies, offer advantages in modeling cracking and other discontinuous phenomena. Within the community of developers of discrete models, there are two main veins of thought: 1) the discrete nature of the model represents physical features of the material; or 2) the discretization strategy should not have a dominant influence on the analysis results. Advocates of the first vein of thought can argue, with some merit, that the discrete approaches effectively capture the effects of large-scale heterogeneity of concrete. From another viewpoint, however, it is attractive for the models to retain selected qualities of the continuum approaches including, for example, elastic homogeneity under uniform straining. Similar qualities are attractive in scalar field analyses (e.g., of moisture or heat transport) that couple with mechanical analyses for simulating the durability of concrete. The research presented herein resides in the second vein. One goal is to provide an unbiased framework without artificial heterogeneity, such that the presence of actual heterogeneity (in the form of phase fractions, interfaces, reinforcing bars, short fibers, etc.) can be explicitly represented.