Keywords: three-dimensional, soil-structure interaction, earthquake, Biot formulation, soil dynamics.

A numerical method for the calculation of the overall behaviour of a non-trivial three-dimensional saturated soil-structure system is presented in this paper. The numerical modelling of saturated soil is discussed in detail together with comparisons with soil-structure physical experiments performed on the centrifuge facilities at the Rensselaer Polytechnic Institute for the VELACS project.

In order to model the saturated soil, three main components are needed for the numerical simulation and they are as follows:

1. The establishment of an adequate mathematical framework to describe the phenomenon
2. The establishment of a numerical (discrete) approximation procedure
3. The establishment of an adequate constitutive relationship for the material behaviour

The numerical procedure employs the Biot formulation as the basic mathematical framework, the Finite Element method for spatial discretisation and the Generalised Newmark scheme for time stepping [1]. The u-p formulation is used with displacement (u) and pore pressure (p) as the primary unknowns and the constitutive relationship used is the Pastor-Zienkiewicz mark III model [2].

The numerical procedure is validated using Test No.12 from the VELACS [3] experiments, is a dynamic three-dimensional soil-structure interaction test with a model of a structure in the form of a block being placed on a saturated sand layer overlaid by a thin silt layer and subjected to earthquake-like base motion. The tests were performed at 100g centrifugal acceleration at Princeton University, Rensselaer Polytechnic Institute and University of California, Davis [4].

Very good comparisons with the results from the physical centrifuges test had been obtained. All the accelerations predicted were in good agreement with the measured values. Very good comparisons were also obtained for most of the pore water pressure transducers though in some locations, the level of excess pore pressure rise was slightly lower than that measured. Around 10cm settlement was predicted by the numerical analysis which is between the value obtained at UC Davis (9cm) and RPI (13cm). But a very wide spread of the measured vertical settlement was observed therefore the measured final settlement value may not be too trustworthy for comparison purposes however the numerical prediction correctly modelled the trend at which the settlement developed.

These results confirmed that the assumptions and the approximation used in the numerical procedure are sound and further analyses on various three-dimensional examples and further investigations on the use of iterative solvers instead of the direct solver used in this study are underway.

[1]

M.G. Katona, O.C. Zienkiewicz, "A unified set of single step algorithms Part 3: The Beta-m method, a generalisation of the Newmark scheme", Int. J. Num. Meth. Engrg., 21, 1345-1359, 1985. doi:10.1002/nme.1620210713

[2]

M. Pastor, O.C. Zienkiewicz, "A generalised plasticity hierarchical model for sand under monotonic and cyclic loading", NUMOG II, Ghent, April, 131-150, 1986.

[3]

K. Arulanandan, "Why VELACS? (VErification of Liquefaction Analysis using Centrifuge Studies)", Proc. VELACS symp., UC Davis, 17-20 Oct., Vol. 2, 1239-1266, 1994.

[4]

J.H. Prevost, I. Krstelj, R. Popescu, "Overview of experimental results for centrifuge model No.12", Verification of Numerical Procedures for the Analysis of Soil Liquefaction Problems, Volume 2, 1619-1634, 1993.

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