Salt pile stability: a mathematical model

Abstract

The maximum height for the salt pile in a circular dome with a 4ft retaining wall was determined by two methods. The first method used rigid-body physics; in this model, the critical angel, the maximum angle of inclination allowed while maintaining static equilibrium, was determined using only the external coefficient of friction for salt. Because the static equilibrium also depended upon internal friction, a second model was developed. Development of the second model utilized particle physics, fluid mechanics and soil stress analysis. Mohr's circle, the internal coefficient of friction for salt and its angle of repose were used to determine the critical angle. These results were combined to form our solution model, Model II, which consisted of two submodels: Model II(a) provides a general solution where the front-end loader is allowed to freely travel to any location on the salt pile. This model yields a maximum height of 17.4ft for a symmetric cone with a critical angle of 14.6°. Model II(b) provides a volume-maximizing solution if the loader's travel is restricted. This model yields a maximum height of 23.7ft for a wedge shape with a ramp slope of 14.6° and a back edge slope of 35.9°, where the loader must not cross the peak. Therefore, the authors recommend that Model II(a) be used in the general situation, since the loader is allowed to drive anywhere on the salt pile in this case. When the maximum volume provided is insufficient, Model II(b) can be utilized to increase the capacity of the dome. (Note: The loader must not cross the peak in this model.)