Rayleigh波作用下非饱和土中单桩水平振动解

Horizontal dynamic response of single-pile in unsaturated soil under Rayleigh waves

非饱和土在自然环境和工程界中普遍存在,对于Rayleigh波作用下非饱和土中单桩的水平振动响应,目前仍没有较完善和准确的理论计算方法。针对该问题,基于三维连续介质力学,先求解非饱和多孔介质波动方程得到Rayleigh波弥散特性下土体的自由场振动响应,再利用平面应变模型和动力Winkler模型模拟非饱和土和桩的耦合振动,进而引入桩土边界条件、势函数并采用分离变量法推导出桩顶水平位移相互作用因子的表达式,并通过其退化解与已有文献中的解的对比验证了本文模型的合理性。利用所得解分析了土体的饱和度、泊松比及桩土模量比对桩身水平动力特性的影响规律。结果表明:随土体饱和度增加,相互作用因子逐渐减小,当饱和度大于0.999时整个桩身的水平位移才出现较为明显的减小;相互作用因子随土体泊松比增加而逐渐减小,且减幅随激励频率的增加而增大;桩土模量比增加时,相互作用因子减小且减幅逐渐变弱,最终稳定于一常值,同时激励频率的增加会导致到达稳定值所对应的桩土模量比越小。

Unsaturated soils are common in the natural environment and engineering field.However,there is still no perfect and strict theoretical calculation method for horizontal vibration response of single pile in unsaturated soil under Rayleigh wave.To solve this problem,based on three-dimensional continuum mechanics,the wave equation of unsaturated porous media was firstly solved to obtain the free field response of soil under the dispersion characteristics of Rayleigh waves,and then the unsaturated soil-pile coupling vibration model was set up based on the plane strain model and Winkler model.By introducing the pile-soil boundary conditions,potential function method and separation variable method,the expression of the horizontal displacement interaction factor of pile head was derived.Furthermore,the rationality of the proposed model was verified by comparing the degradation solution with previous research results.Based on the obtained solutions,the influences of soil saturation,Poisson's ratio of soil and pile-soil modulus ratio on the horizontal dynamic characteristics of piles in unsaturated foundations under Rayleigh waves were analyzed in detail.Results show that with the increase of soil saturation,the interaction factor gradually decreases,and the horizontal displacement along the pile shaft decreases significantly under a soil saturation of greater than 0.999.The interaction factor gradually decreases with the increasing of Poisson's ratio,and the decreasing amplitude increases with the increase of excitation frequency.As the ratio of pile-soil modulus increases,the interaction factor decreases and the decreasing amplitude gradually becomes weaker,and finally remains a constant value.Meanwhile,the increase in excitation frequency will lead to a smaller pile-soil modulus ratio when the constant value is reached.