# A differential quadrature algorithm based on staggered grids for coupled analysis of saturated soils

A differential quadrature algorithm based on staggered grids for coupled analysis of saturated soils Biot’s theory of consolidation is always analyzed numerically for the complexity of the actual problems. The differential quadrature method (DQ) is a high-order numerical algorithm which is popular for its easy implementation and high accuracy and has already been applied successfully in geotechnical engineering. However, spurious pressure oscillations will be observed when strong pressure gradients appear if it is employed directly for coupled consolidation analysis of saturated soils. In the present study, a staggered differential quadrature (SGDQ) algorithm is developed and a non-uniform staggered grid of Chebyshev-Gauss-Lobatto points is proposed to enhance the numerical stability of DQ. Different numbers of grid points are employed to discretize the displacement and the pore pressure. The equations of equilibrium are approximated at the displacement points and the condition of continuity is established at the pressure points. The derivatives of the pore pressure at the displacement points and the derivatives of the displacement at the pressure points are dealt with through a pre-process of polynomial interpolation. Detailed derivations of the formulations are given and one- and two-dimensional numerical tests are provided. It can be seen that non-physical pressure oscillations observed in the differential quadrature method are removed by the present formulation and therefore the stability and numerical accuracy is greatly improved. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Arabian Journal of Geosciences Springer Journals

# A differential quadrature algorithm based on staggered grids for coupled analysis of saturated soils

, Volume 11 (11) – Jun 1, 2018
10 pages

Publisher
Springer Berlin Heidelberg
Subject
Earth Sciences; Earth Sciences, general
ISSN
1866-7511
eISSN
1866-7538
D.O.I.
10.1007/s12517-018-3607-2
Publisher site
See Article on Publisher Site

### Abstract

Biot’s theory of consolidation is always analyzed numerically for the complexity of the actual problems. The differential quadrature method (DQ) is a high-order numerical algorithm which is popular for its easy implementation and high accuracy and has already been applied successfully in geotechnical engineering. However, spurious pressure oscillations will be observed when strong pressure gradients appear if it is employed directly for coupled consolidation analysis of saturated soils. In the present study, a staggered differential quadrature (SGDQ) algorithm is developed and a non-uniform staggered grid of Chebyshev-Gauss-Lobatto points is proposed to enhance the numerical stability of DQ. Different numbers of grid points are employed to discretize the displacement and the pore pressure. The equations of equilibrium are approximated at the displacement points and the condition of continuity is established at the pressure points. The derivatives of the pore pressure at the displacement points and the derivatives of the displacement at the pressure points are dealt with through a pre-process of polynomial interpolation. Detailed derivations of the formulations are given and one- and two-dimensional numerical tests are provided. It can be seen that non-physical pressure oscillations observed in the differential quadrature method are removed by the present formulation and therefore the stability and numerical accuracy is greatly improved.

### Journal

Arabian Journal of GeosciencesSpringer Journals

Published: Jun 1, 2018

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