埋置简谐扭转荷载作用下广义Gibson饱和地基动力响应

Dynamic response of generalized Gibson saturated soil under an embedded harmonic torsional load

考虑地基为饱和半空间,研究了广义Gibson饱和地基内作用简谐扭转动荷载时地基的动力响应问题。从Biot饱和地基固结理论出发,结合扭转振动的特点,建立了剪切模量随深度线性变化的饱和地基扭转振动的动力微分方程,通过Hankel变换求解此微分方程,给出了Hankel变换域内的切向位移和剪应力关于待定系数的表达式。根据饱和地基表面为自由表面,荷载作用面位移连续、剪应力差等于动荷载大小,波的辐射条件等边界条件求解出待定系数,借助Hankel逆变换给出地基内的位移和应力的表达式。通过数值算例研究发现:在同一水平面内,地基内的切向位移和剪应力曲线的实部和虚部都呈现出非常明显的波动变化规律;在竖向平面内,动荷载作用面上部区域内随深度逐渐增大时,地基内切向位移和剪应力曲线的实部逐渐增大,而在动荷载作用面下部区域则正好相反;扭转动荷载的影响范围主要是荷载作用面上下2倍半径区域。

This paper treats the ground soil as a saturated half space. It investigates the dynamic response of a generalized Gibson soil（whose shear modulus increases linearly with depth） subjected to an embeddd harmonic torsional load. It uses Biot’s theory of saturated soil and combines the characteristics of torsional vibration. It establishes the dynamic differential equations of generalized Gibson saturated soil. Using the technique of Hankel transform, it solves the differential equations. The tangential displacement and shear stresses in Hankel transform domain with several undetermined coefficients are formulated. Using the boundary conditions including the free surface at the top of the half-space, the tangential displacements near the loading area are continuous, the shear stresses near the loading area are discontinuous and the radiation boundary condition, the undetermined coefficients are solved. Then, the tangential displacement and the shear stress of the nonhomogeneous saturated soil are expressed explicitly in Hankel inverse transform. Selected numerical examples are presented. The numerical results reveal that in the same horizontal plane, both real and imaginary parts of the tangential displacement and shear stress show very significant fluctuations. In the vertical plane, the real parts of the tangential displacement and shear stress increase with depth in the zone above the loading surface, and decrease with depth in the zone below the loading surface. Besides, the influence range of the torsional dynamic load is about two times of the action radius to the loading surface.