基于非局部Biot理论的矩形移动荷载下饱和土动力响应

Dynamic Response of Saturated Soil Under Rectangular Moving Load Based on Nonlocal Biot Theory

为进一步研究矩形移动荷载下饱和土路基中动力响应问题,首先,基于非局部Biot理论,以饱和土地基为研究对象,建立了考虑孔隙尺寸效应和矩形荷载作用下的非局部孔隙弹性计算模型;然后,考虑路基表面的透水边界条件,采用二次傅里叶逆变换得到饱和土体在矩形移动荷载下的时域内动力响应解析解;最后,分析了在不同模态和不同非局部参数的取值下,矩形荷载移动速度和荷载自振频率的变化对饱和土竖向和水平位移响应的影响。结果表明:在低模态时,非局部参数对饱和土位移响应影响不大,而在高模态时,其影响较大,并且位移响应主要取决于低模态。非局部参数与竖向位移成正比,而与水平位移成负相关关系。当荷载自振频率增大时,位移受到非局部参数的影响,随着非局部参数增大,位移响应峰值会在更低的荷载自振频率处出现,位移响应峰值向左移动。当荷载自振频率增大时,位移受到荷载移动速度的影响,在较低荷载移动速度下会出现位移响应峰值。当荷载移动速度增大时,位移受到荷载自振频率的影响,位移响应峰值出现对应的荷载自振频率减小。

In order to further investigate the dynamic response of saturated soil subgrade under rectangular moving loads,firstly,based on the nonlocal Biot theory,a nonlocal pore elasticity calculation model considering pore size effects and rectangular loads is established for saturated soil subgrade as the study object.Then,considering the permeable boundary conditions on the surface of roadbed,a second-order inverse Fourier transform is used to obtain the analytical solution of the dynamic response of saturated soil in the time domain under rectangular moving loads.Finally,the effects of the changes in rectangular load movement speed and load natural frequency on the vertical and horizontal displacement response of saturated soil are analyzed with different modes and nonlocal parameter values.The result shows that(1)nonlocal parameters have little effect on the displacement response of saturated soil in low modes,while the influences are greater in high modes,and the displacement response mainly depends on low modes;(2)nonlocal parameters are directly proportional to vertical displacement and negatively correlated with horizontal displacement;(3)when the natural frequency of the load increases,the displacement is affected with nonlocal parameters,as the nonlocal parameters increasing,the peak displacement response will appear at lower natural frequencies of the load,and the peak displacement response will shift to the left;(4)when the natural frequency of the load increases,the displacement is affected with the speed of the load movement,and a peak displacement response will occur at lower load movement speeds;(5)when the speed of load movement increases,the displacement is affected with the natural frequency of the load,and the peak displacement response corresponds to a decrease in the natural frequency of the load.