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

Abstract

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 σθas a function of the radial stress σr. 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.Key words: circular tunnel, ground reaction curve, hyperbolic soil model, hodograph method.