A general solution for groundwater flow around deep excavations based on non–dimensionalization techniques

Abstract

In the context of excavations, the seepage flow rate under retaining earth structures can be pre-quantified using numerical methods, analytical solutions, flow networks, or sets of abacuses. The type curves existing in the literature generally examine 2D scenarios of isotropic hydraulic conductivity in which the horizontal extension of the domain is infinite. Employing the protocol of discriminated non-dimensionalization of the governing equations and boundary conditions, the dimensionless groups that govern the solution to seepage in anisotropic scenarios can be derived. This solution is established through an unknown functional dependence by applying the pi theorem. Three scenarios are studied here: i) a finite horizontal extension of the domain, ii) a finite vertical extension of the domain, and iii) a finite domain size in the vertical and horizontal directions. Numerical simulations are used to verify the results, and new type curves are presented for a wide range of values of the deduced groups. A case study consisting of a 400 m-long excavated trench in a free aquifer is presented to illustrate and validate this study by comparing the pumping rate applied during construction with that calculated using the type curves.