Capturing strain localization behind a geosynthetic‐reinforced soil wall

This paper presents the results of finite element (FE) analyses of shear strain localization that occurred in cohesionless soils supported by a geosynthetic‐reinforced retaining wall. The innovative aspects of the analyses include capturing of the localized deformation and the accompanying collapse mechanism using a recently developed embedded strong discontinuity model. The case study analysed, reported in previous publications, consists of a 3.5‐m tall, full‐scale reinforced wall model deforming in plane strain and loaded by surcharge at the surface to failure. Results of the analysis suggest strain localization developing from the toe of the wall and propagating upward to the ground surface, forming a curved failure surface. This is in agreement with a well‐documented failure mechanism experienced by the physical wall model showing internal failure surfaces developing behind the wall as a result of the surface loading. Important features of the analyses include mesh sensitivity studies and a comparison of the localization properties predicted by different pre‐localization constitutive models, including a family of three‐invariant elastoplastic constitutive models appropriate for frictional/dilatant materials. Results of the analysis demonstrate the potential of the enhanced FE method for capturing a collapse mechanism characterized by the presence of a failure, or slip, surface through earthen materials. Copyright © 2003 John Wiley & Sons, Ltd.     

土体应变局部化现象的理论解析

引起土体失稳的应变局部化现象是在特定应力状态下,土体本构产生的分叉特性。基于有限变形理论推导了应变局部化产生的三维解析解。基于应变局部化的理论解析,分析了轴对称和平面应变条件下应变局部化现象在弹塑性硬化阶段的存在性以及剪切带的方向性。 理论分析表明,在轴对称条件下,土体应变局部化产生于土体应力-应变的软化阶段,而平面应变条件下,土体应变局部化一般出现在应力-应变的硬化阶段,其剪切带方向角的理论预测与Arthur等[1]建议值较为一致。     

Thermo-hydro-mechanical modeling of unsaturated soils using isogeometric analysis: Model development and application to strain localization simulation

This study presents a thermo-hydro-mechanical (THM) model of unsaturated soils using isogeometric analysis (IGA). The framework employs Bézier extraction to connect IGA to the conventional finite element analysis (FEA), featuring the current study as one of the first attempts to develop an IGA-FEA framework for solving THM problems in unsaturated soils. IGA offers higher levels of interelement continuity making it an attractive method for solving highly nonlinear problems. The governing equations of linear momentum, mass, and energy balance are coupled based on the averaging procedure within the hybrid mixture theory. The Drucker-Prager yield surface is used to limit the modified effective stress where the model follows small strain, quasi-static loading conditions. Temperature dependency of the surface tension is implemented in the soil-water retention curve. Nonuniform rational B-splines (NURBS) basis functions are used in the standard Galerkin method and weak formulations of the balance equations. Displacement, capillary pressure, gas pressure, and temperature are four independent quantities that are approximated by NURBS in spatial discretization. The framework is used to simulate strain localization in an undrained dense sand subjected to plane strain biaxial compression under different temperatures and displacement velocities. Results show that an increase in the displacement rate leads to reduction in the equivalent plastic strain while an increase in the temperature leads to an increase in the equivalent plastic strain. The findings suggest that the proposed IGA-based framework offers a viable alternative for solving THM problems in unsaturated soils.     

加筋土不同计算方法之间的关系

加筋土中筋材与土的关系与钢筋混凝土中钢筋与混凝土的关系类似。两者的计算方法也具有相似性。等效附加应力法根据附加节点力计算方法的不同分别对应整体式和组合式方法。钢筋混凝土中经典的整体式和组合式方法构成了等效附加应力法的理论基础。反过来,从等效附加应力的角度分析,虽然分离式、整体式、组合式3种方法的单元刚度矩阵不同,但在本质上其实是一致的,区别主要在于边界上等效附加节点力的分配有所不同。（整体式和分离式可看作是特殊的组合式。）等效附加应力法的思想揭示了3种方法内在的处理原理,并且能够用于解释3种方法计算结果异同的原因。借鉴接触面的研究成果,选择合适的应变比例系数计算方法,也能在整体式和组合式方法中考虑筋材和土的滑移情况     

边坡稳定分析中应变局部化的简化计算

采用分岔理论作为局部化判断条件,提出通过弹粘塑性软化模型来捕捉水工结构中的应变局部化剪切带的有限元简化算法。方法的特点是在每个时步,可以得到作为分岔理论所必须的弹塑性矩阵,仅用其作局部化判断,而不影响程序本身的粘塑性迭代。与其他方法相比,该方法理论简洁,易于程序的实现。通过对边坡的稳定分析,结果表明：该方法是合理可行的。     

Experimental study of strain localization in sensitive clays

For evaluation of slope stability in materials displaying strain-softening behavior, knowledge concerning the failed state material response is of importance. Here, soft sensitive clay is studied. Such clays behave contractant at failure, which for undrained conditions yields a strain-softening behavior governed by the generation of excess pore water pressure. Strain softening is further linked with material instability and the phenomenon of strain localization. In the case of shear band formation, internal pore pressure gradients are then expected to be present for globally undrained conditions in the sensitive clay due to its low permeability. In the present study, this hypothesis and its implications on the global response and shear band properties are investigated. Utilizing an experimental setup with a modified triaxial cell allowing for shear band formation, the effect of varying the displacement rate is studied. Onset of strain localization is interpreted to occur just before or at the peak shear strength. A strong rate dependency of the softening response is observed. Increasing displacement rates give raised brittleness in terms of the slope of the global softening curve due to accumulating pore pressure. Also, reduced shear band thickness and a shear band inclination approaching 45° are obtained for increasing rates. In the context of slope failure in such materials, the rate dependency in the post-peak state opens up for a large variation in behavior, all depending on time as an important factor.     

应变局部化问题中的正则化机制探讨

应变局部化问题是当前岩土力学研究的一个重要课题。处理应变局部化问题,一般的方法是引入正则化机制,包括黏性效应、Cosserat理论、非局部化、梯度理论。对应变局部化问题中的各种正则化机制应用进展作了系统总结,并分析讨论了各种正则化机制所存在的问题,最后对应变局部化问题中的正则化机制应用作了展望。     

Microstructural evolution during strain localization in dolomite aggregates

Dolomite aggregates deformed by dislocation creep over a wide range of conditions (T = 700–1000 °C, effective pressure of 900 MPa, strain rates of 10⁻⁷ – 10⁻⁴/s) strain weaken by up to 75% of the peak differential stress. Microstructural study of samples shortened to different finite strains beyond the peak differential stress shows that strain becomes highly localized within shear zones by high-temperature creep processes, with no contribution of brittle cracking. At low strains (8%), dolomite deforms homogeneously by recrystallization-accommodated dislocation creep. At progressively higher sample strains, deformation is localized into narrow shear zones made up of very fine (∼3 μm) recrystallized grains and relict porphyroclasts (20–100 μm). Finely-recrystallized dolomite grains in the shear zones are largely dislocation free and localized shear is facilitated by diffusion creep. In contrast, original dolomite grains and porphyroclasts in shear zones have high dislocation densities and do not deform after shear zone formation. Calculated strain rates in the shear zones are two to three orders of magnitude faster than the imposed bulk strain rate of the samples and these strain rates are consistent with predictions of the diffusion creep flow law for fine-grained dolomite.     

Directional properties of small strain shear stiffness in soils

A compiled database of shear wave velocity measurements in a variety of clays, silts and sands shows directional hierarchies between downhole (V_sVH), standard crosshole (V_sHV), and rotary crosshole (V_sHH) tests. The special in situ database has been collected from 33 well-documented geotechnical test sites. Expressions relating the small-strain shear modulus in terms of effective confining stress level, stress history and void ratio are explored for each of these three modes of directional shear wave velocity. The relationships are separated initially into soil groups (intact clays, fissured clays, sands and silts), and then generalised to consider all soil types together.     

Equal strain consolidation for stone columns reinforced foundation

Column consolidation and deformation are considered by assuming that the quantity of water flowing through the disturbed soil zone into the column is not equal to that flowing out from the column and the difference between them is equal to the volume change of the column. In addition, three patterns of distribution of the horizontal permeability of soil in the disturbed zone are also considered to account for the disturbance effect of columns construction on the surrounding soil. These three patterns include the constant distribution pattern (Pattern I), the linear distribution pattern (Pattern II) and the parabolic distribution pattern (Pattern III). By incorporating the aforementioned characteristics into the analyses, the governing equations containing two variables (i.e. the average excess pore-water pressures within the column and within the entire foundation at any depth) for the consolidation of a composite foundation are derived. The solutions of the governing equations are then obtained using a new initial condition derived from the assumption of equal strain and the equilibrium condition. On the basis of the solutions for excess pore-water pressures, the average degree of consolidation of a composite foundation is obtained and discussed. Finally, a comparison is made of some available solutions. Copyright © 2009 John Wiley & Sons, Ltd.     

Shear strength behaviour of polypropylene fibre reinforced cohesive soils

Soil reinforcement through the inclusion of oriented or randomly distributed discrete elements such as fibres has recently attracted increasing attention in geotechnical engineering. Therefore, the purpose of this paper is to investigate the influence of certain parameters (the strength properties of the fibre, the relative size of the fibres and grains, and the rate of shear) on the shear strength of polypropylene fibre reinforced cohesive soils. A series of consolidated drained or undrained direct shear tests were conducted on unreinforced and reinforced sandy silt and silty clay specimens. Two types of polypropylene fibres with different mechanical indices were used. The fibre content was varied between 0.3% and 1.1% by weight of dry soil. The test results revealed that the inclusion of fibres in soil significantly increases the shear strength. The attainment of the high shear strength is attributed to the micromechanisms involved in the fibre/soil interactions as studied through scanning electron micrographs. The results also showed that the reinforcement effect was more pronounced under undrained shearing conditions. An important outcome from the current work is that, from the data obtained, the strength of the reinforced soil composites is not practically affected by the fibre mechanical indices.     

饱和多孔介质材料的应变局部化萌生条件

在单相介质和非渗流饱和多孔介质应变局部化萌生条件的基础上,应用饱和多孔介质控制方程和Liapunov稳定理论,导出了渗流条件下的固相应力-应变描述和有效应力-应变描述的多孔介质固相部分的应变局部化的萌生条件。不同应力描述下的萌生条件的形式有一定变化。应用简单算例,讨论了Terzaghi有效应力描述的应变局部化萌生条件中两种固、液相对运动特例下的饱和多孔介质应变局部化破坏的形式。     

Phenomenological issues related to strain localization in sensitive clays

A negative second order work, strain softening, is often noticed in contractant material like sensitive clays. Failure in such clays will lead to the formation of localized deformation zone of intense inelastic strain, known as shear band. Conditions, emergence and inclination of shear band has been very well demonstrated in past decades in different manners, however a definite thickness of shear band is still an open question due to several reasons. Mesh dependency, loss of ellipticity is another challenge associated with finite element analyses for strain softening clays. This paper covers a comprehensive review of classical theories of strain localization and associated limitation. Mesh dependency, ill-possed boundary value problem is addressed using finite element simulation examples and experimental results.     

Finite element analysis of strain localization in frictional materials

Numerical examples are given which illustrate the poor performance of conventional finite elements in problems involving strain localization in frictional materials. In one of the cases investigated, that of granular media subjected to plane strain biaxial loading, isoparametric elements are seen to inhibit localization altogether. With these examples by way of motivation, the performance of a recently proposed finite element method in the context of strain localization in frictional materials is assessed, with particular emphasis on three-dimensional problems. In passing, some issues pertaining to the post-bifurcation response of biaxial specimens are examined. In particular, the numerical simulations suggest that the observed softening is a geometrical effect not attributable to constitutive behaviour.     

Magma-induced strain localization in centrifuge models of transfer zones

Scaled centrifuge experiments have been used to investigate the dynamic relations between deformation and magma distribution in rift-related transfer zones. The physical models were built using suitable analogue materials, such as sand to represent the brittle upper crust, various kinds of silicone mixtures to simulate the lower crust and upper mantle and glycerol to reproduce magma. Models simulated the development of transfer zones across pre-existing glycerol reservoirs placed at the base of the analogue continental crust. In plan view, different geometries, dimensions and positions of subcrustal reservoirs were reproduced in three different sets of experiments; to compare results, models were also performed without magma-simulating glycerol.Set 1 experiments, incorporating a narrow rectangular glycerol reservoir, show that the low-viscosity material is able to localise deformation into the overlying crust, giving rise to discrete transfer zones. This concentrated surface deformation corresponds at depth to major magma accumulation. Set 2 experiments, with an initial wide squared glycerol reservoir, show instead that deformation is distributed across the whole model surface, corresponding at depth to relatively minor magma accumulation. Set 3 experiments explored various positions of a small squared reservoir that invariably localised faulting in the overlying analogue brittle crust at the onset of model deformation.The overall model behaviour suggests that magma distribution at depth can effectively control the strain distribution in the overlying crust and the deformative pattern of transfer zones. Strain distribution, in turn, may control magma emplacement as localized deformation would favour major accumulation of magma at transfer zones. Coupled to a strong thermal weakening of the country rocks, this process may ultimately lead to a positive feedback interaction between magma and deformation.     

Gradient plasticity modelling of strain localization in granular materials

The flow stress in the yield surface of plastic constitutive equation is modified with a higher order gradient term of the effective plastic strain to model the effect of inhomogeneous deformation in granular materials. The gradient constitutive model has been incorporated into the finite element code ABAQUS and used to simulate biaxial shear tests on dry sand. It is shown that the shape of the post-peak segment of the load displacement curve predicted by the numerical analysis is dependent on the mesh size when gradient term is not used. Use of an appropriate gradient coefficient is shown to correct this and predict a unique shape of the load displacement curve regardless of the mesh size. The gradient coefficient required turns out to be approximately inversely proportional to the mesh elemental area. Use of the strain gradient term is found to diffuse the concentration of plastic strains within shear band resulting in its consistent width. The coefficient of the higher gradient term appears as a function of the grain size, the mean confining stress, and the plastic softening modulus. Copyright © 2004 John Wiley & Sons, Ltd.     

Spatiotemporal analysis of strain localization in dense granular materials

Acta Geotechnica - Predicting localized failure in granular materials is a problem of great interest from both the scientific and technological perspectives. The initiation and growth of strain...     

含水率对加筋膨胀土强度的影响

通过室内加筋三轴剪切试验,得出最优含水率附近两种不同含水率的加筋膨胀土的应力-应变关系曲线。分析试验曲线可知,相同含水率时试样的强度随着加筋层数、周围压力的增加而增大;同围压、同加筋层数的试样的含水率略微的减少,引起强度明显的增加,表明加筋膨胀土强度的水敏感性。