Approximate equations for the method of fragment

Abstract

The method of fragment is a simple and approximate technique for solving confined seepage flow problems. In this method, the flow domain is divided into few fragments along the equipotential lines that are assumed to be vertical and a dimensionless form factor is defined for each fragment. The flow rate and the exit hydraulic gradient can be computed using the form factors. Griffiths proposed three types of fragments that are adequate to solve most configurations, incorporating anisotropy in permeability, and presented design charts for determining the form factors. In this paper, through extensive numerical modeling simulations, equations are developed for the form factors and they are validated. These equations enable quicker computations and the method of fragment be implemented in spreadsheets.

The dimensional character of permeability: Dimensionless groups that govern Darcy's flow in anisotropic porous media

“…The studies that make direct use of the group obtained in the previous section from the general discrimination are scarce. It is worth mentioning the work of Madanayaka and Sivakugan 24 for the study of two‐dimensional (confined flow) seepage axisymmetric cofferdam problems using the method of fragments 25 . Using classic arguments based on merely dimensional analysis and from the list of relevant variables of the problem, these authors choose two dimensionless groups consistent with those obtained in the previous section.…”