Effects of multiple parallel fractures on apparent attenuation of stress waves in rock masses

Cai, Jiangdong; Zhao, Jun

doi:10.1016/s1365-1609(00)00013-7

Cited by 220 publications

(153 citation statements)

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“…Fig. 1 Characteristics in the nondimensional x-t plane MC can also be used to study wave propagation across discontinuous jointed rock masses (Cai and Zhao 2000;Zhao J et al 2006;Zhao XB et al 2006a, b). When a wave propagates in jointed rock masses, multiple reflections occur between joints.…”

Section: Methods Of Characteristicsmentioning

confidence: 99%

“…Pyrak-Nolte (1988) and Cook (1992) used the displacement discontinuity method (DDM) for studying the influence of a set of parallel joints on the transmission of seismic waves. Other applications of this method are given by Cai and Zhao (2000), Zhao J et al (2006) and Zhao XB et al (2006a, b), who used the method of characteristics (MC) for solving wave propagation across a set of parallel joints, where multiple wave reflections were considered. Besides linearly deformational joints, joints with nonlinear (Zhao and Cai 2001;Zhao J et al 2006) and Coulomb slip behavior (Zhao XB et al 2006a) were also studied with MC.…”

Section: Introductionmentioning

confidence: 99%

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Theoretical Methods for Wave Propagation across Jointed Rock Masses

Perino

Zhu

et al. 2010

Rock Mech Rock Eng

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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.

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Section: Methods Of Characteristicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Theoretical Methods for Wave Propagation across Jointed Rock Masses

Perino

Zhu

et al. 2010

Rock Mech Rock Eng

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“…In the DDM (Cai and Zhao, 2000), a rock fracture is considered as an interface between two elastic half-spaces with the same seismic impedance. When a normally incident P-wave propagates across a single rock fracture, the stresses across the fracture are continuous, whereas the displacements are discontinuous and equal to the stress divided by a constant normal specific stiffness…”

Section: Analytical Modelsmentioning

confidence: 99%

“…opening, closure, and slip) has long been recognized as resulting in rock mass instability (Zhao, 1997;Indraratna et al, 2010). When stress waves propagate across fractured rock masses, fractures are commonly considered as displacement discontinuity boundaries (Schoenberg, 1980;Cai and Zhao, 2000). Each fracture is treated as a non-welded contact with negligible thickness compared with the incident wavelength.…”

Section: Introductionmentioning

confidence: 99%

Dynamic response of a rock fracture filled with viscoelastic materials

Zhu

Zhao

2013

Engineering Geology

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Rock fractures filled with viscoelastic materials, such as sand, usually contribute to rock mass instability under the influence of seismic waves and dynamic loads. The purpose of this study is to verify that the specific fracture stiffness and the specific initial mass of the filling sand are two key fracture parameters in interrelating the physical, mechanical and seismic properties of a rock fracture filled with dry sand. A series of dynamic tests using a split Hopkinson rock bar was conducted on a simulated sand-filled fracture. The experimental results show that stress wave attenuation across the filled fracture is strongly affected by wave reflection and transmission at the fracture interfaces and the dynamic compaction of the filling sand. With the comparison between the analytical predictions by the displacement discontinuity model and the displacement and stress discontinuity model and the experimental results from the laboratory tests, it is found that both models can predict a filled fracture with a smaller thickness (i.e., less than 10 mm). The displacement and stress discontinuity model may be used to predict a fracture with a larger thickness by considering the specific initial mass of filling materials. The wave transmission coefficient for a filled fracture generally increases with increasing specific fracture stiffness.

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“…Stress wave propagation across rock joints has been investigated theoretically (e.g., Pyrak-Nolte et al 1990;Cai and Zhao 2000;Li et al 2010a;Zhu et al 2011) and experimentally (e.g., Leucci and Giorgi 2006;Zhao et al 2006Zhao et al , 2008Li et al 2010b). Many studies focus on the interaction between the stress wave and the rock joints (e.g., Li et al 2011;Ma et al 2011).…”

Section: Introductionmentioning

confidence: 99%