非饱和路基一维瞬态响应精确解
杨相如1，卜力平1，陈雪梅2，赵云2*
1.福建船政交通职业学院土木工程学院，福建 福州 350007；2.河南工业大学土木工程学院，河南 郑州 450001
摘要：为反应路基非饱和三相介质的实际状态，将路基视为固相与液相不可压缩、气相可压缩的非饱和多孔介质，基于非饱和多孔介质表述方法，考虑惯性、黏滞和机械耦合作用，建立无量纲化的非饱和路基一维波动方程，以一类非齐次边界为例，通过边界齐次化和特征函数法将问题转化为二阶常微分方程初值问题，并用状态空间法求解，获得单层非饱和路基一维瞬态响应的精确解，通过算例验证结果的正确性。分析单层非饱和路基在阶跃荷载和正弦荷载下一维瞬态响应的特点，结果表明，与可压缩的饱和土和非饱和土不同，不可压缩非饱和路基中只存在1种压缩波，液相饱和度增大，压缩波波速和振动幅值减小。结论可为复杂环境荷载作用下非饱和路基的优化设计和灾害防控提供参考。
关键词：岩土工程；非饱和路基；瞬态响应；解析解
Analytical investigation of one-dimensional transient response for unsaturated subgrade
YANG Xiangru1, BU Liping1, CHEN Xuemei2, ZHAO Yun2*
1. College of Civil Engineering, Fujian Chuanzheng Communications College, Fuzhou 350007, China；
2. College of Civil Engineering and Architecture, Henan University of Technology, Zhengzhou 450001, China
Abstract: To reflect the actual state of the unsaturated three-phase medium of the subgrade, the subgrade is regarded as an unsaturated porous medium with incompressible solid and liquid phases, and a compressible gas phase. Based on the representation method of unsaturated porous media, considering the effects of inertia, viscosity, and mechanical coupling, a dimensionless one-dimensional wave equation for the unsaturated subgrade is established. Taking a type of non-homogeneous boundary as an example, the problem is transformed into an initial value problem of a second-order ordinary differential equation through boundary homogenization and the method of characteristic functions, and the state-space method is used to obtain the exact solution of the one-dimensional transient response of a single-layer unsaturated subgrade. The correctness of the results is verified through numerical examples. The characteristics of the one-dimensional transient response of the single-layer unsaturated subgrade under step and sinusoidal loads are analyzed. The results show that, unlike compressible saturated and unsaturated soils, there is only one type of compression wave in the incompressible unsaturated subgrade. As the liquid phase saturation increases, the wave speed and vibration amplitude of the compression wave decrease. The conclusion can provide a reference for the optimal design and disaster prevention of unsaturated subgrades under complex environmental loads.
Keywords: geotechnical engineering; unsaturated subgrade; transient response; analytical solution
