Elastic shear stiffness anisotropy and fabric anisotropy of natural clays

Natural clays usually show anisotropic stiffness due to their deposition process and anisotropic in situ stress state. The stiffness anisotropy depends on both of the stress anisotropy and fabric anisotropy, while the latter can be quantified by the stiffness anisotropy at isotropic stress states. This paper measures the K₀ value (i.e., stress anisotropy) and elastic shear stiffness anisotropy of natural Shanghai clay in a triaxial apparatus with horizontal and vertical bender elements. The results show that the K₀ value of Shanghai clay lies in the range of 0.40–0.66, and an empirical equation is proposed to estimate the K₀ value based on the plasticity index and initial void ratio. The fabric anisotropy of natural Shanghai clay lies in the range of 1.2–1.4 with a stronger fabric in the horizontal plane. Moreover, the experimental data of the stiffness anisotropy and fabric anisotropy of different clays in the literature are reviewed and analyzed. It reveals that the stiffness anisotropy generally increases, while the fabric anisotropy remains nearly the same during K₀ consolidation. For normally consolidated clay, the fabric anisotropy generally lies in the range of 1.1–1.7. For overconsolidated clays, the fabric anisotropy generally increases as the overconsolidation ratio increases. Empirical equations are proposed to approximately estimate the fabric anisotropy of clays based on its stress normalized elastic shear stiffness.

     

考虑各向异性的软黏土扰动状态本构模型

以大量试验结果为依据,运用物理意义明确、获取简便快捷、经济实用的土电阻率结构指标进行软黏土扰动变量的表征和测定。以三轴试验与电阻率测试结果为基础,进行了扰动函数的构建。在软黏土扰动状态描述中,引入旋转硬化因子,用以考虑应力诱发各向异性,进而构建了考虑各向异性的软黏土扰动状态概念本构模型。模型从一定程度上克服了传统扰动变量获取方法的弊端,克服了传统借用数学演绎手段建立扰动函数的不足,提高了模型应用的适用性。在模型构建中,融入初始应力各向异性的影响,从而使模型能更好地反映软土实际工程情况。三轴排水剪切试验验证结果表明,该模型可较好反映软黏土受荷下的结构变化情况和受力特性。     

海相沉积软黏土的弹塑性本构模型研究

在深入探讨海相沉积原状软黏土压缩、变形等力学特性和详细分析加载屈服面随荷载情况变化的基础上,确认了海相沉积原状软黏土的强度、变形特性与结构屈服应力密切相关。即当固结压力小于结构屈服应力时,其力学特性与超固结重塑土的力学特性类似;当固结压力大于结构屈服应力时,其力学特性与正常固结重塑土的力学特性类似。为描述海相沉积原状软黏土的上述力学特性,将姚仰平等提出的超固结重塑土本构模型引入到海相沉积软黏土弹塑性本构模型的构建中。在本构模型构建过程中,考虑了海相沉积原状软黏土具有的抗拉强度及其演化规律,软黏土强度包线的特点及其进一步修正的表达式,使模型更符合海相原状软黏土的强度、变形特性。最后,将3种不同海相沉积软黏土固结排水剪切试验得到的应力-应变-体变曲线与模型预测结果进行对比。比较结果显示,本文提出的弹塑性本构模型能很好地描述海相沉积原状软黏土的剪缩硬化、剪胀软化以及变形的应力水平依存性等力学特性。     

天然沉积饱和有明粘性土的Burland 孔隙指数与归一化含水量的关系

如何评价土结构性对天然沉积饱和土的力学性状的影响是一个非常重要的研究课题。Burland在第30届郎肯讲座论文中导入孔隙指数对各种重塑土的压缩曲线进行归一化，提出固有压缩曲线用于评价天然沉积土的压缩性状。通过对广泛沉积在日本九洲岛的有明粘性土进行试验研究，探讨了灵敏有明粘性土的特征，提出一个比Burland孔隙指数更为简单实用的评价天然沉积土力学性状的指标——归一化含水量，定义为含水量与液限之比。根据大量的试验结果，得出了天然沉积有明粘性土的Burland孔隙指数与归一化含水量的相关关系，提出了对应于归一化含水量的固有压缩曲线。     

软土初始应力各向异性弹塑性模型

自然土体处于初始应力状态,其强度和应力-应变关系都呈现出各向异性,而以往广泛使用的剑桥模型是建立在重塑土试验结果的基础上的,因此,计算实际问题时有一定缺陷.在总结了一些在修正剑桥模型基础上进行扩展而得到的各向异性模型,尤其是S-CLAY1模型.然后,假定了初始屈服面的倾角为K0线,这样使S-CLAY1的计算更加简单.此外,还编制了相关程序,进行了比较计算.结果表明,该模型简单合理,参数正确,可以在实际工程中应用.     

上海浅部黏土渗透系数及其各向异性

为研究上海浅部黏土的渗透系数及其各向异性,沿水平及竖直方向对上海浅部主要黏土层进行了不同压力下的固结试验,联合使用时间平方根法和时间对数法获取了试样的渗透系数,探讨了渗透系数与孔隙比及渗流方向之间的关系,并通过电镜扫描,从微观角度分析了水平和竖直方向渗透系数存在差异的原因。研究结果表明：上海浅部主要黏土层的渗透系数均随着孔隙比的增加而增大。对于单组试验来说,渗透系数k与孔隙比e在e lgk坐标系中呈现很好的线性关系,且渗透变化指数Ck大致呈现Ck = 0.5e0的规律;但对于整体试验而言,渗透系数与孔隙比在e lgk坐标系中大致呈现出曲线关系。通过扫描电镜观察,揭示了沉积形成的絮状微观结构是竖直和水平渗透系数差异较小的主要原因。     

On a multilaminate model for soil incorporating small strain stiffness

In this paper a constitutive model for soils incorporating small strain stiffness formulated in the multilaminate framework is presented. In the multilaminate framework, the stress–strain behaviour of a material is obtained by integrating the mechanical response of an infinite number of randomly oriented planes passing through a material point. Such a procedure leads to a number of advantages in describing soil behaviour, the most significant being capture of initial and induced anisotropy due to plastic flow in a physically meaningful manner. In the past, many soil models of varying degree of refinement in the multilaminate framework have been presented by various authors. However, the issue of high initial soil stiffness in the range of very small strains and its degradation with straining, commonly referred to as ‘small strain stiffness’, has not been addressed within the multilaminate framework. In this paper, we adopt a micromechanics‐based approach to derive small strain elastic stiffness of the soil mass. Comparison of laboratory test data with results obtained from numerical simulations based on the proposed constitutive model incorporating small strain stiffness is performed to demonstrate its predictive capabilities. The model is implemented in a finite element code and numerical simulations of a deep excavation are presented with and without incorporation of small strain stiffness to demonstrate its importance in predicting profiles of deformation. Copyright © 2008 John Wiley & Sons, Ltd.     

Hyperelastic modelling of small‐strain stiffness anisotropy of cyclically loaded sand

Experimental evidence shows that soil stiffness at very small strains is strongly anisotropic and depends on the stress level and void ratio. In particular, stiffness anisotropy varies considerably in sand when subjected to cyclic loading, following the stress cycles applied. To model this behaviour, an innovative hyperelastic formulation based on the elastoplastic coupling is incorporated in a new kinematic hardening elastoplastic model. The proposed hyperelastic–plastic model is the first to be capable of correctly simulating all aspects of the small‐strain behaviour of granular materials subjected to monotonic and cyclic loads. This hyperelastic formulation is generally applicable to any elastoplastic model. Copyright © 2009 John Wiley & Sons, Ltd.     

A note on thermomechanical anisotropy of clays

Deep clays exhibit a pronounced strain anisotropy both during mechanical loading as well as during heating and cooling at constant stress in drained isotropic conditions. During mechanical loading vertical strain is larger than the horizontal one. During heating the vertical strain is larger than the horizontal one within the elastic range; the opposite is observed in the elasto-plastic range. The above described response can be interpreted adopting a consistent rotational, kinematic hardening thermo-elasto-plastic constitutive law.     

Undrained expansion of a cylindrical cavity in clays with fabric anisotropy: theoretical solution

This paper presents a novel, exact, semi-analytical solution for the quasi-static undrained expansion of a cylindrical cavity in soft soils with fabric anisotropy. This is the first theoretical solution of the undrained expansion of a cylindrical cavity under plane strain conditions for soft soils with anisotropic behaviour of plastic nature. The solution is rigorously developed in detail, introducing a new stress invariant to deal with the soil fabric. The semi-analytical solution requires numerical evaluation of a system of six first-order ordinary differential equations. The results agree with finite element analyses and show the influence of anisotropic plastic behaviour. The effective stresses at critical state are constant, and they may be analytically related to the undrained shear strength. The initial vertical cross-anisotropy caused by soil deposition changes towards a radial cross-anisotropy after cavity expansion. The analysis of the stress paths shows that proper modelling of anisotropic plastic behaviour involves modelling not only the initial fabric anisotropy but also its evolution with plastic straining.     

Electrical anisotropy of clays - its geological significance

Electrical (resistivity) anisotropy is found to vary directly and closely as thermaland hydrodynamic anisotropy in clays. This effect is strongest in clays deposited where hydrodynamic forces are strong, i.e., in shallow water. This is the environment of deposition for arenites, however. Therefore, anisotropy in clays may indicate the presence of oil or gas reservoirs. The behavior of the parameter depends, in the main, upon data obtained by the long lateral sonde. —M. E. Burgunker     

On hardening anisotropy of K0-consolidated clays

The combined isotropic-kinematic hardening rule for clays is presented using the concept of a multisurface model discussed previously in Reference 1. The mechanical behaviour of clays after one-dimensional consolidation is next simulated for the axisymmetric stress stress state. A general three-dimensional formulation of constitutive relations is also presented.     

天然沉积结构性黏土原位压缩规律及预测模型研究

通过天然沉积黏土的原状样与重塑样的压缩对比试验,揭示了屈服后土结构性的渐进性破损过程以及由常规 曲线确定的压缩指数 随固结压力呈非线性变化性状给实际工程沉降计算参数选取带来不便。采用 双对数坐标表示方法,通过不同初始结构大小的黏土试验数据证实了 压缩曲线在屈服前后段具有良好的线性关系,实现了结构屈服应力、屈服前后压缩指标有效统一确定。在该坐标体系下给出了考虑取样扰动影响的原位压缩曲线恢复方法,建立了结构性黏土的双线性压缩模型,结合文中与文献中试验数据给出了结构屈服应力与不排水强度、屈服后压缩指标与稳定指数SI和液限wL的经验关系。研究结果可为天然沉积土地基固结沉降计算参数的合理选取提供依据。     

Stress–strain model for clays with anisotropic void ratio distribution

The porosity of soils is considered to be a directional measure and its distribution is characterized by a functional form. This form has been used to extend the critical state soil mechanics framework to include the effects of structure in soils. A new internal plastic energy dissipation formulation has been proposed to account for fabric arrangement. New expressions for the yield locus, and the plastic stress–strain response of structural soils have been derived. The applicability of the concepts to model the plastic stress–strain behaviour of a number of soils is illustrated. The advantage of the new model is very well identified in modelling the stress–strain behaviour of K₀ consolidated and natural clays. © 1998 John Wiley & Sons, Ltd.     

Hypoplastic and viscohypoplastic models for soft clays with strength anisotropy

This paper presents a new viscohypoplastic model for soft clays accounting for their typical features—strength anisotropy and rate dependency. The model is based on the hypoplastic model for clays enhanced by the anisotropic shape of the asymptotic state boundary surface. It has been shown that if the surface is skewed, the model predicts different ultimate strength in compression and in extension. Additional enhancement makes the tensor L bilinear in the strain rate, which more realistically predicts the stress paths of K₀ consolidated samples. The new model has been evaluated by simulating laboratory experiments on soft marine clays (Singapore and Bangkok clays). The model can be easily calibrated using only undrained triaxial and odometer tests. The model is subsequently enhanced by the rate effects. The resulting viscohypoplastic model has been evaluated using experiments of remolded kaolin clay and St. Herblain clay. It is shown that the enhanced model can predict important features of soil viscous behavior, such as rate dependency of strength and preconsolidation pressure, relaxation, and creep.     

A multilaminate constitutive model accounting for anisotropic small strain stiffness

In this paper an extension of existing multilaminate soil models is presented, which can account for inherent and stress‐induced cross‐anisotropic elasticity in the small strain range and its dependency on the load history. In the multilaminate framework, material behaviour is formulated on a number of local planes in each stress point, and the macroscopic response of the material is obtained by integration of the local contributions. Strain‐induced anisotropy, which adds to the stiffness anisotropy inherently present in the material, is therefore intrinsically taken into account. Micro–macro relations between local parameters on plane level and global parameters on macroscopic level are obtained by the spectral decomposition of the global elastic compliance matrix. The model is implemented into a finite‐element code, and model predictions are compared with experimental data of triaxial tests on different soils involving small and large load cycles. The importance of cross‐anisotropic elasticity within the small strain range for predicting ground deformations in geotechnical boundary value problems is discussed at the example of an excavation problem. Copyright © 2012 John Wiley & Sons, Ltd.     

Constitutive modeling of inherent anisotropy in a strain space multiple mechanism model for granular materials

Consideration of fabric anisotropy is crucial to gaining an improved understanding of the behavior of granular materials. This paper presents a constitutive model to describe the sand behavior associated with fabric anisotropy within a framework of a strain space multiple mechanism model. In the proposed model, a second-order fabric tensor is extended by incorporating a new function that represents the effect of inherent (or initial fabric) anisotropy, along with three additional parameters: two of them, a₁ and a₂ , control the degree of anisotropy, and the second mode of inherent anisotropy can be expressed by introducing the parameter a₂ as well as the first mode by the parameter a₁ . The third parameter, θ₀ , expresses the principal direction of inherent anisotropy (eg, the normal vector direction of bedding planes relative to horizontal axis). The formulation of the dilative component of dilatancy (ie, positive dilatancy) is also extended to consider the effect of inherent anisotropy based on the interlocking mechanism. Experimental data on the complex anisotropic responses of Fraser River sand and Toyoura sand under monotonic loading is used to validate this model. The proposed model is shown to successfully capture anisotropic responses, which become contractive or dilative depending on different principal-stress directions, with a single set of anisotropy parameters; thus, the model is considered to possess the capability to simulate the anisotropic behaviors of granular materials. In addition to different loadings on the same fabric, the effects of different fabric anisotropies upon the sand behavior under the same loadings are also investigated.     

Effects of geologic time on the initial stiffness of clays

The paper addresses the effect of geologic aging on the initial stiffness of clays through the analysis of in situ shear stiffness data obtained using a seismic cone penetrometer at three sites in Boston blue clay (BBC), a 12,000–14,000-year old post-glacial marine clay deposit. The effects of this aging period are estimated using as reference for the unaged behavior the results of over 90 triaxial shear phases conducted on specimens of resedimented Boston blue clay (RBBC), a soil prepared in the laboratory from natural BBC, and tested after 1 day of laboratory aging.At the same OCR and effective stress level, the natural clay displays an initial stiffness, which on the average, is approximately 50% greater than that of the laboratory resedimented clay. Based on the estimated age of the natural deposit, this corresponds to an increase of the stiffness per log cycle of time of 7%. This value of the aging coefficient, N_G, is at the low end of values presented in the literature for clays, which are however all based on shorter aging durations (days to weeks).     

Coupled hydro-mechanical model for partially saturated soils predicting small strain stiffness

In the paper, we present newly developed hydro-mechanical hypoplastic model for partially saturated soils predicting small strain stiffness. Hysteretic void ratio dependent water retention model has been incorporated into the existing hypoplastic model. This required thorough revision of the model structure to allow for the hydro-mechanical coupling dependencies. The model is formulated in terms of degree of saturation, rather than of suction. Subsequently, the small strain stiffness effects were incorporated using the intergranular strain concept modified for unsaturated conditions. New features included degree of saturation-dependent size of the elastic range and an updated evolution equation for the intergranular strain. The model has been evaluated using two comprehensive data sets on completely decomposed tuff from Hong-Kong and Zenos Kaolin from Iran. It has been shown that the modified intergranular strain formulation coupled with the hysteretic water retention model correctly reproduces the effects of both the stress and suction histories on small strain stiffness evolution. The model can correctly predict also different other aspects of partially saturated soil behaviour, starting from the very small strain range up to the asymptotic large-strain response.