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传统土力学处理岩土工程问题时,经常采用弹性力学方法分析土中应力分布。土中应力通常依据较为简单的Boussinesq解计算,该解答假定荷载作用于土体表面;但是,建筑物基础一般都埋置在地表以下一定深度,此时,应依据Mindlin解计算应力分布。在半无限弹性体内作用竖向矩形和条形均布荷载时的应力分布对计算基础沉降以及分析基坑尺寸对稳定性和变形的影响均有重要意义,在其他岩土工程问题中也有诸多应用。尽管文献[1-2]给出了相关计算公式,但存在几处错误。基于Mindlin解,通过积分重新推导了在半无限体内部作用竖向矩形均布荷载时应力分布的解析表达式,进一步得到了条形均布荷载作用时应力分布的解析表达式,这2组公式均与文献[1-2]给出的结果存在不同。最后,采用数值积分方法验证了新给出的2组公式的正确性。
When traditional geotechnical engineering geotechnical problems, often using elastic mechanics method to analyze soil stress distribution. Soil stress is usually calculated using the simple Boussinesq solution, which assumes that loads act on the surface of the soil; however, the foundation of the building is generally buried some depth below the surface, at which point the stress distribution should be calculated from the Mindlin solution. The stress distribution in vertical rectangular and strip-like distributed loads in a semi-infinite elastic body is of great significance for calculating the foundation settlement and for analyzing the influence of the foundation pit size on the stability and deformation. There are also many applications in other geotechnical problems . Although the relevant formulas are given in [1-2], there are several errors. Based on the Mindlin solution, the analytical expression of stress distribution in vertical rectangular uniform load acting on the semi-infinite body is deduced by integral method. The analytical expression of stress distribution in strip-shaped uniform load is obtained. The two formulas All the results presented in [1-2] are different. Finally, numerical integration is used to verify the correctness of the two new formulas.