A review of underground openings, excavated in varying rock mass types and conditions, indicates that the initiation of brittle failure occurs when the damage index, Di , expressed as the ratio of the maximum tangential boundary stress to the laboratory unconfined compressive strength exceeds 0.4. When the damage index exceeds this value, the depth of brittle failure around a tunnel can be estimated by using a strength envelope based solely on cohesion, which in terms of the Hoek - Brown parameters implies that m D 0. It is proposed that in the brittle failure process peak cohesion and friction are not mobilized together, and that around underground openings the brittle failure process is dominated by a loss of the intrinsic cohesion of the rock mass such that the frictional strength component can be ignored for estimating the depth of brittle failure, an essential component in designing support for the opening.