Differential equations governing slip-induced pore-pressure fluctuations in a water-saturated granular medium

Mathematical Geology



Macroscopic frictional slip in water-saturated granular media occurs commonly during landsliding, surface faulting, and intense bedload transport. A mathematical model of dynamic pore-pressure fluctuations that accompany and influence such sliding is derived here by both inductive and deductive methods. The inductive derivation shows how the governing differential equations represent the physics of the steadily sliding array of cylindrical fiberglass rods investigated experimentally by Iverson and LaHusen (1989). The deductive derivation shows how the same equations result from a novel application of Biot's (1956) dynamic mixture theory to macroscopic deformation. The model consists of two linear differential equations and five initial and boundary conditions that govern solid displacements and pore-water pressures. Solid displacements and water pressures are strongly coupled, in part through a boundary condition that ensures mass conservation during irreversible pore deformation that occurs along the bumpy slip surface. Feedback between this deformation and the pore-pressure field may yield complex system responses. The dual derivations of the model help explicate key assumptions. For example, the model requires that the dimensionless parameter B, defined here through normalization of Biot's equations, is much larger than one. This indicates that solid-fluid coupling forces are dominated by viscous rather than inertial effects. A tabulation of physical and kinematic variables for the rod-array experiments of Iverson and LaHusen and for various geologic phenomena shows that the model assumptions commonly are satisfied. A subsequent paper will describe model tests against experimental data. ?? 1993 International Association for Mathematical Geology.

Additional publication details

Publication type Article
Publication Subtype Journal Article
Title Differential equations governing slip-induced pore-pressure fluctuations in a water-saturated granular medium
Series title Mathematical Geology
DOI 10.1007/BF00911548
Volume 25
Issue 8
Year Published 1993
Language English
Publisher location Kluwer Academic Publishers-Plenum Publishers
Larger Work Type Article
Larger Work Subtype Journal Article
Larger Work Title Mathematical Geology
First page 1027
Last page 1048
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