Critical Span Design Approach is a purely empirical technique that allows the estimation of the maximum unsupported span (or panel width) for an underground stope or crown pillar depending on the quality and geometry of the rock-mass through its comparison with previous case histories. Critical span analysis involves comparing the span of the underground stope and rock-mass classification, (such as RMR or Q), possibly along with some geometry/stress modifier, against span-stability plots or scaled-span equations to make an assessment whether a certain span will prove to be stable enough without any permanent support.
The concept and the basic principles of application (such as historical span-stability plots or critical span plots and newer weak-rock span curves) were formulated by analyzing numerous examples of the successful operation of stopes and crown pillars of different widths and varying rock mass indices (which resulted in a failure or success of the stope) and developing boundaries for stability and instability that can be used by mining engineers when estimating the stability of their stopes or crown pillars.
The use of the technique in evaluating stope stability involves a step-by-step process whereby first one should characterize the rock mass (determine the RMR76 or Q value, control joint sets, groundwater conditions, and mechanical anisotropy) and geometric dimensions (span, height, dip, and crown thickness). Next, one must choose the relevant empirical stability relationship or graph based on the geometry of the orebody (e.g., steep versus shallow scaled-span relationships), and if applicable, apply the appropriate modifiers for stress direction, groundwater, or discontinuity persistence. Finally, one determines the scaled span value (or plots RMR versus span) against the empirical stability curve.
Potential problems associated with critical-span approaches include their empirical basis, the importance of rock mass characteristics that govern rather than represent the average state, and the fact that their applicability is limited to situations falling within the range of case history studies (extremely weak or strong rock masses, complicated jointing conditions, and high stress levels/deep mining). Therefore, it is customary to recommend expert opinion, local information, and other techniques such as structural mapping and numerical or discrete element analysis for verifying the empirical results.
Extensions and contemporary practice typically integrate span design equations with concepts of reliability or probability, as well as numerical simulations: the reliability approach for span design takes into account the uncertainties regarding rock mechanical properties as well as in situ conditions, providing a probability of failure rather than a simple choice between stability and instability, and numerical analysis models (either continuum or discontinuum models) simulate the jointed rock behavior in situations beyond the empirical database. Such an approach uses the empirical curves as a rapid screening tool yet applies a rigorous analysis for design purposes.
For actual application in mine design, one needs to consider the critical span result as a design guideline: do a comprehensive rock mass characterization of the rock mass paying attention to its controlling factors, apply the proper scaled span/critical span equation according to geometrical and rock properties considerations, and verify the span design through numerical/structural analysis when risks are involved, and monitor the process, thus validating the empirical prediction and making adjustments if required. This methodology (screening, rigorous analysis, and monitoring) is the recommended one in contemporary stope design papers.
