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The shearing behavior and permeability of the interfaces between rock and cement are critical for the stability analysis of supporting structures in underground engineering projects, especially after exposure to thermal loads. In the present study, an advanced test method was proposed to preform shearing tests on granite–cement interface samples after pre-heating treatment. The samples consisted of two semi-cylindrical parts. The first part was granite, and the other was cement with two different water–cement ratios (for example, 0.3 and 0.5). The shear stress–strain curves, peak shear strength at shear failure, as well as the residual shear strength at the residual shear stage, cohesion, and internal shear angle, were analyzed. The results were correlated to the pre-heating temperatures and cement–water ratios, while the initial permeability before shear loading, along with the permeability evolution during the shearing process, was also analyzed. It was found that after higher pre-heating treatment the lower the peak shear strength, cohesion, and internal friction angle of the samples would be. Meanwhile, the initial permeability was higher. In addition, during the shearing process, the shear stress and permeability levels increased rapidly, reaching maximum values when shear failure occurred. Then, the shear stress and permeability levels decreased gradually to stable values at the residual shear stage. The degradation in the shear strength, cohesion, and internal friction angle caused by the pre-heating treatment may be attributed to the microcracks induced by the thermal expansion differences between the granite and cement and the evaporation of the chemically bound water in the cement. The shearing behavior and permeability evolution of the granite–cement interface samples were determined to be closely related to the water–cement ratios. For example, under the same normal stress and pre-heating temperature conditions, when the water–cement ratio was higher, the porosity of the cement was greater and the adhesion between the granite–cement interfaces was lower. Therefore, the peak shear strength at the shear failure point was also lower. In addition, the shear stress–strain curves showed stronger ductile behavior, and the cohesion and internal friction angle were lower. Meanwhile, the reductions in the shear stress and permeability levels at the residual shear stage became smaller.

The Callovo-Oxfordian (COx) claystone is chosen as a potential geological barrier for the geological repository of radioactive waste in France, and high-performance concrete is used as a sealing plug and lining in repository facilities. In this study, the shear strength of the interface between the concrete and claystone is investigated in particular. Ultra-high-performance (UHP) concrete is directly cast and cured beside a COx claystone semi-cylinder to make a cylindrical specimen including an interface. First, a microscopic analysis of the interface surfaces using scanned electronic microscope images is presented. It is shown that the adhesion of the UHP concrete to the COx claystone is of good quality and there is almost no initial interface aperture between the two materials. By using a home-designed original device, a series of direct shear tests is performed on cylinder specimens with interface under different confining stresses. The interface deformation and shear strength are quantitatively analysed. It is found that the interface has a bonded cohesion and the shear strength can be approximated by a non-linear function of normal stress. In most cases, the shear deformation does not generate an opening but rather a closure of the interface. The morphology of the sheared interface is also analysed by optical microscopic scanning images.

Thermal shock on tensile behaviour of granite is highly important for understanding of fracturing mechanism in hot dry rock. The effects of heating and water-cooling treatment (HWCT) on tensile behaviour of granite were investigated in this work. The granite samples were first heated to different predetermined temperatures and then rapidly cooled by water. The Brazilian split tests were carried out on the HWCT samples, and the strain gauges were used to measure the evolution of tensile deformation. With the increasing of heating temperature, the tensile stress–strain curves change from linear to nonlinear, the axial tensile strain corresponding to failure point increases, and the tensile strength and tensile elastic modulus undergo a slight increase to decrease as the temperature increases. Finally, the mechanical properties under tensile condition were compared with those under compressive condition. Below 300 °C, the temperature has slight effect on both tensile and compressive strengths. Above 300 °C, the tensile properties decrease significantly after heating temperature threshold of 300 °C, while the heating temperature threshold for compressive properties is 500 °C. The thermal shock has a greater effect on tensile strength than on compressive strength.

Poroelastic properties play an essential role in interaction between deformation and fluid pressure change in porous rocks. These properties can be affected by microstructural evolution such as porosity change and micro-cracks growth. In this study, the modification of poroelastic properties of a hard rock (granite) is investigated in terms of thermally induced micro-cracks. Granite samples are first subjected to a heating–cooling treatment with different values of temperature. The variations of bulk modulus, stiffness of solid grains and Biot’s coefficient of thermally treated samples are determined and analyzed. It is found that both connected and occluded micro-cracks are generated in granite samples. The bulk modulus of porous material is affected by the connected micro-cracks, while the stiffness of solid grains is influenced by the occluded micro-cracks. The Biot’s coefficient is affected by the connectivity of micro-cracks. All poroelastic properties evolve with effective mean stress and a non-linear poroelastic law should be defined.

In this study, three-dimensional non-uniform strain fields and cracking patterns of a clay-rich rock are investigated. Uniaxial compression creep tests are performed on samples drilled in five different orientations with respect to bedding planes. A digital volume correlation method is applied to X-ray micro-tomographic images taken during the creep tests to calculate both full local strain fields and average global strains. Both instantaneous and time-dependent strains, respectively, induced by applied stress and creep mechanism are analysed. Strain heterogeneity inside samples is quantified by calculating strain concentration zones, which are correlated with the presence of stiff inclusions. Cracking patterns of samples are characterized through reconstructed X-ray micro-tomographic images. Correlations between major cracking patterns and strain concentration zones are investigated.

X-ray micro-tomography (XMT) is an efficient technique for non-destructive imaging of morphological structures. It is suitable for monitoring local displacement fields of heterogeneous materials. Digital volume correlation (DVC) methods are widely used for the quantification of local strain fields from highly contrasted XMT images. The aim of this work is to investigate strain localization and cracking process in a hard clayey rock. For this purpose, three-dimensional images have been taken by in situ X-ray micro-tomography on a tested sample under different loading levels and time steps. These images are analyzed with a DVC based method to calculate both local strain fields and averaged global strains. In particular, the progressive localization of strain field with applied stress and creep time is investigated in relation with material heterogeneities. It is found that the strain field localization as well as the cracking process is clearly influenced by the presence of stiff inclusions, pores, weak clayey zones and layered microscopic structure of claystone.

Mechanical behavior and deformation characteristics of rock under unloading conditions are of particular significance for analyzing excavation-induced instability problems of underground rock masses. In this paper, triaxial compression tests with progressive unloading of confining pressure were conducted upon sandstone specimens under different combinations of initial confining pressures and pore pressures. It is shown from the tests that the magnitude of initial confining pressure and pore pressure influences significantly the rock strength, energy conversion, crack propagation, and dilatancy during unloading process. The strength under unloading conditions is in compliance with the linear Mogi-Coulomb criterion. The energy conversion method can be employed to determine the crack damage thresholds during the unloading process. The analysis on cracking process suggests that crack damage thresholds increase linearly with initial confining pressure, but decrease with pore pressure. Under unloading conditions, material yield and brittle failure occur more easily with the increase in pore pressure. Furthermore, given the initial confining pressure, a higher level of pore pressure can accelerate volumetric expansion in the specimens.

Slate frequently encountered in numerous engineering applications basically exhibits significant anisotropies in terms of physico-mechanical properties due to the presence of well-developed foliation structures. The objective of this study is to investigate the mechanisms of foliation effects on the mechanical and failure characteristics of slate in three-dimensional (3D) space under Brazilian test conditions. A series of laboratory tests are conducted on slate with seven different foliation angles (φ), which are defined as the angle between the foliation plane and end surfaces of the specimen. On the basis of each foliation angle, five different loading angles (θ), which are defined as the projection of the angle between the loading surface and the foliation plane on the front side of the specimen, are selected to ensure that 3D space is involved. The high-speed camera and acoustic emission (AE) system are employed to analyse the failure characteristics of slate during loading process. The testing results indicated that the variations of applied failure force (AFF) with respect to loading angle (θ) significantly differ under varied foliation angles. With increase of foliation angle, the anisotropy ratio of the maximum to minimum AFF shows an increasing trend, suggesting that the anisotropy becomes more notable. The high-speed camera visually recorded the initiation and propagation of cracks. The specimen failure can involve two major processes: the local cracks first occurred on the disc flank, and then the fully connected cracks were formed causing the overall failure. The rupture evolution process inside the specimen was characterised by AE energy and AE hits, which was in good agreement with the high-speed camera observations. When the foliation angle is small, i.e. 0° ≤ φ ≤ 15°, or large, i.e. 75° ≤ φ ≤ 90°, the macro-cracks on both sides (i.e., front and back) show similarity to some certain, and the fracture patterns can be considered as two-dimensional (2D). However, when φ is in the range of 30°–60°, the fractured surfaces have 3D spatial distribution characteristics, and the macro-cracks appearing on both sides exhibit an approximately anti-symmetric relationship. It is also revealed that both φ and θ have significant effects on the AFF and the fracture patterns. The results are likely to provide experimental basis for further improving the theory of tensile properties of anisotropic rocks.

This study develops a micro-mechanics-based elastoplastic damage model within the framework of irreversible thermodynamics. In the model, damage is related to growth of micro-cracks, while plastic deformation is induced by frictional sliding along those cracks. The damage criterion and functions of thermodynamic force are used to describe the damage evolution of rocks and determine whether they are damaged. Time-dependent deformation of rock is also taken into account by considering subcritical growth of micro-cracks. For engineering application, the proposed model is implemented in the standard finite element code Abaqus as a user-defined material model (UMAT) by using a specific local integration algorithm. The accuracy of the proposed model is assessed by comparing numerical results with experimental data in conventional triaxial compression tests and triaxial creep tests. The proposed model is then used for simulating the displacement field, damage and plastic zones of the left bank high slope. The predicted results are in a good consistency with field monitored data.

Both experiments and theoretical investigations have evidenced the existence of compressive-shear fracture mode in geomaterials like concrete, rocks and gypsum. Proper description and modeling of intricate fracturing pattern with consideration of strong tension-compression asymmetry in mechanical response remain an open issue in phase-field modeling and simulation. In this work, a new phase field model with plasticity-damage coupling is formulated in the framework of irreversible thermodynamics. Two essential features, tension-compression asymmetry in mechanical response as well as two distinct fracture modes, are taken into account by incorporating two scalar-valued damage variables into the classical modeling framework. By defining a specific free energy density function, the coupling between damage and plasticity is achieved by involving a phase field variable into the yield function. The proposed model is validated at two levels. In the homogeneous cases, the mechanical behaviors of typical geomaterials are investigated in the plane stress condition. Meanwhile, a stress-based crack onset criterion is utilized to capture the distinct failure behavior both in tension and in compression. In numerical simulations, a local numerical integration with implicit return mapping algorithm and plasticity-damage decoupling treatment are developed. Three numerical examples are performed to demonstrate respectively the mode I, mixed-mode and model II fracture in geomaterials. Comparisons between numerical simulations and experimental data make it possible to evaluate the predictive performance of the proposed bi-dissipative phase field damage model. In addition, the local stress analysis is carried out to explain a changing mode of fracture propagation and to demonstrate the existence of tensile-shear (hybrid) fracture mode.

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This paper deals with the impact of climate change on stability of abandoned subsurface cavities in chalk due to its indirect effect on ground water levels. It is the first part of a general work on the hydromechanical behaviour of a partially saturated soft rock (a porous chalk) and the effect of changes in water saturation degree. An experimental investigation including a laboratory-testing program is presented. Different degrees of saturation are imposed by controlled relative humidity conditions. Conventional hydrostatic and triaxial compression tests are performed under drained conditions for saturation degree up to 100% under low confining pressures. The obtained results have allowed to show up fundamental aspects of the chalk behaviour. The high sensitivity of the extracted material to water is described and a water induced plastic deformation is observed.

Granite samples were subjected to heating at different temperatures and rapid water cooling. Hydrostatic compression tests were performed on the thermally treated samples. The initial tangent bulk modulus was measured. The critical value of hydrostatic stress for closing thermally induced micro-cracks was identified and the residual volumetric strain after unloading was determined. Gas permeability of granite samples was also determined under different levels of hydrostatic stress. It is found that the density of thermally induced micro-cracks can be correlated with the residual volumetric strain, both increasing when the pre-treatment temperature is higher. There is a significant increase of gas permeability up to several orders of magnitude as a consequence of micro-cracks induced by the heating and water-cooling process.

A new 2D hydromechanical rigid block spring method is developed for studying hydraulic fracturing in cohesive porous materials. The continuum medium is discretized into an assembly of discrete rigid blocks. Macroscopic deformation and failure are related to local properties of interfaces between blocks. Fluid flow in porous continuum is described by an equivalent discrete fracture network model. Biot's theory is extended to discrete porous interfaces for studying interactions between fluid flow and mechanical behavior. Further, the hydraulic conductivity evolution due to fracture propagation is taken into account through the change of aperture of interfaces. The proposed discrete hydromechanical model is first verified through the response of an elastic isotropic thick-walled cylinder subjected to an inner pressure under the steady state flow condition. The obtained numerical results agree well with the corresponding analytical solutions. Further, the numerical model is applied to studying the hydraulic fracturing of the thick-walled cylinder. The effect of transient flow on fracturing pressure is highlighted. The effect of materials strength anisotropy on fracturing process is also studied. It is shown that the proposed discrete model provides an efficient tool for modeling hydraulic fracturing in cohesive rock-like materials.

In this paper, a micromechanical model is proposed to study the elastoplastic behavior of the Callovo-Oxfordian (COx) argillite. Three scales (i.e., macroscopic, mesoscopic and microscopic) are considered. At the mesoscopic scale, the COx argillite is regarded as a three-phase composite with clay as matrix and calcite and quartz as reinforcements. At the microscale, the clay matrix is a porous medium constituted by clay minerals and interparticle pores. The porous clay is described with an extended Gurson-Tvergaard-Needelman (EGTN) model while the calcite and quartz reinforcements are described with the linear isotropic elastic model. The macroscopic behavior of the COx argillite is determined by adopting the Hill’s incremental formulation. All the numerical aspects including: (1) the integration of the EGTN model with the backward Euler method; (2) the derivation of the corresponding consistent tangent moduli from a new point of view; (3) the realization of the homogenization process, are fully described. The proposed micromechanical model is validated from two aspects. The first aspect is the numerical predictions against the finite element (FE) computations performed on a two-phase unit cell, where the key steps related to the modelling are presented. The second aspect is the comparisons between the numerical predictions and experimental data.

A correlation of creep index (Cα) with high performance is highly recommended for soft clay engineering practice. Current empirical correlations are only acceptable for a few clays. This paper aims to propose a robust and effective evolutionary polynomial regression (EPR) model for Cα of clay. First, a database covering various clays is formed, in which 120 data are randomly selected for training and the remaining data are used for testing. To avoid overfitting, a novel EPR procedure using a newly enhanced differential evolution (DE) algorithm is proposed with two enhancements: (1) a new fitness function is proposed using the structural risk minimization (SRM) with L2 regularization that penalizes polynomial complexity, and (2) an adaptive process for selecting the combination of involved variables and size of polynomial terms is incorporated. By comparing the predictive ability, model complexity, robustness and monotonicity, the EPR formulation for Cα involving clay content, plasticity index and void ratio with three terms is selected as the optimal model. A parametric study is then conducted to assess the importance of each input in the proposed model. All results demonstrate that the proposed model of Cα is simple, robust, and reliable for applications in engineering practice.

In this paper, we investigate the effects of poroelastic properties and permeability on hydraulic fracturing in an anisotropic medium. A hybrid approach combining the EDFM (embedded discrete fracture model) and XFEM (extended finite element method) is proposed. Fractures are embedded into a nonconforming grid used to determine the fluid flow in a porous matrix by the mimetic finite difference method, accounting for an anisotropic permeability tensor. The stress-strain problem is solved by the extended finite element method with the same grid. The fluid flow and rock deformation as well as the fracture propagation are iteratively coupled. The proposed approach is validated against the analytical solutions for Mandel’s problem and the KDG model. A series of calculations are performed, and the obtained results are analyzed to investigate the effects of the anisotropy of permeability, that of the elastic modulus and Biot’s coefficient on the hydraulic fracturing process. It is found that the anisotropy of permeability has a significant influence on the geometrical parameter of a fracture, while the anisotropy of the elastic modulus has a dominating influence on the propagation direction of a fracture. Biot’s coefficient also has an influence on the fracture propagation kinetics.

Fluid flow and fluid-rock interaction mainly take place in fracture network, consequently resulting in deformation and permeability variation of rock and deterioration of the wellbore performance. Mechanical-reactive flow coupling creep tests are performed on cracked granite under various confining pressures and acid and alkaline solution flows. The testing results show that the confining pressure and solution pH significantly influence the creep deformation, creep strain rate, and permeability. A primary creep stage and secondary creep stage are observed in all creep tests in this study; notably, the sample under a confining pressure of 10 MPa and acid solution injection undergoes creep failure for over 2700 hours. The acid solution has a more obvious influence on the creep behavior than that of the alkaline solution. With an increase in confining pressure, the total creep strain and creep strain rate in the samples gradually decrease during the injection of either solution. The permeability of the samples injected with either solution gradually deceases during the testing process, and this deceasing rate increases with the confining pressure. The scanning electron microscopy observations on the crack surfaces after the creep tests show that the surfaces of the fractures injected with the acid solution are smooth due to the dissolution of the matrix, while those injected with the alkaline solution include voids due to the dissolution of quartz. These experimental results could improve the understanding of the long-term transport and mechanical behaviors of wellbore.

In this paper, a new Enhanced Finite Element Method (E-FEM) model is proposed to describe 3D shear fractures of quasi-brittle materials such as concrete. Special attention is made to the failure behaviors in cyclic loadings as it is a common phenomenon in practical engineering. Within the framework of the E-FEM, the discontinuities are locally embedded in the finite elements. Here, two kinds of discontinuity enhancements are used in this model: weak discontinuities allow the model to represent heterogeneities in an unstructured mesh explicitly, and strong discontinuities enable the displacement jumps in finite elements to perform cracks and fractures. In this paper, our interest is focused on the shear sliding discontinuity (mode-II). The closure mechanism is also taken into concern, which simulates frictional sliding forward and backward between the lips of cracks. Then the performance of the proposed model is tested and analyzed by comparing it to experimental results. Certain limitations of the simulation are pointed out, and the corresponding solutions are addressed. Finally, the consistencies and differences between the simulation and the experimental results are discussed.

In this paper, the creep deformations of two representative concrete materials are investigated under thermal-mechanical-hydric conditions. Both basic and drying creeps are considered. Triaxial compression creep tests are first performed under a confining pressure of 5 MPa and three different values of temperature (T = 20 °C, 50 °C or 80 °C). Two different levels of differential stress are considered (50% and 80% of the peak strength at 20 °C). These tests are used for the characterization of basic creep. Then hydric creep tests are conducted on samples subjected to uniaxial compression condition with different prescribed values of axial stress (30%, 50% and 70% of the uniaxial compressive strength) and at constant temperature (20 °C). The samples are progressively dried by decreasing the relative humidity (RH) from 98 to 50%. The relative variations of sample mass are also measured during the drying process. It is found that the basic creep strain rate is enhanced by temperature and differential stress. The drying kinetics is strongly influenced by the compositions of concrete. The drying creep deformation is directly correlated with the mass loss kinetics.

A multi-scale model is developed for modeling of plastic deformation and induced damage in rock-like materials containing pores and mineral inclusions. An analytical macroscopic plastic yield criterion is first determined from three steps of homogenization. This criterion explicitly takes into account respective effects of two populations of pores and mineral inclusions at three different scales. The accuracy of criterion is evaluated by comparisons with numerical results issued from direct simulations on representative volume elements. Then, an induced damage evolution law is defined to describe the onset and growth of micro-cracks inside the solid matrix of materials. The induced damage affects both elastic and strength properties of the solid matrix and its evolution is coupled with the plastic deformation. The performance of the proposed model is first assessed through a series of numerical examples, clearly showing influences of pores and inclusions on macroscopic responses of heterogeneous materials. Finally, the proposed model is applied to describe mechanical behaviors of clayey rocks. Comparisons between numerical results and experimental data are presented.

Cement-based materials usually undergo drying which influences their mechanical behaviour. This study investigates the evolution of mechanical properties of a high-performance self-compacting concrete subjected to drying at an early age and after long-term maturation. Uniaxial compression and bending tests are performed at different drying times. The evolution of the mechanical properties obtained is controlled by a competitive effect between material strengthening (due to capillary depression, disjoining pressure, hygral gradients, and hydration if it still occurs) and drying-induced micro-cracking (due to material heterogeneity and differential shrinkage). The competitive effect shows a great dependence on maturation level. Such couplings have to be taken into account for a reliable durability analysis.

Multi-scale models are developed for heterogeneous concrete materials to estimate their macroscopic mechanical properties in terms of micro-structural data. One crucial challenge of those models is the identification of local properties of constituent phases. In this paper, we present an efficient method based on Artificial Neural Networks (ANN). Typical concrete materials are taken as example. A macroscopic analytical strength criterion is established from three steps of nonlinear homogenization procedure. The macroscopic strength of materials is determined as a function of the frictional coefficient and cohesion of solid cement particles at nanometer scale, intra-particle pores, inter-particle pores and aggregates (inclusions). The objective is to identify the nanoscopic frictional coefficient and cohesion of cement particle from measured macroscopic values of uniaxial compression and tensile strengths. For this purpose, a numerical method based on the ANN is developed. With the analytical macroscopic strength criterion, sensitivity studies are first realized to identify the most important micro-structural parameters influencing the macroscopic strength of concrete. A simplified analytical macroscopic strength criterion is then proposed. A large dataset is further constructed through the inversion of the analytical strength criterion by using the aggregates volume fraction, porosity, macroscopic uniaxial tensile and compressive strengths as input variables and the frictional coefficient and cohesion of cement particles as output unknowns. An ANN model containing four hidden layers and 100 neurons in each layer is constructed and trained by using this dataset. Various types of validation of the ANN model are performed. It is found that the proposed ANN based model can effectively predict the frictional coefficient and cohesion of porous cement paste at the microscopic scale with a very good accuracy.

Peridynamics (PD) has received more and more attention in dealing with discontinuous problems. In this theory, the crack initiates and propagates arbitrarily without any extra remeshing strategy or propagation criteria. To improve the deficiency of computationally more demanding, PD is coupled with the classical finite element method (FEM). One symmetric double notched tension test is taken to verify the effectiveness of PD as well as the coupling method. The influence of parameters on the damage evolution is investigated based on this tension test. It is found that PD is capable to describe the crack propagation process in elastic-brittle materials. The overall force-displacement response is influenced by the size of loading increment. Importantly, the structural response is sensitive to the horizon radius. The results are approximately convergent when the horizon radius is no less than three times the specific mesh size. For a particular (three times) ratio, the peak force and the peak displacement are negatively affected by the mesh size. The critical energy release rate positively influences the peak force as well as the peak displacement. The Young’s modulus has a positive effect on the peak force but the negative effect on the peak displacement.

This paper presents an experimental study on the influence of inclusion rigidity on the shrinkage cracking in a concrete composite. For this purpose, a series of concrete samples are casted with artificial inclusions of different rigidities. These samples are subjected to different levels of drying in order to evaluate cracks induced by the drying shrinkage. The dried samples are then examined by using the non-destructive X-ray micro-tomography imaging method. Three-dimensional (3D) distributions of induced cracks in the dried samples are identified, including their location and shape. The influence of inclusion rigidity on the shrinkage-induced cracking process is clearly demonstrated. It is found that the shrinkage-induced cracking is strongly enhanced by the stiffness difference between the inclusion and cement paste. The experimental results obtained in this study allow for improving understanding of the mechanism of shrinkage cracking in concrete composites.

This work focuses on the study of macroscopic mechanical behavior of cement paste in relation with micro-structural degradation due to chemical leaching. According to experimental evidences, the degradation of cement paste is mainly characterized by a significant increase of porosity due to the dissolution of Portlandite (CH) and the decalcification of calcium silicate hydrates (C–S–H). We shall first establish the explicit relations between macroscopic elastic properties and plastic yield stresses and porosity of cement paste by using analytical homogenization methods. With these relations, the degradation of elastic and plastic properties of cement paste by chemical leaching can be systematically determined. Combining with a specific plastic hardening law, the complete micro-macro constitutive model is formulated to describe the mechanical behavior of cement paste under general loading conditions. The efficiency of the proposed model is assessed through the comparison between numerical results and experimental data in uniaxial and triaxial compression tests performed on both sound and leached samples.

In this study, an adaptive coupling method is proposed for the combination of the state-based peridynamics theory (PD) and the classical finite element method (FEM). The non-local PD theory is used for dealing with localized cracking process while the FEM is adopted for modeling elastic (or plastic) problems without localization. The evolving boundary between cracking domain and the elastic or plastic domain without localization is taken into account. A new bond damage model is implemented into the ordinary state-based PD theory, by considering the progressive degradation of bond strength and residual strength. The proposed coupling method and bond damage model are implemented in MATLAB framework. The accuracy of the PD-FEM coupling method is verified by the analytical solutions in elastic cases. The efficiency of the new bond damage model implemented in the adaptive PD-FEM coupling method for modeling the progressive failure process in cohesive materials is clearly validated through a series of representative laboratory tests on concrete structures.

A new macroscopic yield criterion is derived in the present work to describe the elastoplastic mechanical behavior of composite with a porous matrix-inclusion microstructure. The influences of porosity at the microscopic scale and the bigger inclusions at the mesoscopic scale are explicitly taken into account by this criterion. The solid phase at the microscopic scale obeys to a Drucker-Prager criterion for the dilatant effect. The exact solution can be retrieved in the special case of a porous medium having a Drucker-Prager type matrix. This improves fundamentally the one proposed in Shen et al. (2013) . This criterion is applied to describe the peak stresses of Callovo Oxfordian argillite obtained by the uniaxial and triaxial compression tests with different compositions and different confining pressures. Then, a complete constitutive model is established with a plastic hardening behavior and the non-associated plastic flow rule. The evolutions of the microstructure, such as the variations of the porosity and the volume fraction of inclusions with the loading process, can be fully considered by this micromechanics based model. By comparing the numerical results with the experimental data, the proposed model is able to capture the main features of the studied geomaterial with a porous matrix-inclusion microstructure.

In this study, we present an efficient numerical solution for studying hydraulic fracturing under coupled thermal–hydraulic conditions in an elastic–plastic porous medium. The propagation of macroscopic fracture is described by using an extended finite element method. Both the fluid flow through the porous medium and the exchange between the medium and fracture are taken into account. It is the same for the heat transfer. An efficient iterative scheme is then proposed to deal with the coupling between material deformation with fracture growth, fluid flow and heat transfer. The proposed method is assessed through comparisons with analytical solutions for a number of well-established problems. A series of numerical calculations are further performed in order to investigate the effect of plastic deformation and temperature change on the process of hydraulic fracture propagation.

This paper is devoted to study the elastic–plastic damage behavior of heterogeneous shale rocks. The representative microstructure of this kind of rocks is first studied in order to define the representative elementary volume for the implementation of homogenization procedure. Three relevant material scales are considered. Inter-particle pores are distributed at the nanoscopic scale. Fine grains of calcite and kerogen are immersed at the microscopic scale. Large grains of minerals are embedded at the mesoscopic scale. Effective elastic properties of shale rocks are first determined by using a three-step linear homogenization procedure. The plastic damage behavior is estimated by developing a three-step nonlinear homogenization method. The effective plastic behavior of porous clay matrix with nanoscopic pores is described by an analytical model. The effects of small and large grains of various mineral inclusions are investigated by using a two-step incremental model. The damage due to progressive debonding of mineral inclusions is taken into account. After the implementation of the proposed model, comparisons between numerical results and experimental data are presented.

Mechanical properties of rock-like materials are affected by voids and mineral inclusions. Different kinds of analytical solutions have been established for the determination of effective elastic properties and plastic yield stress or failure strength of those materials. However, voids and inclusions are generally considered at different scales. By adopting the Fast Fourier Transform technique, we propose in this paper a numerical homogenization method for modeling the effective elastic properties and plastic yield stress of rock-like materials having voids and mineral inclusions at the same scale. Both are embedded in an elastic-perfectly plastic matrix. The overall elastic-plastic properties are estimated by taking into account the morphology and spatial distribution of pores and inclusions. It is found that the macroscopic elastic modulus is sensitive to both void and inclusion geometry and orientation. The overall yield stress is mainly controlled by the porosity, the inclusion volumetric fraction, the void shape, distribution and orientation. Due to the presence of voids, the influences of inclusion geometry and orientation on the overall yield stress are significantly reduced. This is an important difference with inclusion-reinforced materials without voids.

This paper aims at analytically determining the limit states of ductile porous media with kinematical hardening solid matrix subjected to cyclic loads. Based on the statical approach, a macroscopic shakedown criterion is established with the hollow sphere model by using the homogenization theory. The approach proposed in the present study does not require the construction of the so-called time-independent self-equilibrium residual stress field, which is the most important point in the classical statical shakedown approaches. This feature leads to a significant simplification of the computation. The final closed-form macroscopic criterion depends on the invariants of the macroscopic stress tensor, the porosity, as well as Poisson's ratio of the solid matrix. It is remarked that the shakedown limit load is not affected by the kinematical hardening law by comparison of different hardening cases. The obtained safety domain is bounded by the limit surface of the proposed criterion and the limit analysis issued yield surface, indicating the mechanism of incremental collapse at the first cycle. Finally, original numerical simulations, inspired from the two-surface model, have been performed for different hardening conditions and porosities to verify the accuracy of the established criterion.

The shakedown safety domain of porous materials is investigated in this work by a direct numerical method based on Melan’s theorem. Considering the critical loading path of the load domain instead of the whole history, the statical shakedown condition is transformed to a large size optimization problem, of which the objective function is the shakedown limit factor, with the discretization of a three dimensional model composed of von Mises matrix. As in limit analysis of the hollow sphere model, we consider pure hydrostatic and deviatoric loads to produce the reference elastic stresses in the fictitious elastic body, for the purpose of capturing the effects of compressive/tensile and shear effects. By the use of a non-linear optimizer IPOPT based on the interior-point method, the proposed optimization problem is solved efficiently, providing not only the shakedown limit load factor, but also the distribution of residual stresses for the limit state. The established method is applied to axisymmetric and non-axisymmetric cyclic loadings, as well as the two independent variable loadings, in order to discover the influence of the loading condition and the solid matrix characteristics on the shakedown safety domain of porous medium (hollow sphere). The obtained results are illustrated and fully compared with reference solutions from literature and with the one from the incremental step-by-step FEM computations. The present method has been accessed and validated by the comparative study.