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对水平与轴向荷载作用下单桩内力变形的求解提出了一种状态空间法。首先,根据线弹性地基反力理论、Euler-Bernoulli梁理论和桩单元平衡条件,建立了地面以上及以下桩身响应的状态方程,其中桩周土体对桩的反力采用三参数模型来模拟。其次,为了使上述状态方程线性化,将地面以上和以下桩身等分为若干桩段,并设各桩段上的地基反力系数、轴力与自由段上水平分布荷载都为常数,建立了地面以上及以下各桩段响应的线性化状态方程。第三,利用桩顶、桩底条件以及各桩段之间的位移内力连续光滑条件,得到了水平轴向荷载共同作用下桩变形内力的状态空间解,编制了计算程序。最后研究了轴向荷载对桩顶水平位移和桩身最大弯矩的影响。计算结果表明:本方法和程序是易于使用且可靠的;当轴向荷载或者水平位移较大时,轴向荷载对桩身弯曲响应的影响很大。
A state space method is proposed to solve the single pile internal force deformation under horizontal and axial loads. Firstly, according to the linear elastic foundation reaction theory, the Euler-Bernoulli beam theory and the pile unit equilibrium conditions, the equation of state of the pile response above and below the ground is established. The reaction force of the soil around the pile to the pile is simulated by the three-parameter model . Secondly, in order to linearize the above equation of state, the pile body above and below the ground is divided into several pile sections, and the foundation reaction coefficient, the horizontal distribution load on the axial force and the free section are both constant and established The linearized equation of state of response for each section above and below the ground. Thirdly, the state space solution of internal force of pile deformation under horizontal axial load is obtained by using the conditions of pile top, bottom of pile and continuous displacement of internal force of each pile. The program is compiled. Finally, the influence of axial load on the horizontal displacement of pile top and the maximum bending moment of pile is studied. The calculation results show that the method and procedure are easy to use and reliable. When the axial load or the horizontal displacement is large, the axial load has a great influence on the bending response of the pile.