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This paper evaluates a simple approximate pseudostatic method for estimating the maximum internal forces and horizontal displacements of a pile group located in a soil slope. The method is an extension of an existing similar method developed by the authors for the case of a horizontal ground surface. The method for horizontal ground involves two main steps: 1. First, the free-field soil movements caused by the earthquake are computed. 2. Second, the response of the pile group is analysed, based on the maximum freefield soil movements as static movements, as well as a static loading at the pile head, which depends on the computed spectral acceleration of the structure being supported. The methodology takes into account the effects of group interaction and soil yielding. Simple modifications are applied to take into account the effect of slope on the seismic deformations of the pile group, making use of the Newmark sliding block method. The applicability of the approach is verified by comparisons with both experimental shaking table tests, and with the results of a more rigorous analysis of a pile-supported wharf. It is demonstrated that the proposed method yields reasonable estimates of the pile maximum moment and horizontal displacement for many practical cases, despite its relative simplicity.

This paper deals with an approach to obtaining the numerical solution of the Lotka–Volterra predator-prey models with discrete delay using Euler polynomials connected with Bernoulli ones. By using the Euler polynomials connected with Bernoulli ones and collocation points, this method transforms the predator-prey model into a matrix equation. The main characteristic of this approach is that it reduces the predator-prey model to a system of algebraic equations, which greatly simplifies the problem. For these models, the explicit formula determining the stability and the direction is given. Numerical examples illustrate the reliability and efficiency of the proposed scheme.

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