基于Mindlin解的单桩竖向附加应力系数

Study on vertical additional stress coefficient for the single piles based on Mindlin's stress solution theory

基于考虑桩径影响的竖向荷载下Mindlin应力解,将单桩端阻、矩形分布侧阻、正三角形分布侧阻产生的应力表达为各分项阻力与相应附加应力系数的乘积,并将附加应力系数表示为以深径比h/d和距径比ρ/d为自变量的函数以描述其空间变化。这样使得附加应力系数物理意义直观明晰,应用简单。通过对单桩附加应力系数的三维图形和附加应力系数表的分析表明:①端阻附加应力系数由桩端平面呈现柱状分布随深度演变为锥形分布,空间衰减迅速;端阻附加应力系数基本不随长径比l/d而变;②侧阻附加应力系数由桩端平面的长桶喇叭形分布演变为漏斗形分布,空间衰减缓慢;正三角形分布侧阻与矩形分布侧阻相比,其附加应力系数上部较大,且衰减较快;③侧阻是群桩应力叠加效应的主要因素,端阻影响甚微。

Based on the Mindlin＇s stress solution theory considering the pile diameter effect, the additional stress coefficient is expressed by the depth -diameter ratio （hid） and the distance- diameter ratio （pi d）. The stress from the pile tip and side resistance is indicated as multiplication of the different part resistance and the corresponding additional stress coefficient. Thus physical meaning of additional stress coefficient is more concise, straight forward and easy to apply in engineering. The results of additional stress coefficient field and table show that the additional stress coefficient from the tip resistance under the pile tip shows a columnar distribution form and it changes in a pyramidal distribution with the depth increasing. It weakens rapidly in the depth direction, but not with the length-diameter ratio. The additional stress coefficient from the pile side resistance under the pile tip surface shows long barrel-trumpet-shape distribution form and it changes to a infundibuliform with the depth increasing. It weakens more slightly than the pile tip resistance in the depth direction. The additional stress coefficient from the side resistance of rectangular distribution change more slightly than triangle distribution in the depth direction but it is smaller than the coefficient from the triangle distribution close to the pile tip. The pile side resistance is the main factor of the stress superposition in the calculation, but the tip resistance has little influence on the stress calculation results.