【作者】 胡育佳；

【导师】 程昌钧；

【作者基本信息】 上海大学 ， 固体力学， 2008， 博士

【摘要】 桩基由于其具有承载能力高、稳定性好、基础沉降及差异变形小、抗震性能好以及能适应各种复杂的地质条件等特点而在各种工程领域中得到广泛应用,同时也使得对桩基力学特性的研究成为工程师和研究人员非常关注的问题。但是由于承台、桩、土的相互作用,桩基的载荷传递与变形过程属于复杂的非线性力学系统,桩基在各种静载荷与动载荷作用下,其载荷传递机理和破坏模式与桩基本身的材料强度、抗弯刚度、桩侧土体的抗力、摩阻力、桩端土体的承载能力以及施加载荷的方式等因素都密切相关,这给桩基的理论分析、数值计算和设计与施工带来很多困难。因此,不论是从理论上还是实际工程需要上,建立桩-土系统非线性静动力学特性分析的数学模型,提供高效的数值计算方法都具有重要的意义。本论文的研究内容主要包括三个方面:(a)从工程力学和连续介质力学相结合的观点出发,建立了具有初始位移的桩基大变形分析的数学模型,发展了相应的数值计算方法,研究了桩基大变形行为的力学特性;(b)从连续介质力学的框架出发,建立了桩—土耦合系统非线性分析的数学模型,发展了相应的数值计算方法,研究了桩—土耦合系统(包括单桩和群桩)的非线性静动力学特性;(c)从连续介质力学混合物理论出发,建立了两相不可压流体饱和多孔介质空间轴对称问题的控制方程,发展了相应的数值计算方法,研究了桩-饱和土耦合系统的动力学特性。主要研究成果如下:(1)利用弧坐标建立了具有初始位移的桩基大变形分析的积分型数学模型及其退化模型,其中,地基抗力采用广义粘弹性Winkler模型来描述。这是一组强非线性变下限积分-微分方程组,并提出了求解这类变下限积分-微分方程组的方法。通过引入一组辅助函数,将变下限积分-微分方程组转化为一组非线性微分方程,然后分别在空间域内和时间域内采用微分求积方法和隐式差分格式来进行离散,得到了离散化的非线性代数方程组并进行迭代求解;最后研究了桩基的非线性静动力学特性,得到了桩基变形前后的构形、弯矩和剪力,考察了两类不同初始位移等参数对桩基大变形力学行为的影响。(2)与积分型数学模型相对应,利用弧坐标建立了具有初始位移的桩基大变形分析的微分型数学模型。这类模型的特点是:(a)避开了求解积分—微分方程的困难;(b)更易于推广应用,包括研究各种间断性条件的影响。作为应用,研究了在弹性或弹塑性土体中具有初始位移的桩基大变形静力学特性,比较了土的弹性和弹塑性性质对桩基力学特性的影响。作为模型的退化,得到了具有初始位移的桩基小变形问题的解析解,并与大变形理论的解进行比较,给出了桩基小变形理论的适用范围。(3)在微分型数学模型的基础上,进一步建立了具有初始位移和间断性条件的桩基大变形分析的数学模型。同时,在空间区域内,采用微分求积单元法(DQEM)来离散非线性数学模型,并提出了在使用DQEM求解桩基大变形分析中处理多个变量具有间断性条件的有效方法,得到了一组非线性DQEM的离散化方程,它是关于时间域内的一组具有奇异性的非线性微分-代数方程,并在时域内采用向后二阶差分求解了这类非线性微分-代数方程组。作为数值算例,分析了弹性土体中具有一个或多个弹性铰接头或弹性层状土中的桩基,受组合载荷作用时的构形、转角、弯矩和剪力,并考察了弹性铰接头的接头刚度和位置等参数对桩基非线性力学特性的影响,得到了一些有益的结论。作为模型的进一步推广和应用,给出了其它工程结构领域中的多种算例,包括各种梁的大变形问题,简单框架的大变形问题,组合框架的大变形问题等,并与现有结果进行了比较,吻合良好。(4)从连续介质力学理论出发,建立了两类桩-土非线性耦合系统的数学模型,其中一类非线性来自于层状土介质的非线性双曲型本构模型,另外一类非线性来自于几何非线性的影响。在考察土的非线性本构模型的基础上,运用无网格迦辽金方法(EFGM)研究了非线性桩-土耦合系统的静动力学特性,包括摩擦桩桩周摩阻力及非线性单桩承载特性等,并进行了参数研究。同时,从单桩的非线性计算结果和试验出发,提出了群桩的非线性相互作用因子的概念和计算群桩非线性沉降的方法。作为应用分析了由两根单桩、三根单桩、四根单桩和九根单桩等所组成的桩群的非线性力学特性,并与有限元计算结果和已有的现场试验结果进行了比较,吻合良好。还研究了单桩和群桩在β-型地震激励下的非线性振动特性,得到了群桩中各桩在β-型地震激励下的承载特性。对于在几何非线性条件下的桩-土耦合系统问题,发展了具有连接条件和间断性条件的空间轴对称问题的微分求积单元法,并用以研究了桩-土非线性耦合系统的力学特性。特别提出了在运用微分求积单元法时处理单元连接条件、边界条件和对称轴处奇异性的有效方法,大大提高了非线性桩—土耦合系统的计算精度和计算效率。(5)从连续介质力学混合物理论出发,在小变形条件下,建立了两相不可压流体饱和多孔介质空间轴对称问题的控制方程,其中,固相材料采用弹性和微分型粘弹性本构关系。推广微分求积方法于两相不可压流体饱和多孔介质并结合二阶向后差分格式,研究了固相为弹性、粘弹性材料的流体饱和土的动力学特性,并与现有解析结果相一致。推广微分求积方法为微分求积单元法研究了饱和流体多孔介质中桩-土耦合系统的动力学特性,提出了在运用微分求积单元法来求解这类问题时弹性结构和流体饱和土间的连接条件及处理方法,得到了良好的计算结果。更多还原

【Abstract】 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.更多还原