Calculation and analysis of single pile settlement based on mathematical programming algorithm

Based on the soil spring model of the load transfer method, a new assumption is proposed, and a mathematical programming model for calculating single pile settlement is established. In the mathematical model, the principle of the minimum potential energy is used as the objective function and the working load at the top of the pile is used as constraints, which is a mathematical approach to find how to distribute the load of soil spring to make the whole system potential energy minimum. Different from the traditional soil spring model, the proposed model defines the element value of a pile settlement as the average value of the top and bottom plane settlements of that pile element. Validated by an example, the Q-s curve calculated by the mathematical programming model and the measured data are in good agreement, which illustrates the proposed method is feasible and effective. And a comparison with the displacement coordination method shows that the proposed method has higher precision under the condition of less subdivision element.