基于滑移线场理论斜坡条基极限承载力解析解

Analytical Solutions of Ultimate Bearing Capacity for Strip Foundations on Slopes Based on Slip Line Theories

在工程建设领域,经常需要把基础设置在斜坡地基上,但在现行成果中,对斜坡地基极限承载力的确定并没有给出具体计算方法。为合理确定斜坡地基极限承载力,从而为斜坡地基上的基础设计提供理论依据,并有效降低基础工程的建设成本,本文基于滑移线场理论,建立了斜坡地基的滑移破坏模型,进而根据斜坡地基坡前、坡后土体的塑性边界条件,推导了无重土斜坡地基极限承载力解析公式。同时,提出了采用有限差分方法获取斜坡地基滑移线场及应力分布场的方法。实例计算表明,滑移线解小于极限平衡解及有限元解,主要误差来自于地基土自重的影响,但总体误差在10%以下,本文所述解析法可用于斜坡地基极限承载力的快速估算。

In the field of engineering construction,foundations are always placed on slopes. However,in the present research work,there is no accurate method to calculate the ultimate bearing capacity of these foundations. In order to accurately calculate the ultimate bearing capacity of foundations on slopes,provide theoretical basis for foundation designing,and effectively reduce the construction cost of these foundations,slip failure model for foundations on slopes is developed based on slip line theories and the analytical formula to calculate the ultimate bearing capacity of these foundations without considering the weight of soil is deduced according to the plastic boundary conditions of soil before and after the slope. Meanwhile,the way how to get the slip line field and stress field in the whole foundation soil by finite difference method is introduced. To verify the feasibility and reliability of the methods described herein,a calculation example is given in this paper. Calculation results from the example indicate that,slip line solution is smaller than the limit equilibrium solution and the finite element solution,the main error is from the soil weight impact,but overall error less than 10%. Therefore,the analytical method herein can be used to quickly estimate the ultimate bearing capacity of foundations on slopes.