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Stress-strain state in soil massif when interacting with incompressible barrette and raft

The statement and solution of problems on the interaction of incompressible barrette with the soil massif as part of a pile-raft foundation are considered, taking into account the barrette steps, diameters, the embedded length, as well as nonlinear soil behaviors by analytical and numerical methods using Plaxis-3d. It is shown that these parameters have a significant effect on the stress-strain state (SSS) of the soil massif interacting with the barrette-raft system. By taking the approach above engineers entirely manage to gain formulas so that to determine the SSS in incompressible barrette, as well as to assess the settlement of this system. For the sake of achieving the solution to problem above, the behaviors of the barrette-raft system, the soil massif are assumed to be elastic.


Introduction
When a barrette-raft system interacts with the surrounding soil, a complex and heterogeneous SSS arises, in which the geometrical parameters such as barrette steps, embedded length, diameters exercise substantial influence. With an increase in the number of barrettes, the quantitative assessment of the SSS of the barrette-raft-soil massif becomes significantly sophisticated. The SSS assessment is necessary to figure out the principle of distribution of the load between surfaces and the heel of the barrette, as a result, the settlement of the barrette-raft-soil massif and the bearing capacity of the barretteraft system absolutely can be estimated accurately. Therefore, the authors present an analytical solution to the problems above and conduct comparison with the results achieved from plaxis-3d in order to estimate the efficiency of the solution.

Statement problem
Considering a barrette-raft system with given soil properties, as well as dimension and boundary conditions of the soil massif, which is presented in the figure 1, we assume that the load p applied to the raft is distributed to the surrounding and underlaying soil in terms of compressive stress, shear stress and punching stress respectively. Hence the following problems are necessitated to be clarified: The  Based on the calculation scheme above, the equilibrium condition of the barrette raft surrounding underlying soil can be described as follow [1]: where N  is the compressive stress at the head of the barrette, s  is the stress in the surrounding soil under the raft plate,  is a non-dimensional parameter and calculated by the ratio / ab AB . The barrette settlement with the load p develops due to the shear deformation of the surrounding soil within the affected zone around the barrette with the range from 2a x 2b to 2A × 2B along the barrette's body and the vertical sides of the soil massif. Thereby, the increment of the settlement at the depth z can be calculated by the following dependency: Putting the attaining the equation of the shear stresses into expression (1), then we achieve the distribution of the settlement on the lateral surfaces corresponding to the edges 2a and 2b of the incompressible barrette Considering the boundary condition of the soil massif and the calculation scheme, it is obvious that when r is taken equal to B and A, respectively, where s m and 0 m are the values of the coefficients of volume compressibility of the soil massif in the range of the barrette's body and the underlying soil, respectively. Substituting the received equation (7) to expressions (5) and (6) we finally get: The settlement of the barrette's heel is procured from the known dependency of the settlement of a rectangular rigid stamp taking into account the coefficient Kl1 on the load p, then we get: 0 G and 0 v are deformation parameters of the underlying soil layer, while w is the coefficient taking into account the shape of the stamp (rectangle, square).
Kl is a non-dimensional coefficient which denotes the effect of the barrette's shape and the embedded depth on the settlement of the underlying soil. We can refer to N M Doroshkevich, V V Znamensky, and V I Kudinov's article [9] for Kl.
Determining the calculated value R  in the linear statement, the degree of its approximation to the limit state should be checked ( . This test can be taken place by the formula of L. Prandtl [11]: Considering the interaction of an incompressible barrette with the soil mass with the origin of coordinates z = 0 at the barrette's heel level, by considering the equilibrium conditions for the element dz (refered to calculation scheme in the figure 1), it is affirmed that the increment of the stress is taken equal to the increment of the shear stress on the lateral surfaces between the barrette and the surrounding soil.
Basing on the equilibrium condition of the settlement on the barrette's side surfaces , we achieve the dependency of the shear stress The value () b z  in expression (15) is replaced by the received from (16), thereby we have: The principle of distribution of the shear stress on the surfaces of the barrette depending on the depth z (m) complies the exponential function proposed by Sidorov V.V. [16] as follow: conspicuously turns out to be as follows: From the equilibrium condition between the settlement of the surrounding soil at the level z = l, taking into account the incompressible property of barrette, we evidently attain the expressions: In the similar way of analyzing above, the expression of compressive stress N  at the head of the barrette appears as follows: Considering the equality of the settlement of the barrette and the underlying soil layer at the level z=0, we decidedly procure the following expressions: Juxtaposing expression (29) with (25) above, we definitely get a new equation:

Conclusions:
• The geometric parameters of the barrette-raft-soil massif, as well as the mechanical and physical properties of the surrounding, and the underlying soil layer exercise a substantial influence in the stress-strain-state (SSS) of them. • It is figured out that the distributed load transferred from the raft to the lateral surfaces and the heel is proportional to their geometric and mechanical parameters and this proportion is variable with depth. The proportion of the stress at the barrette heel and the barrette head accounts for 37%.
• The juxtaposition of the result attained by using analytical and numerical methods is clearly represented (the divergence is about 6%), and the solution to the problems is able to be suggested when carrying out a calculation of the entire settlement as well as bearing capacity of the barrette. • In order to adjust the proportion mentioned above and mobilize dramatically the bearing capacity soil layer under the barrette heel, the dimensional parameters of the soil massif and barrette need to be chosen rationally.