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.     

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.     

Investigation into the effect of fault properties on wave transmission

The estimation of wave transmission across the fractured rock masses is of great importance for rock engineers to assess the stability of rock slopes in open pit mines. Presence of fault, as a major discontinuity, in the jointed rock mass can significantly impact on the peak particle velocity and transmission of blast waves, particularly where a fault contains a thick infilling with weak mechanical properties. This paper aims to study the effect of fault properties on transmission of blasting waves using the distinct element method. First, a validation study was carried out on the wave transmission across a single joint and different rock mediums through undertaking a comparative study against analytical models. Then, the transmission of blast wave across a fault with thick infilling in the Golgohar iron mine, Iran, was numerically studied, and the results were compared with the field measurements. The blast wave was numerically simulated using a hybrid finite element and finite difference code which then the outcome was used as the input for the distinct element method analysis. The measured uplift of hanging wall, as a result of wave transmission across the fault, in the numerical model agrees well with the recorded field measurement. Finally, the validated numerical model was used to study the effect of fault properties on wave transmission. It was found that the fault inclination angle is the most effective parameter on the peak particle velocity and uplift. Copyright © 2017 John Wiley & Sons, Ltd.     

A Numerical Study on Wave Transmission Across Multiple Intersecting Joint Sets in Rock Masses with UDEC

This paper presents a numerical study on wave transmission across jointed rock masses with UDEC, where multiple intersecting joint sets exist. The capability of UDEC of studying wave transmission across rock joints is validated through comparison with analytical solutions and experimental data. Through parametric studies on wave transmission across jointed rock masses, it is found that joint mechanical and spatial parameters including joint normal and shear stiffnesses, nondimensional joint spacing, joint spacing ratio, joint intersecting angle, incident angle, and number of joint sets together determine the wave transmission. And for P wave incidence, compared with other parameters, joint normal stiffness, nondimensional joint spacing, and joint intersecting angle have more significant effects on wave transmission. The physical reasons lying behind those phenomena are explained in detail. Engineering applications and indications of the modeling results are also mentioned.     

酸性干湿循环下充填节理岩石劣化性能试验研究

为探究酸性干湿循环作用对充填节理岩石的损伤劣化规律,首先对预制充填节理岩石进行酸性和中性环境下不同次数的干湿循环前处理,再采用万能试验机和分离式Hopkinson杆（split Hopkinson pressure bar,简称SHPB）装置对其进行单轴压缩试验和动态冲击试验,对充填节理岩石纵波波速、静态抗压强度以及动态抗压强度的劣化效应进行分析,并进一步分析酸性和中性环境干湿循环作用下充填节理岩石动态冲击的破坏形态。结果表明,随着干湿循环次数的增加,无论是酸性环境还是中性环境,充填节理岩石的波速值、静态抗压强度以及动态抗压强度不断减小,劣化程度不断加剧,其中酸性干湿循环作用对静态抗压强度的劣化最显著;此外发现干湿循环作用下充填节理岩石静态、动态抗压强度与波速值之间均存在一致性较强的线性关系;酸性环境干湿循环作用下充填节理层粉化程度和两侧岩石破碎程度更严重。研究成果可为酸性环境干湿循环作用下工程岩体稳定性分析提供科学依据。     

黏弹性节理岩体的位移不连续模型研究

选用三参数标准线性固体作为岩石本构,提出了一种考虑岩体黏弹性的位移不连续模型;根据一维黏弹性波的特征线法,推导了节理处质点速度、应力和应变递推公式。首先,基于分离式霍普金森压杆（SHPB）对砂层进行试验,得到其应力-应变关系,并换算出砂层节理的法向刚度;接着,通过一维强间断黏弹性波的波速公式、高频波衰减系数以及任一频率下的衰减系数,确定出数值算法中的三参数。最后,基于自制的摆锤装置,探讨了一维应力波在节理岩体中的传播规律,试验中以两根长1 000 mm、直径为68.50 m的岩杆作为入射和透射杆,以3 mm砂层模拟节理。试验和数值结果吻合度良好,进一步验证了该方法的可靠性。     

Theoretical Methods for Wave Propagation across Jointed Rock Masses

Different methods are presently available for the analysis of wave propagation across jointed rock masses with the consideration of multiple wave reflections between joints. These methods can be divided into two categories. One is based on the displacement discontinuity model for representing rock joints, where the displacements across a joint are discontinuous and the tractions are continuous, and the other is the equivalent medium method. For the first category, there are three methods, i.e., method of characteristics (MC), scattering matrix method (SMM) and virtual wave source method (VWS). MC solves the equation of motion by using the theory of characteristic curves. SMM is based on the definition of the scattering matrix in which the reflection and transmission coefficients of a set of joints are stored. VWS method replaces the joints in the rock mass with a virtual concept. For the second category, equivalent medium model treats the problem in the frame of continuum mechanics and simplifies it from an explicit wave propagation equation. The objective of this paper is to review and compare these theoretical methods. The comparison shows that the four solutions agree very well with each other. Some additional considerations about the advantages and disadvantages of these methods are also given in the paper.     

基于大直径霍普金森压杆数值试验的非均匀介质动态破坏过程分析

基于细观损伤力学基础而开发的动态岩石破裂过程分析系统RFPA2D代替大直径SHPB试验技术对非均匀介质的动态破坏过程和动态性能进行数值模拟,分析了加载波形和介质的非均匀性对数值试样的动态性能,如应力-时间曲线、应变-时间曲线、应力-应变曲线和应变率-时间曲线的影响。分析表明,大直径SHPB弥散效应对试验结果的影响较大,选择合适的加载波形可以减小SHPB装置中应力波的弥散效应,得到较准确的试验结果,其中三角形波加载可以有效降低大直径SHPB动态测试中的应力波弥散,是岩石等非均匀材料SHPB动态测试的较理想加载波形;在相同加载条件下,岩石的非均匀性对波的弥散效应影响不大,但非均匀岩石的试验曲线比均匀岩石的曲线在波峰后都出现较大的振荡,这主要是由于不同均质度的岩石其单元具有不同的破坏分布造成的,不是波形弥散造成的。     

Numerical study on S-wave transmission across a rough,filled discontinuity

This paper presents a numerical simulation of S-wave propagation across a rough, filled discontinuity using the universal distinct element code (UDEC). The ability of UDEC to simulate a stress wave across a smooth and planar discontinuity filled with an elastic material is validated through comparisons with analytical solutions. Next, the effect of the plastic deformation of the fill on the wave propagation is investigated. The model is extended to further study S-wave propagation across a filled discontinuity with rough interfaces, which is described using a sawtooth. The transmission coefficient defined by the energy is used to measure the wave attenuation. Finally, a parametric study is conducted to investigate the influences of the filled thickness, asperity angle, and incident amplitude on the transmission waves and transmission coefficients. The asperity angle and filled thickness together determine the transmitted waveform and transmission coefficient. The transmitted wave may be cut off when the incident wave amplitude exceeds a threshold value. The transmission coefficient decreases with a different trend with the incident wave amplitude increasing when the asperity angle varies. Compared with planar discontinuity, a filled discontinuity with rough interfaces is more sensitive to the amplitude of the incident wave. The causes of these phenomena are analyzed in detail. In addition, the deformation of the fill material is strongly related to the wave attenuation.     

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。     

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.     

P‐wave transmission across fractures with nonlinear deformational behaviour

Stress wave attenuation across fractured rock masses is a great concern of underground structure safety. When the wave amplitude is large, fractures experience nonlinear deformation during the wave propagation. This paper presents a study on normal transmission of P‐wave across parallel fractures with nonlinear deformational behaviour (static Barton–Bandis model). The results show that the magnitude of transmission coefficient is a function of incident wave amplitude, nondimensional fracture spacing and number of fractures. Two important indices of nondimensional fracture spacing are identified, and they divide the area of nondimensional fracture spacing into three parts (individual fracture area, transition area and small spacing area). In the different areas, the magnitude of transmission coefficient has different trends with nondimensional fracture spacing and number of fractures. In addition, the study reveals that under some circumstances, the magnitude of transmission coefficient increases with increasing number of fractures, and is larger than 1. Copyright © 2006 John Wiley & Sons, Ltd.     

Analytical solutions for dynamic pressures of coupling fluid–porous medium–solid due to SV wave incidence

This paper presents the results of theoretical investigation on the dynamic coupling of an ideal fluid‐porous medium‐elastic half‐space system subjected to SV waves to study the effect of sediment on the seismic response of dams for reservoirs that are deposited with a significant amount of sediment after a long period of operation. The effects of the porous medium and the incident wave angle on dynamic pressures in the overlying ideal fluid are analyzed, and the reflection and transmission coefficients of the wave at the material interfaces are derived using an analytical solution in terms of displacement potentials. The numerical test of modeling shows that the dynamic pressures significantly depend on the properties of porous medium. The fully saturated porous medium reduces the response peaks slightly, while the partially saturated porous medium causes a considerable increase in the resonance peaks. Copyright © 2009 John Wiley & Sons, Ltd.     

Validating the ability of the discontinuous deformation analysis method to model normal P‐wave propagation across rock fractures

The effects of fractures on wave propagation problems are increasingly abstracting the attention of scholars and engineers in rock engineering field. This study aims to fully validate the ability of discontinuous deformation analysis (DDA) to model normal P‐wave propagation across rock fractures. The effects of a single fracture and multiple parallel fractures are all tested. The results indicate that DDA can accurately reflect the fracture effects, including the fractures stiffness, the fracture spacing and the fracture number, and the effects of incident wave frequency on one‐dimensional P‐wave propagation problems. Thus, DDA is able to deal well with normal incident P‐wave propagation problems. Copyright © 2017 John Wiley & Sons, Ltd.     

基于元胞自动机模型的堆积体动力学参数研究

堆积体是一种典型的二元介质,由软弱的基质土与坚硬的碎、块石构成。利用元胞自动机模型对随机离散单元进行演化,模拟堆积体的分布结构、“聚团”特征;利用弹性应力波传播原理计算波的等效速度,研究了堆积体内介质分布、软硬程度对动力学参数的影响规律。研究发现,堆积体内的波速由基质与充填物共同决定,基质材料越弱,地震波传播速度越慢,二者呈对数变化;堆积体内碎石含量越高,则波速越快,波速与充填碎石块含量呈对数关系增长,而振幅系数与碎石含量关系不大,主要取决于碎块石的分布结构;由于堆积体介质密度不均,导致堆积体内波传播速度与入射波频率密切相关,高频波速度快、低频波速度慢,横波速度与入射波频率成指数递增关系。研究表明,采用基于元胞自动机模型研究动变形参数,可以更好地反映出堆积体的波动力学性能,是一种获得复杂介质动参数的重要方法,可以弥补室内及现场试验的不足。     

节理面透射模型及其隔振性能研究

振动波入射到节理界面上,与软弱断层一样会产生波场的分解,能够起到隔振作用。根据线性变形节理的透反射规律研究发现,隔振后各点的波场可由透射P波与透射S波叠加而成,其能量分配服从Zoeppritz方程,不连续位移造成了透射波的衰减;法向刚度增加透射纵波系数会增加,而切向刚度与透射纵波无关,法向与切向刚度对透射S波均有影响,刚度增加透射S波振幅逐渐降低,逐步逼近于0;由于透射后波场相互干涉,不同波场延时不同,透射合成波与入射波相比,振幅降低,持续时间增加,波形尾段有畸变;总能量系数与节理面的刚度无关,而随入射角增加不断降低。     

Application of the numerical manifold method for stress wave propagation across rock masses

In this paper, the numerical manifold method (NMM) is extended to study wave propagation across rock masses. First, improvements to the system equations, contact treatment, and boundary conditions of the NMM are performed, where new system equations are derived based on the Newmark assumption of the space–time relationship, the edge‐to‐edge contact treatment is further developed for the NMM to handle stress wave propagation across discontinuities, and the viscous non‐reflection boundary condition is derived based on the energy minimisation principle. After the modification, numerical comparisons between the original and improved NMM are presented. The results show that the original system equations result in artificial numerical damping, which can be overcome by the Newmark system equations. Meanwhile, the original contact scheme suffers some calculation problems when modelling stress wave propagation across a discontinuity, which can be solved by the proposed edge‐to‐edge contact scheme. Subsequently, the influence of the mesh size and time step on the improved NMM for stress wave propagation is studied. Finally, 2D wave propagation is modelled, and the model's results are in good agreement with the analytical solution. Copyright © 2013 John Wiley & Sons, Ltd.     

不同煤岩介质模型的波场特征研究

准确和形象地分析煤矿微地震波在不同介质中的传播规律,能够为煤矿主动地震勘探以及反演煤矿不同区域内部介质结构提供有效的理论依据。基于二维介质模型,以煤矿典型的煤、岩单一均匀介质模型、煤岩组合多层介质模型、含断层煤岩介质模型以及含水煤岩双相介质模型为例,利用高阶有限差分法对不同煤岩介质进行了波场模拟,分析不同介质的波场特征。研究结果表明,高阶有限差分法可以准确、形象地得到煤岩不同介质条件下的纵横波的波场特征;不同介质模型的波场特征各不相同,在多层煤岩介质中不同介质的分界面会发生纵横波的反射、透射和转换,产生透射波、透射转换波、反射波和反射转换波;在含断层煤岩介质中断层处不仅可以产生透射波、透射转换波、反射波和反射转换波,还可以发生绕射产生绕射波;在含水煤岩双相介质中不仅有快纵波和横波,也会产生慢纵波。不同时刻的波场快照可以进一步形象地描述波场动态特征,都为矿山微震波场分析打下了理论基础。     

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.     

冲击载荷下块系岩体摆型波传播特性的试验研究

摆型波现象是深部开采中块系岩体固有的动力学特征之一。为研究深部块系岩体摆型波传播规律,采用理论分析与室内试验相结合的方法,研究了在冲击载荷作用下摆型波的传播特性。该试验采用12块花岗岩和橡胶夹层材料建立了模型,采用TST5915动态数据采集系统进行信号监测,分别获得了在均质夹层和部分夹层介质增厚情况下的加速度响应曲线,并运用摆型波动力模型理论进行分析。结果表明,摆型波在块体间传播过程中,频率大小不受能量大小的影响,而能量大小决定了波的衰减时间。当块体间介质黏性增加时,加速度幅值均有所下降,但对加速度衰减周期没有影响,而影响加速度衰减的主要因素是冲击载荷的能量大小。此次试验研究将为今后进一步研究摆型波动力传播特性提供一定的基础。