توسعه نمودار ثبات ستون زغال سنگ با استفاده از رگرسیون لجستیک

Logistic regression was utilised to calculate the probability that a particular pillar of a given geometry (width to height ratio) and a known stress condition (strength to stress ratio) will be stable. The stable-failure boundary was also determined. The logistic regression was also used to calculate and draw isoprobability contours. These contours represent the probability of stability of coal pillars based on the probability function for each stability class and are a valuable design tool in quantifying the instability probability of coal pillars.

Pillars in underground coal mines are mainly designed to ensure the protection of roadways and entries. Pillars stability is consequently the most important factor that must be guaranteed through the entire life of mine that can be years or even decades long. Pillar stability can be analysed by a number of methods that are generally based on the ratio between the pillar strength and pillar load that is expressed in Factor of Safety (FoS). The strength characteristics of coal pillars has been studied by many researchers and the subject has been well discussed in the literature, for examples [1], [2], [3], [4] and [5]. A number of fairly intensive new developments relating to coal pillar strength estimation methods have also been carried out. Two coal pillar strength approaches based on a tentative empirical failure criterion for coal seams were proposed [6]. The first, progressive failure type approach, gave incorrect estimates of pillar strength for low width-height ratios while the second pillar strength approach performed satisfactorily for both slender and fiat pillars. The performance of these new equations has been compared with some of the more popular strength formulas and tested against 16 failed and 27 stable pillar case studies. A new coal pillar strength equation was developed and tested, along with existing equations, against 23 failed and 20 stable case studies [7]. The results revealed that in situ strength is more affected by depth of cover than indicated by laboratory tests, and a new safety factor based on depth and width/height ratio was proposed. Alternative methods of coal pillar strength estimation using numerical modelling with strain softening constitutive behaviour of coal were also provided. The numerical models implemented in the researches were three dimensional finite difference [8] and finite element [9] methods. They might give decent results and better than the previous pillar strength estimation method. Furthermore, it was found that the FoS calculated using deterministic approach had some intrinsic limitations in handling uncertainties in material properties, non-regular geometries and different mining operations [10]. A probabilistic expression for FoS was then suggested, which provided a confidence interval to express the reliability of coal pillar stability. In this paper, a statistical approach based on real stable and failed cases of coal pillars was suggested. As pillar stability was only defined as stable or failed, logistic regression was utilised because the method is suitable for categorical dependent variables.

The logistic regression model for predicting the probability of stability of a coal pillar for given geometry (width to height ratio) and stress condition (strength to stress ratio) has been developed. The model prediction is close to the actual stability data, where the model predicts all stable cases correctly and 13 out of 14 failure cases. A coal pillar stability chart has been constructed. A stable-failure boundary line, which will have the same proportion of mismatched points either side of the line, has also been defined and plotted on the stability chart. Isoprobability contours for stable pillars have been developed, which allow the probabilities of risk associated with pillar stability to be determined and presented directly on the stability graph. The contours are a valuable measure of the reliability of the stability zone boundary and allow the statistical meaning of the stability boundaries to be quantified in terms of probable stability outcomes. The use of the contours must be in conjunction with different conditions experienced at mine sites, which define the risk level of acceptance and consequently the choice of isoprobability contour.