饱和半空间表面无限长梁的沉降变形

Bending consolidation of an infinite beam of finite width resting on a saturated poroelastic halfspace

采用解析方法研究了饱和半空间表面无限长欧拉梁的沉降变形特性。假定梁与地基的竖向接触应力沿梁截面均匀分布、梁的挠度与梁截面下地基表面的位移均值相等,分别考虑地基表面完全透水及完全不透水情况,基于Fourier及Laplace联合变换获得了问题的解析解,并通过已有研究结果及ABAQUS^(TM)有限元分析模型对比验证了解的正确性。分析结果表明,梁的弯曲刚度、地基的排水及不排水泊松比以及地基表面的透水条件对梁的沉降变形有明显影响。

The time-dependent flexural behavior of an infinite beam of finite width resting on the surface of a saturated poroelastic halfspace is examined. The vertical contact stress is assumed to be uniformly distributed across the beam section. The displacement continuity is achieved by equaling the beam deflection to the average displacement of the halfspace surface under the beam width. The drainage condition at the surface of the poroelastic halfspace is considered as either completely drained or completely undrained. The problem is analytically solved using the Fourier and Laplace transformations. The developed solutions are verified via comparisons with the existing analytical solutions and computational results by finite element code ABAQUSTM. The numerical results indicate that the beam bending rigidity, the drained and undrained Poisson＇s ratios and the drainage boundary conditions at the halfspace surface have important influences on the flexural responses of the beam.