Effects of non‐uniform traction and specimen height in the direct shear test on stress and deformation in a rock fracture

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

The response of an elastic half‐space under a momentary shear line impulse

The response of an ideal elastic half‐space to a line‐concentrated impulsive vector shear force applied momentarily is obtained by an analytical–numerical computational method based on the theory of characteristics in conjunction with kinematical relations derived across surfaces of strong discontinuities. The shear force is concentrated along an infinite line, drawn on the surface of the half‐space, while being normal to that line as well as to the axis of symmetry of the half‐space. An exact loading model is introduced and built into the computational method for this shear force. With this model, a compatibility exists among the prescribed applied force, the geometric decay of the shear stress component at the precursor shear wave, and the boundary conditions of the half‐space; in this sense, the source configuration is exact. For the transient boundary‐value problem described above, a wave characteristics formulation is presented, where its differential equations are extended to allow for strong discontinuities which occur in the material motion of the half‐space. A numerical integration of these extended differential equations is then carried out in a three‐dimensional spatiotemporal wavegrid formed by the Cartesian bicharacteristic curves of the wave characteristics formulation. This work is devoted to the construction of the computational method and to the concepts involved therein, whereas the interpretation of the resultant transient deformation of the half‐space is presented in a subsequent paper. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

Modeling the behavior of sandstone based on generalized plasticity concept

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

岩石节理分级剪切加载-蠕变-卸载的能量与变形特征

为分析岩石节理在剪切加载-蠕变-卸载下的能量演化与变形特征,利用GCTS（RDS?200型）岩石剪切测试系统对人工劈裂岩石节理进行分级剪切加载-蠕变-卸载试验。结果表明：在法向应力小于6.5 MPa和大于7.8 MPa时,滞回环面积与循环级数分别符合线性和指数关系;总变形能和弹性变形能与法向应力呈正相关,与循环级数呈指数关系;塑性变形能与循环级数和法向载荷呈正相关。各级剪切应力加载终止时的剪切位移外包络线与直剪应力-位移曲线变化趋势相同,具有加速上升段、匀速上升段和匀速下降段;累积剪切塑性变形随循环级数增加而增大,但增大速率逐渐变慢;各级剪切加、卸载曲线均能以剪切滑移点为界分为两个阶段;剪切失稳前,加、卸载阶段的法向位移-剪切应力曲线出现在上一循环前方,循环剪切加载和（或）蠕变结束时的累积法向变形出现从增加到减小的现象。     

地震边坡失稳机理及稳定性分析

通过对汶川地震边坡调研,发现大量边坡破坏形式为坡顶拉裂、下部坡体剪切破坏。本文利用有限差分程序,从边坡土体的应力状态出发,通过监测边坡土体的状态、位移和剪应变增量变化等,分析了岩土体在静力、横向地震和耦合地震作用下的破坏过程,发现坡顶附近发生张破坏,以下部位发生剪切破坏,而非传统的地质工程观点——地震边坡破坏主要是地震惯性力造成的剪切破坏。并提出一种新方法——关键点相对位移法,来判断边坡的动力稳定性,数值模拟结果与已有研究成果及震后灾害调查结果具有良好的一致性。     

Study of rock joints under cyclic loading conditions

Summary A conceptual model for the behaviour of rock joints during cyclic shear and under constant normal stresses was proposed according to results from shear tests with 50 concrete replicas of rock joints. The shear strength and deformability of joint samples were found to be both anisotropic and stress dependent. Based on these experimental results, a two-dimensional constitutive model was developed for rock joints undergoing monotonic or cyclic loading sequences. The joint model was formulated in the framework of non-associated plasticity, coupled with empirical relations representing the surface roughness degradation, appearance of peak and residual shear stresses, different rates of dilatancy and contraction, variable normal stiffness with normal deformation, and dependence of shear strength and deformability on the normal stress. The second law of thermodynamics was represented by an inequality and used to restrict the values of some of the material parameters in the joint model. The new joint model was implemented into a two-dimensional Distinct Element Method Code, UDEC, and its predictions agreed well with some well-known test results.     

非贯通类节理岩体剪切变形规律分析

通过直剪条件下的模型试验研究具有相同连通率、含不同起伏角的共面闭合节理在不同法向应力作用下的剪切变形特征。试验结果表明：在达到峰值剪切强度前,剪切应力-位移曲线具有明显的线性段与非线性段;岩桥在法向与剪切荷载的共同作用下会产生一定程度的弱化,积累到一定程度时宏观表现为剪切应力软化。详细阐述了试验过程中裂纹发展的4个阶段并描述了剪切应力-剪切变形曲线变化的特征,提出一个能反映剪切应力-剪切变形曲线全过程的经验本构模型。新模型采用分段函数描述曲线变化特征。直剪试验数据分析表明,该模型能够拟合剪切应力-剪切变形变化发展趋势且具有较高的拟合精度,验证了模型的正确性。最后,对其存在的不足亦进行了简要分析     

Dilatancy of granular materials in a strain space multiple mechanism model

A granular material consists of an assemblage of particles with contacts newly formed or disappeared, changing the micromechanical structures during macroscopic deformation. These structures are idealized through a strain space multiple mechanism model as a twofold structure consisting of a multitude of virtual two‐dimensional mechanisms, each of which consists of a multitude of virtual simple shear mechanisms of one‐dimensional nature. In particular, a second‐order fabric tensor describes direct macroscopic stress–strain relationship, and a fourth‐order fabric tensor describes incremental relationship. In this framework of modeling, the mechanism of interlocking defined as the energy less component of macroscopic strain provides an appropriate bridge between micromechanical and macroscopic dilative component of dilatancy. Another bridge for contractive component of dilatancy is provided through an obvious hypothesis on micromechanical counterparts being associated with virtual simple shear strain. It is also postulated that the dilatancy along the stress path beyond a line slightly above the phase transformation line is only due to the mechanism of interlocking and increment in dilatancy due to this interlocking eventually vanishing for a large shear strain. These classic postulates form the basis for formulating the dilatancy in the strain space multiple mechanism model. The performance of the proposed model is demonstrated through simulation of undrained behavior of sand under monotonic and cyclic loading. Copyright © 2010 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.     

循环与单调加载作用下冻结黄土的变形与损伤特性

针对冻土工程中地基冻土体受力形式复杂、常处于变应力路径、反复加卸载作用问题, 开展了冻结黄土静力条件下的三轴加卸载试验与单调加载对比试验, 研究了两种应力路径下冻结黄土的变形和损伤特性. 通过对比发现, 加载方式对冻结黄土变形特性随围压的变化规律影响不大. 循环加卸载作用下, 冻结黄土的压密变硬增强了其抵抗变形的能力. 卸载阶段, 冻结黄土表现出卸载体胀的弹性现象, 呈现出与融土不同的体变特征. 基于弹性模量的劣化定义了冻结黄土的损伤变量, 并根据试验结果得出了冻结黄土的损伤演化规律可用双曲线函数来描述. 在较低的围压下, 围压增加对冻土损伤的发展有抑制作用; 而当围压足够大时, 由于冰的压碎和压融的出现, 围压增大加剧了损伤的发展.     

循环荷载作用下软土的孔压模式和强度特征

通过循环三轴剪切试验,研究原状软土的变形和孔压发展规律。建议了一个循环荷载作用下孔隙水压力的发展模式。研究了不排水循环荷载作用下软土的动强度以及作用后饱和软土静强度的衰减特征,讨论了周围固结压力和荷载作用频率对动强度的影响。研究表明,在某一轴向应变条件下,循环次数随循环剪应力比的增加而迅速减小;随循环剪切应力比的增大,饱和软土的静强度有一定衰减。     

NGI‐ADP: Anisotropic shear strength model for clay

Many geotechnical problems involve undrained behavior of clay and the capacity in undrained loading. Most constitutive models used today are effective stress based and only indirectly obtain values for the undrained shear strength. To match the design profiles of undrained shear strengths, in active (A), direct simple shear (D) and passive (P) modes of loading are complicated. This paper presents the elastoplastic constitutive model NGI‐ADP which is based on the undrained shear strength approach with direct input of shear strengths. Consequently, exact match with design undrained shear strengths profiles is obtained and the well‐known anisotropy of undrained shear strength and stiffness is accounted for in the constitutive model. A non‐linear stress path‐dependent hardening relationship is used, defined from direct input of failure strains in the three directions of shearing represented by triaxial compression, direct simple shear and triaxial extension. With its clear input parameters the model has significant advantages for design analysis of undrained problems. The constitutive model is implemented, into finite element codes, with an implicit integration scheme. Its performance is demonstrated by a finite element analysis of a bearing capacity problem. Copyright © 2011 John Wiley & Sons, Ltd.     

Bedform spurs: a result of a trailing helical vortex wake

The formative conditions for bedform spurs and their roles in bedform dynamics and associated sediment transport are described herein. Bedform spurs are formed by helical vortices that trail from the lee surface of oblique segments of bedform crest lines. Trailing helical vortices quickly route sediment away from the lee surface of their parent bedform, scouring troughs and placing this bed material into the body of the spur. The geometric configuration of bedform spurs to their parent bedform crests is predicted by a cross‐stream Strouhal number. When present, spur‐bearing bedforms and their associated trailing helical wakes exert tremendous control on bedform morphology by routing enhanced sediment transport between adjacent bedforms. Field measurements collected at the North Loup River, Nebraska, and flume experiments described in previous studies demonstrate that this trailing helical vortex‐mediated sediment transport is a mechanism for bedform deformation, interactions and transitions between two‐dimensional and three‐dimensional bedforms.     

直剪剪切速率对钙质砂强度及变形特征的影响

为深入研究剪切速率对钙质砂强度和变形特征的影响,对钙质干砂进行不同剪切速率条件下的直剪试验。研究结果表明,随剪切速率从0.1 mm/min增至2.4 mm/min时钙质砂抗剪强度先减小后增大,其内摩擦角亦呈现出先减小后增大趋势,临界剪切速率为1.6 mm/min;低法向应力条件下钙质砂试样随剪切速率的增加更易于呈现剪胀现象,高法向应力条件下剪切速率从0.1 mm/min增长至1.6 mm/min时试样整体剪缩量逐渐减小;当剪切速率继续从1.6 mm/min增长至2.4 mm/min时试样最大剪缩量逐渐增加;不同法向应力水平条件下钙质砂加载速率效应的细观机制不同,较低应力水平条件下钙质砂加载速率效应主要由试样内部颗粒错动、换位、重新排列引起,在较高应力水平条件下钙质砂加载速率效应主要由颗粒破碎引起。     

动静组合作用下刀具破岩机制数值分析

基于细观损伤有限元方法,模拟分析了刀具在单一动载、动静联合荷载、静态围压条件下动静联合荷载3种情况下岩体破碎的全过程。模型采用黏弹性人工边界剔除了边界应力波反射对模拟结果准确性的影响。数值模拟结果表明：在弹性情况下,静压的存在对岩体内部最小主应力值影响不大,却显著提高了材料内部最大主应力水平,增大了剪应力的大小,导致剪切破坏可能性增加;当有围压存在时,岩体内部受拉区域减少,岩体强度有所提高。单一动载和动静联合荷载破岩时,岩体内部除刀头附近呈现少量压破坏外,破坏均以拉破坏为主;而围压条件下,岩体破碎面积相对减小,裂纹在围压的作用下向两侧自由面延伸,岩体内部破坏形式则趋于多样化,压破坏比重明显增大,整体表现为拉压复合作用。模拟结果还表明,刀头侵入量主要受动载力大小影响,在相同幅值增量下,动载力增加导致的刀头侵入量远大于静压增加所导致的侵入量。相对单一动载和静压作用下的岩石破碎机制来说,动静组合加载破岩的研究还需更为深入的探讨。研究结果可望对岩体破坏机制以及地下工程作业等实际应用提供一定的参考。     

岩体的加、卸载状态与能量的分配关系

岩体是流变体,在高地应力的长时间作用下其内部非均匀应力随着时间自我松弛,逐渐趋向于静水压力状态。在这样的状态下,虽然其体积仍维持弹性,但丧失了进一步抵抗剪切变形的能力,处于流动的状态,其能量储存具有体积的特征。采用平面压缩模型,研究岩石在不同应力水平长期作用下的变形性状及能量分配关系,给出在快速卸荷条件下发生自持续动力断裂破坏条件,以期揭示深部岩体初始地应力水平（能量在体变及形变上的分配关系）对卸荷条件下岩体运动过程中表现的惯性、黏性及弹塑性变形的影响规律,为建立深部岩体加卸荷本构关系打下基础。     

宏-细观结合的砂土单剪试验非共轴特性分析

针对传统本构理论无法描述土体单剪试验非共轴变形的不足,采用非共轴修正模型进行改进。模型基于材料状态相关临界状态理论,采用宏-细观结合的方法,将1个新的各向异性状态变量引入本构模型来描述砂土的各向异性。考虑细观组构张量和应力张量的几何关系的变化,模型可以描述砂土在主应力轴旋转条件下材料状态的变化,材料状态变化直接导致模型的硬化规律和剪胀性发生变化,因此,模型可以描述该条件下原生向异性对砂土变形的影响。引入非共轴理论对本构模型进行修正,建立了三维非共轴各向异性模型。单剪试验的加载条件会造成主应力轴相对土体沉积面发生旋转,修正模型不但能够描述砂土在主应力轴旋转条件下其原生各向异性对变形的影响,而且可以描述主应力轴旋转造成的应力诱发各向异性对土体变形的影响,因此,该模型能够对整个单剪试验的变形规律进行描述,而且物理意义清晰。通过铝棒堆积体和Toyoura砂单剪试验验证表明,非共轴修正各向异性模型能对单剪试验的整个变形过程进行较好的模拟。     

CFD-DEM simulation of submarine landslide triggered by seismic loading in methane hydrate rich zone

Submarine landslide due to seismic loading in methane hydrate-rich zone was simulated in this study using coupled computational fluid dynamics and discrete element method. Dynamic features and Magnus force were incorporated in the coupling scheme to improve the simulation fidelity in dynamic problem. A sinusoidal type seismic loading was applied to a steep submarine slope, which was characterized by a strong inter-layer of methane hydrate-bearing sediments. The simulation results show that a flow-type sliding occurs and the sliding ends with a gentle slope of accumulated debris material. The fluid flows in an eddy pattern near the sliding mass. The presence of methane hydrate can increase the strength and decrease the damping of the sediment. When MH saturation is low (25 and 30%), the combined seismic loading and particle-fluid interaction damage the MH-rich layer, which allows settlement behind the slope crest and upheaval in front of the slope toe. The two ground deformation patterns (settlement and upheaval) are not observed when MH saturation is high (40 and 50%) because the sediment strength is great enough to resist seismic damage. The lower damping in higher MH saturation sediment allows more energy to be transferred from ground base to potential sliding mass and consequently the sliding initiates earlier. Implications of the simulation results in the assessment of earthquake-induced submarine hazards are discussed.