Theoretical solution for drained cylindrical cavity expansion in clays with fabric anisotropy and structure

Acta Geotechnica - This paper presents a novel, exact, semi-analytical solution for the quasi-static drained expansion of a cylindrical cavity in soft soils with fabric anisotropy and structure....     

Undrained cavity expansion in anisotropic soils with isotropic and frictional destructuration

This paper proposes a semi-analytical solution of undrained cylindrical cavity expansion in anisotropic soils with both isotropic and frictional destructuration. The rigorous derivation based on the general form of the SANICLAY model with destructuration is provided following a standardized solving procedure, and the features of anisotropy and structuration are then invoked in the cavity expansion solution by adopting the non-associated hierarchical model. Cavity expansion tests in both structured and unstructured clays with various overconsolidation ratio are conducted to investigate the evolutions of effective stresses, excess pore pressure, anisotropic parameters and structuration factors during cylindrical expansion. The results show that the effective stresses at the cavity wall are lower after expansion and the cavity excess pore pressure is oppositely higher in structured clays with slightly smaller plastic regions. The evolutions of anisotropy for structured clays appear to follow similar patterns to unstructured cases, whereas the degree of anisotropy is further developed with gradual loss of inter-particle bonds. Finally, the proposed solution is applied to predict the limit pressure of pressuremeter tests in Bothkennar clay, showing its ability for interpretation of in situ testing data in natural structured clays.

     

初始应力各向异性状态下圆柱孔扩张机制分析

采用静止土压力系数K0描述土体初始应力各向异性程度,建立了压力控制边界条件的柱孔扩张数值模型,分析压力为边界条件的圆柱孔扩张特性。计算结果表明,初始应力条件各向异性时,柱孔周围的土体的径向位移是不相等的,扩张后的柱孔呈椭圆形,初始应力各向异性是柱孔非对称扩张的内在原因;塑性区的分布具有明显的方向性,塑性区最大半径位于柱孔周围初始大主应力方向上;在相同的扩张压力下,随不排水抗剪强度增加,土体的塑性区减小,且土体初始应力各向异性造成的土体塑性区分布各向异性程度也随之减小;在相同的扩张压力下,柱孔初始应力越大,其塑性区范围越大,且土体初始应力各向异性造成的土体塑性区分布的各向异性程度也越大。     

压力控制的圆孔扩张数值模拟分析

受沉积历史的影响,实际工程中土体的初始应力往往呈各向异性,此时传统圆孔扩张理论的假定条件不再成立,故其适用性也受到限制。借助于FLAC有限差分数值软件,建立了以压力为圆孔扩张边界的二维圆孔扩张模型,从圆孔的变形、孔周土屈服范围、圆孔扩张产生的超静孔水压力分布等方面进行分析,获得在初始应力各向异性的条件下压力控制圆孔扩张过程土体响应规律。计算分析结果表明,初始应力各向异性时,压力控制的圆孔扩张孔口径向位移、塑性区分布、超静孔隙水压力影响范围各个方向不相等;塑性区的分布具有明显的方向性,塑性区最大半径位于孔周土体初始大主应力方向上,并且其值比在相同的扩张压力作用下各向同性初始应力条件下的塑性区半径大,因此传统的初始等应力条件下位移控制的圆孔扩张理论用于分析各向异性初始应力的工程是偏于不安全的。     

各向异性初始应力状态下圆柱孔扩张理论弹塑性分析

传统的圆柱孔扩张理论假定初始应力为各向同性的。在城市地下管道的铺设、隧道工程等的水平掘进施工过程中,圆柱孔受到的初始竖向应力不等于初始水平应力,并不满足各向同性初始应力条件。考虑土体的各向异性初始应力条件,假定土体满足Mohr-Coulomb屈服准则,推导了各向异性初始应力状态下的圆柱孔扩张问题弹塑性解答。算例计算结果表明：土性参数一定时,在相同内压力作用下,各向异性初始应力状态下的圆柱孔扩张形成的塑性区半径大于各向同性初始应力状态下的圆柱孔扩张的塑性区半径,但前者的极限扩孔压力小于后者。     

A rigorous semi‐analytical solution for undrained cylindrical cavity expansion in critical state soils

This paper presents a generalized, rigorous and simple large strain solution for the undrained expansion of a vertical cylindrical cavity in critical state soils using a rate‐based plasticity formulation: the initial stress field is taken as anisotropic, that is with horizontal stresses that differ from the vertical stress, and the soil is assumed to satisfy any two‐invariant constitutive model from the critical state (Cam‐clay) family; no simplifying assumption is made during the mathematical derivation; calculating the effective stresses around the cavity requires the solution of a nonlinear equation by means of the Newton–Raphson method in combination with quadrature. Cavity expansion curves and stress distributions in the soil are then presented for different critical state models (including the modified Cam‐clay model). The solution derived can be useful for estimating the instantaneous response of saturated low‐permeability soils around piles and self‐boring pressuremeters and can serve as trustworthy benchmark for numerical analysis codes. Copyright © 2016 John Wiley & Sons, Ltd.     

UNDRAINED CAVITY EXPANSIONS IN CRITICAL STATE SOILS

Boundary value problems for hardening/softening soils, such as Cam-Clay, usually require the extensive use of finite element methods. Here analytical and semi-analytical solutions for the undrained expansion of cylindrical and spherical cavities in critical state soils are presented. The strain is finite, the initial cavity radius is arbitrary and the procedure applicable to any isotropically hardening materials. In all cases only simple quadratures are involved, and in the case of the original Cam-Clay a complete analytical solution can be found. In addition to providing models of the behaviour of displacement piles and pressuremeters these results also provide valuable benchmark solutions for verifying various numerical methods.     

An anisotropically elastoplastic solution to excavation responses of a circular opening considering three-dimensional strength

Circular opening is commonly encountered in wellbore drilling of petroleum engineering, boring for cast-in situ pile installation, and tunneling excavation. This paper presents a rigorous solution for the elastoplastic responses of the anisotropic soft soil mass around a circular opening excavated under undrained and drained conditions. Both the anisotropic elastoplastic behavior and the 3D strength of the soft clay are incorporated in the present solutions. The well-established anisotropic critical state elastoplastic model S-CLAY1, which can represent the initial fabric anisotropy and stress-induced anisotropy of soft soil, is further modified by the Spatially Mobilized Plane criterion to consider the 3D strength of geomaterials. Then, the investigated problems, excavation of a circular opening under both short-term (undrained) and long-term (drained) conditions, are formulated as a system of first-order differential equations and are solved as initial value problems. The distributions of stress components and anisotropy parameters around the opening, the stress trajectory of a soil particle at the opening wall, as well as the stress–displacement curve at the opening wall are presented to investigate the elastoplastic responses of the opening. Extensive parameters show that the overconsolidated ratio and coefficient of earth pressure at rest (K₀) have remarkable effects on the elastoplastic responses around a circular opening.

     

初始组构各向异性对砂土力学特性及临界状态的影响

采用离散元方法,利用半径扩展法和重力沉积法分别生成具有初始各向同性和各向异性内结构的试样,并开展三轴不排水压缩和拉伸试验,研究不同制样方法产生的初始各向异性对砂土宏微观力学特性及其临界状态的影响。运用组构张量对砂土的各向异性进行量化,分析不同初始组构各向异性对组构张量演化的影响并确定了组构张量的临界值。试验结果表明：初始组构各向异性对试样的剪胀性有重要影响,由于受重力影响形成初始各向异性,其各向异性程度越大、组构方向与加载方向越一致,剪胀性越显著;初始组构各向异性对试样的临界状态没有影响,砂土的组构张量具有唯一的临界状态值。     

Analytical solution of undrained cylindrical cavity expansion in saturated soil under anisotropic initial stress

This paper presents an analytical solution for undrained elasto-plastic cylindrical cavity expansion in saturated soil under anisotropic initial stress. The problem is formulated by assuming small-strain deformation in the elastic zone and large-strain deformation in the plastic zone. Plastic yielding is determined by the Tresca failure criterion and an associated flow rule. Two stress functions are used to describe the stress state in the two zones around the cavity. The elasto-plastic boundary can subsequently be determined by solving the two stress functions under the stress boundary conditions. Additionally, the cavity pressure-expansion relationship, the total stress and the excess pore pressure around the cavity wall under anisotropic initial stress can be easily obtained by application of a numerical integration. The results show that the cavity pressure and excess pore pressure under the isotropic initial total stress (K = 1) are larger than those under the anisotropic initial stress (K > 1 and K < 1), which is true at all states of the expansion. The higher value of K develops lower stress and pore pressure around the cavity wall at the ultimate states. However, the stress and excess pore pressure are not sensitive to the value of K. The present solution may be used for analyzing the uplift capacity of plate anchors in soils and Horizontal Directional Drilling (HDD) problems such as the tunneling, and pipeline installation.     

K0固结饱和土柱孔扩张问题弹塑性分析

采用K0固结各向异性土体本构模型,将柱孔扩张后周围土体分为弹性区和塑性区,根据柱孔扩张理论和边界条件,推导出K0固结状态下饱和天然土体柱孔扩张问题弹塑性区的应力、塑性区半径以及超孔隙水压力的理论解答。同时,通过算例与修正剑桥模型解答进行对比分析,结果表明,土的不同初始固结状态对柱孔扩张后孔周围的应力和超孔隙水压力产生很大影响,采用考虑K0固结诱发各向异性土体本构模型所得到的应力和超孔隙水压力解答大于修正剑桥模型的解答,但塑性区影响半径却明显小于后者。     

多因素作用下天然土体渐进破损强度解析

天然沉积土体一般都具有结构性和初始各向异性。在复杂的应力路径的作用下,天然结构性土体的强度与变形一般与重塑土不同。由于结构性、初始各向异性和复杂的应力路径的共同影响,往往使极限状态设计如何确定天然土体渐进破损的强度及参数变得复杂而困难。给出了关于各向异性的天然结构性土体渐进破损的归一化不排水抗剪强度的解析表达式,并研究了天然结构性土体渐进破损的归一化不排水抗剪强度与各向异性和应力路径等因素的相关性。     

A hypoplastic model for granular soils incorporating anisotropic critical state theory

It is well known that soil is inherently anisotropic and its mechanical behavior is significantly influenced by its fabric anisotropy. Hypoplasticity is increasingly being accepted in the constitutive modeling for soils, in which many salient features, such as nonlinear stress-strain relations, dilatancy, and critical state failure, can be described by a single tensorial equation. However, within the framework of hypoplasticity, modeling fabric anisotropy remains challenging, as the fabric and its evolution are often vaguely assumed without a sound basis. This paper presents a hypoplastic constitutive model for granular soils based on the newly developed anisotropic critical state theory, in which the conditions of fabric anisotropy are concurrently satisfied along with the traditional conditions at the critical state. A deviatoric fabric tensor is introduced into the Gudehus-Bauer hypoplastic model, and a scalar-valued anisotropic state variable signifying the interplay between the fabric and the stress state is used to characterize its impact on the dilatancy and strength of the soils. In addition, fabric evolution during shearing can explicitly be addressed. Modifications have also been undertaken to improve the performance of the undrained response of the model. The anisotropic hypoplastic model can simulate experimental tests for sand under various combinations of principle stress direction, intermediate principal stress (or mode of shearing), soil densities, and confining pressures, and the associated drastic effect of different principal stress orientations in reference to the material axes of anisotropy can be well captured.     

Analysis of undrained cavity expansion in elasto‐plastic soils with non‐linear elasticity

A large strain analysis of undrained expansion of a spherical/cylindrical cavity in a soil modelled as non‐linear elastic modified Cam clay material is presented. The stress–strain response of the soil is assumed to obey non‐linear elasticity until yielding. A power‐law characteristic or a hyperbolic stress–strain curve is used to describe the gradual reduction of soil stiffness with shear strain. It is assumed that, after yielding, the elasto‐plastic behaviour of the soil can be described by the modified Cam clay model. Based on a closed‐form stress–strain response in undrained condition, a numerical solution is obtained with the aid of simple numerical integration technique. The results show that the stresses and the pore pressure in the soil around an expanded cavity are significantly affected by the non‐linear elasticity, especially if the soil is overconsolidated. The difference between large strain and small strain solutions in the elastic zone is not significant. The stresses and the pore pressure at the cavity wall can be expressed as an approximate closed‐form solution. Copyright © 2001 John Wiley & Sons, Ltd.     

A general semi-analytical solution for consolidation around an expanded cylindrical and spherical cavity in modified Cam Clay

This paper presents a general semi-analytical solution for undrained cylindrical and spherical cavity expansion in Modified Cam Clay (MCC) and subsequent consolidation. The undrained cylindrical and spherical cavity expansion response in MCC model is obtained through the similarity solution technique. Then, the subsequent consolidation process around the cavity is governed by the classical partial differential equation for consolidation. Finite Difference Method (FDM) is selected for solving the consolidation equation numerically. The proposed semi-analytical solution is validated by comparing the prediction of the dissipations of the pore pressure with Randolph’s closed-form solution for elastic-perfectly plastic soil. Parametric study shows that G₀/p₀′, R and M have significant influence on the cavity wall excess pore pressure dissipation curve, while it is not sensitive to the value of ν′. It is also found that the negative pore pressure generates around the expanded cylindrical and spherical cavity wall during the consolidation process when R > 5 for typical Boston blue clay. The developed solution has potential applications in geotechnical problems, such as the pile foundation, in-situ test, tunnel construction, compaction grouting, and so forth.     

Plasticity solutions for soil behaviour around contracting cavities and tunnels

The action of tunnel excavation reduces the in-situ stresses along the excavated circumference and can therefore be simulated by unloading of cavities from the in-situ stress state. Increasing evidence suggests that soil behavior in the plane perpendicular to the tunnel axis can be modelled reasonably by a contracting cylindrical cavity, while movements ahead of an advancing tunnel heading can be better predicted by spherical cavity contraction theory. In the past, solutions for unloading of cavities from in-situ stresses in cohesive-frictional soils have mainly concentrated on the small strain, cylindrical cavity model. Large strain spherical cavity contraction solutions with a non-associated Mohr–Coulomb model do not seem to be widely available for tunnel applications. Also, cavity unloading solutions in undrained clays have been developed only in terms of total stresses with a linear elastic-perfectly plastic soil model. The total stress analyses do not account for the effects of strain hardening/softening, variable soil stiffness, and soil stress history (OCR). The effect of these simplifying assumptions on the predicted soil behavior around tunnels is not known. In this paper, analytical and semi-analytical solutions are presented for unloading of both cylindrical and spherical cavities from in-situ state of stresses under both drained and undrained conditions. The non-associated Mohr-Coulomb model and various critical state theories are used respectively to describe the drained and undrained stress-strain behaviors of the soils. The analytical solutions presented in this paper are developed in terms of large strain formulations. These solutions can be used to serve two main purposes: (1) to provide models for predicting soil behavior around tunnels; (2) to provide valuable benchmark solutions for verifying various numerical methods involving both Mohr–Coulomb and critical state plasticity models. Copyright © 1999 John Wiley & Sons, Ltd.     

Elastic‐plastic solutions for expanding cavities embedded in two different cohesive‐frictional materials

An analytical solution of cavity expansion in two different concentric regions of soil is developed and investigated in this paper. The cavity is embedded within a soil with finite radial dimension and surrounded by a second soil, which extends to infinity. Large‐strain quasi‐static expansion of both spherical and cylindrical cavities in elastic‐plastic soils is considered. A non‐associated Mohr–Coulomb yield criterion is used for both soils. Closed‐form solutions are derived, which provide the stress and strain fields during the expansion of the cavity from an initial to a final radius. The analytical solution is validated against finite element simulations, and the effect of varying geometric and material parameters is studied. The influence of the two different soils during cavity expansion is discussed by using pressure–expansion curves and by studying the development of plastic regions within the soils. The analytical method may be applied to various geotechnical problems, which involve aspects of soil layering, such as cone penetration test interpretation, ground‐freezing around shafts, tunnelling, and mining. © 2014 The Authors. International Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons Ltd.     

Simulation of yielding and stress–stain behavior of shanghai soft clay

In this paper, a simple bounding surface plasticity model is used to reproduce the yielding and stress–strain behavior of the structured soft clay found at Shanghai of China. A series of undrained triaxial tests and drained stress probe tests under isotropic and anisotropic consolidation modes were performed on undisturbed samples of Shanghai soft clay to study the yielding characteristics. The degradation of the clay structure is modeled with an internal variable that allows the size of the bounding surface to decay with accumulated plastic strain. An anisotropic tensor and rotational hardening law are introduced to reflect the initial anisotropy and the evolution of anisotropy. Combined with the isotropic hardening rule, the rotational hardening rule and the degradation law are incorporated into the bounding surface formulation with an associated flow rule. Validity of the model is verified by the undrained isotropic and anisotropic triaxial test and drained stress probe test results for Shanghai soft clay. The effects of stress anisotropy and loss of structure are well captured by the model.     

基于广义SMP破坏准则的柱形孔扩张问题理论分析

采用应力跌落的简化应力-应变模型考虑土的应变软化特性,同时采用简化的体积应变?v与大主应变?1及大主应变?1与小主应变?3之间的相互关系反映土的剪胀特性,根据空间准滑动面(SMP)理论和平面应变轴对称问题的柱形孔扩张基本方程,推导并给出一般黏性土中柱形孔扩张问题的应力场、应变场、位移场、塑性区半径和孔扩张压力。通过算例分析,探讨了土的剪胀因素、软化特性对孔扩张问题的影响程度。为了反映中主应力的影响,将本文解与基于Mohr-Coulomb破坏准则的解答进行了比较。计算结果表明,土的剪胀性和软化特性及中主应力对孔扩张问题的影响是显著的,基于Mohr－Coulomb破坏准则的孔扩张解答往往偏于保守。