An Experimental Study on Scale-Dependent Velocity and Anisotropy in Fractured Media Based on Artificial Rocks with Controlled Fracture Geometries

Abstract

The scale of the fractures can vary, making the seismic velocity and anisotropy substantially scale dependent. Two mechanisms of the scale-dependent phenomenon may be considered: scattering and wave-induced fluid flow. In this study, we measure the scale-dependent velocity and anisotropy effects through laboratory experiments on porous and non-porous artificial rocks containing aligned fractures. This allows us to isolate the effects of these two mechanisms for the first time, yielding some insights into the scale-dependent phenomenon. For short-wavelength waves, scattering dominates with less wave-induced fluid flow effects. For intermediate- and long-wavelength waves, the P-wave is strongly scale dependent mainly due to wave-induced fluid flow mechanism, and the slow shear-wave is also strongly scale dependent but due to both scattering and wave-induced fluid flow. However, the fast shear-wave is almost scale independent. Moreover, a multi-scale equivalent medium theory can model the P-wave propagation accurately.

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Abbreviations

\({\uplambda }_{{\text{P}}}\). \({\uplambda }_{{\text{s}}}\) :

Wavelength of P- and S-waves

d :

Fracture scale length

\({\uptau }_{{\text{m}}}\) :

Relaxation time at grain scale

\(\uptau_{{\text{f}}}\) :

Relaxation time at fracture scale

\(\eta\) :

Fluid viscosity

\(k\) :

Permeability

\(c_{{\text{v}}}\) :

Volume of the individual cracks

\(K_{{\text{c}}}\) :

Inverse of the crack space compressibility

\(c_{1}\) :

Number of connections to other elements of the pore space

\(\sigma_{{\text{c}}}\) :

Critical stress

\({\upmu }\) :

Shear-wave modulus

r :

Aspect ratio of the crack

ν:

Poisson’s ratio of the isotropic rock matrix

\(\varsigma\),\({ }a_{{\text{f}}}\) :

Grain size and fracture size

\(\phi_{p}\), \(\epsilon_{{\text{c}}}\), \(\epsilon_{f}\) :

Porosity, crack density and fracture deity

\(C_{{{\text{ijkl}}}}\) :

Stiffness tensor of fractured rock

\(C_{{{\text{ijkl}}}}^{0}\) :

Elastic properties of the unfractured porous rock

\({\text{C}}_{{{\text{ijkl}}}}^{1}\), \({\text{C}}_{{{\text{ijkl}}}}^{2}\), \({\text{C}}_{{{\text{ijkl}}}}^{3}\) :

Contributions from the pores, micro-scale cracks and meso-scale fractures, respectively

\(\lambda^{0}\), \(\mu^{0}\) :

Lame parameters of porous background matrix

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Acknowledgements

This work is supported by the National Natural Science Fund Projects (41804105, U19B6003), the Fundamental Research Funds for the Central Universities (2462018YJRC008) and the National Science and Technology Major Project (2017ZX05018005).

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Correspondence to Xiang-Yang Li.

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Ding, P., Wang, D. & Li, X. An Experimental Study on Scale-Dependent Velocity and Anisotropy in Fractured Media Based on Artificial Rocks with Controlled Fracture Geometries. Rock Mech Rock Eng 53, 3149–3159 (2020). https://doi.org/10.1007/s00603-020-02095-2

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Keywords

  • Dispersion
  • Fluid flow
  • Velocity anisotropy
  • Fracture