考虑位移的土压力理论在支护桩受力分析中的应用

针对支护桩所受土反力与土体位移呈非线性关系的问题,通过引入梅国雄提出的考虑位移的土压力计算方法,将计算方法中的土压力代换单桩挠曲四阶微分方程中的土反力,得到一个四阶变系数非齐次非线性常微分方程;然后根据支护桩位于基坑底面上、下所处受力状态的差异和桩顶的初值条件,采用泰勒级数解法求出支护桩任意深度处的挠度解析解;再根据桩体的挠度计算出桩周土体的位移量,并得到桩周土反力的计算式;由此便可计算桩身任意深度以及该深度截面上任意点处的受力情况,使得问题的求解更简捷。最后还给出了计算实例来验证所采用的方法以及所推导出的公式的正确性。

APPLICATION OF EARTH PRESSURE THEORY CONSIDERING DISPLACEMENT TO MECHANICAL ANALYSIS OF BRACING PILE

The non-linear relationship between displacement and soil reaction caused by pile-soil interaction directly results in the complexity of mechanical analysis of bracing pile. Through replacing the soil reaction of fourth-order differential equation of single pile displacement with the earth pressure obtained from the earth pressure theory considering displacement given by MEI, a variable-coefficient, non-homogeneous and non-linear fourth-order differential equation can be obtained. Based on different mechanical characteristics of bracing pile located at upside and downside of excavation surface respectively and initial condition of pile peak, the explicit solution of displacement for random part of bracing pile is presented with the method of Taylor series. Accordingly, the displacement of soil around the pile also can be obtained by the method of geometry. Thus, the force acting on bracing pile at any depth and any point can be calculated directly. Therefore, the solution in the paper is more simple and convenient. A numerical example is presented to verify above solution.