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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 86
Edited by: B.H.V. Topping
Paper 19

Angular Displacement of a Normal in the Foundation-Subsoil Contact Area

R. Cajka and D. Sekanina

Faculty of Civil Engineering, Technical University Ostrava, Czech Republic

Full Bibliographic Reference for this paper
R. Cajka, D. Sekanina, "Angular Displacement of a Normal in the Foundation-Subsoil Contact Area", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 19, 2007. doi:10.4203/ccp.86.19
Keywords: foundation, subsoil, Mindlin's slab, Pasternak's model.

This paper deals with one of possible solution of the foundation-subsoil interaction problem. This solution combines a thick Mindlin slab and the Pasternak's model for the subsoil. According to the theory, the angular displacement of the centreline normal of the slab-subsoil surface does not change. The planar task deals with rotation of nodes in the contact surface. The finite element method (FEM) is employed in various parts where the foundation is in contact with the subsoil.

A thick Mindlin's slab and elastic subsoil represented with a Pasternak's model is considered. Shift and x and y angular displacements of the centreline result from the equation for a thick slab. As contrasted to a Kirchhoff's thin slab, the angular displacement of the normal includes the effects of shearing forces. The Pasternak's model uses C1z (for the vertical z-direction), C2x and C2y. These are the shearing forces among elemental columns of soil. If the three differential equations for the thick Mindlin's slab are combined with the equation for the Pasternak's subsoil, the result is an equation for a thick slab placed on a two-parameter subsoil [1,2,3,4]. To solve the equations, it is assumed that the angular displacement of the normal is the same in the slab and subsoil surface at the contact joint. A parametric study has been undertaken as an example for the foundation with lengths of 3m, 6m and 12m and with a modulus of elasticity of the soil ranging between 20MPa and 10,000MPa.

The results of the parametric studies proved that the rotation of single points on the original normal line to the middle plane is not identical to the rotation of the normal line in the subsoil. The settlement on the basis of the elastic half-space is investigated, and here the shearing forces have been already taken into account in the settlement calculation. Then it does not have to be valid that the rotation of foundation slab's normal line is equal to the rotation of subsoil but the equality of the slab deformation and the subsoil settlement is sufficient.

This interactive task between the foundation and the subsoil has to be solve using the iterative method that results from a combination of the Winkler soil model and a settlement solution with the help of a modified elastic half-space according to CSN 73 1001 [5]. The unknown parameter C1z may be determinated at every point in the finite element model accordingly [5].

R. Cajka, "Using Numerical Integration to Solve Foundation-Soil Interaction", Dissertation work, Ostrava, 1999.
R. Cajka, "Numerical Analysis of Contact Pressure under Shallow Foundation", International Symposium on Shallow Foundations FONDSUP 2003, Paris, France, 5-7 November 2003.
R. Cajka, "Contact Subsoil FEM Element for Soil - Structure Interaction", The Second International Conference on Structural Engineering, Mechanics and Computation SEMC 2004, Cape Town, South Africa, 5-7 July 2004.
R. Cajka, "FEM soil - structure interaction element and EC standards", 24th CADFEM Users' Meeting 2006 - International Congress on FEM Technology with 2006 German ANSYS Conference, Stuttgart/Fellbach, Germany, 25-27 October 2006.
CSN 73 1001, "Foundation of structures. Subsoil under shallow foundations", 1988.

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