Study on S-wave propagation through parallel rock joints under in situ stress

The interaction between rock joints and seismic waves is critical in rock engineering when rock mass is suffered from human-induced or natural earthquakes. Stress wave propagation across rock joints is usually dependent on the seismic response of the joints. Wave propagation may cause joints close or open under the in situ stress. In this paper, the seismic response for wave propagation with an arbitrary incident angle impinging on joints is studied. Both reflection and transmission usually occurring at the two interfaces of the joint are considered, respectively. Wave propagation equations with equally and unequally close-open behaviours are deduced firstly, which can be applied for the general cases of arbitrary incident P- or S-wave. Then, wave propagation across joints with normal and oblique incident P- and S-waves is analyzed by considering the equally and unequally close-open behaviours and verified by comparing with the existing methods. Finally, several parametric studies are conducted to evaluate the effect of in situ stress on transmitted waves, the effect of the incident frequency on the maximum deformation of joints, and the effect of the incident angle on the maximum deformation of joints. The wave propagation equations derived in the study are more feasible and can well analyze the seismic response of wave propagation for the most general cases of different incident waveforms.

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Simulation of seismic waves at the earth's crust (brittle–ductile transition) based on the Burgers model

Solid Earth ◽

10.5194/se-5-1001-2014 ◽

2014 ◽

Vol 5 (2) ◽

pp. 1001-1010 ◽

Cited By ~ 3

Author(s):

J. M. Carcione ◽

F. Poletto ◽

B. Farina ◽

A. Craglietto

Keyword(s):

Seismic Waves ◽

In Situ Stress ◽

Seismic Attenuation ◽

Earth’S Crust ◽

S Wave ◽

Fourier Pseudospectral Method ◽

Stress Criterion ◽

Brittle Ductile Transition ◽

Earth's Crust

Abstract. The earth's crust presents two dissimilar rheological behaviors depending on the in situ stress-temperature conditions. The upper, cooler part is brittle, while deeper zones are ductile. Seismic waves may reveal the presence of the transition but a proper characterization is required. We first obtain a stress–strain relation, including the effects of shear seismic attenuation and ductility due to shear deformations and plastic flow. The anelastic behavior is based on the Burgers mechanical model to describe the effects of seismic attenuation and steady-state creep flow. The shear Lamé constant of the brittle and ductile media depends on the in situ stress and temperature through the shear viscosity, which is obtained by the Arrhenius equation and the octahedral stress criterion. The P and S wave velocities decrease as depth and temperature increase due to the geothermal gradient, an effect which is more pronounced for shear waves. We then obtain the P−S and SH equations of motion recast in the velocity-stress formulation, including memory variables to avoid the computation of time convolutions. The equations correspond to isotropic anelastic and inhomogeneous media and are solved by a direct grid method based on the Runge–Kutta time stepping technique and the Fourier pseudospectral method. The algorithm is tested with success against known analytical solutions for different shear viscosities. A realistic example illustrates the computation of surface and reverse-VSP synthetic seismograms in the presence of an abrupt brittle–ductile transition.

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Simulation of seismic waves at the Earth crust (brittle-ductile transition) based on the Burgers model

Solid Earth Discussions ◽

10.5194/sed-6-1371-2014 ◽

2014 ◽

Vol 6 (1) ◽

pp. 1371-1400 ◽

Cited By ~ 5

Author(s):

J. M. Carcione ◽

F. Poletto ◽

B. Farina ◽

A. Craglietto

Keyword(s):

Seismic Waves ◽

Grid Method ◽

In Situ Stress ◽

Seismic Attenuation ◽

S Wave ◽

Fourier Pseudospectral Method ◽

Stress Criterion ◽

Brittle Ductile Transition ◽

The Earth

Abstract. The Earth crust presents two dissimilar rheological behaviours depending on the in-situ stress-temperature conditions. The upper, cooler, part is brittle while deeper zones are ductile. Seismic waves may reveal the presence of the transition but a proper characterization is required. We first obtain a stress–strain relation including the effects of shear seismic attenuation and ductility due to shear deformations and plastic flow. The anelastic behaviour is based on the Burgers mechanical model to describe the effects of seismic attenuation and steady-state creep flow. The shear Lamé constant of the brittle and ductile media depends on the in-situ stress and temperature through the shear viscosity, which is obtained by the Arrhenius equation and the octahedral stress criterion. The P- and S-wave velocities decrease as depth and temperature increase due to the geothermal gradient, an effect which is more pronounced for shear waves. We then obtain the P-S and SH equations of motion recast in the velocity-stress formulation, including memory variables to avoid the computation of time convolutions. The equations correspond to isotropic anelastic and inhomogeneous media and are solved by a direct grid method based on the Runge–Kutta time stepping technique and the Fourier pseudospectral method. The algorithm is tested with success against known analytical solutions for different shear viscosities. A realistic example illustrates the computation of surface and reverse-VSP synthetic seismograms in the presence of an abrupt brittle-ductile transition.

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Effects of Unidirectional In Situ Stress on Crack Propagation of a Jointed Rock Mass Subjected to Stress Wave

Shock and Vibration ◽

10.1155/2021/5529540 ◽

2021 ◽

Vol 2021 ◽

pp. 1-13

Author(s):

Zhanfeng Fan ◽

Jianhua Cai

Keyword(s):

Wave Propagation ◽

Rock Mass ◽

Crack Propagation ◽

Stress Wave ◽

Large Scale ◽

Jointed Rock ◽

In Situ Stress ◽

Jointed Rock Mass ◽

Stress Wave Propagation

This paper proposes a large-scale experiment combined with multiple cement mortar blocks to simulate stress wave propagation across a jointed rock mass under unidirectional in situ stress. Two identical mortar block models with smooth, dry, and unfilled joints were poured. The stress waves in Model 1 and Model 2 were generated by an electric spark source and a blast-induced source, respectively. The effects of these two excitation sources on stress wave propagation were compared through crack propagation experiments. The experimental results show that the peak value of the transmitted strain wave decreases as the in situ stress increases. The unidirectional in situ stress has a certain inhibitory effect on the stress wave propagation. It also indicates that for Model 1 with the electric spark source, no cracks on the upper surface, but a Livingstone blasting crater at the bottom is generated. For Model 2 with the blast-induced source, cracks on the upper surface and a blasting crater at the bottom are produced. The results verify the similarity between the electric spark source and the explosive source. The two-dimensional finite element program (ANSYS/LS-DYNA) was applied to further simulate the crack propagation of a jointed rock mass under different in situ stresses. The results of numerical simulation verify that the in situ stress has a clear guiding effect on the crack propagation.

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