BEDDINGS AND FOUNDATIONS, SUBTERRANEAN STRUCTURES. SOIL MECHANICS

STRESS-STRAIN STATE OF AN ELASTIC HALF-PLANE AT A LINEAR SHIFT OF A PART OF ITS BOUNDARY

Vestnik MGSU 2/2017 Volume 12

Pages 184-192

Loads cause vertical shifts of foundations of all structures, and the safe operation of buildings depends on the value thereof. The article presents a solution of the problem of stress distribution in a homogeneous and isotropic soil mass under vertical linear shift of a part of its boundary obtained by the complex potentials method. Expressions for stress components and strain components of the second basic boundary plane problem of the theory of elasticity for half-plane at the linear shift (the law of linear shift) of a part of its boundary are determined in a closed form. Patterns of isolines of stress and strain components are built; they illustrate that numerical values of all like-named components located at corresponding points on opposite sides of the symmetry axis are equal in value but opposite in sign. The formula of subsidence that occurs at the shift of the half-plane boundary part was derived. The value of subsidence is directly proportional to the boundary part shift value and inversely proportional to the lateral soil pressure coefficient value. Conclusions: expressions for stress and strain components of the second basic boundary plane problem of the theory of elasticity for half-plane are obtained in a closed form. Values of the stress and strain components are symmetric relative to the origin and opposite in sign; the formula of subsidence for half-plane boundary vertical shift is obtained on the basis of the expression for the vertical strain component.

DOI: 10.22227/1997-0935.2017.2.184-192