Analysis of random anisotropic damage mechanics problems of rock mass

Summary A probabilistic analysis method of random anisotropic damage mechanics problems is proposed in parts I and II. In part I, based on the measured characteristics of random crack distribution on the surface of a rock specimen, a probabilistic distribution law of damage variables for rock mass is presented as a Beta distribution by using the Monte-Carlo statistical simulation method. In part II, statistical estimation of a damage state and properties of random damaged rock mass are evaluated by Rosenblueth's point estimate method. Combining with the F. E. method, rock mechanics problem for random damaged state have been analyzed.     

Fuzzy-random probabilistic analysis of rock mass responses to explosive loads

This paper addresses the effects of randomness of initial damage in a rock mass and the critical tensile strain of the rock material on its dynamic responses and damage under explosive loads. A fuzzy definition is proposed to describe the fuzzy nature of failure phenomenon in a rock mass. The initial damage of the rock mass is estimated using the longitudinal and transverse elastic wave velocities. By using statistical analysis, the initial damage of the rock mass is found having the Beta distribution. The statistical estimation of a damage state and properties of randomly damaged rock mass are evaluated by the Rosenbluth's point estimate method. In numerical calculation, an isotropic continuum damage model with the initial damage and the cumulative damage dependent on an equivalent tensile strain is suggested to model the rock mass behavior under blast loads. A Beta distribution is proposed to represent the probabilistic distribution of the damage variable of the rock mass under explosive loads. Several types of membership functions are suggested to represent the fuzziness of material failure. Based on the fuzzy–random probabilistic theory, a model including both the effects of randomness and fuzziness is proposed for the failure analysis of rock mass under explosive loads. The suggested models are coded and linked with an available computer program AUTODYN2D through its user's subroutine capacity. The fuzzy failure probability and dynamic responses of the rock mass are calculated. Numerical results are compared with those obtained from independent field tests.     

Numerical Analysis of Blast-Induced Stress Waves in a Rock Mass with Anisotropic Continuum Damage Models Part 2: Stochastic Approach

Summary This paper reports the second part of the study carried out by the authors on the underground explosion-induced stress wave propagation and damage in a rock mass. In the accompanying paper reporting the first part of the study, equivalent material properties were used to model the effects of existing cracks and joints in the rock mass. The rock mass and its properties were treated as deterministic. In this paper, existing random cracks and joints are modeled as statistical initial damage of the rock mass. In numerical calculation, an anisotropic continuum damage model including both the statistical anisotropic initial damage and cumulative damage dependent on principal tensile strain and stochastic critical tensile strain is suggested to model rock mass behavior under explosion loads. The statistical estimation of stress wave propagation in the rock mass due to underground explosion is evaluated by Rosenblueth's point estimate method. The suggested models and statistical solution process are also programmed and linked to Autodyn3D as its user's subroutines. Numerical results are compared with the field test data and those presented in the accompanying paper obtained with equivalent material property approach.     

节理岩体力学性能不确定性分析方法研究

基于连续介质损伤力学框架,通过损伤张量和有效应力来描述节理岩体的力学性能,自主研发了基于损伤力学模型的有限元程序（CD-FEM）,用于节理岩体等效力学性能研究。同时,采用Karhunen-Loeve（K-L）展开来分解随机输入场,用混沌多项式来表示随机输出场,采用概率配点法生成配点,再由连续损伤有限元分析系统CD-FEM求解确定性方程组,最终得到输出域的统计数据,从而提出了一种将随机分析与基于连续损伤力学模型的数值分析方法解耦进行节理岩体不确定性力学行为分析的方法。利用该方法,对一典型节理岩体在加载条件下的力学行为进行不确定性分析,并与蒙特卡罗方法进行对比,结果表明,所提方法的计算量大大减少,极大地提高了节理岩体力学性能不确定性分析的效率,可应用于对节理岩体在不同载荷条件下的不确定性进行分析。     

Statistical Analysis of Anisotropic Damage of the Bukit Timah Granite

Summary This paper presents a method to analyze probabilistic anisotropic initial damage of a rock mass. A three-dimensional geometric model of cracks in a rock mass is established in terms of several parameters, such as orientations, spacing and normalized sizes of cracks in the rock mass. The dip, dip direction, spacing, and normalized size of cracks of the Bukit Timah granite in Singapore were obtained from visual inspection of rock cores, color TV imaging, and impression packer tests in the boreholes at a site of geological investigation. Using the measured data, probabilistic distribution laws of geometric parameters of cracks on the surface of the boreholes are derived. Based on these statistical distributions and using Monte-Carlo simulation method, the distribution of anisotropic initial damage of the Bukit Timah granite is derived and found to have a beta distribution. This anisotropic initial damage distribution of a rock mass can be used in probabilistic analysis of rock mass responses to both static and dynamic loads.     

Comparative study on three-dimensional statistical damage constitutive modified model of rock based on power function and Weibull distribution

According to the characteristics of the microscopic unit strength of rock with random distribution, the power function distribution, and the Weibull distribution which is widely used in the past as the distribution function of the strength of the rock. Based on the theory of rock damage and statistical strength theory, two damage constitutive models established under three different confining pressures are modified. Then, the damage constitutive modified model of two kinds of distribution is verified and compared with the existing three axis test data. The results show that: (1) In the stage of elastic deformation of rock, the two theoretical damage constitutive model curves are in high agreement with the three axis test curve; (2) The rock at the plastic stage (hardening and softening), damage constitutive model established by Weibull probability distribution and experimental curve fits better than the damage constitutive model established by power function distribution. Especially in high confining pressure, damage constitutive model based on Weibull distribution can well describe the rock deformation from brittle to ductile transition process and power function is not; (3) In the residual strength in rock, damage variable D of damage constitutive model based on power function distribution appeared more than 1, which is deviation from the actual one and damage constitutive model based on Weibull distribution is not deviating. To summarize, using Weibull distribution statistical probability model to describe the microscopic unit strength of rock is more reasonable.     

参数型岩石几何损伤模型的构建及其应用研究

岩石几何损伤模型是建立统计损伤本构模型的重要基础。在岩石变形力学特性基础上对现有岩石几何损伤模型进行了回顾性分析,针对它们难以较好地反映初始损伤特征和峰后变形破坏特征的缺陷与不足,首先,将岩石材料视为由未损伤部分、初始损伤部分和后继损伤部分组成,提出了考虑初始损伤的岩石几何损伤模型;然后,通过探讨Weibull分布参数m和F0对损伤变量变化产生的影响,构建了参数型岩石几何损伤模型,在此基础上建立了应变软化类岩石统计损伤本构模型并进行了修正,给出了模型参数的确定方法;最后,通过模型验证和参数分析表明,修正后模型能够较好地模拟岩石变形破裂全过程,参数l和h对损伤变量变化产生的影响与m和F0等效,解决了现有岩石几何损伤模型存在的共性问题,该模型和方法具有一定的合理性和可行性。     

基于摩尔-库仑准则的断续节理岩体复合损伤本构模型

针对工程实际中断续节理裂隙岩体的损伤本构模型,假设岩石微元强度服从Weibull随机分布,以摩尔-库仑破坏准则作为描述微元强度的表示方法,推导出细观损伤变量。利用能量和断裂力学理论,综合考虑节理几何特征及力学特性,推导宏观损伤变量计算公式。基于Lemaitre应变等效假设,考虑宏细观缺陷耦合作用,推导出复合损伤变量,建立了基于摩尔-库仑准则的宏细观缺陷耦合作用的断续裂隙岩体损伤本构模型。研究结果表明：（1）采用摩尔-库仑准则作为描述微元强度的统计分布变量建立的损伤模型能够较好地反映岩石内部缺陷分布和变形特征,该模型真实地反映岩石微元强度受应力状态的影响。（2）该模型建立的理论曲线与断续节理岩体的试验曲线吻合较好。（3）节理裂隙岩体宏观损伤变量及峰值强度随节理倾角的变化规律与综合考虑宏细观耦合作用下的损伤变量及裂隙岩体峰值强度随节理倾角的变化规律基本一致。（4）宏细观耦合作用下的等效弹性模量与节理贯通率呈非线性负相关;在节理倾角一定的情况下,损伤变量与节理长度呈非线性正相关;在贯通率较小时,岩体的宏观损伤变量与内摩擦角的关系呈线性负相关变化,贯通率达到一定程度,线性关系变成非线性关系。     

裂隙延展性统计分布离散性对岩体块体化程度REV的影响

表征单元体(REV) 的存在是应用连续介质力学方法对岩体进行研究的前提,REV可以从岩体块体化程度的角度进行研究,裂隙大小及其统计分布是影响岩体块体化程度REV的重要因素。本文利用课题组自主研发的GeneralBlock 软件,建立更一般化实际化的模型,研究裂隙延展性统计分布的离散程度对岩体块体化程度REV的影响。分析时选取了最常用的裂隙延展性统计分布形式:正态分布。由于所建立的岩体结构模型是随机的,需要对每个随机裂隙模型进行多次实现。为节省计算量,当研究范围比较小时,对每种结构的每个研究范围进行9次随机实现。当研究范围足够大,达到REV大小的时候进行100次随机实现。为确定离散程度对表征单元体的影响,本文针对5个不同标准差进行了模拟分析（共建立了1 005个裂隙模型,分别进行了块体识别并计算其块体化程度B）。结果表明,裂隙延展性服从正态分布的情况下,如果其平均值一定,岩体的块体化程度随着统计分布离散程度的增加略有上升,裂隙岩体的REV值基本上由裂隙延展性统计平均值决定。     

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。     

基于三维结构面网络模拟的岩体变形模量确定方法

变形模量作为表征岩体变形特征的重要参数,是岩体工程设计的基础力学参数之一。在综合前人研究的基础上提出了基于三维结构面网络模拟确定岩体变形模量的方法,编制了三维结构面网络模拟及计算RQD值的程序。以西南山区某水电站坝址区岩体为实例,在概率统计各组优势结构面几何要素分布形式的基础上,采用Monte Carlo法生成三维结构面网络模型,据此获得岩体三维RQD值,利用RMR法进行质量评价和变形模量的确定,并与钻孔资料统计法和原位试验结果进行对比分析。结果表明:基于钻孔资料统计的估算结果与原位试验相对误差达31.62%,且其估算值偏低;基于三维结构面网络模拟的估算结果与原位试验相对误差仅为2.56%,估算结果精度较高。该方法考虑了岩体质量的空间各向异性,对岩体的质量评价和参数确定更为合理,研究成果为该工程的优化设计提供了合理的计算参数。      

边坡模糊随机可靠性分析的模糊点估计法

在统计矩点估计法和模糊随机理论的基础之上,提出边坡工程模糊随机可靠性分析的模糊点估计法,将边坡稳定性极限状态方程由模糊随机集向普通随机集转化,然后利用点估计法求解边坡的可靠度指标。鉴于岩土体物理力学参数的近似分布类型,采用区别于梯形模糊数的正态模糊数对随机变量进行模糊随机化处理,使其更趋近于物理力学参数的近似分布类型。该方法考虑了各个力学参数的模糊性,计算结果更能反映边坡的真实工作状态。算例分析结果表明,该法使用简便,计算效率高,结果可靠,避免了传统分析方法的缺点,对复杂边坡或者功能函数为隐式表达的边坡工程可靠性分析具有很大的潜力,为边坡可靠性分析提供了一条新的途径,具有广泛的应用前景。     

裂隙岩体变形模量尺寸效应研究Ⅰ:有限元法

通过对裂隙交叉和非贯通裂隙进行的网格剖分研究,建立了随机裂隙岩体网格生成方法,并编制了裂隙岩体有限元网格自动生成程序。根据锦屏电站辅助洞白山组大理岩裂隙分布调查结果,用蒙特卡洛法生成随机裂隙网络,进行了岩石-裂隙二元岩体网格自动剖分,将试验室获得的岩石和裂隙的力学参数分别赋予岩体模型中的岩石和裂隙,通过有限元方法研究了裂隙岩体等效变形模量的尺寸效应和各向异性。尺寸效应研究结果表明,所研究的裂隙岩体的等效变形模量表征单元体REV为8 m;各向异性研究结果表明,在REV尺寸下,所研究的裂隙岩体各个方向变形模量可以通过柔度张量进行拟合,且张量拟合误差不超过8%。     

岩石时效损伤模型及其在工程爆破中应用

为了实现爆破智能化,降低爆破带来的负面影响,通过数值模拟预估出岩体中爆破诱发损伤的大小以及分布范围在工程上具有重要意义,其中科学合理的爆破损伤模型是关键。基于岩石介质是连续的、各向同性的、且存在初始裂纹的假设,把考虑时效的岩石拉裂损伤演化方程和双线形弹塑性本构结合起来,通过用户自定义简明地嵌入到大型LS-DYNA软件中,并引入了该软件中的侵蚀算法,对半无限岩体中临空面附近爆破漏斗问题进行了重点数值模拟,计算结果比较接近实际。本文方法在工程中将具有一定的参考价值。     

单轴压缩条件下岩溶化裂隙岩体损伤破坏特征研究

岩溶化裂隙岩体是普遍发育于自然界中具有初始损伤的岩体。为了研究岩溶化裂隙岩体损伤破坏特征,本文以贵州某地赋存的溶蚀岩体为研究对象,运用损伤力学理论构建岩溶化裂隙岩体在单轴压缩条件下的损伤演化模型,并建立岩溶化裂隙岩体损伤演化方程。采用颗粒流数值软件进行单轴压缩数值试验,进一步研究岩溶化裂隙岩体试件在单轴压缩条件下的损伤演化特征,分析岩溶化裂隙岩体的微观损伤特征。结果表明：岩溶化裂隙岩体的初始损伤主要包括溶蚀损伤和裂隙损伤。岩溶化裂隙岩体的初始损伤随着溶蚀率的增加而增加,最终增加速率趋于平缓;岩溶化裂隙岩体的损伤演化曲线均呈“S”型变化,先缓慢增加,再迅速增加,最后缓慢增加至损伤值1;岩溶化裂隙岩体存在异构特征,导致破坏裂隙起源于具有初始损伤的溶蚀孔洞和裂隙处,随后裂隙经历萌发、扩张和剪切作用、数量和长度增加以及裂隙贯通4个阶段后发生宏观破坏。     

高地应力条件下爆破开挖诱发围岩损伤的特性研究

高地应力条件下隧道或硐室钻爆开挖需考虑初始地应力动态卸荷效应,同时其最终损伤形态会受多个因素影响。采用三维有限差分软件FLAC3D讨论了爆破荷载与地应力动态卸荷复合作用下隧道围岩损伤分布,并重点研究了侧压力系数、岩体力学性质、卸荷速率对围岩损伤范围的影响,最后通过赣龙铁路梅花山隧道开挖损伤区检测结果进行了验证。研究表明,考虑动态卸荷效应的围岩损伤范围明显大于只考虑爆破荷载作用下的围岩损伤范围,在中高地应力条件下,初始地应力动态卸荷对围岩的损伤破坏作用不可忽视;随着侧压力系数逐渐增大,损伤区形态呈现明显的方向性,当侧压力系数为1时,损伤区沿开挖轮廓面分布较为均匀,侧压力系数不为1时,损伤区主要向小主应力方向集中;岩石力学性质越好,损伤范围越小;卸荷速率越快,围岩损伤范围越大,但影响并不十分显著。结果可为高地应力下隧道开挖稳定性分析和支护设计提供一定参考。     

基于统计强度理论的破裂岩体本构模型研究

借助损伤力学思想,基于统计强度理论,提出一种适用于深部工程破裂区破裂岩体的本构模型建立方法,并通过室内试验和数值试验进行了验证。将破裂岩体划分为无数微元立方体,微元立方体的强度与岩石破裂程度有关,且各立方体强度随机分布,故可用强度反映破裂岩体的破裂程度,据此提出一种破裂岩体本构模型建立方法。其中,根据岩石破裂面间的摩擦力做功等于材料破裂后释放的应变能,得到从力学角度定义的岩石破裂程度变量;另外,假定微元立方体强度分布服从Weibull分布,应力水平满足Hoek-Brown准则。利用泥质砂岩破裂岩体典型三轴试验结果,建立泥质砂岩破裂岩体本构模型,并进行了验证,结果表明模型计算曲线与试验曲线吻合度较好。利用离散元软件PFC进行了补充数值试验验证研究,证明了泥质砂岩破裂岩体理论模型的良好计算效果,进而证明提出的本构模型建立方法的可行性。     

The Dynamic Evaluation of Rock Slope Stability Considering the Effects of Microseismic Damage

A state-of-the-art microseismic monitoring system has been implemented at the left bank slope of the Jinping first stage hydropower station since June 2009. The main objectives are to ensure slope safety under continuous excavation at the left slope, and, very recently, the safety of the concrete arch dam. The safety of the excavated slope is investigated through the development of fast and accurate real-time event location techniques aimed at assessing the evolution and migration of the seismic activity, as well as through the development of prediction capabilities for rock slope instability. Myriads of seismic events at the slope have been recorded by the microseismic monitoring system. Regions of damaged rock mass have been identified and delineated on the basis of the tempo-spatial distribution analysis of microseismic activity during the periods of excavation and consolidation grouting. However, how to effectively utilize the abundant microseismic data in order to quantify the stability of the slope remains a challenge. In this paper, a rock mass damage evolutional model based on microseismic data is proposed, combined with a 3D finite element method (FEM) model for feedback analysis of the left bank slope stability. The model elements with microseismic damage are interrogated and the deteriorated mechanical parameters determined accordingly. The relationship between microseismic activities induced by rock mass damage during slope instability, strength degradation, and dynamic instability of the slope are explored, and the slope stability is quantitatively evaluated. The results indicate that a constitutive relation considering microseismic damage is concordant with the simulation results and the influence of rock mass damage can be allowed for its feedback analysis of 3D slope stability. In addition, the safety coefficient of the rock slope considering microseismic damage is reduced by a value of 0.11, in comparison to the virgin rock slope model. Our results demonstrate that microseismic activity induced by construction disturbance only slightly affects the stability of the slope. The proposed feedback analysis technique provides a novel method for dynamically assessing rock slope stability and can be used to assess the slope stability of other similar rock slopes.     

综合考虑宏微观复合损伤的节理岩体本构模型

针对目前节理岩体损伤本构模型中仅考虑节理等宏观缺陷造成的损伤,而没有考虑岩块中微裂纹等微观损伤的不足,提出了综合考虑宏微观损伤的节理岩体本构模型。其中微观损伤模型采用基于应变强度理论和岩石微元强度服从Weibull分布假定的统计损伤模型,把其应用于被节理切割而成的岩块。而宏观损伤模型主要基于连续介质力学原理,把节理对岩体性质的劣化作为损伤来考虑。在考虑节理传压及传剪系数的基础上,提出了综合考虑宏微观复合损伤的节理岩体本构模型。算例表明宏观节理的存在大大削弱了岩体的强度,降低了其刚度,增大了其柔性。所提出的模型能够较好地反映宏微观两类损伤对岩体应力-应变关系及强度的影响,较为合理。      

Application of extended Kalman filter to back analysis of the natural stress state accounting for measuring uncertainties

In this work, we present a numerical procedure for determining the nature stress state in the rock mass around a tunnel. A finite element method is applied for analyzing the direct problems of tunneling during the back analysis of parameter estimation, in which a no‐tension elastic–plastic model is used to simulate the elastic–tensile and elastic–plastic‐tensile failure states which often occur in the cases of underground excavation in heavily jointed rock masses. By considering the natural stress state as random parameters of the tunneling system, the Kalman filter method is employed for feedback analysis to modify the parameter values in a statistical context, which uses the prior information in the process of estimation and employs a set of displacements obtained from field measurements. To verify the effectiveness of the proposed method of inverse analysis, the developed numerical procedure is applied to a synthetic example of deep tunnels in yielding rock masses. The relative importance of the a priori and updating information is investigated, as is the importance of their uncertainty. The results show great potential of the proposed approach. Copyright © 2010 John Wiley & Sons, Ltd.