SOCIETY FOR MINING, METALLURGY AND EXPLORATION, INC.

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1 SOCIETY FOR MINING, METALLURGY AND EXPLORATION, INC. P.O. BOX 6500 LITTLETON, COLORADO PREPRINT NUMBER 06- Enhancements to the LaModel Stress Analysis Program R. Hardy and K. A. Heasley Department of Mining Engineering College of Engineering and Mineral Resources West Virginia University Morgantown, WV Permission is hereby given to publish with appropriate acknowledgments, excerpts or summaries not to exceed one-fourth of the entire text of the paper. Permission to print in more extended form subsequent to publication by the Society for Mining, Metallurgy, and Exploration, (SME) Inc. must be obtained from the Director of the Society. If and when this paper is published by the SME, it may embody certain changes made by agreement between the Technical Publications Committee and the author, so that the form in which it appears is not necessarily that in which it may be published later. Current year preprints are available from the SME, Preprints, PO Box 6500, Littleton, CO ( ). Prior year preprints may be obtained from the Engineering Societies Library, 345 East 47th Street, New York, NY ( ). PREPRINT AVAILABILITY LIST IS PUBLISHED PERIODICALLY IN MINING ENGINEERING

2 ABSTRACT LaModel is a boundary-element program capable of calculating the displacements and stresses in thin bedded deposits such as coal, salt, or potash. Throughout its history, it has continually been upgraded in order to expand analysis detail and stay current with the latest advances in computer technology. The most recent enhancements include: an increased grid size capability, a significant increase in the speed of the automatic grid generation using an AutoCAD visual interface, implementation of subsidence-based horizontal strain calculations for multiple-seam situations, and pillar safety factor calculations. To demonstrate these new features, a multipleseam case study of a longwall panel undermining an active set of main entries is presented. INTRODUCTION LaModel is a boundary-element computer program capable of calculating the displacements and stresses in thin bedded deposits such as coal, salt, or potash mines. This innovative boundary-element program uses a laminated overburden model as opposed to a traditional homogeneous elastic overburden model. The laminated overburden model has been found to provide more realistic stress and displacement calculations, particularly with layered sedimentary geology commonly associated with bedded mines. Since the initial coding of the laminated solution algorithm in 1994 (Heasley, 1998), the program has continually been upgraded in order to increase userfriendliness, expand analysis detail, and stay current with the latest advances in computer technology. Within the previous year, LaModel has been enhanced to accommodate larger grid sizes with faster automatic grid generation, subsidence-based strain and pillar safety factor calculations. to make grid creation easier and faster, an automatic mine grid generator was created. The automatic grid generation has been implemented for both the mine grid and the overburden grids directly within the AutoCAD visual interface (Figure 1) using optimized algorithms in conjunction with Visual C++ and AutoCAD s runtime extension libraries. The result has been a reduction in grid generation times from hours to minutes, even for large mine grids with complicated geometry. With the automatic mine grid generation, the task of mine-map correction became an additional concern because there are often inconsistencies in actual mine maps such as: non-joined polylines comprising a pillar, nonclosed polylines, and duplicate polylines or pillars. Interactively locating and amending these inconsistencies can be very laborious for most users. This once-tedious process of mine-map correction has been successfully automated and simplified within the AutoCAD interface by the development of a number of utility routines for automatically joining pillar polylines, closing pillar polylines, and moving and deleting duplicate pillars. Now, even the most difficult of mine maps may be cleaned up and generated into a LaModel compatible grid within minutes. SUBSIDENCE-STRAIN PREDICTIONS Subsidence-based horizontal strain calculations have also been implemented as an additional feature in the LaModel suite. This enhancement allows the user to consider both multiple-seam vertical stress transfer and subsidence-based horizontal strains in a multiple-seam undermining situation. The calculations used for inter-seam subsidence or remote displacement prediction in LaModel are essentially an influence function method. The convergence of each INCREASED GRID SIZE The grid size available previously in LaModel was 400 elements by 400 elements. With the latest increases in computer speed and the demand for increased model sizes for mining scenarios, it was apparent that a larger grid size was necessary for the updated LaModel.1 release. Therefore, the grid size was increased to a capacity of 1,000 elements by 1,000 elements. With this new grid size, the program running time has not significantly increased since the personal computer speeds have also been increasing. AUTOMATIC GRID GENERATION Previously, when a user wanted to enter mine map data into the LaModel pre-processor grid editor, the mine map layout and geometries had to be entered manually. With larger and more intricate mine models; this was a very challenging and time consuming task. Therefore, in order Figure 1. AutoCAD interface with LaModel grid menu. 3

3 element within the mining seam causes a small subsidence influence on the seam above it. The small subsidence influences from all of the seam elements are numerically integrated to calculate the total subsidence. The general influence function form used for years was empirically developed (Equation 1) (Heasley et al., 004; Heasley, 1998). x + y π R SMAX f S( x, y) = e R (1) S MAX = the maximum subsidence R = the radius of major influence x, y = local horizontal coordinates The influence function used in LaModel has the same general form as the historical influence function, but it is derived mechanistically (Equation ) (Heasley 1998) using the assumption of laminations in the overburden. Therefore, the constants in the equation have physical meaning relating to the overburden material properties. x + y 4λ z 1 W = e 8 π λ z () W= the vertical displacement λ = derived property (Equation 3)(Heasley 1998) z = local coordinate for depth x, y = local horizontal coordinates displacement within the other seam and this will also cause a remote horizontal stress and strain (Figure ). The calculations used for predicting the horizontal strain from the vertical displacement were modeled after the methodology outlined in the National Coal Board s Subsidence Engineers Handbook (NCB, 1975). This methodology involves determining the subsidence of each element at the seam level, finding the slope between adjacent elements, and then calculating the strain using the differential slope (Figure 3). The final equation (Equation 4) suggested by the National Coal Board s Subsidence Engineers Handbook is (NCB p.35, 1975): 1 Slope Slope 1 = 0.04 (4) ε L E ε = strain L E = element length Slope = differential displacement per length In the program, the subsidence-based strains are calculated in both the x and y directions. Once the strains have been determined, they are included in the output file, and can be plotted like any of the other stress items. t λ = (3) 1 1 ( ν ) λ = property of the laminated overburden t = overburden lamination thickness ν = Poisson s Ratio of overburden material Figure 3. Diagram of strain calculation. SAFETY FACTORS Figure. Remote displacement and stress illustration. Using this laminated influence function, elastic theory dictates that whatever happens within one seam will ultimately have an impact on the other seam or seams. If the local seam converges, there will be a resulting remote Many LaModel users are ultimately interested in the stability of the pillar design in their model. Prior to release.1, the pillar stability had to be meticuously calculated from the stresses and displacements included in the output file. With the new release, a pillar safety factor calculation has been implemented into the calculation and included as one of the standard outputs from the program. In the program, there are two types of safety factors available; the element strain safety factor or the pillar strain safety factor. The calculation of these safety factors is based on the users 4

4 choice of the six material models accessible within the program (Figure 4). For the gob materials (which have already failed), the safety factors are set to a default value of zero. This includes the material models for linear-elastic gob, bi-linear hardening, and strain hardening. Figure 5. Idealized mine plan for case study analysis. CASE STUDY Figure 4. The six material models available in LaModel. For the strain-softening and elastic-plastic material models, the strain safety factor is calculated as the ratio between the peak strain defined for that particular element (see Figure 4) and the applied strain: ε P SF = (5) ε APPLIED SF = calculated Safety Factor ε P = Peak strain ε APPLIED = Applied strain For the linear elastic model, which has no pre-defined peak stress or strain, the safety factor is determined by assuming a Bieniawski coal strength (Heasley, 1998). Conventionally, safety factors are calculated on a stress basis, rather than strain. This can be problematic when determining safety factors in the post-failure range in LaModel as inappropriate values result for the elasticplastic and strain-softening material models (Figure 4). The strain-based safety factor calculation detailed above gives equivalent values as the stress-based calculation in the prefailure range but also gives appropriate values in the postfailure range for all the materials; therefore, this safety factor calculation is used. The second type of safety factor calculation available in LaModel is the pillar safety factor. The principles for calculation are essentially the same as those for the element safety factors; however, in this case, the safety factor from each of the individual element in a pillar is totaled and then averaged for the entire area of the pillar. In order to test the functionality of these new features, a sample case study was performed. This case study was taken from the literature (Ellenberger et al., 003) and documents a situation where a longwall panel undermines an active room-and-pillar, mainline development. The upper room-and-pillar mine was extracting the 9 ft thick Coalburg seam using a seven-entry mainline with 40 ft x 80 ft pillars. The lower longwall mine had a 5.6 ft seam height in the No. Gas and was retreat mining a 1000 ft wide longwall panel directly under the overlying mains of the room-and-pillar mine. The average interburden thickness at this site was approximately 560 ft and the maximum overburden of 400 ft overlaid the upper mine (Figures 5). (For the idealized study in this paper, the mains are modeled as being perfectly aligned with the middle of the longwall panel and all of the pillars in the mains and the gateroads are modeled with consistent sizes. In reality, the mains were somewhat offset from the center of the longwall panel and slightly skewed to the longwall advance. Also, the pillars in both the mains and the longwall gateroads have some variations in dimensions due to practical and operational considerations (Ellenberger et al., 003).) As the longwall advanced, the upper seam experienced tension cracks which developed in the roof when the underlying face approached within 70 ft. Roof and rib control problems continued to intensify and worsen as the longwall progressed and pushed beyond the upper seam. The sandstone in the upper mine roof fractured significantly, creating some fissures measuring in excess of four inches; while numerous roof falls occurred in conjunction with substantial pillar spalling. As the dynamic phase of subsidence passed and a new equilibrium was reestablished, the ruptures in the roof mostly closed and conditions improved considerably. To accurately reflect the mine plan, a three- 5

5 Strain (microstrains) Strain Profile for Upper Seam During Mining 3.5 E-3.5 E E E E E E-3 Distance Across Panel (ft) Figure 6. LamPlot output for Upper Seam Subsidence due to mining lower seam. dimensional LaModel model was developed. A 50 x 50 element grid with ten foot element widths was used to represent the idealized mine plan. After entering the input, using mostly the default material parameters, and appropriately generating the grids, the LaModel program ran in approximately three hours. The resultant remote displacement experienced in the upper seam from the undermining longwall panel was approximately 3.5 feet, as illustrated by the LaModel output (see Figure 6). This resulting predicted subsidence was consistent with measurements and observations recorded in the field. The subsidence induced strain which caused the tension cracks in the roof of the upper seam is illustrated in the LamPlot output for the strain parallel to the x-direction (Figures 7 and 8). (The sign convention used in LaModel is that tension is negative, while compression is positive.) It can be seen in the figures that the tensile stress ahead of the longwall and the compressive stress following the longwall are in excess of 000 micro-strains. Figure 8. A cross section of the strain in the X direction down the centerline of the upper mains. According to the experience of the National Coal Board (NCB, 1975) with surface structures, a strain of 50 microstrains over a distance of 150 ft can cause severe damage; however, the relationship between subsidenceinduced strain and the corresponding damage to the underground roof has not previously been well defined. The calculated 00 microstrains may indeed be consistent with the observed roof cracking and subsequent falls, but more experience with the program is necessary before any predicted results can be considered dependable. Figure 9. Pillar safety factors for the upper seam. Figure 7. Strain in the X-direction for the upper seam. It was reported that there was some pillar spalling in the upper mine; however, there was no observed pillar failure. The pillar and element safety factors shown in Figures 9 and 10 illustrate that most of the safety factors are above 1.00; however, some of the pillars in front of the moving longwall face have safety factors less than one. This is close to the observations, but the calculated pillar safety factor may be a bit conservative. Figure 7. Strain in the X-direction for the upper seam. 6

6 Mines, Department of Mining and Earth Systems Engineering, 187 p. Kratzsch, H. (1983), Mining Subsidence Engineering, translated by R.F.S. Fleming, Springer Verlag, Berlin, 543 p. National Coal Board (NCB) (1975), Subsidence Engineers Handbook, 110 pp. Figure 10. Element safety factors in the upper seam. SUMMARY AND CONCLUSIONS It can easily be seen that the new developments added to the LaModel program improve its functionality and practicality, and in many cases, actually decrease the modeling time and effort. This new release (.1) makes available the first three-dimensional multiple-seam analysis package capable of automatically calculating the safety factors and multiple-seam induced subsidence and strain. Also, the new larger grids and faster grid generation greatly increase the ease-of-use and practicality of the program. REFERENCES Ellenberger, J., F. Chase, C. Mark, K. Heasley and J. Marshal (003), Using Site Case Histories of Multiple Seam Coal Mining to Advance Mine Design. Proceedings of the nd International Conference on Ground Control in Mining, Morgantown, WV, August 5-7, p Heasley, K.A. and O. Akinkugbe (004), A Simple Program for Estimating Multiple Seam Interactions. Proceedings of The Society for Mining, Metallurgy and Exploration, Inc. Annual Conference 004, preprint # Denver, CO; Heasley, K.A. and G. Chekan (1998), Practical Stress Modeling for Mine Planning. Proceedings of 17 th International Conference on Ground Control in Mining. Morgantown, WV, pp Heasley, K.A. (1998), Numerical Modeling of Coal Mines with a Laminated Displacement-Discontinuity Code [Dissertation], Golden, CO: Colorado School of 7