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Deterministic approaches such as the limit equilibrium method (LEM) especially Bishop modified method has been traditionally used to evaluate the stability of embankment dams. However, the uncertainty associated with the material properties necessitates the use of the probabilistic method to account the sensitivity of this uncertainty on the response of the deterministic approaches. In this study, the authors propose the application of design experiment, especially central composite design (CCD) to determine the effects of independent uncertain parameters on the response of stability. A second-order polynomial model with cross terms is used to create an approximating function referred to as response surface for the implicit limit state surface, for which the input data were provided by stability analyses of different heights of homogeneous earth dams (10 m, 20 m, and 30 m) with a depth ratio of DH = 1.5 and a circular slip surface using the Bishop modified limit equilibrium method. The proposed models obtained from this application represent higher prediction accuracy. The study of the effect of geotechnical parameters (material properties of embankment) on safety factor show the importance of individual factors in level of linear effect with a positive effect of c’ or φ’ and a negative effect of H, γd, γsat and significant influence of two-factors interaction, the effect of c’ highly dependent on H, β, γd and φ’. Moreover, the effect of φ’ is dependent on the values of H and β. Lastly, the optimization of safety factor with respect to the range of values of material properties was made, and two failures modes are discussed which are (φ’, c’ reduction and γd increase)

Studying the effect of a variation in the main parameters on stability of homogeneous earth dams using design experiment