Arching in granular soils: limit state equilibrium

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.