低填方加筋路基沉降的Kerr模型解

A simple solution of settlement for low reinforced embankments on Kerr foundation

To predict the settlement of low reinforced embankments on soft soil foundation with high accuracy, the pavement structure is modelled as a Euler-Bernoulli beam, and the reinforced embankment is simulated as composite materials and simplified as Timoshenko beams considering the lateral shearing. The soft soil foundation is simulated by the three-parameter Kerr elastic foundation model considering the stress diffusion. To derive the governing differential equations, the energy balance equation is developed, and the principle of stationary total potential energy is used. Based on the eigenvalue differential method, the differential governing equations of settlement deformation of embankment are derived, and the analytical solutions for the settlement, shear stress and bending moment of reinforced embankment on Kerr foundation are established. The effects of the thickness and the elastic modulus of soft soil foundation and the reinforcement position on the stress and settlement of the reinforced embankments are analyzed. The results show that the Kerr foundation model can simulate the settlement of reinforced embankments with higher accuracy than Winkler and Pasternak models.