Dynamic bulk and shear moduli due to grain-scale local fluid flow in fluid-saturated cracked poroelastic rocks: Theoretical model

Yongjia Song, Hengshan Hu*, John W. Rudnicki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


Grain-scale local fluid flow is an important loss mechanism for attenuating waves in cracked fluid-saturated poroelastic rocks. In this study, a dynamic elastic modulus model is developed to quantify local flow effect on wave attenuation and velocity dispersion in porous isotropic rocks. The Eshelby transform technique, inclusion-based effective medium model (the Mori-Tanaka scheme), fluid dynamics and mass conservation principle are combined to analyze pore-fluid pressure relaxation and its influences on overall elastic properties. The derivation gives fully analytic, frequency-dependent effective bulk and shear moduli of a fluid-saturated porous rock. It is shown that the derived bulk and shear moduli rigorously satisfy the Biot-Gassmann relationship of poroelasticity in the low-frequency limit, while they are consistent with isolated-pore effective medium theory in the high-frequency limit. In particular, a simplified model is proposed to quantify the squirt-flow dispersion for frequencies lower than stiff-pore relaxation frequency. The main advantage of the proposed model over previous models is its ability to predict the dispersion due to squirt flow between pores and cracks with distributed aspect ratio instead of flow in a simply conceptual double-porosity structure. Independent input parameters include pore aspect ratio distribution, fluid bulk modulus and viscosity, and bulk and shear moduli of the solid grain. Physical assumptions made in this model include (1) pores are inter-connected and (2) crack thickness is smaller than the viscous skin depth. This study is restricted to linear elastic, well-consolidated granular rocks.

Original languageEnglish (US)
Pages (from-to)28-54
Number of pages27
JournalJournal of the Mechanics and Physics of Solids
StatePublished - Jul 1 2016
Externally publishedYes


  • Eshelby transform
  • Mori-Tanaka Scheme
  • Porous rocks
  • Squirt flow
  • Wave attenuation

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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