Keywords: foundation structure, soil-structure interaction, linear and nonlinear half-space, Gauss numerical integration, finite element method.

The objective of this paper is the improvement and development of the numerical methods of soil-structure analysis based on the EN standard and the finite element method. The state of stress in an elastic half-space has so far been dealt with for certain simple shapes and for certain loading behaviour only because in practice mathematical difficulties are faced, even in simplest cases [1,2,3,4]. The basis of the proposed subsoil model is numerical integration of an elastic halfspace, which is loaded by the arbitrary shape of the loaded area. Considering the accuracy of the integration, Gauss' quadrature formulae have been used. The spatial integral can be calculated using the numerical integration without any major difficulties only if the loading surface is a rectangle. In the case of other shapes (including a triangle which is often used in the finite element method), the calculation is somewhat complicated because integration limits are variable. The solution that eliminates such drawbacks is the use of transformation relations by means of the transformation Jacobian which utilised the shape functions for isoparametric elements. Any loading surface can be expressed by means of four-node or eight-node isoparametric elements with the general load defined at node points. This proposal's original solution was successfully used for various tasks in structural practice [2]. An advantage of the suggested iteration solution used to solve the non-linear task is the possibility of checking the plate structure stiffness with respect to the cracking limit [5]. New possibilities for finite element solution together with simulation based reliability assessment and decreasing the time for solvers and integration procedures are offered by parallel computing [6].

1

H.G. Poulos, E.H. Davis, "Elastic Solutions for Soil and Rock Mechanics", John Wiley & Sons, Inc., New York, 1974.

2

R. Cajka, P. Manasek, "Building structures in danger of flooding", IABSE Conference on Role of Structural Engineers Towards Reduction of Powerty, February 19-22, New Delhi, India, 2005. doi:10.2749/222137805796272296

3

P. Kuklik, "Preconsolidation, structural strength of soil, and its effect on subsoil upper structure interaction", Engineering Structures, 33(4), 1195-1204, 2011. doi:10.1016/j.engstruct.2010.12.041

4

J. Kralik, N. Jendzelovsky, "Contact problem of reinforced-concrete girder and nonlinear Winkler foundation", International Conference Geomechanics 93, Strata Mechanics/Numerical Methods/Water Jet Cutting/Mechanical Rock Disintegration, 233-236, Ostrava, Czech Republic, Sep 28-30, 1993.

5

O. Sucharda, J. Brozovsky, "Approach to the Assessment of Concrete Structures based on Non-Linear Elasto-Plastic Analysis", in B.H.V. Topping, L.F. Costa Neves, R.C. Barros, (Editors), "Proceedings of the Twelfth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 121, 2009. doi:10.4203/ccp.91.121

6

P. Konecný, J. Brozovský, V. Krivý, "Simulation Based Reliability Assessment Method using Parallel Computing", in B.H.V. Topping, P. Iványi, (Editors), "Proceedings of the First International Conference on Parallel, Distributed and Grid Computing for Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 38, 2009. doi:10.4203/ccp.90.38

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