水平荷载作用下单桩的虚拟桩解法及参数

根据Muki&Sternberg的虚拟桩方法，将水平荷载作用下单桩的问题分解为弹性半空间扩展土和一根虚拟桩的叠加，其中虚拟桩的弹性模量等于桩的弹性模量与土的弹性模量之差。基于水平位移协调条件推导出求解桩土间相互作用所需要的第二类Fredholm积分方程，通过广义胡可定律推导出该积分方程间断点的显式解，从而提高了Fredholm积分方程的数值计算精度并简化了计算程序的编写，根据Mindlin解推导出位移影响函数，简化了位移函数的推导过程。参数分析表明，桩土弹性模量比对单位水平力作用下桩身最大弯矩的位置有明显的影响，随着桩刚度的增加，桩身最大弯矩的位置随之加深。

Fictitious pile approach and parametric analysis of laterally loaded piles

Following the technique proposed by Muki and Sternberg, the problem is decomposed into an extended soil mass and a fictitious pile characterized respectively by Young''s modulus of the soil and that of the difference between the pile and soil. A Fredholm integral equation of the second kind is established which imposes the displacement compatibility condition. According to the generalized Hooke''s law, the explicit solutions for the discontinuous point of the integral equation is derived, which improves the numerical accuracy and simplifies the calculation procedure. Based on the Mindlin''s solution, the displacement influence function is derived which is simple. The results show that the pile-soil stiffness ratios have obvious influence on the position of the maximum bending moment for the pile under unit shear. With the increase of the pile stiffness, the position of the maximum bending moment of the pile is deeper.