Energy method as solution for deformation of geosynthetic-reinforced embankment on Pasternak foundation

To more accurately analyze the settlement of geosynthetic-reinforced embankments on soft soil foundation, we simplified the ground surface structures as an Euler-Bernoulli beam, and the geosynthetic-reinforced layer as a Timoshenko beam. The granular fill and the soft soil foundation were both modelled using two-parameter Pasternak foundation models. We used energy method to establish energy balance equations for the system, and then we used the principle of resident potential energy to derive the governing differential equations of the settlement of the ground surface structures and the geosynthetic-reinforced layer. The MATLAB solver bvp4c was used to obtain numerical solutions for the settlement of the ground surface structures and the geosynthetic-reinforced layer on Pasternak foundations. By comparing to test results and existing models, the validity of the proposed solution is verified. This study analyzed the effects of parameters, such as flexural rigidity of the geosynthetic-reinforced layer, shear modulus of the granular fill, thickness of the soft soil foundation, and horizontal shear modulus of the Timoshenko beam, on the settlement of the ground surface structures and the geosynthetic-reinforced layer. The results showed that the model using a Pasternak foundation and a Timoshenko beam is more accurate at predicting settlement than that using a Winkler foundation and an Euler-Bernoulli beam.