Keywords: structural strength, shear damage of subsoil of buildings, finite differences, FEM.

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 of height from the rock should be taken into account. This fact is verified by experiments, which are partly completed and distribution of eigenstrains in time was studied. The creep for lower loading is stabilized relatively quickly (for 500 kPa after one day one reach a stabilized situation), for higher loading it lasts longer (for 1100 kPa after three days the movement of the subsoil still persists).

Acknowledgment

This research was supported by Grant Agency of the Czech Academy of Sciences, grant number IAA2119402.

1

G.J. Dvorak, P.P. Prochazka, "Thick-walled Composite Cylinders with Optimal Fiber Prestress", Composites, Part B, 27B, 643-649, 1996. doi:10.1016/S1359-8368(96)00001-7

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £95 +P&P)