Long-Wavelength Elastic Wave Propagation Across Naturally Fractured Rock Masses

Geophysical site investigation techniques based on elastic waves have been widely used to characterize rock masses. However, characterizing jointed rock masses by using such techniques remains challenging because of a lack of knowledge about elastic wave propagation in multi-jointed rock masses. In this paper, the roughness of naturally fractured rock joint surfaces is estimated by using a three-dimensional (3D) image-processing technique. The classification of the joint roughness coefficient (JRC) is enhanced by introducing the scan line technique. The peak-to-valley height is selected as a key indicator for JRC classification. Long-wavelength P-wave and torsional S-wave propagation across rock masses containing naturally fractured joints are simulated through the quasi-static resonant column (QSRC) test. In general, as the JRC increases, the S-wave velocity increases within the range of stress levels considered in this paper, whereas the P-wave velocity and the damping ratio of the shear wave decrease. In particular, the two-dimensional joint specimen underestimates the S-wave velocity while overestimating the P-wave velocity. This suggests that 3D joint surfaces should be implicated to obtain the reliable elastic wave velocity in jointed rock masses. The contact characteristic and degree of roughness and waviness of the joint surface are identified as a factor influencing P-wave and S-wave propagation in multi-jointed rock masses. The results indicate a need for a better understanding of the sensitivity of contact area alterations to the elastic wave velocity induced by changes in normal stress. This paper’s framework can be a reference for future research on elastic wave propagation in naturally multi-jointed rock masses.     

爆破荷载应力波在无限弹性介质中传播的特征线法解

双指数爆破荷载的应力时程关系是爆破工程的数值分析常用的动力输入。其在弹性岩石中传播衰减的特征线法解是工程爆破数值分析中弹性以及弹塑性分析的重要参照,也是动力学数值分析算法开发的重要高阶校准工具。应用统一弹性波的特征线法解求解源自圆形孔洞的双指数爆破荷载在理想介质中的传播。介绍了源自圆形孔洞的双指数爆破荷载在周围弹性介质传播过程中的径向应力、周向应力、位移以及速度波的特征线法解的具体过程,在MATLAB中进行了4种波的特征线法解的数值实施。对径向应力、周向应力、位移以及速度波的特征线法解的结果进行了多方面讨论。结果表明,特征线法是求解双曲型偏微分方程的一种有效方法,双指数爆破荷载在弹性岩石中传播衰减的特征线法解可为爆破工程数值分析以及动力学数值分析算法开发提供重要的支撑。     

阻尼对应力波传播的影响

基于一维应力波理论，本文讨论了材料粘性（内阻尼）及作用于杆侧表面外阻尼对应力波传播的影响，应力波在外阻尼作用下，向上传播－应力波，该应力波在端面质点速度方向与入射波质点速度相反，而内阻尼则使材料具有松弛、蠕变行为，作用力终止后，端面质点速度缓慢地回复到零。无论是内阻尼还是外阻尼。受其影响，应力波在向下传播过程中，能量有一定程度的耗损     

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.     

爆炸应力波对新浇混凝土衬砌的影响研究

爆炸应力波作用下新浇混凝土衬砌的破坏模式及安全振动速度是水电、铁道工程隧洞建设中需要解决的重要问题。根据弹性P波及SV波在介质中的传播规律,讨论了P波及SV波在薄层混凝土衬砌中的传播及近似处理方法,依照莫尔-库仑准则、极限拉应力准则、极限拉应变准则,研究了爆炸应力波作用下新混凝土衬砌的破坏模式及安全振动速度。结果表明,入射应力波及衬砌中的折射波对衬砌的破坏作用最主要,折射波在衬砌内产生的反、折射波将降低衬砌中的应力,具有卸载效果;混凝土衬砌的安全振动速度随着龄期的增大而增大,P波入射时,安全振动速度随着入射角的增大而增大,入射角较大时,胶结面容易发生剪切破坏,较小时,容易发生拉伸破坏,SV波入射时,较小角度下容易发生剪切破坏,较大角度时容易发生拉伸破坏;围岩弹性模量越高,衬砌的安全振动速度越小。     

Aligned fractures in carbonate rocks: laboratory and in situ measurements of seismic anisotropy

By vertical seismic profiling and shear wave analysis we show that a packet of carbonate reservoir rocks, found at nearly 3000 m depth in the North German Basin, is seismically anisotropic. For vertical paths of wave propagation the estimated velocity difference of the split shear waves is 10%. No shear wave birefrigence is observed within the hangingwall which, therefore, has to be regarded as isotropic or transversely isotropic. Additional laboratory investigations of the petrography of drilled carbonate samples and of their seismic velocities show that the anisotropy is most probably caused by subvertical fractures with preferred azimuthal orientation. The strike direction of the aligned fractures determined by analysis of split shear waves is approximately N55°E. This value agrees with recently published directions of maximum horizontal tectonic stress in pre-Zechstein sediments in the eastern part of the North German Basin, but it is in contrast to the world stress map. Received: 20 April 1999 / Accepted: 25 August 1999     

单轴加载过程中砂岩声学特性研究

岩体的声学特性与应力状态和破坏程度密切相关,通过岩体声学特性的变化来分析岩体应力状态进而评价工程稳定性是一种行之有效的工程措施。针对砂岩开展了单轴压缩试验,并在加载过程中同步进行3个方向的声波测试,获得了砂岩加载过程中3个不同方向声波波速与应力的演化规律。试验结果表明：随着应力的增加,轴向波速逐渐增大,横向波速表现出先增后减的趋势。考虑到不同方向声波测试结果的差异性,采用含不同倾角裂隙的石膏试样进行声波试验。结果表明,当裂隙方向与声波传播方向一致时,波速最大,与声波传播方向垂直时,波速最小;此外,为分析岩样波速与应力状态的相关性,建立了波速与体应变的关系,结果表明,随着体应变的增加,平均波速逐渐增大,在体应变达到最大值附近时,平均波速达到最大值,在体应变下降阶段,波速开始下降;根据轴向波速与应力的变化规律,得到了应力与波速的指数函数拟合公式,据此可以通过现场测试获得的波速预测现场岩体的应力范围,进而评价工程岩体稳定性。     

Determination of the elastic modulus set of foliated rocks from ultrasonic velocity measurements

Ultrasonic measurements of compressional and shear wave velocities under hydrostatic pressure up to 70 MPa were carried out on cylindrical specimens cored across and along the foliation planes. Our measurements revealed that the foliation of the metamorphic rocks induces a clear velocity anisotropy between two orthogonal directions; faster along the foliation plane and slower across the plane in most rock types. All velocity components monotonically increase with the confining pressure, probably due to the closure of microcracks distributed in rock specimens. We determined the complete set of dynamic moduli of foliated metamorphic rocks with two assumptions; transverse isotropy due to the foliation and ellipsoidal seismic energy propagation from a point source. The calculated elastic moduli referring to different directions could be valuable for the design of various engineering structures in planar textured rock mass.     

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.     

石灰岩和砂岩高温力学特性的试验研究

利用自行研制的岩石加温装置和RMT-150C岩石力学试验机, 对石灰岩和砂岩试样高温后的力学特性进行了试验研究。试验结果表明, 随着温度升高, 两种岩石纵波波速逐渐减小。单轴压缩过程中的全程应力应变曲线经历了压密、弹性、屈服、破坏4个阶段; 达到峰值应力后两种岩石均发生脆性破坏, 砂岩破坏时呈锥形炸裂, 而石灰岩则呈草捆状破坏。高温对两种岩石的强度都有一定的弱化作用, 其峰值应力都随温度升高而降低, 石灰岩700 ℃时强度降幅达84.59 %, 而砂岩强度仅比常温降低22 %左右。两种岩石的峰值应变都随温度升高逐渐增大, 但具体表现不尽相同, 石灰岩500 ℃时应变增加了30.57 %, 500 ℃之后峰值应变基本无变化, 甚至到700 ℃时还略有降低; 砂岩700 ℃时峰值应变增加了80.63 %, 其峰值应变的变化与其微观结构变化相关。随着温度升高, 两种岩石的弹性模量和变形模量均减小, 700 ℃时石灰岩弹性模量降幅为86.8 %, 砂岩弹性模量降幅为46.94 %; 700 ℃时石灰岩变形模量下降了83.9 %, 砂岩的变形模量下降了53.06 %。      

Directional dependence of P- and S-wave propagation and polarization in foliated rocks from the Kola superdeep well: Evidence from laboratory measurements and calculations based on TOF neutron diffraction

We have measured P- and S-wave velocities on two amphibolite and two gneiss samples from the Kola superdeep borehole as a function of pressure (up to 600 MPa) and temperature (up to 600 °C). The velocity measurements include compressional (Vp) and shear wave velocities (Vs1, Vs2) propagating in three orthogonal directions which were in general not parallel to inherent rock symmetry axes or planes. The measurements are accompanied by 3D-velocities calculations based on lattice preferred orientation (LPO) obtained by TOF (Time Of Flight) neutron diffraction analysis which allows the investigation of bulk volumes up to several cubic centimetres due to the high penetration depth of neutrons. The LPO-based numerical velocity calculations give important information on the different contribution of the various rock-forming minerals to bulk elastic anisotropy and on the relations of seismic anisotropy, shear wave splitting, and shear wave polarization to the structural reference frame (foliation and lineation). Comparison with measured velocities obtained for the three propagation directions that were not in accordance with the structural frame of the rocks (foliation and lineation) demonstrate that for shear waves propagating through anisotropic rocks the vibration directions are as important as the propagation directions. The study demonstrates that proper measurement of shear wave splitting by means of two orthogonal polarized sending and receiving shear wave transducers is only possible when their propagation and polarization directions are parallel and normal to foliation and lineation, respectively.     

基于单轴压缩试验的不同风化程度花岗岩分形特征分析

风化花岗岩物理力学性质的弱化给工程稳定性带来很大影响,因此,研究不同风化程度花岗岩的破坏特性具有重要意义。利用河南五岳抽水蓄能电站库区采集的风化花岗岩,结合现场岩芯特征的定性描述及波速比定量评价指标,划分出了微、弱、强3种不同风化程度的花岗岩;对单轴压缩破坏后产生的碎屑进行质量和尺度的特征分析,在此基础上建立了碎屑分形维数值与波速比之间的对应关系,并利用MATLAB对花岗岩破坏后主破裂表面裂缝进行分形维数计算。结果表明：风化试样产生的碎屑以粗粒组为主,且随风化程度增强,粗粒组碎屑质量占比逐渐增大;强风化岩石碎屑长厚比分布范围小,块状碎屑占比低,破坏动力学特性不明显,其形状更单一,主要以板状为主;随着风化程度的降低,块状碎屑含量增多,岩石动力学破坏特征增强,碎屑分形维数随着表征风化程度波速比的增大而呈增大趋势;相较于碎屑质量、宽度和厚度,碎屑数量和长度是影响碎屑分形维数的主控因素,是反映不同风化程度花岗岩破碎分形特征的主要参量;强风化类组花岗岩表面裂缝分形随波速比变化不明显,而弱风化、微风化花岗岩的裂缝分形维数随波速比增大而呈显著增大趋势,说明其自相似程度更高,形状更复杂,而在裂缝形成过...     

Shear wave propagation in granular assemblies

Shear wave velocity is a fundamental property of a granular assembly. It is a measure of the true elastic stiffness of a bulk specimen of discrete grains. Shear wave velocity is typically measured in the laboratory (e.g., using bender elements) or in-situ (e.g., using a seismic cone penetrometer, sCPT). In the current work, shear wave propagation is modeled numerically using the discrete element method (DEM). First, an appropriate method for measuring wave velocity is identified. Then the effects of particle size and elastic properties are investigated. Specimen fabric is then quantified before and after wave excitation and the elasticity of the response at the scale of the particle contacts is investigated. The results show that shear wave velocity may be robustly measured for discrete numerical specimens. The ability to measure shear wave velocity using DEM simulations may provide another tool for researchers seeking to link results from physical and numerical experiments.     

Numerical modelling of the driving response of thin‐walled open‐ended piles

The driving response of thin‐walled open‐ended piles is studied using numerical simulation of the wave propagation inside the soil plug and the pile. An elastic finite element analysis is carried out to identify the stress wave propagation in the vicinity of the pile toe. It is found that the shear stress wave has the highest magnitude above the bottom of the soil plug. Below the bottom of the soil plug, the vertical stress wave has the highest magnitude. Although the shear stress wave propagating in the radial direction is similar in magnitude to the vertical stress wave at the bottom of the soil plug, it decays rapidly while travelling downwards. The highest vertical stress at the bottom of the soil plug appears after the vertical stress wave interacts with the shear stress wave travelling in the radial direction. Initially, the vertical stress wave propagates with the dilation wave velocity in both the radial and vertical directions. After it interacts with the shear stress wave, the vertical stress wave starts to propagate with the shear wave velocity in the radial direction and with the axial wave velocity downwards. It is concluded that at the bottom of the soil plug, the interaction between the waves travelling in radial and vertical directions is important. The capabilities of several one‐dimensional pile‐in‐pile models to reproduce the driving response given by a two‐dimensional axisymmetric finite element model is studied. It is seen that when the base of the soil plug fails, a one‐dimensional pile‐in‐pile model can be used to achieve results in agreement with the finite element model. However, when the pile is unplugged, where the base of the soil plug does not fail, a reduced finite element mesh that permits the radial wave propagation inside the soil plug must be used. Copyright © 2001 John Wiley & Sons, Ltd.     

Source signature and elastic waves in a half‐space under a sustainable line‐concentrated impulsive normal force

First, the response of an ideal elastic half‐space to a line‐concentrated impulsive normal load applied to its surface is obtained by a computational method based on the theory of characteristics in conjunction with kinematical relations derived across surfaces of strong discontinuities. Then, the geometry is determined of the obtained waves and the source signature—the latter is the imprint of the spatiotemporal configuration of the excitation source in the resultant response. Behind the dilatational precursor wave, there exists a pencil of three plane waves extending from the vertex at the impingement point of the precursor wave on the stress‐free surface of the half‐space to three points located on the other two boundaries of the solution domain. These four wave‐arresting points (end points) of the three plane waves constitute the source signature. One wave is an inhibitor front in the behaviour of the normal stress components and the particle velocity, while in the behaviour of the shear stress component, it is a surface‐axis wave. The second is a surface wave in the behaviour of the horizontal components of the dependent variables, while the third is an inhibitor wave in the behaviour of the shear stress component. An inhibitor wave is so named, since beyond it, the material motion is dying or becomes uniform. A surface‐axis wave is so named, since upon its arrival, like a surface wave, the dependent variable in question features an extreme value, but unlike a surface wave, it exists in the entire depth of the solution domain. It is evident from this work that Saint‐Venant's principle for wave propagation problems cannot be formulated; therefore, the above results are a consequence of the particular model proposed here for the line‐concentrated normal load. Copyright © 2002 John Wiley & Sons, Ltd.     

Numerical and analytical investigation of compressional wave propagation in saturated soils

In geotechnical earthquake engineering, wave propagation plays a fundamental role in engineering applications related to the dynamic response of geotechnical structures and to site response analysis. However, current engineering practice is primarily concentrated on the investigation of shear wave propagation and the corresponding site response only to the horizontal components of the ground motion. Due to the repeated recent observations of strong vertical ground motions and compressional damage of engineering structures, there is an increasing need to carry out a comprehensive investigation of vertical site response and the associated compressional wave propagation, particularly when performing the seismic design for critical structures (e.g. nuclear power plants and high dams). Therefore, in this paper, the compressional wave propagation mechanism in saturated soils is investigated by employing hydro-mechanically (HM) coupled analytical and numerical methods. A HM analytical solution for compressional wave propagation is first studied based on Biot’s theory, which shows the existence of two types of compressional waves (fast and slow waves) and indicates that their characteristics (i.e. wave dispersion and attenuation) are highly dependent on some key geotechnical and seismic parameters (i.e. the permeability, soil stiffness and loading frequency). The subsequent HM Finite Element (FE) study reproduces the duality of compressional waves and identifies the dominant permeability ranges for the existence of the two waves. In particular the existence of the slow compression wave is observed for a range of permeability and loading frequency that is relevant for geotechnical earthquake engineering applications. In order to account for the effects of soil permeability on compressional dynamic soil behaviour and soil properties (i.e. P-wave velocities and damping ratios), the coupled consolidation analysis is therefore recommended as the only tool capable of accurately simulating the dynamic response of geotechnical structures to vertical ground motion at intermediate transient states between undrained and drained conditions.     

非饱和土中Rayleigh波的传播特性分析

基于对非饱和多孔介质的研究成果,考虑孔隙中液相和气相的相互影响,研究了非饱和土地基中Rayleigh波的传播特性。通过非饱和土中固相、液相和气相的质量平衡方程、动量平衡方程和非饱和土有效应力原理,建立了问题的弹性波动方程。通过引入势函数及考虑自由透水（透气）的边界条件,经过理论推导给出了非饱和土中Rayleigh波的弥散特征方程。通过数值算例分析了Rayleigh波的波速和衰减系数随饱和度、频率和固有渗透系数等因素的变化规律。结果表明：不同饱和度下波速随频率和固有渗透系数的变化均是先不变,然后小幅下降,再急剧增加,最后趋于一致;衰减系数在不同饱和度下随频率的增大而增大,随固有渗透系数的增大而先增大后减小。     

The transmission of compressional waves in jointed rock

Experiments have been carried out to determine the effect of joints on the propagation of P-waves in specimens of both weak and strong rocks; in particular the effect of normal stress on the transmission of P-waves in jointed rock was studied. These experiments were supported by measurements of seismic wave velocity carried out in tunnels driven in Lower Chalk and Carboniferous strata. The laboratory tests showed that relatively small normal stresses are sufficient to close joints acoustically and this was confirmed by the tunnel site observations. The results show that the interpretation of seismic data for the exploration of engineering sites may be improved by allowing for effects which result in the acoustic closure of joints.     

非饱和土中热弹性波的传播特性分析

基于非饱和多孔介质的研究成果,考虑热效应和孔隙流体迂曲度的影响,研究了非饱和土中热弹性波的传播特性。利用非饱和土中耦合热的固-液-气三相介质的质量平衡方程、渗流连续方程、动量平衡方程和广义非Fourier热传导定律,建立了问题的热弹性波动方程。通过引入势函数,经过理论推导给出了非饱和土中热弹性波的弥散特征方程。结合数值算例,分析了几类热弹性波的波速和衰减系数随迂曲度、热膨胀系数和介质温度等热物理参数的变化规律。结果表明：孔隙水迂曲度的增大将引起P1波、P3波和S波的波速增大,而孔隙气体迂曲度的增大仅使得P2波的波速增大;热膨胀系数的增大将造成P1波波速的增大和热（T）波波速的减小;介质温度的升高将引起各类热弹性波波速的增大;频率、热膨胀系数和介质温度的变化对各类热弹性波的衰减系数均有较大影响,不可忽视。     

表层土剪切波速的不确定性对地表设计谱平台值的影响

土层剪切波速对地表反应谱有重要的影响。选取构建了不同场地类别的235个场地地震反应模型,人工合成了12条强弱及频谱特性不同的加速度时程,运用一维土层地震反应的等效线性化波动方法,研究了不同地震动输入下表层土剪切波速的不确定性对设计谱平台值的影响,统计给出了表层土剪切波速的变异率与地表设计反应谱平台值间的经验公式。结果表明:地表设计反应谱平台值与表层土剪切波速的变异率呈负相关关系,即随表层土剪切波速变异率的增大而减小;不同地震波输入条件下各类场地类别地表设计谱平台高度与表层土剪切波速变异率的数学模型为一阶指数函数。