The analytical presentation of solid border basement in conditions of solid stamp effect

The current level of construction and, moreover, the future value the right apressiation of mechanical capabilities of the structure basement. The calculation of additional resource of strength basement of each structure brings to increasing of value of structure. The increasing of reliability and sustainability of structures is one of the problems of modern applied mechanics. The correct assessment of the strength of basement is very important in solving this problem. It is still conditional to determine the computational depth of basement. Numerous experimental studies have shown that in the case of distributed load of constant intensity, the dependence of sediment from the base sizes is expressed by strict nonlinear connection. The solvation of problem of constant thick layer gives the linear connection by methods of elasticity of theory. The purpose of eliminating that essential discrepancy with experimental results, the solved problem, proposed by the academician S.S. Grigoyan and applied by his students, is an important step towards solving.


Introduction
For projecting the bases of constructions you must select the depth of elastic sphere of its base.
The experimental studies have shown [1,2,3,4] that the depth of the elastic layer of the basement effecting on it from greatness of load and sizes of bases, depends on non-linear link. The solvation of the problem by method of elasticity gives the linear dependence.
For the purpose of elimination of discrepancy with experimental data, the academician S.S. Grigoryan's suggestion [5] concerning the model of solid material, was the fundamental step in the correct assessment work of discrepancy of noted disagreement and the mechanical chances of basement.

Methods
The correct selection of basement in the problems of bases calculation is the most important precondition. It is supposed that the material of basement in conditions of affection of its gravity forces on a certain density is already state of solidity. It means that additional deformations don't emerge in domain of solid material (Fig. 1).
Here u and w are marked to point the replacements in x and z directions, S-is the sediment of stamp. Such problem set like this, is strictly non-linear because the solid edge on which the edge conditions are put, is preliminary unknown and is determined during the solution of the problem. The * h depth of solidity from the weight of the partition is determined by the following formula: where * σis the value of critical comprehensive pressure,  -is the material coefficient of Puason. The problem set like this, is solved by us with the method of [6] local variations for which all the magnitudes are expressed with immeasurable views.
The solvation of the problem by unmeasurable data, we have received numerical data expressing the sediment of hard stamp and the variation of border line of hard material, the values of which on the symmetry Z axis are listed in the table [6] ; So, the function of solidity will have the following aspect; ( ) .
In order to be able to apply the received (12 ) formula in cases of different magnitudes of the sediment stamp, we insert the  coefficient.
Let's determine those coefficient values on the symmetry axe by means of getting the values of changes of solid border by variation method.
For determination of  we get (Table 1). For determination of  we get (Table 4).

Conclusions
For the purpose of verifying the reliability of the (13) formula for determining the solid border of the base material, we have compared the values of having [6] local variation method and (13) calculated by formula. We have done the comparison on the r axis of symmetry by means of replacement of solid edge (table). The comparison shows, that on the symmetric axis of stamp (13), the differences of replacement of the edge of solid material is being determined by method of formula and local variations are very small, and are negligible in the point of practical application. Therefore, (13) the formula can be used for the ribbon base of constructions, in order to receive the determination of initial size of the depth of deformative layer of basement.