CALCULATIONS FOR THE STABILITY OF A SAND BED BY A SOLUTION COMBINING THE THEORIES OF ELASTICITY AND PLASTICITY

Abstract

THE CALCULATIONS OF THE STABILITY OF A SAND BED UNDER A RIGID ROUGH FOOTING RESTING ON THE SURFACE HAVE BEEN CARRIED OUT WITH A VIEW TO THE FORMATION UNDER THE PLATE OF A COMPACTED CORE. THE LATTER CONSISTS OF AN ELASTIC PART ADJOINING THE FOOTING AND A LOWER PLASTIC PART. THE STRESSES AND STRAIN IN THE ELASTIC PART OF THE CORE ARE DETERMINED BY MEANS OF THE THEORY OF ELASTICITY. THE LOWER BOUNDARY OF THE ELASTIC PART IS ESTABLISHED ASSUMING THAT ALL THREE COMPONENTS OF THE STRESSES AT BOTH SIDES OF THE BOUNDARY ARE EQUAL, AND THAT THE LINES OF SLIDING ARE A SMOOTH CONTINUATION OF THE TRAJECTORIES OF THE PARTICLES IN THE ELASTIC PART OF THE CORE. THE STRESSES IN THE PLASTIC PART OF THE COMPACTED CORE AND IN ALL THE REMAINING DISPLACED SOIL ARE DETERMINED IN ACCORDANCE WITH THE THEORY OF CRITICALLY STRESSED SOIL. THE VERTICAL AND TANGENTIAL REACTIONS OF THE SOIL TO THE FOOTING AT THE MOMENT WHEN THE COMPACTED CORE IS FORMED HAVE BEEN ESTABLISHED. THE RESULTS AGREE WITH EXPERIMENTAL DATA AND INDICATE AN INCREASE IN THE VALUE OF THE CRITICAL LOAD. /LCPC/RRL/A/