Stability Graph Method

The Stability Graph Method was developed by Mathews et al. (1980) [1] as a modification of the Q rock mass classification system by Barton (1974) [2]. It provides an empirical approach for assessing stope wall stability in underground mining.

The method relates a Stability Number \(N'\) to the Hydraulic Radius of a stope wall through stability charts. The stability number is defined as:

\[N' = Q' \cdot A \cdot B \cdot C\]

where:

• \(A\) (Factor A) is a stress factor

• \(B\) (Factor B) is a rock defect orientation factor

• \(C\) (Factor C) is a design surface orientation factor

• \(Q'\) is a modified NGI rock mass parameter:

\[Q' = \frac{RQD}{J_{n}} \cdot \frac{J_{r}}{J_{a}} \cdot J_{w}\]

Here, \(RQD\), \(J_n\), \(J_r\), \(J_a\), and \(J_w\) are terms from Barton’s classification, with the stress reduction factor (SRF) omitted to better represent conditions in open stopes.

Factor A (Stress Factor) Accounts for the ratio of intact rock strength to induced stress at the stope surface. - Intact strength is typically measured by the uniaxial compressive strength (UCS). - Induced stress corresponds to the maximum tangential stress acting parallel to the stope wall. This factor is estimated either through numerical modelling or from empirical charts (Mathews et al., 1981).

Application The method distinguishes between three primary stability domains: 1. Stress-controlled failure 2. Structurally controlled failure 3. Combined stress and structural failure

These zones are separated by transition areas and are defined using case histories from mining operations.

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References

[1]

K. E. Mathews, E. Hoek, D. C. Wyllie, and S. B. V. Stewart. Prediction of stable excavation spans for mining at depths below 1,000 metres in hard rock. Report, Golder Associates, Ottawa, Ontario, Canada, 1980. Report to Canada Centre for Mining and Energy Technology (CANMET), Department of Energy and Resources.

[2]

N. Barton, R. Lien, and J. Lunde. Engineering classification of rock masses for the design of tunnel support. Rock Mechanics, 6(4):189–236, 1974. doi:10.1007/BF01239496.