Interaction of reinforced cushion and pile-soil system in embankments based on principle of minimum potential energy

The bearing mechanism of piled embankments is complex as it involves the interaction of piles, soil columns, sand cushions and reinforced geogrids, and its simplified calculation method for layered soils still lacks researches. A mathematical model is proposed for a generalized pile-soil model with geogrids. Considering the potential energy generated by pile-soil load transfer and geotextile tensile, the potential energy equations for the whole system are derived and discreted. An unconstrained nonlinear mathematical optimization model is established, with the potential energy equation as an objective function. The minimum value of the total potential energy equation is obtained by a descent iterative algorithm, and in this way the deformations of piles, soils and sand cushions in the vertical direction are solved. The mathematical model for piled embankment and the solving method are validated through an example without geogrid. The effect of the geogrid interaction is discussed in another engineering example.