Variational Theory Of Linear Elastic Settlement Of The Long-Short Pile Composite Foundation Based On Spline Function

With the application and the theoretical research of engineering, the long-short pile composite foundation is unique in the various forms of foundation treatment means. It fully preserves the characteristicof the traditional forms of composite foundation treatment,which ensures the carrying capacity and allows partial settlement. Meanwhile, according to the characteristics of the foundation soil, it makes the shallow soil and the pile bear loads from the upper structure and pass the ultimate load to the well-compressed deep soil through a long pile. The piles and the soil are not only collaborative bearers in the same work area but also different controllers of settlement in different work areas, which fosters the theoretical studies on composite foundation to a more specific and more efficient stage. In view of this, it is particularly necessary to make further study on the long-short pile composite foundation bearing mechanism and the settlement laws in order to give better guidance in the work practice.Based on the analysis of pile load transfer, this paper assumes that the relationship between the pile load displacement is linear and thus the load and the pile displacement relationship in soil layer is exported through an iterative approach on this basis. Because the load bearing of A pile will impact B pile and B pile will react to the pile in turn, dynamic interaction model between the pile was established and two pile displacement and friction resistance constitution were analyzed based on linear load displacement by displacement field hypothesis. Thus the total complementary energy expression established in accordance with the theory of elasticity could be applied further to the pile group. Given the structural characteristics of basis functions of spline, stress parameter array was constructed by specific transformation matrix with inclusive element (pile of different segments of the same pile) and was finally applied to the total complementary energy expression of long pile groups in layered soil. Inspired by pile interaction, the interaction between the pile and the foundation of the land was quantized by the given solution drawn by Bousinessq or Mindlin, its deficiencies was made up by the average equivalent value with the modulus of elasticity and the coupling model and the interaction equation of pile group and ground land systems were eventually established with full consideration of beam hoop action of pile to land foundation. With the concept of virtual pile and the consideration of pile length factors of the long-short pile composite foundation, the stress parameter array was determined and the relation of load and displacement was also achieved by the functional variation.The conclusions of this paper are as follows:1. The pile displacement relationship in soil layer is exported through an iterative approach by the hypothesis that the relationship between the pile load displacement is linear. Although the hypothesis is not fully consistent with the engineering practice, it should be promoted to the pile group because of its simple concept and convenient calculation. It is found that the barrier effect and reinforcement effect between the pile are actually the balancing process of dynamic effects by establishing interaction model between the pile and analyzing two pile displacement and friction resistance construction. It is also found that the effect is relatively weakened because of the pile length factors of the long-short pile composite foundation.2. In accordance with the characteristics of spline function, basis functions widely used in the pile group are constructed and concrete forms to convert the matrix are presented in this paper. The matrix enables the stress parameters array to be associated with different soil in layered soil. Instead of losing its compactness in the matrix inversion, the matrix makes its programming possible.3. A numerical expression of the total complementary energy of single pile is obtained from the theory of elasticity in the linear load transfer and displacement field and the total complementary energyequation of pile group in layered soil is established by adopting basis function constructed by transformation matrix to describe pile stress. The average equivalent value with the modulus of elasticity is adopted to make up the deficiencies of the given solution drawn by Bousinessq or Mindlin in layered land foundation through the interaction between the pile and the foundation of the land in view of pile interaction. And the coupling model and the interaction equation of pile group and ground land systems are eventually established by converting the length of the pile to a pile of equal length with virtual soil piles and by directly including the amount of deformation of cushion in the pile and pile-soil flexibility matrix.4. On the basis of six long-short pile composite foundation experimental program, the effect of the number of piles, pile spacing and the cushion on composite foundation settlement behavior are calculated and analyzed in this paper. The results better reflect the real model test results and demonstrate the possibility of the practical application of this method. But it is also found that the variational theory presented in this paper does not reflect the maximum load adaptation corresponding to a certain number of piles and pile arrangement under certain circumstances of the foundation. Under this load case, pile side soil plastic deformation occurred and settlement value is relatively stable without jumping difference in other loads less than it; but the response of the theory in this paper to the load lags behind. Although selecting the number of pile segments in sub-soil properly based on simulation of pile stress of spline function is conducive to the accuracy of the final results, the improvement of accuracy might be affected by other factors to some extent. Due to the increased number of segments,It will correspondingly increases the number of the parameters of pile stress column vector. Therefore, for the contradiction between accuracy and speed, the speed of calculation should be optimized under the premise to meet the accuracycombined with the specific engineering practice.