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.     

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.     

Modeling of wave propagation induced by underground explosion

A piecewise linear Drucker–Prager strength criterion and an isotropic continuum damage model with the damage scalar depending on an equivalent tensile strain are suggested to model rock mass behavior under blast loading. A rate-dependent constitutive relation is employed to model the energy dissipation caused by two sources, namely irreversible degradation of damage and permanent deformation caused by plasticity. The suggested model is incorporated with a commercially available software AUTODYN through its user’s subroutine function. Coupling of Euler and Lagrange processors are used to include all the materials under consideration such as explosive, air and rock mass, in the calculation. Using AUTODYN and the suggested model, shock wave propagation in rock mass induced by an underground explosion is simulated. Numerical results obtained agree favorably well with those obtained from an independently conducted field test. It demonstrates that the suggested model can be used to predict the damage area, plastic zone and ground motions generated by underground explosions.     

基于ANSYS/LS-DYNA的岩石爆破结构数值模拟分析

等离子爆破技术是一种新型爆破技术,其爆破孔的设计对整个爆破效果及爆破效率起着决定性的作用。本文基于ANSYS/LS-DYNA建立了爆破孔的有限元模型,并对爆炸荷载作用下掏槽孔孔壁压力及其破碎区进行了数值模拟。研究结果表明,爆破时畸变能的变化自始至终都基本呈椭圆形,孔径越小,积累的能量越大,对岩体破坏越大;孔深长度越短,能量积聚空间越小,爆破对岩体造成的破坏越大;孔深长度的改变对下部岩体影响较小,对中部岩体影响较大。此外由于爆炸实验多为破坏性实验,很难进行原型试验,因此使用数值模拟方法研究爆破孔的结构是可行的,可以作为实际工程的参考。     

隧洞开挖重复爆炸荷载作用下围岩累积损伤特性

隧洞毫秒爆破开挖推进过程中,预留岩体在重复爆炸荷载作用下产生不可逆的损伤叠加。而现有的岩体爆破损伤数值模拟基本都是针对单孔装药和单段爆破,很少涉及实际工程中的重复爆炸。基于LS-DYNA程序的用户自定义材料接口,将统计损伤演化模型嵌入到弹塑性本构材料中,模拟圆形隧洞全断面毫秒爆破过程中重复爆炸荷载作用下的岩体累积损伤效应,并考虑地应力对岩体爆破损伤的影响。计算结果表明,围岩损伤范围和损伤程度随重复爆炸荷载次数而增加,在一个爆破进尺内,围岩损伤的临界峰值质点振动速度较单段爆破降低了12%;爆炸荷载作用下,围岩主要表现为拉损伤,围岩地应力对爆破张拉效应起到非常敏感的"抑制"作用,在2¹0 MPa应力水平时,围岩爆破累积损伤范围随着应力增加而明显减小,围岩损伤的临界峰值质点振动速度增加24%10 MPa应力水平时,围岩爆破累积损伤范围随着应力增加而明显减小,围岩损伤的临界峰值质点振动速度增加24%⁵7%。     

含预制裂纹的水泥砂浆试块在爆炸载荷作用下损伤特征的数值模拟

把能够体现岩体在冲击载荷作用下的响应特点及损伤演化的各向异性特征的损伤模型嵌入到有限元软件中，模拟了含有预制裂纹的水泥砂浆试块在爆炸载荷作用下的损伤特征。模拟结果表明，在爆炸近区产生一个损伤“重灾区”，并可根据模拟结果确定“重灾区”及爆炸损伤的范围，模拟结果与试验结果基本一致。模拟方法可以为岩土工程中经历过爆炸损伤岩体的稳定性研究提供理论依据。     

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。     

Considerations of the discontinuous deformation analysis on wave propagation problems

In rock engineering, the damage criteria of the rock mass under dynamic loads are generally governed by the threshold values of wave amplitudes, such as the peak particle velocity and the peak particle acceleration. Therefore, the prediction of wave attenuation across fractured rock mass is important on assessing the stability and damage of rock mass under dynamic loads. This paper aims to investigate the applications of the discontinuous deformation analysis (DDA) for modeling wave propagation problems in rock mass. Parametric studies are carried out to obtain an insight into the influencing factors on the accuracy of wave propagations, in terms of the block size, the boundary condition and the incident wave frequency. The reflected and transmitted waves from the interface between two materials are also numerically simulated. To study the tensile failure induced by the reflected wave, the spalling phenomena are modeled under various loading frequencies. The numerical results show that the DDA is capable of modeling the wave propagation in jointed rock mass with a good accuracy. Copyright © 2009 John Wiley & Sons, Ltd.     

地震作用下预应力锚索加固危岩体的动力响应分析

针对预应力锚索加固危岩体的特点,以某危岩体加固工程的3个典型工程剖面为实例,通过对不同动荷载作用下预应力锚索加固的危岩位移场、应力场分布特征的数值模拟计算,揭示了预应力锚索加固危岩体在地震作用下的动态响应和变化规律。分析结果表明,随着地震动峰值加速度（PGA）、反应谱特征周期（Tg）的增大,被加固危岩体的位移和应力值明显增大,应力集中区的范围扩大,围岩损伤的可能性增加,稳定性降低。其成果为危岩体抗震加固与减灾提供理论基础和实践依据。     

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。     

爆破荷载作用下岩体振动特征的数值模拟

根据福建牛头山水电站地基岩体爆破开挖监测,运用离散元方法模拟了节理岩体距爆源不同距离处质点的振动速度和频率的变化特征,由此确定岩体质点最大振动速度和振动主频随爆源距离的衰减规律,并得到了距爆源一定距离处质点最大振动速度和振动主频与爆破药量的关系。数值模拟与现场实测的结果表明,用离散元软件UDEC计算得到的岩体振动特征和衰减规律与现场监测结果是基本符合的,误差在工程应用的允许范围之内,因此UDEC用于对岩体动态响应的数值模拟是适合的。     

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.     

深埋隧洞爆破开挖荷载诱发围岩损伤特性

深埋隧洞爆破开挖荷载构成复杂,对围岩损伤区的孕育发展具有重要影响。利用颗粒流程序（PFC）软件,讨论了不同初始地应力状态下爆炸荷载及地应力瞬态卸载所分别诱发围岩损伤的特性,并通过锦屏2级水电站引水隧洞爆破开挖损伤区检测数据对数值模拟的结果进行了验证。研究表明,爆炸荷载和地应力瞬态卸载所诱发的围岩损伤程度和范围均随地应力量级的提高而显著增大;爆炸荷载作用条件下损伤区的分布有随着侧压力系数的增大而向应力集中区发展的趋势,而地应力瞬态卸荷所产生的围岩破坏以受拉破坏为主,表层损伤区沿开挖呈轮廓均匀分布的趋势;在相同的初始地应力状态下,爆炸荷载和地应力瞬态卸荷所分别诱发的围岩损伤区深度均明显小于实测值,考虑二者的耦合效应后,计算值与实测值基本吻合。这说明这两种荷载是高应力条件下爆破开挖荷载的主要成分,但二者耦合作用对围岩的损伤大于它们单独作用效应的线性叠加。     

节理岩体各向异性等效弹性参数研究

采用复合材料力学分析方法,针对规则节理岩体考虑坐标转换及刚度系数,建立各向异性等效弹性参数的解析公式。通过算例证明了解析公式的可行性,同时对规则节理岩体等效参数规律性进行了研究,分析在不同的节理刚度比值下等效弹性参数的变化规律。结合白鹤滩坝址区柱状节理岩体特征,探讨了其等效弹性参数取值和各向异性特征。研究表明：所采用方法在刚度取值相等时岩体可退化为各向同性介质,且该方法计算结果与实测结果较为吻合;同时发现柱体偏转对等效弹性参数的影响较大,偏转后水平向和铅直向弹性模量分别降低约54%和17%,根据曲线规律性,偏转角度越大,降低程度越高,等效弹性参数的曲线变化反映了其具有明显的各向异性特征。     

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。     

考虑累积损伤效应的围岩变形特性研究

隧道爆破开挖诱发的动力扰动作用范围往往远大于其开挖进尺,同一部位围岩受到循环爆破开挖的多次扰动普遍存在累积损伤。对乌东德水电站左岸导流洞爆破开挖过程中的爆破振动和围岩变形监测进行了监测和数值分析,基于累积损伤理论,通过引入损伤判据及损伤变量,考虑计算中产生的不同程度的损伤区域的岩体参数劣化,并将劣化后的参数引入相应损伤单元进行后续开挖爆破数值模拟计算,从而对岩体爆破开挖累积损伤效应进行模拟。通过比较乌东德水电站导流洞的实测数据以及数值模拟计算结果发现,考虑累积损伤的计算结果无论是爆破振动速度还是围岩变形均更接近于实测值。对爆破开挖的分析模拟中应考虑围岩的多次循环爆破累积损伤效应。     

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     

损伤条件下深部岩体巷道光面爆破参数研究

岩体条件复杂多变,为了提高光面爆破的适应性、改善光面爆破效果,对损伤条件下深部岩体巷道光面爆破参数进行研究。通过对深部岩体巷道光爆层原岩应力场、光面爆破机制和振动损伤特征进行分析,基于爆炸应力波和爆生气体综合作用理论,考虑高原岩应力和岩石损伤影响,提出了损伤条件下深部岩体巷道光面爆破参数确定的计算方法。研究表明, （1）高原岩应力相当于提高了岩石的抗拉强度,不利于炮孔初始裂纹的形成及贯通,宜减小周边眼间距;（2）岩石损伤后,其他条件不变,光面爆破的炮孔间距和抵抗线值可适当加大;（3）高原岩应力和损伤条件下,光面爆破的炮孔间距较小时,容易造成爆后围岩损伤,降低围岩的稳定性能,因此,提高爆破效果的同时应及时加强支护,以确保施工安全和围岩稳定;（4）本文提出的光面爆破参数计算公式,经现场爆破验证效果良好,适用于复杂多变的岩体环境。     

岭澳核电站二期工程基岩爆破安全阈值分析

核电站基础爆破开挖过程中必须严格控制岩体爆破损伤深度,确保建基面安全。以广东岭澳核电站二期工程基础爆破开挖为例,通过现场爆破振动监测、岩体声波试验以及数值模拟,综合分析了岩体爆炸振动衰减规律和损伤特征,研究了距爆源一定距离处岩体振动速度与损伤特征的关系,提出了岭澳核电站二期工程岩体爆炸损伤深度的控制方法,确定了相应的安全阈值。分析结果表明,岭澳核电站二期工程基础爆破开挖时,当距爆源30 m处的岩体质点振动速度不超过5 cm/s时,可保证下卧基岩的损伤深度小于2 m,确保建基岩完整性。     

基于小波能量的爆破震动巷道围岩稳定性判据

目前爆破震动荷载作用下地下围岩稳定性判别主要依靠单一强度因子的独立阈值稳定性判据,这类判据多为定性分析,没有同时考虑爆破震动三要素的综合作用效果,且未建立稳定性判据与巷道围岩破坏程度之间的定量关系,在实际工程应用中存在一定的缺陷和不足。通过建立爆破荷载作用下的不同类别巷道围岩有限元模型,提取巷道围岩的响应信号,基于小波变换理论建立时间能量密度函数分析巷道围岩响应信号的时、频域特征,进而将时间能量密度曲线与时间轴围成的面积TEDI作为评估爆破震动效应的判别指标,建立了TEDI与巷道围岩损伤程度的定量关系,为进一步完善基于小波能量理论的巷道围岩损伤预警体系奠定基础。