Recently, a numerical model based approach for support analysis has been developed at the National Institute for Occupational Safety and Health (NIOSH). In this approach calibrated models are used to determine a stability factor for a supported entry. The stability factor is determined using the strength reduction method (SRM). The success of the SRM depends on the ability to accurately identify a collapsing or stable roof condition in the models. A collapse condition can be identified by considering the mechanical ratio and the velocity/acceleration of the roof grid points. It is found that during collapse, grid points of the zones within the collapsing roof move at least 50 to 100 times faster than in the remainder of the model. However, the default local damping scheme in FLAC3D attempts to arrest the collapsing roof, which may result in an incorrect assessment of roof stability. In order to solve this problem, combined damping is used. In addition, unloading of the model to simulate the excavation is controlled strictly with a relaxation algorithm to provide efficient energy dissipation.


The strength reduction modeling technique has a long history in numerical model analysis in rock slope stability engineering (Lorig and Varona, 2000). This modeling technique was adapted to underground coal mine entry analysis by Esterhuizen (2015) to address the need for a method to compare the effectiveness of different support systems when designing ground support in coal mines. The SRM calculates a stability factor of the entry roof by gradually reducing the rock strength until failure is indicated. The stability factor is expressed as the inverse of the strength reduction factor. For example, if collapse occurs when the strength is reduced by a factor of 0.5, the entry stability factor will be 2.0. The stability factor can be used to assist in developing a final support design by comparing the effectiveness of various support systems and the stability of excavations under various geological and loading conditions, as demonstrated by Tulu et al. (2016).

The success of the SRM depends on the ability to accurately identify a collapsing or stable roof condition in the models. In this paper, a procedure to reliably identify the collapsing roof in a FLAC3D model is presented.

The Modelling Approach

The SRM stability factors are determined using the FLAC3D finite difference code (Itasca, 2014). A systematic procedure is used to estimate model inputs based on the Coal Mine Roof Rating (Esterhuizen et al., 2013a). Model calibration and validation studies were conducted to ensure that the developed modeling technique provides realistic estimates of the stability of mine entries. As part of the validation studies, model calculated stability factors were compared to the results of the empirically based Analysis of Roof Bolt Systems (ARBS) method (Mark et al., 2001). Outcomes of the validation studies are presented by Esterhuizen et al. (2013b, 2013c).

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