Slip Line Field of Plane Strain Problem Obeying the GeneralizedHoek Brown Failure Criterion
ZENG Qian bang,LIU Tong and MA Ping
DOI:10.11835/j.issn.1674-4764.2010.01.003
Received September 29, 2009,Revised , Accepted , Available online July 01, 2015
Volume ,2010,Pages 4-11
- Abstract
According to the characteristics of plane strain problem of elastic and plastic mechanics, the bi parametric expressions were derived for stress components satisfying the generalized Hoek Brown failure criterion. Being substituted into the static equilibrium partial differential equations, a group of first order hyperbolic pseudo linear differential equation partial differential equations was obtained. Utilizing the determinant method and proper variable transformation, the characteristic direction and the differential relation equation for the stress partial differential equations were acquired. The characteristic direction indicted that in plastic zone obliquely intersecting conjugate shear slip surfaces formed two families of non orthogonal slip lines, in which conjugate angle varied with the limit stress state and the material physical properties of Hoek Brown rock mass. Since the principal direction of the maximum principal stress was circumferential in perfectly elasto plastic surrounding rock of the plastic zone around a circular opening suffering the symmetric initial stress field, the angle between the tangential direction of slip line with the principal direction of the maximum principal stress was the function of the minimum principal stress(i.e. the radial stress). Combined with the analytical solution, the polar coordinate differential equation was derived and furthermore, the polar coordinate curve equation for the slip line was obtained.