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基于弹性力学Mindlin解,推导了盾构推进时正面推力、盾构与土体间的摩擦力引起的周围土体附加应力沿圆周方向的计算表达式,并运用Gauss-Legendre公式,结合庆春路过江隧道工程进行了数值分析,得到了周围土体附加应力沿圆周方向的分布规律,可以为盾构推进控制及壁后注浆提供参考。通过分析得出:土体中附加应力关于90°/270°轴,即隧道轴线严格对称;σx在90°与270°位置即圆周顶与底达到最大值,且顶部值比底部略大;在腰部偏下位置达到最小值;σy最大值分别在90°与270°位置,即圆周顶与底,且顶部值比底部更大,最小值分别在0°与180°位置,即圆周腰部,整个图形呈眼镜形;σz最大值分别在圆周腰部略偏上位置,最小值分别在90°与270°位置,即圆周顶与底,整个图形呈“8”形;摩阻力引起的土体附加应力的分布规律类似于正面推力引起的土体附加应力的分布规律,但其值远大于正面推力引起的土体附加应力,因此不可忽略摩阻力的影响。
Based on the Mindlin solution of elastic mechanics, the formulas for calculating the additional stress of the surrounding soil caused by the positive thrust of the shield and the friction between the shield and the soil are deduced. Using the Gauss-Legendre formula, Through the numerical analysis of the tunnel project, the distribution rule of the additional stress around the soil in the circumferential direction is obtained, which can provide reference for the shield control and the grouting behind the wall. The results show that the additional stress in the soil is strictly symmetric with respect to the 90 ° / 270 ° axis, ie the axis of the tunnel; σx reaches the maximum value at the top and bottom of the circle at 90 ° and 270 °, and the top is slightly larger than the bottom; The waist lower reaches the minimum position; σy maximum at 90 ° and 270 ° position, the top and bottom of the circle, and the top value is greater than the bottom, the minimum value at 0 ° and 180 ° position, the waist circumference, the whole The shape of the figure is the shape of glasses. The maximum values of σz are slightly above the waist, respectively, with the minimum values of 90 ° and 270 ° respectively, ie the top and bottom of the circle. The whole figure shows “8” shape. The distribution of additional stress is similar to the distribution of additional stress due to positive thrust, but its value is much larger than the additional stress of soil due to positive thrust. Therefore, the influence of friction should not be neglected.