# Identification of soil parameters in an embankment dam by mathematical optimization

Abstract: The finite element method (FEM) has been widely used to analyse earth and rockfill dams. In a finite element analysis a proper constitutive model has to be chosen for each part of the dam in order to simulate the relation between stresses and strains. The zones of an earth and rockfill dam have different functions. Because of that the zones normally consist of various soil types for which the stress/strain response could vary considerably. For each dam zone, suitable values have to be assigned to the parameters included in the constitutive model chosen. In general, laboratory tests and/or field tests of the soil are needed as a basis for this parameter evaluation. However, many dams are old and limited information might be available regarding the soil materials being used in the dam structures. In dams, it is normally very difficult to take up soil samples for testing, especially from the central impervious part, since this might affect the dam performance and the safety of the dam. For dams it would be advantageous if constitutive parameter values could be determined with some non-destructive method. Inverse analysis provides a possibility to determine the constitutive behaviour of different materials within the dam structure under the condition that the dams have been equipped with various instrumentations, for monitoring dam performance, which record data such as pore pressures, deformations, total stresses and seepage etc. In the method of inverse analysis, two separate parts are included: (1) an optimization method consisting of an error function and a search algorithm and (2) a numerical method to solve the partial differential equations arising in stress-strain analysis of structures. In this study, inverse analysis of a dam case was performed with a commercial finite element program Plaxis and the genetic algorithm was utilized as the search algorithm in the optimization method. The genetic algorithm was chosen due to its robustness and efficiency, particularly since it provides a set of solutions close to the optimum solution instead of one unique answer; a set of solutions is more practical from a geotechnical perspective. In the proposed inverse analysis a finite element model is calibrated automatically by changing the values of the input parameters of the selected constitutive model in different dam zones until the discrepancy between the measured results by dam instrumentations and the corresponding computed results is minimized.In order to examine the efficiency and robustness of the genetic algorithm, the research was initially focused on a synthetic case study. The synthetic case, a set of model parameters known in advance, is a good test of the mathematical basis used in the optimization, i.e. the objective function and the search algorithm. The Mohr-Coulomb model was chosen for all dam zones, as an initial choice for this research, chiefly because of its simplicity. A very good agreement for the optimization against the synthetic case was obtained. The practical outcome of an inverse analysis clearly depends on the ability of the constitutive models chosen to capture the real soil behaviour in the different dam zones. A proper choice of a constitutive model provides an opportunity to calibrate the finite element model properly. Therefore, in the next step the Hardening soil model, an advanced constitutive model, was chosen for optimization on the dam. In this part of the research, two cases (A and B) based on different reservoir water levels and number of berms constructed, were analysed. All the data of horizontal displacement were received from exactly the same positions in the geometry as the measurements carried out with the single inclinometer. The results of inverse analyses showed that the Hardening soil model is able to capture better the soil displacements within the dam structure, especially at the crest part, compared to the Mohr-Coulomb model.Finally, it was concluded that inverse analysis is a practical tool for identifying soil material properties of earth and rockfill dams and provides a non-destructive method for dam engineers to obtain more information about the dams. Moreover, if inverse analysis applications become available in commercial finite element software, it would certainly be a valuable tool for dam engineers assessing dam performance and dam safety.