Rock failure is observed around boreholes often with certain types of failure zones, which are called breakouts. Laboratory-scale drilling tests in some high-porosity quartz-rich sandstone have shown breakouts in the form of narrow localized compacted zones in the minimum horizontal stress direction. They are called fracture-like breakouts. Such compaction bands may affect hydrocarbon extraction by forming barriers that inhibit fluid flow and may also be a source of sand production.

This paper presents the results of numerical simulations of borehole breakouts using 3D discrete element method to investigate the mechanism of the fracture-like breakouts and to identify the role of far-field stresses on the breakout dimensions. The numerical tool was first verified against analytical solutions. It was then utilized to investigate the failure mechanism and breakout geometry for drilled cubic rock samples of Castlegate sandstone subjected to different pre-existing far-field stresses.

Results show that failure occurs in the zones of the highest concentration of tangential stress around the borehole. It is concluded that fracture-like breakout develops as a result of a nondilatant failure mechanism consisting of localized grain debonding and repacking and grain crushing that lead to the formation of a compaction band in the minimum horizontal stress direction. In addition, it is found that the length of fracture-like breakouts depends on both the mean stress and stress anisotropy. However, the width of the breakout is not significantly changed by the far-field stresses. Copyright © 2013 John Wiley & Sons, Ltd.

This paper is devoted to develop a theoretical framework to predict the macroscopic transversely isotropic elastoplastic behavior of clay-like material, which is viewed as a porous polycrystal. We consider evolutions of two local plastic mechanisms of grains and interface simultaneously, for which a Schmid criterion is used for the strength of sheet-like grains and a Tresca criterion for the strength of interfaces between particles. By adapting the standard incremental method, we propose firstly a classic self-consistent model, which does not consider the effect of interface, then a generalized self-consistent model in which the solid phase is represented by laminated (or isotropic) spherical grains surrounded by interfaces. Comparisons of numerical predictions between these two methods are performed and have demonstrated the validity of the generalized self-consistent model taking account of interface effects. Numerical simulations of uniaxial compression tests have shown that the macroscopic elastoplastic behavior of polycrystalline (clay-like) material can be successfully predicted by the way of considering the two local plastic mechanisms at microscopic scale. Copyright © 2013 John Wiley & Sons, Ltd.

The primary focus in this work is on proposing a methodology for the assessment of stability of natural/engineered slopes in clayey soils subjected to water infiltration. In natural deposits of fine-grained soils, the presence of water in the vicinity of minerals results in an interparticle bonding. This effect cannot be easily quantified as it involves complex chemical interactions at the micromechanical level. Here, the evolution of strength properties, including the apparent cohesion resulting from initial suction at the irreducible fluid saturation, is described by employing the framework of chemoplasticity. The paper provides first the formulation of the problem; this involves specification of the constitutive relation, development of an implicit return mapping scheme, and the outline of a coupled transient formulation. The framework is then applied to examine the stability of a slope subjected to a prolonged period of intensive rainfall. It is shown that the water infiltration may trigger the loss of stability resulting from the degradation of material properties. Copyright © 2013 John Wiley & Sons, Ltd.

Safety assessment of geosequestration of CO₂ into deep saline aquifers requires a precise understanding of the study of hydro-chemo-mechanical couplings occurring in the rocks and the cement well. To this aim, a coupled chemo-poromechanical model has been developed and implemented into a research code well-suited to the resolution of fully coupled problems. This code is based on the finite volume methods.

In a 1D axisymmetrical configuration, this study aims to simulate the chemo-poromechanical behaviour of a system composed by the cement well and the caprock during CO₂ injection. Major chemical reactions of carbonation occurring into cement paste and rocks are considered in order to evaluate the consequences of the presence of CO₂ on the amount of dissolved matrix and precipitated calcium carbonates. The dissolution of the solid matrix is taken into account through the use of a chemical porosity. Matrix leaching and carbonation lead, as expected, to important variations of porosity, permeability and to alterations of transport properties and mechanical stiffness. These results justify the importance of considering a coupled analysis accounting for the main chemical reactions. It is worth noting that the modelling framework proposed in the present study could be extended to model the chemo-poromechanical behaviour of the reservoir rock and the caprock when subjected to the presence of an acidic pore fluid (CO₂-rich brine). Copyright © 2013 John Wiley & Sons, Ltd.

The solutions of advection–dispersion equation in single fractures were carefully reviewed, and their relationships were addressed. The classic solution, which represents the resident or flux concentration within the semi-infinite fractures under constant concentration or flux boundary conditions, respectively, describes the effluent concentration for a finite fracture. In addition, it also predicts the cumulative distribution of solute particle residence time passing through a single fracture under pulse injection condition, based on which a particle tracking approach was developed to simulate the local advection–dispersion in single fractures. We applied the proposed method to investigate the influence of local dispersion in single fractures on the macrodispersion in different fracture systems with relatively high fracture density. The results show that the effects of local dispersion on macrodispersion are dependent on the heterogeneity of fracture system, but generally the local dispersion plays limited roles on marodispersion at least in dense fracture network. This trend was in agreement with the macrodispersion in heterogeneous porous media. Copyright © 2013 John Wiley & Sons, Ltd.

The macroscopic linear elastic behaviour of inclusion-reinforced soils, regarded as periodic composite media, is investigated by means of the homogenization theory. Special attention is given here to the determination of their longitudinal shear stiffness properties, which strongly govern the reinforced ground response under lateral loading. Combining the use of analytical, variational and numerical methods, we thoroughly examined three particular engineering-relevant configurations: single trench, column and cross trench reinforcements. Fairly accurate closed-form expressions are thus obtained, giving the value of the reinforced soil longitudinal shear stiffness as a function of the individual components shear moduli and reinforcement volume fraction. It is shown in particular that adopting a cross trench reinforcement layout instead of the classical column configuration results in a much higher improvement of the longitudinal shear stiffness. The results are then applied to assessing the reduction of soil liquefaction risk, which can be attributed to the presence of the reinforcing inclusions. Again, they clearly demonstrate the excellent performance of the cross trench configuration as compared with the complete inefficiency of the column reinforcement technique. Copyright © 2013 John Wiley & Sons, Ltd.

Infinite slope (IS) method is the simplest limit equilibrium method for slope stability analysis. It gives reliable results for slides where the longitudinal dimension prevails on the depth of the landslide. Usually results are conservative since ignoring the effects of the strength along lateral bounds. Here, starting from the assumption of considering the effects of the shear strength along lateral bounds by a rectangular cross section, a new expression of the safety factor is investigated, based first on an elliptical and then on a parabolic cross section of the landslide mass. The safety factor evaluated in this way can be quite different from those returned by the classic formula of IS model, in particular when the width of the landslide is narrow with respect to its depth and the ratio between the width and the depth of the landslide is lower than 5. An interesting implication of the proposed model is that if cohesion differs from zero, there is a ‘critical depth’, where the safety factor has a minimum value. Copyright © 2013 John Wiley & Sons, Ltd.

The present work aims at introducing an efficient numerical approach based on the immersed interface method to estimate the effective thermal conductivity and permeability of geomaterials as porous media with either perfect or debonded interfaces. The first part deals with the problem of the overall thermal properties of a medium containing perfectly bonded inclusions. The evolution of the homogenized properties with respect to the properties of individual constituents, the volume fraction, the spatial distribution, and the shape of inclusions is highlighted. The second part of the paper is devoted to the case of imperfectly bonded inclusions. An extension of the immersed interface method in this context makes it possible to study other aspects that have an influence on the effective properties such as the interfacial resistance and the size of inclusions. The application of the proposed numerical tool to some porous rocks in partially saturated condition shows good agreement with the available experimental results and demonstrates the performance and the flexibility of the developed procedure.Copyright © 2013 John Wiley & Sons, Ltd.

By using the upper bound finite-elements limit analysis, with an inclusion of single and two horizontal layers of reinforcements, the ultimate bearing capacity has been computed for a rigid strip footing placed over (i) fully granular, (ii) cohesive-frictional, and (iii) fully cohesive soils. It is assumed that (i) the reinforcements are structurally strong so that no axial tension failure can occur, (ii) the reinforcement sheets have negligible resistance to bending, and (iii) the shear failure can take place between the reinforcement and soil mass. It is expected that the different approximations on which the analysis has been based would generally remain applicable for reinforcements in the form of geogrid sheets. A method has been proposed to incorporate the effect of the reinforcement in the analysis. The efficiency factors, η_c and η_γ, to be multiplied with N_c and N_γ , for finding the bearing capacity of reinforced foundations, have been established. The results have been obtained (i) for different values of ϕ in case of fully granular and cohesive-frictional soils, and (ii) for different rates at which the cohesion increases with depth for a fully cohesive soil. The optimum positions of the reinforcements' layers have also been determined. The effect of the reinforcements' length on the results has also been analyzed. As compared to cohesive soils, the granular soils, especially with higher values of ϕ, cause a much greater increase in the bearing capacity. The results compare reasonably well with the available theoretical and experimental data from literature. Copyright © 2013 John Wiley & Sons, Ltd.

Artificial ground freezing (AGF) is a commonly used technique in geotechnical engineering for ground improvement such as ground water control and temporary excavation support during tunnel construction in soft soils. The main potential problem connected with this technique is that it may produce heave and settlement at the ground surface, which may cause damage to the surface infrastructure. Additionally, the freezing process and the energy needed to obtain a stable frozen ground may be significantly influenced by seepage flow. Evidently, safe design and execution of AGF require a reliable prediction of the coupled thermo-hydro-mechanical behavior of freezing soils. With the theory of poromechanics, a three-phase finite element soil model is proposed, considering solid particles, liquid water, and crystal ice as separate phases and mixture temperature, liquid pressure, and solid displacement as the primary field variables. In addition to the volume expansion of water transforming into ice, the contribution of the micro-cryo-suction mechanism to the frost heave phenomenon is described in the model using the theory of premelting dynamics. Through fundamental physical laws and corresponding state relations, the model captures various couplings among the phase transition, the liquid transport within the pore space, and the accompanying mechanical deformation. The verification and validation of the model are accomplished by means of selected analyses. An application example is related to AGF during tunnel excavation, investigating the influence of seepage flow on the freezing process and the time required to establish a closed supporting frozen arch. Copyright © 2013 John Wiley & Sons, Ltd.

Presented and discussed in this paper is an exact analytical solution of the nonhomogeneous partial differential equation governing the conventional one-dimensional consolidation under haversine repeated loading. The derived analytical solution to the 1D consolidation equation is compared with the numerical solution of the same consolidation problem via FEM. The series solution takes into account the frequency of repeated loading through a dimensionless time factor T₀. The paper reveals that an increase in the frequency of imposed repeated haversine loading (a decrease in period of repeated loading) causes an increase in the number of cycles required to achieve the steady state, whereas the effect of frequency on the maximum excess pore water pressure at the bottom of a clay layer with permeable top and impermeable bottom for the range of frequencies studied is generally insignificant. The effective stress at the bottom of the clay deposit with permeable top and impermeable bottom increases with time but with some fluctuations without changing the sign. These fluctuations become more pronounced for increasing values of T₀. An increase in T₀ also causes an increase in maximum effective stress.Copyright © 2013 John Wiley & Sons, Ltd.

The stability of a tunnel face driven by a pressurized shield is investigated in the light of a limit analysis kinematic approach formulated in the context of the modified Hoek–Brown strength criterion. The analysis focuses on evaluating the destabilizing effects induced by seismic loading. The pseudo-static approach is adopted to account for the effects of inertial forces developed in the rock mass by the passage of seismic waves. Taking advantage of the ability to compute analytically, the expressions of the support functions for the modified Hoek–Brown strength criterion, rigorous limit analysis solutions can be derived semi-analytically for the tunnel face stability. Particular emphasis is given to the description of the Horn failure mechanism and associated lower bound estimates of the limit face supporting pressure. The approach is then applied to investigate the influence of some relevant strength and loading parameters in the tunnel face stability.Copyright © 2013 John Wiley & Sons, Ltd.

At the mesoscopic scale, concrete can be considered as a mix of coarse aggregates with a mortar paste matrix. In this paper, we investigate numerically the influence of aggregates arrangements and loading rate on the tensile response of concrete. Each coarse aggregate is assumed to be circular with six different radiuses following the aggregates size distribution of real gravel. Rate-independent cohesive elements are used to model failure within the mesostructure. Our results show that the spatial distribution of heterogeneities does not influence the peak strength, while it changes the post-peak macroscopic response. This implies that our specimen size is large enough for strength computation but that larger mesostructures should be considered to obtain fully reliable toughness predictions. Although the cohesive approach is able to capture the transition from one macro-crack in quasi-static to multiple micro-cracks in fast dynamics, which increases the dissipated fracture energy, our results suggest that the full extent of the high-rate strengthening of concrete observed experimentally for loading rates greater than 1/s cannot be captured with rate independent constitutive laws.Copyright © 2013 John Wiley & Sons, Ltd.

A triangular wedge, composed of a frictional material such as sand, and accreting additional material at its front, is the classical prototype for accretionary wedges and fold-and-thrust belts. A simplified method is proposed to capture the internal deformation of this structure resulting from a large number of faulting events during compression. The method combines the application of the kinematic approach of limit analysis to predict the optimum thrust-fold and a set of geometrical rules to update the geometry accordingly, at each increment of shortening. It is shown that the structure topography remains approximately planar with a slope predicted by the critical Coulomb wedge theory. Failure by faulting occurs anywhere within the wedge at criticality, and its exact position is sensitive to topographic perturbations resulting from the deformation history. The convergence analysis in terms of the shortening increments and of the topography discretization reveals that the timing and the position of a single faulting event cannot be predicted. The convergence is achieved nevertheless in terms of the statistics of the distribution of the faulting events throughout the structure and during the entire deformation history. It is these two convergence properties that are presented to justify the claim that these compressed frictional wedges are imperfection sensitive, chaotic systems. Copyright © 2013 John Wiley & Sons, Ltd.

We present an explicit extended finite element framework for fault rupture dynamics accommodating bulk plasticity near the fault. The technique is more robust than the standard split-node method because it can accommodate a fault propagating freely through the interior of finite elements. To fully exploit the explicit algorithmic framework, we perform mass lumping on the enriched finite elements that preserve the kinetic energy of the rigid body and enrichment modes. We show that with this technique, the extended FE solution reproduces the standard split-node solution, but with the added advantage that it can also accommodate randomly propagating faults. We use different elastoplastic constitutive models appropriate for geomaterials, including the Mohr–Coulomb, Drucker–Prager, modified Cam-Clay, and a conical plasticity model with a compression cap, to capture off-fault bulk plasticity. More specifically, the cap model adds robustness to the framework because it can accommodate various modes of deformation, including compaction, dilatation, and shearing. Copyright © 2013 John Wiley & Sons, Ltd.

This paper presents a finite-element (FE) model for simulating injection well testing in unconsolidated oil sands reservoir. In injection well testing, the bottom-hole pressure (BHP) is monitored during the injection and shut-in period. The flow characteristics of a reservoir can be determined from transient BHP data using conventional reservoir or well-testing analysis. However, conventional reservoir or well-testing analysis does not consider geomechanics coupling effects. This simplified assumption has limitations when applied to unconsolidated (uncemented) oil sands reservoirs because oil sands deform and dilate subjected to pressure variation. In addition, hydraulic fracturing may occur in unconsolidated oil sands when high water injection rate is used. This research is motivated in numerical modeling of injection well testing in unconsolidated oil sands reservoir considering the geomechanics coupling effects including hydraulic fracturing. To simulate the strong anisotropy in mechanical and hydraulic behaviour of unconsolidated oil sands induced by fluid injection in injection well testing, a nonlinear stress-dependent poro-elasto-plastic constitutive model together with a strain-induced anisotropic permeability model are formulated and implemented into a 3D FE simulator. The 3D FE model is used to history match the BHP response measured from an injection well in an oil sands reservoir. Copyright © 2013 John Wiley & Sons, Ltd.

The phenomenon of excess pore water pressure increase or stagnation and continuing large ground deformation in soft sensitive clay following the completion of construction of embankment is simulated for a case study at Saint Alban, Quebec, Canada. The present model employs an updated Lagrangian finite element framework and is combined with an automatic time increment selection scheme. The simulation based on an elasto-viscoplastic constitutive model considers soil-structure degradation effect. It is shown that without consideration for the microstructural degradation effect, it is not possible to reproduce the field responses of soft sensitive clay even during the construction of the embankment. When the soil-structure degradation effect is considered, the present model can offer reasonably accurate prediction for the consolidation behavior of soft sensitive clay, including the so-called anomalous pore water pressure generation and continuing large deformation even after the end of construction, which has been posing numerous uncertainties on the long-term performance of earth structures. Copyright © 2013 John Wiley & Sons, Ltd.

Wheeler, Sharma and Buisson proposed an elasto-plastic constitutive model for unsaturated soils that couples the mechanical and water retention behaviours. The model was formulated for isotropic stress states and adopts the mean Bishop's stress and modified suction as stress state variables. This paper deals with the extension of this constitutive model to general three-dimensional stress conditions, proposing the generalized stress–strain relationships required for the numerical integration of the constitutive model. A characteristic of the original model is the consideration of a number of elasto-plastic mechanisms to describe the complex behaviour of unsaturated soils. This work presents the three-dimensional formulation of these coupled irreversible mechanisms in a generalized way including anisotropic loading. The paper also compares the results from the model with published experiments performed under different loading conditions. The response of the model is very satisfactory in terms of both mechanical and water retention behaviours. Copyright © 2013 John Wiley & Sons, Ltd.

Modelling failure in geomaterials, concrete or other quasi-brittle materials and proper accounting for size effect, geometry and boundary effects are still pending issues. Regularised failure models are capable of describing size effect on specimens with a specific geometry, but extrapolations to other geometries are rare, mostly because experimental data presenting size effect for different geometries and for the same material are lacking. Three-point bending fracture tests of geometrically similar notched and unnotched specimens are presented. The experimental results are compared with numerical simulations performed with an integral-type non-local model. Comparisons illustrate the shortcomings of this classical formulation, which fails to describe size effect over the investigated range of geometries and sizes. Finally, experimental results are also compared with the universal size effect law. Copyright © 2013 John Wiley & Sons, Ltd.

As is well known, granular soils under cyclic loading dissipate a large amount of energy and accumulate large irreversible strains. Usually, with time, this second effect reduces and the accumulation rate decreases with the number of cycles until obtaining a sort of ideal stationary cyclic state at which ratcheting disappears. In this paper, only this ideal state is taken into consideration and simulated by means of a multi-mechanism constitutive model for plastic adaptation. For this purpose, the concept of cycle is discussed, many different categories of cyclic stress/strain paths are considered and some theoretical issues concerning both the flow and the strain-hardening rules are tackled. Even though the paper focuses on soil behaviour, the conclusions can be extended to all materials exhibiting ratcheting due to volumetric behaviour.Copyright © 2013 John Wiley & Sons, Ltd.

This paper aims at extending the well-known critical state concept, associated with quasi-static conditions, by accounting for the role played by the strain rate when focusing on the steady, simple shear flow of a dry assembly of identical, inelastic, soft spheres. An additional state variable for the system, the granular temperature, is accounted for. The granular temperature is related to the particle velocity fluctuations and measures the agitation of the system. This state variable, as is in the context of kinetic theories of granular gases, is assumed to govern the response of the material at large strain rates and low concentrations. The stresses of the system are associated with enduring, frictional contacts among particles involved in force chains and nearly instantaneous collisions. When the first mechanism prevails, the material behaves like a solid, and constitutive models of soil mechanics hold, whereas when inelastic collisions dominate, the material flows like a granular gas, and kinetic theories apply. Considering a pressure-imposed flow, at large values of the normal stress and small values of the shear rate, the theory predicts a nonmonotonic shear rate dependence of the stress ratio at the steady state, which is likely to govern the evolution of landslides.Copyright © 2013 John Wiley & Sons, Ltd.

It has been established that the second-order work criterion is a general necessary condition for all instabilities by divergence in rate-independent granular materials. The relation between the values of discrete second-order work at the intergranular contact point level and its global macroscopic value is recalled at the beginning of this paper. Then, the basic purpose of the paper is tackled by an analysis of the main features of second-order work criterion in relation with the granular microstructure. For that, it is considered a novel micromechanical model (the so-called ‘H-microdirectional model’), which has the property to involve three scales: grain scale, mesoscale with a specific granular configuration and continuum mechanics macroscale. Eventually, these exhibited features (a bifurcation stress domain and some instability cones) are qualitatively compared with the ones provided by direct numerical simulations issued from a discrete element model. The ultimate goal is to analyse what happens at the granular scale, when the macrosecond-order work is vanishing at the macrolevel. Copyright © 2013 John Wiley & Sons, Ltd.

This paper presents a fracture mapping (FM) approach combined with the extended finite element method (XFEM) to simulate coupled deformation and fluid flow in fractured porous media. Specifically, the method accurately represents the impact of discrete fractures on flow and deformation, although the individual fractures are not part of the finite element mesh. A key feature of FM-XFEM is its ability to model discontinuities in the domain independently of the computational mesh. The proposed FM approach is a continuum-based approach that is used to model the flow interaction between the porous matrix and existing fractures via a transfer function. Fracture geometry is defined using the level set method. Therefore, in contrast to the discrete fracture flow model, the fracture representation is not meshed along with the computational domain. Consequently, the method is able to determine the influence of fractures on fluid flow within a fractured domain without the complexity of meshing the fractures within the domain. The XFEM component of the scheme addresses the discontinuous displacement field within elements that are intersected by existing fractures. In XFEM, enrichment functions are added to the standard finite element approximation to adequately resolve discontinuous fields within the simulation domain. Numerical tests illustrate the ability of the method to adequately describe the displacement and fluid pressure fields within a fractured domain at significantly less computational expense than explicitly resolving the fracture within the finite element mesh. Copyright © 2013 John Wiley & Sons, Ltd.

This paper aims to evaluate the performance of several recent constitutive models in simulating the thermo-mechanical behaviour of saturated clays. A classic thermo-mechanical test on natural Boom Clay, commonly used in constitutive modelling, was first clarified. Different methods commonly used to measure volumetric strain in drained heating tests were then discussed. Model evaluation was performed in terms of thermodynamic and elasto-plastic requirements. The capability of the models to capture the observed behaviour was assessed on the basis of the experimental evidence. It was shown that all the models provide reasonable predictions of the thermo-mechanical behaviour of saturated clays. However, each constitutive model has its own limitations or unclear points from the theoretical point of view. Copyright © 2013 John Wiley & Sons, Ltd.

Observations from earthquakes over the past several decades have highlighted the importance of local site conditions on propagated ground motions. Downhole arrays are deployed to measure motions at the ground surface and within the soil profile, and also to record the pore pressure response within the soft soil profiles during excitation. The degradation of soil stiffness as excess pore pressures are generated during earthquake events has also been observed. An inverse analysis framework is developed and demonstrated to directly extract soil material behavior including pore water pressure (PWP) generation from downhole array measurements that can then be readily used in 1D nonlinear site response analysis. The self-learning simulations (SelfSim) inverse analysis framework, previously developed for total stress site response analysis, is extended to extract PWP generation behavior of the soil in addition to cyclic response during ground shaking. A Neural Network based constitutive model is introduced to represent PWP generation during cyclic loading. A new analysis scheme is introduced that can use data from co-located piezometer and accelerometer sensors. The successful performance of the proposed framework is demonstrated using four synthetic vertical array recordings. Copyright © 2013 John Wiley & Sons, Ltd.

In this note, we examine the flow towards a well in a confined aquifer in the presence of an interaction force defined by the sum of three terms, namely, a Darcy term (linear in the velocity), a Forchheimer term (quadratic in the velocity), and an added-mass term (linear in the acceleration). We obtain the exact dynamic solution for the piezometric head distribution around the well and investigate the relative importance of the non-Darcian terms. Copyright © 2013 John Wiley & Sons, Ltd.

Non-associated flow rule is essential when the popular Mohr–Coulomb model is used to model nonlinear behavior of soil. The global tangent stiffness matrix in nonlinear finite element analysis becomes non-symmetric when this non-associated flow rule is applied. Efficient solution of this large-scale non-symmetric linear system is of practical importance. The standard Krylov solver for a non-symmetric solver is Bi-CGSTAB. The Induced Dimension Reduction [IDR(s)] solver was proposed in the scientific computing literature relatively recently. Numerical studies of a drained strip footing problem on homogenous soil layer show that IDR(s = 6) is more efficient than Bi-CGSTAB when the preconditioner is the incomplete factorization with zero fill-in of global stiffness matrix K_ep (ILU(0)-K_ep). Iteration time is reduced by 40% by using IDR(s = 6) with ILU(0)-K_ep. To further reduce computational cost, the global stiffness matrix K_ep is divided into two parts. The first part is the linear elastic stiffness matrix K_e, which is formed only once at the beginning of solution step. The second part is a low-rank matrix Δ, which is re-formed at each Newton–Raphson iteration. Numerical studies show that IDR(s = 6) with this ILU(0)-K_e preconditioner is more time effective than IDR(s = 6) with ILU(0)-K_ep when the percentage of yielded Gauss points in the mesh is less than 15%. The total computation time is reduced by 60% when all the recommended optimizing methods are used. Copyright © 2013 John Wiley & Sons, Ltd.

One-dimensional consolidation analysis of layered soils conventionally entails solving a system of differential equations subject to the flow conditions at the bounding upper and lower surfaces, as well as the continuity conditions at the interface of every pair of contiguous layers. Formidable computational efforts are required to solve the ensuing transcendental equations expressing the matching conditions at the interfaces, using this method. In this paper, the jump discontinuities in the flow parameters upon crossing from one layer to the other have been systematically built into a single partial differential equation governing the space–time variation of the excess pore pressure in the entire composite medium, by the use of the Heaviside distribution. Despite the presence of the discontinuities in the coefficients of the differential equation, a closed-form solution in the sense of an infinite generalized Fourier series is obtained, in addition to which is the development of a Green's function for the differential problem. The eigenfunctions of the composite medium are the coordinate functions of the series, obtained computationally through the application of the extended equations of Galerkin. The analysis has been illustrated by solving the consolidation problem of a four-layer composite, and the results obtained agree very well with the results obtained by previous researchers. Copyright © 2013 John Wiley & Sons, Ltd.

Stability of a circular earth dam is assessed for radial cracking potential and static slope stability using continuum mechanics-based three-dimensional numerical models. Comparisons of numerical model results for a circular water tank with vertical walls and different radii with their analytical counterparts are included to support the validity of the ideas and their implementation in the continuum mechanics-based computer program used. Effects of sloping wall faces and Poisson's ratio on computed deformations and stresses are also included. The same numerical models are used to assess stability of a circular dam in terms of factor-of-safety and associated failure surface. Three-dimensional slope stability analysis results are compared with continuum based two-dimensional slope stability analysis results to assess the magnitude of 3D effects. Example problems are included to illustrate the use of ideas presented. Published 2013. This article is a U.S. Government work and is in the public domain in the USA.

In the framework of elastostatics, a mathematical treatment is presented for the boundary value problem of the interaction of a flexible cylindrical pile embedded in a transversely isotropic half-space under transverse loadings. Taking the pile region as a stiffened subdomain of an extended half-space, the formulation of the interaction problem is reduced to a Fredholm integral equation of the second kind. The necessary set of Green's functions for the transversely isotropic half-space is obtained by means of a method of potentials. The resulting Green's functions are incorporated into a numerical procedure for the solution of the integral equation. The theoretical response of the pile is presented in terms of bending moment, displacement and slope profiles for a variety of transversely isotropic materials so that the effect of different anisotropy parameters can be meaningfully discussed. Copyright © 2013 John Wiley & Sons, Ltd.

This paper presents a novel analytical solution to the transient, z-dependent, and asymmetric problem of an infinite wellbore drilled into a fluid-saturated porous medium. The formulations are based on Biot's linear theory of poroelasticity, in which the dependency of poroelastic field variables to spatial coordinates as well as time domain is considered in the most general form. This gives flexibility to the solution in cases that cannot be analyzed using the conventional plane strain or symmetric models. One such case is when calculating the stress variations around an inclined wellbore where the far-field stresses are acting over a finite vertical section. The results of our solution to this case with a three-dimensional state of far-field stress are used to analyze the stability of inclined wellbores passing through abnormally stressed formations.

The presented solution is capable of finding expressions for fundamental solutions with stress or flow boundary conditions at the wellbore. These solutions are here adopted to analyze the pressure disturbances generated by multiprobe formation tester, a standard wireline device that is designed for downhole fluid sampling as well as estimating the directional permeabilities of subsurface earth formations. A comparison with the conventional solution for the relevant pressure diffusion equation indicates that the poroelastic effect is relatively significant in relation to the transient response of the pore pressure. Further, it is shown that the finite dimensions of sink probe would, to a great extent, contribute to the formation's pore pressure variations at its immediate proximity. Copyright © 2013 John Wiley & Sons, Ltd.

The dynamic response of an end bearing pile embedded in a linear visco-elastic soil layer with hysteretic type damping is theoretically investigated when the pile is subjected to a time-harmonic vertical loading at the pile top. The soil is modeled as a three-dimensional axisymmetric continuum in which both its radial and vertical displacements are taken into account. The pile is assumed to be vertical, elastic and of uniform circular cross section. By using two potential functions to decompose the displacements of the soil layer and utilizing the separation of variables technique, the dynamic equilibrium equation is uncoupled and solved. At the interface of soil-pile system, the boundary conditions of displacement continuity and force equilibrium are invoked to derive a closed-form solution of the vertical dynamic response of the pile in frequency domain. The corresponding inverted solutions in time domain for the velocity response of a pile subjected to a semi-sine excitation force applied at the pile top are obtained by means of inverse Fourier transform and the convolution theorem. A comparison with two other simplified solutions has been performed to verify the more rigorous solutions presented in this paper. Using the developed solutions, a parametric study has also been conducted to investigate the influence of the major parameters of the soil-pile system on the vertical vibration characteristics of the pile. Copyright © 2013 John Wiley & Sons, Ltd.

An adaptively stabilized finite element scheme is proposed for a strongly coupled hydro-mechanical problem in fluid-infiltrating porous solids at finite strain. We first present the derivation of the poromechanics model via mixture theory in large deformation. By exploiting assumed deformation gradient techniques, we develop a numerical procedure capable of simultaneously curing the multiple-locking phenomena related to shear failure, incompressibility imposed by pore fluid, and/or incompressible solid skeleton and produce solutions that satisfy the inf-sup condition. The template-based generic programming and automatic differentiation (AD) techniques used to implement the stabilized model are also highlighted. Finally, numerical examples are given to show the versatility and efficiency of this model. Copyright © 2013 John Wiley & Sons, Ltd.

Kinematic pile–soil interaction under vertically impinging seismic P waves is revisited through a novel continuum elastodynamic solution of the Tajimi type. The proposed model simulates the steady-state kinematic response of a cylindrical end-bearing pile embedded in a homogeneous viscoelastic soil stratum over a rigid base, subjected to vertically propagating harmonic compressional waves. Closed-form solutions are obtained for the following: (i) the displacement field in the soil and along the pile; (ii) the kinematic Winkler moduli (i.e., distributed springs and dashpots) along the pile; (iii) equivalent, depth-independent, Winkler moduli to match the motion at the pile head. The solution for displacements is expressed in terms of dimensionless transfer functions relating the motion of the pile head to the free-field surface motion and the rock motion. It is shown that (i) a pile foundation may significantly alter (possibly amplify) the vertical seismic excitation transmitted to the base of a structure and (ii) Winkler moduli pertaining to kinematic loading differ from those for inertial loading. Simple approximate expressions for kinematic Winkler moduli are derived for use in applications.Copyright © 2013 John Wiley & Sons, Ltd.

This paper presents two test procedures for evaluating the bond stress–slip and the slip–radial dilation relationships when the prestressing force is transmitted by releasing the steel (wire or strand) in precast prestressed elements. The bond stress–slip relationship is obtained with short length specimens, to guarantee uniform bond stress, for three depths of the wire indentation (shallow, medium and deep). An analytical model for bond stress–slip relationship is proposed and compared with the experimental results. The model is also compared with the experimental results of other researchers. Since numerical models for studying bond-splitting problems in prestressed concrete require experimental data about dilatancy angle (radial dilation), a test procedure is proposed to evaluate these parameters. The obtained values of the radial dilation are compared with the prior estimated by numerical modelling and good agreement is reached. Copyright © 2012 John Wiley & Sons, Ltd.

This paper presents a numerical analysis of the influence of initial stress state on the response of deep excavation supported by retaining wall. Indeed, the influence of diaphragm wall installation prior to excavation works may affect the soil response and lateral wall deflection induced by excavation process. The first part of this paper gives a short review of the numerical methods aimed to reproduce the retaining wall installation. Numerical analysis of a deep excavation in two-dimensional and three-dimensional conditions is then performed according to the methods previously presented. In three-dimensional conditions, diaphragm wall installation is performed considering a sequence of panels, described by their number and length. Results of three-dimensional calculations confirm that stress state is disturbed by wall installation, which has a sensitive effect on the ground response induced by soil excavation. It is also noted that these results are not easily reproduced in two-dimensional conditions. Copyright © 2012 John Wiley & Sons, Ltd.

A meso-scale particle model is presented to simulate the expansion of concrete subjected to alkali-aggregate reaction (AAR) and to analyze the AAR-induced degradation of the mechanical properties. It is the first attempt to evaluate the deterioration mechanism due to AAR using the discrete-element method. A three-phase meso-scale model for concrete composed of aggregates, mortar and the interface is established with the combination of a pre-processing approach and the particle flow code, PFC2D. A homogeneous aggregate expansion approach is applied to model the AAR expansion. Uniaxial compression tests are conducted for the AAR-affected concrete to examine the effects on the mechanical properties. Two specimens with different aggregate sizes are analyzed to consider the effects of aggregate size on AAR. The results show that the meso-scale particle model is valid to predict the expansion and the internal micro-cracking patterns caused by AAR. The two different specimens exhibit similar behavior. The Young's modulus and compressive strength are significantly reduced with the increase of AAR expansion. The shape of the stress–strain curves obtained from the compression tests clearly reflects the influence of internal micro-cracks: an increased nonlinearity before the peak loading and a more gradual softening for more severely affected specimens. Similar macroscopic failure patterns of the specimens under compression are observed in terms of diagonal macroscopic cracks splitting the specimen into several triangular pieces, whereas localized micro-cracks forming in slightly affected specimens are different from branching and diffusing cracks in severely affected ones, demonstrating different failure mechanisms. Copyright © 2012 John Wiley & Sons, Ltd.

Stress history plays an important role in controlling the consolidation behavior of soft clays, but few models exist that can provide quantitative estimate of its influence. In this paper, the Gibson–Lo rheological model is used to simulate the coupled processes of drainage and creep of soft soils that takes stress history into account. A hybrid combination of analytical and numerical methods is adopted to solve the governing equations of consolidation with the nonlinear rheological model. The methodology is applied to a saturated soft soil subjected to surface loading. The soil profile is separated into normally consolidated and overconsolidated layers by a boundary that is allowed to move. Comparisons of the model predictions and its simulations are used to evaluate the effects of stress history, model parameters, and loading pattern on consolidation behavior. It is shown that stress history influences the location of the moving boundary, variations of the profiles of excess pore water pressure dissipation, stress and deformation-based average degrees of consolidation. Parametric studies conducted show that when soil is stiffer, the excess pore water pressure dissipates much more quickly, and thus the soil consolidates much faster especially at the early stages. The results also show that soil viscosity influences the deformation-based average degree of consolidation at the latter stages. The consolidation process of soil layer under linear loading is shown to lag behind those under instantaneous loading: the longer the loading period is, the smaller the average degrees of consolidation are no matter how they are defined. Copyright © 2012 John Wiley & Sons, Ltd.

For prediction of rockfalls, the failure of rock joints is studied. Considering these failures as constitutive instabilities, a second-order work criterion is used because it explains all divergence instabilities (flutter instabilities are excluded). The bifurcation domain and the loading directions of instabilities, which fulfill the criterion, are determined for any piecewise linear constitutive relation. The instability of rock joints appears to be ruled by coupling features of the behavior (e.g., dilatancy). Depending on the loading parameters, instabilities can lead to failure, even before the plastic limit criterion. Results for two given constitutive relations illustrate the approach. Some given loading paths are especially considered. Constant volume (undrained) shear and τ-constant paths are stable or not depending on the link between the deviatoric stress and strain along undrained paths, as found for soils. Some unstable loading paths are illustrated. Along these paths, failure before the plastic limit criterion is possible. The corresponding failure rules are determined. Copyright © 2012 John Wiley & Sons, Ltd.

Understanding the response of partially saturated soils under different loads is important for the design and construction of economical and safe geotechnical engineering structures. This paper presents a coupled elastoplastic constitutive model for predicting the hydraulic and stress–strain–strength behaviour of unsaturated soils. The model proposed is built according to the following principle. A constitutive relation is given for each phase (solid, liquid and gas) and coupling relations between each phases are also derived. In the present case, we assume that each phase is not miscible and that pressure in voids not filled by water remains more or less constant, which is reasonable for most geotechnical problems. Therefore, the model is written in a classical manner with

• a non associated elastoplastic model for the granular skeleton behaviour;

• an incompressible liquid phase;

• a water retention description; and

• an assumption of the existence of an effective stress concept defined by Bishop.

According to the strong hypotheses made earlier about the fluid phases, the perfect gas law is not written for the gas phase. Therefore, the gas volume is defined as being the same as the void volume not filled by water. The main originality of this work is in the description of the water retention behaviour and in that of the coupling parameter using the Bishop relationship. A discussion on this parameter and the description of the so called loading-collapse phenomenon are provided. We demonstrate that this paradox can be explained without introducing suction in the expression of the plastic yield surface. Copyright © 2012 John Wiley & Sons, Ltd.

Thermal recovery from a hot dry rock (HDR) reservoir viewed as a deformable fractured medium is investigated with a focus on the assumption of local thermal non-equilibrium (LTNE).

Hydraulic diffusion, thermal diffusion, forced convection and deformation are considered in a two-phase framework, the solid phase being made by impermeable solid blocks separated by saturated fractures. The finite element approximation of the constitutive and field equations is formulated and applied to obtain the response of a generic HDR reservoir to circulation tests. A change of time profile of the outlet fluid temperature is observed as the fracture spacing increases, switching from a single-step pattern to a double-step pattern, a feature which is viewed as characteristic of established LTNE. A dimensionless number is proposed to delineate between local thermal equilibrium (LTE) and non-equilibrium. This number embodies local physical properties of the mixture, elements of the geometry of the reservoir and the production flow rate. All the above properties being fixed, the resulting fracture spacing threshold between LTNE and LTE is found to decrease with increasing porosity or fluid velocity. The thermally induced effective stress is tensile near the injection well, illustrating the thermal contraction of the rock, while the pressure contribution of the fracture fluid is negligible during the late period. Copyright © 2012 John Wiley & Sons, Ltd.

In the predicting of geological variables, artificial neural networks (ANNs) have some drawbacks including possibility of getting trapped in local minima, over training, subjectivity in the determining of model parameters and the components of its complex structure. Recently, support vector machines (SVM) has been found to be popular in prediction studies due to its some advantages over ANNs. Because the least squares SVM (LS-SVM) provides a computational advantage over SVM by converting quadratic optimization problem into a system of linear equations, LS-SVM method is also tried in study. The main purpose of this study is to examine the capability of these two SVM algorithms for the prediction of tensile strength of rock materials and to compare its performance with ANN and linear regression (MLR) models. Total porosity, sonic velocity, slake durability index and aggregate impact value were used as input in modeling applications. Favorite performance evaluation measures were employed to assess developed models. The results determined in study indicate that the SVM, LS-SVM and ANN methods are successful tools for prediction of tensile strength variable and can give good prediction performances than MLR model. Although these three methods are powerful artificial intelligence techniques, LS-SVM makes the running time considerably faster with the higher accuracy. In terms of accuracy, the LS-SVM model resulted in error reductions relative to that of the other models. Copyright © 2012 John Wiley & Sons, Ltd.

The purpose of this paper is to develop the macroscopic model of hydro-mechanical coupling for the case of a porous medium containing isolated cracks or/and vugs. In the development, we apply the asymptotic expansion homogenization method. It is shown that the general structure of Biot's model is the same as in the case of homogeneous medium, but the poro-elastic parameters are modified. Two numerical examples are presented. They concern the computations of Biot's parameters in isotropic and anisotropic cases. It can also be seen how the presence of near-zero-volume cracks influences Biot's parameters of the porous matrix. It can significantly affect the coupled hydro-mechanical behaviour of damaged porous medium. Copyright © 2012 John Wiley & Sons, Ltd.

Stress–strain modeling of sand–silt mixtures is important in the analysis and design of earth structures. In this paper, we develop a stress–strain model that can predict the behavior of sand–silt mixtures with any amount of fines content. This model is based on a micromechanics approach, which involves mean-field assumptions. For the mixtures with low amount of fines, the mechanical behavior is dominated by sand grains network. On the other hand, for the mixtures with high amount of fines, the mechanical behavior is dominated by silt grains network. Using this concept of dominant grains network, the behavior of mixtures with any amount of fines can be predicted from knowing the behavior of sand and silt, alone. We also modeled the critical state friction angle, critical state void ratio, and elastic stiffness for the mixtures as a function of fines content. The applicability of this developed stress–strain model is shown by comparing the simulated and measured results for two different types of sand–silt mixtures with full range of fines content. Copyright © 2012 John Wiley & Sons, Ltd.

The paper presents a constitutive model for simulating the high strain-rate behavior of sands. Based on the concepts of critical-state soil mechanics, the bounding surface plasticity theory and the overstress theory of viscoplasticity, the constitutive model simulates the high strain-rate behavior of sands under uniaxial, triaxial and multi-axial loading conditions. The model parameters are determined for Ottawa and Fontainebleau sands, and the performance of the model under extreme transient loading conditions is demonstrated through simulations of split Hopkinson pressure bar tests up to a strain rate of 2000/s. The constitutive model is implemented in a finite-element analysis software Abaqus to analyze underground tunnels in sandy soil subjected to internal blast loads. Parametric studies are conducted to examine the effect of relative density and type of sand and of the depth of tunnel on the variation of stresses and deformations in the soil adjacent to the tunnels. Copyright © 2012 John Wiley & Sons, Ltd.

Integration of poromechanics and fracture mechanics plays an important role in understanding a series of thermal fracturing phenomena in subsurface porous media such as cold water flooding for enhanced oil recovery, produced-water reinjection for waste disposal, cold water injection for geothermal energy extraction, and CO₂ injection for geosequestration. Thermal fracturing modeling is important to prevent the potential risks when fractures propagate into undesired zones, and it involves the coupling of heat transfer, mass transport, and stress change as well as the fracture propagation. Analytical method, finite element method, and finite difference method as well as boundary element method have been used to perform the thermal fracturing modeling considering different degrees and combinations of coupling. In this paper, extended finite element method is employed for the thermal fracturing modeling in a fully coupled fashion with remeshing avoided, and the stabilized finite element method is employed to account for the convection-dominated heat transfer in the fracturing process with numerical oscillation circumvented. With the thermal fracturing model, a hypothetical numerical experiment on cold water injection into a deep warm aquifer is conducted. Results show that parameters such as injection rate, injection temperature, aquifer stiffness, and permeability can affect the fracture development in different ways and extended finite element method and stabilized finite element method provide effective tools for thermal fracturing simulation. Copyright © 2012 John Wiley & Sons, Ltd.

Based on hypotheses derived directly from experimental observations of the triaxial behaviour, a constitutive model for fibre reinforced sands is built in this paper. Both the sand matrix and the fibres obey their own constitutive law, whereas their contributions are superimposed using a volumetric homogenization procedure. The Severn-Trent sand model, which combines well-known concepts such as critical state theory, Mohr-Coulomb like strength criterion, bounding surface plasticity and kinematic hardening, is adopted for the sand matrix. Although the fibres are treated as discrete forces with defined orientation, an equivalent continuum stress for the fibre phase is derived to allow the superposition of effects of sand and fibres. The fibres are considered as purely tensile elements following a linear elastic constitutive rule. The strain in the fibres is expressed as a fraction of the strain in the reinforced sample so that imperfect bonding is assumed at the sand-fibre interface. Only those fibres oriented within the tensile strain domain of the sample can mobilize tensile stress—the orientation of fibres is one of the key ingredients to capture the anisotropic behaviour of fibre reinforced soil that is observed for triaxial compression and extension loading. A further mechanism of partition of the volume of voids between the fibres and the sand matrix is introduced and shown to be fundamental for the simulation of the volumetric behaviour of fibre-reinforced soils. Copyright © 2012 John Wiley & Sons, Ltd.

This paper extends the material point method to analyze coupled dynamic, two-phase boundary-valued problems via a velocity formulation, in which solid and fluid phase velocities are the variables. Key components of the proposed approach are the adoption of Verruijt's sequence of update steps when integrating over time and the enhancement of volumetric strains. The connection between fractional step method and the time-stepping algorithm presented in this paper is addressed.

Enhancement of volumetric strains allows lower order variations in pressure and mitigates spurious pressure fields and locking that plague low-order finite-element implementations.

A stress averaging technique to smoothen stress variations is proposed, and the local damping procedure adopted by FLAC is extended to handle two-phase problems. Special Kelvin-Voigt boundaries are developed to suppress reflections at artificial boundaries. Idealized examples are presented to demonstrate the capability of the proposed framework to accurately capture the physics of wave propagation, consolidation and wave attack on a sea dike. Copyright © 2012 John Wiley & Sons, Ltd.

This paper proposes a numerical model for jointed rock masses within the 3-D numerical manifold method (NMM) framework equipped with a customized contact algorithm. The strength of rock sample containing a few sets of discontinuities is first investigated. The results of models with simple geometries are compared with the available analytical solutions to verify the developed computer code, whereas models with complex geometries are simulated to better understand the fundamental behavior and failure mechanism of jointed rock mass. Furthermore, the stability of jointed rock mass in an underground excavation is studied, where rock failure process is determined by the 3-D NMM simulation. The simulation results provide valuable guidance on excavation process design and stabilization design in rock engineering practice. Copyright © 2012 John Wiley & Sons, Ltd.

Groundwater flow in a peninsula or an elongated island is influenced by tidal fluctuations on both sides of the peninsula or island, which is named as dual tidal fluctuations. In this study, semianalytical solutions of transient groundwater flow in response to dual tidal fluctuations in an aquifer–aquitard system were presented for cases with and without the aquitard storage. These solutions were first derived using the Laplace transform and subsequently computed by the Fourier series numerical inverse Laplace transform. The derived solutions were found to agree very well with the results of numerical simulations by MODFLOW. The solution ignoring the aquitard storage approached the quasi-steady state solution quickly when the mean sea level initial condition was used. The solutions with and without the aquitard storage were nearly the same at the early time and were separated from each other during the intermediate time, and the difference of solutions became constant at late time for small aquifer/aquitard storativity ratio and large tidal frequency. The propagation bias, which is the departure from the theoretical ratio of tidal attenuation to tidal lag, was enhanced not only with increase of the dimensionless specific leakage (aquitard/aquifer hydraulic conductance ratio) but also with decrease of the aquifer/aquitard storativity ratio and with the increase of the dimensionless tidal frequency. The solution with the aquitard storage was more sensitive to these three parameters. The newly developed solutions were capable of handling realistic initial conditions that might be approximated by piecewise linear functions. Copyright © 2012 John Wiley & Sons, Ltd.

Key in predicting stability in sands during dynamic events is gaining a fundamental understanding of the physics of its deformation and failure at high pressures. In this paper are reported results of an experimental investigation into the high-pressure (up to 700 MPa) mechanical response of Quikrete sand. During all triaxial compression tests, the material exhibited hardening up to failure while both compressibility and dilatancy regimes of the volumetric response were observed. Furthermore, the transition from compressibility to dilatancy was found to be highly dependent on confining pressure. By performing triaxial compression tests with several creep stages followed by unloading–reloading cycles, the time influence of the overall response was detected. Using the experimental data, a new model that captures both compressibility and dilatancy has been developed. Comparison between model predictions and data showed that the proposed model describes well the main characteristics of the high-pressure response of sand. Copyright © 2012 John Wiley & Sons, Ltd.

In this study, on the basis of the Floquet transform method, a numerical model for the simulation of the vibration isolation via multiple periodic pile rows with infinite number of piles is established. By means of the fictitious pile method due to Muki and Sternberg, the second kind of Fredholm integral equations for the pile rows are developed by using the fundamental solutions for the half-space and the compatibility conditions between the piles and half-space. Employing the Floquet transform method, integral equations for the pile rows in the wavenumber domain are then derived. Solution of the integral equations yields the wavenumber domain solution for the pile rows. The space domain solution can then be retrieved by inversion of the Floquet transform. Numerical results show that the proposed model with the Floquet transform method is in a good agreement with those of the conventional direct superposition method. On the basis of the new model, influences of the spacing between neighboring piles, the Young's modulus of the piles, and the pile length on the vibration isolation effect of the pile rows are investigated. Numerical simulations conducted in this study show that compared with the direct superposition method, the efficiency of the proposed model for simulation of the vibration isolation via pile rows is very high. Copyright © 2012 John Wiley & Sons, Ltd.

An extensive examination of the discontinuous deformation analysis (DDA) in block dynamic sliding modeling is carried out in this paper. Theoretical solutions for a single block sliding on an arbitrarily inclined plane by applying the horizontal/vertical seismic loadings to the sliding block as acceleration time histories or to the base as constraint displacement time histories are derived. As compared with the theoretical solutions, for a single block sliding, the DDA predicts the sliding displacements and block interaction forces accurately under various base incline angles and friction angles under both the harmonic loadings and a real seismic loading. The vertical seismic component may influence the block sliding displacements to different extent, and the DDA can capture these phenomena successfully and give accurate results. For the calculation of the single block relative sliding, both the theoretical and the DDA solutions indicate that applying the seismic accelerations as constraint displacement time histories (derived by integrating the seismic accelerations twice) to the base is equivalent to applying the seismic accelerations as volume forces to the sliding block in the opposite directions. The DDA modeling also demonstrates that this conclusion still stands for the case of multi-block sliding. Copyright © 2012 John Wiley & Sons, Ltd.

An analytical investigation of a half-space containing transversely isotropic material under forced vertical and horizontal displacements applied on a rectangular rigid foundation is presented in this paper. With the goal of a rigorous solution to the shape- and rigidity- induced singular mixed boundary value problem, the formulation employs scalar potential representation, the Fourier expansion and the Hankel integral transforms method to obtain the surface arbitrary point-load solution in cylindrical coordinate system. The obtained Green's functions are rewritten in rectangular coordinate system, allowing the response of the half-space because of an arbitrary distributed load on a rectangular surface area be given in terms of a double integral. The numerical evaluations of stresses are done with the use of an element, which is singular at the edge and the corner of the rectangle. Upon the imposition of the rigidity displacement boundary condition for a rigid foundation and the use of a set of two-dimensional adaptive-gradient elements, which can capture the singular behavior in the contact stress effectively, a set of new numerical results are presented to illustrate the effect of transverse isotropy on the foundation response. Copyright © 2012 John Wiley & Sons, Ltd.

In this article, a typical and representative kinematic hardening soil model is first studied to investigate its capabilities to reproduce soil responses under principal stress rotations (PSR). It is found that the model is capable of reproducing the non-coaxiality very well. It can qualitatively capture the trends of responses of different stress and strain components, without the capability to quantitatively reproduce these responses. Its prediction of volumetric responses is the poorest and can give wrong results in many cases. The underlying reasons for these capabilities and defects are analyzed in detail. The model is subsequently modified to better take into account the PSR influences. An additional new flow rule and plastic modulus for the PSR are developed. One important feature of the model is that it is developed in the general stress space with six stress variables. Therefore, it can take into account multiple PSRs at different directions. Another feature is that it retains the linear stress rate–strain rate relationship, which facilitates its numerical implementations. In addition, the universal characteristic of the theory makes it equally applicable to other kinematic hardening models. Copyright © 2012 John Wiley & Sons, Ltd.

Modeling hydraulic fracturing in the presence of a natural fracture network is a challenging task, owing to the complex interactions between fluid, rock matrix, and rock interfaces, as well as the interactions between propagating fractures and existing natural interfaces. Understanding these complex interactions through numerical modeling is critical to the design of optimum stimulation strategies. In this paper, we present an explicitly integrated, fully coupled discrete-finite element approach for the simulation of hydraulic fracturing in arbitrary fracture networks. The individual physical processes involved in hydraulic fracturing are identified and addressed as separate modules: a finite element approach for geomechanics in the rock matrix, a finite volume approach for resolving hydrodynamics, a geomechanical joint model for interfacial resolution, and an adaptive remeshing module. The model is verified against the Khristianovich–Geertsma–DeKlerk closed-form solution for the propagation of a single hydraulic fracture and validated against laboratory testing results on the interaction between a propagating hydraulic fracture and an existing fracture. Preliminary results of simulating hydraulic fracturing in a natural fracture system consisting of multiple fractures are also presented. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, 3D steady-state fluid flow in a porous medium with a large number of intersecting fractures is derived numerically by using collocation method. Fluid flow in the matrix and fractures is described by Darcy's law and Poiseuille's law, respectively. The recent theoretical development presented a general potential solution to model the steady-state flow in fractured porous media under a far-field condition. This solution is a hypersingular integral equation with pressure field in the fracture surfaces as the main unknown. The numerical procedure can resolve the problem for any form of fractures and also takes into account the interactions and the intersection between fractures. Once the pressure field and then the flux field in fractures have been determined, the pressure field in the porous matrix is computed completely. The basic problem of a single fracture is investigated, and a semi-analytical solution is presented. Using the solution obtained for a single fracture, Mori-Tanaka and self-consistent schemes are employed for upscaling the effective permeability of 3D fractured porous media. Copyright © 2012 John Wiley & Sons, Ltd.

Selected gas pulse tests on initially saturated claystone samples under isotropic confinement pressure are simulated using a 3D thermo-hydro-mechanical code. The constitutive model considers the hydro-mechanical anisotropy of argillaceous rocks. A cross-anisotropic linear elastic law is adopted for the mechanical behaviour. Elements for a proper modelling of gas flow along preferential paths include an embedded fracture permeability model. Rock permeability and its retention curve depend on strains through a fracture aperture. The hydraulic and mechanical behaviours have a common anisotropic structure. Small-scale heterogeneity is considered to enhance the initiation of flow through preferential paths, following the direction of the bedding planes. The numerical simulations were performed considering two different bedding orientations, parallel and normal to the imposed flow in the test. Simulations are in agreement with recorded upstream and downstream pressures in the tests. The evolution of fluid pressures, degree of saturation, element permeability and stress paths are presented for each case analysed. This information provides a good insight into the mechanisms of gas transport. Different flow patterns are obtained depending on bedding orientation, and the results provide an explanation for the results obtained in the tests. Copyright © 2012 John Wiley & Sons, Ltd.

Tunnels constructed using New Austrian Tunnelling Method (NATM) are always based on certain round (unsupported) advance lengths, after which, the temporary lining is placed. The settlement of the ground surface resulting from such construction is of high significance in design and practice. The existing data in this respect, however, is scarce. It is the aim of this paper to propose a semi-analytical procedure based on three-dimensional finite element analyses to predict the maximum surface settlement of the ground in NATM tunnels under different combinations of tunnel diameter, overburden depth, round length and soil and lining properties. The comparison of the results with three case histories of real tunnels reveals reasonable accuracy of the present solution. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, we present the exact solution of the Riemann problem for the nonlinear one-dimensional so-called shallow-water or Saint-Venant equations with friction proposed by SAVAGE and HUTTER to describe debris avalanches. This model is based on the depth-averaged thin layer approximation of granular flows over sloping beds and takes into account a Coulomb type friction law with a constant friction coefficient. A particular configuration of the Riemann problem corresponds to a dam of infinite length in one direction from which granular material is released from rest at a given time over an inclined rigid or erodible bed. We solve analytically and numerically the depth-averaged long-wave equations derived in a topography-linked coordinate system for all the possible Riemann problems. The detailed mathematical proof of the derivation of the analytical solutions and the analysis of their structure and properties is intended, first of all, for geophysicists, mathematicians, and physicists because of the possible extension of this study to more complex problems (geometries, friction laws, …). The numerical solution of the first-order finite-volume method based on a Godunov-type scheme is compared with the proposed exact Riemann problem solution. This solution is used to solve the dam-break problem and analyze the influence of the thickness of the erodible bed on the speed of the granular front. Comparison with existing experimental results shows that, for an erodible bed, the equations lack fundamental physical significance to reproduce the observed dynamics of erosive granular flows. Copyright © 2012 John Wiley & Sons, Ltd.

This paper presents a performance-based reliability design methodology for axially loaded drilled shaft foundations using the Monte Carlo statistical methods. The performance criteria for an axially loaded drilled shaft are defined in terms of the drilled shaft head displacement. The load transfer method is used as the computational model for solving the nonlinear soil–foundation interaction problem and to predict the load–settlement curve at the drilled shaft head. The input to the computational model and the model error are treated as random variables. Particularly, soil properties such as soil strength parameters are modeled as random fields to account for soil spatial variability. Random field samples are generated using local averaging subdivision according to the prescribed statistical descriptors, including mean, variance, and correlation length. Given performance-based acceptance criteria, the probability of failure can be evaluated for the prescribed load effects. A computer program is developed to facilitate the computation of the load–displacement curves of the drilled shaft head by using the commonly adopted load transfer concepts (t–z curves and q–w curves for shaft side and toe, respectively). Two design examples are presented, one for uplift and the other for compression, to illustrate the application of the developed performance-based reliability design methodology. One of the important observations from the examples is that the computed probability of failure can be sensitive to the spatial variations of soil strengths characterized by the correlation structures. It is strongly recommended that spatial variation of soil properties be considered in the reliability-based foundation design. Copyright © 2012 John Wiley & Sons, Ltd.

In the direct shear test (DST), an internal moment is distributed within the rock specimen by non-coaxial shear loads applied to the specimen, which cause non-uniform distributions of both the traction on the loading planes and the stress and deformation in the specimen. To examine the validity of the DST for a rock fracture and to clarify the effect of specimen height, both the stress and deformation in a fracture in the DST were analyzed for specimens with three different heights using a three-dimensional finite element method with quadratic joint elements for a fracture model. The constitutive law of the fracture considers the dependence of the non-linear behavior of closure on shear displacement and that of shear stiffness on normal stress and was implemented in simulation code to give a conceptional fracture with uniform mechanical properties to extract only the effect of non-uniform traction on the stress and deformation in the fracture. The results showed that both normal and shear stresses are concentrated near the end edges of the fracture, and these stress concentrations decrease with a decrease in the specimen height according to the magnitude of the moment produced by the non-coaxial shear loads. Furthermore, although closure is greater near the end edges of the fracture, where normal stress is concentrated, this concentration of closure is not so significant within the range of this study because of the non-linear behavior of closure, that is, closure does not significantly increase with an increase in normal stress at large normal stresses. Copyright © 2012 John Wiley & Sons, Ltd.

Rate effects are examined in the steady pore pressure distribution induced as a result of penetration of standard and ball penetrometers. The incompressible flow field, which develops around the penetrometer is used to define the approximate soil velocity field local to the penetrometer tip. This prescribes the Lagrangian framework for the migration of the fluid saturated porous medium, defining the advection of induced pore pressures relative to the pressure-monitoring locations present on the probe face. In two separate approaches, different source functions are used to define the undrained pore fluid pressures developed either (i) on the face of the penetrometer or (ii) in the material comprising the failure zone surrounding the penetrometer tip. In the first, the sources applied at the tip face balance the volume of fluid mobilized by the piston displacement of the advancing penetrometer. Alternately, a fluid source distribution is evaluated from plasticity solutions and distributed throughout the tip process zone: for a standard penetrometer, the solution is for the expansion of a spherical cavity, and for the ball penetrometer, the solution is an elastic distribution of stresses conditioned by the limit load embedded within an infinite medium. For the standard penetrometer, the transition from drained to undrained behavior occurs over about two orders of magnitude in penetration rate for pore pressures recorded at the tip (U1) and about two-and-a-half orders of magnitude for the shoulder (U2). This response is strongly influenced by the rigidity of the soil and slightly influenced by the model linking induced total stresses to pore pressures. For the ball penetrometer, the transition from drained to undrained behavior also transits two-and-a-half orders of magnitude in penetration rate, although it is offset to higher dimensionless penetration rates than for standard penetration. Copyright © 2012 John Wiley & Sons, Ltd.

Face stability analysis of tunnels excavated under pressurized shields is a major issue in real tunnelling projects. Most of the failure mechanisms used for the stability analysis of tunnels in purely cohesive soils were derived from rigid block failure mechanisms that were developed for frictional soils, by imposing a null friction angle. For a purely cohesive soil, this kind of mechanism is quite far from the actual velocity field. This paper aims at proposing two new continuous velocity fields for both collapse and blowout of an air-pressurized tunnel face. These velocity fields are much more consistent with the actual failures observed in undrained clays. They are based on the normality condition, which states that any plastic deformation in a purely cohesive soil develops without any volume change. The numerical results have shown that the proposed velocity fields significantly improve the best existing bounds for collapse pressures and that their results compare reasonably well with the collapse and blowout pressures provided by a commercial finite difference software, for a much smaller computational cost. A design chart is provided for practical use in geotechnical engineering. Copyright © 2012 John Wiley & Sons, Ltd.

The failure mechanisms induced by a wedge-shaped tool indenting normally against a rock surface are investigated using the discrete element method (DEM). The main focus of this study is to explore the conditions controlling the transition from a ductile to a brittle mode of failure. The development of a damage zone and the initiation and propagation of a brittle fracture is well captured by the DEM simulations. The numerical results support the conjecture that initiation of brittle fractures is governed by a scaled flaw length Λ, a ratio between the flaw size λ and the characteristic length (where K_Ic is the toughness and σ_c the uniaxial compressive strength). The size of the damage zone agrees well with analytical predictions based on the cavity expansion model. The effects of a far-field confining stress and the existence of a relief surface near the indenter are also examined.Copyright © 2012 John Wiley & Sons, Ltd.

With the concept of generalized plasticity, a constitutive model for describing the deformation behavior of sandstone is proposed in this paper. This proposed model is characterized by the following features: (i) nonlinear elasticity under hydrostatic and shear loading; (ii) associated flow rule for pre-peak simulation; (iii) substantial plastic deformation during shear loading; and (iv) significant shear dilation and distortion prior to the failure state. This model requires 10 material parameters, including three for elasticity and seven for plasticity. All of the parameters can be determined, in a straightforward manner, by the suggested procedures. The proposed model has been validated by comparing the triaxial test results of the Mushan sandstone under different hydrostatic stress, different stress paths, and cyclic loading condition. It is also versatile in simulating the deformation behaviors of two other sandstones. Upon slight modification of the model, the post-peak behavior of sandstone can be reasonably predicted using proposed model. Copyright © 2012 John Wiley & Sons, Ltd.

Tool-rock interaction processes can be classified as indentation or cutting depending on the direction of motion of the tool with respect to the rock surface. The modes of failure induced in the rock by an indenting or a cutting tool can be ductile and/or brittle. The ductile mode is associated with the development of a damage zone, whereas the brittle mode involves the growth of macrocracks. This is the first part of a series of two papers concerned with an analysis of the cutting and the indentation processes based on using the discrete element method. In this paper, numerical simulations of the cutting process are conducted to reproduce the transition from a ductile to a brittle failure mode with increasing depth of cut, which is observed in experiments. The numerical results provide evidence that the critical depth of cut d_* controlling the failure mode transition is related to the characteristic length ℓ = (K_Ic ∕ σ_c)² with K_Ic denoting the material toughness and σ_c its unconfined compressive strength. The nature of frictional contact between the cutter face and the rock in the ductile failure mode is also examined. It is shown that the inclination of the total cutting force is controlled by a multi-directional flow mechanism ahead of the cutter that is related to the formation of a wedge of failed material, intermittently adhering to the cutter. As a result, the inclination of the total cutting force varies with the rake angle of the cutter and cannot be considered an intrinsic measure of the interfacial friction between the cutter and the rock. Copyright © 2012 John Wiley & Sons, Ltd.

This paper presents an instability theory that can be used to understand the fundamental behavior of an acidization dissolution front when it propagates in fluid-saturated carbonate rocks. The proposed theory includes two fundamental concepts, namely the intrinsic time and length of an acidization dissolution system, and a theoretical criterion that involves the comparison of the Zhao number and its critical value of the acidization dissolution system. The intrinsic time is used to determine the time scale at which the acidization dissolution front is formed, while the intrinsic length is used to determine the length scale at which the instability of the acidization dissolution front can be initiated. Under the assumption that the acidization dissolution reaction is a fast process, the critical Zhao number, which is used to assess the instability likelihood of an acidization dissolution front propagating in fluid-saturated carbonate rocks, has been derived in a strictly mathematical manner. Based on the proposed instability theory of a propagating acidization dissolution front, it has been theoretically recognized that: (i) the increase of the mineral dissolution ratio can stabilize the acidization dissolution front in fluid-saturated carbonate rocks; (ii) the increase of the final porosity of the carbonate rock can destabilize the acidization dissolution front, while the increase of the initial porosity can stabilize the acidization dissolution front in fluid-saturated carbonate rocks; (iii) the increase of the mineral dissolution ratio can cause an increase in the dimensionless propagation speed of the acidization dissolution front; (iv) the increase of the initial porosity can enable the acidization dissolution front to propagate faster, while the increase of the final porosity can enable the acidization dissolution front to propagate slower in the acidization dissolution system. Copyright © 2012 John Wiley & Sons, Ltd.

A computational method, incorporating the finite element model (FEM) into data assimilation using the particle filter, is presented for identifying elasto-plastic material properties based on sequential measurements under the known changing traction boundary conditions to overcome some difficulties in identifying the parameters for elasto-plastic problems from which the existing inverse analysis strategies have suffered. A soil–water coupled problem, which uses the elasto-plastic constitutive model, is dealt with as the geotechnical application. Measured data on the settlement and the pore pressure are obtained from a synthetic FEM computation as the forward problem under the known parameters to be identified for both the element tests and the ground behavior during the embankment construction sequence. Parameter identification for elasto-plastic problems, such as soil behavior, should be made by considering the measurements of deformation and/or pore pressure step by step from the initial stage of construction and throughout the deformation history under the changing traction boundary conditions because of the embankment or the excavation because the ground behavior is highly dependent on the loading history. Thus, it appears that sequential data assimilation techniques, such as the particle filter, are the preferable tools that can provide estimates of the state variables, that is, deformation, pore pressure, and unknown parameters, for the constitutive model in geotechnical practice. The present paper discusses the priority of the particle filter in its application to initial/boundary value problems for elasto-plastic materials and demonstrates a couple of numerical examples. Copyright © 2012 John Wiley & Sons, Ltd.

A closed-form stability analysis of earth slopes performed in 3D is proposed. The sliding surface is assumed spherical and treated as a rigid body allowing the internal state of stress to be ignored. The proposed closed-formed solution (CFS) can be applied to both homogenous and non-homogenous slopes of either simple or complex geometry and can also deal with any kind of additional loading. Although it is recognized that the critical failure surface is often non-spherical, the CFS methodology for spheres described herein provides an objective tool for the evaluation of the assumptions made by other limit equilibrium methods including the role of intercolumn forces. Copyright © 2012 John Wiley & Sons, Ltd.

Today multiphysics problems applied to various fields of engineering have become increasingly important. Among these, in the areas of civil, environmental and nuclear engineering, the problems related to the behaviour of porous media under extreme conditions in terms of temperature and/or pressure are particularly relevant. The mathematical models used to solve these problems have an increasing complexity leading to increase of computing times. This problem can be solved by using more effective numerical algorithms, or by trying to reduce the complexity of these models. This can be achieved by using a sensitivity analysis to determine the influence of model parameters on the solution. In this paper, the sensitivity analysis of a mathematical/numerical model for the analysis of concrete as multiphase porous medium exposed to high temperatures is presented. This may lead to a reduction of the number of the model parameters, indicating what parameters should be determined in an accurate way and what can be neglected or found directly from the literature. Moreover, the identification parameters influence may allow to proceeding to a simplification of the mathematical model (i.e. model reduction). The technique adopted in this paper to performing the sensitivity analysis is based on the automatic differentiation (AD), which allowed to develop an efficient tool for the computation of the sensitivity coefficients. The results of the application of AD technique have been compared with the results of the more standard finite difference method, showing the superiority of the AD in terms of numerical accuracy and execution times. From the results of the sensitivity analysis, it follows that a drastic simplification of the model for thermo-chemo-hygro-mechanical behaviour of concrete at high temperature, is not possible. Therefore, it is necessary to use different model reduction techniques in order to obtain a simplified version of the model that can be used at industrial level.Copyright © 2012 John Wiley & Sons, Ltd.

A probabilistic model is presented to compute the probability density function (PDF) of the ultimate bearing capacity of a strip footing resting on a spatially varying soil. The soil cohesion and friction angle were considered as two anisotropic cross-correlated non-Gaussian random fields. The deterministic model was based on numerical simulations. An efficient uncertainty propagation methodology that makes use of a non-intrusive approach to build up a sparse polynomial chaos expansion for the system response was employed. The probabilistic numerical results were presented in the case of a weightless soil. Sobol indices have shown that the variability of the ultimate bearing capacity is mainly due to the soil cohesion. An increase in the coefficient of variation of a soil parameter (c or φ) increases its Sobol index, this increase being more significant for the friction angle. The negative correlation between the soil shear strength parameters decreases the response variability. The variability of the ultimate bearing capacity increases with the increase in the coefficients of variation of the random fields, the increase being more significant for the cohesion parameter. The decrease in the autocorrelation distances may lead to a smaller variability of the ultimate bearing capacity. Finally, the probabilistic mean value of the ultimate bearing capacity presents a minimum. This minimum is obtained in the isotropic case when the autocorrelation distance is nearly equal to the footing breadth. However, for the anisotropic case, this minimum is obtained at a given value of the ratio between the horizontal and vertical autocorrelation distances. Copyright © 2012 John Wiley & Sons, Ltd.

Propagation of fractures, especially those emanating from wellbores and closed natural fractures, often involves Mode I and Mode II, and at times Mode III, posing significant challenges to its numerical simulation. When an embedded inclined fracture is subjected to compression, the fracture edge is constrained by the surrounding materials so that its true propagation pattern cannot be simulated by 2D models. In this article, a virtual multidimensional internal bond (VMIB) model is presented to simulate three-dimensional (3D) fracture propagation. The VMIB model bridges the processes of macro fracture and micro bond rupture. The macro 3D constitutive relation in VMIB is derived from the 1D bond in the micro scale and is implemented in a 3D finite element method. To represent the contact and friction between fracture surfaces, a 3D element partition method is employed. The model is applied to simulate fracture propagation and coalescence in typical laboratory experiments and is used to analyze the propagation of an embedded fracture. Simulation results for single and multiple fractures illustrate 3D features of the tensile and compressive fracture propagation, especially the propagation of a Mode III fracture. The results match well with the experimental observation, suggesting that the presented method can capture the main features of 3D fracture propagation and coalescence. Moreover, by developing an algorithm for applying pressure on the fracture surfaces, propagation of a natural fracture is also simulated. The result illustrates an interesting and important phenomenon of Mode III fracture propagation, namely the fracture front segmentation. Copyright © 2012 John Wiley & Sons, Ltd.

This second part of the work deals firstly with carrying out materials characterization, mainly mercury intrusion porosimetry and chloride electrodiffusion tests on two cement pastes. Experimental data allowed fixing the perturbation parameter ϵ and other dimensionless numbers highlighted in part I of this work. Secondly, a series of parametric simulations were performed in order to compute the chloride diffusion coefficient through a gradual complexity of the elementary cell, approaching as close as possible the real microstructure of the cement pastes tested. Results highlighted that taking into account microstructure parameters (porosity, tortuosity and constrictivity) allows to approach the experimental diffusion coefficient. However, they also showed that electrochemical interactions between ions and the liquid-solid interface, and the multi-scale character of cementitious material microstructure, must be considered. Copyright © 2012 John Wiley & Sons, Ltd.

A closed-form solution (CFS) satisfying both equilibrium of moments and forces for the stability analysis of earth slopes in 2D is proposed. The sliding surface is assumed circular and treated as a rigid body, allowing the internal state of stress to be ignored. The proposed solution can be applied to both homogenous and non-homogenous slopes of either simple or complex geometry, and can also deal with any kind of additional loading. The method is based on the fact that, all possible forces acting on the slope can be projected onto the failure surface where they are broken into driving and resisting ones. Comparison of the safety factors obtained by the proposed CFS and those obtained by traditional limit equilibrium methods, as applied to several test examples, indicates that the proposed method is more conservative, whereas moreover, it gives a more realistic point of view for the formation of tension crack in slopes. Copyright © 2012 John Wiley & Sons, Ltd.

In this first part of the work, we develop macroscopic models for migration and diffusion–migration of ionic species in saturated porous media, based on periodic homogenization. The prior application is chloride transport in cementitious materials. The dimensional analysis of Nernst–Planck equation lets appear to dimensionless numbers characterizing the ionic transfer in the porous medium. Using experimental data obtained from electrodiffusion tests on cement-based materials (Part II), these dimensionless numbers are linked to the perturbation parameter ϵ. For a strong imposed electrical field, the asymptotic expansion of Nernst–Planck equation leads to a macroscopic model where the migration is predominant. For a weak imposed electrical field or in natural diffusion, we obtain a macroscopic model coupling diffusion and migration at the same order. In both models, the expression of the homogenized diffusion tensor is identical and only involves the geometric properties of the material microstructure. Copyright © 2012 John Wiley & Sons, Ltd.

This study aims at building a theoretical framework allowing for estimation of the macroscopic friction coefficient of a mixed quartz/clay fault gouge from the description of the microstructure and from relevant properties at the lower scale. The effect of clay content is particularly highlighted through two opposite morphology cases. The first one corresponds to a grain framework-supported microstructure with a predominant content of quartz grains forming a connected structure and some clay filling the intergranular space. The second considered morphology corresponds to a clay matrix-supported microstructure in which quartz grains are embedded. The friction coefficient of the gouge is derived with respect to the clay content for both morphologies because of theoretical homogenization techniques. The models prove to be in good agreement with experimental results from the literature. Copyright © 2012 John Wiley & Sons, Ltd.

This paper presents a computational microstructure model to estimate the progressive moisture damage of multiphase asphaltic paving mixtures. Moisture damage because of water transport is incorporated with mechanical loading through a finite element method. To simulate nonlinear damage evolution in the mixtures, the model includes Fickian moisture diffusion, a cohesive zone model to simulate the gradual fracture process, and a degradation characteristic function to represent the reduction of material properties because of moisture infiltration. With the model developed, various parametric analyses are conducted to investigate how each model parameter affects the material-specific moisture damage mechanism and damage resistance potential of the mixtures. Analysis results clearly demonstrate the significance of physical and mechanical properties of mixture components and geometric characteristics of microstructure for the better design of asphaltic paving mixtures and roadway structures. Copyright © 2012 John Wiley & Sons, Ltd.

A mesoscale model of desiccation of soil based on the evolution of the pore system idealized as bimodal is numerically examined. A simplified evolution of the model reveals a series of characteristics that qualitatively agree with the observed macroscopic experimental findings. The principal mechanism is deemed to be driven by the surface evaporation and water outflow generating a pore pressure gradient resulting in the shrinkage mainly of the largest pores. The amount of shrinkage is a function of (negative) pore pressure and is controlled by the compressibility of the solid matrix. The numerical model includes also the ensuing partial saturation stage initiated by the air entry simulated as a scenario with a moving phase interface inside the pore. The proposed model can be extended beyond the two-mode porosity soils, to include the multi-modal porosity, or its statistical representation.Copyright © 2012 John Wiley & Sons, Ltd.

The Barcelona basic model (BBM) successfully explained many key features of unsaturated soils and received extensive acceptance. It is also one of the few elastoplastic constitutive models for unsaturated soils that have been implemented within finite element codes and applied to the analysis of real boundary value problems. The BBM was proposed in incremental forms according to theories of soil plasticity in which individual aspects of the isotropic virgin behavior are controlled by multiple parameters, whereas at the same time, a single parameter controls more than one aspect of soil behavior. Although a variety of methods have been recently developed for calibrating model parameters for elastoplastic soil models, at present, there are no well-established, simple, and objective methods for selecting parameter values in the BBM from laboratory tests. This has been one of the major obstacles to the dissemination of this constitutive model beyond the research context.

This article presents an optimization approach especially developed for simple and objective identification of material parameters in the BBM. This is achieved by combining a modified state surface approach, recently proposed to model the elastoplastic behavior of unsaturated soils under isotropic stress conditions, with the Newton or quasi-Newton method to simultaneously determine the five parameters governing isotropic virgin behavior in the BBM. The comparison between results using the proposed method and an existing method for the same laboratory tests was discussed from which the simplicity and objectivity of the proposed method were evaluated. Copyright © 2012 John Wiley & Sons, Ltd.

This article is devoted to numerical modeling of anisotropic damage and plasticity in saturated quasi-brittle materials such as rocks and concrete. The damaged materials are represented by an isotropic poroelastic matrix containing a number of families of microcracks. Based on previous works, a discrete thermodynamic approach is proposed. Each family of microcracks exhibits frictional sliding along crack surfaces as well as crack propagation. The frictional sliding is described by a Coulomb–Mohr-type plastic criterion by taking into account the effect of fluid pressure through a generalized effective stress concept. The damage evolution is entirely controlled by and coupled with the frictional sliding. The effective elastic properties as well as Biot's coefficients of cracked porous materials are determined as functions of induced damage. The inelastic deformation due to frictional sliding is also taken into account. The procedure for the identification of the model's parameters is presented. The proposed model is finally applied to study both mechanical and poromechanical responses of a typical porous brittle rock in drained and undrained compression tests as well as in interstitial pressure controlled tests. The main features of material behaviors are well reproduced by the model. Copyright © 2012 John Wiley & Sons, Ltd.

Air sparging (AS) is an in situ soil/groundwater remediation technology, which involves the injection of pressurized air/oxygen through an air sparging well below the zone of contamination. Characterizing the mechanisms governing movement of air through saturated porous media is critical for the design of an effective cleanup treatment system. In this research, micromechanical investigation was performed to understand the physics of air migration and subsequent spatial distribution of air at pore scale during air sparging. The void space in the porous medium was first characterized by pore network consisting of connected pore bodies and bonds. The biconical abscissa asymmetric concentric bond was used to describe the connection between two adjacent pore bodies. Then a rule-based dynamic two-phase flow model was developed and applied to the pore network model. A forward integration of time was performed using the Euler scheme. For each time step, the effective viscosity of the fluid was calculated based on fractions of two phases in each bond, and capillary pressures across the menisci was considered to compute the pressure field. The developed dynamic model was used to study the rate-dependent drainage during air sparging. The effect of the capillary number and geometrical properties of the network on the dynamic flow properties of two-phase flow including residual saturation, spatial distribution of air and water, dynamic phase transitions, and relative permeability-capillary pressure curves were systematically investigated. Results showed that all the above information for describing the air water two-phase flow are not intrinsic properties of the porous medium but are affected by the two-phase flow dynamics and spatial distribution of each phase, providing new insight to air sparging. Copyright © 2012 John Wiley & Sons, Ltd.

Analysis of macroscopic desiccation shrinkage experiments indicates that most, but not all of the shrinkage during drying occurs while soil is still saturated. Shrinkage practically ceases and air starts to penetrate the soil, when the water content is still quite high, for example, above 20% for the tested soils. The remaining, unsaturated drying process occurs with a much-reduced shrinkage rate. In this context, we examine data of the pore system evolution as represented by the mercury porosimetry experimental results. The process is then modeled as a two-stage process of deformation and evacuation of a two-tube vessel system driven by the external evaporation flux. In the first stage, Poiseuille flow occurs through the vessels. The amount of water evaporated in this stage equals to the reduction of volume of the vessel through the deformation of its walls. This stage ends when a negative water pressure (suction) required to further deform the vessel reaches a critical value at which air enters the pore space. Two physical interpretation of such threshold are discussed. In the subsequent stage, evaporation proceeds with a receding liquid/vapor interface starting from the open end, incrementally emptying the vessel but with a marginal water flow and vessel deformation. The leading variables of the process are identified, and a quantifiable multiphysics meso-scale scenario of models is established. Copyright © 2012 John Wiley & Sons, Ltd.

In this article, we investigate the main parameters that influence the propagation of a fluid-driven fracture in a poroelastoplastic continuum. These parameters include the cohesive zone, the stress anisotropy, and the pore pressure field. The fracture is driven in a permeable porous domain that corresponds to weak formation by pumping of an incompressible viscous fluid at the fracture inlet under plane strain conditions. Rock deformation is modeled with the Mohr–Coulomb yield criterion with associative flow rule. Fluid flow in the fracture is modeled by the lubrication theory. The movement of the pore fluid in the surrounding medium is assumed to obey the Darcy law and is of the same nature as the fracturing fluid. The cohesive zone approach is used as the fracture propagation criterion. The problem is modeled numerically with the finite element method to obtain the solution for the fracture length, the fracture opening, and the propagation pressure as a function of the time and distance from the pumping inlet. It is demonstrated that the plastic yielding that is associated with the rock dilation in an elastoplastic saturated porous continuum is significantly affected by the cohesive zone characteristics, the stress anisotropy, and the pore pressure field. These influences result in larger fracture profiles and propagation pressures due to the larger plastic zones that are developing during the fracture propagation. Furthermore, it is also found that the diffusion process that is a major mechanism in hydraulic fracture operations influences further the obtained results on the fracture dimensions, plastic yielding, and fluid pressures. These findings may explain partially the discrepancies in net pressures between field measurements and conventional model predictions. Copyright © 2012 John Wiley & Sons, Ltd.

Formulation and algorithmic treatment of a rate-dependent plastic–damage model modified to capture large tensile cracking in cyclic-loaded concrete structures are presented in detail for a three-dimensional implementation. The plastic–damage model proposed by Lee and Fenves in 1998 was founded based on isotropic damaged elasticity in combination with isotropic multi-hardening plasticity to simulate cracking and crushing of concrete under cyclic or dynamic loadings. In order that the model can capture large crack opening displacements, which are inevitable in plain concrete structures, the excessive increase in plastic strain causing unrealistic results in cyclic behaviors is prevented when the tensile plastic–damage variable controlling the evolution of tensile damage is larger than a critical value. In such a condition, the crack opening/closing mechanism becomes similar to discrete cracking. The consistent tangent operator required to accelerate convergence rate is also formulated for the large cracking state including viscoplasticity. The validation and performance of the modified algorithm implemented in a special finite element program is exemplified through several single-element tests as well as three structural applications. The last example examines the model in the seismic fracture analysis of Koyna dam as a benchmark problem and the resulting crack profile is compared with the available experiment. The numerical experimentations well demonstrate that the developed model whose modification is necessary to properly simulate the cyclic behavior of plain concrete subjected to large tensile strains is robust and reasonably accurate. Copyright © 2012 John Wiley & Sons, Ltd.

A mechanistic constitutive model for fully formed cracks in geomaterials, such as concrete and rock, is presented. A three-dimensional characterisation of the crack morphology is employed in which the crack surface is idealised as a series of conical teeth and corresponding recesses of variable height and slope. Based on this geometrical characterisation, an effective contact function is derived to relate the contact stresses that develop on the sides of the teeth to the net stresses on a crack plane. Plastic embedment and frictional sliding are simulated using a local plasticity model in which the plastic surfaces are expressed in terms of the contact surface function in cylindrical relative displacement space. Finally, the performance of the model is assessed against several sets of experimental data from direct shear tests, and it is concluded that the model is able to capture key characteristics of the behaviour of fully formed cracks in geomaterials. Copyright © 2012 John Wiley & Sons, Ltd.

Surficial slope failures in residual soils are common in tropical and subtropical regions as a result of rainfall infiltration. This study develops an analytical solution for simulating rainfall infiltration into an infinite unsaturated soil slope. The analytical solution is based on the general partial differential equation for water flow through unsaturated soils. It can accept soil–water characteristic curve and unsaturated permeability function of the exponential form into account. Numerical simulations are conducted to verify the assumptions of the analytical solution and demonstrate that the proposed analytical solution is acceptable for the coarse soils with low air entry values. The pore-water pressure (pwp) distributions obtained from the analytical solution can be incorporated into a limit equilibrium method to do infinite slope stability analysis for a rain-induced shallow slip. The analysis method takes into account the influence of the water content change on unit weight and hence on factor of safety. A series of analytical parametric analyses have been performed using the developed model. The analyses indicate that when the residual soil slope, consisting of a completely decomposed granite layer underlain by a less permeable layer, is subjected to a continuous heavy rainfall, the loss of negative pwp and the reduction in factor of safety were found to be most significant for the shallow soil layer and during the first 12 h. The antecedent and subsequent rainfall intensity, depth of a less permeable layer and slope angle all have a significant influence on the pwp response and hence the slope stability. Copyright © 2012 John Wiley & Sons, Ltd.

A numerical model, called CCRS1, is presented for one-dimensional large strain consolidation under constant rate of strain loading conditions. The algorithm accounts for vertical strain, general constitutive relationships, relative velocity of fluid and solid phases, changing compressibility and hydraulic conductivity during consolidation, and an externally applied hydraulic gradient acting across the specimen. Soil compressibility is rate independent, and as such, the current model is most appropriate for less-structured clays. Verification checks show excellent agreement with analytical and numerical solutions for small and large strain conditions. A series of numeric examples indicates that compressibility and hydraulic conductivity constitutive relationships can have an important effect on constant rate of strain consolidation response. Results also indicate that analytical solutions obtained using small strain theory can be in significant error for large strain conditions with changing coefficient of consolidation. Copyright © 2012 John Wiley & Sons, Ltd.

In this study, a simplified analytical closed-form solution, considering plane strain and axial symmetry conditions, for analysis of a circular pressure tunnel excavated underwater table, is developed. The method accounts for the seepage forces with the steady-state flow and is based on the generalized effective stress law. To examine the effect of pore pressure variations and also the boundary conditions at the ground surface, the formulations are derived for different directions around the tunnel. The proposed method can be applied for analysis and design of pressure tunnels. Illustrative examples are given to demonstrate the performance of the proposed solution and also to examine the effect of seepage forces on the stability of tunnels. The simplified analytical solution derived in this study is compared with numerical analyses. It is concluded that the classic solutions (Lame's thick-walled solution), considering the internal pressure as a mechanical load applied to the tunnel surface, are not applicable to pervious media and can result in an unsafe design. Copyright © 2012 John Wiley & Sons, Ltd.

Three porous media flow problems, in which the fluid mechanical interactions are critical, are studied in a mesoscopic–microscopic coupling system. In this system, fluid flow in the pore space is explicitly modeled at mesoscopic level by the lattice Boltzmann method, the geometrical representation and the mechanical behavior of the solid skeleton are modeled at microscopic level by the particulate distinct element method (DEM), and the interfacial interaction between the fluid and the solids is resolved by an immersed boundary scheme. In the first benchmark problem, the well-known and frequently utilized Ergun equation is validated in periodic particle and periodic pore models. In the second problem, the upward seepage problem is simulated over three stages: The settlement of the column of sphere under gravity loading is measured to illustrate the accuracy of the DEM scheme; the system is solved to hydrostatic state with pore space filled with fluid, showing that the buoyancy effect is captured correctly in the mesoscopic–microscopic coupling system; then, the flow with constant rate is supplied at the bottom of the column; the swelling of the ground surface and pore pressure development from the numerical simulation are compared with the predictions of the macroscopic consolidation theory. In the third problem, the fluid-flow-induced collapse of a sand arch inside a perforation cavity is tested to illustrate a more practical application of the developed system. Through comparing simulation results with analytical solutions, empirical law and physical laboratory observations, it is demonstrated that the developed lattice Boltzmann–distinct element coupling system is a powerful fundamental research tool for investigating hydromechanical physics in porous media flow. Copyright © 2012 John Wiley & Sons, Ltd.

Particle manifold method (PMM) is a new extension of the numerical manifold method (NMM). PMM uses a mathematical cover system to describe the motion and deformation of a particle-based physical domain. By introducing the concept of particle into NMM, PMM takes the advantages of easy topological and contact operations with particles. In this article, the methodology, formulations and implementation of the method are presented, together with modelling examples for validation. It is found that good solutions for both continuous and discontinuous problems are obtained by the new developed PMM. Due to the underlying coupled continuum-discontinuum property of PMM, it has great potential for modelling of geomechanical problems. Copyright © 2012 John Wiley & Sons, Ltd.

This article presents the developments of an ongoing research aimed at modelling the influence of fissuring on the behaviour of clays. In particular, it recalls the main results of an extensive laboratory investigation on a fissured bentonite clay from the south of Italy and presents the data of a new investigation on the evolution with shearing of the strain fields developing within the clay, resulting from Digital Image Correlation (DIC).

Element test results are analysed in the framework of continuum mechanics and linked to the clay fissuring features, once characterised using the Fissuring IDentity (F-ID) chart. This article compares the bentonite behaviour with that of other fissured clays of different F-IDs, highlighting the common behavioural features.

Thereafter, the soil response at the macro level is related to the DIC-derived strain fields evolving within the clay with loading. For this purpose, DIC was successfully used to investigate the deformation processes active in the fissured clay and the sources of the localisation phenomena. DIC is shown to provide indications of the extent to which highly to medium fissured clays element test results can be of use to model the clay behaviour according to continuum mechanics. Copyright © 2012 John Wiley & Sons, Ltd.

Effective moisture and chloride ion diffusivity coefficients for concrete are determined by computational homogenization, where concrete is modeled on the mesoscale as a heterogenous three-phase composite material. By imposing moisture and chloride ion gradients on a representative volume element, effective macroscale properties are obtained through finite element analysis. A parametric study of the effects of the ballast content was carried out. The numerical results correspond well with an estimate of the Hashin–Shtrikman type available in the literature. The computational homogenization strategy proposed here also includes the interfacial transition zone, and its influence on the effective diffusivity coefficients is assessed. Copyright © 2012 John Wiley & Sons, Ltd.

A method is presented for coupling cubic-order quadrilateral finite elements with the finite side of a new coordinate ascent hierarchical infinite element. At a common side shared by a hierarchical infinite element and an arbitrary number of finite elements, the displacements are minimized in the least square sense with respect to the degrees-of-freedom of the finite elements. This leads to a set of equations that relate the degrees-of-freedom of the finite and hierarchical infinite elements on the shared side. The method is applied to a non-homogeneous cross-anisotropic half-space subjected to a non-uniform circular loading with Young's and shear moduli varying with depth according to the power law. A constant mesh constructed from coupled finite and hierarchical infinite elements is used and convergence is sought simply by increasing the degree of the interpolating polynomial. The displacements and stresses produced by conical and parabolic circular loads applied on the surface are obtained. The efficiency of the proposed method is demonstrated through convergence and comparison studies. New results produced by a frusto-conical circular load applied on the surface of a half-space made up of heavily consolidated London clay are provided. The non-homogeneity parameter and degree of anisotropy are shown to influence the soil response. Copyright © 2012 John Wiley & Sons, Ltd.

This paper discusses the reliability and the efficiency of a time homogenization method employed to reduce the computational time during cyclic loading for two common geotechnical tests and two elastoplastic models for clays. The method of homogenization is based upon splitting time into two separate scales. The first time scale relates to the period of cyclic loading and the second to the characteristic time of the fatigue phenomenon. The time homogenization method is applied to simulate an undrained triaxial test (homogeneous stress state) and a pressuremeter test (nonhomogeneous stress state) under one-way cyclic loading on normally consolidated clay. This method is coupled with two elastoplastic models dedicated to cyclic behavior of clay (a bounding surface plasticity model and a bubble model). Both linear and nonlinear elasticities are considered. The difficulty encountered when applying this method to models introducing nonlinear elasticity and kinematic hardening is pointed out. The performance of time homogenization related to the main parameters is numerically investigated by comparison with conventional finite element simulations. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, a numerical model is developed for the fully coupled hydro-mechanical analysis of deformable, progressively fracturing porous media interacting with the flow of two immiscible, compressible wetting and non-wetting pore fluids, in which the coupling between various processes is taken into account. The governing equations involving the coupled solid skeleton deformation and two-phase fluid flow in partially saturated porous media including cohesive cracks are derived within the framework of the generalized Biot theory. The fluid flow within the crack is simulated using the Darcy law in which the permeability variation with porosity because of the cracking of the solid skeleton is accounted. The cohesive crack model is integrated into the numerical modeling by means of which the nonlinear fracture processes occurring along the fracture process zone are simulated. The solid phase displacement, the wetting phase pressure and the capillary pressure are taken as the primary variables of the three-phase formulation. The other variables are incorporated into the model via the experimentally determined functions, which specify the relationship between the hydraulic properties of the fracturing porous medium, that is saturation, permeability and capillary pressure. The spatial discretization is implemented by employing the extended finite element method, and the time domain discretization is performed using the generalized Newmark scheme to derive the final system of fully coupled nonlinear equations of the hydro-mechanical problem. It is illustrated that by allowing for the interaction between various processes, that is the solid skeleton deformation, the wetting and the non-wetting pore fluid flow and the cohesive crack propagation, the effect of the presence of the geomechanical discontinuity can be completely captured. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper an extension of existing multilaminate soil models is presented, which can account for inherent and stress-induced cross-anisotropic elasticity in the small strain range and its dependency on the load history. In the multilaminate framework, material behaviour is formulated on a number of local planes in each stress point, and the macroscopic response of the material is obtained by integration of the local contributions. Strain-induced anisotropy, which adds to the stiffness anisotropy inherently present in the material, is therefore intrinsically taken into account. Micro–macro relations between local parameters on plane level and global parameters on macroscopic level are obtained by the spectral decomposition of the global elastic compliance matrix. The model is implemented into a finite-element code, and model predictions are compared with experimental data of triaxial tests on different soils involving small and large load cycles. The importance of cross-anisotropic elasticity within the small strain range for predicting ground deformations in geotechnical boundary value problems is discussed at the example of an excavation problem. Copyright © 2012 John Wiley & Sons, Ltd.

This study extends the limit analysis techniques used for the computation of strict bounds of the load factors in solids to stability problems with interfaces, anchors and joints. The cases considered include the pull-out capacity of multi-belled anchors and the stability of retaining walls for multiple conditions at the anchor/soil and wall/soil interfaces. Three types of wall supports are examined: free standing wall, simply supported wall and anchored wall. The results obtained are compared against available experimental and numerical data. The conclusion drawn confirms the validity of numerical limit analysis for the computation of accurate bounds on limit loads and capturing failure modes of structures with multiple inclusions of complex interfaces and support conditions. Copyright © 2012 John Wiley & Sons, Ltd.

This study investigated non-Darcian flow to a well in a leaky aquifer considering wellbore storage and a finite-thickness skin. The non-Darcian flow is described by the Izbash equation. We have used a linearization procedure associated with the Laplace transform to solve such a non-Darcian flow model. Besides, the Stehfest method has been used to invert the Laplace domain solutions for the drawdowns. We further analyzed the drawdowns inside the well for different cases. The results indicated that a smaller B_D results in a smaller drawdown at late times and the leakage has little effect on the drawdown inside the well at early times, where B_D is a dimensionless parameter reflecting the leakage. We have also found that the flow for the negative skin case approaches the steady-state earlier than that for the positive skin. In addition, the drawdown inside the well with a positive skin is larger than that without skin effect at late times, and a larger thickness of the skin results in a greater drawdown inside the well at late times for the positive skin case. A reverse result has been found for the negative skin case. Finally, we have developed a finite-difference solution for such a non-Darcian flow model and compared the numerical solution with the approximate analytical solution. It has been shown that the linearization procedure works very well for such a non-Darcian flow model at late times, and it underestimates the drawdowns at early times. Copyright © 2012 John Wiley & Sons, Ltd.

Surface movements were measured in the Gotthard massif as the Gotthard Base Tunnel was excavated. These movements might damage concrete dams constructed on the surface valleys. The leading assumption of this work is that deformation is induced by the dissipation of pore pressures in the massif caused by tunnel drainage. Deformations induce both horizontal and vertical surface displacements. Horizontal displacements, may lead to valley closures if they are in opposite direction, which would induce negative effects on arch dams. An analytical solution is derived using the method of images and an approximated integration of deformations to calculate the movements and the flow rate collected in the tunnel. Numerical calculations were carried out in 2D (vertical cross section) and 3D to investigate the problem under different conditions and to study the effect of parameters. The 3D models permit to incorporate the presence of a vertical fracture perpendicular to the tunnel that increases the drainage and pressure drop as it is hit by the tunnel. It was also possible to simulate the impermeabilization works in the tunnel to reduce drainage and consequently, movements. Copyright © 2012 John Wiley & Sons, Ltd.

Although high-modulus columns are widely used in both soil improvement and liquefaction mitigation, there is not much research, which validates their effects numerically. The aim of this paper is to investigate the role of high-modulus columns on liquefaction mitigation and propose an empirical and simplified formula to assess this effect. For this purpose, an intensive numerical analyses scheme has been performed. These analyses include three-dimensional, finite difference-based total stress analyses on generic soil, high-modulus column and earthquake combinations. The effect of the number, length, diameter of high-modulus columns, the replacement ratio, peak acceleration of the shaking event and soil strength has been discussed in detail. A factor, called as improvement ratio, defining the ratio of liquefaction resistance of free field to resistance of treated cases was then developed using probabilistic methods. The descriptive (input) parameters are selected based on regression analyses, and they are soil stiffness, replacement ratio, stiffness of high-modulus column and the depth of consideration. The model coefficients were estimated through maximum likelihood methodology. A satisfactory fit was achieved among improvement ratio estimations and numerical model results. A validation of the improvement ratio with a centrifuge test also is presented at the end of the paper. As the concluding remark, it is proven that the high-modulus column can be used safely to prevent liquefaction. The effects of these columns increase with increasing replacement ratio, stiffness of the column and increasing soil stiffness and not depend on the magnitude or the peak ground acceleration of the earthquake. Copyright © 2012 John Wiley & Sons, Ltd.

This paper describes a soil-structure coupling method to simulate blast loading in soil and structure response. For the last decade, simulation of soil behavior under blast loading and its interaction with semi buried structure in soil becomes the focus of computational engineering in civil and mechanical engineering communities. In current design practice, soil-structure interaction analysis often assumes linear elastic properties of the soil and uses small displacement theory. However, there are numerous problems, which require a more advanced approach that account for soil-structure interaction and appropriate constitutive models for soil. In simplified approaches, the effect of soil on structure is considered using spring-dashpot-mass system, and the blast loading is modeled using linearly decaying pressure–time history based on equivalent trinitrotoluene and standoff distance, using ConWep, a computer program based on semi-empirical equations. This strategy is very efficient from a CPU time computing point of view but may not provide accurate results for the dynamic response of the structure, because of its significant limitations, mainly when soil behavior is strongly nonlinear and when the buried charge is close to the structure. In this paper, both soil and explosive are modeled using solid elements with a constitutive material law for soil, and a Jones–Wilkins–Lee equation of state for explosive. One of the problems we have encountered when solving fluid structure interaction problems is the high mesh distortion at the contact interface because of high fluid nodal displacements and velocities. Similar problems have been encountered in soil structure interaction problems. To prevent high mesh distortion for soil, a new coupling algorithm is performed at the soil structure interface for structure loading. The coupling method is commonly used for fluid structure interaction problems in automotive and aerospace industry for fuel sloshing tank, and bird impact problems, but rarely used for soil structure interaction problems, where Lagrangian contact type algorithms are still dominant. Copyright © 2012 John Wiley & Sons, Ltd.

This paper is concerned with diffuse and other ensuing failure modes in geomaterials when tested under homogeneous states of shearing in various loading programs and drainage conditions. Material instability is indeed the basic property that accounts for the instability of an initially homogeneous deformation field leading to diffuse failure and strain localization in geomaterials. The former is normally characterized by a runaway type of failure accompanied with a sudden and violent collapse of the material in the absence of any localization phenomena. Against this backdrop, we present a brief overview of material instability in elastoplastic solids where one finds a rich source of theoretical concepts including bifurcation, strain localization, diffuse failure and second-order work, as well as a considerable body of experiments. Some compelling laboratory experimental studies of material instability with focus to diffuse failure are then presented and interpreted based on the second-order work. Finally, various material instability analyses using an elastoplastic constitutive and a general finite element analysis of the above-mentioned laboratory experimental tests are presented as a boundary value problem. It is shown that instability can be captured from otherwise uniform stress, density and hydraulic states, whereas uniform deviatoric loads are being applied on the external boundaries of a specimen. Although the numerical simulations reproduce well the laboratory experimental results, they also highlight the hierarchy of failure modes where localization phenomena emerge in the post-bifurcation regime as a result of a degradation of homogeneity starting from a diffuse mode signalled by a zero second-order work. Copyright © 2012 John Wiley & Sons, Ltd.

The strain space multiple mechanism model idealizes the behavior of granular materials based on a multitude of virtual simple shear mechanisms oriented in arbitrary directions. Within this modeling framework, the virtual simple shear stress is defined as a quantity that depends on the contact distribution function as well as the normal and tangential components of inter-particle contact forces, which evolve independently during the loading process. In other terms, the virtual simple shear stress is an intermediate quantity in the upscaling process from the microscopic level (characterized by the contact distribution and inter-particle contact forces). The stress space fabric (i.e. the orientation distribution of the virtual simple shear stress) produces macroscopic stress through the tensorial average. Thus, the stress space fabric characterizes the fundamental and higher modes of anisotropy induced in granular materials. Comparing an induced fabric associated with the biaxial shear of plane granular assemblies obtained via a simulation using Discrete Element Method to the strain space multiple mechanism model suggests that the strain space multiple mechanism model has the capability to capture the essential features in the evolution of an induced fabric in granular materials. Copyright © 2012 John Wiley & Sons, Ltd.

This paper presents the finite strain formulation of a strain space multiple mechanism model for granular materials. Because the strain space multiple mechanism model has an appropriate micromechanical background in which the branch and complementary vectors are defined in the material (or referential) coordinate, the finite strain formulation is carried out by following the change in these vectors, in direction and magnitude, associated with deformation in the material. By applying the methodology for compressible materials established in the finite strain continuum mechanics, decoupled formulation that decomposes the kinematic mechanisms into volumetric and isochoric components is adopted for the strain space multiple mechanism model. Lagrangian (material) description of integrated form is given by a relation between the second Piola–Kirchhoff effective stress tensor and the Green–Lagrange strain tensor; Eulerian (spatial) description by a relation between the Cauchy effective stress tensor and the Euler–Almansi strain tensor. In particular, the volumetric strain is defined as a logarithm of Jacobian determinant. Lagrangian (material) description of incremental form is derived through the material time derivative of the integrated form. The counterpart in the spatial description is derived through the Lie time derivative, given as a relation between the Oldroyd stress rate of Kirchhoff stress and the rate of deformation tensor (sometimes called stretching in the literatures). An example is shown to discuss the applicability of the finite strain formulation. Copyright © 2012 John Wiley & Sons, Ltd.

The study of surface wave in a layered medium has their possible application in geophysical prospecting. In the present work, dispersion equation for torsional wave in an inhomogeneous isotropic layer between inhomogeneous isotropic half-spaces has been derived. Two cases are discussed separately for torsional wave propagation in inhomogeneous layer between homogeneous and non-homogeneous half-spaces, respectively. Further, two possible modes for torsional wave propagation are obtained in case of inhomogeneous layer sandwiched between non-homogeneous half-spaces. Closed form solutions for displacement in the layer and half-spaces are obtained in each case. The study reveals that the layer width, layer inhomogeneity, frequency of inhomogeneity, as well as inhomogeneity in the half-space has significant effect on the propagation of torsional surface waves. Displacement and implicit dispersion equation for torsional wave velocities are expressed in terms of Heun functions and their derivatives. Effects of inhomogeneity on torsional wave velocity are also discussed graphically by plotting the dimensionless phase velocity against dimensionless and scaled wave number for different values of inhomogeneity parameter. Copyright © 2012 John Wiley & Sons, Ltd.

Effects of recoverable deformation induced anisotropy in the elastic stiffness of isotropic materials are described. In isotropic materials, thermodynamics predicts coupling of hydrostatic and deviatoric responses. It is shown that the coupling of the two responses is more significant than previously recognized in the literature. Properly accounting for the coupling of hydrostatic and deviatoric responses requires re-evaluating elastic materials characterization data, allowing for the coupled response. The result is an apparent decrease in the pressure sensitivity of the elastic shear modulus. The decrease in the pressure sensitivity of the shear modulus leads to stress paths that are more tangential to the yield surface in stress space, resulting in an increase in predicted elastic strain at each step of an elastic–plastic stress update. Consequently, predicted plastic strains and, in particular, volumetric plastic strains, are smaller than if recoverable deformation induced anisotropy had been neglected. The result is an associated plasticity model, which appears to be non-associated. Copyright © 2012 John Wiley & Sons, Ltd.

This article adopts least square support vector machine (LSSVM) for determination of liquefactions susceptibility of soil based on standard penetration test data. Two models (Models I and II) have been developed. For Model I, input variables are cyclic stress ratio and standard penetration test value (N). Model II employs peak ground acceleration and N as input variables. The developed LSSVM models (Models I and II) give equations for determination of liquefaction susceptibility of soil. The performances of Models I and II are the same. The developed LSSVM gives probabilistic output. The results of LSSVM have been compared with the artificial neural network model. This article shows that N and the peak ground acceleration are sufficient input parameters for determination of liquefaction susceptibility of soil. Copyright © 2012 John Wiley & Sons, Ltd.

Finite element simulations of the behavior of a piled raft foundation have been carried out using a multiphase model conceived as an improved homogenization approach. According to this model, the ground reinforced by a group of piles is treated as a homogeneous continuous medium. In this approach, no specific interface elements are necessary to account for the mechanical interaction between the piles and the ground: this interaction is described by means of two scalar parameters, one stiffness parameter and one which can easily be derived from the maximum ground-pile friction. The implementation of the model into a finite element code provides an efficient tool for the analysis of the influence of the pile number or length on the settlement and bearing capacity of a square piled raft foundation and of the way the total applied load is shared between the raft and the piles. Results are compared with a standard 3D finite element analysis. The comparison highlights the fact that the proposed approach remains to be improved to account for tip resistance. Copyright © 2012 John Wiley & Sons, Ltd.

A hybrid finite element method and differential quadrature method (DQM) is developed to estimate the dynamic response of two-dimensional multilayered half-spaces subjected to impulsive point loading. Nonreflecting absorbing boundary conditions consist of appropriate springs, and dampers are considered. The capabilities of the finite element method for solving boundary value problems with general domain, loading and systematic boundary treatment are combined with accurate and stable time marching capabilities of the DQM to develop an accurate and efficient numerical technique. The capability, efficiency, robustness and convergence of the DQM for solving the dynamic problem are demonstrated through numerical simulations of various half-spaces with different time increments and layer arrangement. Also, comparison study when using Newmark's time integration scheme for the same problem is done. It can be concluded that the DQM as an unconditionally stable method is suitable for solving such a problem. Also, parametric study is performed to show the effect of the absorbing boundary conditions on the dynamic response. Copyright © 2012 John Wiley & Sons, Ltd.

This work investigates the profiles of surface water flow over a pervious pavement, for example, highway, during a uniform rainfall. The pavement, such as porous asphalt or open-graded asphalt friction course, is regarded as a porous medium, and the flow inside the layer is porous media flow. At first, the velocity distributions are solved based on the simplified Navier–Stokes equations and Biot's theory of poroelasticity for the water layer and the permeable layer, respectively. Then, the flow profiles can be found via the continuity equation. Because the closed form of the water depth cannot be obtained, a numerical technique is employed to find the flow profiles on the pavement surface. A critical permeability factor related to the material and structure of pavement is illustrated to be η = 1.36 × 10^− 4m as the half road width L = 20 m, the cross slope S = 0.02,the pavement thickness H = 0.05 m, and rainfall intensity i = 100 mm/h. The water on the road surface can be drained very fast, whereas the parameter is greater than the critical value. Another illustration of allowable/safety water depth is made for the design of the pavement thickness. Copyright © 2012 John Wiley & Sons, Ltd.

This paper presents the calibration of an experiment based on filtration tests, able to provide the cumulative constriction size distribution of granular materials. Here, simulations of these tests are performed using a discrete element method. Filters of same density but different thicknesses are created with a poly-sized spherical material. Lateral periodic boundaries for the samples are used, and their size is calibrated so that a representative elementary volume is obtained. Fine particles are released on the created samples, and the particle size distribution of the collected material that successfully crossed the filters is computed. These particle size distributions are related to the underlying cumulative constriction size distribution (CSD) of the granular material involved in the samples. The CSD is derived using a probabilistic approach for the path length of individual particles through a granular material. We settle all the requisites related to the technique and to the fine particles that are released to allow reaching a correct CSD for the filter. The reference CSD used for the calibration of the experiment is obtained after a radical partition of the void space into Delaunay tetrahedra and a geometrical characterisation of constrictions on each tetrahedron face. Copyright © 2012 John Wiley & Sons, Ltd.

We presented a finite-element-based algorithm to simulate plane-strain, straight hydraulic fractures in an impermeable elastic medium. The algorithm accounts for the nonlinear coupling between the fluid pressure and the crack opening and separately tracks the evolution of the crack tip and the fluid front. It therefore allows the existence of a fluid lag. The fluid front is advanced explicitly in time, but an implicit strategy is needed for the crack tip to guarantee the satisfaction of Griffith's criterion at each time step. We enforced the coupling between the fluid and the rock by simultaneously solving for the pressure field in the fluid and the crack opening at each time step. We provided verification of our algorithm by performing sample simulations and comparing them with two known similarity solutions. Copyright © 2012 John Wiley & Sons, Ltd.

A three-dimensional phenomenological model is developed to describe the long-term creep of gypsum rock materials. The approach is based on the framework of continuum damage mechanics where coupling with viscoelasticity is adopted. Specifically, a local damage model based on the concept of yield surface is proposed and deeply investigated. Among the many possibilities, we choose in this work its coupling with a generalized Kelvin–Voigt rheological model to formulate the whole behavior. Long-term as well as short-term relaxation processes can be integrated in the model by means of as many as necessary viscoelastic processes. The numerical discretization is described for an easy integration within a finite element procedure. Finally, a set of numerical simulations is given to show the possibilities of the presented model. It shows good agreement with some experimental results found in the literature. Copyright © 2012 John Wiley & Sons, Ltd.

This paper discusses the formation of stable arches in frictional soils. A series of laboratory tests are performed to explore the formation of arches in granular materials, either cohesionless or with small apparent cohesion. By considering the stable soil arch as a stress-free surface, the analysis in the framework of continuum mechanics reveals that such an arch can only form in cohesive frictional materials. The shape of the arch mainly depends on the material's friction angle, while the critical width of the arch is primarily dominated by cohesion. The formation of stable arches in cohesionless materials is interpreted by taking into account the discrete nature of the material, with the failure of the arch being considered as buckling of particle columns. It is shown that the width of stable arches in cohesionless materials is generally five to seven times of the particle size. Copyright © 2012 John Wiley & Sons, Ltd.

A micromechanical analysis is presented for the description of elastic and plastic behavior of a cement-based material (mortar). The mortar is considered as a composite material constituted with cement paste and sand grain. The mechanical behavior of cement paste is described by an elastoplastic model, while a linear elastic behavior is adopted for sand grains. A non-linear homogenization approach based on Hill's incremental model is proposed for the determination of macroscopic properties of mortar composite. Further, influences of water saturation degree on mechanical behavior are taken into account by considering capillary effects on plastic deformation of cement paste. Comparisons between numerical simulations and experimental data are presented.

Highlights:

We propose a homogenization method for non-linear cement-based materials.

We take into account local properties of constituent phases of composite.

The effects of drying process on effective behavior are considered.

Numerical simulations agree well with experimental data. Copyright © 2012 John Wiley & Sons, Ltd.

The paper deals with inferring the mechanical layer properties of pavement systems by way of inverse analysis. The proposed scheme is based on the availability of sensory gear embedded within the system - collecting different types of response traces resulting from moving wheel loads. The inverse analysis task simultaneously exploits the readings from all available sensors and therefore formulated as a multicriterion optimization problem. Data from an experimental asphalt pavement are employed to demonstrate the scheme. A versatile and computationally efficient layered viscoelastic pavement model is offered and implemented as a forward solver. Recoverable layer properties, elastic and viscoelastic, are derived and also compared with laboratory values. Results and possible future uses of the work are discussed. Copyright © 2012 John Wiley & Sons, Ltd.

The magnitude of clamping forces has a significant influence on the estimated ultimate pullout force of a block. The Crawford–Bray equation, which is fundamental in considering clamping forces, is only a function of horizontal stress and block height. Further research to incorporate the influence of induced stress in block stability analysis was considered, but all the previous analytical solutions for analyzing block stability assume a continuum medium to estimate clamping forces and do not allow joint deformations to occur before block movement due to gravity. Assuming a continuous medium to estimate clamping forces leads to an overestimation of block stability and therefore unsafe design. In this paper, an attempt has been made to deepen the understanding of the block failure mechanism and correct the estimated magnitude of clamping forces in a discontinuous medium. A conceptual model is proposed based on the loading–unloading of the block from an in-situ state to failure. Based on this model, an analytical solution has been developed that calculates clamping forces in a discontinuous medium. The validity and model uncertainty of the solution were checked for different conditions. The new analytical solution is both precise and accurate and can be used as a design tool to estimate block stability. Copyright © 2011 John Wiley & Sons, Ltd.

During several triaxial compression experiments on plastic hardening, softening, and failure properties of dense sand specimens, it was found on various stress paths that the size of the failure surface was not constant. Instead, it changed depending on the current state of hydrostatic pressure. This finding is in contrast to the standard opinion consisting of the fact that the failure surface remains constant, once it has been reached during an experiment or in situ.

In general, the behaviour of cohesionless granular-material-like sand is somehow characterised in between fluid and solid, where the solid behaviour results from the angle of internal friction and the confining pressure. Although the friction angle is an intrinsic material property, the confining pressure varies with the boundary conditions, thus defining different solid properties like plastic hardening, softening, and also failure.

Based on our findings, it was the goal of the present contribution to introduce an improved setting for the plastic strain hardening and softening behaviour including the newly found yield properties at the limit state. For the identification of the material parameters, a complete triaxial experimental analysis of the tested sand is given. The overall elasto-plasticity concept is validated by numerical computations of several laboratory foundation- and slope-failure experiments. The performance of the proposed approach is compared with the standard concept of a constant failure surface, where the corresponding yield surfaces are understood as contours of equivalent plastic work or plastic strain. Copyright © 2012 John Wiley & Sons, Ltd.

The model proposed in this article relates permeability to porosity measurements that can easily be performed in the laboratory. The pore size distribution (PSD) curve is updated with strains and damage. The updated volumetric fractions of natural pores and cracks are introduced in the expression of permeability. Contrary to classical permeability models based on PSD integrations, the model proposed in this article accounts for possible changes in the porosity modes: one mode for undamaged samples and two modes for cracked samples. The proposed approach also accounts for varying states of damage, as opposed to classical fracture network models, in which the cracks pattern is fixed. The only material parameters that are required to describe the microstructure are the lower and upper bounds of the pores size for both natural pores and cracks. All the other PSD parameters involved in the model are related to macroscopic parameters that can easily be determined in the laboratory, such as the initial void ratio. The framework proposed in this article can be used in any damage constitutive model to determine the permeability of a brittle porous medium. Drained triaxial compression tests have been simulated. Before cracks initiation, permeability decreases while the larger natural pores are getting squeezed. After the occurrence of damage, permeability grows due to the increase of cracks density. The model performs well to represent the influence of the confining pressure on damage evolution and permeability variations. Copyright © 2012 John Wiley & Sons, Ltd.

This article presents a fundamental study on the role of particle breakage on the shear behavior of granular soils using the three-dimensional (3-D) discrete element method. The effects of particle breakage on the stress ratio, volumetric strain, plastic deformation, and shear failure behavior of dense crushable specimens undergoing plane strain shearing conditions are thoroughly investigated through a variety of micromechanical analyses and mechanism demonstrations. The simulation of a granular specimen is based on the effective modeling of realistic fracture behavior of single soil particles, which is demonstrated by the qualitative agreement between the results from platen compression simulations and those from physical laboratory tests.

The simulation results show that the major effects of particle breakage include the reduction of volumetric dilation and peak stress ratio and more importantly the plastic deformation mechanisms and the shear failure modes vary as a function of soil crushability. Consistent macro- and micromechanical evidence demonstrates that shear banding and massive volumetric contraction depict the two end failure modes of a dense specimen, which is dominated by particle rearrangement–induced dilation and particle crushing–induced compression, respectively, with a more general case being the combination and competition of the two failure modes in the medium range of soil crushability and confining stress. However, it is further shown that a highly crushable specimen will eventually develop a shear band at a large strain because of the continuous decay of particle breakage. Copyright © 2011 John Wiley & Sons, Ltd.

Experimental results have shown very different stress–dilatancy behavior for sand under loading and unloading conditions. Experimental results have also shown significant effects of inherent anisotropy. In this article, a micromechanics-based method is presented, by which the stress–dilatancy relation is obtained through the consideration of slips at the interparticle contacts in all orientations. The method also accounts for the effect of inherent anisotropy in sand. Experimental results on Toyoura sand and Hostun sand are used for illustration of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.

The finite element (FE) simulation of large-scale soil–structure interaction problems (e.g. piled-raft, tunnelling, and excavation) typically involves structural and geomaterials with significant differences in stiffness and permeability. The symmetric quasi-minimal residual solver coupled with recently developed generalized Jacobi, modified symmetric successive over-relaxation (MSSOR), or standard incomplete LU factorization (ILU) preconditioners can be ineffective for this class of problems. Inexact block diagonal preconditioners that are inexpensive approximations of the theoretical form are systematically evaluated for mitigating the coupled adverse effects because of such heterogeneous material properties (stiffness and permeability) and because of the percentage of the structural component in the system in piled-raft foundations. Such mitigation led the proposed preconditioners to offer a significant saving in runtime (up to more than 10 times faster) in comparison with generalized Jacobi, modified symmetric successive over-relaxation, and ILU preconditioners in simulating piled-raft foundations. Copyright © 2012 John Wiley & Sons, Ltd.

A new approach is proposed to analyze the surface flow and subsurface flow passing over a pervious ground under a uniform rainfall excess. The flow field is divided into two regions that are called water layer and soil layer. To figure out the hydraulic behavior of overland flow on an inclined plane under a rainfall event, the simplified Navier–Stokes equations are employed for the surface water flow, and the flow inside the soil layer is porous media flow, which is governed by Biot's (1956, 1962) theory of poroelasticity. The velocity distribution of overland flow is nonzero at the ground surface. The relation between water depth and slope length was developed first. The profile of surface water flow was then found backwards from the downstream end of the flow section by the Runge–Kutta method. After that, the flow velocity and flow discharge of each layer could also be obtained via the water depth. Finally, the variation of fluid shear stress inside the soil layer is also discussed. Copyright © 2011 John Wiley & Sons, Ltd.

Using pile segment analysis, the mobilized shaft resistance of axially loaded nondisplacement piles in sand is investigated here. It is accepted that the shaft capacity of piles constructed in granular soils is highly influenced by the mechanical behavior of soil–structure interfaces forming adjacent the piles skin. Adopting the thin interface layer as a load transfer mechanism, a simple but accurate critical state compatible interface constitutive model is introduced. After evaluation, the interface model in conjunction with the pile segment analysis is applied for the prediction of the shaft resistance mobilized in nondisplacement piles. The proposed approach takes into account the influences of pile diameter and surface roughness together with the effects of the surrounding soil density and stiffness on the mobilized shaft resistance. The performance of the proposed method is verified by comparing its predictions with the experimental data of various model piles covering wide ranges of length, diameter, roughness, and surrounding soil properties. Copyright © 2012 John Wiley & Sons, Ltd.

This paper describes a random solid-porous model capable of simulating the structure of porous materials. To this purpose, the grain and pore size distributions as well as the void ratio of the material are required. Solids and pores are distributed at random in the model's space according to a size strategy. Herein, the model is used to simulate the retention curves of soils. The Laplace equation is used to determine the size of the pores able to saturate or dry during a wetting or drying process, respectively. The continuous path principle is used to define those elements that effectively saturate or dry during these processes. With this procedure, it is possible to simulate the main retention curves as well as the scanning curves during wetting–drying cycles. Some experimental results reported in the international literature have been used to test the model. This model can be enhanced to study the mechanical behavior of unsaturated soils. Copyright © 2012 John Wiley & Sons, Ltd.

Analytical solutions for the steady-state response of an infinite beam resting on a visco-elastic foundation and subjected to a concentrated load moving with a constant velocity are developed in this paper. The beam responses investigated are deflection, bending moment, shear force and contact pressure. The mechanical resistance of the foundation is modeled using two parameters k_s and t_s — k_s accounts for soil resistance due to compressive strains in the soil and t_s accounts for the resistance due to shear strains. Since this model represents the ground behavior more accurately than the Winkler spring model, the developed solutions produce beam responses that are closer to reality than those obtained using the existing solutions for Winkler model. The dynamic beam responses depend on the damping present in the system and on the velocity of the moving load. Based on the study, dynamic amplification curves are developed for beam deflection. Such amplification curves for deflection, bending moment, shear force and contact pressure can be developed for any beam-foundation system and can be used in design. Copyright © 2012 John Wiley & Sons, Ltd.

Fractional calculus has been successfully applied to characterize the rheological property of viscoelastic materials; however, geomaterials were seldom involved in fractional order constitutive models (FOCM), and the topic of first loading and then unloading is rarely discussed through fractional calculus. In this paper, mechanical properties are considered as a ‘spectrum’, both ends of which are elasticity and viscosity, and the fractional order can be utilized to describe such properties quantitatively. In addition to conditions such as creep, stress-relaxation, and constant-strain-rate loading, stress-strain relationship under the condition of first loading and then unloading was also derived using FOCM. FOCM is then adopted to simulate triaxial tests of geomaterials under corresponding conditions. A comparison of test and numerical results demonstrates that FOCM can reasonably describe the mechanical characteristics of geomaterials.Copyright © 2012 John Wiley & Sons, Ltd.

The description of damaged zones in large scale structures can nowadays be assessed by means of a finite element approach using an appropriate damage model. Nevertheless, a fine description of cracking (crack pattern, crack length, crack opening, crack tortuosity) is of primary importance to satisfy new requirements in design codes, especially when dealing with structure durability. In this paper, a computational strategy to quantify cracking at structural case is proposed. A continuous damage model is used to perform a full resolution at the global scale. Then, a reanalysis (implemented as a post-treatment) of the damaged zones is performed at the local scale with a discrete element model. A non-intrusive and decoupled numerical scheme allows for a two-scale analysis using each mechanical model (continuous as well as discrete) within its more efficient level. 2D and 3D test cases will be treated to illustrate the non-intrusive global/local analysis. Copyright © 2013 John Wiley & Sons, Ltd.