Condition for liquefaction instability in fluid-saturated granular soils

High-porosity granular materials such as loose sands can implode when subjected to compressive stresses. The mechanism of deformation is diffuse in that the jump in the strain rate tensor has three independent eigenvalues (full rank), in contrast to the jump in the strain rate tensor for a deformation band-type instability that has one eigenvalue (rank one). Recently, the mechanism of volume implosion has been studied in the context of material instability. In this paper we move one step further and consider the effect of a volume constraint associated with the presence of fluids in the pores of granular materials that have a tendency to implode. The upshot of this constraint is that at the onset of liquefaction the solid matrix deforms in a nearly isochoric fashion at the same time that the pore fluid pressure increases. The corresponding eigenmode (e-mode) is represented by jumps in the strain rate tensor and rate of pore fluid pressure. The framework presented in this work is used to analyze the onset of liquefaction instability in very loose Hostun RF sand tested in undrained triaxial compression and extension.     

ELASTOPLASTIC RESPONSE OF PRESSURE SENSITIVE SOLIDS

Tensorially invariant constitutive relations are systematically derived for large strain elastoplastic response of geomaterials. The analysis centres on Mohr–Coulomb (MC) and Drucker–Prager (DP) models with arbitrary hardening and non-associated response. Both flow and deformation theories are constructed for each model with emphasis on linear incremental relations between the Eulerian strain rate tensor and the objective Jaumann stress rate tensor. Specifying the results for plane strain compression we find that deformation theory produces a much smaller tangent instantaneous shear modulus than flow theory. It follows that failure of ellipticity and onset of surface instabilities predicted by deformation theory for associated solids occur at much lower levels of strain than the corresponding flow theory results. On the other hand, flow theory predictions admit a considerable sensitivity to the level of non-associativity. In fact, at high levels of non-associativity flow theory predictions for loss of ellipticity can be at strains below those obtained from deformation theory. © 1997 John Wiley & Sons, Ltd.     

The present-day active deformation in the central and northern parts of the Gulf of Suez area,Egypt, from earthquake focal mechanism data

The average seismic strain rate is estimated for the seismotectonic zone of the northern/central parts of the Gulf of Suez. The principal strain rate tensor and velocity tensor were derived from a combination of earthquake focal mechanisms data and seismic moment of small-sized earthquakes covering a time span of 13 years (1992–2004). A total of 17 focal mechanism solutions have been used in the calculation of the moment tensor summation. The local magnitudes (MLs) of these events range from 2.8 to 4.7. The analysis indicates that the dominant mode of deformation in the central and northern parts of the Gulf of Suez is extension at a rate of 0.008 mm/year in N28°E direction and a small crustal thinning of 0.0034 mm/year. This low level of strain means that this zone experienced a little seismic deformation. There is also a right lateral shear motion along the ESE–WNW direction. This strain pattern is consistent with the predominant NW–SE normal faulting and ESE–WNW dextral transtensive faults in this zone. Comparing the results obtained from both stress and strain tensors, we find that the orientations of the principal axes of both tensors have the same direction with a small difference between them. Both tensors show a predominantly extensional domain. The nearly good correspondence between principal stress and strain orientations in the area suggests that the tectonic strength is relatively uniform for this crustal volume.     

Diffuse instabilities with transition to localization in loose granular materials

This paper is concerned with diffuse and other ensuing failure modes in geomaterials when tested under homogeneous states of shearing in various loading programs and drainage conditions. Material instability is indeed the basic property that accounts for the instability of an initially homogeneous deformation field leading to diffuse failure and strain localization in geomaterials. The former is normally characterized by a runaway type of failure accompanied with a sudden and violent collapse of the material in the absence of any localization phenomena. Against this backdrop, we present a brief overview of material instability in elastoplastic solids where one finds a rich source of theoretical concepts including bifurcation, strain localization, diffuse failure and second‐order work, as well as a considerable body of experiments. Some compelling laboratory experimental studies of material instability with focus to diffuse failure are then presented and interpreted based on the second‐order work. Finally, various material instability analyses using an elastoplastic constitutive and a general finite element analysis of the above‐mentioned laboratory experimental tests are presented as a boundary value problem. It is shown that instability can be captured from otherwise uniform stress, density and hydraulic states, whereas uniform deviatoric loads are being applied on the external boundaries of a specimen. Although the numerical simulations reproduce well the laboratory experimental results, they also highlight the hierarchy of failure modes where localization phenomena emerge in the post‐bifurcation regime as a result of a degradation of homogeneity starting from a diffuse mode signalled by a zero second‐order work. Copyright © 2012 John Wiley & Sons, Ltd.     

Changes in strain trajectories in three different types of plate tectonic boundary deduced from earthquake focal mechanisms

Principal strain orientations (minimum horizontal compression—ex and maximum horizontal compression—ey) were established at three different types of plate tectonic boundary: two transform faults, an oceanic ridge located on the Southeast Indian Ridge and a trench located close to the South Sandwich Archipelago. To establish the strain patterns in each zone, 104 earthquake focal mechanisms (centroid-moment tensor solutions for earthquakes with mb≥4; Harvard seismology data, CMT) were examined by fault population analysis. Despite the existence of only one tectonic process that controlled deformation in these zones (divergence, convergence or passive displacement), and only one main strain tensor, several coeval strain ellipsoids were found. These differed from the main strain tensor in the location of the principal strains. In general, permutations were observed between the principal strains, i.e., interchanges between the location of the principal strain axes maintaining the strain ellipsoids in the same 3D orientation. Only in some cases were changes in the ellipsoid orientation associated with major structures.     

Evaluating magnetic lineations (AMS) in deformed rocks

Magnetic lineation in rocks is given by a cluster of the principal axes of maximum susceptibility (K_max) of the Anisotropy of Magnetic Susceptibility (AMS) tensor. In deformed rocks, magnetic lineations are generally considered to be the result of either bedding and cleavage intersection or they parallel the tectonic extension direction in high strain zones. Our AMS determinations, based on a variety of samples that were taken from mudstones, slates and schists from the Pyrenees and Appalachians, show that strain is not the only factor controlling the development of magnetic lineation. We find that the development and extent to which the magnetic lineation parallels the tectonic extension direction depends on both the original AMS tensor, which in turn depends on the lithology, and the deformation intensity. Rocks having a weak pre-deformational fabric will develop magnetic lineations that more readily will track the tectonic extension.     

A physical and numerical investigation of the failure mechanism of weak rocks surrounding tunnels

The large-scale construction of railway tunnels in China is hindered by several challenges, including large depths, large tunnel cross-sections, and fragile geological conditions. In this paper, we explored a new physical and numerical simulation method that improves upon the currently used methods to investigate the deformation and failure modes of weak rocks surrounding a tunnel. We also compared the results from physical tests and numerical simulations with the field measurements to demonstrate the effectiveness of the proposed numerical simulation method. In the physical model test, an artificial speckle field was developed by staining quartz sand particles and mixing the particles with barite powder and petroleum jelly in preset proportions. The artificial speckle field was employed in the digital speckle correlation method (DSCM) to monitor the evolution of the strain field on the surface of the plain strain model for tunneling during loading. A secondary strain-softening constitutive model using the numerical modeling code FLAC^3D was developed (degradation constitutive model) by considering the deformation modulus degradation in the numerical simulation. The failure mode of weak rocks surrounding a tunnel in the physical model test was examined using the developed degradation constitutive model. Both the physical and numerical results revealed that the least stable area was the shear wedge along the minimum principal stress, which was confirmed in the damage zone of the surrounding rocks. The results were consistent with previous research findings. The results of the DSCM in the physical model test indicated that the shear wedge in the middle part of the tunnel and the cracks around the arch of the tunnel were induced by shear strain, whereas the collapse of the arch was attributed to a combination of tensile strain and shear strain. A comparison of the physical and numerical simulation results demonstrated that the degradation constitutive model can be used to describe the extent and depth of the excavation damage zone of tunneling. A comparison of the displacements from the numerical simulation and field measurements indicated that the degradation model can be used to capture the displacement of weak rocks surrounding tunnels.     

Rotation and strain of linear and planar structures in three-dimensional progressive deformation

Rotation and progressive strain have been studied for a sheet embedded in a matrix which undergoes rotational three-dimensional strain under constant volume conditions. The mathematics gives explicit information on the following features:

1. (1) The length and position (relative to a defined coordinate system) of the principal axes of the strain ellipsoid at any stage of the progressive deformation.

2. (2) The position and length of the principal axes in any plane intersecting the strain ellipsoid, also at any stage of the deformation.

3. (3) The position and length of passive markers which initially coincided with the principal axes in an intersecting plane. This is of consequence for the distinction between passively rotating structures and actively forming structures.

4. (4) The shear strain parallel to an intersecting plane or sheet, as indicated by the angular difference between the normal to an intersecting plane at any time and the marker at the same time which initially, however, was parallel to the normal. This layer-parallel shear causes boudins to rotate and the axial plane of buckles to tilt.

The relationships have been expressed quantitatively in the bulk of the paper and illustrated in diagrams. The analysis presented is basic for the study of the deformational behavior of competent sheets of rocks embedded in less competent ones.     

白银厂矿区劈理成因的磁组构分析

将磁性组构方法用于甘肃白银厂矿区的构造分析.结果表明该区岩石的磁性组构与岩石组构具有同一分布规律.岩石的磁线理与岩石的拉长线理L~a近于一致,磁面理与第一期劈理S_1基本平行,并垂直于岩石的磁化率椭球的最小主轴,也垂直于应变椭球的最短主轴方位,故推断第一期劈理S_1的成因主要属压扁成因.同时受到后期的多次变形与褶皱迭加影响.S_1轴面的优选面状分布发生变位不大,表明该区多次构造变形主要来自早期的同一主应力场作用所致.矿区岩石的磁面理与应变椭球拉长轴面或第一期劈理面S_1存在某些的角度差,表明该区岩石的劈理面由于受后期多次构造变形影响,可能发生剪切运动或旋转机制.     

基于内变量和张量函数表示定理的本构方程

针对各向同性材料,基于张量函数表示定理,建立了本构关系的张量不变性表示,其中,3个不可约基张量取决于应力的0～2次幂,且相互正交,3个系数由塑性应变增量和应力的不变量表示。基于塑性应变增量的不变量定义内变量,本构关系归结为确定内变量的演化。使用张量函数表示定理,给出了内变量演化方程的一般表达式,它取决于应力不变量的增量,因而与主轴旋转无关。讨论了如何根据试验资料和引入适当的假定,确定具体的演化方程。通过与塑性势理论和多重屈服面理论进行比较,表明所建模型是这些理论的最一般表示,且简捷直观、使用方便。     

Particle paths, displacement and progressive strain applicable to rocks

If the particle paths are known for deforming continuous media such as rocks, the strain is determined at all stages of the deformation. The particle paths are studied for various types of simultaneous combinations of pure shear and simple shear. Any kind of progressive plane homogeneous strain can be expressed as a simultaneous superposition of pure shear and simple shear by selecting the proper ratio between the two strain rates and the proper angle between the slide direction of the simple-shear part and the principal axes of the pure-shear part. In the cases studied — except one — the angle between the slide direction of the simple-shear part and the principal strain rate of the pure-shear part is 45°. Several combinations of the simple-shear rate, γ, and the pure-shear rate, , are tested. These combinations give particle paths varying from sets of straight parallel lines to orthogonal hyperbolas. Distorted hyperbolas, ellipses and circles constitute the particle paths at intermediate ratios. From the particle-path equations — which are found by integration of the rate-of-deformation equations — the strain ellipse is readily determined at any stage of the deformation. One particularly intriguing result is the rotating and pulsating strain ellipse found in the cases when the particle paths are closed curves (ellipses). Application of the results to various fold-, thrust- and inclusion structures is suggested. In an appendix the treatment of rotational deformation as a superposition of irrttational strain and rigid rotation is considered for comparison.     

Structural Setting and Kinematic Analysis of the Halaban Region,Eastern Arabian Shield,Saudi Arabia

The vorticity analysis technique was applied to measure the different lithological units,such as schist,metagranite and metavolcano-sedimentary rocks,which are present in the Halaban region.This work aims to interpret the relationship between the different lithologies and the tectonic setting,in order to elucidate the nature of kinematic analysis in the Halaban region.The kinematic analyses were applied to feldspar porphyroclasts,quartz and hornblende for twentysix samples.The kinematic vorticity number (W_m) for deformed rocks in the study area ranged from～0.6 to 0.9.The direction of the long axes for finite strain data (X axes) revealed a WNW trend with shallow dipping.The direction of the short axes for finite strain data (Z axes) were represented by vertical with associated horizontal foliation.The results of the kinematic vorticity and strain analyses are characterized by simple shear with different degrees of deformation in the Halaban region.Furthermore,our finite strain data shows no significant volume change during deformation.The subhorizontal foliation was synchronized with thrusting and deformation.Furthermore,throughout the overlying nappes,the same attitudes of tectonic contacts are observable,the nappes in the orogens being formed from simple shear deformation.     

Axial directions of folds in rocks with linear/planar fabrics

This paper examines the geological implications of an analysis of constraints on the orientation of fold axes in orthotropic materials. We argue that rocks with penetrative linear and planar shape fabrics may have orthotropic (anisotropic) properties during deformation. Two forms of anisotropy (rheological and structural) could be potentially important in the control of fold axial directions. We discuss a model of deformation of rocks with linear/planar fabrics where, in a single deformation event, major fold axes need not be parallel to minor fold axes and neither need be perpendicular to the principal compressive stress direction. Geological and model examples of anistropic control on fold axial directions are given.     

基于广义塑性力学的黄土湿陷变形本构关系

分析了黄土湿陷变形的塑性特性,基于广义塑性力学原理建立了湿陷变形的增量本构关系。将增湿含水量作为内应力,应用常规三轴浸水试验拟合得出了湿陷体积屈服面和剪切屈服面,并且给出了黄土湿陷变形的起始屈服面。该模型能够反映湿陷性黄土在不同湿陷作用,即水和力的不同组合作用下的湿陷变形特性,考虑了湿陷体积变形和湿陷剪切变形以及球应力和偏应力对它们的交叉影响。     

Theory of chocolate tablet boudinage

Two-dimensional boudinage in a flattening type of bulk deformation, with equal layer-parallel extensions in all directions, leads to the development of roundish or polygonal outlines of boudins in plan-view. As combined experimental and theoretical studies show, chocolate tablet boudinage with two sets of mutually perpendicular boudin axes may form in different ways. (1) Unequal layer-parallel extension in the matrix results in one set of extension fractures forming perpendicular to the greatest principal stress in the matrix. Once these long narrow boudins are formed, the greatest principal stress in the brittle layer becomes approximately parallel to the long axis of the boudin. As a result a second set of fractures forms normal to the first set. (2) In lineated rocks the anisotropy of tensile strength leads to the sequential formation of two sets of extension fractures, parallel and perpendicular to the lineation. Depending on the orientation of the lineation the boudin axes may or may not be parallel to the principal stresses in the matrix. (3) Boudins with rectangular plan-view may also form when two successive events of unidirectional boudinage are superposed on one another. Irrespective of the direction of principal extensional strain rate in the matrix, the second generation extension fractures are likely to form approximately perpendicular to the first generation boudin axes.     

地壳岩石半脆性非均匀蠕变破坏-失稳的判别

本文通过分析地壳半脆性域岩石蠕变破坏-失稳的复杂性,提出应该建立能够判别地壳岩石半脆性蠕变破坏-失稳基本规律的准则,以便尽可能准确地预测地壳半脆性域岩石蠕变破坏-失稳的类型及其与温度压力等环境条件的关系。     

软弱破碎围岩变形特性

本文在连续十余年原位监测试验资料的基础上,描述了全断面开挖的软弱围岩变形u-t全过程曲线;阐明了不同变形阶段的变形速率、变形量以及这些变形的时空效应;探讨了岩体工程地质特性、埋深、洞径、开挖方式和支护及时性等主要因素对围岩变形特性的影响;并针对具体工程提出了围岩稳定性状态划分及其判别标准、失稳险情预报原则、变形控制标准与初期支护抗力的确定原则、后期支护最佳施作时期的选择以及合理开挖方式。     

考虑初始损伤和残余强度的岩石变形过程模拟

针对现有损伤模型的不足,提出同时反映岩石初始损伤和残余强度的岩石变形过程模拟方法.将岩石材料分为未损伤部分、损伤部分和微缺陷,未损伤部分和损伤部分共同承担岩石所受的应力.通过岩石材料几何条件及微观受力分析建立未损伤部分的应变分析.再考虑岩石的形变比能只与损伤部分材料相关,从而建立损伤部分的应变分析.然后探讨岩石损伤和耗散能的关系,提出了可以反映岩石初始损伤的损伤演化方程,基于各部分应变分析建立模拟岩石变形过程的损伤本构模型,同时给出模型各参数的确定方法.结果表明:损伤演化方程不仅表现了岩石的初始损伤特征,也可以完整地体现岩石变形破坏过程的5个阶段;与前人模型相比,提出的岩石变形模拟方法与试验曲线更加吻合,体现了岩石的变形全过程,特别是更加直观地反映了岩石的初始损伤和残余强度特征.综合体现了本文模型在模拟岩石变形全过程时的优势.     

考虑渗流和变形耦合的黄土湿陷数值计算

以甘肃陇西地区自重湿陷性黄土作为研究对象,建立了渗流和变形耦合的黄土湿陷变形模型,然后利用Galerkin有限元法对基本方程进行空间离散,在时间域内用差分方法离散,并用Fortran语言编程计算。结合具体的试验条件计算得知：渗流计算结果与实际较为吻合;计算湿陷变形量比实测的大,并且土体非饱和程度越大,差异越大。因此,建议在建立湿陷变形本构关系时考虑时间因素。     

Drained instability analysis of sand under biaxial loading using a 3D material model

The diffused and localized instabilities in sand under drained biaxial loading have been analyzed here following a plane strain bifurcation framework, where the rate independent material is defined using a generalized 3D non-associative constitutive model. This study is focused on how various instability modes emerge with respect to initial density, confining pressure, and the applied boundary conditions. Results from large deformation framework have been compared with those from small deformation approximation and the later is noticed to fail in capturing the emergence of diffused modes and predicts delayed onset of localization. The theoretical predictions compares well with existing experimental observations.