Studies on the determination of shear wave velocity in sands

Laboratory investigations such as resonant column, cyclic triaxial, and torsional shear tests are usually conducted on undisturbed and reconstituted sand samples in order to determine their shear modulus, which can be used to compute shear wave velocity. However, these methods are extremely cumbersome and indirect, they employ cost-intensive instrumentation, and they require trained manpower. These problems can be overcome by using bender elements, which yield the shear wave velocity of sands directly, easily, and quite rapidly. In this context, efforts made by earlier researchers in developing empirical relationships (based on bender elements and resonant column techniques) which can be employed to compute shear wave velocity in sands are worth consideration. Although these relationships take into account parameters like effective stress and void ratio, they do not directly incorporate fundamental characteristics of sands such as their state (i.e. dry or saturated) and the particle size. Thus a generalized relationship, which can be used to compute shear wave velocity in sands in either the dry or saturated state, has been developed. Experiments were conducted on samples of sand and glass beads of different sizes and the results were used to demonstrate the utility and efficiency of the relationship. Details of the methodology developed for this purpose are also presented in this paper.     

Bearing capacity of strip and circular footings in sand using finite elements

Design of shallow foundations relies on bearing capacity values calculated using procedures that are based in part on solutions obtained using the method of characteristics, which assumes a soil following an associated flow rule. In this paper, we use the finite element method to determine the vertical bearing capacity of strip and circular footings resting on a sand layer. Analyses were performed using an elastic–perfectly plastic Mohr–Coulomb constitutive model. To investigate the effect of dilatancy angle on the footing bearing capacity, two series of analyses were performed, one using an associated flow rule and one using a non-associated flow rule. The study focuses on the values of the bearing capacity factors N_q and N_γ and of the shape factors s_q and s_γ for circular footings. Relationships for these factors that are valid for realistic pairs of friction angle and dilatancy angle values are also proposed.     

Role of pressure and temperature in inclusion-induced shear localization: An analogue experimental approach

Using analogue model experiments this study investigates the effects of lithostatic pressure and temperature in controlling the pattern of shear localization around rigid inclusions. Compression experiments were conducted on polymethylmethaacrylate (PMMA) by varying confining pressure (P = 30–70 MPa), homologous temperature (T_o = 0.67–0.80 corresponding to room temperature – 80 °C) and axial strain (yield – 15%) in a triaxial setup. Mechanical data showed temperature has a greater influence on the bulk yield strength and steady-state flow of the analogue material than confining pressure. Increasing confining pressures multiply the shear bands in number, and their overall pattern becomes progressively more complex, leading to composite band structures. On the other hand, under ambient pressure increasing temperature results in a transition from incipient high-strain zones to shear bands with sharp boundaries. Further increase in temperature switches the mode of shear localization, sharp to diffuse type. We finally show the inclusion-induced shear localization as a two-stage process, and provide a micro-mechanical explanation for the P-T dependent shear band patterns, attributed to three mechanically distinct domains of the inclusion-matrix interface: compression, extensional and shear localization.     

Stress‐dependent hardening and failure surfaces of dry sand

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.     

Non‐linear analysis of shear band formation in sand

The paper investigates the incipience of shear band with an incrementally non‐linear constitutive equation. Necessary conditions for the emergence of shear band are derived. The lower bound solution is obtained by taking the strain rate inside and outside the shear band into consideration. Numerical results of localized bifurcation for general stress and strain are presented and compared with experiments. In the principal stress space, the stresses at the onset of shear band form a surface, which is partially enclosed by the failure surface for homogeneous straining. The significance of the analysis for identification of the material parameters and verification of the constitutive model against experiments is discussed. Copyright © 2000 John Wiley & Sons, Ltd.     

Numerical investigations of shear localization in a micro‐polar hypoplastic material

In this paper a micro‐polar continuum approach is proposed to model the essential properties of cohesionless granular materials like sand. The model takes into account the influence of particle rotations, the mean grain size, the void ratio, the stresses and couple stresses. The constitutive equations for the stresses and couple stresses are incrementally non‐linear and based on the concept of hypoplasticity. For plane strain problems the implementation of the model in a finite element program is described. Numerical studies of the evolution of micro‐polar effects within a granular strip under plane shearing are presented. It is shown that the location and evolution of shear localization is strongly influenced by the initial state and the micro‐polar boundary conditions. For large shearing the state quantities tend towards a stationary state for which a certain coupling between the norm of the stress deviator and the norm of the couple stress tensor can be derived. Copyright © 2003 John Wiley & Sons, Ltd.     

Effects of transport of pore water and material heterogeneity on strain localization of fluid‐saturated gradient‐dependent viscoplastic geomaterial

The purpose of the present paper is to clarify the effects of permeability and initial heterogeneity on the strain localization of fluid‐saturated cohesive soil modelled by a strain gradient‐dependent poro‐viscoplastic constitutive model. The effects of permeability and gradient parameters on the growth rate of the fluctuation were obtained by a linear instability analysis. Deformation behaviour of clay specimens modelled as a viscoplastic model with a second order strain gradient during shear was numerically analysed by a soil–water coupled FEM under both globally undrained and partially drained conditions. It was found that the deformation pattern and the stress–strain curve greatly depend on the permeability, the drainage conditions and the initial non‐homogeneous properties. Copyright © 2005 John Wiley & Sons, Ltd.     

Simulation of localization failure with strain‐gradient‐enhanced damage mechanics

Strain gradient implies an important characteristic in localized damage deformation, which can be observed in the softening state of brittle materials, and strain gradients constitute the basic behaviours of localization failure area of the materials. The most important point in strain gradient is its damaging function including an internal length scale, which can be used to express the scale effects of mechanical responses of brittle rock mass. By extending the strain gradient theory and introducing an intrinsic material length scale into the constitutive law, the authors develop an isotropic damage model as well as a micro‐crack‐based anisotropic damage model for rock‐like materials in this paper. The proposed models were used to simulate the damage localization under uniaxial tension and plain strain compression, respectively. The simulated results well illustrated the potential of these models in dealing with the well‐known mesh‐sensitivity problem in FEM. In the computation, elements with C₁ continuity have been implemented to incorporate the proposed models for failure localization. When regular rectangle elements are encountered, the coupling between finite difference method (FDM) and conventional finite element method (FEM) is used to avoid large modification to the existing FEM code, and to obtain relatively higher efficiency and reasonably good accuracy. Application of the anisotropic model to the 3D‐non‐linear FEM analysis of Ertan arch dam has been conducted and the results of its numerical simulation coincide well with those from the failure behaviours obtained by Ertan geophysical model test. In this paper, new applications of gradient theories and models for a feasible approach to simulate localized damage in brittle materials are presented. Copyright © 2002 John Wiley & Sons, Ltd.     

Failure criteria for cohesive‐frictional materials based on Mohr–Coulomb failure function

This study presents two three‐parameter failure criteria for cohesive‐frictional materials based on the Mohr–Coulomb failure function. One proposed failure criterion can be linked to Mogi's empirical formula and incorporates the well‐known Von‐Mises, Drucker–Prager, and Linear Mogi criteria as special cases. Another one with smooth and convex cross sections contains a general Lode dependence in the deviatoric plane and includes the Matsuoka–Nakai and Lade–Duncan Lode dependences as special cases. The effect of the intermediate principal stress on the strength of the material can be taken into account in both criteria. The proposed criteria are numerically calibrated against polyaxial data sets of many different types of rocks and concrete_. The comparison results show that the performance of the proposed criteria is excellent, and the failure criterion with a general Lode dependence performs better than the other one for concrete. Copyright © 2015 John Wiley & Sons, Ltd.     

Strain localization in soft rock—a typical rate‐dependent solid: experimental and numerical studies

Strain localization developing inside soft rock specimens is examined through experimental observation and numerical simulation. In the experimental study, soft rock specimens are sheared at different strain rates under plane strain conditions and deformation and strain localization characteristics are analysed. Transition of localization mode from highly localized mode for higher strain rate to distributed and diffused mode of strain localization for lower strain rates was observed. In the numerical study, simulations of plane strain compression tests are carried out at different strain rates by using an overstressed‐type elasto‐viscoplastic model in finite element computations. The role of strain rates on setting gradients of strain fields across shear band is clarified. The probable mechanism for transition of localization mode is discussed. Copyright © 2005 John Wiley & Sons, Ltd.     

剪切带倾角尺度律与局部化启动跳跃稳定研究

研究了剪切带倾角是如何依赖于岩样高度以及剪切带的不稳定性。建立了准脆性材料试件剪切带倾角尺度效应模型,得到了剪切带倾角尺度效应的解析解,且与实验结果比较相符。研究结果表明:剪切带倾角随着试件高度的增加而增加,但其增加幅逐渐减缓,最终趋于稳定值。笔者还对剪应变局部化启动、跳跃和稳定进行了理论分析,解释了实验所观测到的剪切带跳跃现象和砂岩岩样应变局部化较煤样滞后的原因。剪应变局部化是否发生跳跃,关键取决于全程应力-应变曲线软化段是否存在拐点。对于没有拐点的情形,宏观剪切带图案不跳跃。局部化是导致准脆性材料试件剪切带倾角尺度效应的原因。     

Dynamic analysis of strain localization in water‐saturated clay using a cyclic elasto‐viscoplastic model

A computational framework is presented for dynamic strain localization and deformation analyses of water‐saturated clay by using a cyclic elasto‐viscoplastic constitutive model. In the model, the nonlinear kinematic hardening rule and softening due to the structural degradation of soil particles are considered. In order to appropriately simulate the large deformation phenomenon in strain localization analysis, the dynamic finite element formulation for a two‐phase mixture is derived in the updated Lagrangian framework. The shear band development is shown through the distributions of viscoplastic shear strain, the axial strain, the mean effective stress, and the pore water pressure in a normally consolidated clay specimen. From the local stress–strain relations, more brittleness is found inside the shear bands than outside of them. The effects of partially drained conditions and mesh‐size dependency on the shear banding are also investigated. The effect of a partially drained boundary is found to be insignificant on the dynamic shear band propagation because of the rapid rate of applied loading and low permeability of the clay. Using the finer mesh results in slightly narrower shear bands; nonetheless, the results manifest convergency through the mesh refinement in terms of the overall shape of shear banding and stress–strain relations. Copyright © 2013 John Wiley & Sons, Ltd.     

上海黏性土剪切带形成的数值模拟分析

各种工程事故表明：现有的土力学计算模型均未考虑应变局部化问题,故不能解释这些工程事故的发生,因此应变局部化和剪切带形成的研究成为国际土力学界研究热点之一。数值模拟是研究剪切带形成的一个重要内容。在数值模拟中首先进行剪切带形成条件的研究,接着考虑土质不均匀性的影响,引入弱单元和强单元,进行弱单元与强单元影响力的研究。     

Influence of heterogeneity on 3D slope reliability and failure consequence

This paper investigates the influence of heterogeneity of undrained shear strength on the reliability of, and risk posed by, a long slope cut in clay, for different depths of foundation layer. The clay has been idealised as a linear elastic, perfectly plastic Von Mises material and its spatial variability has been modelled using random field theory, whereas slope performance has been computed using a parallel 3D finite element program. The results of Monte Carlo simulations confirm previous findings that three categories of failure mode are possible and that these are significantly influenced by the horizontal scale of fluctuation relative to the slope geometry. In particular, discrete 3D failures are likely for intermediate scales of fluctuation and, in this case, reliability is a function of slope length. The risk posed by potential slides has been quantified in terms of slide volumes and slide lengths, which have been estimated by considering the computed out-of-face displacements. The results show that, for a given horizontal scale of fluctuation relative to the slope geometry, there is a wide range of possible slide volumes and slide geometries. Indeed, the results highlight just how difficult it is to compute a 2D slope failure in a heterogeneous soil. However, they also indicate that, for low probabilities of failure, the volumes of potential slides can be small. This suggests that, for some problems, it may not be necessary to design to very small probabilities of failure, due to the reduced consequence of failure in this case. The techniques developed in this paper will be important in benchmarking simpler 2D and 3D solutions used in design, as there is a need to quantify slide geometries when benchmarking simpler methods based on predefined failure mechanisms.     

The strain‐dependent spatial evolution of garnet in a high‐P ductile shear zone from the Western Gneiss Region (Norway): a synchrotron X‐ray microtomography study

Reaction and deformation microfabrics provide key information to understand the thermodynamic and kinetic controls of tectono‐metamorphic processes, however, they are usually analysed in two dimensions, omitting important information regarding the third spatial dimension. We applied synchrotron‐based X‐ray microtomography to document the evolution of a pristine olivine gabbro into a deformed omphacite–garnet eclogite in four dimensions, where the 4^th dimension is represented by the degree of strain. In the investigated samples, which cover a strain gradient into a shear zone from the Western Gneiss Region (Norway), we focused on the spatial transformation of garnet coronas into elongated garnet clusters with increasing strain. The microtomographic data allowed quantification of garnet volume, shape and spatial arrangement evolution with increasing strain. The microtomographic observations were combined with light microscope and backscatter electron images as well as electron microprobe (EMPA) and electron backscatter diffraction (EBSD) analysis to correlate mineral composition and orientation data with the X‐ray absorption signal of the same mineral grains. With increasing deformation, the garnet volume almost triples. In the low‐strain domain, garnet grains form a well interconnected large garnet aggregate that develops throughout the entire sample. We also observed that garnet coronas in the gabbros never completely encapsulate olivine grains. In the most highly deformed eclogites, the oblate shapes of garnet clusters reflect a deformational origin of the microfabrics. We interpret the aligned garnet aggregates to direct synkinematic fluid flow, and consequently influence the transport of dissolved chemical components. EBSD analyses reveal that garnet shows a near‐random crystal preferred orientation that testifies no evidence for crystal plasticity. There is, however evidence for minor fracturing, neo‐nucleation and overgrowth. Microprobe chemical analysis revealed that garnet compositions progressively equilibrate to eclogite facies, becoming more almandine‐rich. We interpret these observations as pointing to a mechanical disintegration of the garnet coronas during strain localization, and their rearrangement into individual garnet clusters through a combination of garnet coalescence and overgrowth while the rock was deforming.     

Influence of shear speed and normal stress on the shear behavior and shear zone structure of granular materials in naturally drained ring shear tests

“Sliding Surface Liquefaction” is a process causing strength loss and consequent rapid motion and long runout of certain landslides. Using a new ring shear apparatus with a transparent shear-box and digital video camera system, shear-speed-controlled tests were conducted on mixed grains (mixture of three different sizes of sand and gravel) and mixed beads to study shear behavior and shear zone development process under the naturally drained condition in which pore pressure is allowed to dissipate through the opened upper drainage valve during shearing. Higher excess pore water pressure and lower minimum apparent friction were observed in the tests where grain crushing was more extensive under higher normal stress and higher shear speed. Along with the diffusion of silty water generated by grain crushing, smaller particles were transported upward and downward from the shear zone. Concentration of larger grains to the central and upper part of the shear zone was confirmed by means of visual observation together with grain size analysis of sliced samples from several layers after the test. On the other hand, smaller particles were accumulated mostly below the layer where larger grains were accumulated. The reason why larger grains were accumulated into the shear zone may be interpreted as follows: grains under shearing are also subjected to vertical movement, the penetration resistance of larger grains into a layer of moving particles is smaller than that into the static layer. Therefore, larger grains tend to move into the layer of moving grains. At the same time, smaller particles can drop into the pores of underlying larger grains downward due to gravity.     

基于梯度塑性理论的岩样拉压剪破坏统一失稳判据

提出了单轴拉伸,直剪及单轴压缩剪切破坏失稳判据的统一形式。首先对de Borst R及Muhlhaus H B关于单轴拉伸试件梯度塑性理论解析解方面的开创性工作进行了回顾、评论,并指出了他们工作的缺憾。受de Borst R等工作的启发,对直接剪切试件进行了分析,得到了快速回跳条件。并发现:岩样的快速回跳条件就是系统(由剪切带及带外弹性岩石构成)的失稳判据。又对单轴压缩岩样剪切破坏进行了分析,得到了其失稳判据。通过对单轴拉伸失稳判据、直接剪切失稳判据及单轴压缩剪切破坏失稳判据的类比,得到了失稳判据的统一形式。统一失稳判据表明:岩石材料的局部化带宽度及压缩或剪切弹性模量越小,软化模量及等效试件高度越大,试件越容易发生失稳破坏。     

Effects of periodic fluctuations of micro‐polar boundary conditions on shear localizations in granular soil–structure interaction

In this work, the interface behavior between an infinite extended narrow granular layer and a rough surface of rigid body is investigated numerically, using finite element method in the updated Lagrangian (UL) frame. In this regard, the elasto‐plastic micro‐polar (Cosserat) continuum approach is employed to remove the limitations caused by strain‐softening of materials in the classical continuum. The mechanical properties of cohesionless granular soil are described with Lade's model enhanced by polar terms, including Cosserat rotations, curvatures, and couple stresses. Furthermore, the mean grain diameter as the internal length is incorporated into the constitutive relations accordingly. Here, the evolution and location of shear band, within the granular layer in contact with the rigid body, are mainly focused. In this regard, particular attention is paid to the effects of homogeneous distribution and periodic fluctuation of micro‐polar boundary conditions, prescribed along the interface. Correspondingly, the effects of pressure level, mean grain diameter, and stratified soil are also considered. The finite element results demonstrate that the location and evolution of shear band in the granular soil layer are strongly affected by the non‐uniform micro‐polar boundary conditions, prescribed along the interface. It is found that the shear band is located closer to the boundary with less restriction of grain rotations. Furthermore, the predicted thickness of shear band is larger for higher rotation resistance of soil grains along the interface, larger mean grain diameter, and higher vertical pressure. Regarding the stratified soil, comprising a thin layer with slightly different initial void ratio, the shear band moves towards the layer with initially higher void ratio. Copyright © 2011 John Wiley & Sons, Ltd.     

Interaction between different internal length scales in strain localization analysis of fully and partially saturated porous media—the 1‐D case

The paper analyses the interaction between two internal length scales during dynamic strain localization in multiphase porous materials. The first internal length is introduced in the mathematical model by the gradient‐dependent plasticity for the solid skeleton, while the second one is naturally contained in the multiphase model and is due to the seepage process of the water via Darcy's law, which induces a rate‐dependent behaviour of the solid skeleton. Numerical results of a one‐dimensional example of water saturated porous medium demonstrate the competing effect between these two length scales. The porous medium is here treated as a multiphase continuum, with the pores filled by water and air, the last one at constant atmospheric pressure. Copyright © 2005 John Wiley & Sons, Ltd.