上海粘性土剪切带倾角的试验研究

采用可量测局部侧向应变的平面应变仪，对上海地区第（2）层褐黄色粉质粘土和第（6）层暗绿色粉质粘土的原状土样，进行固结不排水平面应变压缩试验，观察土样的局部化变形过程，量测剪切带倾角，研究剪切带倾角随固结压力的变化情况，计算剪切带倾角的传统土力学理论解并与实测值进行比较，根据剪切带内局部剪胀角的近似估算，初步研究剪切带内的变形机理，认为剪切带的形成与孔隙水的运动密切相关。     

基于力矩与地下水的黏性土剪切带倾角分析

土体剪切破坏时剪切带倾角是一个一直在研究的问题,传统理论解为Mohr-Coulomb解和Roscoe解。从剪切带厚度和剪切力矩角度重新考虑这一问题,在引入力矩分析及土体本构方程的基础上,对剪切带倾角进行了探讨,得出了新的理论解。同时分析了剪切带上的水压力效应,探讨了孔隙水压力对剪切带倾角的影响。     

Shear band inclination and shear modulus of sand in biaxial tests

The spontaneous shear band formation in the biaxial test on dry sand samples with constant cell pressure is treated as a bifurcation problem. The constitutive response of sand is described in terms of mobilized friction and dilatancy. Dilatancy is looked upon as an internal constraint and the hardening rule is expressed in terms of an adequate dimensionless stress measure. Owing to fail of normality in sand, localization always occurs in the hardening regime. The theoretical solution of the shear band inclination is a geometrical mean of the classical Coulomb and Roscoe solutions and is in good agreement with the experimental data. The incipient shear modulus is proportional to the stress level and can be estimated to be also proportional to these cant modulus.     

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。     

A numerical method for the study of shear band propagation in soft rocks

This paper investigates the possibility of interpreting progressive shear failure in hard soils and soft rocks as the result of shear propagation of a pre‐existing natural defect. This is done through the application of the principles of fracture mechanics, a slip‐weakening model (SWM) being used to simulate the non‐linear zone at the tips of the discontinuity. A numerical implementation of the SWM in a computation method based on the boundary element technique of the displacement discontinuity method (DDM) is presented. The crack and the non‐linear zone at the advancing tip are represented through a set of elements, where the displacement discontinuity (DD) in the tangential direction is determined on the basis of a friction law. A residual friction angle is assumed on the crack elements. Shear resistance decreases on elements in the non‐linear zone from a peak value at the tip, which is characteristic of intact material, to the residual value. The simulation of a uniaxial compressive test in plane strain conditions is carried out to exemplify the numerical methodology. The results emphasize the role played by the critical DD on the mechanical behaviour of the specimen. A validation of the model is shown through the back analysis of some experimental observations. The results of this back analysis show that a non‐linear fracture mechanics approach seems very promising to simulate experimental results, in particular with regards to the shear band evolution pattern. Copyright © 2009 John Wiley & Sons, Ltd.     

Stick-slip model for kink band formation in shear zones and faults

Differential shear stresses acting along or adjacent to a non-planar fault surface or shear zone may cause uneven acceleration during slip. Alternatively, at the initiating and closing stages of motion of parts of a stick-slip fault, localised shear stresses may be variable. Stress variation of this nature causes zones of relative compression and tension, especially close to the “stick” zones on the fault. In fissile rocks adjacent to the fault, kink bands form in zones of local relative compression, while stratal extension features such as veins, fractures and extensional crenulations might be expected in the corresponding zones of relative tension. Repetitive motion on the fault should therefore cause the development of a suite of kink bands superimposed on each other and on any complementary extensional structures. Field evidence indicates that the extensional structures are not developed to the same extent as the kinks, perhaps due to ductile flow during layer-parallel extension of phyllosilicate rocks.

The advantages of this model are that it does not require bulk shortening of the shear zone relative to the enclosing less strained rocks, nor does it depend on complex stress orientation changes.     

Propagation of a shear band in sandstone

Closed‐loop, servo‐controlled experiments were conducted to investigate the development of a shear band in Berea sandstone at various confining pressures. The tests were performed with the University of Minnesota Plane‐Strain Apparatus, which was designed to allow the shear band to develop in an unrestricted manner. Measured load and displacements provided estimates of the stress and deformation states whereby dilatancy and friction were evaluated prior to localization. Experiments were stopped at various stages of shear‐band development within the strain‐softening regime. The specimens displayed a progression of deformation from inception, where the shear band was characterized by a high density of intragranular microcracks and crushed grains, to the tip where the intragranular microcracks were significantly less dense and separated by intact grains. Decreased slip deformation towards the tip of the shear band indicated that localization developed and propagated in plane. Thin‐section microscopy showed porosity increase within the shear band was 3–4 grain diameters wide. Increased porosity did not extend beyond the tip of the shear band. A cohesive zone model of shear fracture, used to examine the stress field near the tip, showed similarities to principal compressive stress orientations interpreted from intragranular microcracks. Thus, propagation of the shear band could be associated with in‐plane mode II fracture. Copyright © 2006 John Wiley & Sons, Ltd.     

Analytical solution of the problem for a set of shear fractures with Coulomb friction

A simplified solution of a two-dimensional problem on a set of interaction shear fractures with Coulomb friction along their wings is proposed. In the classical statement of this problem, the equality between shear stresses and friction stresses must necessarily hold in a new equilibrium state at each point along the fracture plane. The solution of the problem is reduced to the solution of a set of singular integral equations with respect to unknown functions of a shear jump on fractures. In reality, our knowledge of fracture conditions is rather approximate. In addition, in the problems of seismology and tectonophysics it is sufficient to approximately estimate dynamic (taking into account the inertia forces) and static perturbations from a fracture in the form of the first terms of a true solution series. With this aim in view, point models of an earthquake source or continual representation of discontinuous deformations are used. Within the framework of the requirements of such approaches, it is assumed that the condition of equality between the sum of shear stresses and friction stresses on the shear fractures in a new equilibrium state is met. In addition, the complex potential function is calculated for each fracture based on the function of the jump of its wings obtained in the problem for a solitary fracture. Such statement of the problem of a set of neighboring and even intersecting fractures makes it possible to reduce its solution to a set of linear algebraic equations with respect to shear stresses relieved at each fracture and the average along its length, they being the unknown values.     

Effects of crack inclination on shear failure of brittle geomaterials under compression

A micromechanics-based approach is proposed to predict the shear failure of brittle rocks under compression. Formulation of this approach is based on an improved wing microcrack model, the Mohr-Coulomb failure criterion, and a micro-macro damage model. The improved wing microcrack model considers the effects of crack inclination angle on mechanical behaviors of rocks. The micro-macro damage model describes the relation between crack growth and axial strain. Furthermore, comparing experimental and theoretical relations between crack initiation stress and confining pressure, model parameters (i.e., μ, a, β, and φ) hardly measured by test are solved. Effects of crack inclination angle, crack size, and friction coefficient on stress-strain relation, compressive strength, internal friction angle, cohesion, shear failure plane angle, and shear strength are discussed in details. A most disadvantaged crack angle is found, which is corresponding to the smallest compressive strength, cohesion, internal friction angle, and shear strength of rocks. Rationality of the theoretical results is verified by the published experimental results. This approach provides a theoretical prediction for effects of microcrack geometry on macroscopic shear properties in brittle rocks under compression.     

A simulation study of microstructure evolution inside the shear band in biaxial compression test

We study the development of microstructure inside the shear band in granular media consisting of elliptical‐shaped particles. Plane strain biaxial compression test was simulated using two‐dimensional distinct element method. The generation of large voids and concentration of excessive particle rotation inside a shear band are found in a quite similar manner to those observed in natural soils. Evolution of the microstructure inside and outside the shear band is studied. The magnitude and direction of particle rotation inside the shear band is influenced by orientation of long axes of elliptical particles. Because of such particle rotations inside the shear band, the preferred alignment of particles becomes horizontal in the residual state, which results in a more anisotropic contact normal distribution oriented along the major principal stress axis. Copyright © 2010 John Wiley & Sons, Ltd.     

超固结粘土的剪切带数值模拟

基于中井的子负荷面本构关系模型,采用高精度的隐式应力积分算法,研究了平面应变试验中超固结粘土试样的变形局部化问题。模拟了不同的加载速度和边界约束条件,得到了超固结比为8的藤森粘土土体内部明显可见的X型剪切带和单一型剪切带。结果表明：土体的剪胀特性、孔隙水在土体内的移动规律以及边界约束条件对剪切带的形成和发展起着控制作用。     

Numerical simulation of shear band formation in soils

Zones of localized shear strain, called bands, are initiated numerically within idealized cohesive and frictional soil specimens both by inhomogeneities and by imperfect boundaries. Qualitatively the results agree with experimental evidence, and give promise of quantitative analyses using better soil models, when the presence of porewater pressures will be of particular significance.     

剪切带图案的复杂性及应力-应变曲线的离散性

在平面应变压缩条件下,通过在岩样左边界靠近下端面的位置及右边界的不同位置预制材料缺陷,采用拉格朗日元法研究了材料缺陷位置不同时的剪切带图案启动、演变及试样的宏观力学行为。在数值计算中,采用了莫尔-库仑与拉破坏复合的破坏准则,峰后岩石的本构关系为线性应变软化。当试样左、右边界上的缺陷距离较远时,剪切带仅出现1条,以通过两缺陷形式贯通试样两边界;当两缺陷距离较近时,启动于缺陷附近的剪切带按各自其固有方向发展,剪切带图案十分复杂。当右缺陷距离试样上端面较近时,由于上端面的约束,仅位于缺陷下方的剪切带能得到充分的发展。若剪切带数量较少且贯通试样两边界时,试样发生脆性剪切破坏,应力-变形曲线软化段比较陡峭;反之,发生韧性剪切破坏,软化段比较平缓。当剪切带的前端迎面遇到试样上、下端面附近的上、下三角形区域时,由于端面的约束,剪切带的方向将改变。当剪切带的前端与试样的纵向对称线距离较近时,剪切带发生折射现象;当距离较远时,剪切带将发生反射现象。     

A strain model for antithetic fabric rotation in shear band structures

A numerical strain model based on infinitesimal strain theory is presented which simulates the progressive deformation and rotation of a foliated microlithon. It can be shown that an antithetical rotation of the microlithon's foliation with respect to the bulk sense of shear is a geometric consequence of specified strain conditions. The application of the model to asymmetric shear band structures described from the Gurktal Nappe, Eastern Alps, reveals that even the internal foliation of these structures must have been rotated antithetically. This corresponds with rare field observations and supports the suitability of asymmetric shear band structures as indicators for the local sense of shear.     

单轴压缩黏性土剪切带相互作用及损伤试验研究

剪切带损伤研究对于理解材料破坏机制和建立剪切带本构模型具有重要意义。为了研究单轴压缩黏性土样的剪切带损伤演化规律,根据纵向应变较高时清晰剪切带位置布置切向测线,对数字图像相关方法获得的结果进行双三次样条插值,从而获得光滑性较好的各种应变场。将土样整体的损伤变量-纵向应变曲线与各条剪切带的损伤演化曲线进行了对比。研究发现：（1）总体上,土样整体的损伤变量演化曲线呈线性,而各条剪切带的损伤变量演化曲线均上凹,这表明随着纵向应变的增加,各条剪切带的损伤发展越来越快;（2）各条剪切带的损伤变量演化曲线的轮廓线呈马尾形,这说明随着剪切带的逐渐发育,各条剪切带的相互影响和作用规律变强;（3）对于含水率较低的土样,平行或共线剪切带的损伤变量变化基本同步,特别是在剪切带充分发育之后,但两条剪切带的距离应较小;在一定时期,共轭或交叉剪切带中剪切带的损伤占优,这与剪切带的相互竞争有关,但若两条剪切带达到独立发展的程度,则二者的损伤变量变化可以同步;对于含水率较高的土样,各条平行或共轭剪切带的损伤变量变化基本同步,剪切带的相互作用不明显。     

重复剪切作用下结构面起伏角度对其力学特性影响研究

在室内直剪试验的基础上,研究了重复剪切作用下起伏角对结构面变形和强度的影响。采用钢制模具和混凝土材料预制4种起伏角度结构面,分别在5级法向应力下进行6次直剪试验,记录每次剪切过程中的切向应力和法向位移随切向位移的变化。通过对切向应力和法向位移随切向位移变化曲线分析可知,首次剪切时,法向应力和起伏角度越大,结构面剪切破坏方式越容易从滑移破坏过渡为剪断破坏,对于同一种剪切破坏方式,法向应力越大,对结构面磨损或剪断的作用越强烈,峰值剪胀位移越小,起伏角度越大,锯齿被磨损或剪断的高度越大;第2次剪切开始,不论法向应力和起伏角度如何,结构面的剪切破坏方式基本上都转变为滑移破坏。     

An approximate method for evaluating the shear band thickness in saturated soils

A formula for the thickness of a shear band formed in saturated soils under a simple shear or a combined stress state has been proposed. It is shown that the shear band thickness is dependent on the pore pressure properties of the material and the dilatancy rate, but is independent of the details of the combined stress state. This is in accordance with some separate experimental observations. Copyright © 2004 John Wiley & Sons, Ltd.     

粘性土局部化剪切带变形的机理研究

根据上海典型粘性土的平面应变不排水压缩试验,观察了剪切带的形成和发展过程,并结合有限元数值模拟再现剪切带的形成过程,对剪切带形成机理作了探讨。     

结构性黄土二元介质本构模型在局部化剪切带中的应用

基于破损力学理论,将结构性黄土抽象成具有一定结构强度的结构块和摩擦带组成的二元介质模型。对结构性黄土体来说,局部化剪切带问题也是土体的破损问题,剪切带萌生发展的实质就是结构块向摩擦带转化的动态过程。应用结构性土的双参数破损率二元介质本构模型,采用数值分析方法模拟了平面应变压缩条件下结构性土中局部化剪切带萌生、扩展的过程,研究了不同缺陷方案下局部化剪切带的形态、特性与规律,发现结构性土中局部化剪切带的发展起初是由一段段不连续的微小局部破坏区域在外荷载逐步作用下渐进扩展连接贯通而形成整体剪切带的破坏形式。二元介质本构模型和常规有限元的结合,形象生动地再现了局部化剪切带萌生、发展的过程。     

Kinematic modelling of shear band localization using discrete finite elements

Modelling shear band is an important problem in analysing failure of earth structures in soil mechanics. Shear banding is the result of localization of deformation in soil masses. Most finite element schemes are unable to model discrete shear band formation and propagation due to the difficulties in modelling strain and displacement discontinuities. In this paper, a framework to generate shear band elements automatically and continuously is developed. The propagating shear band is modelled using discrete shear band elements by splitting the original finite element mesh. The location or orientation of the shear band is not predetermined in the original finite element mesh. Based on the elasto‐perfect plasticity with an associated flow rule, empirical bifurcation and location criteria are proposed which make band propagation as realistic as possible. Using the Mohr–Coulomb material model, various results from numerical simulations of biaxial tests and passive earth pressure problems have shown that the proposed framework is able to display actual patterns of shear banding in geomaterials. In the numerical examples, the occurrence of multiple shear bands in biaxial test and in the passive earth pressure problem is confirmed by field and laboratory observations. The effects of mesh density and mesh alignment on the shear band patterns and limit loads are also investigated. Copyright © 2003 John Wiley & Sons, Ltd.