Response of a circular opening in a friable low-permeability medium to temperature and pore pressure changes

A general analysis using an incremental elastic, perfectly plastic constitutive stress–strain relationship for poroelastoplastic materials is presented to simulate an opening in a low-permeability friable porous medium under non-isothermal conditions. Analytical solutions are obtained for the stresses and strains around a 2-D plane strain circular borehole. An expansion potential is introduced by combining the strains induced by temperature and pore pressure changes. Steady-state pressures and temperatures are considered, and a non-associated plastic flow rule is applied to calculate plastic strains. Focusing on stress distribution near a circular opening, the classic solutions for those stresses under dry and isothermal conditions are used to compare with the newly derived solution. The general poroelastoplastic effect and the thermal effect on sand production and borehole stability are addressed. We suggest that the knowledge of stress history is critical to achieve adequate solutions for displacement and stress in friable media such as clays, shales and oil sands.     

A kinematic hardening constitutive model for sands: the multiaxial formulation

This paper explores the possibility of using well-accepted concepts—Mohr-Coulomb-like strength criterion, critical state, existence of a small strain elastic region, hyperbolic relationship for representing global plastic stress–strain behaviour, dependence of strength on state parameter and flow rules derived from the Cam-Clay Model—to represent the general multiaxial stress–strain behaviour of granular materials over the full range of void ratios and stress level (neglecting grain crushing). The result is a simple model based on bounding surface and kinematic hardening plasticity, which is based on a single set of constitutive parameters, namely two for the elastic behaviour plus eight for the plastic behaviour, which all have a clear and easily understandable physical meaning. In order to assist the convenience of the numerical implementation, the model is defined in a ‘normalized’ stress space in which the stress–strain behaviour does not undergo any strain softening and so certain potential numerical difficulties are avoided. In the first part the multiaxial formulation of the model is described in detail, using appropriate mixed invariants, which rationally combine stress history and stress. The model simulations are compared with some experimental results for tests on granular soils along stress paths lying outside the triaxial plane over a wide range of densities and mean stresses, using constitutive parameters calibrated using triaxial tests. Furthermore, the study is extended to the analysis of the effects induced by the different shapes of the yield and bounding surfaces, revealing the different role played by the size and the curvature of the bounding surface on the simulated behaviour of completely stress- and partly strain-driven tests. Copyright © 1999 John Wiley & Sons, Ltd.     

Marble decay induced by thermal strains: simulations and experiments

Thermoelastic behavior of different marble types was analyzed using computational modeling and experimental measurements. Eight marble samples with different composition, grain size, grain boundary geometry, and texture were investigated. Calcitic and dolomitic marbles were considered. The average grain size varies from 75 μm to 1.75 mm; grain boundary geometry differs from nearly equigranular straight grain boundaries to inequigranular-interlobate grain boundaries. Four typical marble texture types were observed by EBSD measurements: weak texture; strong texture; girdle texture and high-temperature texture. These crystallographic orientations were used in conjunction with microstructure-based finite element analysis to compute the thermoelastic responses of marble upon heating. Microstructural response maps highlight regions and conditions in the marble fabric that are susceptible to degradation phenomena. This behavior was compared to the measured thermal expansion behavior, which shows increasing residual strains upon repetitive heating–cooling cycles. The thermal expansion behavior as a function of temperature changes can be classified into four categories: (a) isotropic thermal expansion with small or no residual strain; (b) anisotropic thermal expansion with small or no residual strain; (c) isotropic thermal expansion with a residual strain; and (d) anisotropic thermal expansion with residual strain. Thermal expansion coefficients were calculated for both simulated and experimental data and also modeled from the texture using the MTEX software. Fabric parameters control the amount and directional dependence of the thermal expansion. Marbles with strong texture show higher directional dependence of the thermal expansion coefficients and have smaller microstructural values of the maximum principal stress and strain energy density, the main precursors of microcracking throughout the marble fabric. In contrast, marbles with weak texture show isotropic thermal expansion behavior, have a higher propensity to microcracking, and exhibit higher values of maximum principal stress and strain energy density. Good agreement between the experimental and computational results is observed, demonstrating that microstructure-based finite-element simulations are an excellent tool for elucidating influences of rock fabric on thermoelastic behavior.     

基于广义SMP准则及应力路径法的柱孔扩张分析

柱孔扩张理论广泛用于旁压试验机制分析、沉桩挤土效应等岩土工程问题中。基于经典的Vesic孔扩张理论,采用能够考虑中主应力效应的广义SMP屈服准则,并结合有限应变理论对均质土体中柱孔扩张问题进行分析,根据应力路径假设提出确定塑性区平均体应变的解析步骤。通过大量变参数计算给出具有不同刚度指标 、泊松比 和内摩擦角 的土中柱孔扩张极限状态下的塑性区平均体应变、孔扩张半径比和孔扩张系数。分析结果表明, 、 、 越大,塑性区平均体应变越小,塑性区半径比越大,孔扩张系数越大;随着 增加, 的变化对孔扩张系数的影响更显著。同时,将结果与基于Mohr-Coulomb准则的孔扩张解答进行比较,探讨不同土性参数时中主应力效应对孔扩张系数的影响。文中分析方法及给出的考虑中主应力效应的柱孔扩张系数表可为原位试验分析及桩侧摩阻力估算提供参考。     

单轴压缩非贯通节理岩石尖端塑性区及弹塑性断裂模型研究

基于Drucker-Prager（下简称D-P）准则,建立压缩载荷作用下的非贯通节理岩石的弹塑性断裂模型。针对节理岩石小范围屈服翼裂纹尖端塑性区,推导了D-P屈服准则的纯I、纯II及I、II复合型3种翼裂纹无量纲塑性区径长函数,并与Mises准则的塑性区进行对比;结果表明,D-P准则的I型和复合型塑性区较Mises屈服准则的塑性区大,且其II型及I、II复合型塑性区在翼裂纹上下表面不连续。进一步,引入断裂软化因子以表征节理岩石裂隙断裂扩展后的断裂软化规律,考虑非贯通节理岩石复合型断裂软化,是由于节理尖端翼裂纹应变能密度超过最小应变能密度导致其成核扩展引起的,提出用应变能密度的指数函数形式表征断裂软化变量的演化;塑性屈服函数采用Borja等的应力张量3个不变量的硬化/软化函数,反映塑性内变量及应力状态对硬化函数的影响;建立节理岩石的弹塑性断裂本构关系及其数值算法,并用回映隐式积分算法编制了弹塑性断裂模型的程序。以单轴压缩下非贯通节理岩石为例,分析岩石断裂韧度、节理摩擦系数和节理倾角等参数的影响,结果表明,所提出的弹塑性断裂模型与数值和试验结果比较吻合。     

Probabilistic elasto-plasticity: solution and verification in 1D

In this paper, a solution is presented for evolution of probability density function (PDF) of elastic–plastic stress–strain relationship for material models with uncertain parameters. Developments in this paper are based on already derived general formulation presented in the companion paper. The solution presented is then specialized to a specific Drucker–Prager elastic–plastic material model. Three numerical problems are used to illustrate the developed solution. The stress–strain response (1D) is given as a PDF of stress as a function of strain. The presentation of the stress–strain response through the PDF differs significantly from the traditional presentation of such results, which are represented by a single, unique curve in stress–strain space. In addition to that the numerical solutions are verified against closed form solutions where available (elastic). In cases where the closed form solution does not exist (elastic–plastic), Monte Carlo simulations are used for verification.     

基于SMP准则柱孔扩张问题相似解

以柱孔扩张理论为基础,将柱孔扩张后塑性区半径b作为时间刻度,引入扩孔速度概念,将塑性区内任意一点的应力、应变描述成塑性区半径b和柱孔扩张后扩张体单元距孔心距离r的函数,采用平面应变条件下无黏性土的SMP准则和不相关联流动法则,考虑到无黏性土的剪胀性,推导出柱孔扩张后极限扩张力 的相似解。通过参数分析表明,土体强度和剪胀性对塑性区半径和极限扩张力产生很大的影响,即随着土体强度和剪胀性的增加,极限扩张力明显增加,相应塑性区半径却随之减小。通过与基于摩尔-库仑准则解答进行对比分析表明,考虑中间主应力影响的SMP准则所得到的极限扩张力明显高于基于摩尔-库仑准则的解答。该解答为无黏性土中进行静力触探（CPT）试验和静压桩等岩土工程问题提供必要的理论依据。     

基于混合常应力−光滑应变单元的极限分析方法

极限分析是岩土工程稳定性评价的重要方法之一。传统的有限元极限分析方法,采用低阶三角形单元时需要引入速度间断面并采用特殊网格布局,或者采用高阶三角形单元等措施来克服体积锁定问题和提高数值精度。在光滑有限元法（smoothed finite element method,简称SFEM）的基础上,提出了一种基于新型混合常应力−光滑应变单元的极限分析方法（mixed constant stress-smoothed strain element limit analysis,简称MCSE-LA方法）。在服从关联流动法则和Mohr-Coulomb屈服准则的基础上,MCSE-LA方法最终将数值极限分析转化为以应力和极限荷载乘子为基本未知量的二阶锥规划（second order cone programming,简称SOCP）问题。MCSE-LA方法具有形式简单、优化变量相对较少和无需显式的写出塑性内能耗散函数的优点,并且根据凸锥优化的对偶理论,可以从对偶问题中获得速度场和塑性乘子等信息。此外,还采用基于最大塑性剪应变率的网格自适应加密算法,该算法在塑性区细化网格,显著提高了新数值极限分析方法的计算效率和精度。最后通过边坡稳定分析的结果对比,验证了MCSE-LA方法的计算精度和效率均高于传统的有限元极限分析方法。     

循环荷载下饱和重塑黏质粉土的动力特性研究

选取宁波饱和重塑黏质粉土,开展了黏质粉土的动三轴试验,研究了围压、动应力、排水条件、温度及频率等因素对土动力特性的影响,提出了采用相对动应力来分析不同围压、不同动应力下土的累积塑性应变变化规律,并建立了孔压—累积塑性应变关系的经验公式,结果表明:累积塑性应变随着相对动应力的增大而增大;温度越高,累积塑性应变值越小,且相同温度增量（△T=15℃）条件下的累积塑性应变增量也随之减小;建立的孔压-累积塑性应变经验公式可用于长期振动荷载作用后黏质粉土的孔压计算。     

Application of the exact constitutive relationship of modified Cam clay to the undrained expansion of a spherical cavity

The modified Cam clay (MCC) model is used to study the response of virgin‐compressed clay subjected to undrained triaxial compression. The MCC constitutive relationship is obtained in a closed form. Both elastic and plastic deviatoric strains are considered in the analysis. The solution allows to obtain total and effective stress paths followed by the clay in undrained spherical expansion. Pore water pressures are determined from the difference between total and effective mean stresses. For illustration purposes, the analysis is also applied to the well‐known reconstituted normally consolidated London clay and the results are compared with the recently published data obtained by a numerical approach. In addition, the Almansi large strains are used in the analysis, as these allow to obtain limit expansion and pore pressures, whereas both small‐strain and logarithmic‐strain approaches do not permit to determine them. Copyright © 2010 John Wiley & Sons, Ltd.     

Ground response curves for rock masses exhibiting strain‐softening behaviour

A literature review has shown that there exist adequate techniques to obtain ground reaction curves for tunnels excavated in elastic‐brittle and perfectly plastic materials. However, for strain‐softening materials it seems that the problem has not been sufficiently analysed. In this paper, a one‐dimensional numerical solution to obtain the ground reaction curve (GRC) for circular tunnels excavated in strain‐softening materials is presented. The problem is formulated in a very general form and leads to a system of ordinary differential equations. By adequately defining a fictitious ‘time’ variable and re‐scaling some variables the problem is converted into an initial value one, which can be solved numerically by a Runge–Kutta–Fehlberg method, which is implemented in MATLAB environment. The method has been developed for various common particular behaviour models including Tresca, Mohr–Coulomb and Hoek–Brown failure criteria, in all cases with non‐associative flow rules and two‐segment piecewise linear functions related to a principal strain‐dependent plastic parameter to model the transition between peak and residual failure criteria. Some particular examples for the different failure criteria have been run, which agree well with closed‐form solutions—if existing—or with FDM‐based code results. Parametric studies and specific charts are created to highlight the influence of different parameters. The proposed methodology intends to be a wider and general numerical basis where standard and newly featured behaviour modes focusing on obtaining GRC for tunnels excavated in strain‐softening materials can be implemented. This way of solving such problems has proved to be more efficient and less time consuming than using FEM‐ or FDM‐based numerical 2D codes. Copyright © 2003 John Wiley & Sons, Ltd.     

基于Drucker-Prager准则的岩石弹塑性损伤本构模型研究

大多数岩石材料软化本构模型在硬化函数中引入塑性内变量来表示材料的硬化/软化性质,但并不能反映岩石微裂隙损伤对材料力学性能的影响及单轴拉伸和压缩所表现的初始屈服强度f0与屈服极限fu的差异。基于D-P准则同时考虑塑性软化及损伤软化,建立岩石类材料的弹塑性本构关系及其数值算法。塑性屈服函数采用Borja等的应力张量的硬化/软化函数,反映塑性内变量及应力状态对硬化函数的影响;由于岩石损伤软化是微裂隙扩展所导致的体积膨胀引起的,因此,提出用体积应变表征岩石损伤变量的演化,并用回映隐式积分算法编制了岩石的弹塑性损伤本构程序。对单轴压缩及拉伸荷载作用下的岩石材料试验进行数值模拟,结果表明,所提出的岩石弹塑性损伤本构模型可以较好地符合岩石材料的力学特性。     

土体小应变特性研究中的边界面模型

研究表明，土体小应变特性对准确预测土体的变形起着十分重要的作用，而这一特性很难用传统的本构模型对它加以描述。边界面模型能描述一些经典塑性理论所不能描述的土的真实特性，如何将之进一步加以改进，并有效地应用于土体小应变特性的模拟中是一个有待深入研究的课题。     

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。     

多级线性荷载下饱和软黏土一维大应变固结解析解

在软土地基工程中,荷载往往都是分级施加,随着固结地基强度增加到一定值后,再施加下一级荷载以确保地基稳定。基于谢康和饱和软黏土一维大应变固结解析解,采用数学归纳法推导了任意形式多级线性荷载作用下的解,并编制了相应的通用计算程序,可以方便进行计算分析。通过与线性小应变假定下解的计算对比表明,在实际工程中基于非线性大应变进行计算分析更为合理。     

基于能量耗散的球孔扩张理论解答

以空间准滑动面（SMP）准则为基础,推导了扩底桩扩孔压力的理论解。从能量耗散的角度分析球孔扩张的全过程,利用应力不变量推导了符合球孔扩张的屈服准则;化简微分方程得到了弹塑性区应力表达式,进而求出位移、应变表达式;分别利用体积守恒和能量守恒性推导出扩孔压力的表达式。该法考虑了塑性区弹性变形,并得到了扩孔压力p、塑性区半径R与扩孔半径a的关系。算例分析表明,该方法计算的扩孔压力与现场试验得出的结果较好地吻合,塑性区半径和扩孔压力均随扩孔半径的增加而增大,但增幅逐渐减小而趋于稳定值,剪胀角对塑性区半径和扩孔压力影响显著,随着剪胀角的增加,塑性区半径和扩孔压力明显增加。     

Analysis of double shearing in frictional materials

The concept that the flow of granular materials is governed by shear on certain critical planes is used to formulate an elastic–plastic model. When the elastic strains are neglected, the Double Shearing model becomes identical to the rigid-plastic model of de Josselin de Jong which he named the Double Sliding model. After a discussion of the model, the small strain formulation is used to describe general boundary-value problems. A comparison is then made between the coaxial Mohr–Coulomb yielding and the Double Shearing model on the basis of several numerical simulations. The non-coaxiality of the axes of principal plastic strain rate and principal stress in the Double Shearing model leads to essentially different behaviour for stress rotations in comparison to the coaxial model. The Double Shearing model predicts in general lower limit loads because, for a given state of stress, it allows for several possible directions of plastic flow rather than a unique direction which derives from a plastic potential.     

Shear wave propagation along infinite slopes: A theoretically based numerical study

In this paper, the seismic response of ‘infinitely’ long slopes is numerically analysed via the formulation of a 1D analytical/numerical model, in which the soil mechanical behaviour is assumed to be elasto‐perfectly viscoplastic and simple shear (SS) kinematical constraints are imposed. In order to simplify the problem, a theoretically based procedure to set up a fully 1D shear constitutive model is defined, within which the mechanical response of a multiaxial relationship is condensed. The use of a 1D shear constitutive model is aimed at reducing the number of unknowns and, therefore, the computational costs. In particular, the case of the Mohr–Coulomb yield criterion is considered, while an enhanced Taylor–Galerkin finite element algorithm is employed to simulate the seismic wave propagation within the soil stratum. The proposed ‘condensation’/calibration procedure captures both the ‘pseudo’‐hardening pre‐failure behaviour and the influence of dilation on the occurrence of strain‐localization, which characterize, under SS conditions, the static response of virgin perfectly plastic soils. The effectiveness of the conceived method is shown with reference to freshly deposited deposits, while, in the case of highly overconsolidated strata, some difficulties arise because of the brittle behaviour induced both by unloading and non‐associativeness. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical modeling of stress and strain associated with the bending of an oil pipeline by a migrating pingo in the permafrost region of the northern Tibetan Plateau

Small seasonal pingos formed in Quaternary deposits along active fault zones in permafrost of the northern Tibetan Plateau exert destructive forces to oil pipelines, bridges, culverts and other engineering facilities along the Golmud–Lhasa railway and highway. The pingos are particularly hazardous as they change position, or migrate, nearly every year. Three-dimensional finite element modeling reveals the enormous force from exerted by a pingo at the 86th station of the highway. A good representation of the stress and strain fields resulting from an expansion of a pingo and bending of an oil pipeline at the station are calculated after due consideration of the interaction between permafrost, pingo and pipeline. This followed establishing an engineering-geologic model from the field data and determining the mechanical properties of the media from field and laboratory tests. The maximum, intermediate and the minimal principal compressive stresses are calculated as well as those for the plastic strain. Concentrations of principal stress and plastic strain occur beneath the pipeline bend and both the principal compressive stress and resulting plastic strain become very small away from the pingo. Also, the bottom of the pingo is dominated by minimal values of principal stress and strain and the potential bending of a buried pipe caused by an expansion of a pingo is indicated to decrease as depth of burial increases.The pingo growth at the 86th station resulted in the bending upward of a 20m section of a buried oil pipeline, but it did not break and spill oil. Analysis of the pipe within the bend found the maximum, intermediate, and minimal principal compressive stress ranges that leads to plastic strain within the bent pipe. Compressive stress and plastic strain concentrations form in the inner sides of inflexions in the pipe bend, and tensional stress and plastic strain concentrations form in their outer sides where stress exceeds the yield limit of the pipe, but many irregularities are present. Such numerical modeling of stress and strain may offer key parameters for designing oil pipelines and engineered facilities to decrease the hazard from migrating pingos in similar geologic settings in the permafrost of the northern Tibetan Plateau.