Limit analysis solutions for spherical cavities in sandy soils under overloading

An investigation on the stability of spherical cavities in sandy soils under overloading at the ground surface is carried out in this study. By using finite element limit analysis, a spherical cavity is numerically simulated under an axisymmetric condition, and the lower and upper bound solutions of the stability of spherical cavities can be obtained. For practical use, the results of the overload are displayed in the form of the dimensionless load factor, where the effects of three dimensionless parameters including the cover depth ratio of the spherical cavity, the dimensionless overburden factor, and the friction angle of the soil are taken into account. The influences of three dimensionless parameters on the failure mechanisms of collapsed spherical cavities in sandy soils under overloading are comprehensively studied and discussed. From the results, it can be observed that these three parameters have significant influences on the magnitude of the dimensionless load factor as well as the dimensions of the plastic shear zones of the failure mechanisms of collapsed spherical cavities. Note that there is no investigation regarding the effect of the friction angle on the stability of spherical cavities in the past, but many applications of the effect of the friction angle have concerned about tunnel problems; however, for spherical cavities, this type of shape is not really representative for practice applications of the friction angle. The results of the load factors and the predicted failure mechanisms can be used for several practical works dealing with the sinkhole problems under drained conditions.