# Dynamic Response of Buried Torsional Load in Vertically Non-Homogeneous Saturated Soil

#### Abstract

To discuss the dynamic response of buried harmonic torsional load in vertically non-homogeneous saturated soil，the soil shear modulus was assumed as a nonlinear distribution with the depth defined as an exponential function，and the dynamic differential equations of half space were established by using the Biot's consolidation theory and elastic-dynamic theory. The expressions of stress and tangential displacement in the Hankel transform domain were then acquired by solving the dynamic differential equations using the method of Hankel transform，and the true stress and tangential displacement can be obtained by Hankel inverse transformation as well. The corresponding calculation program by Mathematica was compiled based on the obtained solutions. A detailed parameter analysis completed by the program indicates that，the stress and tangential displacement of the soil show obvious fluctuations with the change of radius，and the frequency of fluctuant curves increases with the loading frequency. In addition，the maximum tangential displacement of soil occurs and there is a sharp change of stress on the loading surface. The influence range of the buried harmonic torsional load is about two times the action radius to the loading surface. Furthermore，the largest tangential displacement of the soil is negatively correlated with the depth of buried load，and it is reduced by 90% when the depth of buried load is 2 times the action radius. When the depth of buried load is greater than 4 times the action radius，the largest tangential displacement is approximately equal to zero.

**Keywords:** saturated soil, buried torsional load, dynamic response, shear modulus, Hankel transform

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