复杂应力状态下条形基础的临塑荷载公式

莫尔-库仑强度准则的临塑荷载公式由于没有考虑中主应力在强度上的作用使计算结果偏于保守。利用具有线性形式的双剪应力强度准则替换原有的莫尔-库仑强度准则,将中主应力引入临塑荷载的计算中,推导出平面应变条件下考虑中主应力影响的临塑荷载公式,并通过算例说明了新临塑荷载公式的计算结果比原有公式有较大的偏高。     

条带煤柱设计的强度准则效应研究

条带开采广泛应用于深部煤层,合理的条带煤柱尺寸对提高煤炭采出率和保护地表地貌都具有十分重要的意义。通过总结平面应变状态下Wilson准则、Mohr-Coulomb(M-C)准则、广义Matsuoka-Nakai(M-N)准则、广义Lade-Duncan(L-D)准则和外接圆Drucker-Prager(D-P)准则等5种强度准则的统一表达式,进而建立条带煤柱的极限强度、屈服宽度和留设宽度的统一计算公式,探究条带煤柱设计的强度准则效应,并得出煤层黏聚力和内摩擦角的影响特性。研究结果表明：建立的统一计算式涵盖文献已有解,且应用非常方便;条带煤柱设计的强度准则效应显著,Wilson准则和M-C准则的结果过于保守,外接圆D-P准则应用需谨慎,应优先选用广义M-N准则或广义L-D准则;煤层黏聚力和内摩擦角对条带煤柱设计的影响明显,应充分考虑煤层的强度参数变化。该研究结果可为条带煤柱的合理设计与施工提供一定的理论指导。     

平面应变条件下M-C材料屈服时的中主应力公式

基于Mohr-Coulomb准则,通过引入罗德角参数及Mohr-Coulomb准则平面应变等效广义Mises准则,推导了平面应变条件下材料屈服时的中主应力公式,并给出其与基于SMP准则（Spatial Mobiliaztion Piane）的平面应变中主应力公式之间的关系式。对平面应变条件下的条形地基进行了有限元数值模拟,计算结果验证了所推导的平面应变条件下M-C材料屈服时的中主应力公式的正确性,其公式为岩土体的强度和变形分析、中主应力的强度效应的进一步研究,以及Mohr-Coulomb准则的修正提供了有力的基础。     

平面应变状态下边坡安全系数的近似求解

Mohr—Coulomb屈服准则不考虑中间主应力对材料强度的贡献,是一个保守的强度屈服准则,在近似平面应变状态下,匹配于Mohr-Coulomb屈服准则的Drucker-Prager屈服准则能给出边坡安全系数偏保守一些的估计;相对而言,Matsuoka—Nakai和Lade-Duncan屈服准则均考虑了中间主应力对土体强度的影响,在近似平面应变状态下,匹配于Matsuoka-Nakai和Lade-Duncan屈服准则的Drucker-Prager屈服准则能给出岩土类材料较为合理的破坏强度预测,土体的抗剪强度能被更有效地发挥出来,因而借助这些转化的Drucker-Prager屈服准则能给出平面应变状态下土坡安全系数较为合理和真实的预测。文中的边坡稳定算例证实了这些观点。     

Axisymmetric compression of a Mohr–Coulomb medium around a circular hole

An analytical solution is presented for the stress and strain fields in a Mohr–Coulomb material in plane strain around a circular hole when it is compressed by an axisymmetric far-field pressure. It is shown that several solutions arise involving one to three plastic zones depending on the values of Poisson's ratio and the friction angle. The solution chosen for presentation was obtained and used to validate the functioning of the Mohr–Coulomb yield condition that was added to the NONSAP finite element code. Stress and strain field comparisons are made.     

The influence of the plastic potential on plane strain failure

The influence of the shape of the plastic potential in the deviatoric plane on plane strain collapse is investigated. The most commonly employed elastic‐perfect plastic models are considered, which adopt well‐known failure criteria for defining the yield and plastic potential surfaces, namely the von Mises, the Drucker–Prager, the Tresca, the Mohr–Coulomb and the Matsuoka–Nakai criteria. Finally, the conclusions are also extended to strain hardening/softening models. For simple constitutive models based on perfect plasticity, it is shown that the value of the Lode's angle at plastic collapse in plane strain conditions strongly depends on the specific failure surface adopted for reproducing the plastic potential surface. If the value of the Lode's angle at yield coincides with the failure value prescribed by the plastic potential, the stress–strain curves exhibit the typical perfect plastic behaviour with yield coinciding with failure, otherwise the stress changes after yield and the stress‐strain curves resemble those of strain hardening/softening models. The infinite strength which is in some situations exhibited by the Drucker–Prager model in plane strain condition is investigated and explained, and it is shown that this can also affect strain hardening/softening models. Copyright © 2013 John Wiley & Sons, Ltd.     

Kinematical analysis of 3D passive earth pressure with nonlinear yield criterion

Conventional methods for calculation of passive earth pressure were mainly based on the assumptions of the linear Mohr‐Coulomb yield condition and plane strain failure mechanism. However, both theoretical and experimental studies have shown that such assumptions are not satisfied in some geotechnical projects. Herein, a novel method incorporating a kinematically admissible 3‐dimensional (3D) rotational failure mechanism and the nonlinear power‐law yield criterion is proposed to compute the passive earth pressure acting on the inclined retaining walls. Instead of using the nonlinear yield criterion directly, a straight line tangential to the nonlinear yield curve is employed to represent the strength of soils, and therefore, the nonlinear problem is transformed into the traditional linear problem. The 3D failure mechanism is generated through rotating a circle defined by 2 log‐spirals, and a plane strain block is inserted into the mechanism to consider the retaining walls with different widths. Earthquake effects are taken into account by using quasi‐static representation, and the horizontal seismic coefficient concept is adopted for the estimation of passive earth pressure under seismic conditions. An analytical expression about the 3D passive earth pressure is educed by means of the upper bound theorem of limit analysis. Numerical results for different practical parameters are obtained from an optimization scheme where the minimum of passive earth pressure is sought. Compared with available 2‐dimensional and 3D solutions, the proposed method is validated. A parametric study is conducted to investigate the effects of different parameters on the 3D static and seismic passive earth pressure.     

Non-associative constitutive laws for low porosity rocks

Two simple constitutive laws appropriate for elastic–plastic deformation up to peak load of low porosity rocks are presented. Both laws account for mean stress dependence of yield hardening between yield and peak strength and non-associative plastic straining. The two constitutive laws are based on the Mohr–Coulomb and the Mises–Schleicher yield criteria. The yield criteria are matched at axisymmetric compression and the relationships among the constitutive parameters are given. The parameters are then evaluated for two evaporite rocks anhydrite and polyhalite based on axisymmetric compression data. Comparison of predicted stress–strain laws with those measured in the laboratory show that these laws can be used for engineering analysis.     

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.     

Experimental and discrete element modeling studies of the trapdoor problem: influence of the macro-mechanical frictional parameters

Granular soils have the inherent ability to develop load transfers in their mass. Mechanisms of load transfers are used as a basic principle of many civil and geotechnical engineering applications. However, their complexity makes it difficult to formulate relevant design methods for such works. The trapdoor problem is one of the ways to reproduce load transfers by the arching effect in a granular layer in non-complex conditions. In addition, many analytical solutions for the prediction of load transfer mechanisms are based on the trapdoor problem. However, some of the parameters required are still being widely discussed, in particular the ratio of horizontal stress to vertical stress. For this paper, an experimental device for trapdoor tests in plane strain conditions was created and several geomaterials were tested. Three phases in the response of the materials were consistently observed. Each of these phases corresponded to a specific displacement of the trapdoor. A first phase of high load transfer was observed followed by a transition phase which was followed by a critical phase for which the load transfer amplitude increased and stabilized. Analytical solutions and experimental values of load transfers were compared. Considerable differences between the stress ratio needed to fit the experimental data and the stress ratio proposed in the analytical models were noted. Based on the conclusions of the experimental study, the discrete element method was used to model the same trapdoor problem. A wide range of granular materials was modeled and tested in the trapdoor problem. The three phases in the response of the layer were also observed in the numerical modeling. In addition, it was shown that the shear strength of the material is the key parameter of load transfers: peak shear resistance for the small displacements of the trapdoor and critical shear strength for the larger displacements. A micro-mechanical analysis showed that the effective stress ratio in the sheared zone does not vary as much with shear strength. Stress ratios here were again greater than those proposed in the analytical solutions. Nevertheless, the relevance of the solution of Terzaghi was confirmed as soon as the stress ratio was correctly chosen.     

Solutions for the deformations and stability of elastoplastic hollow cylinders subjected to boundary pressures

In this paper, a closed-form solution is presented for the stress and displacement distributions throughout a hollow cylinder subjected to uniform pressures acting on its internal and external boundary surfaces under plane strain conditions. The material is assumed to be elastoplastic, obeying a Mohr–Coulomb failure criterion, and exhibiting dilatant plastic deformation according to a non-associated flow rule. The newly developed analytical solution is verified through comparison with the solutions obtained from an infinite boundary problem (for which a closed-form solution exists), and numerical analyses using the program FLAC. The solution is also compared with the results of a borehole collapse test on a thick-walled hollow cylinder of synthetic shale. The analytical solution can be used to calculate the stress and displacement distributions around boreholes and other cylindrical cavities under both infinite and finite boundary conditions under both drained and undrained conditions. Copyright © 1999 John Wiley & Sons, Ltd.     

A generalized nonlinear failure criterion for frictional materials

A generalized nonlinear failure criterion formulated in terms of stress invariants is proposed for describing the failure characteristics of different frictional materials. This failure criterion combines a power function and a versatile function in the meridian and deviatoric plane, respectively, which is a generalization of several classic criteria, including the Tresca, Drucker–Prager, Mohr–Coulomb, Lade–Duncan and Matsuoka–Nakai failure criterion. The procedure for determination of the strength parameters was demonstrated in detail. Comparisons between the failure criterion and experimental results were presented for uncemented/cemented Monterey sand, normally consolidated Fujinomori clay, rockfill, concrete, Mu-San sandstone and granite, which reveal that the proposed failure criterion captures experimental trend quite well.     

节理岩体地基极限承载力研究

由于节理岩体具有复杂的力学特性,节理岩体地基的极限承载力问题一直都没有很好解决。利用非线性统一强度准则考虑中间主应力影响和岩性、岩体结构特性可以通过参数m,s和σc 来反映的优点,将非连续介质特性的节理岩体等效为连续介质,在确定即时摩擦角后,结合滑移线场理论获得了节理岩体地基极限承载力的封闭形式的理论解,其解考虑了边界条件和基础的几何形状,举例说明了计算裂隙岩体极限承载力的过程和所需的参数。结果表明：节理岩体的材料特性和中间主应力对极限承载力具有重要影响。     

复杂介质广义权限平衡理论

经过系统的塑性分析，建立了各向异性非线性广义极限平衡理论。考虑到岩土材料复杂特性，提出了有中主应力影响、拉任强度不等、材料各向异性、破坏曲线非线性、受非均匀温度场影响的综合屈服准则。应用塑性位势理论，导出了关联的流动法则。在平面应变条件下，给出了应力场基本方程。采用特征线方法求解，导出了滑移线斜率公式、应力沿滑移线微分方程。应用电算程序，可计算非正交、不对称的滑移线场解答。作为实际应用，导出了各向异性地基极限承载力公式。本文理论可简化得到许多经典理论解答。     

基于弹性应变能的岩石强度准则

为建立更符合岩石屈服与破坏机制的强度准则,基于能量转化是岩石屈服与破坏的本质属性,采用试验与理论分析相结合的方法,对岩石屈服与破坏准则进行了研究。以岩石强度与整体破坏准则为基础,通过引入弹性应变能释放分散系数,建立基于弹性应变能强度准则;分别采用M-C准则、Murrell准则、三剪能量准则、统一能量准则、三维H-B强度准则及基于弹性应变能岩石强度准则对盐岩和花岗岩的破坏强度进行了计算。结果表明,基于弹性应变能岩石强度准则的计算结果与试验值比较吻合（尤其是真三轴试验条件下）,并且分析了产生上述结果的内在机制。所建立的强度准则仅需测定常规岩石力学参数（单轴抗压强度与泊松比）,物理力学意义明确,对于定量描述岩石的屈服与破坏特性具有重要的意义。     

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.     

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。     

An anisotropic strength criterion for jointed rock masses and its application in wellbore stability analyses

In this paper, an anisotropic strength criterion is established for jointed rock masses. An orientation distribution function (ODF) of joint connectivity, is introduced to characterize the anisotropic strength of jointed rock masses related to directional distributed joint sets. Coulomb failure condition is formulated for each plane of jointed rock masses by joint connectivity, where the friction coefficient and cohesion of the jointed rock mass are related to those of the intact rock and joint and become orientation dependent. When approximating joint connectivity by its second‐order fabric tensor, an anisotropic strength criterion is derived through an approximate analytical solution to the critical plane problem. To demonstrate the effects of joint distribution on the anisotropic strength of jointed rock masses, the failure envelopes are worked out for different relative orientations of material anisotropy and principal stress axes. The anisotropic strength criterion is also applied to wellbore stability analyses. It is shown that a borehole drilled in the direction of the maximum principal in situ stress is not always the safest due to the anisotropic strength of the jointed rock mass. Copyright © 2007 John Wiley & Sons, Ltd.     

岩土面上抗剪强度与破坏面位置

通过理论推导出在平面应变条件下岩土任意面上的抗剪强度通式和破坏时中主应力与大小主应力的关系,给出了破坏面位置与强度准则的一般关系。为岩土滑移面的确定提供了理论依据,对研究岩土强度准则具有指导意义。     

基于系列Drucker-Prager破坏准则评述土坡的稳定性

各种在? 平面上等效面积的Drucker-Prager屈服准则,如DP4(Drucker-Prager与Mohr-Coulomb两屈服准则在? 平面上的投影面积相等)、DP5(Drucker-Prager与Matsuoka-Nakai两屈服准则在? 平面上的投影面积相等)和DP6(Drucker-Prager与Lade-Duncan两屈服准则在? 平面上的投影面积相等)等模型都不同程度地模拟了平面应变条件下土体的破坏强度,这就是为什么等效面积的Drucker-Prager屈服准则在二维土坡稳定分析中被推广应用的原因。结合砂土的真三轴强度破坏试验结果,从量化角度论证了DP4模型求出的土坡安全系数可能会保守一些,而DP5和DP6两模型求出的土坡安全系数可能会更真实一些,能更好地发挥材料的承载潜力,因而进一步改善了土坡稳定安全系数的计算精度。