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.     

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。     

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.     

Modified predictor-corrector solution approach for efficient discontinuous deformation analysis of jointed rock masses

The high computational costs associated with the implicit formulation of discontinuous deformation analysis (DDA) have been one of the major obstacles for its implementation to engineering problems involving jointed rock masses with large numbers of blocks. In this paper, the Newmark-based predictor-corrector solution (NPC) approach was modified to improve the performance of the original DDA solution module in modeling discontinuous problems. The equation of motion for a discrete block system is first established with emphasis on the consideration of contact constraints. A family of modified Newmark-based predictor-corrector integration (MNPC) scheme is then proposed and implemented into a unified analysis framework. Comparisons are made between the proposed approach and the widely used constant acceleration (CA) integration approach and central difference (CD) approach, regarding the stability and numerical damping features for a single-degree-of-freedom model, where the implications of the proposed approach on open-close iteration are also discussed. The validity of the proposed approach is verified by several benchmarking examples, and it is then applied to two typical problems with different numbers of blocks. The results show that the original CA approach in DDA is efficient for the simulation of quasi-static deformation of jointed rock masses, while the proposed MNPC approach leads to improved computational efficiency for dynamic analysis of large-scale jointed rock masses. The MNPC approach therefore provides an additional option for efficient DDA of jointed rock masses.     

节理岩体中应力波传播规律研究的进展

讨论了位移不连续模型与特征值法结合的方法,对垂直于单一线性变形节理、多个平行线性变形节理、单一非线性变形节理,分别采用线性变形不连续模型、双曲线变形不连续模型(BB模型)进行的理论与相应的实验研究。用离散元程序UDEC,对上述问题进行数值模拟;用三维离散元程序3DEC,对节理岩体中三维波的传播进行的数值模拟。并用UDEC与有限差分程序AUTODYN-2D耦合,模拟爆炸过程及爆炸波在节理岩体中的传播。同时提出了几个有待研究的问题。     

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 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.     

A numerical study on 2-D compressive wave propagation in rock masses with a set of joints along the radial direction normal to the joints

An explosion in a borehole or an accidental explosion in a tunnel will generate a two-dimensional (2-D) compressive wave that travels through the surrounding rock mass. For the problem of 2-D compressive wave propagation in a rock mass with parallel joints in the radial direction normal to the joints, parametric studies on the transmission ratio and the maximum rebound ratio are performed in universal distinct element code. The variation of the transmission ratio with the ratio of joint spacing to wavelength is generalized into a characteristic curve, which can be used as a prediction model for estimating the transmission ratio. The relationship between the maximum rebound ratio and the influence factors is obtained in charts. The charts can be used as a prediction model for estimating the maximum rebound ratio. The proposed prediction models for estimating the transmission ratio and the maximum rebound ratio are applied to a field explosion test, Mandai test in Singapore. The minimum possible values of peak particle velocity (PPV) at the monitoring points are estimated by using the proposed prediction model for estimating the transmission ratio along the radial direction normal to the joints. On the other hand, the maximum possible values of PPV are estimated by using the proposed prediction model for estimating the maximum rebound ratio along the same radial direction. The comparison shows a good agreement between the field-recorded PPVs and the estimated range of PPVs given by the minimum possible PPVs and the maximum possible PPVs at the monitoring points in Mandai test. The good agreement between the estimated and field-recorded values validates the proposed prediction models for estimating peak particle velocity in a rock mass with a set of joints due to application of a compressive wave at the boundary of a tunnel or a borehole.     

Validation study of the distinct lattice spring model (DLSM) on P-wave propagation across multiple parallel joints

A validation study of the distinct lattice spring model (DLSM) for wave propagation problems is performed. DLSM is a microstructure-based numerical model, which is meshless and has advantages in modelling dynamic problems where stress wave propagation is important. To verify the applicability of DLSM to modelling wave propagation through a discontinuous medium, the virtual wave source (VWS) method is used to obtain analytical solutions for wave propagation across a jointed rock mass. Numerical modelling results of the commercial code UDEC are selected as the reference. The effects of particle size and lattice rotation angle on wave propagation are first studied. Then, the results of wave transmission across a single joint with a different joint stiffness and across multiple parallel joints with different joint spacings are derived with DLSM, UDEC and VWS. These results are in good agreement with each other. Therefore, the capability of DLSM to model P-wave propagation across jointed rock mass is verified, which provides confidence for the further application of DLSM to modelling more complex problems.     

Thermal shock weakening of granite rock under dynamic loading: 3D numerical modeling based on embedded discontinuity finite elements

This paper presents a numerical study of thermal shock weakening of granite rock under dynamic loading. A fully 3D numerical scheme based on a combined continuum viscodamage-embedded discontinuity model and an explicit scheme to solve the underlying thermomechanical problem was developed and validated through numerical examples. First, the dynamic Brazilian disc test is simulated on intact numerical rock. Then, thermal shock-induced cracking due to a moving external heat flux boundary condition, mimicking experiments based on plasma jet treatment, is numerically predicted. Finally, numerical Brazilian disc test is conducted on the thermal shocked numerical samples. The predicted and experimental weakening effects are in good agreement demonstrating that the present modeling approach has good predictive capabilities. The practical significance of the results is that heat shock pretreatment can substantially enhance rock gravel and rubble crushing.     

底摩擦重力试验在倾倒变形岩体稳定性研究中的应用

底摩擦重力试验(底摩擦试验)是利用相似理论分析原理,将研究原形按几何比例和各种物理力学参数,制作相似模型及确定相应的边界条件。然后按照相似边界条件进行加载试验,再现曾经发生过或今后将会出现的物理力学现象,进而了解其发展演化规律及其对工程的影响。澜沧江某水电站坝肩主要为典型的倾倒变形岩体,为探讨倾倒变形岩体在天然重力场条件的变形破裂发展趋势。试验采用模拟重力场条件的岩体底摩擦模型试验技术模拟分析岩体倾倒变形进一步发展演变过程及特征。     

基于复杂结构精细描述的岩质高边坡稳定性分析

用数值方法对岩质高边坡进行稳定性分析时,描述岩体结构对的精细程度会影响分析结果,但常见的有限单元法程序仍难以对复杂节理岩体进行精细建模。为解决这一问题,将结构面网络模拟与离散单元法相结合,在UDEC软件中,利用FISH语言编写网络模拟程序,依据结构面统计资料和结构面分级,实现对复杂岩体结构的精细描述。以某大型水电工程边坡为例,在对岩体结构进行精细描述的基础上,采用离散元强度折减法对边坡进行稳定性分析。通过与极限平衡法和一般离散元结果的对比,表明基于复杂岩体结构精细描述确定的边坡潜在滑动面和安全系数是合理的,为复杂岩质边坡破坏模式和稳定性的分析提供了新的途径。     

倾倒变形岩体发育强度与极限深度的确定方法

以澜沧江某水电站右坝肩倾倒变形岩体为例,根据倾倒变形岩体的宏观地质特征及其地质环境背景条件,系统分析了影响倾倒变形岩体发育的地质因素。运用离散元数值分析方法,模拟了不同影响因素对岩体变形强度的影响程度,并与实际边坡开挖揭露的岩体变形特征进行对比分析,得到了发生岩体变形的控制因素、变形发展过程的时间效应与空间分布特征。研究结果表明,导致岩体发生倾倒变形的外部因素是重力、地应力、卸荷方向与卸荷强度,提出了倾倒变形极限深度的概念。通过地质成因分析、离散元数值分析和理论公式推导,建立了由地表变形弯折强度确定变形随深度变化的计算模型,为开挖边坡的稳定性评价及系统锚索深度设计提供了重要的依据。     

锚杆垫板形式对洞室抗爆效果的影响试验研究

为了研究爆炸条件下不同垫板形式锚杆对洞室加固效果的影响,现场试验中选择了平板和碗形两种不同的垫板形式。通过抗爆试验,对锚固洞室宏观破坏形态、洞壁位移特征、拱顶位移与比例距离之间的关系以及爆心两侧拱顶各点位移进行了对比,分析了两种垫板形式在爆炸条件下对洞室加固效果的影响。试验结果表明：在爆炸条件下,碗形垫板可以充分发挥锚杆抗拉能力高的特点,拱部围岩经碗形垫板加固后,整体刚度能够得到较大提高,对岩体的加固效果较好。     

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.     

层状岩体深埋长隧道锚杆支护优化设计

层状岩体是地下工程中经常遇到的一种岩体,力学性质具有明显的各向异性。选择合适的屈服准则和强度参数变化规律,结合各向异性弹性本构方程,获得横观各向同性弹塑性本构关系,利用该本构模型对共和隧道锚杆支护方案进行数值计算。首先考虑地应力、岩性的影响,从围岩的变形、破坏形式、塑性区及锚杆拉力的大小等方面改进、优化支护设计方案;其次从实际工程出发,考虑施工难度、工程造价等因素的影响,得到改进方案Ⅰ效果较理想,通过试验段现场监测确定改进方案I。本构模型对计算结果的影响很大,正确模型的计算结果可以为实际工程提供科学依据。     

高填石路堤模型密实度动测方法的研究

通过在高填石路堤模型上的密实度动测实验,提出了用修正单模态法测试衰减系数评价压实效果的方法,并将修正单模态法与冲击响应频谱法、动刚度法做了对比。试验结果表明,衰减系数基本能够反映路堤压实过程中的平均沉降量。此外,实验还进行了附加质量法测试,其结果表明附加质量法测得的参振质量也基本能够反映填石路堤修筑压实后达到的密度,最后还给出了参振质量与高填石路堤密度之间的回归公式。      

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.     

节理几何特征对预裂爆破效果影响的数值模拟

运用有限元软件AUTODYN 2D计算爆炸荷载与离散元软件UDEC模拟节理岩体相结合的方法研究了节理几何特征对预裂爆破的影响。通过计算可知,预裂爆破时炮孔间的节理组对预裂成缝的影响明显,当节理法线与炮孔连线夹角在一定范围内时,预裂缝沿炮孔连线方向的平直程度随节理与炮孔连线夹角的增大而逐渐趋于平直,其中当节理组与炮孔连线夹角为90°时成缝效果最好,裂缝与炮孔连线基本重合,与理论分析较一致;节理间距对预裂爆破有较大影响,相同条件下节理间距越小,越难形成连通裂缝,减小炮孔间距有利于小节理间距情况下的预裂缝贯通     

一种改进的光滑粒子动力学法在地震条件下岩质边坡中的验证与应用

开发一种改进损伤框架的粒子流算法,被称为核断裂的光滑粒子流法（kernel-broken smoothed particle hydrodynamics,KBSPH）,用于模拟地震条件下岩质边坡的裂纹扩展和变形破坏过程.在KBSPH中,提出一种改进的损伤框架,通过引入断裂标志来改进损伤粒子的核函数,使损伤粒子的虚拟应力键直接断裂,裂纹在断裂的应力键间生成,从而模拟岩石的裂纹扩展过程.在地震边界上采用了双层边界,将动力输入边界与黏滞边界分离.首先通过薄板振动实验验证KBSPH的动力特性.其次以单裂隙岩体单轴压缩试验验证KBSPH的断裂力学特性.最后模拟地震条件下多节理岩质边坡中裂纹扩展过程和动力响应.薄板振动实验验证了KBSPH的动力特性的准确性.单裂隙岩体单轴压缩试验,证明了KBSPH可以正确模拟预制裂隙尖端的翼型裂纹.通过对比以往数值模拟方法和现场案例,表明KBSPH正确揭示了加速度放大效应以及地震条件下岩质边坡的裂纹扩展过程.KBSPH避免了传统算法的网格畸变,损伤粒子应力分量重新分配的问题,降低了编程难度,提高了运行速率,可为SPH在地震条件下岩石力学中的应用和理解岩石断裂机理提...