Abstract:

Under the framework of Biot porous media theory, the fractional order Kelvin model is used to describe the rheological effect of soil skeleton, considering the coupling effect of pore pressure dissipation and skeleton rheology. By establishing a spatiotemporal analytical function for periodic cyclic loads, a three-dimensional axisymmetric dynamic consolidation control equation for a half space saturated clay foundation is constructed in a cylindrical coordinate system. The analytical solution of the control equation in the transformed domain is derived using Hankel-Laplace joint transformation and tensor operations, followed by numerical inversion to acquire the spatiotemporal solution of the physical field. By analyzing numerical examples, the dynamic consolidation characteristics of a saturated clay foundation under cyclic loading are studied. The results indicate that the settlement rate of saturated clay is slower during primary consolidation but faster during secondary consolidation. With cyclic loading, the soil's cumulative settlement development accelerates as the rheological properties of the soil skeleton strengthen. The amplitude of soil displacement fluctuations decreases as the order of viscosity increases, and the more significant the order of viscosity, the more pronounced the displacement hysteresis becomes. The rheological properties of the soil skeleton lead to a lag in pore pressure response compared to effective stress, resulting in horizontal movement of the spiral curve between pore pressure and effective stress under cyclic loading. In the unloading stage of cyclic loads, due to the decrease of normal stress with the decrease of external load, but the increase of shear stress, the soil undergoes shear dilation phenomenon, resulting in negative pore pressure in the soil.

Key words: fractional Kelvin model, saturated clay foundation, dynamic consolidation, cyclic load, Hankel-Laplace transformation