This paper extends the material point method to analyze coupled dynamic, two‐phase boundary‐valued problems via a velocity formulation, in which solid and fluid phase velocities are the variables. Key components of the proposed approach are the adoption of Verruijt's sequence of update steps when integrating over time and the enhancement of volumetric strains. The connection between fractional step method and the time‐stepping algorithm presented in this paper is addressed.
Enhancement of volumetric strains allows lower order variations in pressure and mitigates spurious pressure fields and locking that plague low‐order finite‐element implementations.
A stress averaging technique to smoothen stress variations is proposed, and the local damping procedure adopted by FLAC is extended to handle two‐phase problems. Special Kelvin‐Voigt boundaries are developed to suppress reflections at artificial boundaries. Idealized examples are presented to demonstrate the capability of the proposed framework to accurately capture the physics of wave propagation, consolidation and wave attack on a sea dike. Copyright © 2012 John Wiley & Sons, Ltd.