Abstract
A closed-form analytical solution to rheological phenomena is obtained based on Hoek-Brown (HB) yield criterion and the generalized Bingham model. Once the circular tunnel is excavated, an initial plastic region is formed. When the total stresses fulfil the yield condition, the initial plastic region steps into the viscoplastic region, in which the displacement develops with time. The one-dimensional constitutive equation of the generalized Bingham model is transformed into a three-dimensional expression in polar coordinates by combining the plane strain condition. With the help of equilibrium differential equation, geometric equation and boundary condition, the stress and displacement in the initial plastic region can be expressed. At the moment of t, the stresses and displacements are described similar to the solutions of the elasto-plastic state. The stresses, strains and displacements after transformation can be expressed in the viscoplastic region. The proposed solution was verified by the closed-form solution of circular tunnels in elastic-brittle-plastic rock mass.
Highlights
Because of the urgent need of mineral resources, the mining dramatically deep into the earth, many coal and metal mines have been mined to a depth of more than 1 km
The strain of the generalized Bingham model is a function of time, the one-dimensional constitutive equation can expressed as Eq (14)
Rock rheology is the result of the continuous accumulation of internal damage, which eventually leads to rock burst
Summary
List of Symbols a Excavation radius σr, σθ Radial and tangential stresses εr, εθ Radial and tangential strains σrvp, σθvp Radial and tangential viscoplastic stresses εrvp, εθvp Radial and tangential viscoplastic strains u Radial displacement uvp Radial viscoplastic displacement E Young’s modulus G Shear modulus σc Uniaxial compression strength μ Poisson’s ratio ψ Dilatancy angle c Cohesive strength φ Friction angle m, s The first and section strength parameters pi Internal supporting pressure pc Radial stress at elasto-plastic interface ρ0 The radius of the initial plastic region Rt The radius of the viscoplastic region Derivative of variable to time
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