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The Consolidated Mathews Stability Graph for Open Stope Design

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Abstract

The stability graph method for open stope design is one of the most widely used approaches for predicting the stability of stopes in underground metalliferous mines. The primary purpose of this work is to propose a new stability chart, which includes all relevant case histories, and to exclude parameters with uncertainties for determining stability number. The modified stability number was used to achieve this goal, and the Extended Mathews database was recalculated and compared with the new stability graph. In this study, a new refined Consolidated stability graph was developed by excluding the entry mining methods data from the Extended graph data, and only the non-entry methods data was used. The applicability of the proposed Consolidated stability chart was demonstrated by an open stope example. The probabilities of stability for each stope surface were determined using the logistic regression model and the developed Consolidated stability chart. Comparing the stability analysis results with that of other published works of the same example shows that the determined Consolidated chart, in which the entry-method data is excluded, produces a more conservative and safer design. In conclusion, the size and quality of the dataset dictate the reliability of this approach.

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Abbreviations

A:

Rock stress factor

B:

Joint orientation adjustment factor

C:

Gravity adjustment factor

CDF:

Cumulative distribution function

ELOS:

Equivalent linear overbreak/slough

F:

Fault factor

HR:

Hydraulic radius (in meters)

Ja :

Joint alteration number

Jn :

Joint set number

Jr :

Joint roughness number

Jw :

Joint water reduction factor

JKMRC:

Julius Kruttschnitt Mineral Research Centre

K:

Stress ratio (σH:σV)

N:

Mathews stability number

N′:

Modified stability number

NGI:

Norwegian Geotechnical Institute

P:

Predicted logit value

Q:

Tunnelling Quality Index, referred to as the Q value

Q′:

Modified Q value

RF:

Radius factor

RMR:

Rock mass rating (Bieniawski)

S:

Shape factor

SRF:

Stress reduction factor

X1 … Xk :

Dependent X variables in the logit model

Z:

Predicted log odds value

a:

Regression parameter without dependent X variable. A constant in the logit regression equation

f(z):

Predicted logit probability value

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Authors and Affiliations

  1. School of Mining and Geosciences, Nazarbayev University, 53 Kabanbay Batyr Ave., Nur-Sultan, 010000, Kazakhstan

    Ali Mortazavi & Bakytzhan Osserbay

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  1. Ali Mortazavi
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  2. Bakytzhan Osserbay
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Correspondence to Ali Mortazavi.

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The authors declare that they have no conflict of interest, and this study was not funded by any organization.

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Mortazavi, A., Osserbay, B. The Consolidated Mathews Stability Graph for Open Stope Design. Geotech Geol Eng 40, 2409–2424 (2022). https://doi.org/10.1007/s10706-021-02034-0

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  • DOI: https://doi.org/10.1007/s10706-021-02034-0

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