Bumps and other types of dynamic failure have been a persistent, worldwide problem in the underground coal mining industry, spanning decades. For example, in just five states in the U.S. from 1983 to 2014, there were 388 reportable bumps. Despite significant advances in mine design tools and mining practices, these events continue to occur. Many conditions have been associated with bump potential, such as the presence of stiff units in the local geology. The effect of a stiff sandstone unit on the potential for coal bumps depends on the location of the stiff unit in the stratigraphic column, the relative stiffness and strength of other structural members, and stress concentrations caused by mining. This study describes the results of a robust design to consider the impact of different lithologic risk factors impacting dynamic failure risk. Because the inherent variability of stratigraphic characteristics in sedimentary formations, such as thickness, engineering material properties, and location, is significant and the number of influential parameters in determining a parametric study is large, it is impractical to consider every simulation case by varying each parameter individually. Therefore, to save time and honor the statistical distributions of the parameters, it is necessary to develop a robust design to collect sufficient sample data and develop a statistical analysis method to draw accurate conclusions from the collected data. In this study, orthogonal arrays, which were developed using the robust design, are used to define the combination of the (a) thickness of a stiff sandstone inserted on the top and bottom of a coal seam in a massive shale mine roof and floor, (b) location of the stiff sandstone inserted on the top and bottom of the coal seam, and (c) material properties of the stiff sandstone and contacts as interfaces using the 3-dimensional numerical model, FLAC3D. After completion of the numerical experiments, statistical and multivariate analysis are performed using the calculated results from the orthogonal arrays to analyze the effect of these variables. As a consequence, the impact of each of the parameters on the potential for bumps is quantitatively classified in terms of a normalized intensity of plastic dissipated energy. By multiple regression, the intensity of plastic dissipated energy and migration of the risk from the roof to the floor via the pillars is predicted based on the value of the variables. The results demonstrate and suggest a possible capability to predict the bump potential in a given rock mass adjacent to the underground excavations and pillars. Assessing the risk of bumps is important to preventing fatalities and injuries resulting from bumps.

This paper is developed as part of an effort by the National Institute for Occupational Safety and Health (NIOSH) to identify risk factors associated with bumps in order to prevent fatalities and accidents in highly stressed, bump-prone ground conditions. The main objective of this study is to demonstrate the application of a robust design procedure by using factors affecting coal bumps based on the previous works by Lawson et al. as an example application [

A robust design (the Taguchi method [

Orthogonal arrays provide a set of well-balanced (or minimum) experiments and serve as objective functions for optimization. The aim is to reduce the number of experiments in order to minimize the resources such as equipment, materials, manpower, or time. However, doing all of the factorial experiments is suitable when conducting experiments is cheap and quick but measurements are expensive and take too long, and when the experimental facility will not be available later to conduct the verification experiment. Conducting separate experiments for studying interactions between factors is not desirable. The general steps involved in the Taguchi method are as follows: (1) define the process objective, or more specifically, a target value for a performance measure of the process, and (2) determine the design parameters affecting the process. The number of levels that the parameters should be varied at must be specified in order to: (1) create orthogonal arrays for the parameter design indicating the number of and conditions for each experiment. The selection of orthogonal arrays is based on the number of parameters and the levels of variation for each parameter, and will be expounded; (2) conduct the experiments indicated in the completed array to collect data on the effect on the performance measure; and finally (3) complete data analysis to determine the effect of the different parameters on the performance measure.

The effect of many different factors on the performance characteristic in a condensed set of experiments can be examined by using the orthogonal array experimental design. The levels at which these parameters should be varied must be determined. Determining what levels of a variable to test requires an indepth understanding of the process, including the minimum, maximum, and current value of the parameter. Orthogonal arrays created by the robust design are used to define the combination of the (a) thickness of a stiff sandstone inserted on the top and bottom of a coal seam in a massive shale mine roof and floor, (b) location of the stiff sandstone inserted on the top and bottom of the coal seam, and (c) material properties of the stiff sandstone and contacts as interfaces using FLAC3D. When there are many parameters to be studied, the main effect of each parameter and some of the reciprocal actions are estimated, while other reciprocal actions are disregarded to reduce the number of tests. The benefits of orthogonal array design are that it calculates the parameter changes from experimental or field-mapping data, facilitates the easy preparation of input data for analysis of variance, and accommodates many parameters in experiments or simulations without increasing the test scale [_{25}(5^{6}), this means that six parameters can be used in the experiment, and there are five stages in which the parameter values can be varied. In this case, 15,625(=5^{6}) experiments in total are required to obtain results that are statistically significant and representative. If the orthogonal array is used, however, only 25 experiments are needed. After completion of the numerical experiments, multivariate analysis, such as principal component analysis and multiple regression, is performed using the calculated results from the orthogonal arrays. The effect of each variable on the intensity of dissipated plastic energy and consequent retained potential energy are investigated and quantified in order to predict the bump potential in the roof, floor, and pillars. In short, this method provides an efficient, practical way to estimate the amount of energy retained in the rock mass that may be subsequently released in the form of a dynamic failure event.

The next section introduces stochastic simulation for the estimation of engineering properties of the rock masses and describes the FLAC3D modeling approach, including assumptions and conditions. Finally, methodologies appropriate to evaluate the bump potential adjacent to the underground excavations and in the coal pillar are explained and demonstrated by means of the robust design and numerical modeling technique.

For this study, the engineering material properties for the sandstone, the coal seam, and other lithologies which are modeled as an elasto-plastic model are estimated using the geological strength index (GSI). A stochastic approach is used to estimate the rock mass strength for the FLAC3D modeling. Monte Carlo simulations are used to obtain statistical distributions of engineering material properties of rock mass strength, based on the Hoek-Brown strength criterion using the available geotechnical data. The GSI, illustrated in

Harr provides some coefficients of variation for parameters common to civil engineering design [

The Monte Carlo simulations are accomplished with the @Risk^{®} software, using the methodology proposed by Hoek et al., to determine a value of the engineering material properties (i.e., modulus and strength parameters associated with variability) [_{i}

Quantitative values of the engineering material properties in terms of percentiles from 5% to 95% for the rock masses were estimated by the Monte Carlo simulations using the software @Risk. The representative values of each engineering material property for sandstone and coal seam and rock masses are summarized in

A FLAC3D model with dimensions of 476 m (W) × 368 m (H) × 10 m (L) was constructed, simulating a longwall mine gateroad similar to that considered for the study of brittle failure mechanism by Kim and Larson [_{H}_{h}_{v}

For the boundary condition, both sides of the model were fixed in the _{25}(5^{6}), was prepared to consider the (a) thickness of a stiff sandstone inserted on the top and bottom of a coal seam in a massive shale mine roof and floor, (b) location of the stiff sandstone inserted on the top and bottom of the coal seam, and (c) the elastic modulus of the sandstone and friction angle of the interfaces with five levels, respectively. This resulted in an orthogonal array that contained 25 numerical experiments, as shown in

Kim and Larson investigated and reported that the floor-heave and no floor-heave phenomenon associated with brittle failure in bump-prone ground was demonstrated by comparing the depth of floor yield in the vicinity of the gate roads, vertical displacement measured of the floor, and the ratio of elastic-to-dissipated plastic energy [

In this study, it is assumed that, if the magnitude of plastic dissipated energy working to fail the rock mass in the vicinity of underground excavation is greater than that of the baseline case (Case 1 in which all the properties are considered to be the default values), the risk of a bump in the rock mass would be relatively increased. In FLAC3D, elastic strain energy and dissipated plastic energy can be tracked for zones containing a mechanical model. FLAC3D uses an incremental solution procedure—i.e., the equations of motion at the grid points and the stress-strain calculations at the zones are solved at every time step. In the stress-strain equations, the incremental change in energy components is determined and accumulated as the system attempts to reach equilibrium. Energy is dissipated through plastic work as the zones undergo irreversible deformation based on the input material properties. Using FLAC3D, the strain in any zone can be divided into elastic and plastic parts [

The geometries of the gate roads and pillars used in this study are simplified so that the gate road entries are 6 m wide and 4 m high, leaving pillars that are 22 m (narrow pillar) and 52 m wide (wide pillar). In the discussion of

Compared to the results of case 1, the results for cases 9, 8, and 5 show that 7%, 8%, and 21% more plastic energy was released in the region of the gate roads with narrow pillars as shown in

In order to evaluate the potential for bumps associated with plastic dissipated energy at the different locations, all of the results of the energy calculations from each case are normalized as a ratio to the results of case 1.

Lawson et al. report that both the thickness of a discrete stiff member and its distance to the seam must be considered to anticipate areas of elevated rupture-induced hazards [

To learn more about the relationship between the given parameters and the bump potential, multiple regression is performed to predict the relative change of the risk based on the orthogonal array. By using

The individual ratio of plastic dissipated energy in terms of the intensity of energy release on the different locations can be characterized and quantified by the multiple regression. From the analysis, the shear strength of the adjacent contacts in terms of internal friction angle is, in general, the most critical parameter contributing to dissipation of the plastic energy no matter where it is adjacent to the gate roads. Also, the Young’s modulus of the stiff sandstone significantly contributes to the energy release in the narrow pillar and floor and in the wide roof and floor. In addition, the intensity of plastic dissipated energy in the wide and narrow roof is substantially controlled by the distance of the top stiff sandstone. As a consequence, the risk of bumps associated with plastic dissipated energy in the pillars is primarily influenced by the strength characteristics of the adjacent contacts. The risk in the roof is mainly dictated by the stiffness of discrete stiff member and its distance from the coal seam. Both the strength characteristics of the adjacent contacts and the stiffness of discrete stiff member principally contribute to the risk in the floor, as shown by the following equations:
_{p}_{sst}_{ssb}_{if}_{ss}_{sst}_{ssb}

In this study, the effect of a stiff sandstone unit on the potential for dynamic failure is shown to depend on the location of the stiff unit in the stratigraphic column and the relative stiffness and strength of other structural members. These effects are investigated using a combination of statistical and numerical techniques. The results suggest that the robust experimental design is a practical and effective method with which to consider the impact of different lithologic risk factors impacting dynamic failure potential.

In summary, the following are the results of the numerical investigation using an orthogonal array and the FLAC3D software, and based on the assumptions and methodologies described herein:

A robust design (i.e., the Taguchi method) is a very useful tool to consider a large number of possible statistical scenarios for a given mine site. As the inherent variability of the independent parameters is significant and the number of influential parameters in determining a parametric study is large, this represents a significant advantage over individually varying each parameter.

The results of the FLAC3D model show that a change in plastic dissipated energy is significantly impacted by the stratigraphic and engineering characteristics of the rock mass.

According to this research, the risk of bumps in narrow pillars is relatively high and is independent of the thickness or location of stiff sandstone and other engineering parameters.

Compared to the baseline case conditions, the bump potential in the roof of gate roads with narrow pillars is more sensitive to the variability of the parameters. The risk is dependent on the thickness, location of the stiff sandstone, and other parameters.

Using the regression formulas, a change in the risk at the different locations can be predicted as a ratio of intensity of plastic dissipated energy.

The magnitude of plastic dissipated energy in the vicinity of mine openings appears to be a reasonable indicator of the higher potential for dynamic failure.

For future work, continuous investigations should be conducted to systematically quantify the risk of bump associated not only with the factor of safety in deep coal mines but also with a surveillance system for mining-induced seismicity.

This study illustrates a method with which to estimate risk for dynamic failure events as a function of changing conditions. The results of this study indicate that friction angle of the sliding surfaces greatly affects elevated risk. Periodic testing of those surfaces and observations of physical indicators of friction angle might be used to map areas or regions with elevated risk for bumps. The method can be applied to other geometries and conditions, such as different stratigraphy and ranges of material properties. A better understanding of risk is a very critical step in improving miner safety with respect to bump potential in coal mines.

The findings and conclusions in this report are those of the authors and do not necessarily represent the views of the National Institute for Occupational Safety and Health. Mention of any company or product does not constitute endorsement by NIOSH.

Geological strength index (GSI) chart for heterogeneous rock masses [after 10].

Cumulative probability distributions for intact coal UCS (a) and GSI (b).

Cumulative probability distributions for cohesion (a) and internal friction angle (b) for the rock mass of coal estimated by Monte Carlo simulation.

Examples of FLAC3D model as per experimental number generated by orthogonal array.

Maximum plastic energy dissipated in wide roof (Case 7, 28% increased).

Maximum plastic energy dissipated in wide pillar (Case 15, 18% increased).

Maximum plastic energy dissipated in wide floor (Case 21, 12% increased).

Maximum plastic energy dissipated in narrow roof (Case 9, 7% increased).

Maximum plastic energy dissipated in narrow pillar (Case 8, 8% increased).

Maximum plastic energy dissipated in narrow floor (Case 5, 21% increased).

Estimated material properties for the rock masses.

Input parameter | Rock mass type | Value |
---|---|---|

Unit weight | Stiff sandstone | 0.027 MN/m^{3} |

Coal seam | 0.022 MN/m^{3} | |

Rock masses in top and bottom | 0.027 MN/m^{3} | |

Young’s modulus | Stiff sandstone | 13.5 GPa |

Coal seam | 0.8 GPa | |

Rock masses in top and bottom | 11.7 GPa | |

Poisson’s ratio | Stiff sandstone | 0.25 |

Coal seam | 0.30 | |

Rock masses in top and bottom | 0.25 | |

Cohesion | Stiff sandstone | 2.4 MPa |

Coal seam | 1.0 MPa | |

Rock masses in top and bottom | 1.1–1.5 MPa | |

Internal friction angle | Stiff sandstone | 54° |

Coal seam | 26° | |

Rock masses in top and bottom | 41° | |

Tensile strength | Stiff sandstone | 0.20 MPa |

Coal seam | 0.01 MPa | |

Rock masses in top and bottom | 0.10 MPa |

Orthogonal array, L_{25}(5^{6}) for FLAC3D modeling.

Experimental case No. | Thickness of stiff sandstone in top (m) | Thickness of stiff sandstone in bottom (m) | Friction angle of interfaces (°) | Modulus of stiff sandstone (GPa) | Distance of stiff sandstone from the roof of seam (m) | Distance of stiff sandstone from the floor of seam (m) |
---|---|---|---|---|---|---|

1 | 2 | 2 | 40 | 13.5 | 0 | 0 |

2 | 2 | 4 | 45 | 21.9 | 4 | 4 |

3 | 2 | 8 | 50 | 24.9 | 8 | 8 |

4 | 2 | 16 | 55 | 33.5 | 16 | 16 |

5 | 2 | 32 | 60 | 41.9 | 32 | 32 |

6 | 4 | 2 | 45 | 24.9 | 16 | 32 |

7 | 4 | 4 | 50 | 33.5 | 32 | 0 |

8 | 4 | 8 | 55 | 41.9 | 0 | 4 |

9 | 4 | 16 | 60 | 13.5 | 4 | 8 |

10 | 4 | 32 | 40 | 21.9 | 8 | 16 |

11 | 8 | 2 | 50 | 41.9 | 4 | 16 |

12 | 8 | 4 | 55 | 13.5 | 8 | 32 |

13 | 8 | 8 | 60 | 21.9 | 16 | 0 |

14 | 8 | 16 | 40 | 24.9 | 32 | 4 |

15 | 8 | 32 | 45 | 33.5 | 0 | 8 |

16 | 16 | 2 | 55 | 21.9 | 32 | 8 |

17 | 16 | 4 | 60 | 24.9 | 0 | 16 |

18 | 16 | 8 | 40 | 33.5 | 4 | 32 |

19 | 16 | 16 | 45 | 41.9 | 8 | 0 |

20 | 16 | 32 | 50 | 13.5 | 16 | 4 |

21 | 32 | 2 | 60 | 33.5 | 8 | 4 |

22 | 32 | 4 | 40 | 41.9 | 16 | 8 |

23 | 32 | 8 | 45 | 13.5 | 32 | 16 |

24 | 32 | 16 | 50 | 21.9 | 0 | 32 |

25 | 32 | 32 | 55 | 21.9 | 4 | 0 |

Normalized floor displacement and plastic dissipated energy measured in different locations.

Case No. | Dissipated energy (wide pillar) | Dissipated energy (narrow pillar) | Dissipated energy (wide roof) | Dissipated energy (narrow roof) | Dissipated energy (wide floor) | Dissipated energy (narrow floor) |
---|---|---|---|---|---|---|

1 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |

2 | 0.866 | 1.020 | 1.218 | 1.290 | 1.108 | 1.105 |

3 | 0.789 | 1.057 | 1.246 | 1.032 | 1.007 | 1.170 |

4 | 0.821 | 0.874 | 1.122 | 1.038 | 1.035 | 1.192 |

5 | 0.696 | 1.031 | 1.150 | 1.043 | 1.051 | 1.208 |

6 | 0.858 | 1.009 | 1.113 | 1.081 | 1.042 | 1.169 |

7 | 0.792 | 0.935 | 1.275 | 1.037 | 0.650 | 0.439 |

8 | 1.129 | 1.084 | 0.962 | 0.334 | 1.117 | 1.122 |

9 | 0.894 | 1.066 | 1.219 | 1.354 | 1.040 | 1.162 |

10 | 0.777 | 0.827 | 1.126 | 1.033 | 1.026 | 1.177 |

11 | 0.777 | 0.956 | 1.138 | 1.107 | 1.036 | 1.202 |

12 | 1.081 | 0.612 | 0.445 | 0.109 | 0.361 | 0.296 |

13 | 0.797 | 0.927 | 1.146 | 1.023 | 0.579 | 0.427 |

14 | 0.842 | 0.806 | 1.110 | 1.043 | 1.053 | 1.168 |

15 | 1.184 | 0.922 | 0.034 | 0.054 | 0.991 | 1.174 |

16 | 0.793 | 0.909 | 1.155 | 1.045 | 1.026 | 1.159 |

17 | 0.958 | 0.938 | 0.038 | 0.038 | 1.014 | 1.201 |

18 | 0.769 | 0.814 | 1.111 | 1.083 | 1.040 | 1.176 |

19 | 0.696 | 0.729 | 1.228 | 1.018 | 0.474 | 0.279 |

20 | 1.096 | 0.952 | 1.096 | 1.059 | 1.045 | 1.197 |

21 | 0.995 | 0.785 | 1.208 | 1.015 | 1.122 | 1.116 |

22 | 0.878 | 0.769 | 1.132 | 1.027 | 1.009 | 1.152 |

23 | 1.000 | 0.988 | 1.109 | 1.046 | 1.059 | 1.206 |

24 | 1.051 | 0.822 | 0.045 | 0.042 | 1.011 | 1.190 |

25 | 0.677 | 0.618 | 1.119 | 0.971 | 0.459 | 0.324 |

Calculated coefficient of variation.

Dissipated energy (wide pillar) | Dissipated energy (narrow pillar) | Dissipated energy (wide roof) | Dissipated energy (narrow roof) | Dissipated energy (wide floor) | Dissipated energy (narrow floor) | |
---|---|---|---|---|---|---|

Coefficient of variation | 0.162 | 0.145 | 0.395 | 0.457 | 0.242 | 0.334 |

Correlation matrix by principal component analysis.

Dissipated energy (wide pillar) | Dissipated energy (narrow pillar) | Dissipated energy (wide roof) | Dissipated energy (narrow roof) | Dissipated energy (wide floor) | Dissipated energy (narrow floor) | |
---|---|---|---|---|---|---|

Dissipated energy (wide pillar) | 1.000 | |||||

Dissipated energy (narrow pillar) | 0.143 | 1.000 | ||||

Dissipated energy (wide roof) | −0.607 | 0.159 | 1.000 | |||

Dissipated energy (narrow roof) | −0.630 | 0.207 | 0.928 | 1.000 | ||

Dissipated energy (wide floor) | 0.243 | 0.616 | 0.035 | 0.151 | 1.000 | |

Dissipated energy (narrow floor) | 0.252 | 0.547 | −0.086 | 0.058 | 0.970 | 1 |