Explicit Model for Excess Porewater Pressure Computation in Fine-Grained Soils with Arbitrary Initial Conditions

Abstract

The consolidation process in fine-grained soils involves changes in excess pore water pressure (EPWP) and void ratio with time. An analytical solution for this problem was presented by Terzaghi (1943). Their solutions included several simplifying assumptions and applied to a constant initial EPWP distributions with depth. The solution is widely used for educational purposes and is of limited practical use where the initial EPWP is complex. The Terzaghi solution is not valid for complex and/or arbitrary applied loading. In such cases, numerical methods are used for EPWP calculation versus time. The finite differences and the finite element methods are powerful tools that are effectively used for modeling the compression behavior of fine-grained soil deposits. Unfortunately, these methods often require large number of calculations and suffer from round-off errors when large number of time increments is required. The proposed model minimizes the round-off errors and eliminates the large number of calculations associated with numerical techniques. The basis of the proposed method is the development of eigenvalues and eigenvectors associated with time-rate of settlement. The proposed explicit model in effect produces a direct solution at any given time and depth. The solution permits the evaluation of EPWP at even a fraction of a time increment. Two models are presented for doubly-drained soil layers and singly-drained layers. Unlike the finite differences method, the proposed model allows arbitrary initial EPWP distribution and for any number of time increments by multiplying four matrices involving soil properties, time increment used and the initial EPWP.