Displacement Analytic Solution of a Deep Elliptical Tunnel in Transversely Isotropic Rock Mass

Abstract

Sedimentary rocks with layered structure account for two third of global land area, and this proportion is 77.3% in China, lots of metamorphic rocks also have significant features of layered structure, so there are a large number of stability problems about layered rock mass in mining engineering. Layered rock mass is generally considered to be transversely isotropic solid in mechanics. Based on the complex variable expression of displacement components of transversely isotropy, the displacement analytical solution of a deep elliptical tunnel in transversely isotropic rock mass is derived by conformal mapping method.

Displacement Analytical Solution of a Circular Hole in Layered Composite Materials considering Shear Stress Effect

“…(20) reduces to solution with two unequal normal stresses. 10 If E E   ,     , Eq. (20) reduces to solution in isotropy.…”

Simulation of Well Wall Stress Distribution Model and Well Stability

“…The authors separated the pressure field around the well into four parts according to the cause of pressure fields, maximum horizontal principal stress σ H1 , minimum horizontal principal stress σ H2 , vertical stress σ v , and wellbore pressure p wf Fig. (1). To make it easier to calculate, they changed the coordinates into rectangular coordinates whose Z axis coincides with well axis, so that the original σ H1 , σ H2 and σ v will be changed into σ xx , σ yy , σ zz , τ xy , τ xz , and τ yz under new coordinates Fig.…”

“…In 1898s, Kirsch established the 2-D stress distribution formulae around borehole in elastic plates [1]. And then Jaeger and Cook made a thorough derivation of Kirsch's formulae [2].…”