水平受荷单桩变形内力的新解法

针对水平受荷单桩变形内力的求解提出了一种新解法.根据基地反力系数三参数模型、线弹性地基上的Euler-Bernoulli梁理论和微段平衡条件,建立了以桩身响应表示的状态空间方程组.为了使状态空间方程线性化,将桩均匀化为若干小段,并且假定任一小段上地基反力系数为常数.利用所有桩小段的状态空间方程组、桩顶及桩底处的边界条件、桩段之间的变形内力连续条件和矩阵分析理论,获得了求解水平荷载单桩内力与变形的状态空间解.采用Matlab编制了计算程序,通过特例的解与已有半解析解进行对比来验证解的可靠性.最后,分析了桩底约束条件以及土体参数对桩身响应的影响.计算结果表明：状态空间法是一种易于程序编制、计算精度又易于控制的方法;当桩长较大时,桩底约束条件对桩身响应的影响很小;地基反力系数中的指数以及反映地表处土体抗侧向变形能力的参数对桩身响应的影响很大,不容忽视.

Novel Solution Method of Deformations and Internal Forces for Piles Under Lateral Loads

A novel solution method has been put forward for finding deformations and internal forces of piles subjected to lateral loads.A set of state space equations expressed in pile shaft responses is established according to a three parameter model for sub-grade reaction coefficient,Euler-Bernoulli＇s beam theory on linearly elastic foundation and the equilibrium condition of a tiny section.To make the state space equations linearized,apile is evenly divided into a number of subsections and the coefficient of sub-grade reaction for a subsection is assumed to be constant.A state space solution of internal forces and deformations for a pile subjected to lateral loads was obtained using the sets of state space equations for all the subsections,the boundary conditions at the pile head and bottom and the continuous conditions of deformations and internal forces between any two subsections.The relevant computational program was developed by Matlab,and the obtained solutions are compared with the pre-existing semi-analytical ones corresponding to a special example.At last the influences of pile bottom constraint and soil parameters on the pile shaft responses were analyzed.The calculation results indicated that the state space method is an easy-programmed and easy-controlled accuracy method;the pile bottom constraint condition has a little impact on the pile responses when the pile length is comparatively large,and the index parameter and the parameter which reflects ability of soil at the ground surface to resist the lateral deflection in the sub-grade reaction coefficient,are too great to be neglected.