An empirical strength criterion for heterogeneous tuff

An empirical failure criterion is formulated by expressing the second invariant of stress deviation at failure as a function of the first invariant of stress, key parameter, and volume. Strength data from Apache Leap tuff specimens are analyzed as a demonstration example. The density variable included as a key parameter for this tuff minimizes the effect of heterogeneity caused by nonuniform distribution of pores, mineralogy, inclusions, welding and grain bonding. The criterion incorporates all principal stresses and the scale effect, and hence allows predicting the strength toward in-situ conditions. The proposed derivation improves the correlations between test results and failure envelope for the heterogeneous tuff. The criterion formulated from the uniaxial and triaxial test data adequately predicts the strengths for biaxial compression tests.