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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。
Considering the foundation as saturated half space, the dynamic response of the foundation during the harmonic torsional dynamic loading acting on the generalized Gibson saturated ground is studied. Based on Biot’s theory of consolidation of saturated ground and combining with the characteristics of torsional vibration, a dynamic differential equation of torsional vibration of saturated soil with varying shear modulus linearly with depth was established. The differential equation was solved by Hankel transform and Hankel transform Tangential Displacement and Shear Stress Expression of Undetermined Coefficients. According to the boundary condition of saturated surface, such as free surface, continuous displacement of load acting surface, difference of shear stress equal to dynamic load, radiation condition of wave, and other boundary conditions, the expression of displacement and stress in foundation is given by Hankel inverse transform. The numerical example shows that the real and imaginary parts of the tangential and shear stress curves in the ground show a very obvious variation rule in the same horizontal plane. In the vertical plane, the upper part of the dynamic loading surface When the depth increases, the real part of the tangential displacement and shear stress curve in the foundation gradually increases, while in the lower part of the dynamic load acting surface, the opposite is true. The influence range of the twisting dynamic load is mainly twofold Radius area.