The impact of turbulent flow on plane strain fluid-driven crack propagation is an important but still poorly understood consideration in hydraulic fracture modeling. The changes that hydraulic fracturing has experienced over the past decade, especially in the area of fracturing fluids, have played a major role in the transition of the typical fluid regime from laminar to turbulent flow. Motivated by the increasing preponderance of high-rate, water-driven hydraulic fractures with high Reynolds number, we present a semianalytical solution for the propagation of a plane strain hydraulic fracture driven by a turbulent fluid in an impermeable formation. The formulation uses a power law relationship between the Darcy-Weisbach friction factor and the scale of the fracture roughness, where one specific manifestation of this generalized friction factor is the classical Gauckler-Manning-Strickler approximation for turbulent flow in a rough-walled channel. Conservation of mass, elasticity, and crack propagation are also solved simultaneously. We obtain a semianalytical solution using an orthogonal polynomial series. An approximate closed-form solution is enabled by a choice of orthogonal polynomials embedding the near-tip asymptotic behavior and thus giving very rapid convergence; a precise solution is obtained with 2 terms of the series. By comparison with numerical simulations, we show that the transition region between the laminar and turbulent regimes can be relatively small so that full solutions can often be well approximated by either a fully laminar or fully turbulent solution.

The dynamic problem of a transversely isotropic multilayered medium is reducible to quasi-static problem by introducing a moving system that travels synchronously with the load. Based on the governing equations in the moving system, the ordinary differential equations in the Fourier transformed domain are deduced. An extended precise integration method is adopted to solve the ordinary differential equations, and the solution in the physical domain is recovered by the inverse Fourier transform. Numerical examples are performed to verify the accuracy of the presented method and to analyze the influence of material properties and the load characteristic.

This paper proposes a new approach for the assessment of the dynamic response of continuously supported infinite beams under high-speed moving loads. A change in the representation of equations of motion in the dynamics of discrete structures is proposed to obtain an improved accuracy of the numerical integration in the time domain. The proposed numerical method called the “periodic configuration update” or “PCU method” is applied to solve the problem of a vertical moving harmonic load on an infinite classical Euler-Bernoulli beam resting on a continuous viscoelastic foundation. This study shows the superiority of the proposed method in comparison with other methods presented in the literature that suffer from the material time derivative, i.e., convective terms, that arises from the Galilean transformation. To confront this numerical problem, the PCU method retains the principle of the spatial follow of loads while zeroing the relative velocity with the traversed beam via a step-by-step adaptive integration of the equation of structural dynamics. The dynamic load is modeled with high theoretical velocities that can reach the critical velocity of the studied beam with different angular frequencies belonging to moderate frequency range. A parametric study is carried out to analyze the influence of key parameters on the convergence. The obtained results show a high efficiency of the PCU method for solving these types of problems relative to the dynamics of high speed trains/tracks.

In this paper, mesoscale hydromechanical simulations are performed to study (1) fracture features and (2) crack-gas permeability coupling evolution in the context of the tensile splitting test. The mesostructure is based on a 2-phase 3-D representation of heterogeneous materials, such as concrete, where stiff aggregates are embedded into a mortar matrix. To take into account these heterogeneities without any mesh adaptation, a weak discontinuity is introduced into the strain field. In addition, a strong discontinuity is also added to take into account microcracking. This mechanical model is cast into the framework of the enhanced finite element method. Concerning the coupling with gas permeability, a double-porosity method is used to simulate the flow through the cracks and the porosity. The apparent gas permeability is afterwards evaluated by a homogenization method. On the basis of finite element simulations, influence of aggregate size on ultimate crack opening, macroscopic ultimate tensile stress, total dissipated energy, and gas permeability evolution is numerically investigated. Furthermore, gas permeability evolution is also compared with experimental results from the literature. In addition, in the spirit of a sequential multiscale approach, macroscale gas permeability equations are identified from the hydromechanical results coming from the mesoscale computations. These equations lead to a relation between macroscale gas permeability evolution and crack opening. Besides, we show how the aggregate size influences the percolation threshold and that after this threshold, a cubic relation between macroscale gas permeability and crack opening is obtained.

In the present study an analytical procedure based on finite element technique is proposed to investigate the influence of vertical load on deflection and bending moment of a laterally loaded pile embedded in liquefiable soil, subjected to permanent ground displacement. The degradation of subgrade modulus due to soil liquefaction and effect of nonlinearity are also considered. A free headed vertical concrete elastic nonyielding pile with a floating tip subjected to vertical compressive loading, lateral load, and permanent ground displacement due to earthquake motions, in liquefiable soil underlain by nonliquefiable stratum, is considered. The input seismic motions, having varying range of ground motion parameters, considered here include 1989 Loma Gilroy, 1995 Kobe, 2001 Bhuj, and 2011 Sikkim motions. It is calculated that maximum bending moment occurred at the interface of liquefiable and nonliquefiable soil layers and when thickness of liquefiable soil layer is around 60% of total pile length. Maximum bending moment of 1210 kNm and pile head deflection of 110 cm is observed because of 1995 Kobe motion, while 2001 Bhuj and 2011 Sikkim motions amplify the pile head deflection by 14.2 and 14.4 times and bending moment approximately by 4 times, when compared to nonliquefiable soil. Further, the presence of inertial load at the pile head increases bending moment and deflection by approximately 52% when subjected to 1995 Kobe motion. Thus, it is necessary to have a proper assessment of both kinematic and inertial interactions due to free field seismic motions and vertical loads for evaluating pile response in liquefiable soil.

After placement of cemented tailings backfill (CTB), which is a mixture of tailings (man-made soil), water, and binder, into underground mined-out voids (stopes), the hydration reaction of the binder converts the capillary water into chemically bound water, which results in the reduction of the water content in the pores of the CTB, thereby causing a reduction in the pore-water pressure in the CTB (self-desiccation). Self-desiccation has a significant impact on the pore-water pressure and effective stress development in CTB and paramount and practical importance for the stability assessment and design of CTB structures and barricades. However, self-desiccation in CTB structures is complex because it is a function of the multiphysics or coupled (i.e., thermal, hydraulic, mechanical, and chemical) processes that occur in CTB. To understand the self-desiccation behavior of CTB, an integrated multiphysics model of self-desiccation is developed in this study, which fully considers the coupled thermal, hydraulic, mechanical, and chemical processes and the consolidation process in CTB. All model coefficients are determined in measurable parameters. Moreover, the predictive ability of the model is verified with extensive case studies. A series of engineering issues are examined with the validated model to investigate the self-desiccation process in CTB structures with respect to the changes in the mixture recipe, backfilling, and the surrounding rock and curing conditions. The obtained results provide in-depth insight into the self-desiccation behavior of CTB structures. The developed multiphysics model is therefore a potential tool for assessing and predicting self-desiccation in CTB structures.

The method of stress characteristics has been used for computing the ultimate bearing capacity of strip and circular footings placed on rock mass. The modified Hoek-and-Brown failure criterion has been used. Both smooth and rough footing-rock interfaces have been modeled. The bearing capacity has been expressed in terms of nondimensional factors *N*_{σ0} and *N _{σ}*, corresponding to rock mass with (1) γ = 0 and (2)

Improved, microfabric-inspired rotational hardening rules for the plastic potential and bounding surfaces associated with the generalized bounding surface model for cohesive soils are presented. These hardening rules include 2 new functions, *f*_{η} and
, that improve the simulation of anisotropically consolidated cohesive soils. Three model parameters are associated with the improved hardening rules. A detailed procedure for obtaining suitable values for these parameters is presented. The first 2 parameters affect the simulation of constant stress ratio loading where, because of the presence of *f*_{η}, the third parameter is inactive. The second new function,
, accelerates the rotation of the plastic potential and bounding surfaces during shearing, which is particularly important for overconsolidated soils tested in extension. This paper also describes the proper manner in which to define the inherent anisotropy. This seemingly straightforward test has rarely been discussed in sufficient detail.

A constitutive model that captures the material behavior under a wide range of loading conditions is essential for simulating complex boundary value problems. In recent years, some attempts have been made to develop constitutive models for finite element analysis using self-learning simulation (SelfSim). Self-learning simulation is an inverse analysis technique that extracts material behavior from some boundary measurements (eg, load and displacement). In the heart of the self-learning framework is a neural network which is used to train and develop a constitutive model that represents the material behavior. It is generally known that neural networks suffer from a number of drawbacks. This paper utilizes evolutionary polynomial regression (EPR) in the framework of SelfSim within an automation process which is coded in Matlab environment. EPR is a hybrid data mining technique that uses a combination of a genetic algorithm and the least square method to search for mathematical equations to represent the behavior of a system. Two strategies of material modeling have been considered in the SelfSim-based finite element analysis. These include a total stress-strain strategy applied to analysis of a truss structure using synthetic measurement data and an incremental stress-strain strategy applied to simulation of triaxial tests using experimental data. The results show that effective and accurate constitutive models can be developed from the proposed EPR-based self-learning finite element method. The EPR-based self-learning FEM can provide accurate predictions to engineering problems. The main advantages of using EPR over neural network are highlighted.

This paper presents a model which can be used for fast landslides where coupling between solid and pore fluid plays a fundamental role. The proposed model is able to describe debris flows where the difference of velocities between solid grains and fluid is important. The approach is based on the mathematical model proposed by Zienkiewicz and Shiomi, which is similar to those of Pitman and Le and Pudasaini. The novelty of the present work is the numerical technique used, the smoothed particle hydrodynamics (SPH). We propose to use a double set of nodes for soil and water phases, the interaction between them being described by a suitable drag law. The paper presents both mathematical and numerical models, describing the main assumptions and their limitations. Then, the model is applied to (1) a simple case where shocks and expansion waves appear, (2) a dam break problem on a horizontal plane with a frictional soil phase, and (3) a debris flow which happened in Hong Kong. The main conclusions that can be drawn from the applications are:

- Debris flows having 2 phases with important relative mobility present a rich structure of shocks and rarefaction waves, which has to be properly modeled. Otherwise, the model will have numerical damping or dispersion.
- Dambreak exercises provide interesting information in simple and controlled situations. We can see how both phases move relative to each other.
- Real debris flows can be simulated with the proposed model, obtaining reasonable results.

A probability-based model is presented to estimate particle crushing and the associated grading evolution in granular soils during isotropic compression and prepeak shearing in biaxial tests. The model is based on probability density functions of interparticle and intraparticle stress (ie, particle normalized maximum shear stress and particle average maximum shear stress) derived from discrete element method simulations of biaxial tests. We find that the probability density functions of normalized maximum shear stress are dependent on the current sample grading, implying coupling effects between particle crushing and sample grading such that the particle crushing is affected by the current sample grading, and the grading change is also dependent on the current particle crushing extent. To incorporate these coupling effects into the model, particle crushing and grading change are calculated for each load increment, in which the crushing probability of a particle during any loading increment is denoted as the corresponding increment of probability of the internal maximum shear stress exceeding its maximum shear strength. The model shows qualitative agreement with published experimental data. The effects of the model parameters, including initial porosity, particle strength, initial grading, and crushing mode, on the calculated results are discussed and compared with previous studies. Finally, the strengths and limitations of the model are discussed.

The smooth-joint contact model based on distinct element method has been widely used to represent discontinuity in the simulation of fractured rock mass, but there is rare efficient guidance for the selection of proper parameters of smooth-joint contact model, which is the basement for using this model properly. In this paper, the effect of smooth joint parameters on the macroscopic properties and failure mechanism of jointed rock under triaxial compression test is investigated. The numerical results reveal that the friction coefficient of smooth joint plays a dominant role in controlling mechanical behaviors. The stiffness of smooth joint has a relative small influence on the mechanical behaviors. Poisson ratio decreases with the reduction of normal stiffness but increases with the reduction of shear stiffness. The reduction of smooth joint strength, which is determined by normal strength, cohesion, and friction angle of smooth joint, contributes to the breakage of bonded smooth joint and ultimately decreases the strength of the specimen. We proposed a detailed calibration process for smooth-joint contact model according to the relationship between smooth-joint parameters and mechanical properties. By following this process, the numerical results are validated against corresponding experimental results and good agreement between them can be found in stress-strain curves and failure modes of different joint orientations. Further analyses from the microperspective are performed by looking at transmission of contact force, the nature and distribution of microcracks, and the particle displacement to show the failure process and failure modes.

This paper presents a theoretical framework to interpret the inception of unstable undrained creep in quasi-saturated soils. For this purpose, the effect of gas bubbles occluded in the fluid phase is embedded into an augmented compressibility of the fluid mixture, while the mechanical characteristics of the solid skeleton have been simulated through a viscoplastic strain-hardening model. This constitutive framework has been been used to formulate a theoretical platform able to detect runaway failures resulting from extended stages of undrained creep. It is shown that the conditions identifying the onset of spontaneous accelerations are governed by the same stability index associated with the initiation of static liquefaction. At variance with soils saturated by incompressible fluids, the conditions for undrained instability are altered by the appearance of the Skempton coefficient *B*, thus reflecting the beneficial effect of the fluid compressibility and its ability to decrease the liquefaction potential. The capabilities of the theory are verified through a sequence of undrained creep simulations showing the transition from stable to unstable behavior resulting from an increase of the degree of saturation. The proposed findings provide a conceptual framework to interpret the effects of gas bubbles in loose soils, as well as to assess effectiveness and longevity of liquefaction mitigation strategies based on desaturation technologies.

This paper presents an analytical solution for cavity expansion in thermoplastic soil considering non-isothermal conditions. The constitutive relationship of thermoplasticity is described by Laloui's advanced and unified constitutive model for environmental geomechanical thermal effect (ACMEG-T), which is based on multi-mechanism plasticity and bounding surface theory. The problem is formulated by incorporating ACMEG-T into the theoretical framework of cavity expansion, yielding a series of partial differential equations (PDEs). Subsequently, the PDEs are transformed into a system of first-order ordinary differential equations (ODEs) using a similarity solution technique. Solutions to the response parameters of cavity expansion (stress, excess pore pressure, and displacement) can then be obtained by solving the ODEs numerically using mathematical software. The results suggest that soil temperature has a significant influence on the pressure-expansion relationships and distributions of stress and excess pore pressure around the cavity wall. The proposed solution quantifies the influence of temperature on cavity expansion for the first time and provides a theoretical framework for predicting thermoplastic soil behavior around the cavity wall. The solution found in this paper can be used as a theoretical tool that can potentially be employed in geotechnical engineering problems, such as thermal cone penetration tests, and nuclear waste disposal problems.

The objective of the present paper is to present a numerical study on the penetration performance of concrete targets with 2 different water contents. Numerical analysis has been performed by using the finite element code Abaqus/Explicit, in which a coupled elastoplastic damage model has been developed for saturated/unsaturated concrete under a wide range of confining pressures. The performance of proposed model has been firstly verified by simulating the triaxial compression tests and penetration tests realized with saturated/dry concretes. Comparisons of available experimental results and numerical simulations show that the proposed model is able to reproduce satisfactorily the mechanical behavior of saturated and dry concretes. A higher failure stress and a more important pores closing are generally obtained in dry concrete samples with respect to saturated ones. Furthermore, the main observed patterns of penetration test realized with saturated concrete targets are also satisfactorily simulated by the numerical results. Therefore, the proposed model is used to numerically predict the penetration performance of dry concrete target, and the penetration performance of dry/saturated concrete target is discussed. We observe that in dry concrete target, the penetration of projectile is strongly declined, and a smaller damage zone is created. The numerical predictions and discussions can help engineers to enhance their understandings on the influence of hydraulic conditions on structural vulnerability of concrete structures subjected to near-field detonations or impacts.

The shear behavior at the interface between the soil and a structure is investigated at the macroscale and particle-scale levels using a 3-dimensional discrete element method (DEM). The macroscopic mechanical properties and microscopic quantities affected by the normalized interface roughness and the loading parameters are analyzed. The macro-response shows that the shear strength of the interface increases as the normalized roughness of the interface increases, and stress softening and dilatancy of the soil material are observed in the tests that feature rough interfaces. The particle-scale analysis illustrates that a localized band characterized by intense shear deformation emerges from the contact plane and gradually expands as shearing progresses before stabilizing at the residual stress state. The thickness of the localized band is affected by the normalized roughness of the interface and the normal stress, which ranges between 4 and 5 times that of the median grain diameter. A thicker localized band is formed when the soil has a rough shearing interface. After the localized band appears, the granular material structuralizes into 2 regions: the interface zone and the upper zone. The mechanical behavior in the interface zone is representative of the interface according to the local average stress analysis. Certain microscopic quantities in the interface zone are analyzed, including the coordination number and the material fabric. Shear at the interface creates an anisotropic material fabric and leads to the rotation of the major principal stress.

This paper presents a *u-p* (displacement-pressure) semi-Lagrangian reproducing kernel (RK) formulation to effectively analyze landslide processes. The semi-Lagrangian RK approximation is constructed based on Lagrangian discretization points with fixed kernel supports in the current configuration. As a result, it tracks state variables at discretization points while allowing extreme deformation and material separation that is beyond the capability of Lagrangian formulations. The *u-p* formulation following Biot theory is incorporated into the formulation to describe poromechanics of saturated geomaterials. In addition, a stabilized nodal integration method to ensure stability of the domain integration and kernel contact algorithms to model contact between bodies are introduced in the *u-p* semi-Lagrangian RK formulation. The proposed method is verified with several numerical examples and validated with an experimental result and the field data of an actual landslide.

Vertical drains are widely used in soft ground improvements to accelerate the consolidation process. This paper develops a new simplified Hypothesis B method for calculating the consolidation settlement of a soil layer improved by vertical drains under the instant and ramp loadings. As a comparison, the traditional Hypothesis A method is also used to calculate the settlement. Then, a fully coupled finite element consolidation analysis is utilized to examine and verify this simplified method and Hypothesis A method. For the instant loading, Carrillo-Barron method and Zhu-Yin method are used to obtain the average degree of consolidation for vertical drain system. Typical parameters, such as over-consolidation ratio (*OCR*), smear zone, and space ratio of vertical drains, are considered. It is found that the calculation results from the new simplified method in this study agree well with finite element simulations, and *relative errors* are in the range of 0.1% to 12.3%. Comparatively, there are obvious differences between the calculated results from Hypothesis A method and finite element results. Carrillo-Olson method and Zhu-Yin method are utilized to obtain the average degree of consolidation for the vertical drain system to consider the ramp loading. Equivalent time is determined from half of the construction period to calculate the creep compression under the ramp loading. The accuracy of this simplified Hypothesis B method using both Carrillo-Olson method and Zhu-Yin method is acceptable with the *relative errors* less than 9.4%.

In this paper, we propose a method to detect the damage and estimate the degree of damage by means of a multifield-based inverse analysis. The fields being considered are displacement, temperature, and water pressure. Furthermore, the uncertainties due to the size of the damage, the errors in the measurement data, and the errors in the model parameters are also investigated. The uncertainty due to the measurements is quantified by assuming different sources of noise in the measurements. The inverse problem is solved repeatedly by a sampling process. The uncertainties in the inverse solutions can be quantified by their probability distributions. This method can be applied to identify damages in masonry dams using coupled nonlinear thermo-hydro-mechanical problems.

This paper presents a thermo-hydro-mechanical framework to model the drying behavior of Boom clay. First, the experimental campaign conducted Noémie Prime is briefly presented because it is used to validate the model. The data acquisition and processing is emphasized because of the use of X-ray microtomography to be able to more accurately compare experimental and numerical strain fields. The different submodels are introduced. Numerical simulations are performed to illustrate the capability of the proposed model to reproduce the observed behavior. Finally, a comprehensive sensitivity study on several key model parameters associated with the water retention curve, and the permeability of the medium, is performed to get a better understanding of the physics behind the coupled model.

The effect of heterogeneity in meso level geometric and material properties on tensile strength and size effect in split cylinder specimens is investigated. Critical meso geometric parameters are identified by studying their influence on the evolution of the fracture process zone. A statistical analysis is used to account for dependencies between the parameters. A reversal of the size effect, important for the strength of field specimens, is observed for certain meso geometries. Meso level explanations for this are proposed, and meso geometries likely to show such a reversal are identified. For moderately sized specimens, major trends in the size effect are seen to be almost entirely explained by heterogeneity in the meso geometry.

This paper presents an algorithm and a fully coupled hydromechanical-fracture formulation for the simulation of three-dimensional nonplanar hydraulic fracture propagation. The propagation algorithm automatically estimates the magnitude of time steps such that a regularized form of Irwin's criterion is satisfied along the predicted 3-D fracture front at every fracture propagation step.

A generalized finite element method is used for the discretization of elasticity equations governing the deformation of the rock, and a finite element method is adopted for the solution of the fluid flow equation on the basis of Poiseuille's cubic law. Adaptive mesh refinement is used for discretization error control, leading to significantly fewer degrees of freedom than available nonadaptive methods. An efficient computational scheme to handle nonlinear time-dependent problems with adaptive mesh refinement is presented. Explicit fracture surface representations are used to avoid mapping of 3-D solutions between generalized finite element method meshes. Examples demonstrating the accuracy, robustness, and computational efficiency of the proposed formulation, regularized Irwin's criterion, and propagation algorithm are presented.

Shear bands with characteristic spatial patterns observed in an experiment for a cubic or parallelepiped specimen of dry dense sand were simulated by numerical bifurcation analysis using the Cam-clay plasticity model. By incorporating the subloading surface concept into the plasticity model, the model became capable of reproducing hardening/softening and contractive/dilative behavior observed in the experiment. The model was reformulated to be compatible with the multiplicative hyperelasto-plasticity for finite strains. This enhanced constitutive model was implemented into a finite-element code reinforced by a stress updating algorithm based on the return-mapping scheme, and by an efficient numerical procedure to compute critical eigenvectors of elastoplastic tangent stiffness matrix at bifurcation points. The emergence of diamond- and column-like diffuse bifurcation modes breaking uniformity of the materials, followed by the evolution of shear bands through strain localization, was observed in the analysis. In the bifurcation analysis of plane strain compression test, unexpected bifurcation modes, which broke out-of-plane uniformity and led to 3-dimensional diamond-like patterns, were detected. Diffuse bifurcations, which were difficult to observe by experiments, have thus been found as a catalyst creating diverse shear band patterns.

A rigorous semianalytical solution for the drained expansion of a cylindrical cavity in frictional soils is presented. Following the restrict material (Lagrangian) description approach recently developed by the authors, the cavity analysis has been extended to the 3-invariant plasticity soil model, which is governed by the Matsuoka-Nakai yield criterion combined with the friction angle hardening depending on the development of deviatoric plastic strain. The 4 desired first-order ordinary differential equations are subsequently derived, which enable the 3 stress components, volumetric strain, and plastic shear strain in the plastic zone to be readily calculated through the standard numerical procedure. Numerical examples illustrate how the major constitutive parameter, in situ stress state, and the third stress invariant impact the overall response of the cavity as well as its ultimate pressure. Specific consideration is given to the influence of the plastic hardening parameter on the stress path of a soil element at the cavity wall.

Studying seismic wave propagation across rock masses and the induced ground motion is an important topic, which receives considerable attention in design and construction of underground cavern/tunnel constructions and mining activities. The current study investigates wave propagation across a rock mass with one fault and the induced ground motion using a recursive approach. The rocks beside the fault are assumed as viscoelastic media with seismic quality factors, *Q*_{p} and *Q*_{s}. Two kinds of interactions between stress waves and a discontinuity and between stress waves and a free surface are analyzed, respectively. As the result of the wave superposition, the mathematical expressions for induced ground vibration are deduced. The proposed approach is then compared with the existing analysis for special cases. Finally, parametric studies are carried out, which includes the influences of fault stiffness, incident angle, and frequency of incident waves on the peak particle velocities of the ground motions.

Data assimilation, using the particle filter and incorporating the soil-water coupled finite element method, is applied to identify the yield function of the elastoplastic constitutive model and corresponding parameters based on the sequential measurements of hypothetical soil tests and an actual construction sequence. In the proposed framework of the inverse analysis, the unknowns are both the particular parameter within the exponential contractancy model, *n*_{E}, which parameterizes various shapes for the yield function of the competing constitutive models, including the original/the modified Cam-Clay models and in-between models and the parameters of the corresponding constitutive model. An appropriate set, consisting of the yield function of the constitutive model and the parameters of the constitutive model, can be simultaneously identified by the particle filter to describe the most suitable soil behavior. To examine the validity of the proposed procedure, hypothetical and actual measurements for the displacements of a soil specimen were obtained for consolidated and undrained tests through a synthetic FEM computation and for consolidated and drained tests, respectively. After examining the applicability of the proposed procedure to these test results, the present paper then focuses on the actual measured data, ie, the settlement behavior including the lateral deformation of the Kobe Airport Island constructed on reclaimed land.

In this paper, the analytical dual-porosity dual-permeability poromechanics solution for saturated cylinders is extended to account for electrokinetic effects and material transverse isotropy, which simulate the responses of chemically active naturally fractured shale under time-dependent mechanical loading and ionic solution exposure. The solution addresses the stresses, fracture pore pressure, matrix pore pressure, fluid fluxes, ion concentration evolution, and displacements due to the applied stress, pore pressure, and solute concentration difference between the sample and the circulation fluid. The presented solution will not only help validate numerical simulations but also assist in calibrating and interpreting laboratory results on dual-porosity dual-permeability shale. It is recommended that the analytical solutions of radial and axial displacements be used to match the corresponding laboratory-recorded data to determine shale dual permeability and chemo-electrical parameters including membrane coefficient, ions diffusion coefficients, and electro-osmotic permeability.

A comparative study of optimization techniques for identifying soil parameters in geotechnical engineering was first presented. The identification methodology with its 3 main parts, error function, search strategy, and identification procedure, was introduced and summarized. Then, current optimization methods were reviewed and classified into 3 categories with an introduction to their basic principles and applications in geotechnical engineering. A comparative study on the identification of model parameters from a synthetic pressuremeter and an excavation tests was then performed by using 5 among the mostly common optimization methods, including genetic algorithms, particle swarm optimization, simulated annealing, the differential evolution algorithm and the artificial bee colony algorithm. The results demonstrated that the differential evolution had the strongest search ability but the slowest convergence speed. All the selected methods could reach approximate solutions with very small objective errors, but these solutions were different from the preset parameters. To improve the identification performance, an enhanced algorithm was developed by implementing the Nelder-Mead simplex method in a differential algorithm to accelerate the convergence speed with strong reliable search ability. The performance of the enhanced optimization algorithm was finally highlighted by identifying the Mohr-Coulomb parameters from the 2 same synthetic cases and from 2 real pressuremeter tests in sand, and ANICREEP parameters from 2 real pressuremeter tests in soft clay.

No abstract is available for this article.

]]>This paper introduces sequential limit analysis (SLA) as a method for modelling large plastic deformations of purely cohesive materials such as undrained clay. The method involves solving a series of consecutive small-deformation plastic collapse problems using finite element limit analysis, thus ensuring high levels of accuracy, efficiency, and robustness. The techniques needed to develop an SLA implementation for two-dimensional (plane strain) problems are described in detail, including model geometry updating routines, treatment of rigid bodies, interfaces and boundaries, and periodic remeshing and interpolation of field variables. A simple total stress-based constitutive model is used to account for strain softening and strain rate effects. Extensive verifications and validations are performed using analytical solutions and physical model test results, comparing both collapse loads and failure mechanisms, to demonstrate the effectiveness of the SLA approach. Additional solution quality checks on the bracketing discrepancy between lower-bound and upper-bound limit analysis solutions, and on the incompressibility of the rigid-plastic material, are also presented.

A Fokker-Planck-Kolmogorov (FPK) equation approach has recently been developed to probabilistically solve any elastic-plastic constitutive equation with uncertain material parameters by transforming the nonlinear, stochastic constitutive rate equation into a linear, deterministic partial differential equation (PDE) and thereby simplifying the numerical solution process. For an uniaxial problem, conventional numerical techniques, such as the finite difference or finite element methods, may be used to solve the resulting univariate FPK PDE. However, for a multiaxial problem, an efficient algorithm is necessary for tractability of the numerical solution of the multivariate FPK PDE. In this paper, computationally efficient algorithms, based on a Fourier spectral approach, are presented for solving FPK PDEs in (stress) space and (pseudo) time, having space-independent but time-dependent coefficients and both space- and time-dependent coefficients, that commonly arise in probabilistic elasto-plasticity. The algorithms are illustrated by probabilistically simulating 2 common laboratory constitutive experiments in geotechnical engineering, namely, the unconfined compression test and the unconsolidated undrained triaxial compression test.

The capability of a bounding surface plasticity model with a vanishing elastic region to capture the multiaxial dynamic hysteretic responses of soil deposits under broadband (eg, earthquake) excitations is explored by using data from centrifuge tests. The said model was proposed by Borja and Amies in 1994 (*J. Geotech. Eng.*, 120, 6, 1051-1070), which is theoretically capable of representing nonlinear soil behavior in a multiaxial setting. This is an important capability that is required for exploring and quantifying site topography, soil stratigraphy, and kinematic effects in ground motion and soil-structure interaction analyses. Results obtained herein indicate that the model can accurately predict key response data recorded during centrifuge tests on embedded specimens—including soil pressures and bending strains for structural walls, structures' racking displacements, and surface settlements—under both low- and high-amplitude seismic input motions, which was achieved after performing only a basic material parameter calibration procedure. Comparisons are also made with results obtained using equivalent linear models and a well-known pressure-dependent multisurface plasticity model, which suggested that the present model is generally more accurate. The numerical convergence behavior of the model in nonlinear equilibrium iterations is also explored for a variety of numerical implementation and model parameter options. To facilitate broader use by researchers and practicing engineers alike, the model is implemented as a “user material” in ABAQUS Standard for implicit time stepping.

Based on relevant experimental data of a petroleum cement paste under mechanical loading and chemical leaching, an elastic-plastic model is first proposed by taking into account plastic shearing and pore collapse. The degradation of mechanical properties induced by the chemical leaching is characterized by a chemical damage variable which is defined as the increase of porosity. Both elastic and plastic properties of the cement paste are affected by the chemical damage. The proposed model is calibrated from and applied to describe mechanical responses in triaxial compression tests respectively on sound and fully leached samples. In the second part, a phenomenological chemical model is defined to establish the relationship between porosity change and calcium dissolution process. The dissolution kinetics is governed by a diffusion law taking into account the variation of diffusion coefficient with calcium concentration. The chemical model is coupled with the mechanical model, and both are applied to describe mechanical response of cement paste samples subjected to progressive chemical leaching and compressive stresses. Comparisons between experimental data and numerical results are presented.

Predicting the deformations of deep reservoirs due to fluid withdrawal/injection is a challenging task that could have important environmental, social, and economical impacts. Finite element models, if endowed with an appropriate constitutive law, represent a useful tool for computing the displacements, the deformations, and the stress distributions in reservoir applications. Several studies show that hypoelastic laws, based on a stress-dependent vertical compressibility, are able to provide accurate results, confirmed by in situ and satellite measurements. On the other hand, such laws present some weaknesses related to the numerical implementation, in particular due to the nonsymmetry of the tangent operator. This paper presents a new constitutive model based on 2 invariants (the mean normal and deviatoric stresses), characterized by a variable pressure-dependent bulk modulus *K*. This constitutive law allows for overcoming most shortcomings of the hypoelastic law, although preserving the same accuracy, reliability, and ease of use and calibration. This paper presents a procedure to identify the parameters of the new model, starting from the typically available data on the vertical compressibility. Numerical results show a good agreement between the 2 laws, suggesting the proposed approach as a valid alternative in reservoir applications.

The effective stress concept for solid-fluid 2-phase media was revisited in this work. In particular, the effects of the compressibility of both the pore fluid and the soil particles were studied under 3 different conditions, i.e., undrained, drained, and unjacketed conditions based on a Biot-type theory for 2-phase porous media. It was confirmed that Terzaghi effective stress holds at the moment when soil grains are assumed to be incompressible and when the compressibility of the pore fluid is small enough compared to that of the soil skeleton. Then, isotropic compression tests for dry sand under undrained conditions were conducted within the triaxial apparatus in which the changes in the pore air pressure could be measured. The ratio of the increment in the cell pressure to the increment in the pore air pressure, *m*, corresponds to the inverse of the *B* value by Bishop and was obtained during the step loading of the cell pressure. In addition, the *m* values were evaluated by comparing them with theoretically obtained values based on the solid-fluid 2-phase mixture theory. The experimental *m* values were close to the theoretical values, as they were in the range of approximately 40 to 185, depending on the cell pressure. Finally, it was found that the soil material with a highly compressible pore fluid, such as air, must be analyzed with the multi-phase porous mixture theory. However, Terzaghi effective stress is practically applicable when the compressibilities of both the soil particles and the pore fluid are small enough compared to that of the soil skeleton.

Two theories may be used to analyze overdamped variable-head (slug) tests in aquifer materials. The first theory assumes that the solid matrix strain has a negligible influence. The second theory takes into account some elastic and immediate strain. Something is wrong with these theories because they yield different hydraulic conductivity values. This paper explains what is wrong after establishing the strain-stress elastic equations for a slug test in 2 ideal conditions: plane strain and spherical symmetry. The equations show that the radial contraction (or elongation) and tangential elongation (or contraction) yield a null volumetric strain. As a result, the conservation is described by the Laplace equation, which is used by the first theory. This first theory is the only one to yield correct solutions. The diffusion equation, with storativity, which is used by the second theory, is physically ill founded for slug tests in aquifers. This new proof scientifically confirms previously raised doubts and experimental proofs that the second theory is ill founded.

In this paper, a numerical model to predict flow-induced shear failure along pre-existing fractures is presented. The framework is based on a discrete fracture representation embedded in a continuum describing the damaged matrix. A finite volume method is used to compute both flow and mechanical equilibrium, whereas specifically tailored basis functions are used to account for the physics at discontinuities. The failure criterion is based on a maximum shear strength limit, which changes with varying compressive stress on the fracture manifold. The displacements along fracture manifolds are obtained such that force balance is achieved under conditions, where shear stress of the failing fracture segment is constrained to the maximum shear strength at the segment. Simultaneously, the fluid pressure is computed independently of the shear slip. A relaxation model approach is used to obtain the maximum shear limit on the fracture manifold, which leads to grid convergence.

This paper presents a numerical scheme for fluid-particle coupling that uses the discrete element method by taking into consideration solid deformation and pore pressure generation. A new water particle element is introduced to calculate pore water pressure due to porosity changes. The water particle element has the same size and shape as the solid element and experiences the same amount of deformation. On the basis of the effective stress principle at the element contact, the total force is equal to the sum of the force transmitted through the solid element contact and the water particle force due to pore water pressure. Analytical solutions of traditional soil mechanics problems, such as isotropic compression and consolidated triaxial undrained test, are used to quantitatively validate the proposed model. The numerical results show good agreement between the model and the analytical solutions. The model therefore provides an effective method to calculate pore pressure in a porous medium in discrete modeling.

This paper presents a system reliability analysis method for soil slopes on the basis of artificial neural networks with computer experiments. Two types of artificial neural networks, multilayer perceptrop (MLP) and radial basis function networks (RBFNs), are tested on the studied problems. Computer experiments are adopted to generate samples for constructing the response surfaces. On the basis of the samples, MLP and RBFN are used for establishing the response surface to approximate the limit state function, and Monte Carlo simulation is performed via the MLP and RBFN response surfaces to estimate the system failure probability of slopes. Experimental results on 3 examples show the effectiveness of the proposed methodology.

Numerical models based on the discrete element method are used to study the fracturing process in brittle rock-like materials under direct and indirect tension. The results demonstrate the capacity of the model to capture the essential characteristics of fracture including the onset of crack propagation, stable and unstable crack growth, arrest and reinitiation of fracturing, and crack branching. Simulations of Brazilian indirect tension tests serve to calibrate the numerical model, relating macroscopic tensile strength of specimens to their micromechanical breakage parameters. A second suite of simulations reveals a linear relationship between the tensile strength of specimens and the loading stress for which mode I tensile crack propagation ensues. Based on these results, a crack initiation criterion for brittle materials is proposed, prescribing the stressing conditions required to induce tensile failure. Such a criterion, if broadly applicable, provides a practical means to rapidly assess the failure potential of brittle materials under tensile loads.

The problem of predicting the geometric structure of induced fractures is highly complex and significant in the fracturing stimulation of rock reservoirs. In the traditional continuous fracturing models, the mechanical properties of reservoir rock are input as macroscopic quantities. These models neglect the microcracks and discontinuous characteristics of rock, which are important factors influencing the geometric structure of the induced fractures. In this paper, we simulate supercritical CO_{2} fracturing based on the bonded particle model to investigate the effect of original natural microcracks on the induced-fracture network distribution. The microcracks are simulated explicitly as broken bonds that form and coalesce into macroscopic fractures in the supercritical CO_{2} fracturing process. A calculation method for the distribution uniformity index (DUI) is proposed. The influence of the total number and DUI of initial microcracks on the mechanical properties of the rock sample is studied. The DUI of the induced fractures of supercritical CO_{2} fracturing and hydraulic fracturing for different DUIs of initial microcracks are compared, holding other conditions constant. The sensitivity of the DUI of the induced fractures to that of initial natural microcracks under different horizontal stress ratios is also probed. The numerical results indicate that the distribution of induced fractures of supercritical CO_{2} fracturing is more uniform than that of common hydraulic fracturing when the horizontal stress ratio is small.