New true-triaxial rock strength criteria considering intrinsic material characteristics

A reasonable strength criterion should reflect the hydrostatic pressure effect, minimum principal stress effect,and intermediate principal stress effect. The former two effects can be described by the meridian curves, and the last one mainly depends on the Lode angle dependence function. Among three conventional strength criteria, i.e.Mohr–Coulomb(MC), Hoek–Brown(HB), and Exponent(EP) criteria, the difference between generalized compression and extension strength of EP criterion experience a firstly increase then decrease process, and tends to be zero when hydrostatic pressure is big enough. This is in accordance with intrinsic rock strength characterization. Moreover, the critical hydrostatic pressure Icorresponding to the maximum difference of between generalized compression and extension strength can be easily adjusted by minimum principal stress influence parameter K. So, the exponent function is a more reasonable meridian curves, which well reflects the hydrostatic pressure effect and is employed to describe the generalized compression and extension strength.Meanwhile, three Lode angle dependence functions of L,L, and L, which unconditionally satisfy the convexity and differential requirements, are employed to represent the intermediate principal stress effect. Realizing the actual strength surface should be located between the generalized compression and extension surface, new true-triaxial criteria are proposed by combining the two states of EP criterion by Lode angle dependence function with a same lode angle. The proposed new true-triaxial criteria have the same strength parameters as EP criterion. Finally, 14 groups of triaxial test data are employed to validate the proposed criteria. The results show that the three new true-triaxial exponent criteria,especially the Exponent Willam-Warnke criterion(EPWW)criterion, give much lower misfits, which illustrates that the EP criterion and Lhave more reasonable meridian and deviatoric function form, respectively. The proposed new true-triaxial strength criteria can provide theoretical foundation for stability analysis and optimization of support design of rock engineering.

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.

A new three-dimensional Hoek-Brown strength criterion

The Hoek-Brown （HB） strength criterion has been widely applied to the estimation of strength of intact rock and rock mass, while evolving ever since. However, negligence of the effect of the intermediate principal stress still remains in the criterion＇s latest version. At the same time, several three-dimensional （3D） HB strength, which can takes into account the influence of the intermediate principal stress, have already been proposed, among which the 3D HB criterion proposed by Zhang and Zhu seems to be the most reasonable one. However, the Zhang 3D HB criterion may have problems with some stress path close to triaxial extension state because of the non-convexity characteristic of its failure surface. In this paper, a new 3D HB strength criterion is presented based on a generalized form of the HB criterion, which also considers the effect of the intermediate principal stress and inherits all the merits of the original version of the HB criterion. In addition, this new criterion can remedy to some extent the shortcomings observed in the Zhang 3D HB criterion. Polyaxial tests for five different rocks from pub- lished literatures are used for evaluating this new criterion and comparing it with the Zhang 3D HB criterion. The re- sults show that this new criterion may over-predict or under- predict the polyaxial strength of rocks but the errors are rela- tively small, and similar results are also found for the Zhang 3D HB criterion, which one is better depends on the type of the rock under estimation.

Bayesian data analysis to quantify the uncertainty of intact rock strength

One of the main difficulties in the geotechnical design process lies in dealing with uncertainty. Uncertainty is associated with natural variation of properties, and the imprecision and unpredictability caused by insufficient information on parameters or models. Probabilistic methods are normally used to quantify uncertainty. However, the frequentist approach commonly used for this purpose has some drawbacks.First, it lacks a formal framework for incorporating knowledge not represented by data. Second, it has limitations in providing a proper measure of the confidence of parameters inferred from data. The Bayesian approach offers a better framework for treating uncertainty in geotechnical design. The advantages of the Bayesian approach for uncertainty quantification are highlighted in this paper with the Bayesian regression analysis of laboratory test data to infer the intact rock strength parameters σand mused in the Hoek-Brown strength criterion. Two case examples are used to illustrate different aspects of the Bayesian methodology and to contrast the approach with a frequentist approach represented by the nonlinear least squares(NLLS) method. The paper discusses the use of a Student’s t-distribution versus a normal distribution to handle outliers, the consideration of absolute versus relative residuals, and the comparison of quality of fitting results based on standard errors and Bayes factors. Uncertainty quantification with confidence and prediction intervals of the frequentist approach is compared with that based on scatter plots and bands of fitted envelopes of the Bayesian approach. Finally, the Bayesian method is extended to consider two improvements of the fitting analysis. The first is the case in which the Hoek-Brown parameter, a, is treated as a variable to improve the fitting in the triaxial region. The second is the incorporation of the uncertainty in the estimation of the direct tensile strength from Brazilian test results within the overall evaluation of the intact rock strength.

Anisotropy of strength and deformability of fractured rocks

Anisotropy of the strength and deformation behaviors of fractured rock masses is a crucial issue for design and stability assessments of rock engineering structures, due mainly to the non-uniform and non- regular geometries of the fracture systems. However, no adequate efforts have been made to study this issue due to the current practical impossibility of laboratory tests with samples of large volumes con- taining many fractures, and the difficulty for controlling reliable initial and boundary conditions for large-scale in situ tests. Therefore, a reliable numerical predicting approach for evaluating anisotropy of fractured rock masses is needed. The objective of this study is to systematically investigate anisotropy of strength and deformability of fractured rocks, which has not been conducted in the past, using a nu- merical modeling method. A series of realistic two-dimensional （2D） discrete fracture network （DFN） models were established based on site investigation data, which were then loaded in different directions, using the code UDEC of discrete element method （DEM）, with changing confining pressures. Numerical results show that strength envelopes and elastic deformability parameters of tested numerical models are significantly anisotropic, and vary with changing axial loading and confining pressures. The results indicate that for design and safety assessments of rock engineering projects, the directional variations of strength and deformability of the fractured rock mass concerned must be treated properly with respect to the directions of in situ stresses. Traditional practice for simply positioning axial orientation of tunnels in association with principal stress directions only may not be adequate for safety requirements. Outstanding issues of the present study and su^zestions for future study are also oresented.

Three independent parameters to describe conventional triaxial compressive strength of intact rocks

The strengths of 12 rocks cited from literatures increase in a nonlinear way with increasing confining pressure against the Coulomb criterion. The criteria with power forms like the generalized Hoek-Brown criterion are not available for describing the strength properties in the whole test range for Indiana limestone, Yamaguchi marble and Vosges sandstone, of which the differential stresses are approximately constant at high confining pressures. The exponential criterion with three parameters fits the test data of those 12 rocks well with a low misfit. The three parameters are independent of the uniaxial compressive strength (UCS), the initial increasing rate of strength with confining pressure, and the limitation of differential stress.

Rock mechanics for design of Brisbane tunnels and implications of recent thinking in relation to rock mass strength

This paper explores the potential implications of recent thinking in relation to rock mass strength for future tunnelling projects in Brisbane,Australia,particularly as they are constructed within deep horizons where the in situ stress magnitudes is larger.Rock mass failure mechanisms for the current tunnels in Brisbane are generally discontinuity controlled and the potential for stress-induced failure is relatively rare.For the road tunnels which have been constructed in Brisbane over the last 12 years,the strength of the more massive rock masses for continuum analysis has been estimated by the application of the Hoek-Brown(H-B)failure criterion using the geological strength index(GSI)to determine the H-B parameters mb,s and a.Over the last few years,alternative approaches to estimating rock mass strength for‘massive to moderately jointed hard rock masses’have been proposed by others,which are built on the work completed by E.Hoek and E.T.Brown in this area over their joint careers.This paper explores one of these alternative approaches to estimating rock mass strength for one of the geological units(the Brisbane Tuff),which is often encountered in tunnelling projects in Brisbane.The potential implications of these strength forecasts for future tunnelling projects are discussed along with the additional work which will need to be undertaken to confirm the applicability of such alternative strength criteria for this rock mass.

巷道蝶形破坏强度准则低敏感性研究及工程应用

巷道围岩的塑性区形态对巷道的破坏形式及破坏程度有重要影响。为探究三向应力场下塑性区形态演化过程,基于弹性力学推导了轴向应力表达式,并依据蝶形塑性区边界方程求解思路,确定了三维强度准则下三向塑性区近似解的求解方法。通过等球应力p、等偏应力q以及不同Lode角θσ来确定围岩应力加载方案,对不同三维强度准则下的围岩塑性区形态演化规律进行深入研究,论证了蝶形破坏的准则低敏感性。基于蝶形破坏理论对羊场湾160206回风巷道的非对称变形破坏机制及控制技术进行深入分析。研究结果表明:(1)在相同p、q及不同θσ的应力加载条件下,5种强度准则下的塑性区形态均呈现圆形、类椭圆及蝶形的演化规律,且每种强度准则在相同θσ的情况下围岩的塑性区形态基本一致。(2)相同应力大小、不同应力方向的加载方案下,围岩的塑性区形态大不相同。圆巷围岩的塑性区形态很大程度上由水平侧压比决定,轴向侧压对围岩的塑性区尺寸影响较大,对塑性区形态影响较小。(3)羊场湾160206回风巷道在叠加采动影响下顶板呈现非对称大变形破坏,基于蝶形塑性区支护思路,应用非对称锚杆索+超前单元支架+钻孔卸压的协同支护技术,取得了良好的支护效果。

考虑中间主应力效应的修正Hoek-Brown真三轴强度准则

为改善Hoek-Brown强度准则未考虑中间主应力对岩石强度的影响,通过岩石真三轴试验结果分析了岩石强度的演化规律,引入中间主应力系数,量化分析主应力系数对岩石真三轴强度的影响,考虑Hoek-Brown强度准则中的参数和岩石应力水平间的关联性,提出了基于拉格朗日插值方法的修正岩石真三轴Hoek-Brown强度准则,分析了其空间包络特征。最后,利用7种岩石的真三轴试验数据与其它3种真三轴强度准则进行最优拟合误差分析,探讨了修正强度准则的合理性。研究结果表明:岩石强度随着最小主应力的增加逐渐增大,随着中间主应力的增加则呈现先增大后减小的变化规律,表现出显著的区间效应;修正强度准则不仅能够继承Hoek-Brown强度准则在子午面上的非线性优点,且能够表征岩石强度在应力空间中的基本特性;线性和非线性插值形式的修正强度准则空间包络面分别为非等边的六棱锥面以及能够满足拉压子午面区间连续光滑要求的圆锥面;修正强度准则能够较好地预测岩石真三轴试验强度,较为合理地反映中间主应力对岩石强度的影响;相比于线性插值形式强度准则,二次插值形式强度准则能够提高岩石强度的预测精度1.2~2.0倍;相较于其他真三轴强度准则,修正强度准则对不同硬脆性岩石的真三轴试验结果均具有良好的强度预测精度,体现了修正强度准则的适用性和可靠性。

考虑温度作用的岩石统计损伤本构模型及验证

为了预测和评估深部高温岩体的稳定性,运用理论推导的方法研究温度作用下(后)岩石的本构关系。首先,基于已有的岩石统计损伤本构模型,考虑温度对岩石损伤变量的影响,引入了损伤变量修正系数、损伤起裂应力和起裂应变等参数;其次,假设微元体强度服从幂函数分布,并符合Hoek-Brown(H-B)强度准则,针对统计损伤本构模型无法反映峰前较强的微裂纹压密效应的弊端,引入了相应的模型修正系数;再次,建立了考虑温度作用的岩石统计损伤本构模型,并确定了模型参数的表达式;最后,对比不同温度作用下(后)的花岗岩在单轴和常规三轴压缩试验条件下所得的结果与文献中模型的计算结果,验证本文模型的准确性。研究结果表明:所提出的模型的计算结果与文献的试验结果在数值、分布规律和趋势上具有良好的一致性;对于全过程σ-ε曲线的各阶段,本文模型的计算效果较文献中本构模型计算效果更好,与试验曲线的贴合度更高,能够更好地反映高温作用下(后)岩石的损伤本构特征。该模型的参数具有常规性,适用于各类温-压组合作用工况下的岩石。

岩石卸荷的Mogi-Coulomb强度准则适用性研究

大量工程实践表明:岩石在卸荷条件下的强度特性与加载条件下相比,存在本质上的不同。结合岩石卸荷的破坏特征和强度特性,建立了岩桥贯通力计算模型,并基于应力强度因子叠加减原理,推导了岩石卸荷条件下的岩桥贯通力计算公式,从而探究Mogi-Coulomb强度准则对于岩石卸荷强度的适用性。将岩桥贯通力作为表征岩石卸荷破坏的强度参数,并与Mogi-Coulomb强度准则的核心参数——八面体剪应力进行对比,发现二者的量值具有极高相似性,这一发现可以间接证明Mogi-Coulomb强度准则适用于岩石卸荷强度方面的相关研究。本文揭示了岩石卸荷破坏时其岩桥贯通与八面体剪应力之间存在的紧密联系,可为岩石卸荷破坏的研究提供借鉴与参考。

考虑刚度与强度劣化的洞室围岩弹塑性分析

地下洞室锚固围岩进入塑性状态后其刚度与强度均会产生一定程度的劣化。将锚固围岩视为复合岩体并借助参数等效原则求出其刚度与强度参数后,基于D-P屈服准则得到了考虑劣化效应的深埋圆形洞室锚固围岩弹塑性解,借助FLAC-3D有限差分软件验证了该方法的可靠性后对相关影响因素进行了具体分析。研究结果表明:①考虑锚固围岩的刚度与强度同时劣化后得到的围岩变形量更符合实际;②残余黏聚力c"、残余内摩擦角φ"、残余弹性模量E"的大小对锚固塑性残余区半径Rb、洞壁位移u具有控制性作用,当c",φ",E"取值越大时,Rb,u便会越小,反之Rp、Rb、u便会越大;③软化模量Mc、Mφ对塑性残余区半径Rb、洞壁位移u的影响较大,对塑性软化区半径Rp的影响可以忽略;④系统锚杆与支护阻力pi协调作用下可以有效控制塑性残余区范围及围岩变形。

基于量化GSI系统对地下岩体力学参数的估算

地下岩体力学参数的准确获取可以为破碎岩体支护设计、采矿方法优化提供一定数据支撑,对保护井下作业人员安全起着重要作用。为准确、便捷获得地下岩体力学参数,采用岩体结构等级SR、岩体结构面等级SCR以及岩体完整性系数Kv 3个指标,通过多指标交集定量化获取GSI值,并结合地质强度指标GSI与扰动参数D之间存在的数理关系,量化扰动参数D,并应用Hoek-Brown强度准则确定岩体力学参数。将实际地质调查结果与室内岩石力学试验相结合,估算某地下铁矿岩体力学性能指标,发现矿体力学性能明显弱于围岩约60%,表明需加强进路巷道以及矿岩边界处的支护强度,该估算方法对地下岩体稳定性优化设计具有重要的指导意义。

缓倾软岩隧道底部结构劣化因素及影响机制分析

【目的】探明缓倾软岩隧道底部结构劣化的影响因素及影响机制,研究在不同围岩强度、岩层产状、地应力作用下的缓倾软岩隧道底部变形及塑性区发展趋势。【方法】基于Hoek-Brown强度准则和遍布节理本构模型确定数值模拟的力学参数并构建开挖模型,通过改变Hoek-Brown参数、岩层产状、地应力状态分析隧道的变形规律。【结果】深埋缓倾软岩隧道拱底两侧具有明显非对称变形,随着Hoek-Brown参数和围岩强度的提高,隧道拱底隆起量不断降低,且拱底两侧的非对称变形有所减弱并趋向于对称变形。当围岩强度较低时,围岩混合剪切型塑性区主要分布在拱底,基体剪切破坏主要分布在边墙,且剪切破坏范围随围岩强度的提高呈不断减小趋势。在倾角为0°~30°条件下,随着岩层倾角的增大,隧道底部隆起呈不断减小趋势,且拱底塑性区分布深度逐渐减小。随着岩层倾向角增大,隧道底部非对称变形和变形量增加,且拱底混合剪切塑性破坏区不断向深处延伸。随着侧压力系数和隧道埋深的增大,隧道仰拱处的变形量和变形速率比其他位置的大,且埋深的改变主要影响围岩塑性区体积和分布深度,而侧压力系数的改变还影响塑性区的分布形态。【结论】缓倾软岩隧道的变形发展趋势和塑性区破坏模式均与岩层产状有关,缓倾角条件下的拱底变形较大,且围岩节理剪切破坏主要发生在岩层倾斜方向上。该研究结果可为类似工程在施工过程中确定不利变形位置及优化支护方案提供参考。

寒区露天矿板岩冻融力学特性及边坡稳定性研究

为了探究寒区板岩边坡在冻融条件下的力学参数劣化规律及其失稳机理,通过室内冻融循环力学试验,并基于广义Hoek-Brown强度准则计算岩体内聚力和内摩擦角随冻融循环次数的衰减规律,以此修正未考虑冻融损伤的白云鄂博南帮内聚力和内摩擦角块体模型,实现南帮岩体力学参数的时空演化表征,最后通过数值模拟分析白云鄂博铁矿主矿区南帮边坡在冻融效应下的循序破坏机理。结果表明:经20次冻融循环后,矽质板岩、云母化板岩、碳化板岩、断层岩内聚力降低率分别为21.64%、22.66%、28.09%、28.53%,内摩擦角降低率分别为12.76%、14.72%、19.37%、21.35%;在冻融效应下,南帮边坡稳定系数由1.19逐渐降至0.92,1650~1570 m区域剪应变逐渐增大,最终滑体于1570 m平台滑移剪出。

基于双边滤波石质文物逆向建模及其稳定性分析

石质文物的长期稳定性问题是文物保护工作中的重点。以大足石刻卧佛前的目犍连菩萨像为研究对象,基于双边滤波算法,将三维激光扫描仪获取的点云数据导入PCL平台,实现文物表面噪声点的去除,建立包含裂隙结构面在内的菩萨像三维精细化实体模型。基于强度折减原理采用有限差分软件FLAC3D,对菩萨像现存状态展开稳定性分析,结果表明:1)双边滤波法去噪后的菩萨像模型平均偏差为-5.0~4.0 mm,标准值为1.1 mm,在去除噪声的同时完整保留了文物表面特征;2)重力荷载下,菩萨像颈部受压,项部受拉;头部裂隙的出现导致内部应力发生重分布,峰值拉应力由项部移动至裂隙端;3)菩萨像头部位移变化与折减系数呈正相关,当折减系数为1.28时,头部位移敏感度急剧增大,向临空面倾倒;4)菩萨像破坏面沿裂隙端、颈部向内部延伸,塑性区体积、最大剪应变增量逐步增大,在两区域形成抛物线贯通破坏面。该研究方法为小型、具有复杂几何特征的石质文物稳定性分析提供思路。

基于强度折减法的M-C强度准则在边坡中的稳定性分析

岩体是一种非均质、各向异性的非连续性材料,其力学特性研究较为复杂。Mohr-Coulomb强度准则(以下简称M-C)是岩土工程当中使用较多,且应用经验较为丰富的强度准则,采用能量型的M-C强度准则开展岩体理论研究具有一定的研究意义。基于此,以弹性应变能广义M-C强度准则(简称为GM-C)为基础,建立能量型广义M-C岩体强度准则(简称为EGM-C强度准则),同时将EGM-C强度准则嵌入到FLAC 3D软件中并进行模拟计算,验证该准则的适用性。理论分析表明:当岩体完整性系数K v等于1时该准则蜕变为GM-C强度准则;当岩体完整性系数K v等于1、材料变形参数νmc等于0.5时该准则蜕变为M-C强度准则。EGM-C强度准则是对GM-C强度准则和M-C强度准则的继承与发展,是以材料变形参数νmc、岩体完整性系数K v为参数的强度准则集合,并非单一强度准则;EGM-C岩体强度准则能够完全利用已有的M-C强度准则的研究成果,并将其应用于实际工程中;两组岩体试验数据验证得出:EGM-C强度准则略高于L.Y.Zhang提出的广义三维H-B岩体强度准则的计算值;同时将EGM-C本构模型嵌入到FLAC 3D有限元软件中并成功调用,在有限元软件中建立一个坡高为30m、未设边坡支护的边坡模型,采用M-C本构模型与EGM-C本构模型作对比分析,结果表明:M-C本构模型与EGM-C本构模型的塑性变形区域大致相似,但EGM-C本构模型与M-C本构模型计算得出的位移分别为8.6318cm、4.6117cm,EGM-C本构模型计算出的结果更偏于安全,这可能与EGM-C本构模型考虑了岩体完整性系数和材料变形参数有关。

基于多重判据的六苴矿区深部岩爆倾向性研究

以大姚六苴礅区矿山6个中段的3种岩性为研究对象,通过地应力测量、室内单轴抗压强度、巴西圆盘劈裂强度、弹性变形测量,结合E.Hoek判据、Russenes判据、徐林生判据、脆性判据对不同中段的岩爆倾向性进行分析。四种判据通过复合判据结合进行研判。研究结果表明:670中段会发生轻微岩爆~中等岩爆,710、740、770均无岩爆,800的紫红色细粒砂岩及860的矿石会发生轻微岩爆。基于多重判据的六苴矿区岩爆倾向性分析为地下矿山的岩爆灾害预防提供了一定的参考价值。

基于Mohr-Coulomb准则隧道围岩-支护体系协同作用下支护强度分析

确定围岩-支护结构体系动态协同变形关系是地下工程支护需要解决的关键问题之一。运用Mohr-Coulomb准则推导隧道开挖支护后围岩径向变形与支护结构径向变形的协同方程,探讨Ⅳ级围岩塑性半径、围岩位移及支护刚度随支护强度的变化关系;并运用FLAC3D数值模拟验证协同变形方程的合理性和有效性。结果表明,围岩-支护结构体系协同变形方程能很好地反映围岩位移和塑性区半径随支护强度变化的关系,且相互关系是非线性的。支护强度为0.75 MPa时,理论计算拱顶沉降为18.9 mm,数值模拟拱顶沉降为21.6 mm;支护强度为1.5 MPa时,理论计算拱顶沉降为11.2 mm,数值模拟拱顶沉降为11.1 mm,表明围岩-支护结构动态协同变形方程的有效性。针对Ⅳ级围岩在采用超前支护和交叉中隔壁法(cross diaphragm,CRD)施工时,建议支护强度设计为0.75~1.5 MPa,支护刚度设计为59.8~375.0 kN/mm。

基于图表法的岩质斜坡永久位移快速计算方法

岩质斜坡地震稳定性的快速评价是学者们关注的热点和难点。传统上,大多数研究采用图表法得到的安全系数快速评价岩质斜坡的地震稳定性,目前缺乏快速计算岩质斜坡临界加速度的方法。如何构建临界加速度模型是计算斜坡永久位移的前提条件。为此,采用有限元极限分析方法(平均界解)和广义Hoek-Brown强度准则,提出了一种快速计算岩质斜坡临界加速度的新方法。对概化岩质斜坡进行数值建模,基于1 960次的案例计算结果,绘制了岩质斜坡临界加速度图,通过2次拟合统计分析,构建了岩质斜坡临界加速度与斜坡几何条件和强度参数的函数表达式,并将本文方法与Newmark模型和数值解进行了比较。结果表明,本文方法的计算精度比Newmark模型更接近数值解。所开发的岩质斜坡永久位移计算方法高效、便捷,不仅能够用于单体斜坡地震稳定性的快速计算,还可以为计算区域尺度内大量斜坡的永久位移提供技术支撑。