Mindlin解积分的方形荷载竖向应力系数初等解  

Elementary solution of vertical stress coefficient of square load based on Mindlin solution integration

作　　者：邱明兵[1] 高文生[1] Qiu Mingbing;Gao Wensheng(China Academy of Building Research,100013,Beijing,China)

机构地区：[1]中国建筑科学研究院,北京100013

出　　处：《应用力学学报》2021年第2期655-662,共8页Chinese Journal of Applied Mechanics

基　　金：中国建筑科学研究院基础研究项目(20171602330710007)。

摘　　要：在求解端阻在土中的应力时通常假定端阻为集中力,使得桩端附近应力突增,与实际应力的误差极大,无法有效考察桩端附近土体的应力分布特征。本文基于Mindlin应力解,利用积分代换和回代,求出方形均布荷载作用下半无限空间内任意一点的竖向应力系数初等解。当荷载深度接近0时,理论上该解退化为Boussinesq解,通过计算可知二者得出的应力系数一致。本文还首次给出了应力系数沿荷载埋深衰减的规律,当荷载埋深与宽度比小于1.0时,衰减很快;当大于1.0时,则衰减较慢,且逼近0.5。对方形端阻应力系数和圆形端阻应力系数进行比较发现,在桩端2倍桩径范围内的应力系数差别仅为约20%,在2倍桩径之外,两种应力系数一致。因此,用方形端阻应力系数替代圆形端阻应力系数产生的误差较小。按照本文的积分方法,还可以求解矩形分布荷载下的应力场和位移场。本初等解也可为研究基坑开挖产生的应力场提供参考。At present,when calculating the stress of end resistance in soil,it is usually assumed that the end resistance is a concentrated force,which makes the stress near the pile tip increase suddenly,and the error is great with the actual stress,so it is unable to effectively investigate the stress distribution characteristics of soil near the pile tip.In this paper,based on Mindlin’s stress solution,the elementary solution of vertical stress coefficient at any point in a semi-infinite space under square uniform load is obtained by integral substitution and back substitution.When the load depth is close to 0,the solution theoretically degenerates to Boussinesq solution,and the stress coefficients obtained by the two solutions are consistent.This paper also gives the law of stress coefficient attenuation along the buried depth of load for the first time.When the ratio of buried depth to width is less than 1.0,the attenuation is very fast;when the ratio is greater than 1.0,the attenuation is slow and approaches 0.5.By comparing the square end resistance stress coefficient with the circular end resistance stress coefficient,it is found that the difference of stress coefficient is only about 20%in the range of two times of pile diameter,and the two kinds of stress coefficients are the same except for two times of pile diameter.Therefore,the error of using the square end resistance stress coefficient to replace the circular end resistance stress system is small.According to the integral method,the stress field and displacement field of rectangular distributed load can also be solved.The primary solution can also be used as a reference for studying the stress field caused by excavation.

关 键 词：桩 MINDLIN解 均布荷载 初等解 弹性半无限空间体 

分 类 号：TU43[建筑科学—岩土工程]