A Procedure for Determining Rock-Type Specific Hoek-Brown Brittle Parameter <Emphasis Type="Italic">s</Emphasis>

The Hoek-Brown failure criterion constants m and s are equivalent rock friction and cohesion parameters, respectively. On the laboratory scale, m depends on the rock type and texture (grain size), while s = 1 for all rocks. On the field scale, m is a function of rock type, texture, and rock mass quality (geological strength index, GSI), while s is simply a function of rock mass quality. The brittle Hoek-Brown damage initiation criterion (m-zero criterion) is a modification to the conventional Hoek-Brown failure criterion with m = 0 and s = 0.11. The m-zero damage initiation criterion has been shown to better predict depths of failure in excavations in some moderate to massive (GSI ≥ 75) rock masses, but over predicts depths of failure in other rock types. It is now recognized that the Hoek-Brown brittle parameter (s) is not the same for all hard, strong, brittle, moderate to massive rock masses, but depends on the rock type. However, there are no guidelines for its determination for specific rock types. This paper presents a semi-empirical procedure for the determination of rock-type specific brittle Hoek-Brown parameter s from the rock texture, mineralogical composition, and microstructure. The paper also differentiates between brittle and tenuous rocks. It is shown that, while the use of the term ‘brittle’ is appropriate for rock mechanical excavation and mode of failure in weak rocks with limited deformability, it is inappropriate for use in explaining the difference in resistance to stress-induced damage in different rock types, and can cause confusion. The terms ‘tenacity/toughness’ are introduced to describe rock resistance to stress-induced damage in excavation performance assessment, and a rock tenacity/toughness rating system is presented.     

基于残余强度修正的岩石损伤软化统计本构模型研究

岩石随着围压的增大,残余强度的增加幅度比峰值强度大,残余强度逐渐成为影响岩石全应力-应变曲线峰后段的主要因素,因此,建立岩石损伤软化统计本构模型时,对残余强度进行修正是非常必要的。基于岩石应变强度理论以及岩石微元强度服从Weibull随机分布的假设,考虑岩石峰后残余强度对损伤变量进行修正,在微元破坏符合Hoek-Brown屈服准则条件下,建立了能够反映岩石峰后软化特征的三维损伤统计本构模型;依据岩石试验全应力-应变曲线的几何特征,推导出本构模型参数的数学表达式,并基于花岗岩室内试验数据对模型参数进行探讨,研究了Weibull分布参数与本构模型的关系,探讨了损伤修正系数的取值和岩石累积损伤的扩展过程;将建立的本构模型理论曲线与4种岩石（斑状二长花岗岩、细晶大理岩、砂岩和粉砂质泥岩）不同围压下的常规三轴压缩试验曲线进行对比分析,结果表明,该模型能很好地描述岩石破裂过程的全应力-应变关系和表征岩石残余强度特征。这对于岩石损伤软化问题以及岩石加固处理措施的研究均具有重要的意义。     

Elastic Solution for Deep Tunnels. Application to Excavation Damage Zone and Rockbolt Support

Summary  A new formulation is presented for deep circular tunnels in rock with cylindrical anisotropy. The formulation is an exact solution since it satisfies equilibrium, strain compatibility, and the anisotropic constitutive model. Complete solutions have been found for two scenarios: tunnel with excavation damage zone, and tunnel with rockbolt support. The solution is based on the assumption of a deep, circular tunnel in a medium with two homogeneous zones: an inner zone surrounding the tunnel, which is either isotropic or anisotropic, and an outer zone, for the remainder of the medium, which is isotropic. Plane strain conditions, elastic response of rock, rockbolts and support, and simultaneous excavation and support installation are also assumed. For tunnels surrounded by an excavation damage zone with reduced rock properties, the tangential stresses and the radial deformations at the tunnel wall are very sensitive to both the magnitude of stiffness reduction of the damaged rock and the size of the damaged zone. The effect of the rockbolts on the rock is approximated by treating the rockbolt-rock composite as a material with cylindrical anisotropy with stiffnesses related to the properties of the rock and rockbolts, and spacing of the rockbolts. Comparisons between the analytical solution and a numerical method show small differences and provide confidence in the approach suggested.     

多孔隙岩石加卸载力学特性及本构模型研究

为了研究岩石在加载-卸载过程中的应力-应变关系,以砂岩为例,对其进行常规三轴加卸载试验。分析了峰后卸载阶段岩石的非线性特性,对岩石的损伤变量进行定义,给出了峰后卸载过程中用于描述应力-应变关系的弹性模量模型。通过分析加载-卸载过程中的轴向应变与径向应变的关系,得到了卸载过程中泊松比模型。引入D-P塑性模型,针对砂岩的塑性硬化特性,对硬化函数进行修正,建立了与等效塑性应变相关联的损伤模型。将计算模型矩阵化后进行数值计算。在此过程中得到如下结论:多孔隙岩石在加载过程中表现出明显的非线性特征,随着体应力的增大,岩石的弹性模量逐渐增大。岩石峰后卸载过程中,当轴向应力大于围压时,应力-应变可以利用峰前弹性阶段的弹性模量模型乘以连续性因子进行描述。随着等效塑性应变的增大,泊松比先增大后减小,最终趋于稳定。峰后卸载过程中,等效塑性应变不发生变化,此时泊松比保持不变。利用提出的本构模型进行了数值计算,数值计算结果与试验结果进行对比,结果表明,提出的模型能够反映出岩石在峰后卸载过程中的应力-应变规律。     

岩体特性和岩体应力推算的回归分析

岩体的开挖改变了岩体的边界条件,扰动了岩体的原始应力场,并使岩体产生变形。岩体的这种变形综合地反映了岩体的结构和地质构造环境,变形的量值及其变化规律直观地反映了岩体的稳定性。量测分析岩体的变形对监视预测岩体的失稳和不支护安全运营的期限、确定岩体加固处理的方法等都有重要的意义。因此,岩体变形的量测在地下洞室、边坡等岩体工程的勘探、施工和运营中都广泛地开展着。     

基于摩尔-库仑模型的非线性本构模型的开发及其在应变局部化中的应用

以FLAC中的Mohr-Coulomb（M-C）本构模型为基础,在C++环境下实现了考虑拉伸截断的非线性本构模型的二次开发。针对应力及位移的分布规律,将理想弹塑性的Hoek-Brown（H-B）本构模型、M-C本构模型及自定义本构模型的数值解及H-B本构模型的理论解进行了比较,验证了自定义本构模型的正确性。采用弹-脆-塑性的自定义本构模型,以先加载,后挖洞的方式模拟了圆形巷道围岩的应变局部化过程,在计算模型的边界条件对称及均质本构参数的条件下,模拟出了4个对称的V型坑,模拟结果与静水压力条件下岩爆的现场观测及试验结果吻合,而采用接近脆性的H-B应变软化模型所得结果的对称性较差     

Determination of Shear Strength and Three-dimensional Yield Strength for the Hoek-Brown Criterion

Summary. Most currently used techniques for analysing the stability of near surface structures, such as rock slopes, are based on the application of the effective Coulomb shear strength parameters cohesion c′, and the angle of friction φ′ on some known or anticipated shear surface subjected to an effective normal stress σ′_n. The most widely used of these techniques are the variants of the method of slices and related upper bound techniques. If the Hoek-Brown criterion is to be used to model the strength of near surface fractured rocks, it is necessary to determine equivalent Coulomb shear strength parameters for the specified level of effective normal stress. Calculation of the equivalent Coulomb parameters for the Hoek-Brown criterion for cases when a ≠ 0.5 is not a straightforward matter. A simple procedure for calculating instantaneous values of c′_i and φ′_i has been developed based on spreadsheet calculations and the application of a numerical optimisation routine. This procedure can also be applied to calculating the Hoek-Brown envelope plotted in shear stress/normal stress space. A simple closed form solution for c′_i and tan φ′_i has also been developed for the special case when a = 1. A three-dimensional version of the Hoek-Brown criterion has been developed by combining it with the Drucker-Prager criterion. This new yield criterion has been implemented by numerical solution of the governing equations. A simplification of this three-dimensional yield criterion has been developed by introducing an intermediate principal stress weighting factor. Comparison with published results demonstrates that this simplified criterion has the capacity to model the results of true triaxial tests for a range of different rock types over a wide range of stress levels. The new three-dimensional yield criterion has the advantage that its input parameters can be determined from routine uniaxial compression tests and mineralogical examination.     

The importance of the effective intermediate principal stress (σ′2) to fault slip patterns

In normal faulting regimes, the magnitudes and orientations of the maximum and minimum principal compressive stresses may be known with some confidence. However, the magnitude of the intermediate principal compressive stress is generally much more difficult to constrain and is often not considered to be an important factor. In this paper, we show that the slip characteristics of faults and fractures with complex or nonoptimal geometry are highly sensitive to variation or uncertainty in the ambient effective intermediate principal stress (σ′₂). Optimally oriented faults and fractures may be less sensitive to such variations or uncertainties. Slip tendency (T_s) analysis provides a basis for quantifying the effects of uncertainty in the magnitudes and orientations of all principal stresses and in any stress regime, thereby focusing efforts on the most important components of the system. We also show, for a normal faulting stress regime, that the proportion of potential surfaces experiencing high slip tendency (e.g., T_s ≥ 0.6) decreases from a maximum of about 38% where σ′₂ = σ′₃, to a minimum of approximately 14% where σ′₂ is halfway between σ′₃ and σ′₁, and increases to another high of approximately 29% where σ′₂ = σ′₁. This analysis illustrates the influence of the magnitude of σ′₂ on rock mass strength, an observation previously documented by experimental rock deformation studies. Because of the link between fault and fracture slip characteristics and transmissivity in critically stressed rock, this analysis can provide new insights into stress-controlled fault transmissivity.     

偏压分岔隧道施工过程损伤破坏分析与优化研究

正在施工的沪蓉西高速公路八字岭分岔隧道属于偏压隧道,而且分岔隧道包括连拱段和小净距段,施工过程转换复杂,因此,采用正确的施工方案对于隧道的稳定性非常重要。为更真实地模拟岩体的力学特性,研究施工过程中岩体的损伤破坏,根据不可逆热力学理论建立了弹塑性损伤耦合模型,并编制了三维弹塑性损伤有限元程序D-FEM。建立了分岔隧道大型三维数值模型,采用弹塑性损伤有限元D-FEM模拟了分岔隧道不同的施工过程,通过分析施工过程中隧道围岩的位移、应力和损伤屈服区,最终确定采用左洞超前右洞32 m,左右洞同步开挖的施工方法。     

隧道开挖中围岩损伤演化分析及力学参数预测

数值方法所得出结论的可靠性很大程度上取决于岩体力学参数的选取,因此基于损伤演化分析,对损伤变量与围岩力学参数之间关系进行了研究。在各向同性损伤的假定下,通过分析开挖过程中围岩损伤演化,建立了采用损伤变量对弹性模量、泊松比、黏聚力、摩擦角等围岩材料参数进行估算的方法。采用弹性纵波波速定义初始损伤,根据壁城隧道现场监测资料建立ANSYS渐进性数值模型,反演典型断面开挖过程中围岩的宏观力学参数。分析结果表明,该方法可以有效地确定围岩力学参数的变化情况,与实际情况吻合较好。     

A Strain Rate Dependent Constitutive Model for the Lower Silurian Longmaxi Formation Shale in the Fuling Gas Field of the Sichuan Basin,China

Shale, as a kind of brittle rock, often exhibits different nonlinear stress-strain behavior, failure and time-dependent behavior under different strain rates. To capture these features, this work conducted triaxial compression tests under axial strain rates ranging from 5×10?6 s?1 to 1×10?3 s?1. The results show that both elastic modulus and peak strength have a positive correlation relationship with strain rates. These strain rate-dependent mechanical behaviors of shale are originated from damage growth, which is described by a damage parameter. When axial strain is the same, the damage parameter is positively correlated with strain rate. When strain rate is the same, with an increase of axial strain, the damage parameter decreases firstly from an initial value (about 0.1 to 0.2), soon reaches its minimum (about 0.1), and then increases to an asymptotic value of 0.8. Based on the experimental results, taking yield stress as the cut-off point and considering damage variable evolution, a new measure of micro-mechanical strength is proposed. Based on the Lemaitre’s equivalent strain assumption and the new measure of micro-mechanical strength, a statistical strain-rate dependent damage constitutive model for shale that couples physically meaningful model parameters was established. Numerical back-calculations of these triaxial compression tests results demonstrate the ability of the model to reproduce the primary features of the strain rate dependent mechanical behavior of shale.     

Application of the strain energy to estimate the rock load in squeezing ground condition of Eamzade Hashem tunnel in Iran

Estimation of rock load is a very important issue because the selection of a support system is highly related to this parameter. Several methods are used to estimate this parameter such as experimental, empirical, and numerical methods. This study propose a new empirical method to estimate the rock load in squeezing ground condition using actual collapses data of Emamzade Hashem tunnel of Iran based on the ration of the post-failure residual strain energy to the pre-failure stored strain energy. Prediction of squeezing ground condition in this study is performed based on Jethwa, Singh, and Hoek criterions. Results show that some sections in shale and sandstone of the Shemshak formation are prone to squeezing. Finally, the relation between the rock load and the ratio of the post-failure residual strain energy to the pre-failure stored strain energy, Ψ, in squeezing ground condition is estimated. Based on the statistical analysis, the maximum correlation between both parameters is achieved when Alejano’s equations are used to estimate the drop modulus. As the rock mass behavior changes from elastic–plastic to elastic–brittle, the drop modulus changes from 0 to infinite. The reason is that by increasing the quality of rock mass and reducing the minimum principal stresses, the ratio of post-failure residual strain energy to pre-failure stored strain energy and rock load height (H _p) reduce. So, regression analysis is used to investigate the relation between the rock load height and the ratio of post-failure residual strain energy to pre-failure stored strain energy, and finally, a formulation is presented to determine rock load height based on power function.     

Numerical analysis of the failure process around a circular opening in rock

Damage and fracture propagation around underground excavations are important issues in rock engineering. The analysis of quasi-brittle materials can be performed using constitutive laws based upon damage mechanics. The finite element code RFPA2D (Rock Failure Process Analysis) based on damage mechanics was used to simulate a loading-type failure process around an underground excavation (model tunnel) in brittle rock. One of the features of RFPA2D is the capability of modeling heterogeneous materials. In the current model, the effect of the homogeneous index (m) of rock on the failure modes of a model tunnel in rock was studied. In addition, by recording the number of damaged elements and the associated amount of energy released, RFPA2D is able to simulate acoustic activities around circular openings in rock. The results of a numerical simulation of a model tunnel were in very good agreement with the experimental test using the acoustic emission technique. Finally, the influence of the lateral confining pressure on the failure mechanism of the rock around the model tunnel was also investigated by numerical simulations.     

Characteristic Curves for Deep Circular Tunnels in Poroplastic Rock

A complete analytical solution for an axisymmetric deep tunnel excavated in a saturated poroplastic rock is presented. Results are found for short- and long-term analyses and for different drainage conditions at the rock–liner interface. In the derivation, the following assumptions are made: (1) circular cross-section, (2) deep tunnel, (3) plane strain conditions on a cross-section perpendicular to the tunnel axis, (4) axisymmetric loading, (5) the rock is saturated, homogeneous and isotropic, and (6) the rock is elastic-perfectly plastic with brittle failure and non-associated flow rule. The results obtained indicate that, if the rock remains elastic during construction, the stresses of the liner and the tunnel deformations are the same for short- and long-term conditions and are independent of the drainage conditions at the rock–liner interface and on the magnitude of Biot’s parameter α. If the rock yields, the stresses in the liner and the tunnel deformations strongly depend on the type of analysis. Effective radial and tangential stresses inside the rock decrease with Biot’s parameter α, while radial displacements increase. The response of the liner in terms of stresses and deformations strongly depends on its stiffness relative to the rock, yielding of the rock, groundwater and drainage conditions, and construction operations, while it is somewhat less sensitive to the rock’s poroplastic properties. Stresses and deformations inside the rock, however, show a much stronger dependency.     

Analysis of Critical Excavation Depth for a Jointed Rock Slope Using a Face-to-Face Discrete Element Method

Summary The critical excavation depth of a jointed rock slope is an important problem in rock engineering. This paper studies the critical excavation depth for two idealized jointed rock slopes by employing a face-to-face discrete element method (DEM). The DEM is based on the discontinuity analysis which can consider anisotropic and discontinuous deformations due to joints and their orientations. It uses four lump-points at each surface of rock blocks to describe their interactions. The relationship between the critical excavation depth D _s and the natural slope angle α, the joint inclination angle θ as well as the strength parameters of the joints c _r ,φ _r is analyzed, and the critical excavation depth obtained with this DEM and the limit equilibrium method (LEM) is compared. Furthermore, effects of joints on the failure modes are compared between DEM simulations and experimental observations. It is found that the DEM predicts a lower critical excavation depth than the LEM if the joint structures in the rock mass are not ignored.     

地应力与岩体模量关系的理论及试验研究

岩体模量（弹性模量及变形模量）是工程岩体力学特性的基础参数之一,研究地应力状态与岩体模量之间的关系具有重要意义.基于静弹性热力学模型原理,结合弹性理论,推导了水平主应力与岩体性质参数的定量关系,并对地应力与岩体模量的关系进行了探讨.在此基础上,以赣龙铁路梅花山隧道为依托,开展了围岩应力及岩体模量参数的现场测试工作,并将实测成果与理论分析进行对比.结果表明：当埋深影响较小时,花岗岩中的水平主应力与岩体模量呈线性正相关关系;当埋深相差较大时,深度对地应力及岩体模量的影响均不可忽略,水平主应力与岩体模量一般呈非线性关系,需要进一步研究;对花岗岩中的岩体弹性模量和变形模量与水平主应力之间的相关性进行对比发现,岩体变形模量与水平主应力的相关性更好.研究成果可为工程岩体力学参数取值及评价提供借鉴.     

利用室内和现场水压致裂试验联合确定地应力与岩石抗拉强度

钻杆式水压致裂原地应力测试系统的柔性会影响最大水平主应力的计算精度。利用空心岩柱液压致裂试验获得的岩石抗拉强度来取代重张压力计算最大水平主应力是降低钻杆式测试系统柔性的负面影响的重要途径。在福建某隧道深度为65 m的钻孔内开展了8段的高质量水压致裂原地应力测试,随后利用钻孔所揭露的完整岩芯开展了17个岩样的空心岩柱液压致裂试验。利用空心岩柱液压致裂所得的抗拉强度平均值为8.40 MPa,与经典水压致裂法确定的岩体抗拉强度8.22 MPa接近。对于20 m的范围内8个测段的原地应力量值,最小水平主应力平均值为8.41 MPa,基于重张压力P_r的最大水平主应力平均值为16.70 MPa;基于空心岩柱抗拉强度的最大水平主应力量值平均值为16.88 MPa,两种方法获得的最大水平主应力平均值基本一致。最大最小水平主应力与垂直主应力之间的关系表现为σ_H > σ_V > σ_h,这种应力状态有利于区域走滑断层活动。通过对比分析可知,对于钻杆式水压致裂原地应力测试系统,当测试深度小且测试系统柔性小时,基于重张压力和基于空心岩柱抗拉强度得到的最大水平主应力量值差别不大,这说明基于空心岩柱的岩石抗拉强度完全可以用于水压致裂最大水平主应力的计算,同时基于微小系统柔性的水压致裂测试系统获得的现场岩体强度也是可靠的。      

Rate constants of dissolution derived from the measurements of mass balance in hydrological catchments

The experimental rate constant of dissolution of oligoclase, 1.7 × 10 ^{? 2} mol · m^?2 · s^?1 (Busenberg and Clemency, 1976), is compared with rate constants, 5.2 × 10^?15 to 6.8 × 10^?13 mol · m^?2· s^?1, derived from mass-balance measurements of sodium in hydrological catchments. The wide range of the field-based rate constants mainly reflects the uncertainty in the evaluation of the specific wetted surface of rock in aquifer. The most probable order of magnitude of the field rate constant is 10^?14 mol · m^?2· s^?1. The difference between the experimental and field rate constant is only partly caused by lower temperature and lowerP_CO2 in the aquifer. The main reason for the discrepancy is the diverse history of the mineral surfaces undergoing reaction.It is suggested that the feldspar surfaces in an aquifer are old, compared to those of feldspars utilized in laboratory experiments. They have fewer defects and are smooth. The fresh surfaces of feldspars studied in the laboratory consist of many kinks and ledges and small-area terraces which dissolve faster.The differences in rate constants derived from field data on several specific catchments indicate that the anthropogenic processes which have operated during this century in Central Europe speed up the rate of dissolution by a factor of three. Modern agricultural practices speed up the rate by a factor of five.     

Memory Effects in Rock Salt Under Triaxial Stress State and Their Use for Stress Measurement in a Rock Mass

Summary Regularities of memory effects in rock salt specimens under triaxial stress state were investigated. Each specimen was subjected to two loading cycles. The first cycle was axisymmetric triaxial compression (σ₁ >σ₂=σ₃). The second cycle was uniaxial compression in the direction of σ₁ of the first cycle. Distinct acoustic emission (AE) and deformation memory effects were observed in the second cycle at the stress value equal to a linear combination of the first cycle principal stresses given by σ₁− (k + 1) σ₃, where k is about 0.5–0.6 for rock salt. Anomalies in deformation curves were found to be more reliable than the AE methods in distinguishing memory symptoms. The necessary pre-requisite for memory formation in the first cycle was that σ₁ exceeded the elastic limit, corresponding to the given confining stress σ₃. Inflections in uniaxial stress versus axial strain and lateral strain curves, in the second cycle, were observed at equal stress values if in the first cycle σ₁ exceeded the elastic limit and memory-forming damage was induced. If there was no memory-forming damage, those inflections were seen at different stress values. This characteristic was used to distinguish between true memory effects and natural characteristic points in deformation curves derived from rock salt testing. A new memory symptom was established, namely a turn point in curve “uniaxial stress versus differential coefficient of lateral strains”. The results form a basis for application of the memory effects for stress measurement in rock salt masses.