Determination of ground reaction curve for hyperbolic soil model using the hodograph method

This paper reintroduces an efficient method for analyzing the problem of a deep circular tunnel and for determining the ground reaction curve (GRC). It is assumed that the tunnel is excavated in soil-rock mass subjected to a hydrostatic in situ stress field under a plane strain condition. The constitutive law for the surrounding material is assumed to follow Duncan-Chang's hyperbolic stress-strain relation. The technique for analysis is known as Biot's hodograph method, which relies on expressing principal strains as functions of principal stresses. The problem is reduced to solving a first order differential equation for the hoop stress σ_θ as a function of the radial stress σ_r. The GRCs are graphically presented in dimensionless form. It is shown that the hodograph method is straightforward and can be easily applied in engineering practice.