A failure criterion for transversely isotropic rocks

In this paper, a new failure criterion for the transversely isotropic rocks is presented. The new criterion is based on two distinct failure modes; one is the sliding mode where the failure is caused by sliding along the discontinuity, and the other is the non-sliding mode where the failure is controlled by the rock material and is not dependent on discontinuity. This failure criterion is defined with seven material parameters. The physical meanings of, and the procedures for determining, these parameters are described. Both the original Jaeger criterion and the extended Jaeger criterion are shown to be special cases of the proposed criterion. The accuracy and applicability of the proposed failure criterion are examined using the published experimental data. The data used cover various types of transversely isotropic rocks, different orientation angels and confining pressures. The predicted strength behaviors of the transversely isotropic rocks agree well with the experimental data from various investigators. The accuracy and applicability of the proposed empirical failure criterion are demonstrated in this paper.     

An approximate nonlinear modified Mohr-Coulomb shear strength criterion with critical state for intact rocks

In this paper, the Mohr-Coulomb shear strength criterion is modified by mobilising the cohesion and internal friction angle with normal stress, in order to capture the nonlinearity and critical state concept for intact rocks reported in the literature. The mathematical expression for the strength is the same as the classical form, but the terms of cohesion and internal friction angle depend on the normal stress now, leading to a nonlinear relationship between the strength and normal stress. It covers both the tension and compression regions with different expressions for cohesion and internal friction angle. The strengths from the two regions join continuously at the transition of zero normal stress. The part in the compression region approximately satisfies the conditions of critical state, where the maximum shear strength is reached. Due to the nonlinearity, the classical simple relationship between the parameters of cohesion, internal friction angle and uniaxial compressive strength from the linear Mohr-Coulomb criterion does not hold anymore. The equation for determining one of the three parameters in terms of the other two is supplied. This equation is nonlinear and thus a nonlinear equation solver is needed. For simplicity, the classical linear relationship is used as a local approximation. The approximate modified Mohr-Coulomb criterion has been implemented in a fracture mechanics based numerical code FRACOD, and an example case of deep tunnel failure is presented to demonstrate the difference between the original and modified Mohr-Coulomb criteria. It is shown that the nonlinear modified Mohr-Coulomb criterion predicts somewhat deeper and more intensive fracturing regions in the surrounding rock mass than the original linear Mohr-Coulomb criterion. A more comprehensive piecewise nonlinear shear strength criterion is also included in Appendix B for those readers who are interested. It covers the tensile, compressive, brittle-ductile behaviour transition and the critical state, and gives smooth transitions.     

A modified Hoek–Brown failure criterion for anisotropic intact rock

The Hoek–Brown criterion parameters (σ_ci, m_i and s) are significantly influenced by the strength anisotropy of intact rock. In the present study, the criterion was modified by incorporating a new parameter (k_β) to account for the effect of strength anisotropy, thus being able to determine the strength of intact anisotropic rock under loading in different orientations of the plane of anisotropy. The range of the parameter (k_β) for the rocks tested has been analytically investigated by carrying out triaxial tests, in different orientations of the foliation plane. The proposed modification was studied for metamorphic rocks (gneiss, schist, marble), but could also be applied to other rock types exhibiting “inherent” anisotropy, e.g. sedimentary as well as igneous rocks. The proposed modified criterion is intended for use for prediction of strength of intact rock, but can also be extended to rock masses.     

各向异性内摩擦材料强度准则的规范空间理论

利用固体力学规范空间理论 ,研究了内摩擦材料的强度机理 ,并从理论上给出了统一形式的各向异性强度准则 ,其中强度参数的个数等于材料异性子空间的数目。对各向同性情况 ,它退化成广义莫尔强度模型 ,对简单压剪受力状态 ,它退化成库仑强度模型。对工程常见各向异性 ,文章给出了强度准则公式 ,并详细讨论了强度参数的实验确定方法。最后给出了算例 ,并与现有强度模型进行了数值比较     

基于Griffith强度理论的岩石裂纹起裂经验预测方法研究

 裂纹起裂强度是岩石破坏过程中的重要应力阈值,研究岩石起裂准则对于揭示其破坏机制及预测围岩工程性质有着重要意义。首先进行青砂岩试样的单轴及三轴压缩起裂试验,并基于多种应变响应分析其中的起裂机制及细观破坏特征,指出局部张拉应力集中是起裂破坏的主因,总结提出低围压条件下的张开型起裂模型及高围压条件下的滑动型起裂模型。然后基于Griffith强度理论分析压应力场中岩石缺陷端部的局部最大张拉应力,其大小随差应力 的升高而增大,同时在围压条件下受表面摩擦作用的影响较大。针对岩石细观起裂机制提出起裂预测经验准则,准则中引入起裂参数 作为围压影响系数以表征摩擦作用,从而适用于不同围压条件下的起裂破坏预测。利用3组起裂试验结果对经验准则进行验证,其准确性及实用性明显优于传统线性起裂准则。最后通过分析不同围压下岩石起裂强度与峰值强度之比 ,发现试样在围压60 MPa以下时其起裂破坏属于细观张拉破坏机制。     

节理岩体Hoek-Brown经验强度准则可靠度分析

基于二滩水电站和溪洛渡的工程岩体实例,提出了岩体 Ｈｏｅｋ Ｂｒｏｗｎ 经验强度准则的可靠度计算方法,同时讨论了准则可靠度对 ｍ ,ｓ 等强度参数的变异系数的敏感性以及在三维岩体 Ｈｏｅｋ Ｂｒｏｗ ｎ 经验强度准则中第二主应力对可靠度的影响程度。通过分析指出, 强度参数的变异性是准则可靠度的决定性因素之一,因此, 岩体工程的详细勘察和试验以及对参数的变异性进行统计分析,对于工程设计来说是具有重大意义的。     

节理岩体Hoek-Brown经验强度准则可靠度分析

基于二滩水电站和溪洛渡的工程岩体实例,提出了岩体 Ｈｏｅｋ Ｂｒｏｗｎ 经验强度准则的可靠度计算方法,同时讨论了准则可靠度对 ｍ ,ｓ 等强度参数的变异系数的敏感性以及在三维岩体 Ｈｏｅｋ Ｂｒｏｗ ｎ 经验强度准则中第二主应力对可靠度的影响程度。通过分析指出, 强度参数的变异性是准则可靠度的决定性因素之一,因此, 岩体工程的详细勘察和试验以及对参数的变异性进行统计分析,对于工程设计来说是具有重大意义的。     

岩石黏结摩擦特性及非线性强度的指数准则描述

 岩石具有黏结和摩擦特性,但两者在同一位置并不同时存在。裂隙摩擦力随围压增加,达到邻近完整岩石黏结力后将不再滑移引起材料破坏,影响试样强度的裂隙倾角范围随之减小,引起强度非线性增加。主控裂隙引起强度在低围压下线性变化,但不能以Coulomb准则直接确定岩石的内摩擦角。砂岩内存在多种倾角的自然裂隙,引起单轴压缩及低围压的强度离散,围压增高裂隙影响减小,强度随围压规则变化而以指数准则描述;轴向压缩塑性变形引起大理岩黏结力由低向高逐步丧失,而热力损伤引起黏结力整体降低;冻结使岩石黏结力提高而内摩擦角不变。若岩石具有宏观各向同性特征,则常规三轴强度可用指数准则描述,据其确定的初始围压影响系数可估计裂隙摩擦系数;进而理解裂隙对试样强度影响的非线性特征,评价岩石材料的真实黏结力和损伤。     

Hoek-Brown强度准则的断裂力学理论研究

采用Griffith关于岩石内部微裂纹分布的假定,用一个角量 来表征三轴压力下岩石内微破裂密度,依据线弹性断裂力学中复合裂纹问题的有关准则,导出了 与外载的关系,进而以岩石受压过程中的细观现象为基础,选取 (即 对轴向应力的变化率)作为岩石在三轴压力下的破坏特征量,从理论上导出了与Hoek-Brown经验强度准则完全一致的强度公式。     

Stress influence Charts for transversely isotropic rocks

A graphical procedure to calculate stresses in a transversely isotropic half-space subjected to a three-dimensional surface load has been developed. The surface load can be distributed on an irregularly-shaped area. The planes of transverse isotropy are assumed to be parallel to the horizontal surface of the half-space. The closed-form solutions for stresses at a point under the vertex of a loading sector, with a unit load intensity are presented first. Based on these solutions, five influence charts are constructed for calculating the six components of a stress tensor at any given point in the half-space. The charts are composed of unit blocks. Each unit block is bounded by two adjacent radii and arcs, and contributes the same level of influence to the stress within the half-space. An example is presented to demonstrate the use of the new graphical method. For the case analyzed, results from the new graphical method agree with those of analytical solutions within 3%. The new influence charts can be a practical alternative to the existing analytical or numerical solutions, and provides results with reasonable accuracy.     

一种横观各向同性沉积岩的失效准则

通过定义初始屈服函数及由试验测定沉积岩的参数,提出了一般应力条件下岩石材料的失效准则,给出了该准则的数学表达式,对两种典型横观各向同性岩石强度特性的模拟结果表明,该准则能较好地反映沉积岩类材料在一般应力条件下的强度变化规律。     

基于非线性动态强度准则的岩石动态变形过程统计损伤模拟方法

 岩石动态应变率对岩石动态变形过程具有极其重要的影响,因此,首先考虑岩石动态应变率对岩石强度的非线性影响特点,通过对现有岩石动态强度准则进行改进,建立反映应变率影响的非线性岩石动态强度准则,为岩石动态变形过程模拟方法研究奠定了坚实的基础;然后,采用本文非线性动态强度准则,在重点探讨考虑应变率影响的岩石微元强度度量方法基础上,引入统计损伤理论建立岩石动态统计损伤本构模型,并提出基于岩石动三轴试验曲线的模型参数确定方法,进而建立岩石动态变形过程模拟方法。它不仅能反映应力状态而且能反映应变率对岩石变形过程的影响;最后,通过与现有同类模型理论曲线以及相应试验曲线的比较分析,表明了提出模型与方法的合理性与优越性。     

A new strength criterion for structured soils

Existing strength criteria are mostly formulated to describe the mechanical properties of reconstituted soils. However, the engineering characteristics of structured soils are different from those of reconstituted soils in many aspects, especially in their strength properties. Thus, the influence of soil structure (bonding and fabric) on the mechanical properties of structured soils cannot be correctly described. By analyzing the breakage mechanism of natural soils, the structured soils can be conceptualized as binary medium materials consisting of bonded blocks and weakened bands. On this basis, a new strength criterion is proposed for structured soils. The expressions of the strength criterion on both meridian and deviator planes are given to describe the strength properties of structured soils on these planes. The proposed strength criterion is compared with available test data under conventional and true triaxial stress conditions in the literature. It is observed that the proposed strength criterion agrees well with the test data.     

横观各向同性砂土的强度准则

提出了一个物理意义清晰且满足客观性原理的横观各向同性砂土的强度准则。通过对典型试验结果的观察,总结了各向异性粒状材料峰值强度随加载方向的变化规律。分析了强度发挥的物理机制,定义了一个新的无量纲各向异性参量Λ(σ,F),用于度量应力张量与组构张量的相对方位。利用该各向异性参量将SMP准则推广,得到一个新的适用于横观各向同性砂土的强度准则。在沉积面方位已知的情况下,该准则只需确定两个试验参数kf0和k,其中kf0代表基准强度,k代表各向异性程度的大小。kf0和k通过两个加载方向不同的破坏试验即可确定。通过物理试验和数值试验结果初步验证了该准则的有效性。     

Foliation index determination for fine-grained metamorphic rocks

The fine grain size of rocks such as slates, phyllites and hornfelses limits the accurate determinations of their foliation index values using the optical microscope. An experimental study has therefore been undertaken for a more relevant approach to evaluating the index. X-ray diffractometry on rock specimens at extreme orientations is ideal. The rock types studied fit well into a proposed classification scheme. This reaffirms that foliation index is a reliable parameter for the quantitative fabric characterization of metamorphic rocks which bears a practical significance to their engineering performance.