Constitutive modeling of three-dimensional non-coaxial characteristics of clay

Acta Geotechnica - A simple critical state-based constitutive model is proposed to represent the non-coaxial plastic deformations of saturated clay subjected to monotonic shearing with fixed...     

考虑各向异性的原状软黏土微观结构变化机制研究

采用电镜扫描仪（SEM）对在复杂应力路径作用下剪切前后的黏土样进行微观观察,并从剪切前后孔隙排列、孔隙形态、孔隙尺度变化特征3方面分析宏观试验原状软黏土归一化抗剪强度各向异性的微观本质。试验表明：剪切前后孔隙排列无序,孔隙排列方向变化很小,对黏土宏观性质影响很小;当中主应力参数b=0时,剪切过程中孔隙形态的变化对剪切后黏土归一化抗剪强度表现出的各向异性贡献较大;当b =0.5时,剪切过程中孔隙尺度的变化对剪切后黏土归一化抗剪强度表现出的各向异性贡献较大。因此,当中主应力参数不同时,影响剪切后黏土归一化抗剪强度各向异性的土的微观变化因素不同。     

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。     

软土地基上土工织物加筋堤的离心模型试验研究

以黄骅港防波堤工程为依托,对有、无土工织物加筋垫层及不同织物加筋条件下堤坝和软土地基的变形与稳定进行了离心模型试验对比研究。得到了地基土体的竖向与水平位移分布规律以及孔隙水压力的消散特性。研究表明：土工织物加筋垫层的加筋机理源于其对土体的侧限效果,铺设土工织物后能有效地减小地基的沉降,并能够限制浅层土体的侧向变形;为使土工织物的加筋效果能够得以充分发挥,要求织物的强度及模量要与垫层的界面强度相匹配。     

Constitutive modeling of principal stress rotation by considering inherent and induced anisotropy of soils

In order to simulate the soil response during principal stress rotation, anisotropic unified hardening (UH) model is developed within the framework of elastoplastic theory. Without introducing any additional mechanism to display the role of stress rotation specifically, this model achieves the simulation by considering the material anisotropy. The effect of inherent anisotropy is reflected using the anisotropic transformed stress method, but a new formula for the stress mapping is adopted to keep the mean stress unchanged. Analysis indicates that from the view of the transformed stress tensor, the anisotropic soil is subjected to loading during pure rotation of principal stress axes, so that plastic strains can be calculated. To represent the induced anisotropy, a fabric evolution law is proposed based on laboratory and numerical test results. At the critical state, the fabric tensor reaches a stable value determined by the stress state, while the critical state line is unique in the plane of void ratio versus mean stress. The anisotropic UH model has concise formulation and explicit elastoplastic flexibility matrix and can provide reasonable predictions for the deformation of anisotropic soils when principal stresses rotate.     

软土地基路堤施工控制的离心模拟试验研究

软土路基上快速填筑路堤时的稳定控制是非常重要的。为此在现行规范中,采用了一些位移或位移速率的控制标准。但实践表明,采用现行的标准仍然出现一些地基失稳的事例,说明这些标准需要进一步求证和改进。除了继续收集、分析失效事例之外,通过离心模型试验也可以进一步理解堤基失稳的机制。离心模型试验结果表明：路堤快速填筑使得地基破坏时,地基变形略呈马鞍形,坡肩处沉降比道中处沉降略大,坡脚水平位移增加较快;破坏时的位移速率与现有规范建议的控制标准基本符合,但地基内的孔隙水压力是在地基进入破坏状态并发生较大变形之后才有突然增加的趋势;此外,坡脚水平位移和道中沉降的速率比,可能是一个较好的稳定性控制的指标。     

防波堤土工织物加筋地基离心模型试验及数值模拟

以黄骅港北防波堤工程为依托,对土工织物加筋软粘土地基及斜坡式防波堤体系的固结过程进行了离心模型试验和有限元数值模拟,通过分析地基土体固结过程中防波堤-加筋垫层-基体系的位移场和应力场的发展及织物拉应力分布和发展,验证离心试验及数值模拟方法的合理性,并得出以下几点主要结论:(1)土工织物加筋垫层的作用机理为其抗拉性限制自身横向变形,通过与附近土体的摩擦作用限制其侧向变形;(2)加筋减小防波堤-垫层-地基体系的高应力水平区,避免堤身与地基高应力水平区域的连通,增强系统稳定性;(3)在离心试验采用的分层地基的条件下,加筋减小了浅层软基和堤身的侧向位移量,对系统总位移有抑制作用;(4)试验中织物替代材料的极限拉伸强度发挥程度较低,其与砂垫层间摩擦强度的发挥水平约为23.8％。     

An elastoplastic description of frictional destructuration in natural clays and shales

The existence of structuration in natural clays and shales is believed to change their stiffness, yielding, dilatancy and strength characteristics. These constitutive features are widely known to ultimately reunite with those of the reconstituted parent soil upon large straining. However, some experimental results show that such reunification may not occur in isotropic/one-dimensional compression, especially with regard to the critical state friction angle. This peculiar phenomenon has been barely addressed in constitutive models for natural geomaterials. Hence, the present study aims at introducing a structure-dependent critical state friction angle within the subloading yield framework. A new internal variable is introduced in the model of Nakai et al. (Soils Found 51(6):1149–1168, 2011) to capture subtle irreversible degradation of the structured critical state line which also serves as the threshold between contractive and dilatant volume changes. Additionally, a new evolution rule for the proposed destructuration factor is developed by considering important microstructural information revealed by discrete element method simulations. The proposed new modifications not only enhance the model capabilities in predicting bonding effects, but also enrich the classical stress-dilatancy equation by rendering it a function of void ratio, mean stress and the microstructural state. Model simulations of laboratory experimental tests on the Colorado shale as well as Bacinetto clay are presented in order to illustrate the improved predictive capabilities of the new model.     

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.     

Constitutive analysis of the mechanical anisotropy of Opalinus Clay

This paper aims to analyse the anisotropic features of behaviour of Opalinus Clay using the theory of plastic multi-mechanisms. The results of triaxial tests conducted with different load levels and directions showed that the mechanical behaviour of this shale is cross-anisotropic. The stiffer samples are those in which the loading direction is parallel to the bedding plane. This indicates that the preconsolidation stress depends on the orientation of the load with respect to the fabric of Opalinus Clay. It is proposed to interpret the observed cross-anisotropy with an elastoplastic model based on four plastic strain mechanisms that may be successively mobilised depending on the loading direction. The predicted stress–strain responses vary according to the directions of the space as a result of the hardening process, depending on the number of plastic strain mechanisms that have been mobilised. The numerical predictions show overall good agreement with the experimental data in terms of deviatoric stress versus axial strain, demonstrating that multi-mechanism plasticity is a suitable constitutive tool for the interpretation of the mechanical anisotropy of this shale.     

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.

     

Constitutive modeling of unsaturated aggregated soils

A coupled water retention–mechanical constitutive model for unsaturated aggregated soils is presented here. Based on the multi‐scale experimental results, the model incorporates the inter‐particle bonding, fabric and partial saturation effects in a single framework. It is formulated within the framework of hardening elasto‐plasticity and is based on the critical state concept. Prior to model validation, we evaluate the model parameters and propose determination procedures for the main new parameters. Finally, the model is examined for its capability in simulating the experimental results of aggregated and bonded soils. Results of these simulations show that the model addresses the most features arising from the combined effects of soil structure and partial saturation. Copyright © 2010 John Wiley & Sons, Ltd.     

结构性软土的黏滞系数

黏滞系数是表征土的蠕变和流动特性的重要指标。对黄石、漳州、青岛地区结构性软土进行电子显微镜扫描、颗粒分析、X衍射试验和化学分析试验,测试结果表明,软土的粒度成分、矿物成分、物理化学性质、结构类型对黏滞系数影响较大。软土蠕变过程中,结构单元体发生定向排列或产生滑动,其相对运动使结合水的黏滞性反映出来,进而引起黏滞系数的变化。进行直接剪切蠕变试验,并通过陈氏法处理蠕变试验数据。试验结果表明,黏滞系数随剪应力的增加达到峰值,固结压力越大,峰值体现越明显,峰值对应的剪应力也越大,这主要是微观结构随剪应力增大逐渐破损所引起的。固结压力增大,结合水膜厚度变薄,土颗粒间连接力增强,黏滞系数也随之增大。用不同固结压力下黏滞系数峰值对应的剪应力代替临界抗剪强度,提出了一个新的求取长期强度的方法,并通过试验数据验证了方法的正确性。该研究有助于进一步认清蠕变机制,对修正或建立较为符合实际的本构模型有一定意义。     

Compression and consolidation anisotropy of some soft soils

The compression and consolidation anisotropy of 11 soft soils were studied by conducting oedometer tests on sets of duplicate undisturbed specimens prepared in the vertical and horizontal directions from adjacent sections of carefully sampled borehole cores. The one-dimensional compression, yield and creep characteristics of the various silts, clays and amorphous peaty material tested were similar for the vertical and horizontal directions. The exception was the structured, coarse fibrous peaty material which was strongly cross-anisotropic. Drainage occurred more rapidly in the horizontal direction with horizontal-to-vertical permeability ratios r _k of 1.0–1.7. Higher r _k values were associated with more marked fabrics, namely for clays with fine sand partings, fibrous organic inclusions or fine root-holes and the laminated silts. The r _k value was for practical purposes independent of the stress level. Brendan C. O’Kelly: Formerly Scott Wilson Consulting Engineers, UK     

Impacts of saturation-dependent anisotropy on the shrinkage behavior of clay rocks

Geomaterials such as soils and rocks can exhibit inherent anisotropy due to the preferred orientation of mineral grains and/or cracks. They can also be partially saturated with multiple types of fluids occupying the pore space. The anisotropic and unsaturated behaviors of geomaterials can be highly interdependent. Experimental studies have shown that the elastic parameters of rocks evolve with saturation. The effect of saturation has also been shown to differ between directions in transversely isotropic clay rock. This gives rise to saturation-dependent stiffness anisotropy. Similarly, permeability anisotropy can also be saturation-dependent. In this study, constitutive equations accommodating saturation-dependent stiffness and hydraulic anisotropy are presented. A linear function is used to describe the relationship between the elastic parameters and saturation, while the relative permeability–saturation relationship is characterized with a log-linear function. These equations are implemented into a hydromechanical framework to investigate the effects of saturation-dependent properties on the shrinkage behavior of clay rocks. Numerical simulations are presented to demonstrate the role of saturation-dependent stiffness and hydraulic anisotropy in shrinkage behavior. The results highlight that strain anisotropy and time evolution of pore pressures are substantially influenced by saturation-dependent stiffness and hydraulic anisotropy.

     

武汉软土固结不排水应力-应变归一化特性分析

基于武汉软土的固结不排水三轴剪切试验,分析了武汉软土的应力-应变关系特性：在低围压下,土体表现出稳定型或弱应变硬化型;在高围压下,土体呈现出弱应变软化型;土体的应力-应变关系曲线为典型的双曲线。为实现武汉软土应力-应变关系的归一化,基于典型的双曲线方程,从理论上推导了为实现应力-应变方程归一化而必须满足的归一化条件,并提出了用主应力差渐近值作为标准归一化因子。通过运用标准归一化因子和常用的以固结围压为归一化因子,对武汉软土应力-应变特性进行归一化分析和比较,得出用主应力差渐近值作为标准归一化因子,软土的应力-应变特性归一化程度更高,效果更好。同时,运用标准归一化因子,建立了武汉软土固结不排水条件下应力-应变特性的归一化方程。     

A comparison of the fabric and permeability anisotropy of consolidated and sheared silty clay

This paper reports the geotechnical aspects of an experimental programme investigating the permeability of shear zones in clay-rich sediments. Oedometric and ring shear permeameters were used to investigate and compare permeability anisotropy in consolidated and sheared silty clay, to simulate the behaviour of wall-rock sediments and shear zone sediments respectively. In line with other studies, consolidated silty clay was found to have no significant permeability anisotropy, although clay fabric anisotropy was well developed. However, sheared silty clay showed an increase in permeability anisotropy (r_k = 3−16) with decreasing void ratio (e = 0.8−0.4), corresponding to effective stresses of 100 kPa to 4 MPa. This level of anisotropy was retained during shearing along the unloading path, and no significant dilation or enhancement of permeability was observed.     

从各向异性的角度解释和模拟土的非共轴特性

从发挥面的角度出发,分析论证各向异性是引起岩土材料出现非共轴现象的根本原因,得到与材料力学一致的结论。当共轭的两发挥面与沉积面的夹角不相等时,主应力面上将出现塑性应变增量的切向分量,所以塑性应变增量的主方向与应力的主方向非共轴。按照这一结论,对非共轴的数值模拟,也应当根据各向异性本构模型进行。为考虑各向异性影响新近提出的各向异性变换应力法,改变了各应力分量的相对大小,得到的各向异性变换应力张量与真实应力张量的主方向不一致,因此也能反映非共轴。利用各向异性变换应力法,能够在现有的弹塑性本构模型的框架下,描述土的非共轴现象。以各向异性UH模型为例,预测各种加载条件下的非共轴变形,验证了该方法的有效性。