垂直均布荷载矩形基础地基任意点附加应力系数公式推导

摘要

At present,the additional stress coefficient at any point of the rectangular foundation subsoil under the vertically even distributed load is mainly obtained by the corner point method with the help of the “table look-up”and the interpolation.Although the method seems to be easy to use, the results may vary from person to person.In this paper,the author uses the integration method derivates the computational formulas about the additional stress coefficient at any point of the rectangular foundation subsoil under the vertically even distributed load.Moreover,The author also presents some specific formulas for calculating a corner point,a central point,a mid-point on the long side as well as a corner point of a 2l×2b region beyond the rectangular foundation.By comparing with the formulas for the additional stress coefficients under the corner points listed in the related literature,it is found that the derivated formulas in this paper are completely correct.Although the formulas seem complicated,they are easy to use with the help of the Excel Program Calculation Sheet.They can avoid the interpolation values differences due to different users and the possible confusion due to different rectangle area of l/b and z/b during the calculation by the corner point method.As long as the length l and width b of the rectangular area are given,the additional stress coefficient at any point of (x ,y ,z )can be calculated,which,to some extent,makes the rapid calculation possible.Therefore,the formulas can be very conveniently applied to the practical work for the engineering technicians.%目前，垂直均布荷载作用下，矩形基础地基中任意点附加应力系数都是通过角点法查表内插求得，虽然用起来方便，但结果可能因人而异。笔者通过积分导出了垂直均布荷载作用下，矩形基础地基中任意点附加应力系数的计算公式，并给出了角点、中心点、边中点及基础外2l×2b 区域角点下的计算公式。通过与有关文献所列角点下附加应力系数公式对比，本文所推导的公式是完全正确的。虽然公式复杂，但借助 Excel 很容易进行计算，达到了“速算”程度，只要给出矩形面的长度、宽度，就可计算任意点（x，y ，z）的附加应力系数，避免了内插取值因人而异的差异及角点法计算过程中因不同矩形的 l／b、z／b 可能出现混乱导致的错误，极大地方便了工程技术人员在实际工作中的运用。