Spectral element analysis for the pore-pressrure of earth dams

The paper demonstrates the derivation of conversion of governing differential equation of earth-dam pore-pressure to an integral one by the weighted residuals. As per the orthogonality of Chebyshev polynomials on the domain [-1,1]; the approximation of the unknown, earth-dams pore-pressure function, is expanded as spectral Chebyshev series. For the sake of complicated configuration of general problem domain, it´s necessary to adopt spectral-isoparametric mapping onto regular domain, [-1,1] × [-1,1] in two-dimensional formulation, so called spectral element method(SEM). The overall procedure, how to get a spectral element matrix equations combining with initial boundary value conditions, are illustrated in detail. For its excellent characteristics of SEM, particularly in numerical precision, SEM is becoming more and more popular as a numerical tool applied to difficult problems, such as the pore-pressure of earth dams.