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1.
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. 相似文献
2.
Propagation of elastic waves in discontinuous media is studied in this paper by the scattering matrix method (SMM). An electromagnetic transmission line analogy is also used to set up the mathematical model. The SMM operates in the frequency domain and allows for all wave polarizations (P, SV and SH). Rock masses are examples of discontinuous media in which the discontinuities (fractures or joints) influence wave propagation. Both elastic and viscoelastic joints are considered and the latter are described by Kelvin–Voigt, Maxwell and Burgers models. Rock joints with Coulomb slip behavior are also analyzed, by applying the averaging principle of Caughy (J Appl Mech 27:640–643, 1960). The evaluation of the effects of periodic discontinuities in a homogeneous medium is presented by introducing the concept of Bloch waves. The dispersion curves of these waves are useful to explain the existence of frequency bands of strong attenuation, also in the case of lossless (perfectly elastic) structures. Simple expressions of transmission and reflection coefficients are obtained. Finally, the SMM results are compared with those computed via the distinct element method (DEM). The comparisons are performed on a medium with joints with Coulomb slip behavior and the agreement is satisfactory, although the SMM must be applied in conjunction with the equivalent linearization technique. Even if the DEM is much more general, the SMM in these simple cases is extremely faster and provides a higher physical insight. 相似文献
3.
This paper evaluates the existing equivalent medium methods for jointed rock mass and further develops the equivalent viscoelastic medium method proposed by the authors. The advantages and limitations of different equivalences to the discontinuous rock mass are discussed. Theoretical derivation of stress wave propagation through the equivalent viscoelastic medium is carried out by adopting the Fourier transformation method, and the parameters of the equivalent viscoelastic medium method are determined analytically. The frequency dependence and the wave attenuation phenomenon can be properly described when the imaginary terms of the complex moduli of the rock mass are included. The results show that the equivalent viscoelastic medium method is able to predict the effective velocity and the stress wave transmission coefficient in a rock mass more accurately than the conventional effective elastic moduli methods. An example of the stress wave propagation through rock mass with parallel joints shows that the equivalent viscoelastic medium method is promising and worthy to be further explored for application in practical rock engineering problems. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
4.
Analysis of Blast Wave Interaction with a Rock Joint 总被引：8，自引：3，他引：5
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. 相似文献
5.
6.
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. 相似文献
7.
地震波在跨越岩体中节理时的透反射特性是岩石地下工程抗震分析问题中的重要基础,目前开展的研究工作中尚未有针对连续屈服（CY）非线性节理模型透反射特性的研究报导。在前人提出的非线性节理透反射系数时域递归法解答的基础上,将这一方法拓展至CY模型。并采用3DEC离散元软件,对比了CY模型的时域递归解与数值模拟结果的差异。在此基础上以时域递归解为手段,辅以离散元数值模拟,开展了CY模型的参数影响研究。最终比较了库仑（MC）模型与CY模型在正弦脉冲激励和真实地震动激励下表现的差异。结果表明：CY模型的时域递归解与3DEC数值模拟结果显示了良好的一致性,证明了时域递归解用以进行后续参数研究的合理性。法向应力、入射波幅值、节理初始刚度、节理间距等参数对CY模型具有显著影响。相比库仑模型,连续屈服模型可以更好地反映地震波穿越节理时发生的复杂力学现象,如切向刚度退化、抗剪强度劣化、法向应力依赖性、滞回现象等。研究成果可为岩石地下工程的抗震设计与分析工作提供一定参考。 相似文献
8.
多裂隙岩体的损伤断裂模型及模型试验 总被引：5，自引：0，他引：5
对于由裂隙、岩石组成的多裂隙岩体,本文通过对裂隙岩体内的应力、应变的体积平均,提出了适合于这种岩体的等效连续模型。运用损伤力学以及断裂力学理论,定义了岩体损伤张量、有效应力张量、损伤应变等,建立了损伤演化方程,从而建立了多裂隙岩体的损伤断裂模型。对岩体裂隙的扩展方式进行了模拟试验。 相似文献
9.
Hatem Gasmi Essaïeb Hamdi Nejla Bouden Romdhane 《Rock Mechanics and Rock Engineering》2014,47(4):1393-1409
Homogenization in fractured rock analyses is essentially based on the calculation of equivalent elastic parameters. In this paper, a new numerical homogenization method that was programmed by means of a MATLAB code, called HLA-Dissim, is presented. The developed approach simulates a discontinuity network of real rock masses based on the International Society of Rock Mechanics (ISRM) scanline field mapping methodology. Then, it evaluates a series of classic joint parameters to characterize density (RQD, specific length of discontinuities). A pulse wave, characterized by its amplitude, central frequency, and duration, is propagated from a source point to a receiver point of the simulated jointed rock mass using a complex recursive method for evaluating the transmission and reflection coefficient for each simulated discontinuity. The seismic parameters, such as delay, velocity, and attenuation, are then calculated. Finally, the equivalent medium model parameters of the rock mass are computed numerically while taking into account the natural discontinuity distribution. This methodology was applied to 17 bench fronts from six aggregate quarries located in Tunisia, Spain, Austria, and Sweden. It allowed characterizing the rock mass discontinuity network, the resulting seismic performance, and the equivalent medium stiffness. The relationship between the equivalent Young’s modulus and rock discontinuity parameters was also analyzed. For these different bench fronts, the proposed numerical approach was also compared to several empirical formulas, based on RQD and fracture density values, published in previous research studies, showing its usefulness and efficiency in estimating rapidly the Young’s modulus of equivalent medium for wave propagation analysis. 相似文献
10.
The wave propagation in jointed rock mass depends on many factors, in particular the wave frequency, existing stress conditions and the induced strain levels. When the wavelength of the propagating wave is much longer than the spacing of the joints, it is referred to as long-wavelength condition. This is a dominant condition in seismological studies due to the presence of closely spaced joints in rocks. A comprehensive study on long-wavelength propagation of shear and compression waves in very weak rocks has been carried out with the help of a resonant column apparatus using a model material (plaster of Paris) at various strain levels. The working principle and suitability of the apparatus for testing stiff samples are discussed. The velocity reductions of shear and compression waves across joints are obtained. The influence of frictional and filled joints in attenuating stress waves under various strain levels is analysed. Wave velocities are found to be reduced with increasing strain levels and decreasing joint spacing. The joints with gouge material are more efficient at damping the waves. It is recognised that wave velocity reductions and damping across joints are functions of confining stress and strain levels induced in very weak rocks. 相似文献
11.
裂隙型单斜介质中弹性系数的计算及波的传播特性研究 总被引：3，自引：1，他引：3
根据Hudson等关于裂隙介质弹性系数计算的扰动理论及Bond变换矩阵原理，给出了各向同性介质中含多组垂直裂隙时等效弹性系数的计算方法。计算了含两组斜交的垂直裂隙形成的单斜各向异性介质中的等效弹性系数，并根据Christoffel方程推导、得出水平面内平面波传播的相速度和群速度随方位变化的特性。 相似文献
12.
Analysis of Wave Propagation Through a Filled Rock Joint 总被引：1，自引：1，他引：0
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. 相似文献
13.
14.
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. 相似文献
15.
引言岩石和岩体的本构关系(包括适用于可压缩流体的状态方程)是岩石介质的应力(或压力)、应变(或比容)、比内能(或温度)、及加载路径、应变率等之间的普遍关系式.它是研究应力波在岩石介质中的传播规律及其与地下结构相互作用的基础;在估价地下结构对各种爆炸作用的抵抗能力以设计经得起这些作用的防护结构时,在预报周围环境地运动及确定结构--介质相互作用时,都需要岩石和岩体介质的动力响应的精确描述; 相似文献
16.
Wang Wu-ling Feng Yi-xing 《岩土力学》1980,2(1):15-36
The constitutive relations of rock and rock mass are essential to the study of propagation of stress wave in rock medium and its interaction with structure .in this paper ,the development of the research on constitutive relations of rock and rock mass is briefly reviewed ;the equations of state of rock in fluid state at high pressures and the con equations of rock in solid state are mainly described .The cop model as the constitutive equation of rock and its generaligations especially discussed . 相似文献
17.
Mohd Mustaqim Mohd-Nordin Ki-Il Song Gye-Chun Cho Zainab Mohamed 《Rock Mechanics and Rock Engineering》2014,47(2):561-573
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. 相似文献
18.
A three‐phase medium model is proposed in describing the dynamic property of filled rock joints and an analytical study on longitudinal wave transmission normally across a three‐phase rock joint is presented. Parameters in the three‐phase medium model were determined by a series of modified split Hopkinson pressure bar (SHPB) tests, where a sand or clay layer was used to represent an artificially filled rock joint. The effect of the unloading path on the transmitted wave was discussed by comparing the analytical and SHPB test results. The derived wave transmission coefficients across the filled joint agreed very well with those from the test results. Both the analytical and the test results showed that the wave transmission coefficients were affected by the mechanical properties of the fillings. Parametric studies with respect to the volume ratios of water and air in the three‐phase medium and the type of filling material have also been performed. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
19.
Seepage-stress coupling is a key problem in the field of geotechnical engineering, and the finite element method is one of the main methods to study seepage-stress coupling in rock masses. However, the finite element method has issues of poor stability, low efficiency, and low accuracy in the simulation of the seepage-stress coupling problem. In this paper, the homogeneous saturated rock mass is taken as the object to deduce the control equation based on the Biot's theory. Considering the singularity of the coupling matrix, the discrete equation is converted into a precise integral format, and the equation is solved by the precise integration method to avoid instability and low precision. The precise integration method in this paper has good numerical stability, fast convergence speed, and high simulation accuracy, which effectively facilitates the rapid and stable numerical simulation of the seepage-stress coupling problem using the equivalent continuum medium model. The validity and accuracy of the precise integration method for seepage-stress coupling problems are verified by numerical examples. 相似文献
20.
通常地层介质都是粘滞性的,由于地层的吸收作用,地震波在向下传播过程中能量被衰减,特别是高频能量的衰减,使反射信号频带宽度变窄。为了补偿被吸收的能量,笔者采用粘滞声波方程波场延拓方法进行能量吸收和衰减补偿。首先,从粘滞性波动方程波场延拓函数理论出发,推导了波场延拓函数稳定性条件;其次,对其有效性进行了测试和分析;最后,通过设计数值模型进行正演模拟对比试验,证明了基于粘滞性声波方程的吸收补偿方法能够很好地对粘性介质吸收衰减进行能量补偿,改善处理效果。 相似文献