Engineering Transactions, 47, 2, pp. 173–181, 1999
10.24423/engtrans.627.1999

### 2-D And 3-D Analysis of Stochastic, Elastic Soil Medium

J. Przewłócki
Poland

J. Górski
Technical University of Gdansk
Poland

The paper presents a stochastic description of a three-dimensional soil medium and its modelling under plane strain conditions. The main aim of the paper is to work out a computational model enabling incorporation of three-dimensional variability of soil properties into the plane strain state analysis. It is assumed that the soil medium is statistically homogeneous and its mechanical behaviour is governed by the linear elasticity theory. It is also assumed that elastic parameters can be modelled as the multidimensional random fields. The strip foundation on a soil layer in the 3-D and the 2-D strain states is analysed. Stochastic 2-D and 3-D finite element methods, based on the Monte Carlo technique, were used. The analysis performed enables determination of the standard deviations of components of the stress tensor and the displacement vector for the 3-D state, based on the solution for the 2-D plane strain state. Transfer functions between both states are determined.
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#### References

R. BAKER, Modelling soil variability as a random field, Mathematical Geology, 16, 5, 1984.

E. BIELEWICZ, J. GÓRSKI, R. SCHMIDT and H. WALUKIEWICZ, Random fields in the limit analysis of elastic-plastic shell structures, Int. J. Comp. & Struct. 51, 3, 267–275, 1996.

C.G. BUCHER and M. SHINOZUKA, Structural response, Mechanics, 114, 12, 1988.

W. KNABE, J. PRZEWŁÓCKI and G. ROŻYŃSKI, Spatial averages for linear elements for two-parameter random field, Probabilistic Engineering Mechanics, 13, 3, 147–167, 1997.

J. PRZEWŁÓCKI and E. CALLE, Planar representation of three-dimensional problems, Studia Geotechnica et Mechanica, 16, 3–4, 1994.

J. PRZEWŁÓCKI, Estimation of the random field of mechanical soil medium (Estymacja pola losowego parametrów mechanicznych ośrodka gruntowego) [in Polish], XI Krajowa Konferencja Mechaniki Gruntów i Fundamentowania, Gdańsk 1997. II.

M. SHINOZUKA, Structural response ility, J. of Engineering Mechanics, 113, 1, 1987.

P.D. SPANOS and R. GHANEN, Stochastic finite elements: A spectral approach, Springer-Verlag 1991.

E. VANMARCKE, Random fields: is and synthesis, The MIT Press, Cambridge 1983.

F. YAMAZAKI, M. SHINOZUKA and G. DASGUPTA, Neumann expansion for stochastic finite element analysis, J. of Engineering Mechanics, 114, 8, 1988.

D.G. ZEITOUN, R. BAKER and J. UZAN, Application of random elasticity to soil engineering, Structural Safety, 5, 1987.

DOI: 10.24423/engtrans.627.1999