SEEPAGE ANALYSIS AIDED OPTIMAL DESIGN OF HOMOGENEOUS EARTH DAMS

Abstract

The present study is aimed at evolving a procedure for arriving at an optimal design of a homogeneous earth dam laid on an impervious foundation and provided with a drain. The procedure, heavily dependent on variably saturated flow modelling, involves optimizing a multi-objective function comprising a weighted summation of four objective functions, viz., the dam section area, seepage discharge, wetted area and the drain area. The design variables considered in the optimization are the upstream and downstream slopes and drain dimensions. The optimization is carried out subject to the constraints ensuring safe upstream and downstream slopes and sufficient distance between the free surface and downstream face. The optimization is conducted by employing sequential unconstraint minimization technique (SUMT) (Rao, 2000). The objective functions representing the seepage discharge and the wetted area, and all the constraints are viewed as implicit functions of the pore water pressure/ soil moisture content distributions in the section. These distributions are obtained by modelling two-dimensional (vertical plane) variably saturatedflow (Ahmad et al., 1993) in a homogeneous earth dam. This is followed by computing the implicit state variables, viz., seepage discharge, wetted area, factors of safety and the minimum distance between the free surface and the downstream face, which in turn leads to computation of the implicit objective functions and all the constraints. These computations (except for the constraint on the stability of upstream slope) are based upon the computed steady state pore water pressure/ soil moisture contentdistributions corresponding to reservoirfull condition. The constraint on the stability of upstream slope is evaluated employing the pore water pressure/ soil moisture content distributions computed under sudden draw down condition. The variably saturated flow model developed for simulating the pore water pressure/ soil moisture content distributions is validated employing an analytical solution (Harr, 1962) and a reported data set (Giu et al., 2000). The factors of safety in respect of stability of upstream and downstream slopes are computed using simplified Bishop's method (Bishop, 1955) and employing the computed pore water pressure/ soil moisture content distributions. An algorithm is developed for the necessary numerical generation of the slip circles. This is validated employing a set of published data (Desai, 1977). Optimization procedure described above requires repeated runs of the variably saturated flow model and computation of the implicit state variables with varying values of the design variables. The computer time requirement for such large number of model runs is bound to be prohibitively large. This problem, in the present study, is overcome by conducting the model runs for several combinations of the design variables and computing the corresponding implicit state variables. Subsequently, these set of discrete data are employed to interpolate the state variables for various values of the design variables during the optimization. This apparently eliminates necessity of the model runs during the optimization. The results of the optimization are presented in the form of non-dimensional design curves or tables for different weights and non-dimensional parameters. These curves/tables can be used for arriving at optimal design of a homogeneous dam section by a simple interpolation procedure which is illustrated with an example. Studies are conducted to illustrate the sensitivity of the optimal design to the weights assigned to the four objective functions in the multi-objective function, and to the degree of hydraulic conductivity.