A failure criterion for shale considering the anisotropy and hydration based on the shear slide failure model

A failure criterion fully considering the anisotropy and hydration of shale is essential for shale formation stability evaluation.Thus,a novel failure criterion for hydration shale is developed by using Jaeger’s shear failure criterion to describe the anisotropy and using the shear strength reduction caused by clay minerals hydration to evaluate the hydration.This failure criterion is defined with four parameters in Jaeger’s shear failure criterion(S_(1),S_(2),a andφ),three hydration parameters(k,ω_(sh)andσ_(s))and two material size parameters(d and l0).The physical meanings and determining procedures of these parameters are described.The accuracy and applicability of this failure criterion are examined using the published experimental data,showing a cohesive agreement between the predicted values and the testing results,R^(2)=0.916 and AAREP(average absolute relative error percentage)of 9.260%.The error(|D_(p)|)is then discussed considering the effects ofβ(angle between bedding plane versus axial loading),moisture content and confining pressure,presenting that|Dp|increases whenβis closer to 30°,and|D_(p)|decreases with decreasing moisture content and with increasing confining pressure.Moreover,|D_(p)|is demonstrated as being sensitive to S1and being steady with decrease in the data set whenβis 0°,30°,45°and 90°.

Upper bound analysis of slope stability with nonlinear failure criterion based on strength reduction technique

Based on the upper bound limit analysis theorem and the shear strength reduction technique,the equation for expressing critical limit-equilibrium state was employed to define the safety factor of a given slope and its corresponding critical failure mechanism by means of the kinematical approach of limit analysis theory.The nonlinear shear strength parameters were treated as variable parameters and a kinematically admissible failure mechanism was considered for calculation schemes.The iterative optimization method was adopted to obtain the safety factors.Case study and comparative analysis show that solutions presented here agree with available predictions when nonlinear criterion reduces to linear criterion,and the validity of present method could be illuminated.From the numerical results,it can also be seen that nonlinear parameter m,slope foot gradient β,height of slope H,slope top gradient α and soil bulk density γ have significant effects on the safety factor of the slope.

Strength Regularity and Failure Criterion of High-Strength High-Performance Concrete under Multiaxial Compression

Multiaxial compression tests were performed on 100 mm×100 mm×100 mm high-strength high-performance concrete （HSI-IPC） cubes and normal strength concrete （NSC） cubes. The failure modes of specimens were presented, the static compressive strengths in principal directions were measured, the influence of the stress ratios was analyzed. The experimental results show that the ultimate strengths for HSHPC and NSC under multiaxial compression are greater than the uniaxial compressive strengths at all stress ratios, and the multiaxial strength is dependent on the brittleness and stiffness of concrete, the stress state and the stress ratios. In addition, the Kupfer-Gersfle and Ottosen＇s failure criteria for plain HSHPC and NSC under multiaxial compressive loading were modified.

A modified failure criterion for transversely isotropic rocks

A modified failure criterion is proposed to determine the strength of transversely isotropic rocks. Me-chanical properties of some metamorphic and sedimentary rocks including gneiss, slate, marble, schist, shale, sandstone and limestone, which show transversely isotropic behavior, were taken into consider-ation. Afterward, introduced triaxial rock strength criterion was modified for transversely isotropic rocks. Through modification process an index was obtained that can be considered as a strength reduction parameter due to rock strength anisotropy. Comparison of the parameter with previous anisotropy in-dexes in literature showed reasonable results for the studied rock samples. The modified criterion was compared to modified Hoek-Brown and Ramamurthy criteria for different transversely isotropic rocks. It can be concluded that the modified failure criterion proposed in this study can be used for predicting the strength of transversely isotropic rocks.

Failure criterion for soft rocks considering intermediate principal stress

The significant differences between hard rocks(more brittle)and soft rocks(more ductile)may suggest the use of different failure criteria.A strength criterion for soft rocks that includes intermediate principal stress was proposed.The new criterion includes two independent parameters:the uniaxial compressive strength(σ_(ci)),which can be obtained from common laboratory tests or indirectly estimated by alternative index tests in the laboratory or field;and f(joint),which is used to characterize the rock mass quality and can be easily estimated.The authors compared the predictive capabilities of the new criterion with other criteria using the database of soft rocks under two conditions:with and without triaxial data.For the estimation of triaxial and true-triaxial strengths,the new criterion generally produced a better fit.The proposed criterion is practical for an approximate first estimation of rock mass strength,even without triaxial data,as it balances accuracy(lower prediction error)and simplicity(fewer independent parameters).

FAILURE MODE AND CONSTITUTIVE MODEL OF PLAIN HIGH-STRENGTH HIGH-PERFORMANCE CONCRETE UNDER BIAXIAL COMPRESSION AFTER EXPOSURE TO HIGH TEMPERATURES

An orthotropic constitutive relationship with temperature parameters for plain highstrength high-performance concrete （HSHPC） under biaxial compression is developed. It is based on the experiments performed for characterizing the strength and deformation behavior at two strength levels of HSHPC at 7 different stress ratios including a=σs ： σ3=0.00：-1,-0.20：-1,-0.30 ： -1,-0.40：-1,-0.50：-1,-0.75：-1,-1.00：-1, after the exposure to normal and high temperatures of 20, 200, 300, 400, 500 and 600℃, and using a large static-dynamic true triaxial machine. The biaxial tests were performed on 100 mm×100 mm×100 mm cubic specimens, and friction-reducing pads were used consisting of three layers of plastic membrane with glycerine in-between for the compressive loading plane. Based on the experimental results, failure modes of HSHPC specimens were described. The principal static compressive strengths, strains at the peak stress and stress-strain curves were measured; and the influence of the temperature and stress ratios on them was also analyzed. The experimental results showed that the uniaxial compressive strength of plain HSHPC after exposure to high temperatures does not decrease dramatically with the increase of temperature. The ratio of the biaxial to its uniaxial compressive strength depends on the stress ratios and brittleness-stiffness of HSHPC after exposure to different temperature levels. Comparison of the stress-strain results obtained from the theoretical model and the experimental data indicates good agreement.

Retrospective and prospective review of the generalized nonlinear strength theory for geomaterials

Strength theory is the basic theory for calculating and designing the strength of engineering materials in civil,hydraulic,mechanical,aerospace,military,and other engineering disciplines.Therefore,the comprehensive study of the generalized nonlinear strength theory(GNST)of geomaterials has significance for the construction of engineering rock strength.This paper reviews the GNST of geomaterials to demonstrate the research status of nonlinear strength characteristics of geomaterials under complex stress paths.First,it systematically summarizes the research progress of GNST(classical and empirical criteria).Then,the latest research the authors conducted over the past five years on the GNST is introduced,and a generalized three-dimensional(3D)nonlinear Hoek‒Brown(HB)criterion(NGHB criterion)is proposed for practical applications.This criterion can be degenerated into the existing three modified HB criteria and has a better prediction performance.The strength prediction errors for six rocks and two in-situ rock masses are 2.0724%-3.5091%and 1.0144%-3.2321%,respectively.Finally,the development and outlook of the GNST are expounded,and a new topic about the building strength index of rock mass and determining the strength of in-situ engineering rock mass is proposed.The summarization of the GNST provides theoretical traceability and optimization for constructing in-situ engineering rock mass strength.

Analysis on the turning point of dynamic in-plane compressive strength for a plain weave composite

Experimental investigations on dynamic in-plane compressive behavior of a plain weave composite were performed using the split Hopkinson pressure bar. A quantitative criterion for calculating the constant strain rate of composites was established. Then the upper limit of strain rate, restricted by stress equilibrium and constant loading rate, was rationally estimated and confirmed by tests. Within the achievable range of 0.001/s-895/s, it was found that the strength increased first and subsequently decreased as the strain rate increased. This feature was also reflected by the turning point(579/s) of the bilinear model for strength prediction. The transition in failure mechanism, from local opening damage to completely splitting destruction, was mainly responsible for such strain rate effects. And three major failure modes were summarized under microscopic observations: fiber fracture, inter-fiber fracture, and interface delamination. Finally, by introducing a nonlinear damage variable, a simplified ZWT model was developed to characterize the dynamic mechanical response. Excellent agreement was shown between the experimental and simulated results.

RELIABILITY ANALYSIS OF FRP LAMINATED PLATES WITH CONSIDERATION OF BOTH INITIAL IMPERFECTION AND FAILURE SEQUENCE

A probabilistic progressive failure analyzing method is applied to estimating the reliability of a simply supported laminated composite plate with an initial imperfection under bi-axial compression load. The initial imperfection and the strength parameters are considered as random variables. Ply-level failure probability is evaluated by the first order reliability method (FORM) together with the Tsai-Wu strength criterion and Tan criterion. Current stresses in the laminated structure are calculated by the classical lamination theory with the stiffness modified based on the last step ply failure. Probabilistically dominant ply-level failure sequences leading to overall system failure are identified, based on which the system failure probability is estimated. A numerical example is presented to demonstrate the methodology proposed. Through parameter studies it is shown that the deviation of the initial imperfection and some of the strength parameters largely influence the system reliability.

A simplified three-dimensional extension of Hoek-Brown strength criterion

The Hoek-Brown(HB)strength criterion has been applied widely in a large number of projects around the world.However,this criterion ignores the intermediate principal stress s2.Many evidences have demonstrated that the rock strength is dependent on s2.Thus it is necessary to extend the HB criterion into a three-dimensional(3D)form.In this study,the effect of s2 on the strength of rocks is identified by reviewing the true triaxial tests of various rock types reported in the literature.A simple 3D strength criterion is developed.The modified criterion is verified by the true triaxial tests of 13 rock types.The results indicate that the modified criterion can achieve a good fit to most of rock types.It can represent a series of criteria as b varies.For comparisons,several existing 3D versions of the HB criterion are selected to predict the strengths of these rock types.It is indicated that the proposed criterion works better than other criteria.A substantial relationship between parameter b and the unconfined compressive strength is established,which guarantees that the proposed criterion can still work well even in the absence of true triaxial test data.

Comprehensive compressive-tensile strength criterion for intact rock

This paper presents a strength criterion for intact rock, which can well describe triaxial test data under compressive or tensile stress state. The proposed criterion is defined in terms of three parameters. One parameter expresses the apparent unconfined compressive strength （AUCS）, obtained from the Coulomb-Mohr criterion, as a regulated unconfined compressive strength （RUCS）. Two other parameters, 2~ and （, are material-dependent that can be determined by regression analysis. The proposed criterion is compared with selected applicable strength criteria separately for compressive and tensile strengths. Coefficient of determination and accordance coefficient are considered in comparisons between the proposed and selected strength criteria.

Numerical modeling of permeability evolution based on degradation approach during progressive failure of brittle rocks

The permeability evolution of rock during the progressive failure process is described.In combination with the strength degradation index,the degradation formulas of s and a,which are dependent on the plastic confining strain component,the material constants of Hoek–Brown failure criterion are presented,and a modified elemental scale elastic–brittle–plastic constitutive model of rock is established.The relationship between volumetric strain and permeability through tri-axial compression is investigated.Based on the above,a permeability evolution model is established.The model incorporates confining pressuredependent degradation of strength,dilatancy and corresponding permeability evolution.The model is implemented in FLAC by the FISH function method.The permeability evolution behavior of rock is investigated during the progressive failure process in a numerical case.The results show that the model is capable of reproducing,and allowing visualization of a range of hydro-mechanical responses of rock.The effects of confining pressure on degradation of strength,dilatancy and permeability evolution are also reflected.

Modified Mohr-Coulomb strength criterion considering rock mass intrinsic material strength factorization

With the increase of mining depth of mineral resources,the rock mass stress state is being more and more complex.The rock mass show different features,namely,with the increase of hydrostatic pressure,rock mass failure mode turns from brittle tension failure to structure ductile failure and its limit strength also increases.The restriction of minimal principal stress on the initiation and development of microcrack and the change of micro-unit stress state by the intermediate principal stress play a decisive role in the increase of rock mass limit strength.Based on the rock mass failure behavior law under complex stress state and the σ2-dependence on the rock mass strength,we proposed a Modified Mohr-Coulomb(M-MC) strength criterion which is smooth and convex.Finally,the M-MC criterion is validated by multiaxial test data of eight kinds of rock mass.We also compared the fitting results with Mohr-Coulomb criterion(MC).It shows that the new criterion fits the test data better than the Mohr-Coulomb criterion.So the M-MC strength criterion well reveals the rock mass bearing behavior and can be widely used in the rock mass strength analysis.The results can provide theoretical foundations for stability analysis and reinforcement design of complex underground engineering.

THREE-DIMENSIONAL SLOPE STABILITY ANALYSIS BASED ON NONLINEAR FAILURE ENVELOPE

The effects of nonlinearity of strength envelopes on 3D slope stability analysis are investigated.A power relation for the nonlinear envelope is employed to derive the 3D factor of safety equations of an extended Spencer method hich satisfies boty force equilibrium and moment equilibrium.Then,a search procedure is presented based on dynamic programming to determine the 3D critical slip surface for a general slope,Linear and nonlinear strength envelopes used for slope stability computations are obtained by fitting curves to the 103 strength data of consolidated-undrained(CU)triaxial compression tests for compacted Israeli clay.Results of a typical 3D problem show that a linear approximation of the nonlinear strength envelope may lead to a significant overestimation of calculated safety factors.

Limestone mechanical deformation behavior and failure mechanisms： a review

In this paper, several mechanical deformation curves of limestone are reviewed, and the effects of temperature, confining pressure, and fluid are discussed. Generally, Mohr–Coulomb is used for limestone brittle fracture. The characteristic of low temperature cataclastic flow and the conditions and constitutive equations of intracrystal plastic deformation such as dislocation creep,diffusion creep, and superplastic flow are discussed in detail. Specifically, from the macroscopic and microscopic view, inelastic compression deformation(shear-enhanced compaction) of large porosity limestone is elaborated.Compared with other mechanics models and strength equations, the dual porosity(macroporosity and microporosity) model is superior and more consistent with experimental data. Previous research has suffered from a shortage of high temperature and high pressure limestone research; we propose several suggestions to avoid this problem in the future:(1) fluid-rock interaction research;(2) mutual transition between natural conditions and laboratory research;(3) the uniform strength criterion forshear-enhanced compaction deformation;(4) test equipment; and(5) superplastic flow mechanism research.

考虑水力效应的裂缝边坡稳定性非线性能耗分析

现有考虑水力效应的裂缝边坡稳定性分析大多基于线性破坏准则,而岩土体破坏往往呈现非线性特征,因此开展水力效应影响下的裂缝边坡稳定性非线性极限上限分析具有重要意义。基于极限分析上限定理及强度折减技术,结合“外切线法”非线性破坏准则,构建坡顶含竖直裂缝的边坡对数螺旋线破坏模式,根据虚功原理推导出裂缝边坡安全系数解析式,通过MATLAB优化计算,结合边坡工程实例探讨了典型因素对裂缝边坡稳定性、临界裂缝及滑动面位置的影响规律。研究结果表明:随着地下水位h的持续上升,边坡安全系数不断降低,临界裂缝深度逐渐增大且临界裂缝位置逐渐向坡顶缘偏移;非线性系数m明显影响边坡的稳定性,边坡安全系数随着非线性系数的增大显著减小,采用线性破坏准则会高估地下水位变化对边坡稳定性的影响;随着非线性系数的增大,临界裂缝深度随之增大,临界裂缝位置距离坡顶缘越来越远,滑坡体体积逐渐增大;裂缝与坡顶缘距离l m随着非线性系数m的增大而增大(当m增大0.2时,l m增大约1 m),且随着裂缝与坡顶缘距离的增大,边坡安全系数无明显变化,临界裂缝深度先逐渐减小后趋于稳定。

直接剪切下页岩的各向异性破坏特征和强度预测模型

了解页岩剪切破坏特性对页岩气储层改造和井壁稳定性控制具有重要意义。然而,由于页岩本身的各向异性属性,页岩的剪切破坏行为复杂。本文对6种不同层理倾角(0°、30°、60°、90°、120°和150°)的立方体页岩进行了系统的直接剪切破坏测试,详细分析了在层理弱面影响下页岩的剪切应力–剪切位移、抗剪强度、剪切模量和破坏模式的各向异性特征。结果表明:页岩的剪切破坏表现为典型的非线性渐进破坏特征;页岩平均抗剪强度和剪切模量随层理倾角的增加均呈现“M”型变化趋势;在90°~180°的层理倾角区间,平均抗剪强度的极值差明显大于0°~90°区间,而剪切模量近似关于90°呈对称变化;当层理倾角从0°变化到180°时,页岩剪切各向异性行为呈现非对称演化规律。在层理倾角和直接剪切荷载作用下,页岩的破坏模式有3类:层理倾角为0°时,沿层理面剪切滑移破坏;层理倾角为30°、60°和90°时,表现为穿透层理和基质的剪切滑移破坏;其他倾角下呈现穿透层理和基质的剪切滑移与沿层理的拉伸劈裂相结合的复合破坏。基于试验结果和组构张量,构建了一个可考虑页岩本征各向异性和剪应力诱导各向异性影响的直接剪切破坏准则,其理论预测值与试验结果的平均偏差率低于3%,能够定量表征黏聚力和摩擦系数的各向异性程度,合理评估页岩直接剪切强度对外加法向应力的敏感性,可推广应用于理论表征所有层状岩土材料的直接剪切强度。

各向异性复合材料强度失效判据综述

失效判据在复合材料的渐进损伤模拟和极限强度预测中具有极其重要的意义.针对各向异性复合材料的损伤-破坏问题,根据理论架构与发展脉络,对现有失效判据进行了分类汇总和全面综述,重点总结了破坏模式无关判据和破坏模式相关判据,分析了基于破坏面假设的相关理论成果,阐述了基于应力不变量进行判据构建的基本理论、方法和模型,并论述了基于应变能和基于损伤参量的两类失效判据.研究表明,各向异性复合材料强度理论发展的基础和主线仍然是二次应力判据,高阶唯象失效判据的合理性和适用性尚需验证;能量判据和损伤判据对于非线性-准脆性复合材料显示出了合理性和适用性,但表达式较为复杂.在深入分析研究的基础上,对复合材料强度理论的发展趋势进行了展望,提出了“损伤-断裂协同理论”这一重点与难点方向,以期对复合材料及其结构的设计、评估与应用提供更有价值的参考.

基于残余位移增量判据的土石围堰边坡稳定性分析

针对有限元强度折减法在复杂水文地质环境下土石围堰边坡稳定性评价中效果欠佳的问题,引入残余位移增量判据,基于有限元强度折减法,考虑深厚覆盖层土石围堰不同水位下的渗流特征,通过计算坡面节点平均残余位移增量,获取边坡稳定系数,进一步通过位移增量分布图,探讨了围堰边坡潜在滑面位置及其形成机制。结果表明,在复杂水文地质环境下的土石围堰边坡稳定性评价中,残余位移增量判据相较经典失稳判据适用性更强。研究结果能够为工程实践提供指导。