Failure Criteria and Strength Characterization in Rock Materials

Rock masses display a complex interplay of brittle fracture and plastic deformation under diverse stress states, making the prediction of failure and strength a cornerstone of geoscience and engineering. Classical approaches capture this behaviour through empirical and semi‐empirical criteria that define the stress‐dependent envelopes within which rock remains intact. The Mohr–Coulomb criterion characterises failure by linear relationships between shear and normal stresses, while the Hoek–Brown criterion introduces non‐linear descriptions that account for rock mass heterogeneity via parameters such as the Geological Strength Index and the material constant mi. Strength characterisation hinges on laboratory and field tests—including uniaxial and triaxial loading, in situ stress measurements and probabilistic sampling methods—to derive cohesion, friction angle and confining stress thresholds. Recent advances integrate finite element modelling, probabilistic frameworks and data‐driven algorithms to refine parameter estimation, offering more reliable designs for tunnels, slopes and foundations. These developments underscore global imperatives to improve the safety and sustainability of infrastructure in variable geological settings.

Research from Nature Portfolio

A new study has dissected the estimation of the maximum minimum principal stress on potential failure surfaces by combining strength reduction with three‐dimensional finite element analyses of a wide range of slope geometries and rock mass properties. By evaluating 425 synthetic slopes, the research demonstrates that slope angle and Geological Strength Index exert dominant control on the confining stress limit, whereas intact rock strength and the Hoek–Brown parameter mi are of secondary influence. Two analytical formulae are proposed to estimate this critical stress directly from slope angle and GSI, and validation against 31 real‐world case studies confirms their broad applicability for translating non‐linear Hoek–Brown behaviour into equivalent Mohr–Coulomb parameters.

Failure Criteria and Strength Characterization in Rock Materials publication trend

The graph below shows the total number of articles in failure criteria and strength characterization in rock materials across all publications each year (not limited to Nature Index journals).

Technical terms

Hoek–Brown failure criterion: A non‐linear empirical model relating major and minor principal stresses at failure, incorporating rock mass quality parameters.

Mohr–Coulomb criterion: A linear failure envelope defining shear strength as a function of normal stress via cohesion and internal friction angle.

Geological Strength Index (GSI): A qualitative system for estimating rock mass quality based on discontinuity characteristics and intact rock properties.

Terminating Mohr’s circle (TMC): A parabolic construct used to cap the tensile end of a quadratic Mohr failure envelope in generalised formulations.

Uniaxial compressive strength (UCS): The maximum axial compressive stress a rock specimen can sustain under uniaxial loading.

Cohesion: The shear strength parameter representing internal cementation or binding forces at zero normal stress.

Internal friction angle: The slope of the shear-normal stress envelope, indicating the granular interlocking resistance of rock or rock mass.

References

1. Rational implementation of the Mohr criterion in its general form. International Journal of Mechanical Sciences (2024).
2. Rock slope stability analysis under Hoek–Brown failure criterion with different flow rules. Bulletin of Engineering Geology and the Environment (2024).
3. Probabilistic Characterization of Hoek–Brown Constant mi of Rock Using Hoek’s Guideline Chart, Regression Model and Uniaxial Compression Test. Geotechnical and Geological Engineering (2019).
4. Modified minimum principal stress estimation formula based on Hoek–Brown criterion and equivalent Mohr–Coulomb strength parameters. Scientific Reports (2023).