Showing papers in "International Journal for Numerical and Analytical Methods in Geomechanics in 2013"

Discrete element modeling of tool-rock interaction I: rock cutting

Abstract: SUMMARY 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 = (KIc ∕ σc)2 with KIc denoting the material toughness and σc 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.

Hydro‐mechanical modeling of cohesive crack propagation in multiphase porous media using the extended finite element method

Abstract: SUMMARY 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.

An improved SPH method for saturated soils and its application to investigate the mechanisms of embankment failure: Case of hydrostatic pore-water pressure

Abstract: SUMMARY The method of smoothed particle hydrodynamics (SPH) has recently been applied to computational geomechanics and has been shown to be a powerful alternative to the standard numerical method, that is, the finite element method, for handling large deformation and post-failure of geomaterials. However, very few studies apply the SPH method to model saturated or submerged soil problems. Our recent studies of this matter revealed that significant errors may be made if the gradient of the pore-water pressure is handled using the standard SPH formulation. To overcome this problem and to enhance the SPH applications to computational geomechanics, this article proposes a general SPH formulation, which can be applied straightforwardly to dry and saturated soils. For simplicity, the current work assumes hydrostatic pore-water pressure. It is shown that the proposed formulation can remove the numerical error mentioned earlier. Moreover, this formulation automatically satisfies the dynamic boundary conditions at a submerged ground surface, thereby saving computational cost. Discussions on the applications of the standard and new SPH formulations are also given through some numerical tests. Furthermore, techniques to obtain the correct SPH solution are also proposed and discussed throughout. As an application of the proposed method, the effect of the dilatancy angle on the failure mechanism of a two-sided embankment subjected to a high groundwater table is presented and compared with that of other solutions. Finally, the proposed formulation can be considered a basic formulation for further developments of SPH for saturated soils. Copyright © 2011 John Wiley & Sons, Ltd.

Two-phase dynamic analysis by material point method

Abstract: SUMMARY 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.

LBM-DEM modeling of fluid-solid interaction in porous media

Abstract: SUMMARY 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

On the role of particle breakage in the shear failure behavior of granular soils by DEM

Abstract: SUMMARY 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.

Continuous velocity fields for collapse and blowout of a pressurized tunnel face in purely cohesive soil

Abstract: 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.

A stabilized assumed deformation gradient finite element formulation for strongly coupled poromechanical simulations at finite strain

Abstract: SUMMARY 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.

Failure and size effect for notched and unnotched concrete beams

Abstract: 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

Modeling of fluid–solid interaction in granular media with coupled lattice Boltzmann/discrete element methods: application to piping erosion

Abstract: SUMMARY In this article, we present a numerical method to deal with fluid–solid interactions and simulate particle–fluid systems as encountered in soils. This method is based on a coupling between two methods, now widely used in mechanics of granular media and fluid dynamics respectively: the discrete element (DE) method and the lattice Boltzmann (LB) method. The DE method is employed to model interactions between particles, whereas the LB method is used to describe an interstitial Newtonian fluid flow. The coupling presented here is a full one in the sense that particle motions act on fluid flow and reciprocally. This article presents in details each of the two methods and the principle of the coupling scheme. Determination of hydrodynamic forces and torques is also detailed, and the treatment of boundaries is explained. The coupled method is finally illustrated on a simple example of piping erosion, which puts in evidence that the combined LB–DE scheme constitutes a promising tool to study coupled problems in geomechanics. Copyright © 2011 John Wiley & Sons, Ltd.

Bivariate simulation using copula and its application to probabilistic pile settlement analysis

Abstract: SUMMARY This paper aims to propose a procedure for modeling the joint probability distribution of bivariate uncertain data with a nonlinear dependence structure. First, the concept of dependence measures is briefly introduced. Then, both the Akaike Information Criterion and the Bayesian Information Criterion are adopted for identifying the best-fit copula. Thereafter, simulation of copulas and bivariate distributions based on Monte Carlo simulation are presented. Practical application for serviceability limit state reliability analysis of piles is conducted. Finally, four load–test datasets of load–displacement curves of piles are used to illustrate the proposed procedure. The results indicate that the proposed copula-based procedure can model and simulate the bivariate probability distribution of two curve-fitting parameters underlying the load–displacement models of piles in a more general way. The simulated load–displacement curves using the proposed procedure are found to be in good agreement with the measured results. In most cases, the Gaussian copula, often adopted out of expedience without proper validation, is not the best-fit copula for modeling the dependence structure underlying two curve-fitting parameters. The conditional probability density functions obtained from the Gaussian copula differ considerably from those obtained from the best-fit copula. The probabilities of failure associated with the Gaussian copula are significantly smaller than the reference solutions, which are very unconservative for pile safety assessment. If the strong negative correlation between the two curve-fitting parameters is ignored, the scatter in the measured load–displacement curves cannot be simulated properly, and the probabilities of failure will be highly overestimated. Copyright © 2011 John Wiley & Sons, Ltd.

Stress–dilatancy behavior for sand under loading and unloading conditions

Abstract: SUMMARY 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.

A fully coupled elastic–plastic hydromechanical model for compacted soils accounting for clay activity

Abstract: A constitutive model, accounting for multiphase and multiscale coupling, is proposed for the water retention domain and the stress–strain response of compacted clayey soils. The model is based on a conceptual interpretation of the microfabric evolution of compacted soils along generalised hydromechanical paths, detected by means of mercury intrusion porosimeter tests. Multiphase coupling is provided by the mutual interaction between the mechanical and the hydraulic states. Multiscale coupling is introduced by a measure of the size of the aggregates, which influences both the retention and the stress–strain response, in the phenomenological constitutive equations. Model capabilities are verified by comparison with relevant experimental data from laboratory tests on compacted Boom clay and other selected experimental data on different compacted clayey soils.

A three-phase thermo-hydro-mechanical finite element model for freezing soils

Abstract: SUMMARY 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.

Soil-pile interaction in the pile vertical vibration considering true three-dimensional wave effect of soil

Abstract: SUMMARY 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.

A finite element approach to the simulation of hydraulic fractures with lag

Abstract: Summary 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.

Analytical solutions for Euler–Bernoulli beam on visco‐elastic foundation subjected to moving load

Abstract: SUMMARY 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 ks and ts — ks accounts for soil resistance due to compressive strains in the soil and ts 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.

Prediction of the shaft resistance of nondisplacement piles in sand

Abstract: SUMMARY 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.

Exact solution for granular flows

Abstract: In this paper we present the exact solution of the Riemann problem for the non-linear one-dimensional socalled 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 topographylinked 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 a first-order finitevolume 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

Discrete element modeling of tool-rock interaction II: Rock indentation

Abstract: SUMMARY 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 KIc is the toughness and σc 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.

An analytical solution for rainfall infiltration into an unsaturated infinite slope and its application to slope stability analysis

Abstract: SUMMARY 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.

Fractional order constitutive model of geomaterials under the condition of triaxial test

Abstract: 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 issue of first loading and then unloading is rarely discussed through fractional calculus. It is considered that all materials are arranged in a queue and ideal solid and Newtonian fluid are located at both ends of the queue in FOCM. On the basis of FOCM, stress-strain relation under the condition of first loading and then unloading, besides creep, stress-relaxation and loading of constant strain rate are obtained. The stress-strain relation is utilized to fit triaxial test results of geomaterials under the corresponding conditions. The comparison between the test and fitting results reveals that FOCM can reasonably describe the stress-strain, stress-time or strain-time characteristics of geomaterials, which shows that fractional calculus is a good tool to constitutive model research of geomaterials.

Fibre reinforced sands: from experiments to modelling and beyond

Abstract: SUMMARY 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.

Theoretical analyses of acidization dissolution front instability in fluid-saturated carbonate rocks

Abstract: SUMMARY 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

Influence of damage on pore size distribution and permeability of rocks

Abstract: SUMMARY 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.

Bearing capacity of strip footings on spatially random soils using sparse polynomial chaos expansion

Abstract: 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 phi) 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.

Numerical modeling of fluid-driven fractures in cohesive poroelastoplastic continuum

Abstract: SUMMARY 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.

A meshfree method for fully coupled analysis of flow and deformation in unsaturated porous media

Abstract: SUMMARY A meshfree algorithm is proposed for the fully coupled analysis of flow and deformation in unsaturated poro-elastic media. A brief description of the governing differential equations is presented followed by the spatial discretization of the governing equations using the Galerkin approach and the radial point interpolation method. Temporal discretization is achieved using a three-point approximation technique with second order accuracy. Particular attention is given to the determination of constitutive coefficients and effective stress parameters of the medium taking into account hydraulic hysteresis. Application of the model to several experimental data is demonstrated. Good agreement is obtained between the numerical and experimental results in all cases highlighting the ability of the proposed model in capturing the volume change and suction dependency of the model parameters as well as the coupled behaviour of unsaturated porous media subject to hydraulic hysteresis. Copyright © 2012 John Wiley & Sons, Ltd.

A detailed investigation of block dynamic sliding by the discontinuous deformation analysis

Abstract: SUMMARY 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.