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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 80
PROCEEDINGS OF THE FOURTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: B.H.V. Topping and C.A. Mota Soares
Paper 118
Coupled Modelling of Shear Damage in Subsoil using the FEM and Finite Differences P.P. Procházka+, N. Starikov+ and J. Trcková*
+Department of Structural Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Czech Republic
Full Bibliographic Reference for this paper
, "Coupled Modelling of Shear Damage in Subsoil using the FEM and Finite Differences", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Proceedings of the Fourth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 118, 2004. doi:10.4203/ccp.80.118
Keywords: structural strength, shear damage of subsoil of buildings, finite differences, FEM.
Summary
In the paper coupled modelling based on comparison of numerical models and
experimental scale modelling is put forward. Possible time dependent behaviour,
creep for example, can be very precisely obtained from the coupled modelling. The
scale models are prepared from physically equivalent materials, while for numerical
modelling classical finite differences are revived and 24 nodal point degrees of
freedom finite elements are used for comparison.
The problem of searching for the structural strength in subsoil under foundations of tall buildings, heavy industrial halls, sport halls of large spans, etc., leads to extraordinarily advantageous application of the finite difference method, since the shape of the domain describing the body of the subsoil is suitable for such an application. Diagonal dominancy, symmetry of the system, very fast iterative algorithms, which are much faster then that suitable for the FEM or the BEM, strong positive definiteness (the FEM are generally ill-posed, which is not the case of the BEM; the latter method bears other disadvantages in comparison with the finite differences), etc. call for revival of this method for solving such problems. The comparative approach consists in the following idea. First, select subdomains with uniform distribution of eigenparameters, see [1], for example. Theoretically one can select as many subdomains as nodal points used in the computation. But in this case the calculation can exceed reasonable computational time and from the nature of the problem the subdomains can be estimated in advance to lower the number of free eigenparameters. Then, one can write the overall stress as a linear hull of stresses due to external load in purely linear elastic medium and uniformly distributed eigenparameters in subdomains, which are selected in advance. The components of influence matrix are created by successive application of unit impulses of selected eigenparameters in the selected subdomains; no external loading is taken into account in the latter case and elastic medium is again considered. A natural requirement is the following: the difference between measured and computed stresses should be as small as possible. This requirement can be formulated in terms of optimisation of an appropriate functional. The functional will express the variance of deviations of measured and computed values of stress components. Variation of the functional with respect to individual eigenparameters (which serve here a design parameters of the optimisation problem) leads us to a system of linear algebraic equations for unknown eigenparameters. Very important circumstance has to be mentioned: The algebraic system its solution leads to the solution of non-linear problem is linear. The time of non-linear iterative computation for finite differences is approximately 10 times shorter then that for finite elements, providing the same iterative procedure for each pseudo-elastic step is used; in our case it was the over-relaxation method. Such computations are carried out for each time step. In our case we adopted the computation to the measurements accomplished on scale models. The results from 10 time-equidistant measurements were involved in the numerical computations. Consequently, 100 times faster computation was achieved from the finite differences in comparison with the finite elements.
The displacements were mainly observed, although the stresses play very
important role in plastic and creep computation. The greatest values of the
displacements are attained below the loading of the ditch, and the influence of the
loading on the displacement field is recorded in relatively deep positions of the
subsoil. From the hypsography of the displacements it is seen that the negligible
displacements are approximately only one fourth of the length between the terrain
and the rock; this is measured from the bedrock. The lower the rock is positioned
below the terrain, the larger zone of significant displacements has to be considered.
For shallow rock bedding approximately
AcknowledgmentThis research was supported by Grant Agency of the Czech Academy of Sciences, grant number IAA2119402.References
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