The Research On Nonlinear Static And Dynamic Characteristics Of Piles

Pile foundation has been widely used in many engineering fields due to that it has many advantages including high carrying capacity, good stability, little settlement and deformation difference, good earthquake resistance and broad applicability to complicated geological conditions. At the same time, the research on mechanical characteristics of piles has also been of interest to engineers and researches. However, duo to that the interactions among the cap, the piles and soil, the load transfers and deformation processes of pile foundations are all complicated, so the pile-soil system belongs to one of nonlinear mechanical systems essentially. The load transmission mechanism and breakage patterns of a pile are related with the material strength and the bending rigidity of the pile itself, the resistance, friction and the bearing capacity of the soil as well as the manners of loadings imposed to the pile, this makes the academic analysis, numerical simulation and design of piles become very difficult. Therefore, whether in theory or in practice, it is significant to establish the rational mathematical models of pile-soil systems and to provide efficient numerical methods.The main contents of this thesis include the following three parts: (a) Based on the view of the engineering mechanics and continuum mechanics, mathematical models for the analysis of the large deformation of piles with initial displacements are established by using the arc-coordinate, the corresponding numerical methods are developed, the nonlinear mechanical characteristics of piles are analyzed; (b) Based on the theoretical framework of continuum mechanics, mathematical models for the nonlinear analysis of pile-soil coupling systems are established, the corresponding numerical methods are developed, the nonlinear static and dynamic characteristics of pile-soil coupling systems including single pile and pile-groups are analyzed; (c) Based on the porous theory of continuum mechanics, governing equations of space-axisymmetrical problems for incompressible fluid-saturated visco-elastic porous media are presented in the case of small deformations, the corresponding numerical methods are developed, and then the dynamic characteristics of saturated soil and pile are analyzed. The main research results are as follows:(1) An integral-type mathematical model and its degenerated models of the large deformation analysis of piles with initial displacements are established by using the arc-coordinate, in which a generalized viso-elastic Winkler model is used to describe the resistance of the soil. This is a set of strong nonlinear integral-differential equations, and a method is proposed to solve this kind of integral-differential equations by introducing new functions, and the integral-differential equations are transformed into a set of nonlinear differential equations. And then, the differential quadrature method (DQM) and the implicit difference scheme are applied to discretize the set of nonlinear differential equations in the spatial and temporal domain, respectively. A set of nonlinear discretization algebraic equations are obtained and solved by the iterative method. Finally, the nonlinear static and dynamic characteristics of piles are analyzed. The configuration, the bending moment and shear force of the deformed pile are yielded. The effects of initial displacements and the other parameters on the mechanical behaviors of the deformed pile are considered in detail.(2) Corresponding to the integral-type mathematical mode above, the differential-type mathematical model of the large deformation analysis of piles with initial displacements is established. The characteristics of this model are: (a) avoid the difficulty to solve the integral-differential equations; (b) easily extend and apply to analyze nonlinear mechanical problems of structures with various discontinuity conditions. As application, the static characteristics of large deformation of piles with the initial displacements are analyzed under the elastic or plastic soil. The effect of the characteristics of elastic and plastic soils on the pile is compared. As a degradation of model, the analytical solutions of the problem under the case of small deformations are presented for two initial displacements given. The range of application of the small deformation theory of piles is given by comparing the solutions with the large deformation theory.(3) Base on the differential-type model above, the nonlinear mathematical model of large deformation analysis of piles with the discontinuities and the initial displacements is further established. At the same time, the differential quadrature element method (DQEM) is used to discretze the nonlinear mathematical model in the spatial domain, and an effective method is presented to deal with problems of multivariable with discontinuity conditions in large deformation analysis. A set of nonlinear DQEM discretization algebraic equations are obtained, which are a set of nonlinear differential-algebra equations with singularity in the temporal domain. The second order backward differentiation scheme is applied to solve this kind of differential-algebra equations. Finally, numerical examples are given and the responses of deformed piles with one or more elastic joints or pile in layered soil under the combined loadings are yielded, including the configuration, the angle and the bending moment and so on. The effects of parameters, such as the rigidity and the position of joint, on the responses of deformed piles are analyzed. Some useful conclusions are given.As the further promotions and applications of the model, some numerical examples in other structures are presented, including the large deformation analysis of beams, simple frames and combined frames and so on. The obtained results are compared with those in the existing results; they are good agreement with each other.(4) Based on the theory of continuum mechanics, two nonlinear pile-soil coupling models are established, in which the non-linearity comes from two aspects: one is the nonlinear constitutive relation of the soil, another is the geometrical nonlinearity. Based on the nonlinear constitutive relation of the soil, the element free Galerkin method (EFGM) is used to analyze the nonlinear static and dynamic mechanical behaviors of pile-soil coupling systems, such as the friction resistance and the load bearing capacities, while the study of parameters is carried through.At the same time, the nonlinear interaction factor and a method for solving the settlement of pile-groups are developed from the results of the nonlinear single pile and field tests obtained. As application, the mechanical characteristics of pile-groups, such as, 2 piles, 3 piles, 2×2 piles and 3×3 piles and so on, are analyzed. Comparison with the FEM results and field tests point out that they are very close.On the other hand, the nonlinear vibration characteristics of pile-groups under the type-βearthquake impulse are studied and the load bearing characteristics of the individual pile in pile-groups are obtained.Under the case of geometrical nonlinearity, the DQEM of space-axisymmetric body for the pile-soil coupling system with continuity conditions and discontinuity conditions is developed. And the nonlinear mechanical characteristics of pile-soil coupling system are further studied by using the DQEM developed in this paper. In especial, an effective method of applying DQEM to deal with the unit connection conditions, the boundary conditions and the singularity conditions is presented, this makes the calculation accuracy and efficiency of nonlinear pile-soil coupling systems are increased and improved.(5) Based on the porous media theory (PMT), governing equations of space-axisymmetrical problem for incompressible fluid-saturated visco-elastic porous media are presented in the case of small deformations, in which the elastic or the differential-type constitutive relation is applied to describe the characteristics of solid skeleton. The differential quadrature method (DQM) and the second-order backward difference scheme are used to analyze the dynamic characteristics of the fluid-saturated elastic or visco-elastic porous soil. Comparison with the analytical results points out that they are agreement. And then, extend the DQM to DQEM and analyze the dynamic characteristics of pile-soil system in the fluid-saturated porous media. An effective method to deal with the connection conditions between the elastic structure and the fluid-saturated porous soil as well as the pile is developed in applying DQEM and good results are obtained.