A cap model for partially saturated soils

The present paper deals with the extension of a cap model in order to describe the material behavior of partially saturated soils, in particular, of partially saturated sands and silts. The soil model is formulated in terms of two stress state variables, using net stress and matric suction and, alternatively, the average soil skeleton stress and suction, the latter playing the role of a stress‐like plastic internal variable. The yield surface, consisting of a shear failure surface and a hardening cap surface, the plastic potentials for the non‐associated flow rule and the hardening law for the cap are extended by taking into account the effects of matric suction on the material behavior. Furthermore, the third invariant of the deviatoric stress tensor is taken into account in the formulation of the yield surfaces. The developed model is validated by the numerical simulation of an extensive series of suction controlled tests for a silty sand, which were conducted at different constant values of suction. Although both versions of the soil model yield identical results for stress paths at constant values of matric suction, differences are encountered for stress paths involving wetting. Copyright © 2007 John Wiley & Sons, Ltd.     

A fully implicit and consistent finite element framework for modeling reservoir compaction with large deformation and nonlinear flow model. Part I: theory and formulation

Reservoir depletion results in rock failure, wellbore instability, hydrocarbon production loss, oil sand production, and ground surface subsidence. Specifically, the compaction of carbonate reservoirs with soft rocks often induces large plastic deformation due to rock pore collapse. On the other hand, following the compaction of reservoirs and failure of rock formations, the porosity and permeability of formations will, in general, decrease. These bring a challenge for reservoir simulations because of high nonlinearity of coupled geomechanics and fluid flow fields. In this work, we present a fully implicit, fully coupled, and fully consistent finite element formulation for coupled geomechanics and fluid flow problems with finite deformation and nonlinear flow models. The Pelessone smooth cap plasticity model, an important material model to capture rock compaction behavior and a challenging material model for implicit numerical formulations, is incorporated in the proposed formulation. Furthermore, a stress-dependent permeability model is taken into account in the formulation. A co-rotational framework is adopted for finite deformation, and an implicit material integrator for cap plasticity models is consistently derived. Furthermore, the coupled field equations are consistently linearized including nonlinear flow models. The physical theories, nonlinear material and flow models, and numerical formulations are the focus of part I of this work. In part II, we verify the proposed numerical framework and demonstrate the performance of our numerical formulation using several numerical examples including a field reservoir with soft rocks undergoing serious compaction.     

An improved implicit numerical integration of a non‐associated,three‐invariant cap plasticity model with mixed isotropic–kinematic hardening for geomaterials

The Sandia GeoModel is a continuum elastoplastic constitutive model that captures many features of the mechanical response for geological materials over a wide range of porosities and strain rates. Among the specific features incorporated into the formulation are a smooth compression cap, isotropic/kinematic hardening, nonlinear pressure dependence, strength differential effect, and rate sensitivity. This study attempts to provide enhancements regarding computational tractability, domain of applicability, and robustness of the model. A new functional form is presented for the yield and plastic potential functions. This reformulation renders a more accurate, robust, and efficient model as it eliminates spurious solutions attributed to the original form. In addition, we achieve a high‐performance implementation, because the local iterative method is allowed to recast residual vectors with a uniform dimensionality. The model is also furnished with a smooth, elliptical tension cap to account for the tensile yielding. Moreover, an efficient algorithm is introduced, which decreases the computational cost by differentiating the updated shear yield surface from the cap surface based on the trial relative stress state. Finally, various numerical examples including a large‐scale boundary value problem are presented to demonstrate the fidelity of the modified model and to analyze its numerical performance. Copyright © 2015 John Wiley & Sons, Ltd.     

A rigorous semi‐analytical solution for undrained cylindrical cavity expansion in critical state soils

This paper presents a generalized, rigorous and simple large strain solution for the undrained expansion of a vertical cylindrical cavity in critical state soils using a rate‐based plasticity formulation: the initial stress field is taken as anisotropic, that is with horizontal stresses that differ from the vertical stress, and the soil is assumed to satisfy any two‐invariant constitutive model from the critical state (Cam‐clay) family; no simplifying assumption is made during the mathematical derivation; calculating the effective stresses around the cavity requires the solution of a nonlinear equation by means of the Newton–Raphson method in combination with quadrature. Cavity expansion curves and stress distributions in the soil are then presented for different critical state models (including the modified Cam‐clay model). The solution derived can be useful for estimating the instantaneous response of saturated low‐permeability soils around piles and self‐boring pressuremeters and can serve as trustworthy benchmark for numerical analysis codes. Copyright © 2016 John Wiley & Sons, Ltd.     

On double shearing in frictional materials

This paper evaluates the mechanical behaviour of yielding frictional geomaterials. The general Double Shearing model describes this behaviour. Non‐coaxiality of stress and plastic strain increments for plane strain conditions forms an important part of this model. The model is based on a micro‐mechanical and macro‐mechanical formulation. The stress–dilatancy theory in the model combines the mechanical behaviour on both scales. It is shown that the general Double Shearing formulation comprises other Double Shearing models. These models differ in the relation between the mobilized friction and dilatancy and in non‐coaxiality. In order to describe reversible and irreversible deformations the general Double Shearing model is extended with elasticity. The failure of soil masses is controlled by shear mechanisms. These shear mechanisms are determined by the conditions along the shear band. The shear stress ratio of a shear band depends on the orientation of the stress in the shear band. There is a difference between the peak strength and the residual strength in the shear band. While peak stress depends on strength properties only, the residual strength depends upon the yield conditions and the plastic deformation mechanisms and is generally considerably lower than the maximum strength. It is shown that non‐coaxial models give non‐unique solutions for the shear stress ratio on the shear band. The Double Shearing model is applied to various failure problems of soils such as the direct simple shear test, the biaxial test, infinite slopes, interfaces and for the calculation of the undrained shear strength. Copyright © 2006 John Wiley & Sons, Ltd.     

洞周岩体内裂纹水力劈裂临界水压分析计算

水力劈裂是深埋隧洞施工涌水重要因素之一,对其破坏机制研究是岩土工程界的热点课题。根据裂纹面的应力状态,从断裂力学角度将岩体的裂纹扩展分为拉剪复合扩展和压剪复合扩展。应用地下岩体复合失稳扩展判据分别推导出两种破坏模式的临界水压计算公式,并对其随裂纹在隧洞洞周围的位置、方位变化规律进行分析。分析结果表明,在发生拉剪复合扩展情况下,裂纹方向与最大地应力方向平行时,最易失稳扩展;在压剪复合扩展情况下,裂纹与最大地应力夹角约介于30°～75°之间时,最易失稳扩展。     

A coupled chemo‐viscoplastic cap model for simulating the behavior of hydrating cemented tailings backfill under blast loading

Although the use of blasting has become a routine in contemporary mine operations, there is a lack of knowledge on the response of cement tailings backfills subjected to sudden dynamic loading. To rationally describe such a phenomenon, a new coupled chemo‐viscoplastic cap model is proposed in the present study to describe the behavior of hydrating cemented tailings backfill under blast loading. A modified Perzyna type of visco‐plasticity model is adopted to represent the rate‐dependent behavior of the cemented tailings backfill under blast loading. A modified smooth surface cap model is consequently developed to characterize the yield of the material, which also facilitates hysteresis and full compaction as well as dilation control. Then, the viscoplastic formulation is further augmented with a variable bulk modulus derived from a Mie–Gruneisen equation of state, in order to capture the nonlinear hydrostatic response of cemented backfills subjected to high pressure. Subsequently, the material properties required in the viscoplastic cap model are coupled with a chemical model, which captures and quantifies the degree of cement hydration. Thus, the behavior of hydrating cemented backfills under the impact of blast loading can be evaluated under any curing time of interest. The validation results of the developed model show a good agreement between the experimental and the predicted results. The authors believe that the proposed model will contribute to a better understanding of the performance of cemented backfills under mine blasting and contribute to evaluating and managing the risk of failure of backfill structures under such a dynamic condition. Copyright © 2015 John Wiley & Sons, Ltd.     

Vertical bearing capacity behaviour of single T-shaped soil–cement column in soft ground: laboratory modelling,field test,and calculation

The T-shaped soil–cement column is a variable-diameter column, which has an enlarged column cap at the shallow depth, resulting in the column shape being analogous to the letter “T”. In this study, 1-g laboratory and full-scale field loading tests were employed to investigate the vertical bearing capacity behaviour of a single T-shaped column in soft ground. Pressure cells were set in a T-shaped column in the field to measure the vertical column stress above and below the column cap during the loading test. After the loading test, several columns were excavated to investigate their failure modes. The results indicated that, since the section area of the column cap was remarkably higher than that of the deep-depth column, the stress concentration occurred in the deep-depth column just under the cap, leading to column failure. Based on this failure mode, a simplified method was proposed to estimate the ultimate bearing capacity of a single T-shaped column; the comparison of estimated and measured results indicated the applicability of the proposed method.     

岩石裂纹水力劈裂分析与临界水压计算

水力劈裂是深埋隧洞施工涌水或高压隧洞洞周岩体开裂渗漏的重要因素之一,对其破坏机理研究是岩土工程界的热点课题。根据裂纹面的应力状态,从断裂力学角度将岩体的裂纹扩展分为拉剪复合断裂及压剪复合断裂。应用工程近似裂纹失稳准则,分别推导出两种破坏模式的临界水压计算公式,并对其随裂纹方向及地应力侧压系数变化规律进行分析。结果表明,当侧压力系数等于1.0时,临界水压并不随裂纹的方向而变化;在拉剪复合断裂模式下,裂纹与主应力方向平行时最易发生水力劈裂;在压剪复合断裂模式下,当压剪断裂参数与裂纹面间摩擦系数之差大于零时,其规律性与拉剪复合断裂模式基本一致;但当其差值小于零时,裂纹与最大主应力夹角呈45°及135°时最易发生水力劈裂。     

A fully convex reformulation of the original Matsuoka–Nakai failure criterion and its implicit numerically efficient integration algorithm

This paper presents a reformulation of the original Matsuoka–Nakai criterion for overcoming the limitations which make its use in a stress point algorithm problematic. In fact, its graphical representation in the principal stress space is not convex as it comprises more branches, plotting also in negative octants, and it does not increase monotonically as the distance of the stress point from the failure surface rises. The proposed mathematical reformulation plots as a single, convex surface, which entirely lies in the positive octant of the stress space and evaluates to a quantity which monotonically increases as the stress point moves away from the failure surface. It is an exact reproduction, and not an approximated one, of the only significant branch of the original criterion. It is also suitable for shaping in the deviatoric plane the yield and plastic potential surfaces of complex constitutive models. A very efficient numerical algorithm for the implicit integration of the proposed formulation is presented, which enables the evaluation of the stress at the end of each increment by solving a single scalar equation, both for associated and non‐associated plasticity. The algorithm can be easily adapted for other smooth surfaces with linear meridian section. Finally, a close expression of the consistent Jacobian matrix is given for achieving quadratic convergence in the external structural newton loop. It is shown that all this results in extremely fast solutions of boundary value problems. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptation of an existing constitutive model for describing mechanical behaviour of cemented granular soils

In this paper, an existing elastoplastic constitutive model, originally developed for granular soils, is adapted to describe the stress–strain behaviour of cemented granular soils. The existing model (CJS), due to its modular formulation, can be easily developed to take into account different supplementary behavioural aspects in soil mechanics. In the present study, the failure mechanism of the CJS model is modified by introducing the essential aspects in the behaviour of cemented granular soils in its formulation. All of the model parameters have clear physical meaning and can be identified using classical laboratory tests. A set of direct relations between model parameters and famous mechanical parameters of soils such as internal friction angle and cohesion at peak and residual states is presented. In order to validate the model, the results of triaxial and uniaxial tests in the compression and extension performed on cemented granular materials are used. The validation results indicate the good capability of the proposed model.     

An empirical strength criterion for heterogeneous tuff

An empirical failure criterion is formulated by expressing the second invariant of stress deviation at failure as a function of the first invariant of stress, key parameter, and volume. Strength data from Apache Leap tuff specimens are analyzed as a demonstration example. The density variable included as a key parameter for this tuff minimizes the effect of heterogeneity caused by nonuniform distribution of pores, mineralogy, inclusions, welding and grain bonding. The criterion incorporates all principal stresses and the scale effect, and hence allows predicting the strength toward in-situ conditions. The proposed derivation improves the correlations between test results and failure envelope for the heterogeneous tuff. The criterion formulated from the uniaxial and triaxial test data adequately predicts the strengths for biaxial compression tests.     

A fully implicit and consistent finite element framework for modeling reservoir compaction with large deformation and nonlinear flow model. Part II: verification and numerical example

A fully implicit, fully coupled, and fully consistent finite element framework has been formulated in part I of this work for modeling reservoir compaction through linearizing coupled solid and flow field equations and constructing a local material integrator. In part II of this work, we focus on verification and performance analysis of our numerical formulation and computer implementation using several numerical examples. First, we design a cube problem in triaxial compression to verify our numerical formulation and computer code implementation especially for rock formation in compaction using cap plasticity models. The finite element prediction on stresses is compared with the analytical solution. The second problem we select is a strip footing problem popular in the geotechnical area where the evolution of soil consolidation degrees following the diffusion of pore pressure is the main interest. In this example, we demonstrate a good performance of the proposed numerical formulation on solving different shear and compaction-dominated deformation behaviors by varying the footing length. Importantly, an extremely sharp cap model based on real experimental data for Leda clays, a challenging cap model, is successfully applied in this footing problem. Our focus in this work is to model field reservoirs undergoing serious compaction. A reservoir with complex payzone geometries, multiple horizontal wells, and cap plasticity models with sharp cap surfaces has been successfully solved using our fully implicit formulation. The last example is to model a horizontal wellbore damage problem. Finally, the sensitivity of predicted subsidence to nonlinear flow model, cap hardening parameters, and Lode angles have been systemically investigated and documented in detail, which can provide a constructive guidance on how to successfully model field reservoir compaction problems with cap plasticity models.     

绿泥石片岩各向异性特性研究

为研究十堰地区片岩的各向异性特性,开展了武当群绿泥石片岩长方体试样的单轴压缩和圆盘试样的间接拉伸试验,探讨了试样各向异性的力学特性和在不同受力状态下的变形破裂特性,揭示了不同变形破裂的力学机制。研究表明,武当群绿泥石片岩具有明显的各向异性性质,平行片理方向强度高,垂直片理方向强度低。该片岩特殊的定向排列片束状构造和片理间的弱胶结作用,致使不同方向上的破坏特征具有明显差异,其力学机制也不相同。在压应力作用下,泊松效应容易引起平行片理面的张拉劈裂和压杆失稳,垂直片理方向容易发生片理面间的剪切破坏。在同一方向上强度具有一致性,即平行片理面抗压和抗拉强度均较垂直片理面强度大。由于片理面间的抗拉承载力极低,在小角度劈裂荷载下,容易发生张拉劈裂和拉剪破坏,因此,实际工程中应尽可能避免片理面间的受拉破坏和沿片理的拉剪破坏。研究结果可以为隧道、边坡支护加固和防水处理提供参考。     

桩承式路堤承载特性的颗粒流模拟

现有的土拱效应计算方法中,由于采用的计算模型不同,计算结果差异很大。文中克服传统连续介质力学模型的宏观连续性假设,采用二维颗粒流程序（PFC）建立基于模型试验的细观数值分析模型,对桩承式路堤中土体接触力、应力分布、主应力方向、竖向位移进行分析,并比较计算和实测结果,研究土拱效应的荷载传递机制。同时,对不同桩帽、桩间距、填土高度、颗粒大小、摩擦角的情况进行PFC方法的参数敏感性分析。研究结果表明,桩承式路堤桩顶处局部范围可按弹性核考虑;土拱的分布型式受桩帽型式、桩净距、格栅的影响;实际土拱作用的影响范围主要集中在路堤底面以上约1倍桩净距的区域;土拱内部的竖向应力和水平应力均随深度非线性改变,桩土应力比随着荷载水平、土体内摩擦角、颗粒大小的增大而增加。     

A single numerically efficient equation for approximating the Mohr–Coulomb and the Matsuoka–Nakai failure criteria with rounded edges and apex

This paper presents a novel formulation for defining soil failure. It plots in the principal stress space as a surface with the shape ranging between an approximation of the Matsuoka–Nakai and of the Mohr–Coulomb criteria depending on the value of a single parameter. The new function can be used as a replacement of the original equations of these well‐established criteria for implementing in a program for numerical analyses, and it is particularly effective for approximating the Matsuoka–Nakai criterion. Both the Mohr–Coulomb and the Matsuoka–Nakai failure criteria present numerical difficulties during implementation and also at run‐time. In the case of the Matsuoka–Nakai, the new formulation plots in the first octant only, whereas the original criterion plots in all octants, which causes severe convergence problems particularly for those Gauss points with low stress state, such as those on the side of a shallow footing. When the shape parameter is set to reproduce the Mohr–Coulomb failure criterion, on the other hand, the new formulation plots as a pyramid with rounded edges. Moreover, as the new function is at least of class C², the second derivatives are continuous, thus ensuring quadratic convergence of the Newton's method used within the integration scheme of the constitutive law. The proposed formulation can also provide both sharp and rounded apex of the surface at the origin of the stress space by setting accordingly one additional parameter. Copyright © 2013 John Wiley & Sons, Ltd.     

粗粒料三维颗粒流数值模拟及其破坏准则研究

采用三维颗粒流程序,进行了粗粒料的三维颗粒流数值模拟试验,试验过程中保持平均主应力和中主应力系数不变,研究了不同平均主应力和中主应力系数下粗粒料的变形和强度特性。通过比较粗粒料真三轴颗粒流模型试验结果和室内真三轴试验结果,发现三维颗粒流程序能够较好地模拟该种材料的三维力学特性。基于已提出的统一破坏准则理论,通过调整准则中的材料参数,发现该准则能够较好地描述粗粒料的室内真三轴试验和数值模拟试验结果。     

A simple hypoplastic constitutive model for sand

The paper presents a hypoplastic constitutive model for the three-dimensional non-linear stress–strain and dilatant volume change behaviour of sand. The model is developed without recourse to the concept in elastoplasticity theory such as yield surface, plastic potential and decomposition into elastic and plastic parts. Benefited from the non-linear tensorial functions available from the representation theorem the model possesses simple mathematical formulation and contains only four material parameters, which can be easily identified with triaxial compression tests. Comparison of the predictions with the experimental results shows that the model is capable of capturing the salient behaviour of sand under monotonic loading and is applicable to both drained and undrained conditions.     

The influence of anisotropy on compaction bands: The case of coaxiality between stress and fabric anisotropy tensors

Compaction bands are localized failure patterns that appear in highly porous rock material under the effect of relatively high confining pressure. Being affected mainly by volumetric compression, these bands appear to be almost perpendicular to the most compressive principal stress of a stress state at the so-called “cap” of the yield surface (YS). In this study, we focus on the mechanism that leads to the onset of compaction bands by using a viscoplasticity model able to describe the post-localization response of these materials. The proposed constitutive framework is based on the overstress theory of Perzyna (1966) and the anisotropic clay plasticity model of Dafalias (1986), which provides not only the necessary “cap” of the YS, but introduces a rotational hardening (RH) mechanism, thus, accounting for the effect of fabric anisotropy. Following the analysis of Veveakis and Regenauer-Lieb (2015), we identify the compaction bands as “static” cnoidal wave formations in the medium that occur at a post-yield regime, and we study the effect of rotational and isotropic hardening on their onset. Moreover, we determine a theoretical range of confining pressures in triaxial compression tests for the compaction bands to develop. Under the assumption of coaxiality between stress and anisotropy tensors, the results show that the isotropic hardening promotes compaction localization, whereas the RH has a slightly negative effect on the onset of compaction localization.