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The prediction of pillar stability (PS) in hard rock mines is a crucial task for which many techniques and methods have been proposed in the literature including machine learning classification. In order to make the best use of the large variety of statistical and machine learning classification methods available, it is necessary to assess their performance before selecting a classifier and suggesting improvement. The objective of this paper is to compare different classification techniques for PS detection in hard rock mines. The data of this study consist of six features, namely pillar width, pillar height, the ratio of pillar width to its height, uniaxial compressive strength of the rock, pillar strength, and pillar stress. A total of 251 pillar cases between 1972 and 2011 are analyzed. Six supervised learning algorithms, including linear discriminant analysis, multinomial logistic regression, multilayer perceptron neural networks, support vector machine (SVM), random forest (RF), and gradient boosting machine, are evaluated for their ability to learn for PS based on different input parameter combinations. In this study, the available data set is randomly split into two parts: training set (70 %) and test set (30 %). A repeated tenfold cross-validation procedure (ten repeats) is applied to determine the optimal parameter values during modeling, and an external testing set is employed to validate the prediction performance of models. Two performance measures, namely classification accuracy rate and Cohen’s kappa, are employed. The analysis of the accuracy together with kappa for the PS data set demonstrates that SVM and RF achieve comparable median classification accuracy rate and Cohen’s kappa values. All models are fitted by “R” programs with the libraries and functions described in this study.

The crown pillar in the stope structure belongs to the category of thick plate, and its thickness determines the stability of the engineering structure. The key to determining the safe thickness of the crown pillar lies in solving its deflection function. Previous researchers often used the Galerkin method and other methods except the Ritz method to solve the deflection function of the crown pillar under simple boundary conditions. However, these methods are difficult to solve for the deflection function of the crown pillar under complex boundary conditions. Therefore, this paper builds upon the Reissner plate theory and introduces the Ritz method while considering the influence of strain components εz, γyz, and γzx on the flexural deformation of the crown pillar. Thus, the Reissner–Ritz method for solving the deflection function of the crown pillar in the stope is developed. Taking the failure of the crown pillar in stope 27 in the + 280 m section of the Daxin Manganese Mine as an example, firstly, the maximum tensile stress of the crown pillar is compared with its tensile strength to determine the safe thickness of the crown pillar in stope 27. The correctness of the chosen safe thickness for the crown pillar in stope 27 is verified using the Reissner–Ritz method. Then, FLAC3D is used to model and analyze the 8 m thick crown pillar in stope 27, and the accuracy of the Reissner–Ritz method in determining the safe thickness of the crown pillar is verified through finite element analysis. Finally, a comparison is made between the Reissner–Ritz method and the Galerkin method in solving the deflection function of the crown pillar under the uniformly distributed load, considering both simple and complex boundary conditions. The research results show that the Reissner–Ritz method has significant advantages over the Galerkin method in solving the deflection function of the crown pillar under the uniformly distributed load, even under complex boundary conditions. The findings are of great significance for solving the deflection function of thick plates under both simple and complex boundary conditions under the uniformly distributed load and determining the safe thickness of thick plates.HighlightsBased on the Reissner thick plate theory, the Ritz method is introduced, taking into account the influence of strain components εz, γyz, and γzx on the bending deformation of the crown pillar, forming the Reissner–Ritz method for solving the deflection function of the crown pillar in the stope.The range of safe thickness values for the crown pillar is determined based on the thickness-span ratio and safety factor, incorporating engineering experience to finalize the safe thickness of the crown pillar in the stope.The accuracy of the Reissner–Ritz method in determining the safe thickness of the four-sided fixed support crown pillar under the uniformly distributed load is verified through finite element analysis.Comparing and analyzing the calculation results of the Reissner Ritz method with the Galerkin method.

This translation of Khutabat covers themes such as Iman, Islam, the prayer, fasting, almsgiving, pilgramage and Jihad.

In order to reveal the load transfer mechanism during cascading pillar failure, compressive tests on treble-pillar specimens were conducted under soft and stiff loading conditions, where the stiffness of the test machine was adjusted with a disc spring group. Experimental results showed that the load transfer behavior of treble-pillar specimen could only be reproduced under soft loading condition when the rapid elastic rebound is achievable with disc spring group. The load transfer behavior of treble-pillar specimen is governed by energy storage characteristics of test machine and the mechanical properties of three rock specimens. In this respect, the failure behavior of treble-pillar specimen under soft loading condition was summarized into the following three failure modes: successive failure mode, compound failure mode and domino failure mode. Additionally, a theoretical model was proposed to further explain the physical mechanism of load transfer behavior, where the theoretical results of load transfer and elastic rebound of disc spring group were in good agreement with the experimental results. Finally, it was concluded that the elastic deformation of near-field surrounding rockmass (or the soft loading condition) was the necessary condition for load transfer of multiple pillars; and the rapid elastic rebound of near-field surrounding rockmass was the physical essence of load transfer behavior. This study may contribute to understanding the load transfer mechanism among pillars and to optimizing the design of room-and-pillar stopes during underground mining.HighlightsThe soft loading condition of test machine is realized by adjusting the stiffness of disc spring group.The experiments on treble-pillar specimens are conducted to reveal the load transfer mechanism during cascading pillar failure.Three failure modes of treble-pillar specimen are successive failure, compound failure and domino failure.

This paper describes the results of a back analysis of pillar failures at Troy Mine, Montana, and the use of this experience to make forward predictions on pillar stability in the nearby Montanore deposit which lies in a similar geomechanical setting. At Troy Mine, a progression of pillar failures in areas within the Middle Quartzite of the Revett formation led to the observed surface subsidence. The Troy Mine experience was used to understand the level of stresses and failure mechanism leading to the collapse of some pillars in the North Orebody to estimate pillar strength in quartzite beds within Troy’s mountainous terrain. The model elucidated that the dipping orebody geometry in relation to topography led to shear stresses in pillars at Troy Mine. Shear stresses resulted in significant loss of confinement in pillar cores (many theoretically in tension), even at width-to-height ratios that would be deemed stable under zero shear stress (flat seam under flat topography). A calibrated model was achieved, which allowed us to evaluate the impact that different pillar geometric characteristics (such as width, length, height, and shape) have on pillar performance under shear conditions for different depths and extraction ratios. Design charts were then generated to provide guidance on pillar geometry based on expected demand. Mine-wide models were developed to predict the level of vertical stress and horizontal shear stress for pillars in the different ore-bearing beds at Montanore. A sensitivity study was performed for various conditions, including extraction ratio, spatial location under the mountainous terrain, and local orebody geometry with the aim of performing a mine-wide evaluation of the factor of safety against shear. The results of the analyses performed in the present work show that the use of design methods that do not take the effect of shear stresses into account may result in under-designed pillars, while a false impression of rock mass strength could be derived from back analysis.

Pillars are often used to support the roof in underground mining. The multi-pillar and roof system is regarded as a multi-pillar and rock beam model. For a system composed of n pillars, the interaction force between the roof and pillars is obtained by a semi-analytical and semi-numerical method. Pillar failure may be progressive or sudden, depending on the equilibrium stability of the system in the post-peak stage. The initial conditions of multi-pillar failure and influence of one pillar progressive failure or unstable failure on adjacent pillars are analyzed based on the instability theory. If one pillar fails gradually, the stress transfer between pillars is also progressive. Once the first pillar fails suddenly, part of the stress is transferred to adjacent pillars, which may lead to further unstable failure of adjacent pillars and cascading failure of multiple pillars. The factors of pillar unstable failure mainly include geometric and mechanical parameters of the system. The mechanical parameters cannot be changed; however, entry (or stope in metal mine) geometrical parameters can be adjusted to reduce the possibility of unstable failure. The variations of pillar stability with entry widths are analyzed according to the factor of safety (FoS) and roof-to-pillar stiffness ratio rk. If the pillars are arranged in a properly concentrated manner, FoS increases, rk decreases and the tendency of pillar unstable failure increases. Conversely, if the pillars are scattered close to the barrier pillars, the possibility of pillar unstable failure is reduced but the overall strength of all pillars is also reduced. Therefore, for a multi-pillar and roof system, the entry widths should be properly adjusted from an overall system perspective to ensure that both FoS and rk values are sufficiently large to minimize the possibility of pillar unstable failure.

The collapse of abandoned room-and-pillar mines is often violent and unpredictable. Safety concerns often resulted in mine closures with no post-mining stability evaluations. As a result, large amounts of land resources over room-and-pillar mines are wasted. This paper attempts to establish an understanding of the long-term stability issues of goafs (abandoned mines). Considering progressive pillar failures and the effect of single pillar failure on surrounding pillars, this paper proposes a pillar peeling model to evaluate the long-term stability of coal mines and the associated criteria for evaluating the long-term stability of room-and-pillar mines. The validity of the peeling model was verified by numerical simulation, and field data from 500 pillar cases from China, South Africa, and India. It is found that the damage level of pillar peeling is affected by the peel angle and pillar height and is controlled by the pillar width–height ratio.