Mining Engineering Department West Virginia University

Transcription

1 Mining Engineering Department West Virginia University 1600 Calibrating the LaModel Program for Deep Cover Pillar Retreat Coal Mining Final Report September 28, A. Pillar Safety Factors Keith A. Heasley WVU Mining Engineering 1600

2 Final Report (Draft 3/31/10) Calibrating the LaModel Program for Deep Cover Pillar Retreat Coal Mining By Dr. Keith A. Heasley, Ph.D., P.E. March 31, 2010 i

3 Executive Summary The research presented in this report has produced a number of significant results that will undoubtedly raise the quality of mine design in the United States in the future, particularly for deep cover, pillar retreat coal mines. Initially, a database of 47 deep cover pillar retreat case studies was developed. With this database, a standardized LaModel calculation for deep cover pillar retreat mines was developed, verified and calibrated. As a result of this process it was ultimately determined that if the LaModel user designs a deep cover pillar retreat section with the calibration method presented in this report and keeps the safety factor above 1.40, then they should have a 79% chance of success, or if the user keeps the safety factor above 1.50 they should have a 100% chance of success (based on the given database analysis). This recommended calibration method and associated safety factor represents a major milestone in the development of LaModel, since this is the first time that such recommendations have been made for use with LaModel. The deep cover database was also used to conduct a detailed comparison between ARMPS and LaModel. The results of this comparison show that the standardized LaModel safety factor averages 37% higher than the ARMPS stability factor. This difference seems to be primarily a result of LaModel s natural shedding of load from the active mining zone (AMZ) and active gob onto the adjacent barrier pillars and adjacent panel gobs. The load analysis indicates that for deeper and narrower panels, the LaModel loading on the AMZ further decreases in relation to the calculated ARMPS loading. In the last part of this report, the protocols for the standardized LaModel calibration are rigorously developed. Essentially, for the standard calibration of the critical input parameters: 1) The lamination thickness is calibrated to match the expected abutment extent; 2) The final gob modulus is calibrated to an abutment loading that is consistent with a 21 abutment load angle; and 3) The coal material is calibrated to provide a 900 psi, Mark-Bieniawski pillar strength. These calibration protocols have also been implemented into individual Wizards in LamPre3.0 in order to assist the LaModel user in quickly, easily and accurately producing a standard calibrated model. ii

4 Table of Contents Executive Summary... ii List of Figures...v 1. Introduction Background Statement of the Problem Statement of Work Modeling of the Deep-Cover Case Histories Development of Best practices for Using LaModel Implementation of Efficiency and Accuracy Enhancements to LaModel Acknowledgements Deep Cover Case History Database Database Overview ARMPS Analysis LaModel Analysis Idealized Analysis Detailed LaModel Analysis Comparison of ARMPS and LaModel Stability factor Comparison Detailed Load Analysis Best Practices for Calibrating LaModel Background The Critical Input Parameters Calibrating Rock mass Stiffness Rock Mass Modulus Rock Mass Lamination Thickness Yield Zone Distance Implementation in LamPre Calibrating Gob Stiffness Critical Panel Width Laminated Model Gob Stress Abutment Angle Gob Stress Adjusted Abutment Angle Stress Implementation in LamPre Calibrating Coal Strength...32 Page iii

5 3.5.1 Mark-Bieniawski Formula Back Analysis Implementation in LamPre Summary and Conclusions References APPENDIX A Deep Cover Pillar Retreat Database iv

6 List of Figures 2.1 ARMPS stability factors for the case studies LaModel safety factors for the idealized case studies LaModel safety factors for the detailed case studies Comparison between ARMPS and LaModel stability factors Influence of the mining height on the safety factor ratio Influence of the depth on the safety factor ratio Influence of the panel width on the safety factor ratio Influence of the panel width-to-depth ratio on the safety factor ratio Schematic of the loading zones in the load analysis Influence of the panel depth on the difference in AMZ loading A comparison of abutment stresses from field measurements and LaModel A comparison of laminated abutment load to the Mark-Bieniawski coal load New Lamination Thickness Wizard in LamPre The six material models in LaModel Conceptualization of the abutment angle Suggested stability factors for the ARMPS deep-cover database New wizard for calibrating the final modulus of the gob Schematic of pillar loading and material code representation New wizard for defining Mark-Bieniawski coal properties...35 Page v

7 1. Introduction 1.1 Background On August 6 th, 2007, the Crandall Canyon Mine in Utah collapsed trapping six miners. It appeared that a large area of pillars in the Main West and South Barrier sections of the mine had bumped in a brief time period, filling the mine entries with coal from the failed pillars and entrapping the six miners working in the South Barrier section (MSHA, 2008). The seismic event associated with the initial accident registered 3.9 on the Richter scale. Ten days later during the heroic rescue effort, another collapse occurred thereby killing three of the rescue workers, including one federal inspector. At the time of the initial collapse, the Crandall Canyon Mine was performing pillar retreat mining at cover deeper than 1500 ft (MSHA, 2008). In reviewing the mining plan after the collapse, several questions were raised concerning the accuracy of the currently available analysis tools and the methods that can be used for design purposes to help ensure that these types of tragic events are not repeated. 1.2 Statement of the Problem The LaModel boundary-element program was one of the analysis tools that was used in the design of the original mine plan. This program has a long history of successful application at coal mines in the U.S. and around the world. So, why was the mine design unsuccessful? As with any numerical method, the success and accuracy of the LaModel program is largely dependent on the accuracy of the input parameters. LaModel has default properties for most of the input parameters that were developed to give reasonable output for average mining conditions. However, to really design a specific mining plan and pillar layout well, the LaModel parameters need to be specifically calibrated to the unique conditions at the specific mine. The problem is that the process for calibrating LaModel for a specific mine site, and in particular a deep-cover pillar retreat mine, is not well established or standardized. Different users have developed different calibration processes that suit their particular application, and these various calibration processes have various degrees of success. What is needed is a standardized method of calibrating LaModel that has been thoroughly evaluated and verified on actual case studies. This standardized or best practice calibration process for LaModel would greatly raise the quality of mine design in this country, and would allow both the designers and the evaluators to work with the same calibration process. In fact, the need for an improved design methodology for deep cover pillar retreat mines was recognized by the U.S. Congress after the Crandall Canyon accident and included in the final 2008 Budget Appropriations Bill. 1.3 Statement of Work This report addresses the need for improving the design of deep-cover retreat mining at depths greater than 1500 ft as mandated by the legislature. Specifically, three tasks have been completed: 1

8 1.3.1 Modeling of the Deep-Cover Case Histories: Forty seven deep cover pillar retreat case histories from eleven different mines have been analyzed using the ARMPS and the LaModel numerical software. Raw data for these case histories (including AutoCAD mine map files) were provided by NIOSH. With this case history information, three different analyses of each case history were performed: 1) An ARMPS analysis 2) An idealized LaModel analysis - designed to match the ARMPS input. 3) A full LaModel analysis with the real pillar plan and the real topography. With the result from these detailed analyses, the LaModel program was calibrated with the deep cover pillar retreat case histories, and a detailed comparison between the Analysis of Retreat Mining Pillar Stability (ARMPS) and LaModel was performed Development of Best Practices for Using LaModel: In this task, an in-depth evaluation of the critical input parameters for LaModels (the lamination thickness, the gob modulus and the coal strength) was performed. This evaluation identified a number of new parameter evaluations and calibration procedures for making the program more accurate and effective. As these new input procedures were developed, they were implemented into various new Wizards in the LamPre3.0 program (the Lamination Thickness Wizard, the Strain-Hardening for Gob Material Wizard, and the Elastic Plastic for Coal Material Wizard). Also, to help achieve the objective of developing a standardized or best practice method of calibrating LaModel in order to raise the quality of mine design, a training manual is being developed. This training manual will document the technical aspects of the new optimized calibration process for the rock mass stiffness, the gob stiffness, the coal strength and the yielding coal properties. The training manual will also provide step-by-step directions and practical hints and considerations for performing a fully calibrated LaModel analysis. Also, the training manual will document a number of complete LaModel analyses of case histories beginning with the original AutoCAD mine map and grid generation through the calibration of the optimum input parameters and finally to running the model and analyzing the results Implementation of Efficiency and Accuracy Enhancements to LaModel: Along with implementing the new calibration techniques into wizards in LamPre3.0, a number of other enhancement and general updates are being programmed into the LaModel3.0 program: 1) The grid size has been increased to 2000 x ) The automatic grid generator now recognizes gob areas in the mine plan 3) The new coal strength wizard allows for more than 4 yield zones 4) The new grid editor has a change all and an undo command 2

9 1.4 Acknowledgements First, I would like to acknowledge the support for this project, Calibrating the LaModel Program for Deep Cover Pillar Retreat Coal Mining, from the National Institute for Occupational Safety and Health (NIOSH) and the Centers for Disease Control (CDC) through contract Also, I would like to acknowledge the assistance of the personnel in the ground control group at the NIOSH Pittsburgh Research Laboratory for supplying the raw data from the case histories, including AutoCAD mine map files. In particular, Tom Barczak, Chris Mark, Gabriel Essie Esterhuizen and Ted Klemetti have been extremely helpful during this cooperative research. Finally, I would like to acknowledge the team of graduate and undergraduate students (Christian Calderon-Arteaga, Larry Jimison, Morgan Sears and Ihsan Berk Tulu) who have performed the majority of the work in analyzing the case histories with ARMPS and LaModel. Without their dedicated and quality work, the results of this report would not have been possible. 3

10 2.1 Database Overview 2. Deep Cover Case History Database In order to help evaluate and verify a standardized method for calibrating LaModel, a database of deep cover retreat mining case studies was developed. For this database, NIOSH gathered the field data and mine maps, and provided them to the West Virginia University research team for analysis with LaModel. In this database, there are 47 deep cover pillar retreat case studies from 11 different mines (see Appendix A, Table A.1). Seven of these mines are in the Central Appalachian coal fields and 4 are in the Western coal fields. These are presently the only areas in the United States where deep cover pillar retreat is presently being performed. The depths at the case study sites ranged from 750 ft to 2200 ft with an average of The extraction thicknesses at the case study sites went from a low of 3.6 ft to a high of 9.0 ft with an average of 6.9 ft. This is probably higher than the average seam thicknesses in the given mining areas, but for deep covering pillaring to be economically successful, a thicker coal is very helpful. The number of entries in the sections ranged from 3 to 13 with an average of 6.2 entries. Pillar widths ranged from 50 to 100 ft and crosscuts spacing ranged from 80 to 150 ft (centercenter) with the average pillar size being 78 ft by 101 ft. The panel widths ranged from 160 ft to 940 ft with an average of 410 ft. Thirty of the case studies included loading from a single side gob, while 14 of the panels only had an active gob, 2 of the sections had loading from two side gobs and one situation was development loading. Sixteen of the case study sites were considered failures, 28 were considered successful and 3 were considered marginal, or middlings. The NIOSH personnel made the determination of success or failure during their visit to the mine and conversations with the mine staff. A case study is considered a success when an entire panel was recovered without any significant ground incidents (Mark, 2009). Generally, the unsuccessful cases include (after Mark, 2009): 1) Squeezes, which are non-violent pillar failures that may take hours, days or even weeks to develop; 2) Collapses, which occur when large areas supported by slender pillars (w/h < 4) fail almost simultaneously, resulting in an air blast, and; 3) Bumps, which are sudden, violent failures of one or more highly stresses pillars. The database analysis does not specifically consider: the geology, the cut sequence, the specific coal strength or the type and amount of roof support. 2.2 ARMPS Analysis The first analysis to be performed on each of the case studies was to calculate the ARMPS stability factor (Chase et al., 2002; Mark and Tuchman, 1997). These results are tabulated in Appendix A, Table A.1 and are shown in Figure 2.1. For the 47 case histories, the ARMPS stability factors ranged from 0.33 to 1.55 with an average of As can be seen in Figure 2.1, the stability factors cluster within a stability factor deviation of about 0.30 around the design line. There does not appear to be much separation between the successes and failures with a 4

11 fairly equal number of each above and below the line (a few more successes above the line than below). ARMPS Stability Factor Depth (ft) Failures Middling Success Figure 2.1 ARMPS stability factors for the case studies. Design Line When examining these results it is important to consider how the case histories were obtained. For each failure, the mine typically retreated the panel until the active gob distance, depth of cover or some other factor became so adverse that the face was abandoned (for the reasons as discussed above). Therefore, these failures are just below the stability factor that was successful. For each of the failure points in the above plot, one can consider that all stability factors above that point were successful while all of the stability factors below that point were unsuccessful. Similarly, when a section was successful, the point with the deepest cover or most adverse conditions was analyzed to determine the minimum successful stability factor. Thus, for each of the success points in the above graph, one can consider all of the stability factors above that point to have been successful. So in essence, the points in Figure 2.1 plot the design curve between success and failure, and they do appear to track the present design curve fairly well. The vertical spread of these points essentially defines the magnitude of the uncertainty or grey area in the design line. This uncertainly appears to encompass a stability factor deviation of approximately ± 0.40 on either side of the design line. With an average stability factor of 0.98, this translates into a discrepancy of about 41%. Considering that the AMRPS analysis is performed for non-homogeneous, non-isotropic overburden and does not consider the specific: topography, geology, cut sequence, specific coal strength, or roof support, etc., this is a pretty good fit for the simplified geometric analysis implemented in ARMPS. 5

12 2.3 LaModel Analysis Idealized Analysis: The next analysis that was performed on the database was to use LaModel to calculate a safety factor for each of the case studies (Heasley, 1998). For the LaModel analysis, two different approaches were perfomed. In the first approach, what is called the idealized LaModel analysis, the LaModel grid was built to exactly duplicate the idealized mining plan simulated in ARMPS for each case study. The pillars were perfectly rectangular, the mine plan was rigidly organized and the overburden was set at a constant depth. To calibrate the input parameters for the models: the lamination thickness was set to match the expected abutment extent according to equation 3.13 using the Lamination Thickness Wizard (see section 3.3), the final gob modulus was set to provide a gob load that was consistent with a 21 abutment angle using equations 3.21 or 3.22 through the Strain Hardening for Gob Material Wizard (see section 3.4), and the coal materials were set to provide a Mark-Bieniawski elastic-perfectly-plastic strength according to equation 3.25 using the Elastic-Plastic for Coal Material Wizard (see section 3.5). To calculate the safety factor for the idealized case study, the average stress-based pillar safety factor for the area within the ARMPS Active Mining Zone (AMZ) was used. LaModel Safety Factor Failures Middling Success Depth (ft) Design Line Even Split Figure 2.2 LaModel safety factors for the idealized case studies. The results of this idealized analysis are tabulated in Appendix A, Table A.1 and are shown in Figure 2.2. For the case histories, the idealized LaModel safety factors ranged from 0.74 to 2.28 with an average of Similar to the ARMPS analysis results, for each of the failure points in the above plot, one can consider that all stability factors above that point were successful while all of the stability factors below that point were unsuccessful. Similarly, for each of the success points in the above graph, one can consider all of the stability factors above that point to have been successful. 6

13 The area where the successful and failed designs overlap (the grey area ) appears to go from a safety factor of 0.75 to a safety factor of This grey area encompasses a safety factor deviation of ± 0.50 on either side of a theoretical center line. With an average stability factor of 1.39, this translates into an uncertainty of about 36%. If a few outliers on the graph are not considered, the overlap appears to generally cover the area between a safety factor or 1.00 and 1.50, and encompasses a safety factor deviation of ± 0.25 on either side of a theoretical center line. This translates into an uncertainty of about 18%. This 36% (or 18%) uncertainty (see Figure 2.2) shows that the idealized LaModel analysis does appear to provide a little more delineation between the successes and failures than the ARMPS analysis. In the case studies, only 4 failures (and middlings) out of 19 (21%) occurred with an idealized safety factor above 1.5, and only one success out 30 (3%) occurred with an idealized safety factor below 1.0. Dr. Chris Mark performed a logistic regression on the safety factor data from the idealized LaModel analyses. One of the first outcomes from this analysis was that the depth was not statistically significant. The analysis also determined that a safety factor of 1.16 best splits the successes and failures with 86% of the successes properly classified, 44% of the failures properly classified and an overall correct classification of 70%. The LROC value, which is a measure of the goodness of the fit somewhat comparable to the R 2 value in a linear regression, for the analysis was determined to be Considering that the idealized LaModel results are from a geo-technical analysis that does not consider site specific: topography, geology, cut sequence, coal strength, roof support, etc., this is a pretty good fit Detailed LaModel Analysis: For the second approach to the LaModel analysis, what is called the detailed LaModel analysis, the LaModel grid was built directly from the mine map and included all of the typically abnormalities associated with retreat pillar mining: variable pillar sizes, variable panel width, variable surrounding rooms, variable pillar stumps, etc. Also, the true topography from the mine map was gridded into LaModel and used in the analysis. This detailed LaModel analysis was intended to simulate the true underground geometry and topography as closely as possible with LaModel. For the detailed analysis, the critical input parameters were calibrated exactly as for the idealized analysis using: the Lamination Thickness Wizard for determining the lamination thickness, the Strain Hardening for Gob Material Wizard for determining the final gob modulus, and the Elastic-Plastic for Coal Material Wizard for determining the coal materials. This approach resulted in the values of the critical input parameters being identical between the two LaModel analysis approaches. The safety factors for the detailed case study analysis were calculated in the same manner as for the idealized case studies, by using the average stress-based pillar safety factor for the area within the ARMPS (AMZ). The results of this detailed LaModel analysis are tabulated in Appendix A, Table A.1 and are shown in Figure 2.3. For the case histories, the detailed LaModel safety factors ranged from 0.85 to 2.14 with an average of This spread is a little less than for the idealized analysis, and as can be seen in Figure 2.3, the separation of the successes and failures was improved a bit with the detailed analysis. Including the real geometry and topography in the LaModel analysis changes the safety factors for the specific case studies about 11% on average with a range from 0% to 58%. One would hope that the more detailed analysis would have a tendency to 7

14 LaModel Safety Factor Failures Middling Success Even Split Design Line Depth (ft) Figure 2.3 LaModel safety factors for the detailed case studies. lower the safety factors of the failures and raise the safety factors for the successes. For 11 out of 19 of the failures (or middlings), the safety factor was indeed reduced, but for 4 cases the safety factor was increased. However, for 10 out of 29 successful case studies, the safety factor was reduced; while for 8 of the case studies, the safety factor was indeed increased (11 stayed the same). Examining the separation of the successes and failures as was done for the idealized analysis (see Figure 2.2) it can be seen that the bulk of the safety factors may have indeed become better separated. In fact, the detailed analysis brought one of the failures below the design line, although it took one of the middling cases to a higher safety factor. Looking at the graph in Figure 2.3, the area where the successful and failed designs overlap (the grey area ) appears to go from a safety factor of 0.86 to a safety factor of This grey area encompasses a safety factor deviation of ± 0.32 on either side of a theoretical center line. With an average stability factor of 1.33, this translates into an uncertainty of about 24%. This 24% uncertainty (see Figure 2.3) compares very favorably with the 36% uncertainty for the idealized analysis and the 41% uncertainty in the ARMPS analysis. It shows that the detailed LaModel analysis does indeed provides a better delineation between the successes and failures than either the idealized LaModel analysis or the ARMPS analysis. In the case studies, only 4 failures (and middlings) out of 19 (21%) occurred with an idealized safety factor above the design line at 1.40 (and 0 failures above a safety factor of 1.50). And only 1 success occurred with an idealized safety factor below A logistic regression on the safety factor data from the detailed LaModel analyses was performed by Dr. Chris Mark of NIOSH. Again, depth was found to not be statistically significant and the same safety factor value of 1.16 best splits the successes and failures. For the detailed analysis, the 1.16 safety factor successfully classifies 79% of the successes and 50% of 8

15 the failures with an overall correct classification of 69%. The LROC value for the detailed analysis was 5% better at Again, considering that the detailed LaModel results are from a geo-technical analysis that does not consider site specific: geology, cut sequence, coal strength, roof support, etc., this is a pretty decent fit. 2.4 Comparison of ARMPS and LaModel The next step in the analysis of the database was to conduct a detailed comparison between the ARMPS and the idealized LaModel results. The idealized LaModel case studies use the exact same mining geometry, seam thickness and overburden depth as the ARMPS analyses. Also, through the calibration process, the extent of the abutment loads, the gob/abutment loading distribution and the pillar strength in the idealized LaModel analyses have been set as close as possible to the ARMPS analysis algorithms. The idealized LaModel results (as opposed to the detailed results) were used for this comparison in order to remove the influence of topography and variable pillar plans. In this comparison, the biggest significant difference between the ARMPS and the idealized LaModel analysis techniques is that ARMPS essentially uses a geometric loading algorithm while LaModel uses the laminated overburden model in conjunction with elastic-plastic coal and strain-hardening gob materials to calculate seam loading. So, it would be expected that the two different program s analysis results would be fairly close with any difference due to the different loading mechanisms Stability Factor Comparison: Figure 2.4 shows the comparison between the ARMPS stability factors and the idealized LaModel safety factors for the deep cover retreat mining case studies. As expected, there is a fairly good correlation between the stability factors with an R 2 value of for the best fit line and an R 2 value of for the line forced to go through the origin. This means that 41% of the difference in the LaModel stability factors can be explained by the ARMPS safety factor for the case study. The absolute magnitudes of the different stability factors are consistently a bit different, with the idealized LaModel safety factors averaging about 37% higher than the ARMPS stability factors. In order to find other site specific parameters that may be significantly influencing the difference between the ARMPS and LaModel stability factors, a stability factor (SF) ratio was created by dividing the LaModel safety factor by the ARMPS stability factor for each case study. This SF ratio was then compared with the: mining height, seam depth, panel width and panel width-to-depth ratio. The plots of these comparisons are shown in Figures 2.5 to 2.8. Reviewing Figures 2.5 through 2.8, there does not appear to be any significant correlation between the mining height and the safety factor ratio (R 2 = ). However, there does appear to be some correlation between the mining depth (R 2 = 0.33), panel width (R 2 = 0.15) and the panel width-to-depth ratio (R 2 = 0.26) and the safety factor ratio. In particular, it appears that the safety factor ratio increases as the depth increases and decreases as the panel width increase. This means that the LaModel safety factor becomes larger in relation to the ARMPS stability factor as the depth increases, and the idealized LaModel safety factor gets closer to the ARMPS stability factor as the panel width increases. 9

16 LaModel Safety Factor y = x R² = y = x R² = ARMPS Stability Factor Idealized Stability Factor Detailed Stability Factor Figure 2.4 Comparison between ARMPS and LaModel stability factors. It is believed that the safety factors from the two methods separate as the depth increases because the laminated model starts to redistribute load away from the AMZ to the surrounding gob and pillars as the section convergences more with depth, in contrast to ARMPS were the gob load is fixed after a certain depth and the adjacent barrier pillars shed load before complete failure. It is believed that the safety factor values get closer with an increasing panel width because ARMPS assumes a tributary area load while the laminated overburden allows some load from the pillars at the edge of the section to be carried by the barrier. This difference in loading would naturally decrease as the panel gets wider and the tributary area loading model more closely matches the LaModel loading model. 10

17 Safety Factor Ratio Idealized SF Ratio y = x R² = Mining Height Figure 2.5 Influence of the mining height on the safety factor ratio. Stress Safety Factor Ratio Idealized SF Ratio y = x R² = Depth (ft) Figure 2.6 Influence of the depth on the safety factor ratio. 11

18 Stress Safety Factor Ratio Idealized SF Ratio y = x R² = Panel Width (ft) Figure 2.7 Influence of the panel width on the safety factor ratio Safety Factor Ratio Idealized SF Ratio y = x R² = Width-to-Depth Ratio Figure 2.8 Influence of the panel width-to-depth ratio on the safety factor ratio 12

19 2.4.2 Detailed Load Analysis: To further investigate the difference between the ARMPS stability factor and the LaModel safety factor, and in particular, the difference in the loading mechanism between the two methods, a detailed analysis of the magnitude of the loads in several different zones and at different times in the mining cycle for the two methods was performed. For this detailed loading analysis, the 4 different zones were (see Figure 2.9): 1) The Active Mining Zone (AMZ) (defined by 5(H) 1/2 ) 2) The immediate gob at the pillar line (defined by H tan(β)) 3) The first side outby barrier pillar 4) The first side inby barrier pillar H*TAN(ß) GOB INBY BARRIER PILLAR WSC 1/2 AMZ = 5(H) OUTBY BARRIER PILLAR W_Panel WBP Figure 2.9 Schematic of the loading zones in the load analysis. 13

20 and the 4 different loading cases were: 1) Development load 2) Development and first side gob load 3) Development, first side and active gob load 4) Development, first side, active gob and the slab cut load For each of these loading cases a different LaModel step was created. Then, for each of the loading cases and for each of the zones, the load used by ARMPS was calculated (using a specially constructed spreadsheet version of ARMPS) and the load from the idealized LaModel was determined from the LaModel output. The various different loads between the ARMPS calculation and the LaModel case study were then compared. This load analysis revealed that, in general, the load on the AMZ in LaModel was less than the load on the AMZ in ARMPS. 1) For development loading, the LaModel load averaged 12% less; 2) For development and first side gob loading, the load averaged 13% less; 3) For development, first side and active gob loading, the load averaged 19% less; and 4) For development, first side, active gob and the slab cut loading, the load averaged 22% less. This 22% lower loading for LaModel for case 4 helps directly explain the higher safety factors in LaModel as seen in Figure 2.4. Next, the difference in AMZ loading was compared to the: panel depth, panel width, active gob extent, side gob extent, barrier pillar width and safety factor. The only parameter which seemed to have some significant impact on the observed difference in AMZ loading was the panel depth (see Figure 2.10). This figure indicates that the difference in AMZ loading between ARMPS and LaModel increases with increasing panel depth. (This is consistent with Figure 2.6 where the safety factor ration is seen to increase with depth.) We know that the ARMPS calculation essentially puts full development load and the full abutment loads on the AMZ with no consideration for load shedding to the stiffer surrounding barriers as more load is applied. On the other hand, the elastic (and yielding) behavior built into the LaModel overburden and pillars will naturally shed load to the stiffer surrounding barrier pillars and solid coal areas. The load shedding from the AMZ in LaModel will naturally increase as the loading increases (case 1 to 4) and as the panels get deeper. Also, it is expected that the load shedding will naturally be greater for narrower panel where the stiff barriers are closer to the AMZ pillars, although the panel width did not appear to have a significant impact in this dataset. So, where does the shed load go? To more fully investigate the relative loading between ARMPS and LaModel, the load on the immediate gob (within a distance of H tan (β) of the pillar line, see Figure 2.9 and 3.5) was determined for both models. This immediate gob loading averaged 35% lower in LaModel than in ARMPS, so the shed load is not going to the gob. This lack of gob load appears to be due to the 3D effect at the face line, where the overburden load above the gob is spread to: the inby 14

21 LaModel Percent Difference 0% -10% -20% -30% -40% -50% AMZ Loading y = x R² = Panel Depth (ft) Figure 2.10 Influence of the panel depth on the difference in AMZ loading. barrier pillars on either side of the gob, the AMZ, and the outby barrier pillars on either side of the AMZ. Upon further investigating the gob loading, it is seen that the difference in gob loading between ARMPS and LaModel is seen to decrease as the gob gets wider and/or longer. This observation also supports the hypothesis that the 3D support of the overburden over the gob as calculated in LaModel is causing a lower gob load than the modified 2D geometric analysis used in ARMPS. So, if the AMZ and the gob both carry less load in LaModel than in ARMPS, then the load must be going to surrounding coal, and indeed this is the case. The inby barrier pillar in LaModel is seen to carry 15% more load and the outby barrier pillar is seen to carry 17% more load than in ARMPS. In the case of the barrier pillars, LaModel maintains the pillars at peak load after failure using an elastic, perfectly-plastic coal model, while ARMPS has an algorithm for shedding barrier pillar load as the stability factor drops; therefore, LaModel has a tendency to carry more load on the barrier pillars. Also, the side gob (the first side gob adjacent to the AMZ and active gob) is seen to carry some 35% to 45% more load in LaModel than in ARMPS. In LaModel, as the active gob is formed it causes additional convergence and associated load on the adjacent side gob, so that the side gob is carrying more load than the abutment angle concept for an isolated panel would suggest. In contrast, ARMPS maintains the load on the gob suggested by the abutment angle concept, even though the two adjacent gobs may be influencing the stresses on each other. 15

22 3.1 Background 3. Best Practices for Calibrating LaModel The LaModel program is used to model the stresses and displacements on thin tabular deposits such as coal seams. It uses the displacement-discontinuity (DD) variation of the boundary-element method, and because of this formulation, it is able to analyze large areas of single or multiple-seam coal mines (Heasley, 1998). What makes LaModel unique among boundary element codes is that the overburden material includes laminations which give the model a very accurate flexibility for stratified sedimentary geologies and multiple-seam mines. Using LaModel, the total vertical stresses and displacements in the coal seam are calculated, and also, the individual effects of multiple-seam stress interactions and topographic relief can be separated and analyzed individually. Since LaModel s original introduction in 1996, it has continually been upgraded (based on user requests) and modernized as operating systems and programming languages have changed. The present program is written in Microsoft Visual C++ and runs in the windows operating system. It can be used to calculate convergence, vertical stress, overburden stress, pillar safety factors, intra-seam subsidence, etc. on single and multiple seams with complex geometries and variable topography. Presently, the program can analyze a 2000 x 2000 grid with 6 different material models and 52 different individual in-seam materials. It uses a forms-based system for inputting model parameters and a graphical interface for creating the mine grid. Also, it includes a number of Wizards for: 1) Calculating the lamination thickness based on the extent of abutment loading 2) Calculating coal material properties based on a Mark-Bienawski pillar strength 3) Calculating gob properties based on expected gob loading, and 4) Calculating strain-softening coal properties. Recently, the LaModel program has been interfaced with AutoCAD and can take an AutoCAD map of the pillar plan and overburden and automatically convert these into the appropriate seam and overburden grids. Also, the output from LaModel can be downloaded into AutoCAD and overlain on the mine map for enhanced analysis and graphical display (Heasley, 2008). 3.2 The Critical Input Parameters The accuracy of a LaModel analysis depends entirely on the accuracy of the input parameters. Therefore, the input parameters need to be calibrated with the best available information, either: measured, observed, or empirically or numerically derived. However, in calibrating the model, the user also needs to consider that the mathematics in LaModel are only a simplified approximation of the true mechanical response of the overburden and because of the mathematical simplifications built into the program, the input parameters may need to be appropriately adjusted to reconcile the program limitations. In particular, after many years of experience with the program, it is clear that in many situations the overburden model in LaModel is not as flexible as the true overburden. The laminated overburden model in LaModel is inherently more flexible than a homogeneous elastic overburden as used in previous displacement-discontinuity codes and it is more flexible than a 16

23 stratified elastic model without bedding plane slip as used in many finite-element programs. However, using reasonable values of input parameters, the LaModel program still does not produce the level of seam convergence and/or surface subsidence as measured in the field. It is believed that this displacement limitation in the model may be due to the lack of any consideration for vertical joint movement in the program. The laminated model makes a good attempt at simulating bedding plane slip in the overburden, but it does not consider any overburden movement due to vertical/sub-vertical joint slip, thereby limiting the amount of calculated displacements. Knowing this inherent limitation of LaModel, the user can either calibrate for realistic stress output or for realistic displacement output. In general, it is not possible to accurately model both with the same set of material parameters. If the user calibrates the model to produce realistic stress values, then the input parameters are optimized to match as closely as possible the observed/measured stress levels from the field, and it is likely that the calculated displacement values will be low. On the other hand, if the user optimizes the input parameters to produce realistic displacement/subsidence values, then generally, the calculated stress values will be inaccurate. Historically, the vast majority of LaModel users have been interested in calculating realistic stresses and loads, and that is the calibration process presented in the remaining sections of this report. When actually building a model, the geometry of the mining in the seams and the topography are fairly well know and fairly accurately discretized into LaModel. The most critical input parameters with regard to accurately calculating stresses and loads, and therefore, pillar stability and safety factors are then: 1) The Rock Mass Stiffness 2) The Gob Stiffness 3) The Coal Strength These three parameters are always fundamentally important to accurate modeling with LaModel and particularly so in simulations analyzing abutment stress transfer (from gob areas) and pillar stability as in deep cover pillar retreat. During model calibration, it is critical to note that these parameters are strongly interrelated, and because of the model geo-mechanics, the parameters need to be calibrated in the order shown above. With this sequence of parameter calibration, the calibrated value of the subsequent parameters is determined by the chosen value of the previous parameters, and changing the value of any of the preceding parameters will require re-calibration of the subsequent parameters. The calibration derivation and recommended calibration process as it relates to each of these parameters is discussed in more detail below. 3.3 Calibrating Rock Mass Stiffness The stiffness of the rock mass in LaModel is primarily determined by two parameters, the rock mass modulus and the rock mass lamination thickness. Increasing the modulus or increasing the lamination thickness of the rock mass will increase the stiffness of the overburden. With a stiffer overburden: 1) The extent of the abutment stresses will increase, 2) The convergence and stress over the gob areas will decrease and 17

24 3) The multiple seam stress concentrations will be smoothed over a larger area Rock Mass Modulus: When calibrating for good stress output, it is recommended that the rock mass stiffness be calibrated to produce a reasonable extent of abutment zone at the edge of the critical gob areas. Since changes in either the modulus or lamination thickness cause a similar response in the model, it is logical and most efficient to keep one parameter constant and only adjust the other. When calibrating the rock mass stiffness, it has been found to be most efficient to initially select a rock mass modulus and then solely adjust the lamination thickness for the model calibration. It is recommended to determine the average rock mass modulus as a thickness weighted average of the elastic modulus of the overburden layers (Karabin and Evanto, 1999), or second best, to use the default rock mass modulus in LaModel. If the rock mass lamination thickness is calibrated to match the extent of the abutment zone as described below, then the choice of rock mass elastic modulus is not very critical to the final objective, since the lamination thickness will be adjusted as needed with regard to the elastic modulus to ultimately match the desired extent of the abutment zone Rock Mass Lamination Thickness: In calibrating the lamination thickness for a model based on the extent of the abutment zone, it would be best to use specific field measurements of the abutment zone from the given mine. However, often these field measurements are not available. In this case, visual observations of the extent of the abutment zone can often be used. Most operations personnel in a mine have a fairly good idea of how far the stress effects can be seen from an adjacent gob. For visually determining the abutment extent, the user is looking for the extent of the abutment zone from the full side abutment of a longwall or room-and-pillar gob area, NOT necessarily the distance outby the face where the front abutment zone is first observed. Also, if visually determining the extent of the abutment zone, the user should consider that the extent of the abutment zone as determined from sensitive field measurements as used in the derivation of equations 3.1 and 3.2 below is probably larger than what can be visually observed in the rib of the entries. Without any field measurements or underground observations to guide the LaModel user, then historical empirical information can be used. For instance, historical field measurements would indicate that, on average, the extent of the abutment zone (D) at depth (H) should be (Peng, 2006): D = 9.3 H (3.1) or that 90% of the abutment load should be within (Mark and Chase, 1997): D.9 = 5 H (3.2) Once the desired extent of the abutment zone has been determined, the next step is to calculate the lamination thickness that will match that abutment extent for the particular site. In the original development of LaModel (Heasley, 1998), an equation (3.3) was developed which gives the abutment stress magnitude (σ l ) for the laminated overburden model as a function of the distance (x) from the panel rib (also see Figure 3.1): 18

25 2 E P 2 E s x s σ (x) q e E λ h l = (3.3) 2 E λ h where: q = the insitu stress P = the width of the panel E s = the elastic modulus of the seam E = the elastic modulus of the overburden λ = a parameter of the laminated model h = the seam thickness In this equation, the insitu stress (q) is determined as: q = γ H (3.4) where: γ = the overburden density H = the seam depth and λ = t 2 12 ( 1 υ ) (3.5) where: t = the lamination thickness in the rock mass υ = Poisson s Ratio of the rock mass In equation 3.3, the panel is assumed to be open with no gob loading; therefore, the total abutment load is the full weight of the overburden for one half of the panel (qp/2). Also, equation 3.3 assumes the coal seam is perfectly elastic and there is no yield zone at the rib of the panel. For the extent of the abutment stress given in equation 3.1, the empirically determined distribution of the abutment stress (σ a ) within the abutment zone has been found to be (Mark, 1992) (see Figure 3.1): where: L s = the total side abutment load 3Ls (x) = D σa 3 ( D x) 2 (3.6) Based on the stress distribution generated by equation 3.6, it can be determined that essentially 90% of the abutment load should be within the distance (D.9 ) from the edge of the panel (as previously shown in equation 3.2) (Mark and Chase, 1997): D.9 = 5 H (3.7) 19

26 Stress (psi) 14,000 12,000 10,000 8,000 6,000 4,000 Laminated Model Abutment Stress Empirical Abutment Stress 2, Distance from Edge of Panel (ft) Figure 3.1 A comparison of abutment stresses from field measurements and LaModel. To determine the distance from the panel edge which contains a given percentage (n) of the side abutment load for the laminated overburden model, first, the stress as defined by equation 3.3 needs to be integrated over the distance, x, to determine the load: 2 Es P x σ (x) dx = -q e E λ h l (3.8) 2 Then the fraction (n) of the total side abutment load (qp/2) which is contained in a given distance (D n ) can be determined as: D n P nq = σl (x) 2 0 P = -q e 2 P = -q e 2 2 Es D E λ h 2 Es D E λ h n n P -q e 2 P + q 2 2 Es 0 E λ h (3.9) Simplifying, by dividing through by the total abutment load (qp/2) gives: 20

27 2 E s D n - e E λ h n = + 1 (3.10) Then, solving for the abutment distance (D n ) for the given percent load (n) and substituting back in for λ, we get: 1- n = e 2 Es D E λ h n ln ( 1- n) D D n n = = ln = ln 2 Es D E λ h ( 1- n) ( 1- n) n E λ h 2 E 2 E s s E h t 12 2 ( 1 υ ) (3.11) This equation (3.11) says that the extent of the abutment load is proportional to the square root of the rock mass modulus, seam thickness and lamination thickness and inversely proportional to the square root of the seam modulus. Next, to determine the lamination thickness to use to get a given abutment distance with given rock and seam properties, equation 3.11 is solved for t: ln D D ln ( 1- n) 2 2 E 12 ( 1 υ ) n n 2 = = ( 1- n) 2 Es 2 12 ( 1 υ ) 2 E 2 12 ( 1 υ ) t = s s E h t E h t E h ln D n ( 1- n) 2 (3.12) Equation 3.12 shows that the lamination thickness (t) required to match a given abutment extent (D n ) is proportional to the square of the abutment extent, linearly proportional to the seam modulus and inversely proportional to the rock mass modulus and seam thickness. A comparison of the empirical abutment stress and the matching laminated model abutment stress as calculated by equation 3.12 is shown in Figure 3.1. One adjustment needs to be made to equation 3.12 to use it in practice. For the original derivation of equation 3.1, the seam was assumed to be linearly elastic. Generally, this is not the case and there is some distance (d) of coal yielding at the edge of the panel. On the other hand, the field measurements used to determine the extent of the abutment stress in equation 3.5 and 3.6 naturally included the distance of the yielding zone in the measurements. Therefore, to use an abutment extent measured in the field for input to equation 3.12, the extent of the actual yield zone in the field needs to be subtracted from the field measurement to be more consistent with 21

28 the derivation of equation (This adjustment essentially neglects the amount of overburden load carried in the yield zone.) After making this yield zone adjustment to the extent of the abutment zone and substituting equation 3.7 for the distance of 90% load, an equation which determines the lamination thickness (t) required to match the field measurements for 90% of the abutment load is derived: 2 ( 1 υ ) 2 Es 12 5 H d t = E h ln(.1) (3.13) where: E = the elastic modulus of the overburden υ = the Poisson s Ratio of the overburden E s = the elastic modulus of the seam h = the seam thickness d = the extent of the coal yielding at the edge of the gob H = the seam depth Yield Zone Distance: In equation 3.13, the only parameter that is not necessarily known ahead of time is d, the extent of the yield zone. This value can be developed by running LaModel and observing the calculated yield zone for the given conditions. Or, to get a first approximation of the yield zone extent, one can find the point (x) into the pillar rib where the total load carrying capability of the coal rib is equal to the load distributed by the side abutment. First, to determine the load carrying capability of the coal rib, we start with the stress gradient implied by the Mark- Bieniawski coal strength formula (Mark, 1999): σ p (x) = Si x h (3.14) where: σ p (x) = peak coal stress (psi) x = distance into the coal S i = insitu coal strength (psi) h = pillar height This equation (3.14) is then integrated with respect to x and evaluated from the rib (x=0) to the distance x into the pillar to determine the total load carried by the edge of the pillar rib (see Figure 3.2): x σ p (x) dx = Si x x (3.15) h

29 6,000 5,000 Laminated Abutment Load Mark-Bieniawski Coal Load Load (tons) 4,000 3,000 2,000 1, Distance from Edge of Panel (ft) Figure 3.2 A comparison of laminated abutment load to the Mark-Bieniawski coal load. The load distributed by the side abutment within the distance x was previously determined in equation 3.9. If these two loads are set equal, the following equation is determined: P q e 2 2 Es x E λ h P Si + q 1.08 x 2 h 2 - i 0.64 S x = 0 (3.16) In the original derivation of equation 3.9, it was assumed that there was no gob and the total overburden load over half of the panel became the total abutment load. In the more general case, the gob is supporting some percentage of the overburden load and the remainder of the overburden load becomes abutment load. If the percentage of the total overburden load over the gob that becomes abutment load at the edge of the panel is (m), then 3.16 can be written as: P m q e 2 2 Es x E λ h P Si + m q 1.08 x 2 h 2 - i 0.64 S x = 0 (3.17) Therefore, the value of x which solves equation 3.16 is the point where the cumulative load carrying capability of the pillar rib equates to the load distributed by the abutment stress gradient. This is the point in Figure 3.2 where the loading curves cross and this value gives a fair estimate of the depth of the yield zone, d. Equation 3.17 is obviously non-linear and cannot be solved 23

30 analytically; however, a numerical solution can easily be determined through using different trial values of x to find the zero point of the equation. So, for determining the rock mass stiffness to use in LaModel, it is recommended to: 1) Determine the average rock mass modulus as a thickness weighted average of the elastic modulus of the overburden layers, or to use the default rock mass modulus in LaModel. 2) Then, determine the lamination thickness that matches the observed behavior (equation 3.12) or average field measurements (equation 3.13) 3) For estimating the depth of the yield zone at the coal rib of the abutment, use observations from the field or use equation Implementation in LamPre3.0: To simplify applying the above protocols and equations in LaModel, a Lamination Thickness Wizard form has been added to the new LamPre 3.0 (see Figure 3.3). This wizard implements the previous equations in a user-friendly manner to assist the LaModel user in calibrating the lamination thickness as suggested above. The first section of the form contains the Rock Mass Parameters. These values (Elastic Modulus, Poisson s Ratio and Vertical Stress Gradient) were previously entered in the Rock Mass Parameter form in LamPre and are used in the calculation, so they are displayed on this form. The next set of Seam Parameters (Elastic Modulus, Extraction Thickness, Depth, Width of Gob and In-Situ Coal Strength) is the critical site specific input for calculating the rock mass lamination thickness (see Figure 3.3). Default values for the Seam Elastic Modulus (300,000 psi) and In-Situ Coal Strength (900 psi) are provided, but these values can be changed by the user if desired. In this section of the form, the user does have to enter the site specific values for the; Extraction Thickness, Depth and Width of Gob. The third section of the form is for entering or calculating the extent of the abutment load (see Figure 3.3). The first line in this section implements equation 3.2 (or 3.7) and calculates the extent of 90% of the abutment load based on field measurement and the given seam depth. In the next line ( Extent of Abutment Load ), the user can enter a site specific value of the abutment extent determined from field measurements, observations, etc., or the user can check the box to the right ( Use the Suggested Value ) and the empirically suggested value from the line above will automatically be entered for the extent of the abutment load to be used in subsequent calculations. The third and last line in this section is the Portion of Load within the Given Extent and this value has been fixed at 90% (0.90) for the calculation and is displayed here for the user s information. The fourth section of the form is for entering or calculating the width of the yield zone. The first line contains the Suggested Percentage of the Overburden load that is transferred from over the gob to the abutment zone. This suggested percentage is calculated using the abutment angle concept with a 21 abutment angle. In the next line ( Percentage of the Overburden Load ), the user can enter a site specific value of the percentage overburden load on the abutment as determined from field measurements, observations, etc., or the user can check the box to the right ( Use the Suggested Value ) and the 21 abutment angle value from the line above will automatically be entered for the percentage of the overburden load to be used in subsequent calculations. The next line contains the Trial Lamination Thickness which is used in equation 3.17 for calculating the yield zone. This value is not editable by the user. (The Trial Lamination Thickness defaults to 50 ft, but is automatically updated when the lamination 24

31 thickness is calculated at the bottom of the form.) On the fourth line, there is a Calculate button and the Calculated Yield Zone parameter. When the user clicks this yield zone Calculate button, equation 3.17 is solved with the Trial Lamination Thickness and the other parameters previously entered in the form, and the resultant calculated width of the yield zone is shown in the Calculated Yield Zone parameter box. In the fifth and last line of this section ( Width of Yield Zone ), the user can enter a site specific value of the yield zone width determined from field measurements, observations, etc., or the user can check the box to the right ( Use the Calculated Value ) and the calculated value from the line above will automatically be entered for the Width of Yield Zone to be used in subsequent calculations. Figure 3.3 New Lamination Thickness Wizard in LamPre

32 The final parameter line on the form contains a Calculate button and the Calculated Lamination Thickness parameter. At this point, once the Seam Parameters, Extent of Abutment Load and the Width of the Yield Zone have been input, the user can click the lamination thickness calculate button and equation 3.13 will be used to calculate the calibrated lamination thickness. If the Use the Calculated Value button is checked for the Width of the Yield Zone, then a brief iteration will occur where the Trial Lamination Thickness, Width of Yield Zone and Calculated Lamination Thickness are sequentially updated until convergence on a final Width of Yield Zone and Calculated Lamination Thickness. To use the Calculated Lamination Thickness for the input to LaModel, the user clicks the OK button and the calculated lamination thickness is automatically entered as the Lamination Thickness for the Overburden / Rock Mass Parameters. So to briefly recap, for the user to calculate a calibrated lamination thickness based on the protocols and equations presented in this report using the new Lamination Thickness Wizard, they should: 1) Enter the site specific Seam Parameters 2) Enter a measured or observed Extent of Abutment Zone, or use the suggested value 3) Enter a measured or observed Width of Yield Zone, or use the calculated value 4) Calculate the calibrated Lamination Thickness. 3.4 Calibrating Gob Stiffness In a LaModel analysis with gob areas, an accurate stiffness for the gob (in relation to the stiffness of the rock) is critical to accurately calculating the overburden load distribution and therefore the pillar stresses and safety factors. The relative stiffness of the gob determines how much overburden weight is carried by the gob; and therefore, not carried by the surrounding pillars. This means that a stiffer gob carries more load and the surrounding pillars carry less, while a softer gob carries less load and the surrounding pillars carry more. In LaModel, the stiffness of the gob is primarily determined by adjusting the Final Modulus of the strainhardening gob model (Heasley 1998) (see Figure 3.4). A higher final modulus gives a stiffer gob and a lower modulus value produces a softer gob material. Given that the behavior of the gob is so critical in determining the pillar stresses and safety factor, it is a sad fact that our knowledge of insitu gob properties is very poor. For a calibrated LaModel analysis, it is imperative that the gob stiffness be calibrated with the best available information on the amount of abutment load (or gob load) experienced at that mine. It would be best to use specific field measurements of the abutment load (or gob load) from the mine in order to calibrating the gob stiffness. However, these types of field measurements are quite rare (and often of questionable accuracy). For estimating abutment loads or gob loads, visual observations are not very useful; and therefore, general historical measurements and/or empirical information are quite often the only available data Critical Panel Width: In order to calibrate the gob stiffness for a practical situation, it is best to consider a number of general guiding factors. First, a comparison of the present gob width with the critical gob 26

33 Figure 3.4 The six material models in LaModel. width for the given depth can provide some useful insight. The critical gob width (P c ) for a given gob depth (H) and abutment angle (β) can be calculated as: where: P c = critical panel width H = depth β = abutment angle P c = 2 H tan(β ) (3.18) For a critical (or supercritical) panel width (where the maximum amount of subsidence has been achieved), it would be expected that the peak gob load in the middle of the panel would approach the insitu overburden load. As the depth increases and the gob width becomes more subcritical, I would expect that the peak gob load would similarly decrease from the insitu load. As a first cut, I might expect the peak stress on the longwall gob to be around the same percentage of the insitu stress as the gob width is a percentage of the critical gob width Laminated Model Gob Stress: For a laminated overburden model, as the depth increases from the critical situation and the gob width becomes more subcritical, a linear elastic gob material would suggest that the peak gob load would increase linearly with depth from the load level in the critical case (Chase et al., 2002; Heasley, 2000). The critical depth (H c ) for a given gob width (P) and abutment angle (β) can be calculated as: 27

34 where: H c = Critical Depth P = Panel Width β = Abutment Angle P H c = (3.19) 2 tan(β ) and then the expected average gob stress (σ gob-lam-av ) at the actual seam depth (H) (greater than H c ) can be calculated as: where: H = Seam Depth (ft) γ = Overburden Density (lbs/cu ft) H H c γ H γ σ gob -lam av = = (3.20) H c Equation 3.20, which is based on a laminated overburden and a linear elastic gob, implies that the average gob stress for a subcritical panel is solely a function of the depth and equal to half of the insitu stress. (In reality, gob material is generally considered to be strain-hardening and therefore, equation 3.20 may underestimate the actual gob loading. On the other hand, the optimum lamination thickness may increase with depth and counteract the effect of the strainhardening gob.) Abutment Angle Gob Stress: Next, for estimating the gob and abutment loading, we can look at ALPS and ARMPS, which have a large empirical database supporting them. In both of these programs, an average abutment angle of 21º was determined from an empirical database and is used to calculate the abutment loading. Using the abutment angle concept, the average gob stress (σ g-av ) for a supercritical panel (see Figure 3.5) can be calculated as: ( H tanβ) H γ P σ g av = (3.21) 144 P where: H = Seam Depth (in ft) γ = Overburden Density (in lbs/cu ft) P = Panel Width (in ft) Β = Abutment Angle 28

35 H tanβ P/2 H L S - Side Abutment Load L SS β - Abutment Angle Mined out panel Supercritical P β Subcritical Figure 3.5 Conceptualization of the abutment angle. Similarly, the average gob stress (σ g-av ) for a subcritical panel (see Figure 3.5) can be calculated as: P 1 γ σ g av = (3.22) 4 tanβ 144 Equation 3.22, which is based on the abutment angle concept of gob loading, implies that the average gob stress for a subcritical panel (with an assumed abutment angle) is solely a function of the panel width, and not influenced by depth past the critical point Adjusted Abutment Angle Stress: Recent work has noted that the concept of a constant abutment angle as used in ALPS and ARMPS appears to breakdown under deeper cover (see Figure 3.6)(Chase et al., 2002; Heasley, 2000). In particular, for room-and-pillar retreat panels deeper than 1250 ft, it was found that a stability factor of 0.8 (for strong roof) could be successfully used in ARMPS, as opposed to a required stability factor of 1.5 for panels less than 650 ft deep. One of the more likely explanations for this reduction in allowable stability factor is that the actual pillar abutment loading may be less than predicted by using the constant abutment angle concept (Chase et al., 2002). Colwell found a similar situation with deep longwall panels in Australia where the measured abutment stresses were much less than predicted with a 21º abutment angle (Colwell et al., 1999). 29

36 ARMPS Stability Factor Design Line Successful Case Unsuccessful Case Depth of Cover (ft) Figure 3.6 Suggested stability factors for the ARMPS deep-cover database. The degree to which a constant abutment angle might overestimate the abutment loading can be investigated by comparing the recommended NIOSH stability factors for shallow and deep cover. Below 650 ft, a stability factor greater than 1.5 is recommended but, at depths greater than 1250 ft, 0.8 is acceptable. Since higher coal strengths have not been correlated with greater depth, it is most likely that the lower stability factor recommendation is due to an overestimate of applied stress or load. Based on the NIOSH recommendations, it appears that the abutment loading based on the constant abutment angle of 21 could be as much as (1.5/0.8) times higher than actual loading experienced in the field. Implementing this adjustment produces the following equation for an adjusted average gob load for a subcritical panel based on the abutment angle concept (given without derivation): ( 4H tanβ) 0.8 P H γ σgob -adj av = 1 (3.23) 1.5 4H tanβ 144 where: H = Seam Depth (ft) γ = Overburden Density (lbs/cu ft) P = Panel Width (ft) β = Abutment Angle The preceding discussion on gob stiffness and loading has produced several competing concepts/equations. Equation 3.20, which is based on a laminated overburden model and a linear elastic gob, implies that the average gob stress for a subcritical panel is solely a function of the depth. Equation 3.22, which is based on the abutment angle concept of gob loading, implies that the average gob stress for a subcritical panel is solely a function of the panel width. Equation 3.23 modifies the abutment angle concept in an attempt to produce more realistic results for panels deeper than 1250 ft. 30

37 At this time, it is not entirely clear which concept or equation provides the most realistic estimates of gob stress. From recent experience, Equation 3.22 appears to provide a lower bound for realistic gob stresses and Equation 3.23 appears to provide an upper bound. Equation 3.20 is between the bounds set by equations 3.22 and 3.23 and may provide a reasonable starting point for further calibration. Regardless of which equation is chosen as a starting point, it is clear that a realistic gob/abutment loading is critical to a realistic model result and that the gob stiffness should be carefully analyzed and calibrated in a realistic model. A major improvement in mine design can be achieved by just getting the designer to carefully considering how the overburden load is distributed between the gob and the abutment. Certainly, gaining a better understanding of the true gob/abutment loading in coal mining is an area for future research, and the deep cover database presented earlier will undoubtedly be used for this analysis in the future Implementation in LamPre3.0: To simplify applying the above equations in LaModel and to get the LaModel user to consider the load distribution between the gob and the abutments, a new wizard for defining the properties for the Strain Hardening Gob material has been added to the new LamPre 3.0. This wizard implements the previous equations (3.21 and 3.22) for an abutment angle loading in a user-friendly manner to assist the LaModel user in calibrating the Final Modulus value for the strain-hardening gob material (see Figure 3.7). As part of this calibration process, the wizard actually produces a two dimensional laminated model with the site specific geometry (depth, seam thickness, gob width, etc) and geo-mechanical properties (rock mass stiffness, coal properties, etc.), and iteratively determines the Final Gob Modulus which will provide the desired overburden load on the gob. Figure 3.7 New wizard for calibrating the final modulus of the gob. The first section of the Strain Hardening for Gob material wizard contains the Geometry and Overburden Parameters (see Figure 3.7). Four of these parameter values (Elastic Modulus, Poisson s Ratio, Lamination Thickness, and Vertical Stress Gradient) were previously entered in the Rock Mass Parameter form of LamPre and are used in the calculation, so they are displayed on this form. The next parameter is the Current Seam Number and setting this value 31

38 fills the next two parameters (Seam Thickness and Overburden Depth) from the values previously entered in the Seam Geometry and Boundary Condition form. The second set of parameters is for the Coal Properties (Coal Modulus, Plastic Modulus and Coal Strength) and they are used to define the nature of the coal yielding at the edge of the gob area (see Figure 3.7). The initial values for these parameters are taken from those used in the Elastic-Plastic for Coal material wizard, but the user can edit them as they see fit. It is highly recommended that the user keep the default properties for the coal strength, but if either the coal strength or the coal modulus are changed, then they should be consistently used between the Elastic Plastic for Coal wizard and the Strain-Hardening for Gob wizard. The third section of the form (Gob Input Parameters) is for entering or calculating the % Overburden Load on the Gob (see Figure 3.7). The first line in this section is for inputting the Width of the Gob Area for which the gob material properties are desired. The user must input the site specific value (rib-to-rib), but several different gob materials for different widths of gob in a single model can certainly be developed. The second line under Gob Input Parameters for the Suggested % Overburden Load on the Gob implements equation 3.21 or 3.22 (as appropriate) to calculate the percentage of overburden load on the gob based on the depth, gob width and abutment angle theory. In the third and final input line in this section ( % Overburden Load on the Gob ), the user can enter a site specific value of the percent overburden load determined from field measurements, observations, etc., or the user can check the box to the right ( Use the Suggested Value ) and the empirically suggested value from the line above will automatically be entered for the % of Overburden Load on the Gob to be used in subsequent calculations. The fourth section of the form is for calculating the Final Gob Modulus that will give the user the desired gob loading. The first three parameters in this Gob Default Parameters section contain default values for the: the Initial Gob Modulus, the Upper Limit Stress for the Gob, and the Gob Height Factor. It is strongly recommended that these default gob parameters be used, but the form does allow a very experienced user to input other values. On the fourth and final line, there is a Define Material Properties for Gob button and the Final Modulus parameter. When the user clicks this final modulus calculate button, the program wizard takes the parameters input on the form and actually produces a two dimensional laminated model with a trial Final Modulus. For this trial final modulus, the corresponding percentage of abutment load on the gob is calculated. The wizard then continues to iteratively select better approximations of the Final Modulus until the Final Gob Modulus which provides the desired percentage overburden load on the gob is determined. This new gob material will then be entered as one of the model materials. So to briefly recap, for the user to calculate a calibrated gob material based on the protocols and equations presented in this report using the new Strain-Hardening for Gob material wizard, they should: 1) Check or Enter the site specific Seam Geometry parameters 2) Check or Enter the site specific Coal Properties 3) Enter the site specific gob width 4) Enter a measured or observed percentage of Overburden Load on the Gob, or use the suggested value 5) Calculate the calibrated Final Modulus for the gob. 32

39 3.5 Calibrating Coal Strength Accurate in situ coal strength is another value which is very difficult to obtain and yet is critical to determining accurate pillar safety factors. It is difficult to get a representative laboratory test value for the coal strength, and then scaling the laboratory values to accurate insitu coal pillar values is not very straightforward or precise (Mark and Barton, 1997) Mark-Bieniawski Formula: For the default coal strength in LaModel, 900 psi is used in conjunction with the Mark- Bieniawski pillar strength formula (Mark, 1999): 2 w w S p = Si (3.24) h lh where: S p = Pillar Strength (psi) S i = Insitu Coal Strength (psi) w = Pillar Width l = Pillar Length h = Pillar Height This formula also implies a stress gradient from the pillar rib that was previously presented as equation 3.14 and is shown here: x σp (x) = Si (3.25) h where: σ p (x) = Peak Coal Stress (psi) x = Distance into Pillar S i = Insitu Coal Strength (psi) h = Pillar Height The 900 psi insitu coal strength that is the default in LaModel comes from the databases used to create the ALPS and ARMPS program and is supported by considerable empirical data. It is the author s opinion that insitu coal strengths calculated from laboratory tests are not more valid than the default 900 psi, due to the inaccuracies inherent to the testing and scaling process for coal strength. If the LaModel user chooses to deviate very much from the default 900 psi, they should have a very strong justification, preferably a suitable back analysis as described below or very accurate field measurements Back Analysis: If the user desires to improve upon the default average 900 psi coal strength, the best technique to determine a more accurate coal strength for LaModel is to back analyze a previous mining situation (similar to the situation in question) where the coal was close to, or past, failure. Back-analysis is an iterative process in which the coal strength is increased or decreased to determine a value that provides model results consistent with the actual measured/observed behavior. This back analysis should, of course, use the previously determined optimum values 33

40 of the lamination thickness and gob stiffness. If there are no situations available where the coal was close to failure, then the back-analysis can at least determine a minimum insitu coal strength with some thought of how much stronger the coal may be. In the users manual, a detailed example of back analyzing accurate coal strength is given Implementation in LamPre3.0: To numerically simulate a yield zone in LAMODEL, concentric rings of different materials are used against the openings and the material properties of the ribs are set such that the pillar yields from the rib inward. This type of yielding behavior matches that observed in the field (see Figure 3.8). In the last few years, a systematic technique for calculating these yielding coal properties based on the Mark-Bieniawski coal strength formula (equation 3.24) and associated stress gradient (equation 3.25) has been developed. Essentially, for an element at the side of a pillar (such as A, C and E in Figure 3.8), the element average peak strength is equal to the stress at the midpoint of the element as determined by equation For the corner elements, (such as B, D, F in Figure 3.8) which are needed to accurately approximate the Mark-Bieniawski pillar strength, the pyramid-like geometry produces an element average peak stress that is equal to the stress at the point one third of the distance across the element as determined by equation Load Bearing Capacity Rectangular Pillar LAMODEL Material Code Representation Figure 3.8 Schematic of pillar loading and material code representation In order to assist the user in implementing the Mark-Bieniawski pillar strength formula in LaModel, a new wizard for defining the properties for the Elastic-Plastic for Coal material has been added to the new LamPre 3.0. The wizard assumes an elastic, perfectly-plastic material model and uses the Mark-Bieniawski pillar strength formula to produce sets of realistic coal material properties for the yield zone at the edge of a pillar or longwall panel (see Figure 3.9). 34

41 The first section of the Elastic Plastic for Coal material wizard contains the Geometry Parameters (see Figure 3.9). The two parameter values (Extraction Thickness and Element Width) were previously entered in the Seam Geometry and Boundary Conditions form of LamPre and are used in the calculation, so they are displayed on this form. The Extraction Thickness can be set to the value previously entered for a particular seam by using the Seam Number edit box or slider. The Extraction Thickness value is site specific and needs to be entered by the user in the Seam Geometry and Boundary Conditions form. Figure 3.9 New wizard for defining Mark-Bieniawski coal properties. The next set of Coal Properties includes: the Coal Modulus, the Plastic Modulus and the Coal Strength. These coal properties are used to define the nature of the coal yielding at the edge of the pillar. The program provides default values for these parameters. The Coal Modulus can be modified to fit the user s conditions. The Plastic Modulus is fixed at 0 psi so that the wizard can accurate match the Mark-Bieniawski pillar strength. The Coal Strength defaults to 900 psi, but the program allows the user to edit it as they see fit. However, it is highly recommended that the user keep the default 900 psi for the coal strength or have a strong justification for changing 35