The properties of anisotropic conical failure surfaces in relation to the Mohr–Coulomb criterion

An earlier publication¹ considered the properties of circular conical failure surfaces whose axes coincide with the space diagonal in principal stress space. The present work uses a similar approach to analyse conical surfaces that are offset from the space diagonal. It is shown that cones fitted to the Mohr–Coulomb surface in triaxial compression contain a potential singularity. The occurrence and location of the singularity depends on the Mohr–Coulomb friction angle to which the surface is fitted in triaxial extension. It is shown that for a cone fitted to the same friction angle in both triaxial extension and compression, singular conditions occur when that angle reaches \documentclass{article}\pagestyle{empty}\begin{document}$ \sin ^{ - 1} \left({\sqrt 7 - 2} \right)\left({ = 40.22^\circ } \right) $\end{document}. Even cones fitted to smaller friction angles give significant overestimations of material strength for certain stress paths.     

无粘性土的一种破坏准则

研究表明,在三轴压缩和伸长试验条件下,土的抗剪强度与莫尔-库仑准则是一致的,而对于一般应力状态下,土体破坏时的应力状态与莫尔-库仑准则有一定的出入。结合以往的真三轴试验结果,建议了一个复杂应力状态下的等效内摩擦角,在此基础上提出了一个考虑中主应力影响的无粘性土（c＝0）的破坏准则。通过和真三轴试验结果比较,发现该准则在π平面内比莫尔-库仑准则更接近于试验结果。该准则有望推广应用到粘性土中。     

Plane Strain Testing with Passive Restraint

A plane strain condition for testing rock is developed through passive restraint in the form of a thick-walled cylinder. The so-called biaxial frame generates the intermediate principal stress that imposes a triaxial state of stress on a prismatic specimen. Major and minor principal stresses and corresponding strains are accurately measured, providing data to calculate the elastic (Young’s modulus and Poisson’s ratio), inelastic (dilatancy angle), and strength (friction angle and cohesion) parameters of the rock. Results of experiments conducted on Indiana limestone in plane strain compression are compared with the results of axisymmetric compression and extension. With proper system calibration, Young’s modulus and Poisson’s ratio are consistent among the tests. The plane strain apparatus enforces in-plane deformation with the three principal stresses at failure being different, and it allows one to determine the Paul-Mohr-Coulomb failure surface, which includes an intermediate stress effect.     

含裂隙岩体单轴压缩裂纹扩展机制离散元分析

将由室内试验总结得到的岩石微观胶结模型嵌入离散元软件,对Lac du Bonnet花岗岩石进行预制单裂隙单轴压缩试验DEM数值模拟,分析了压缩过程中裂隙试样中应力的分布,并与理论计算结果进行对比分析,同时对各种断裂判据中裂纹起裂角的预测值进行了适用性的对比分析。结果表明,离散元模拟试样破坏形态与试验结果相近;离散元分析得到的应力分布与理论解在定性上相似;当预制角度较小时,侧向应力都处于拉压状态;由于裂隙左右两端压应变的集中造成了裂隙上下面拉应变的产生,造成了裂隙周围特殊的应力分布;当裂隙角度较大时,应力集中现象已不明显,因而,理论值与试验值有偏差;在断裂判据中最大周应力准则和最大能量释放率准则得到的裂纹扩展角与室内试验与DEM结果中的数值较为吻合。     

Experimental study of mechanical and hydraulic properties of bedded rock salt from the Jintan location

A series of triaxial compression tests, triaxial extension tests, and triaxial compression creep tests were conducted to evaluate the strength, deformability, and permeability of rock salt from the Jintan location. Based on a previous analysis, the measured data can be physically modeled very well as shown by the constitutive model Hou/Lux and indicate that China’s representative bedded rock salt from the Jintan location is characterized by good ductility and deformation properties, similar to the European high-purity rock salt. Based on a comparison of compression as well as extension failure strength determined at rock salt from Jintan location, a similarity of compression and extension failure strength could be demonstrated. Permeation flow seems to be an anisotropic process because the permeability measured at samples prior to failure by compression tests differs to those measured at samples prior to failure by extension tests. The anisotropy of damage and destruction of rock salt has a significant influence on permeability. In case of triaxial compression tests, the measured permeability increases two to six orders of magnitude because of consistent direction of injection and cracks. In case of triaxial extension tests, however, the permeability increases less with a maximum of two orders in magnitude. The test results are significant for understanding the load-bearing behavior of rock salt from Jintan location and investigations with reference to the stability and tightness of underground caverns.     

DEM analyses of crack propagation in flawed rock mass under uniaxial compressionEI北大核心CSCD

A contact model for rock is established and imbedded into a DEM software by summarizing the bond granule tests. DEM simulation of uniaxial compression test on the pre-cracked Lac du Bonnet granite is performed, and then stress distributions are further analyzed and compared with the theoretical results. Different fracture criteria are employed to predict the crack initiation angles that are compared with theoretical ones. The results show that the failure modes obtained from DEM simulation are similar to experimental results, and stress distributions in DEM simulation are qualitatively similar to theoretical values. When the angle of pre-crack is small, the lateral stresses are compressive and tensile. The compressive strains concentrate at two edges, resulting in the tensile strains in the up-and downward cracks. When the angle of the pre-crack is large enough, the stress concentration is unobvious, leading to a discrepancy between the DEM and theoretical results. The crack extension angle resulting from uniaxial compression measured from DEM tests are in good agreement with those acquired from experimental tests. These angles are consistent with theoretical predictions by the maximum circumferential stress criterion and the maximum energy release rate criterion.     

硬脆性大理岩拉剪破坏特征与屈服准则研究

岩土工程中常用的屈服准则多以压缩剪切为其破坏机制,然而硬脆性岩体的脆性破坏包括拉伸破坏、张拉剪切破坏和压缩剪切破坏3类,且随着岩体工程向深部发展,张拉剪切破坏成为了洞壁围岩的主要破坏机制。针对此问题,开展了硬脆性大理岩的室内拉剪试验,分析了大理岩拉剪破坏特征,并结合压剪试验结果,建立了考虑张拉剪切破坏机制和应力状态影响的Mohr-Coulomb准则。研究结果表明,硬脆性大理岩破裂面在拉剪应力状态和低正应力压剪应力状态下均具有张拉剪切破坏特征,高正应力压剪应力状态下则只具有压缩剪切滑移特征;拉剪应力状态下,大理岩破裂面张拉破坏特征明显,无明显剪切痕迹,剪切力固定时,剪切位移随着轴向拉力增加而增加;凝聚力和内摩擦角受应力状态影响,凝聚力随正应力增大先减小后增大,内摩擦角则随正应力的增大而减小;凝聚力、内摩擦角随正应力的变化趋势可分为4段,拉剪段、低压应力段、中压应力段和高压应力段,每段的凝聚力、内摩擦角与正应力皆可认为是线性关系,靠近抗拉强度处,内摩擦角趋近90°,凝聚力趋于无穷大;考虑张拉剪切破坏机制和应力状态影响的Mohr-Coulomb准则曲线分为两部分,可采用二次抛物线进行拟合的拉剪段和考虑凝聚力、内摩擦角随正应力演化的压剪段,由此建立的Mohr-Coulomb准则更全面、精度也更高。     

砂与黏土混合物强度特性环剪试验研究

为分析砂和黏土混合物的强度特性,将石英砂和高岭土按不同质量比配制试验土样,开展了一系列固结排水条件下的环剪试验。通过设置轴压为75 kPa、150 kPa、300 kPa和600 kPa状态下开展试验,得到土样剪切角与剪切应力的关系曲线。根据试验曲线的峰值剪应力,通过莫尔-库仑准则得到土样的黏聚力和摩擦角。结果表明,砂和黏土混合物的黏聚力在5~18 kPa范围内波动,当高岭土含量为50%时黏聚力值达到最小值。当高岭土含量小于50%时,摩擦角随高岭土含量增加略有减小;当高岭土含量超过50%时,摩擦角随高岭土含量增加而减小的趋势更明显。     

Influence of Lode angle‐dependent failure criteria on shear localization analysis in sand

Geotechnical experiments show that Lode angle‐dependent constitutive formulations are appropriate to describe the failure of geomaterials. In the present study, we have adopted one such class of failure criteria along with a versatile constitutive relationship to theoretically analyze the effects of Lode angle on localized shear deformation or shear band formation in loose sand for both drained and undrained conditions. We determine the variation in the possible stress states for shear localization due to the introduction of Lode angle by considering the localized deformation as a bifurcation problem. Further, similar bifurcation analysis is performed for the stress states along a specific loading path, namely, plane strain compression at the constitutive level. In addition, the plane strain compression tests have been simulated as a boundary value finite element problem to see how Lode angle affects the post‐localization response. Results show that the inclusion of a Lode angle parameter within the failure criterion has considerable effects on the onset, plastic strain, and propagation of shear localization in loose sand specimens. For drained condition, we notice early inception of shear localization and multiple band formation when the Lode angle‐dependent failure criterion is used. Undrained localization characteristics, however, found to be independent of Lode angle consideration.     

装配式型钢基础抗压抗拔承载力的试验及计算

通过在两个不同基础底面尺寸的装配式型钢基础进行抗压、抗拔承载力和变形特性试验研究,考察了型钢基础及土体的变形及破坏型式,试验中该类基础发生土体剪切破坏而失效,最后提出了基于试验研究的抗压、抗拔承载力计算理论,其中抗压承载力根据有效底面积计算;抗拔承载力应考虑基础上拔产生应力扩散形成的破坏土体进行计算;计算中建议按土体的内摩擦角取用不同土体的上拔扩散角;地下水位以下土体上拔扩散角建议取为0 º。研究成果为该类基础的承载力计算理论、设计方法及实际工程应用提供理论依据。     

基于颗粒离散元模型的花岗岩压缩试验模拟研究

基于颗粒流理论,以黄岛国家石油储备库地下洞库的花岗岩室内试验测试为背景,借助PFC2D（particle flow code）的黏结颗粒模型（bonded particle model, BPM）建立双轴压缩模型。以花岗岩室内试验的宏观力学参数和破坏形态为参照,通过“试错法”得出黏结颗粒模型相对应的细观物理力学性质参数。模拟试验的弹性模量、泊松比与室内试验值吻合较好,BPM模型由于选用圆形颗粒导致黏聚力和内摩擦角与室内试验值相比有一定偏差。模拟试验与室内试验的试件破坏形态均以单斜面剪切破坏为主。采用校准的细观物理力学性质参数,应用BPM模型再现花岗岩压缩试验全过程,深入分析微裂纹萌生演化及能量变化规律。研究表明,压缩过程中岩石试件内裂纹扩展主要经历平稳发展-急剧增加-平稳发展3个阶段;变形过程中,花岗岩试件边界能、应变能、黏结能、摩擦能及动能在各个阶段的变化很好地解释花岗岩受力破坏的细观力学机制。     

Strength criterion for cross-anisotropic sand under general stress conditions

By incorporating the fabric effect and Lode’s angle dependence into the Mohr–Coulomb failure criterion, a strength criterion for cross-anisotropic sand under general stress conditions was proposed. The obtained criterion has only three material parameters which can be specified by conventional triaxial tests. The formula to calculate the friction angle under any loading direction and intermediate principal stress ratio condition was deduced, and the influence of the degree of the cross-anisotropy was quantified. The friction angles of sand in triaxial, true triaxial, and hollow cylinder torsional shear tests were obtained, and a parametric analysis was used to detect the varying characteristics. The friction angle becomes smaller when the major principal stress changes from perpendicular to parallel to the bedding plane. The loading direction and intermediate principal stress ratio are unrelated in true triaxial tests, and their influences on the friction angle can be well captured by the proposed criterion. In hollow cylinder torsional shear tests with the same internal and external pressures, the loading direction and intermediate principal stress ratio are related. This property results in a lower friction angle in the hollow cylinder torsional shear test than that in the true triaxial test under the same intermediate principal stress ratio condition. By comparing the calculated friction angle with the experimental results under various loading conditions (e.g., triaxial, true triaxial, and hollow cylinder torsional shear test), the proposed criterion was verified to be able to characterize the shear strength of cross-anisotropic sand under general stress conditions.     

Adaptation of an existing constitutive model for describing mechanical behaviour of cemented granular soils

In this paper, an existing elastoplastic constitutive model, originally developed for granular soils, is adapted to describe the stress–strain behaviour of cemented granular soils. The existing model (CJS), due to its modular formulation, can be easily developed to take into account different supplementary behavioural aspects in soil mechanics. In the present study, the failure mechanism of the CJS model is modified by introducing the essential aspects in the behaviour of cemented granular soils in its formulation. All of the model parameters have clear physical meaning and can be identified using classical laboratory tests. A set of direct relations between model parameters and famous mechanical parameters of soils such as internal friction angle and cohesion at peak and residual states is presented. In order to validate the model, the results of triaxial and uniaxial tests in the compression and extension performed on cemented granular materials are used. The validation results indicate the good capability of the proposed model.     

An experimental study on deformation and failure mechanical behavior of granite containing a single fissure under different confining pressures

Fissures in natural rocks play an important role in determining the strength, deformability and failure behavior of rock mass. However in the past, triaxial compression experiments have rarely been conducted for rock materials containing three-dimensional (3-D) fissures and the failure mechanical behavior of fissured rocks is not well known due to the difficulty of conducting triaxial experiments on fissured rocks. Therefore in this research, conventional triaxial compression experiments were performed to study the strength, deformability and failure behavior of granite specimens with one preexisting open fissure. Thirty-one specimens were prepared to perform conventional triaxial compression tests for intact and fissured granite. First, based on the experimental results, the effects of the confining pressure and the fissure angle on the elastic modulus and the peak axial strain of granite specimens are analyzed. Second, the influence of the confining pressure on the crack damage threshold and the peak strength of granite with respect to various fissure angles are evaluated. For the same fissure angle, the crack damage threshold and the peak strength of granite both increase with the confining pressure, which is in good agreement with the linear Mohr–Coulomb criterion. With increasing fissure angle, the cohesion of granite first increases and later decreases, but the internal friction angle is not obviously dependent on the fissure angle. Third, nine crack types are identified to analyze the failure characteristics of granite specimens containing a single fissure under conventional triaxial compression. Finally, a series of X-ray microcomputed tomography (CT) observations were conducted to analyze the internal damage mechanism of granite specimens with respect to various fissure angles. Reconstructed 3-D CT images indicate obvious effects of confining pressure and fissure angle on the crack system of granite specimens. The study helps to elucidate the fundamental nature of rock failure under conventional triaxial compression.     

IV级软弱围岩相似材料的试验研究

以IV级围岩为参照对象,研制可用于隧道围岩稳定性物理模型试验的软弱围岩相似材料。采用的5种原材料（重晶石粉、石膏、细砂、洗衣液和水）,通过直剪试验、无侧限抗压强度试验及三轴压缩试验测得所配相似材料的强度特征和物理力学参数,包括黏聚力c、内摩擦角?、单轴抗压强度Rc、弹性模量E和泊松比?。首先,通过试验分析每种原材料的不同比例对所配相似材料强度特征及物理力学参数的影响,选择适合于模拟IV级围岩相似材料的原材料配比;其次,针对优选的材料配比所配制的相似材料,开展大量的三轴压缩试验,研究在不同围压下该相似材料的强度及其破坏特征。结果表明,含水率减少或石膏含量增加导致Rc、E和c明显增大,而?降低不明显;增加砂含量可增大E 和?,但Rc值减少;石膏含量对相似材料的脆性和延性影响最明显,而含水率对相似材料的强度影响最为突出。试验结果还表明,相似材料在低围压时呈现脆性,在高围压时呈延性;就破坏准则而言,试验所得结果小于Mohr-Coulomb准则,略大于Hoek-Brown准则,但更符合Hoek-Brown准则。研制软岩相似材料的试验数据可为下一步拟开展的隧道围岩稳定性模型试验和数值模拟提供重要的参考和依据。     

土工格栅加筋砂土的变形与破坏机理解析

利用可考虑局部破坏的非线性弹塑性有限元，对无加筋和加筋砂土的平面应变压缩试验结果进行了从小变形到破坏的全过程数值解析。加筋砂土试验体用土工格栅分6层和11层进行加筋加固。将等价二维有限元解析所得到的解析结果与试验得到的实测值进行了较为伞面的比较，结果表明：合理的二维非线性弹塑性有限元解析，不仅可以较为精确的模拟加筋砂土的平均心力-应变特性，而且还可以全面地调查试验体的局部应力-应变分布以及剪切破坏发生状况，从而，对加筋砂土的变彤破坏以及加筋材的加州机理有一个更加全面合理的认识。     

冻结饱水砂卵石三轴压缩强度试验研究

为研究北京富水砂卵石地层冻结后的强度特性,以北京某地铁暗挖车站砂卵石为研究对象,进行不同温度（?5、?10、?15、?20℃）,不同围压（0.0、0.3、0.8、1.3、2.0、3.0、4.0、8.0 MPa）条件下三轴压缩试验。试验结果表明：冻结砂卵石的应力-应变曲线以应变软化形态为主,高负温、高围压条件下,呈现理想塑性破坏形态;砂卵石强度、黏聚力和摩擦角均随温度降低而增大,其中强度呈指数分布,黏聚力和摩擦角呈线性分布;强度和弹性模量随围压增加而增大,但增大趋势逐渐减小,低围压压缩区强度满足线性Morh-Coulomb（简称M-C）准则;冻结砂卵石的破坏形态以破裂面始/终于试样侧面的剪切破坏为代表,张拉型破坏受冰影响显著,仅存在于低围压条件下,高围压、高负温时易出现体胀型破坏。     

Evaluation of a constitutive model for clays and sands: Part I – sand behaviour

This paper evaluates the performance of a generalized effective stress soil model for predicting the rate independent behaviour of freshly deposited sands, while a companion paper describes model capabilities for clays and silts. Most material parameters can be obtained from standard laboratory data, including hydrostatic or one‐dimensional compression, drained and undrained triaxial shear testing. A compilation of data on compression behaviour allows for estimation of compression parameters when this type of data is not available. Extensive comparisons of model predictions with measured data from undrained triaxial shear tests shows that the model gives excellent predictions of the transition from dilative to contractive shear response as the confining pressure and/or the initial formation void ratio increases. A parametric study of drained response shows that the model describes realistically the variation of peak friction angle and dilation rate as a function of confining pressure and density when compared with an empirical correlation valid for many sands. The proposed formulation predicts a unique critical state locus for both drained and undrained triaxial testing which is non‐linear over the entire range of stresses and is in excellent agreement with recent experimental data. Overall, the model provides excellent predictions of the stress–strain–strength relationships over a wide range of confining pressures and formation densities. Copyright © 2002 John Wiley & Sons, Ltd.     

含水量对晋西黄土抗剪强度影响的试验

以晋西黄土为研究对象,采用常规直剪试验和不排水不固结三轴试验,对不同含水量下土样的抗剪强度参数进行了测定,得出晋西黄土抗剪强度随含水量变化的规律。试验表明:直剪试验条件下,随着含水量的增加,土的抗剪强度降低。当含水量小于12%左右时,随着含水量的增大,黏聚力c降低迅速;当含水量在12%~23%时,随含水量的增大,黏聚力降低缓慢,降低幅度较小,当含水量大于23%左右时,随含水量的增大,黏聚力降低趋势再次变陡;抗剪强度参数内摩擦角φ随着含水量的增大,变化趋势不明显,其取值大致在14°~32°。三轴不固结不排水剪切试验中,随着含水量的增加,抗剪强度参数c降低,在小于12%含水量时,降低趋势陡,大于12%含水量后,降低趋势变缓;内摩擦角φ随着含水量的增大呈线性降低,且相关性较好。      

修正应变能密度因子准则及岩石裂纹扩展研究

由应变能密度因子理论得出裂纹沿着形状改变比能密度因子最小的方向扩展,但理论中所使用的应力强度因子是在拉应力作用下计算得出的,而自然界中的岩体通常处于压应力场中。因此,在修正的应变能密度因子理论的基础上,结合压缩荷载作用下的裂纹尖端应力强度因子,并考虑裂纹面之间的摩擦作用得出了针对压缩荷载作用下的岩石裂纹扩展的应变能密度因子理论,并运用该理论分析了裂纹倾角、围压以及裂面摩擦力对破裂角的影响,将分析结果与已有的试验和数值分析结果进行比较,取得了良好的一致性。分析得出,在单轴压缩荷载作用下临界破裂荷载随着裂纹倾角的增大而先减小、后增大,并且一个裂纹倾角对应多个破裂角,即裂纹朝多个方向发展;在三轴压缩荷载作用下,破裂角与围压大小有关。此研究成果可为压应力场中岩石裂纹扩展的数值模拟提供参考。