矩形深基础地基极限承载力的理论解

THEORETICAL SOLUTION OF ULTIMATE BEARING CAPACITY OF DEEP RECTANGLE FOUNDATION

现有深基础地基极限承载力理论一般仅适用于条形深基础,而实际工程中经常遇到的矩形深基础属于三维问题,对矩形深基础的极限承载力研究较少。根据刚塑性体的平衡条件,在分别考虑黏聚力和重度的情况下,推导方形深基础地基极限承载力的理论解,再结合条形深基础地基极限承载力的理论解,叠加后得到矩形深基础地基极限承载力的通用解析解。针对基础深度与宽度之比为2的情况,探讨在不同内摩擦角下承载力系数Nc,Nq与矩形深基础长宽比的变化关系以及在不同长宽比下系数Nc,Nq与内摩擦角的变化关系;针对基础长度与宽度之比为2情况,给出在不同内摩擦角下系数Nc,Nq与矩形深基础深宽比的变化规律。并与几种典型的深基础地基极限承载力半经验修正公式进行对比分析,结果表明承载力系数Nc,Nq的曲线变化趋势与现有半经验修正公式结果基本相同,但系数的具体数值有差异,表现为Nc的计算值与修正公式的结果相差不大,而Nq的计算值与修正公式的结果差别明显。由此,建议进一步研究现有深基础极限承载力的半经验修正公式。

Most of the existing ultimate bearing capacity theories can only be used in deep strip foundation. There are less researches on the three dimensional problems of deep rectangle foundation that are often encountered in practical engineering so far. According to the static equilibrium of rigid-plasticity body,a new analytical solution of deep square foundation is presented. With considering the bearing capacity factors of cohesion and density of soil,the analytical universal solution of deep rectangle foundation is received combined with the analytical solution of deep strip foundation. The relationship between bearing capacity factors Nc,Nq and ratio of length and width of deep rectangle foundation in different internal friction angle of soil and the relationship between bearing capacity factors Nc,Nq and internal friction angle of soil in different ratio of length and width of deep rectangle foundation are investigated when the ratio of depth and width of foundation is two. And the relationship between bearing capacity factors Nc,Nq and ratio of depth and width of foundation in different internal friction angle of soil are investigated when the ratio of length and width of foundation is two. The results show that the changing trend of the curve of bearing capacity factors Nc,Nq are almost the same,but the value of bearing capacity factors are different when compared with the semi-empiric formulas. The value of Nc are almost the same,on the other hand,the difference of the value of Nq is obvious. There will be more researches to do to perfect the semi-empiric formulas.