Fillunger–Heinrich’s Theory of Porodynamics: Predictive Power and Analytical Solution

Abstract

The first articulation of the second type of dilatational wave propagating through fluid-saturated geomaterials has been traced to Heinrich’s formulation built on Fillunger’s framework of the mixture theory and Terzaghi’s principle of effective stress. Although this Fillunger–Heinrich theory (FHT) precedes the celebrated Biot’s wave theory and Frenkel’s theory, research has yet to systematically investigate the FHT’s predictive ability. To value the scientific heritage, the original formulation of FHT was first revisited with minor corrections and then reformulated in a dimensionless form. Using the method of separation of variables, an analytical solution was developed for the dimensionless FHT in the context of consolidation under instantaneously applied surcharge and with one-way drainage at the top boundary of the consolidating stratum. The predictive power of FHT was validated against available wave measurements; the proposed solution was verified against the finite-difference method with nonclassical Newmark’s integration schemes. The parametric analysis conducted herein further suggests that FHT can qualitatively interpret observed complex phenomena, including the consolidation delay effect, the top-down progressive pattern, and the initial settlement overestimation. FHT significantly fills the knowledge gap between Terzaghi’s classic theory and Biot’s theory, thus enabling engineers to analyze the one-dimensional dynamic behavior of saturated geo-/poro-materials with incompressible constituents.