One of the most critical assumptions in the application of arching theory is an accurate estimate of the coefficient of lateral stress, K, used to relate vertical and horizontal stresses on the assumed failure plane. Historically, this has been treated as an empirical constant, and previous mathematical estimates based on consideration of principal stress rotations in the soil have not been able to match experimental values. This paper presents an analytical solution based on limit equilibrium to calculate K based on the rotation of principal stresses at the failure plane and the formation of a continuous arc of major principal stresses across the trapdoor, as observed from centrifuge tests specifically conducted to study arching in granular soils. The predicted K values from the analytical method showed a good match to historical measurements of K, and were successfully used to predict the vertical stresses from the centrifuge tests conducted in this study. The proposed method gives a new analytical basis from soil mechanics principles and an understanding of the rotation of principal stresses to calculate this factor.

中文翻译：

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颗粒土中的拱起：极限状态平衡

拱形理论应用中最关键的假设之一是对横向应力系数K的准确估计，该系数用于关联假定破坏平面上的垂直和水平应力。从历史上看，这被视为一个经验常数，以前基于土壤中主应力旋转的数学估计无法匹配实验值。本文提出了一种基于极限平衡的解析解，以根据破坏平面处主应力的旋转和穿过活板门的主要主应力的连续弧的形成来计算K，这是从专门用于研究拱起的离心机试验中观察到的。粒状土壤。预测的K来自分析方法的值显示出与K 的历史测量值的良好匹配，并成功地用于预测本研究中进行的离心机测试的垂直应力。所提出的方法从土力学原理和对主应力旋转的理解来计算该因子提供了新的分析基础。