An empirical nonlinear stress-dependent constitutive relationship for rock masses based on rock mass classification

The design of support systems in most underground excavations in the United States makes use of rock mass classification systems. However, classification systems do not provide a means for quantitatively assessing the performance of supports. As a result excessive supports have often been recommended. The advent of the computer age has made possible tremendous advances in numerical modeling techniques, thus providing a means, at least theoretically, of assessing support performance. However, numerical models are not considered to be reliable design tools because of the geotechnical engineer's inability to provide realistic input parameters to necessary constitutive relationships attempting to model stress-strain response.;Recognizing that rock masses of similar condition behave in a similar manner, an empirical constitutive relationship was developed linking the finite element numerical modeling method with an empirical rock mass classification system, in particular, the Geomechanics System. The constitutive relationship defines the modulus of deformation as the ratio of the deviator stress at failure to the major principal strain at failure. The Hoek and Brown failure criterion is used to predict the deviator stress at failure. Research was directed toward developing a failure criterion defining the major principal strain at failure. The constitutive relationship was developed, in part, through correlations with observed deformation from case history studies and predicted deformations from finite element analysis.;The empirical constitutive relationship developed from this research effort expresses the deformation modulus as a nonlinear function dependent upon the uniaxial compressive strength and strain at failure, the minor principal stress, and rock mass condition as determined by the Geomechanics Classification System. The constitutive relationship, when incorporated into a suitable finite element code, offers an equivalent continuum approach for quantitatively assessing the performance of rock support systems in underground excavations.