Quantifying uncertainty in Hoek–Brown intact strength envelopes

• Sources of uncertainty in intact rock parameters were presented.
• A set of new regression methods were proposed to select an accurate mean fit and quantify uncertainty using prediction intervals for the Hoek–Brown intact strength envelope.
• Methods for varying intact strength based on rock homogeneity were also proposed that can be used in a reliability assessment.
• This approach was used to assess ground response for a hydro tunnel in an altered rockmass.
• Treating UCS and mi as uncorrelated parameters results in an inaccurate assessment of variable ground response and extreme ground response conditions that can complicate design.

Uncertainty plays a critical role in geotechnical design projects. In addition to the natural variability of geomaterials, testing, transformation and modelling errors must also be considered to accurately characterize rockmass behaviour. By using statistical methods to quantify the intact rock strength and a measure of rockmass quality, a greater understanding of the variability in ground response and support performance can be achieved. This paper examines the issue of quantifying uncertainty in rockmass strength by using the generalized Hoek–Brown approach, which defines rockmass strength according to the intact strength envelope (based on test data) and the geological strength index (GSI). While uncertainty in GSI can be quantified through either a qualitative or quantitative approach, it is more difficult to assess the uncertainty in the intact strength envelope as it is defined by two correlated variables: the uniaxial compressive strength (UCS) and the Hoek–Brown material constant. A new set of linear and nonlinear regression approaches is proposed that can be used to accurately determine the mean intact strength envelope and quantify uncertainty from test data. A reliability-based design method is then presented that quantifies and utilizes uncertainty information at each stage of design to obtain a more complete understanding of rockmass behaviour. To demonstrate the usefulness of this approach, a reliability assessment is performed for a circular excavation under hydrostatic loading conditions.