Analysis of Stochastic Seismic Wave Interaction with a Slippery Rock Fault

Stochastic seismic wave interaction with a slippery rock fault is studied, based on the principle of conservation of momentum at the wave fronts along the fault. By using the displacement discontinuity method, the wave propagation equations are derived for incident longitudinal-(P-) and shear-(S-) waves, respectively. This is an extension of the study by Li and Ma (2010) for blast-induced wave propagation across a linear rock joint. Stochastic seismic waves are generated from a frequency spectrum and used to analyze the seismic wave interaction with a rock fault having a Coulomb-slip behavior. Parametric studies are carried out to investigate the effect of the intensity and impinging angle of the incident seismic waves on wave propagation across a slippery rock fault. Results show that the transmission of the incident P-wave is almost not affected by the fault, on the contrary, this is not the case for an incident S-wave, due to the occurrence of a relative slip which is related to the impinging angle of the incident S-wave. A quantitative study is presented which is of help in understanding the propagation and attenuation laws of seismic waves in discontinuous rock masses.     

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.     

Coupling of two methods,waveform superposition and numerical,to model blast vibration effect on slope stability in jointed rock masses

Drilling and blasting is a major technology in mining since it is necessary for the initial breakage of rock masses in mining. Only a fraction of the explosive energy is efficiently consumed in the actual breakage and displacement of the rock mass, and the rest of the energy is spent in undesirable effects, such as ground vibrations. The prediction of induced ground vibrations across a fractured rock mass is of great concern to rock engineers in assessing the stability of rock slopes in open pit mines. The waveform superposition method was used in the Gol-E-Gohar iron mine to simulate the production blast seismograms based upon the single-hole shot vibration measurements carried out at a distance of 39 m from the blast. The simulated production blast seismograms were then used as input to predict particle velocity time histories of blast vibrations in the mine wall using the universal distinct element code (UDEC). Simulated time histories of particle velocity showed a good agreement with the measured production blast time histories. Displacements and peak particle velocities were determined at various points of the engineered slope. The maximum displacement at the crest of the nearest bench in the X and Y directions was 26 mm, which is acceptable in regard to open pit slope stability.     

Analysis of Wave Propagation Through a Filled Rock Joint

An analytical and experimental study on a longitudinal wave (P-wave) transmission normally across a filled rock joint is presented in this paper. The dynamic property of the filling material for the artificial rock joints is derived from a series of modified split Hopkinson pressure bar (SHPB) tests. The incident and transmitted waves in granitic pressure bars are calculated by wave separations of the strain gauge readings. The incident wave is approximated by a series of half-sinusoidal waves, and an analytical model on wave propagation across a filled rock joint is then deduced. The derived wave transmission coefficients across the filled joint agree very well with those from the test results. Both the analytical and test results show that the wave transmission coefficients are influenced by the mechanical properties and the input energy of the incident waves. Analytical parametric studies with respect to pre-compaction of the filling material, the frequency and amplitude of the incident wave have also been conducted.     

节理对爆炸波传播影响的数值研究

采用加入无反射边界条件的DDA程序,研究了节理面对应力波传播的影响。结果表明,节理面能阻碍波的传播,有利于波的衰减,节理面越多,波的反射越强,而波的透射越弱。模拟了一个现场爆炸试验,研究爆炸产生的应力波在节理岩体中传播、衰减的规律,模拟结果与现场试验结果比较吻合。研究表明,DDA方法可以模拟节理面对应力波传播的阻碍作用,用它来模拟爆炸波在节理岩体中的传播是适用的。     

基于离散颗粒模型的岩体结构面动-静态刚度系数对比的数值模拟研究

岩体工程计算分析中结构面刚度系数是至关重要的力学参数,计算分析的精度和可靠程度与这个参数密不可分,结构面刚度系数取值仍然是一个难点。岩体中应力波传播至结构面处将会发生反射和透射现象,利用应力波透射系数可反演结构面动态刚度系数。本文从细观力学角度运用颗粒离散元方法,开发分段线性接触模型及应力波吸收边界模型,开展宏观岩体中应力波传播的模拟,结合准静态压缩试验模拟,研究了较为平直的岩体结构面分别在不同正应力条件下的动、静态刚度系数的变化特征。模拟结果表明:(1)利用C++语言开发的分段线性接触模型很好地实现了结构面非线性变形特征的模拟;(2)基于颗粒离散元方法能够准确地反映岩体中应力波传播规律,应力波通过不同刚度结构面的透射系数与理论解一致;(3)在离散颗粒模型中加入黏滞吸收边界条件很好地实现了在有限尺寸模型中远场应力波传播模拟;(4)在岩体模型中结构面接触部位运用分段线性接触模型,通过模拟应力波传播与单轴压缩试验分别获得了一致性较好的结构面动、静态刚度系数,结构面动/静态刚度系数之比值约为1.0。本文对岩体中结构面刚度的测试和取值具有重要的指导意义。     

Analytical study of ground motion caused by seismic wave propagation across faulted rock masses

Studying seismic wave propagation across rock masses and the induced ground motion is an important topic, which receives considerable attention in design and construction of underground cavern/tunnel constructions and mining activities. The current study investigates wave propagation across a rock mass with one fault and the induced ground motion using a recursive approach. The rocks beside the fault are assumed as viscoelastic media with seismic quality factors, Q_p and Q_s. Two kinds of interactions between stress waves and a discontinuity and between stress waves and a free surface are analyzed, respectively. As the result of the wave superposition, the mathematical expressions for induced ground vibration are deduced. The proposed approach is then compared with the existing analysis for special cases. Finally, parametric studies are carried out, which includes the influences of fault stiffness, incident angle, and frequency of incident waves on the peak particle velocities of the ground motions.     

Propagation Characteristics of Blasting Stress Waves in Layered and Jointed Rock Caverns

The existence of joint fissures makes explosive actions between rock masses more complex. Therefore, it is of great significance to carry out experiments studying blasting stress waves propagating in jointed rock masses. Based on the Froude Similarity principle, the geological mechanical models of intact rock masses and jointed rocks have been proposed. A blasting vibration experiment was carried out and demonstrated that the propagation of the blasting stress waves and changing structures have an important relationship. A numerical simulation of the blasting stress wave propagation law in a layered jointed rock mass was carried out. This study found that with an increase in the joint angle, the peak velocity of blasting stress wave, transmission coefficient and reflection coefficient all gradually increased, while the attenuation coefficient gradually decreased. With an increase in joint spacing, the attenuation rate of the blasting stress waves increased.     

Analysis of Blast Wave Interaction with a Rock Joint

The interaction between rock joints and blast waves is crucial in rock engineering when rock mass is suffered from artificial or accidental explosions, bursts or weapon attacks. Based on the conservation of momentum at the wave fronts and the displacement discontinuity method, quantitative analysis for the interaction between obliquely incident P- or S-blast wave and a linear elastic rock joint is carried out in the present study, so as to deduce a wave propagation equation. For some special cases, such as normal or tangential incidence, rigid or weak joint, the analytical solution of the stress wave interaction with a rock joint is obtained by simplifying the wave propagation equation. By verification, it is found that the transmission and reflection coefficients from the wave propagation equation agree very well with the existing results. Parametric studies are then conducted to evaluate the effects of the joint stiffness and incident waves on wave transmission and reflection. The wave propagation equation derived in the present study can be straightforwardly extended for different incident waveforms and nonlinear rock joints to calculate the transmitted and reflected waves without mathematical methods such as the Fourier and inverse Fourier transforms.     

斜入射线弹性节理应力波传播特征的数值模拟

依据弹性波理论,应力波斜入射线弹性节理时会发生波场分解。根据入射、透射及反射各波形的不同到时,运用离散元软件UDEC模拟应力波在含倾斜节理岩体中的传播并计算其透射、反射系数,并分析其波型转换规律。应力波斜入射单节理时,模拟得到的透射、反射系数随节理刚度、入射角度的变化规律,与已有的理论解是吻合的。应力波斜入射一组平行节理时,随着节理间距的增大,其同类波的透射系数Tpp、Tss先增大后减小,最后趋于稳定值;节理条数越多,Tpp、Tss越小。此外,不同条数的节理,透射系数达到最大值的临界节理间距值基本一致,但趋于稳定时的节理间距值随节理条数的增加而逐渐增大。     

Effects of weak layers on particle velocity measurements

Summary Results are presented from a testing program to study the effect weak layers embedded in a strong rock strata have on particle velocity when subjected to explosive loading. A similar computational study had been conducted earlier with WONDY — a finite difference Langrangian code developed at Sandia National Laboratory. The experiments were conducted using models fabricated from Hydrocal containing a single dry sand layer or clay layer through which the stress wave traveled. Particle velocity was measured in front of and past the weak layer to determine attenuation, pulse shape changes, and displacement loss. The results from the model testing indicated that particle velocity amplitude decreased significantly when the stress wave passed through the weak layer. The velocity pulse width on the other hand was found to remain relatively constant when passing through the weak layer. The computational results from WONDY predicted similar behavior and hence were in good agreement with the tests. In the experiments, the velocity loss across a sand layer was found to be much larger than the loss across a clay layer. The stress wave velocity in the sand layer was found to be significantly smaller than in the Hydrocal while the experimentally determined wave velocity in the clay was nearly equal to the wave velocity in the Hydrocal.     

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。     

Theoretical Derivation of a Peak Particle Velocity–Distance Law for the Prediction of Vibrations from Blasting

I would like to suggest a theoretical justification for the mathematical structure of some laws for predicting the maximum particle velocity vibration from blasting operations in the light of some basic notions of elastic and anelastic wave theory. Within this point of view, in dimensionally correct expressions, the terms pertaining to the rock, to the blast and to the seismic wave become evident and recognisable. A law is presented that can be used to forecast the maximum particle velocity on the basis of some blast design and rock parameters. Four tests of the proposed law performed with real data sets seem to confirm fairly well its reliability.     

扭转导波在锚固锚杆中传播的数值模拟

采用有限元数值模拟的方法研究了扭转导波在锚固锚杆中的传播性质。建立了自由锚杆和锚固锚杆的有限元模型,在锚杆顶端激发20～60 kHz扭转导波信号,计算得到导波在自由锚杆和锚杆锚固段的传播速度值与理论值吻合很好,证明了扭转导波数值模拟方法的有效性。数值模拟结果表明：随着激发波频率的增大,扭转导波在自由锚杆和锚杆锚固段中的衰减值均呈线性递增趋势,导波在锚杆锚固段上界面的反射回波逐渐减弱;扭转导波在锚杆锚固段的衰减值较大,无法在锚杆顶端采集到锚杆底端反射回波信号,所以扭转导波不适用于锚杆长度的检测;随着锚固介质弹性模量的增大,同一频率扭转导波在锚杆锚固段上界面的反射波逐渐增强。通过检测扭转导波在锚杆锚固段上界面的反射回波,可以确定锚固介质弹性模量的大小。     

采矿爆破振动波在岩溶区的传播影响因素分析

为研究不同情况下爆破振动强度衰变规律和振动对岩溶塌陷的影响,为当地矿山合理开采及减少地面塌陷灾害的发生提供可靠依据,对湖南水口山铅锌矿区进行现场爆破振动测试,并利用古丹铅锌矿实测数据作对比分析;试验矿区共布设4条测线,接收8组爆破振动数据。采用萨道夫斯基修正公式对采集的数据进行计算,以爆破产生的振动波频率及振动速度作为测试指标,对实测数据进行提取、处理,确定爆破振动波的频率及其在介质中的传播速度及地震波引发的质点振动峰值振速。试验结果表明:采矿活动是岩溶地面塌陷的主要影响因素;爆破振动波的频率衰减强度与其在岩土体中的传播距离和断层有关,振动波的传播速度受到岩土体性质、岩层结构特征、岩层走向等因素的影响。      

海原断裂带断层通道波观测与破碎带宽度

断层通道波是低速断层破碎带与高速围岩之间的边界相干多重反射形成的,其振幅和频率强烈依赖于断层的几何形态和物理性质,故能用于探测断裂带的内部结构.在宁夏海原西安州附近海原断裂带上,横跨1920年海原8.6级地震地表破裂带布设2条测线,接收测线之间人工爆破激发的断层通道波.每条测线由1台3分量数字地震仪组成,靠近破裂带台间距30～40 m,远离破裂带台间距增大至230～250 m.对测线1的台站接收到的一炮垂直道地震波数据进行了0.1～4.0 Hz频段的滤波,结果表明在S波到时之后存在多组强振幅、低频率、长波链的断层通道波.由断层通道波揭示的海原断裂带在西安州附近的断裂破碎带宽度约为250 m.     

红透山铜矿区F8断层构造应力场的有限元数值模拟

针对断层对周围岩石地层影响的问题,本文提出了一种有限元算法计算模拟该断层对周围地层产生的应力场和位移场。首先,根据最大主应力、中间主应力和最小主应力来研究正断层、逆断层以及走滑断层的应力状态;其次,基于弹性力学相关理论研究应力—应变关系,采用线性四面体单元有限元分析方法进行算法实现;最后,在考虑到断层两侧岩体的物理性质(弹性模量和泊松比)、断层几何形态以及边界条件等情况下,应用有限元法模拟正断层、逆断层以及走滑断层在层状岩体中产生的应力场和位移场。以红透山铜矿区F₈断层为例,通过地质勘探获得的资料判别该断层性质及其周围地层属性,使用本文构建的有限元算法模拟了该断层对周围地层产生的应力场和位移场。     

Evaluation of ground vibrations and the effect of air blast in open-pit phosphate mines

Blasting constitutes a beneficial industrial technology, used in quarries and mining production processes, which ensures the achievement of the expected results in a short period of time with relatively low cost. Nevertheless, a significant part of the used blasting energy is wasted in the form of ground vibration and air blast. Hence, blasting-induced ground vibrations are one of the fundamental problems in the mining industry which may cause severe damage to structures and plants nearby. Therefore, a vibration control study plays an important part in the minimization of the environmental effects of blasting in mines. This study represents an investigation reporting ground motion (measured in terms of peak particle velocity (mm/s)) and air blast overpressure measurements around the open-pit phosphate mine near Metlaoui area (southwestern Tunisia). It aimed to calculate the site’s constants: K (ground transmission coefficient) and n (site attenuation curve slope). The obtained site parameters allowed determining the propagation equation of the blast-induced seismic waves in the study area. The scope of this study was to predict the peak particle velocity when the amount of explosive charge and/or the distance were altered with minimum spoil to the environment. Also, a frequency overview of the study area revealed the dominance of low frequencies (>?40 Hz). Such values can cause damage to the nearby structures when a specific peak particle velocity value is reached by blasting. Moreover, this study demonstrated that all overpressure magnitudes were less than 134 dB, which is the safe limit of air blast level.     

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.     

断层导波研究加利福尼亚兰德斯和海克特曼恩地震断层带的四维特征(英文)

美国加利福尼亚州兰德斯和海克特曼恩地区于1992年和1999年先后发生7.4级和7.1级地震,分别在地面产生80km和40km长的断裂带。震后在断裂带布置的密集地震站台记录到明显的断层导波(fault-zone guided waves)。这些导波由断层带内的余震和人工震源激发产生,走时在S波之后,但具有比体波更强的振幅和更长的波列,并具有频散特征。通过对2～7 Hz断层导波的定量分析和三维有限差分数字模拟,获得了震深区断裂带的高分辨内部构造图像以及岩石的物理特性。数字模拟结果表明这些断裂带上存在被严重破碎了的核心层,形成低速、低Q值地震波导。核心破碎带宽约100～200 m,其内地震波波速降为周围岩石的40％～50％,Q值约为10～50。根据岩石断裂力学观点,这一低速、低Q值带可被解释为地震过程中处于断层动态断裂前端的非弹性区(或称之为破碎区,相干过程区)。在兰德斯和海克特曼恩断裂带测得的破碎区宽度与断裂带长度之比约为0.005,基本上符合岩石断裂力学预期的结果。观察到的断层导波还显示兰德斯和海克特曼恩地震中多条断层发生滑移和破碎。兰德斯地震时多条阶梯形断层相继断裂;而在海克特曼恩地震中,断裂带南北两端均出现分枝断裂,深处的分枝断裂较地表出现的破裂状况更为复杂。由三维有限元模拟的动态断裂过程表明,?