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.     

Numerical prediction of blast‐induced stress wave from large‐scale underground explosion

This paper presents a numerical model for predicting the dynamic response of rock mass subjected to large‐scale underground explosion. The model is calibrated against data obtained from large‐scale field tests. The Hugoniot equation of state for rock mass is adopted to calculate the pressure as a function of mass density. A piecewise linear Drucker–Prager strength criterion including the strain rate effect is employed to model the rock mass behaviour subjected to blast loading. A double scalar damage model accounting for both the compression and tension damage is introduced to simulate the damage zone around the charge chamber caused by blast loading. The model is incorporated into Autodyn3D through its user subroutines. The numerical model is then used to predict the dynamic response of rock mass, in terms of the peak particle velocity (PPV) and peak particle acceleration (PPA) attenuation laws, the damage zone, the particle velocity time histories and their frequency contents for large‐scale underground explosion tests. The computed results are found in good agreement with the field measured data; hence, the proposed model is proven to be adequate for simulating the dynamic response of rock mass subjected to large‐scale underground explosion. Extended numerical analyses indicate that, apart from the charge loading density, the stress wave intensity is also affected, but to a lesser extent, by the charge weight and the charge chamber geometry for large‐scale underground explosions. Copyright © 2004 John Wiley & Sons, Ltd.     

某地下电站厂房围岩稳定性及锚固效应研究

某地下电站厂房围岩属于一种断续节理裂隙切割的节理岩体,其围岩采用了锚杆、锚索加固。作者采用三维断续节理岩体的弹性损伤本构模型、损伤演化方程及损伤岩锚柱单元支护模型分析围岩加固前后的稳定情况,结果表明,能较好地反应围岩的渐近破坏过程和锚杆（索）的加固效果。这些理论成果对设计有参考价值,并对工程实践有指导意义。     

Numerical Analysis of Blast-Induced Stress Waves in a Rock Mass with Anisotropic Continuum Damage Models Part 1: Equivalent Material Property Approach

Summary This paper uses the concept of anisotropic damage mechanics to analyze dynamic responses of a granite site under blasting loads. An anisotropic continuum damage model is suggested to model rock mass behavior under blasting loads. The effects of existing cracks and joints in the rock mass are considered by using equivalent rock material properties obtained from both field and laboratory test data. The anisotropic damage accumulations are simulated by continuous degradation of equivalent material stiffness and strength during loading process and are calculated using the exponential function with respect to the principal tensile strain in three directions. The suggested models are programmed and linked to an available computer program Autodyn3D through its user's subroutine capability. Stress wave propagation and damage zone in the rock mass induced by underground explosions are simulated. Numerical results of damaged area, peak particle velocity and acceleration attenuation as well as acceleration time histories and Fourier spectra are compared with those from independent field tests.     

Discrete element modelling of an underground explosion in a jointed rock mass

The purpose of this paper is to investigate the application of the discrete element program UDEC for modelling underground explosions in a jointed rock mass. A field underground explosion test has been conducted and UDEC and AUTODYN were utilised in a coupled manner to predict the rock mass response due to the underground explosion. The dynamic equation for the state of the rock material obtained from impact tests was incorporated into the calibration modelling. The comparison of modelling results with test results and empirical formulas shows that UDEC is capable of modelling explosion wave propagation in jointed rock mass with high reliability.     

不同倾角节理组和锚固效应对岩体特性的影响

首先采用DDARF(discontinuous deformation analysis for rock failure)分析方法对双裂隙岩块进行单轴和双轴压缩模拟试验,研究了裂隙角度和侧向应力大小对岩块特性的影响,得到了裂隙岩块在这两种加载试验中的破坏过程、应力-应变曲线以及岩块中裂隙的起裂应力和岩块的峰值强度。在双轴压缩模拟试验中绘制了裂隙角度为45°的岩块在不同侧向压力下的强度包络线。其次,采用DDARF分析方法模拟劈裂试验中含裂隙试块的锚固效果,得到了4种不同锚固角度试块的轴向荷载–位移变化曲线和裂隙扩展规律。模拟结果与前人的类似条件下的试验结果相符良好。随后又将双裂隙试块双轴压缩模拟试验中得到的参数运用到一个地下洞室的工程实例中,用等效力学特性的方法分析对比了完整岩体和节理岩体洞室开挖完成后的破损状态的差异。最后运用DDARF分析方法研究了随机生成4组节理岩体的地下洞室的稳定性,得到了洞室节理围岩的裂隙扩展过程。同时通过对关键点位移的监测分析了锚杆的锚固效应。     

考虑岩体劣化的大型地下厂房围岩变形动态监测预警方法研究

针对大型地下厂房洞室开挖后围岩力学参数发生劣化的事实,以及大型地下厂房允许变形无相关规范参考的缺陷,在分析地下厂房围岩失稳机制基础之上,基于强度折减法思想,提出大型地下厂房围岩劣化折减计算方法,建立围岩变形的动态预警路线体系。该体系应用屈服接近度指标确定围岩的劣化区域,折减劣化区域内的变形模量、凝聚力及抗拉强度值,在折减计算过程中依据围岩的变形、劣化区体积、释放能量三者之一发生突变作为围岩失稳判据,获得围岩失稳的变形预警值,并与现场变形监测值对比分析,从而实现围岩稳定状况的快速判别。地下厂房实例分析表明,该方法可为洞室稳定性判断提供定量依据,较好地满足了地下工程建设需要。     

单轴压缩荷载下非贯通闭合节理岩体损伤本构模型

目前损伤力学已被认为是研究节理岩体力学行为的有效工具,但是在目前的节理岩体损伤变量定义中大多仅考虑节理几何特征而未考虑节理内摩擦角等力学参数,这显然不能很好地反映节理岩体的力学特征。为此,拟推导出一个能够综合考虑节理几何及力学参数的损伤变量（张量）,并由此建立单轴压缩荷载下岩体损伤本构模型。首先,基于断裂力学的由于单个节理存在引起的附加应变能增量与损伤力学的损伤应变能释放量相关联的观点,推导出了含非贯通节理岩体的损伤变量计算公式;其次,根据断裂力学理论对单轴压缩荷载下的单个节理尖端应力强度因子计算方法进行了研究,得出了应力强度因子K_Ⅰ、K_Ⅱ的计算公式;同时考虑多节理间的相互作用给出了单组单排及多排非贯通节理应力强度因子计算公式。最后,利用该模型对含单条非贯通节理的岩体在单轴压缩荷载作用下的峰值强度及损伤变量进行了分析计算。结果表明,当节理倾角小于其内摩擦角时,岩体强度与完整岩石相同,岩体损伤为零,而后随着节理倾角增加,岩体强度、损伤随节理倾角的变化分别呈开口向上及向下的抛物线,当节理倾角约为60°时,岩体损伤最大,强度最低。随着节理长度增加,岩体损伤增加,而随着节理内摩擦角的增加,岩体损伤则减小。      

基于渗流-损伤-应力耦合作用下考虑力学参数弱化的巷道围岩变形破坏分析

地下工程岩体渗流-损伤-应力耦合问题的研究对于巷道围岩的稳定性分析具有重要意义。本文在总结分析了巷道变形破坏类型影响因素的基础上,基于弹塑性力学、渗流力学以及损伤理论建立了岩体渗流-损伤-应力耦合模型。该模型充分考虑了多物理场耦合过程中,工程岩体的非均质性,岩体力学参数发生的动态弱化过程,围岩塑性屈服的峰后特性以及渗透系数在损伤过程中的突变性。基于多物理场耦合软件,数值模拟结果分析得到,使用该模型能更好地反映巷道围岩的屈服破坏程度和渐进破坏过程。应用该模型分析不同深度下的巷道围岩渐进性破坏过程可以得出:水平地应力为主导的地层中的巷道,屈服破坏主要发生在顶拱和底板,竖直地应力为主导的地层中的巷道,屈服破坏主要发生在两侧边墙,水平地应力和竖直地应力相近的地层中,巷道四周均发生不同程度的破坏,这与工程实际有很好的符合。     

双江口工程地下洞室群围岩损伤及稳定性研究

对四川省双江口水电站工程的地下洞群的节理岩体围岩稳定性进行研究,分别采用了弹塑性模型、节理岩体断裂损伤模型进行数值分析。在弹塑性模型中,采用锚固等效法来模拟锚杆及锚索的支护效果。断裂损伤模型以损伤及断裂力学原理为基础,运用损伤本构模型和损伤演化方程在FLAC3D软件的框架下开发出子程序,考虑了岩体中节理裂隙对洞室围岩稳定性的影响,进而得到用上述的模型和计算程序分析出的围岩塑性区、损伤演化区和位移规律。将两种模型的计算结果与相应工程模型试验的结果进行了比较分析。研究结果表明,损伤模型更接近工程实际情况,与模型试验结果更为接近     

考虑损伤效应的岩锚梁光面爆破数值分析

在地下厂房岩锚梁爆破施工中,为获得良好的开挖轮廓面和较小的损伤区,常采用光面爆破的开挖方式,但在光面爆破施工中,主爆孔爆破对光爆层岩石造成较大程度的损伤,使岩石的力学参数发生变化,而在爆破设计与施工中未考虑这种损伤效应,结果造成单孔装药量偏大,岩石受到过度破坏,出现超挖或产生大量的爆振裂隙。应用动力有限元程序,建立岩体二维弹塑性模型,对不考虑损伤和考虑损伤的光面爆破过程进行了数值模拟,并比较两种模型最大有效应力随距离的变化关系。研究结果表明,在相同情况下,考虑损伤影响时可适当加大光面爆破的炮孔间距和抵抗线。在现场进行了考虑爆破损伤和未考虑爆破损伤的两组爆破试验,观察爆后效果表明：考虑爆破损伤效应的参数设计爆破效果好、损伤作用小。     

岩石破坏非连续变形分析弹脆性本构模型的二次开发

岩石非连续变形分析方法DDARF成功实现了模拟岩体裂纹萌生、扩展、贯通、破碎的全过程,但算法只考虑了岩体的线弹性本构模型,没有分析岩体的非线性应力-应变关系。为更符合真实岩体工程,同时扩展岩石非线性本构模型的应用范围,分别采用摩尔-库仑强度准则和最大拉应力强度准则对岩体进行剪切和拉伸破坏判断;对理想弹脆性本构模型进行算法分析,并在VC++平台下程序实现;对“自定义”的岩体非连续变形分析方法弹脆性本构模型与室内单轴压缩试验进行比较分析;将岩体非连续变形分析方法弹脆性本构模型应用于大型地下洞室开挖,并与线弹性本构模型进行对比。结果表明,非连续变形分析方法中自定义岩体弹脆性本构模型是可行的,它能够反映岩体变形的非线性特征,与室内试验吻合度较好;非连续变形分析方法弹脆性本构模型应用于大型地下工程,能更安全且真实地分析洞室围岩的稳定性,进而更好地指导地下洞室的防护措施。     

深部洞室开挖卸荷分区破裂机制的动力分析

随着地下工程开挖深度的增加,深部岩体将处于高应力和复杂的地质环境中,产生与浅埋洞室破坏模式迥异的分区破裂现象。深部洞室在动力卸荷作用下,基于应变梯度理论和损伤软化模型,建立了弹塑性损伤软化动力模型,推导了含有应变梯度项的运动方程、平衡方程和边界条件,提出相应的破坏判据,采用Runge-Kutta方法和Matlab数值软件求得不同卸载时刻围岩附加位移场、应力场和开挖后围岩总位移场、应力场,得到深部洞室围岩分区破裂的动态形成过程和发展规律。由理论计算值与地质力学模型试验实测值对比分析得知,围岩的径向位移、径向应力和切向应力出现波峰和波谷交替振荡的变化规律,理论计算得到的破裂区和非破裂区的宽度和数量与试验实测值有很好的一致性,证实了该模型分析分区破裂现象的适用性,对以后深部地下工程围岩变形破坏和支护设计提供理论支持。     

基于声速变化的岩体爆破累积损伤效应

声速变化是表征损伤变量的有效参数。为揭示岩体爆破累积损伤效应及损伤演化规律,在某地下工程中开展了反复爆破作用下围岩损伤的声波测试,并对测试数据进行了回归分析。在此基础上,分析了多次爆破作用下岩体损伤与声速变化的对应关系,建立了以岩体声速降低率为基准量的岩体爆破累积损伤扩展模型。研究表明：（1）回归分析的相关系数大于0.981 6,说明岩体爆破损伤非线性累积回归预测模型是正确的;（2）岩体爆破累积损伤模型将岩体损伤总量定义为初始损伤和爆破损伤之和,综合考虑了爆破损伤累积效应和岩体初始损伤的影响,能够真实反映岩体损伤程度,是合理可行的。     

大型地下洞室群围岩应力-损伤-渗流耦合分析

以渗透体力来考虑渗流场的力学效应,建立了应力-损伤-渗透系数关系方程来考虑应力和损伤对渗流场的影响,结合岩体结构的三维弹塑性损伤有限元分析,建立了大型地下洞室开挖围岩应力-损伤-渗流耦合的计算模型。该计算模型求解的难度主要体现在岩体材料弹塑性、损伤、渗流自由面边界、渗流溢出边界、应力-损伤-渗流相互影响关系等。提出分步迭代法对以上因素进行归纳后按一定顺序分别进行迭代求解,取得了良好的计算效果。将该方法应用于某水电站大型地下洞室群分析,得出了一系列有意义的结论。     

金川矿区深部巷道开挖损伤数值模拟研究

在地下深处开挖巷道会诱发应力的急剧调整,无疑会使围岩产生不同程度的损伤.开挖的动态作用虽然持续时间较短,但造成的损伤为后续时效变形和工程扰动影响下的失稳破坏提供了基础条件.为了能够得到开挖作用引起的金川矿区深部巷道损伤区演化规律,从而对巷道损伤破坏进行针对性的防治,本文基于矿区的实际巷道埋深和岩体结构种类,采用等效开挖...     

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。      

地下洞室开挖过程围岩应变能调整力学机制

深埋洞室岩体开挖过程中,围岩应变能的聚集和释放是洞室发生灾变破坏的重要诱因。针对圆形洞室开挖,分析和比较初始地应力准静态和动态两种不同卸载方式下围岩应变能的调整过程,基于能量角度判定了围岩损伤范围。研究表明：伴随地下洞室的开挖,岩体能量靠径向应力做功的方式在围岩中由远及近传递,并导致近区围岩应变能聚集;初始地应力动态卸载诱发围岩应变能先减小后增大,先对靠近开挖面的相邻岩体通过径向应力做功的方式释放自身的应变能,随着卸载应力波的继续向前传播,远离开挖面的相邻岩体又通过径向应力对其做功的方式促使其应变能聚集;相比初始地应力准静态卸载,动态卸载条件下高应变能聚集程度导致围岩损伤破坏范围更大。     

拉应力条件下岩石细观力学本构模型和渗透系数张量研究(I):各向异性损伤本构模型

在拉应力作用下的考虑渗流的岩石本构模型研究尚且很少。采用细观力学研究了岩石损伤变形过程,考虑了渗流过程。由于选用了新的微裂纹扩展准则,提高了解方程效率;采用细观力学成果建立了考虑渗流的微裂纹面不连续变形对岩石变形影响规律,并采用断裂力学成果建立了考虑渗流的微裂纹应力强度因子;建立了同时考虑微裂纹扩展过程和渗流过程的岩石各向异性损伤本构模型,该模型也适用于岩体。