Variational Approach For The Settlement Of Pile Groups

Piles is widely used in civil engineering with much its advantages such as large bearing capacity, small deformation and fast construction. If the bearing capacity of soil between piles is taken into consideration,controlling settlement become extremely important. The calculated settlement of pile groups by common interaction factors method is large in that it cannot consider the reinforcing effect of piles. In an attempt to overcome some of the limitations of the existing methods,a variational solution for the analysis of pile groups is presented in this paper. The variational approach does not involve the discretization of piles so that it is feasible to perform rigorous and total analysis of large pile groups.In the analysis of pile groups by variational method,the stiffness matrix of soil for pile groups system is vital.When soil is isotropic,the deformations and shear stresses of piles are each be represented by a finite series with a set of unknown constants.Based on the shear displacement method, the stiffness matrix of soil is created.In layered soil piecewise function is needed to substitude for the two finite series.Considering the interaction of pile-soil-shaft,the stresses and displacements of soil elements between piles is incorporated in the stiffness matrix of soil of pile groups,so that a new stiffness matrix of soil of the pile-soil supported system is created. By the coupling of the stiffness matrix of the pile-soil supported system based on the principle of minimum potential energy and the stiffness matrix of raft based on the rectangular plates in bending,the basic equation of pile-soil-shaft is created.In a pile-soil supported system which has rigid caps on the top of piles,the deformations of soil elements under one pile cap are equal.As a result,the interrelated elements in the stiffness matrix of soil of pile-soil supported system can be incorporated. And the interrelated elements in the stiffness matrix of pile-soil supported system can also be incorporated for the displacement on the top of pile is equal to that of the soil elements under the same pile cap.Finally,the stiffness matrix of pile cap-soil elements between pile caps is created.In the variational method the symmetry of piles and soil elements can be taken into accounted.According to the symmetry,the addition of some rows and columns in stiffness matrix of soil of the pile-soil supported system corresponding to the components of the contribution of each pile can be carried out. Thus,a new stiffness matrix only for the proportion of symmetry is created.Performing variation of the function of the proportion of symmetry,the stiffness matrix which can perfectly represent the behaviour of the total pile-soil supported system. is established quickly.