Introduction
Background
The tragic coal bump accidents at Crandall Canyon Mine in August 2007 highlighted the persistent issue of coal bumps, reigniting public interest in the topic Ongoing incidents at Aberdeen and West Ridge Mines, along with new bump occurrences at Bowie and West Elk Mines, further emphasized the need for research in this area Over the decades, the Bureau of Mines and NIOSH, alongside various researchers, have made significant advancements in understanding the conditions that lead to coal bumps and developing effective mitigation techniques.
1995) However, we are still a long way from accurately predicting exactly when and where coal bumps will occur The exact mechanics that generate a coal bump are not understood
A promising technique for analyzing coal bumps is the calculation of the Energy Release Rate (ERR), which quantifies the gravitational potential energy released from the rock mass during mining This energy can manifest passively as heat and sound or dynamically as pillar bumps and rock bursts Significant energy releases over a short duration may indicate the timing and location of these coal bumps or rock bursts By adjusting the mine plan, it is possible to distribute energy releases over time and space, potentially reducing the risk of dynamic failures.
Statement of the Problem
In the United States, the Energy Release Rate (ERR) has been utilized in the MULSIM/NL program, yielding significant findings in various studies Heasley and Zelanko (1992) established a correlation between ERR values and the occurrence of coal bumps, while Zipf and Heasley (1990) optimized retreat mining cut sequences using ERR to mitigate coal bump risks in room-and-pillar operations Although the LaModel program has largely replaced MULSIM/NL for boundary-element modeling of coal mines, it has yet to integrate Energy Release Rate calculations.
Statement of Work
This report introduces energy calculations into the LaModel program, enhancing it as a modern coal mine modeling tool that assesses the bump proneness of mining plans using energy principles By integrating these calculations, users can utilize advanced features such as automatic grid generation and various wizards to efficiently create energy release maps, ultimately reducing the risk of bumps in mining operations.
LaModel incorporates various energy calculations for its material models, categorized into two primary groups: Static (input energy) and Dynamic (released energy) Static energies pertain to the strain energy input and stored in seam materials at specific strain levels The system features several calculations for static energy to accurately assess these parameters.
2) The stored elastic energy, and
Dynamic energy values reflect the energy changes in materials during mining processes, primarily linked to variations in an element's stress and deformation while remaining on the same material curve However, for certain elements, energy changes coincide with nearby mining activities when transitioning between material types The model incorporates specific dynamic energy calculations for each element.
1) An increase in dissipated energy,
After the energy calculations were implemented into LaModel, the mathematics and coding were validated (in addition to manual check calculations) by using four pillar cut sequences that
In the studies conducted by Heasley (1990) and Heasley and Zelanko (1992), four cut sequences were identified: open ending, pocket and wing, split and fender, and the Olga method The validation analysis revealed that the general trends from the previous analysis were consistent with the new LaModel ERR calculations, although some variations were noted.
1.3.3 Case Study Demonstration of ERR Calculations:
The energy release calculations in LaModel are applied to a case study that highlights their utility and accuracy This analysis focuses on various pillar recovery cut sequences attempted at a bump-prone mine in Southern Appalachia, originally examined by Newman (2008) through pillar stress distributions and field observations The LaModel energy calculations for these cut sequences demonstrate a good correlation with both field observations and Newman’s original stress analyses, providing a quantifiable index of bump potential.
Literature Review
Background
The former U.S Bureau of Mines and NIOSH have extensively researched coal bumps, which are sudden expulsions of coal from mining faces In the early 1990s, studies by Zipf and Heasley aimed to investigate the geologic strain energy associated with these events, hypothesizing that energy calculations could enhance understanding and potentially predict coal bumps It is well-established that mining activities redistribute the gravitational potential and tectonic strain energy within the rock mass, leading to increased elastic strain energy in surrounding rocks This redistributed energy can either be dissipated as passive forms like heat and sound or manifest as dynamic energy, resulting in damaging occurrences such as rock bursts or coal bumps.
The Energy Release Rate (ERR) has historically been linked to the risk of damaging rock bursts, with its concept originating in the 1960s in South African deep hard-rock mines Over time, advancements in ERR computation have made its application in burst-prone hard-rock mines more prevalent However, its use in bump-prone coal mines remains limited Crouch and Fairhurst demonstrated a technique for optimizing cut sequences to control bumps using energy release calculations, while Maleki et al analyzed mining plans for active mines facing bump issues through energy and stress calculations The U.S Bureau of Mines showcased a unique cut sequence that maintained uniform energy release to minimize bump potential Heasley later confirmed the correlation between energy release and bump behavior through back analysis of actual events, and further studies evaluated dissipated energy in various mining scenarios, establishing a fair correlation with coal bumps.
In the 1990s, energy release rate calculations by the Bureau of Mines utilized the MULSIM/NL program, which employed the displacement-discontinuity variant of the boundary-element method (BEM) to analyze stresses and displacements in coal seams This program calculated energy quantities based on the resulting stresses and displacements in the seam materials However, over the past decade, the LaModel program has largely supplanted MULSIM/NL for modeling stresses and displacements in coal mines, thanks to its laminated overburden model that provides greater accuracy for horizontally bedded sedimentary rocks Unlike MULSIM/NL, LaModel has seen continuous updates to adapt to evolving operating systems and programming languages, although it lacks built-in energy release rate calculations.
The Energy Release Rate (ERR), developed in South Africa, is closely linked to the risk of dangerous bumps and rock outbursts in mining Initial research by Cook et al (1966) highlighted significant energy changes during mining operations, leading to the development of various energy calculations, including the ERR, which aid engineers in managing these hazards Despite establishing a foundational understanding of the ERR, Cook and his colleagues did not provide a sufficiently rigorous derivation of the concept, as noted by Salamon (1984).
In 1984, Salamon conducted the first thorough analysis of energy calculation and the energy release rate (ERR), building on Cook's earlier observations from over two decades prior Salamon's overview highlights that the initial part of the energy balance encompasses all recognized forms of energy expenditure, while the subsequent part addresses the surplus energy that needs to be dissipated This surplus energy can manifest as either passive forms, such as sound and heat, or kinetic forms, like bumps.
In his paper, Salamon elaborates on key energy quantities essential for assessing the ERR, including the work performed by external and body forces through induced displacements (W), the strain energy content of the mined rock volume (Vm) (U'), the change in strain energy in the unmined system volume (V) (U), and the total work exerted by contact and body forces on permanent supports (Ws) Figures 2.1 and 2.2 illustrate these concepts, with Salamon's notations indicating areas in state I (S0) and state II (Sm), as well as the volume of the opening in state I (V0).
Figure 2.2: Mining configuration and notations in the reference state, in state I (a), and after mining, state II (b), (after Salamon, 1984)
The work done in deforming the permanent supports is modeled as nonlinear with a strain hardening response
Based on these energy quantities, the released energy (WR) can be calculated with the following equality for tabular excavations:
Salamon outlined the application methods for tabular excavations, primarily employing the displacement discontinuity, or "slit," concept He identifies four key advantages of utilizing the displacement discontinuity model in energy analysis, enhancing its effectiveness and accuracy.
1) While the displacements are discontinuous when moving perpendicularly across the seam, say from the roof to the floor of the excavation, the stresses remain continuous
2) The weights of the extracted rock and of the backfill are neglected, and their volumes are taken to be zero
3) As a result of (1) and (2), the induced traction, T i (i) , can be taken to be zero on S, which is on the surface enveloping the whole system
4) A further consequence of (1) and (2) is that the work done by forces acting on the surfaces of excavations can be expressed as an integral of the forces acting through the relative displacement on the roof and floor
The final expression derived by Salamon for the total released energy is a function of the primitive stress or traction vector (Qi) This expression is crucial for calculating energy release rates in tabular deposits.
Ri = traction vector of the support si = displacement vector αi = nonlinearity parameter dA = elementary area
Salamon’s derivation of released energy is accurate, but there are concerns regarding its validity, particularly as the mined volume (Vm) decreases, leading to a corresponding reduction in energy release In the limit where Vm approaches zero, energy release also diminishes, necessitating the assumption of equal step sizes for valid comparisons of energy release and associated ERR Additionally, the assumption of elasticity in seam material, especially under high stress conditions in coal, raises questions The subsequent section will discuss how the ERR is integrated into the MULSIM/NL program to address these concerns.
In LaModel 3.0, the strain energy remains consistent, while modifications are made to the kinetic energy and the energy released during the deformation of supports Unlike Salamon's assumption of linear elastic material behavior, LaModel 3.0 allows for transitions between different materials or openings under a linear shift assumption Additionally, the calculation for energy released in deforming supports has been updated to eliminate the linear shift assumption and the non-linearity factor (α), opting instead for a direct calculation using the gob energy equation.
2.1.2 ERR Implementation into MULSIM/NL:
The ERR calculation, previously absent from the LaModel software, was featured in its predecessor, MULSIM/NL, utilizing equations derived by Salamon and adapted by Zipf (1992) In this context, the stored energy release (WRS) and kinetic energy release (WRK) are represented by the first and second bracketed terms, respectively The first term of WRS accounts for the elastic energy stored in elements at step I, which is released during mining between steps I and II, while the second term typically considers body forces to be zero in the displacement discontinuity method In the kinetic energy release calculation, the first term reflects the gravitational potential energy input into mined elements, and the second term quantifies the kinetic energy released from compressing the non-linear gob area.
TI = rock mass stress in state I u I = displacements in state I Δu = change in displacement from state I to state II ΔR = change in gob (backfill) stress from state I to state II
S M = surface area mined this step
In the context of backfill materials, SGII represents the surface area of the gob in state II, while α denotes a nonlinearity factor that varies depending on the material properties; it equals 1 for linear materials and is less than 1 for strain-hardening materials Additionally, ds refers to the differential area, and dv signifies the differential volume.
Zipf’s notation illustrates the transition from state I to state II in mining, as depicted in Figure 2.3 He suggests that the ERR (Energy Release Rate) can serve as a quantitative measure for both rock burst and coal bump potential Additionally, Zipf acknowledges Salamon’s findings regarding the dependence of step size in ERR calculations, indicating that as the mining step diminishes, the kinetic energy released also approaches zero Consequently, when the step size nears zero, the released energy is primarily derived from the strain energy of the mined material, while the kinetic energy release decreases rapidly, as shown in Figure 2.4.
Figure 2.3: Basic notation for energy calculations as mining progresses from state I to state II
Figure 2.4: Step-size dependence of energy release components for radial expansion of a circular tunnel (Zipf, 1992)
In MULSIM/NL energy quantity calculations, three specific scenarios can complicate the mathematics involved Case A occurs when the newly-mined area, regardless of its shape, perfectly balances the newly gobbed/backfilled area, resulting in the open area remaining the same in both state I and state II In Case B, the gob/backfilling process lags behind the mining, leading to an increase in the open area Conversely, Case C arises when the gob/backfilling surpasses the mining activity, causing a decrease in the open area.
Figure 2.5: The three special cases of mining progress from state I to state II showing how elements can undergo six different status changes between state I and state II (after Zipf, 1992)
The ERR subroutine in MULSIM/NL calculates six energy quantities for each element Three dynamic energy quantities:
1) Strain Energy Release (Stored Energy Release)
Nonlinear component (backfill and/or gob)
3) Total Energy Release and three static energy quantities (See Figure 3.2):
Implementation of Energy Release Calculations in LaModel
Linear Elastic Coal
The static energy equations for all linear elastic materials are uniform Specifically, the equations for Linear Elastic Coal and Linear Elastic Gob are presented in the following formulas.
WT = total input energy σ = element stress
SM = the surface area of the element ε = strain h = mining height and where the displacement (u) of the element is equal to the element strain (ε) times the mining height (h): ε h u (3.4)
Equation 3.1 is essentially equal to equation 2.4 and the first term of the stored energy release in equation 2.3.
Strain Softening Coal
The second coal material in LaModel exhibits a stress-strain behavior characterized by an initial increase in stress along a linear curve until reaching peak stress and strain Beyond this peak, stress decreases while strain continues to rise until reaching residual stress, where strain increases at a constant residual level For this material, calculating dissipated energy is beneficial, defined as the difference between total input energy and stored elastic energy The equations for static energy quantities depend on the position on the stress-strain curve; if the location is at or below peak strain (ε ≤ εp), the area under the curve is calculated as a triangle, utilizing the same equations as linear material models.
In the strain softening region of the curve, the strain level is defined between the peak strain (εp) and the residual strain (εr), specifically where εp ≤ ε ≤ εr To facilitate calculations, the incremental strain (εi1) beyond the peak strain is measured The area under this curve represents the total energy input, combining the energy up to the peak strain and the energy from the peak strain to the current strain level Assuming consistent loading and unloading moduli, the energy values for the strain-softening segment can be derived using Equation 3.5b.
When the material is in the residual portion of the stress-strain curve, the strain level exceeds the residual strain (ε > εr) In this scenario, the total energy is calculated by summing the energy input across all three sections of the curve For accurate calculations, the incremental strain between the peak and residual strain (εi1) and the incremental strain beyond the residual strain (εi2) are identified It is also assumed that the loading modulus and unloading modulus are equal.
Where: σp = peak stress σ p = peak strain r = residual strain i1 = first incremental strain i2 = second incremental strain
Elastic Plastic Coal
The most widely used material model for simulating coal is integrated into the LamPre material wizard This model demonstrates an increase in stress along the initial linear segment of the curve until it reaches peak stress, after which it transitions into the plastic curve During the linear phase, static energy values are computed using equations applicable to linear elastic materials Specifically, Equation 3.6a outlines the static energy calculations for elastic-plastic materials when the strain level is less than the plastic strain (ε ≤ εp).
When the strain value exceeds the plastic strain (ε > εp) on the stress-strain curve, the total input energy comprises both the triangular area beneath the linear segment and the area under the plastic region of the curve Equation 3.6b illustrates the static energy calculations specific to the plastic portion of the curve.
Where: σp = peak stress p = peak strain
Linear Elastic Gob
The linear elastic gob material closely resembles linear elastic coal material, with the inclusion of the gob height factor To calculate static energy quantities for both materials, specific equations are utilized to determine the static energy values.
Strain Hardening Gob
This material model is the most widely used gob material since it is incorporated into the
The Gob Wizard in the LamPre program utilizes a non-linear model for gob material, characterized by hardening as stress increases The total input energy for this material is represented by the area under the stress-strain curve, as illustrated in Figure 3.2.
The derivation of this equation can be found in Appendix A
Sp = current strain n = gob height factor
The total energy input to the element (WT) can be calculated by multiplying the element area (SM) by the seam height (h), as outlined in equation 3.10 Assuming the unloading modulus is equal to the final modulus (Ef) and utilizing effective stress and strain values, the static energy quantities for the strain hardening gob can be expressed as h/2E S.
Bilinear Hardening Gob
The gob material facilitates initial hardening along a linear segment of the stress-strain curve until the offset stress is achieved Once this threshold is reached, the gob exhibits a more rapid hardening rate along the final linear section of the curve For strain levels within the initial hardening phase (ε ≤ εo), energy values can be calculated using equations 3.14a.
When the material is in the final hardening stage of the stress-strain curve (ε > ε₀), the total input energy is determined by calculating the area under both sections of the curve In this scenario, the unloading modulus is considered equivalent to the hardening modulus, and the energy values are specified by equations 3.14b.
Where: σo = offset stress o = offset strain
Implementation of Dynamic Energy Calculations into LaModel
Dynamic energy values reflect the energy changes in materials during mining processes Typically, these energy changes correlate with variations in an element's stress and deformation while remaining on the same material curve However, for certain elements, energy changes are linked to one of three significant material transformations that occur between mining steps.
1) The element can change from one material to another (a cut can be taken nearby and the element changes to a weaker element, or a coal element can change to a gob element after it is mined);
2) The element changes from a material to an opening (typically immediately after it is mined), or;
3) The element changes from an opening to a material (typically a gob material as the element moves into the gob)
For each element in the model, there are specific dynamic energy changes that occur These dynamic energy changes are:
1) An increase in dissipated energy,
2) A stored energy release (Zipf’s strain energy release),
The increase in dissipated energy applies only to an element that remains the same material between steps and is equivalent to the change in dissipated energy between the first and second steps This increase is determined by the difference between the energy input along the stress-strain curve and the change in energy stored in the element during these steps Specifically, it is calculated by subtracting the dissipated strain energy in the first step from that in the second step.
WD= change in dissipated energy
WDII = step two dissipated energy
WDI = step one dissipated energy
Figure 3.3: Increase in dissipated energy between step 1 (left) and step 2 (right)
The release of stored energy is determined by the difference in elastic energy between the first and second steps, equating to the negative change in stored energy This energy value can be calculated for all elements, regardless of whether they remain the same material or transition to a different material between the steps.
Where: ΔWS = the change in stored energy
WSI = step one stored energy
WSII = step two stored energy
Kinetic energy represents the energy transferred to an element as it transitions between different stress/strain points on distinct material curves This concept is crucial in understanding material behavior under varying conditions.
In the original work from 1984, the focus was on the energy released from elastic elements transitioning to an opening Initially, the elastic element was at point B on the stress-strain curve and moved to point D, representing an opening with zero stress and increased displacement The energy released during this material change is calculated by subtracting the total stored energy at point D (zero) from the total stored energy at point B (area ABC) The kinetic energy input during this transition is determined by the average stress multiplied by the displacement (area BCD), which represents the gravitational potential energy from the overburden as the roof converges Since the element at point D has no stored energy, the kinetic energy release equals the total kinetic energy input between the steps (area BCD), resulting in the total energy release for the element being represented by area ABD.
In the calculation of kinetic energy release during material changes, an element transitions from one material curve to another, similar to the removal of an elastic element For example, when an elastic coal element shifts to an elastic gob element, the kinetic energy and energy release values are determined by comparing the stored energy at different points on their respective stress-strain curves The energy release is calculated by subtracting the total stored energy of the gob element from the initial stored energy of the coal element The kinetic energy input during this transition is represented by the average stress multiplied by the displacement between the two material states Ultimately, the kinetic energy release is derived from the total energy input minus the final stored energy, and this calculation specifically applies to elements undergoing material code changes, assuming a linear transition between stress/strain locations on the material curves.
II= stress at step two u= change in displacement
Figure 3.4: Figure showing kinetic energy released from Salamon (left) and the extrapolation to the release from a material to material change (right)
After calculating the three types of energy release for an element, the total energy release is the cumulative sum of all energies released during the mining process For elements remaining on the same material curve, the total energy release (E R) corresponds to the increase in dissipated energy between the mining steps.
For an element that changes material curves, the total energy release is the sum of the stored energy release and the kinetic energy release between the given steps
Validation of the ERR Calculations
Prior Research Using MULSIM/NL
This thesis reexamines a case study on pillar recovery cut sequences using the LaModel program, originally published by the US Bureau of Mines based on data from the Olga Mine in southern West Virginia (Zipf and Heasley, 1990) The study investigates how modifications in cut sequences can influence changes in the Energy Release Rate (ERR) By modeling various cut sequences—including single split and fender, pocket and wing, open ending, and the Olga Mine method—the research aims to chart the maximum ERR and its uniformity over time The primary objective is to identify which cut sequence minimizes the risk of bumps, based on energy release rate calculations.
The initial study was conducted in two phases, beginning with a linear elastic coal model followed by a non-linear coal model The material properties for these coal models were derived through back calculation using field data collected from the mine in 1989 by Campoli (Zipf and Heasley).
A study conducted in 1990 found that the non-linear coal model likely provided a more accurate representation of coal recovery methods The research indicated that while the Olga Mine method showed only slight improvements in maximum observed extraction recovery rate (ERR) compared to other methods, it significantly excelled in ERR uniformity Consequently, the findings suggest that both the uniformity of ERR and its absolute magnitude should be evaluated together when assessing recovery methods.
Zipf and Heasley (1990) highlight the challenges in ERR calculations, emphasizing that the area mined per step must remain consistent to ensure valid comparisons between cut sequences, as noted by Salamon Unequal step sizes can lead to misleading results, masking energy release spikes and creating a false sense of uniformity Ideally, each mining step should minimize the extraction area, balancing this with practical computing limitations Non-linear material models are essential for accurately representing coal yield and load transfer in real-world scenarios Additionally, identifying the optimal mining method based on maximum ERR is complicated, as changes are often minimal (typically less than 10%) A more effective approach may be to assess cut sequence superiority by examining the uniformity of ERR over time and space Significant ERR increases are commonly observed during the extraction of highly stressed pillar cores, and as discussed in Chapter 5, strategically cutting into these stressed areas before full extraction can help mitigate the risk of bumps.
When comparing different models, it is essential to use the same rock mass modulus, which leads to a paradox in the application of the Energy Release Rate (ERR) to coal mine bumps Generally, coal bumps are more likely to occur in seams surrounded by strong, competent strata like thick sandstone, while they are less likely in seams surrounded by weaker strata such as shale Sandstone typically has a high rock mass modulus, whereas shale has a lower one However, Boundary Element Model (BEM) calculations show that the ERR inversely correlates with the rock mass modulus, suggesting that seams surrounded by softer rock like shale would have a higher bump risk, contradicting practical observations Despite this paradox, the ERR calculation remains valuable; using a consistent rock mass modulus allows for meaningful comparisons between different cut sequence models Nonetheless, the current ERR value cannot serve as a definitive threshold for predicting bump occurrences.
The case study by Zipf and Heasley (1990) demonstrates that the Olga Mine method for pillar recovery is more effective in bump-prone mines compared to other methods This technique gradually reduces pillar stiffness several rows ahead of the advancing gob line, which helps decrease overall strain energy and maintains uniformity in the energy release rate (ERR) To further mitigate coal bump risks, a nonlinear boundary element method (BEM) like MULSIM/NL, utilizing nonlinear material models, can be employed to assess various mining cut sequences, ensuring that necessary precautions are taken.
Cut Sequence Analysis with LaModel
The validation of the ERR calculations in LaModel involved replicating the analysis of four previously published pillar retreat cut sequences (Zipf and Heasley, 1990; Heasley and Zelanko, 1992), alongside manual test calculations (refer to Appendix B) These sequences were initially analyzed using the MULSIM/NL boundary element program, which employs a homogeneous overburden model, contrasting with LaModel's laminated overburden model Due to this fundamental difference, an exact match between LaModel's energy results and those from MULSIM/NL was not anticipated; however, similar trends were expected The analysis focused on the Open Ending (OE), Pocket and Wing (P&W), Single Split and Fender (SS&F), and Olga cut sequences, as illustrated in Figure 4.1 (Zipf and Heasley, 1990; Heasley and Zelanko, 1992).
The first verification study examined the total energy release from four different pillar retreat cut sequences, replicating the elastic material models developed by Zipf and Heasley (1990) Total energy release was calculated over the area of the extracted pillar, specifically analyzing the Olga cut sequence, which involved multiple pillars Similar trends to those observed by Zipf and Heasley with MULSIM/NL were noted with LaModel, albeit with some variations; notably, LaModel's total energy release was approximately half that of MULSIM/NL, likely due to differences in roof stiffness between the models Both programs indicated that the Olga cut sequence produced the highest peak energy releases, while the open ending cut sequence yielded the lowest The energy release curves for the Olga and split and fender cut sequences were very similar, with differences attributed to variations in element stress locations and failure timing, influenced by differing overburden responses Additionally, minor changes in coal behavior could significantly alter the timing and location of calculated energy releases.
Figure 4.2: MULSIM/NL total energy released versus cut (after Zipf and Heasley, 1990)
Figure 4.3: LaModel total energy released versus cut
The second verification study examines the change in dissipated energy across mining steps for four cut sequences, utilizing strain-softening coal properties from the Olga Mine as established by Heasley and Zelanko (1992) The total dissipated energy was calculated over the entire model area, revealing consistent trends between the MULSIM/NL and LaModel analyses, albeit with some variations Notably, energy values from MULSIM/NL were approximately four times higher than those from LaModel Both models indicated that the first three steps of the cut sequences exhibited the highest energy releases, while the open ending cut sequence showed the lowest peak energy releases, with significant energy distribution occurring after cut 4 In LaModel, the highest dissipated energy was observed in cut 1, contrasting with cut 2 in MULSIM/NL, and the peak energies between the two models appeared somewhat disordered These minor discrepancies in results can likely be attributed to differences in element stress locations and timing of failures, influenced by varying overburden responses.
Figure 4.4: MULSIM/NL dissipated energy release versus cut (after Heasley and Zelanko,
Figure 4.5: LaModel dissipated energy release versus cut.
Case Study Demonstration of ERR Calculations
Prior Research Using LaModel
Prior to this research, the ERR calculation was absent from the LaModel program, unlike in MULSIM/NL Despite this limitation, LaModel has remained a valuable tool for assessing potential risks Newman (2008) highlighted two instances where LaModel effectively determined a safe pillar recovery plan through comprehensive stress analysis.
The Darby Seam in Eastern Kentucky features high-quality metallurgical-grade coal known for its low sulfur content and high BTU, making it suitable for stoker applications This coal exhibits both brittleness and strength, with an insitu strength of 984 psi Harlan County, the focus of the case studies, has a history of extensive mining in the Darby seam, which is also recognized for coal bump occurrences These coal bumps are linked to the area's distinctive geology, significant topographic relief, and rigid overburden characteristics.
The local geology features a roof of competent sandstone, typically around 50 feet thick, and a floor composed of hard shale or sandy shale The area is characterized by long, steep ridges, with relief ranging from 1,800 to 2,000 feet Consequently, while mines usually access the coal seam from the outcrop, they can encounter overburden depths of 1,000 to 1,500 feet rapidly.
Multiple seam mining is commonly practiced in the region, but stacking pillars is usually not feasible due to various factors Different operators often mine simultaneously without sharing proprietary information, while distinct mineral owners aim to maximize their recovery Additionally, previous workings may feature random pillar layouts with irregularly shaped remnants Consequently, coal bumps in the area can be attributed to thick overburden, massive competent formations surrounding the coal seam, and stress concentrations resulting from multiple seam mining.
In the mine studied by Newman, full retreat mining was performed utilizing continuous haulage centers with an average mining height of 66 inches To address the challenges posed by the continuous haulage system and to reduce the occurrence of bumps, five distinct cut sequences were implemented Throughout the year, a total of eight bumps were recorded.
Mine No 1 - History of Bump Events Event Date Section Cross-cut Entry Cover Plan Lift
Table 5.1: Timing, Location, and Circumstances of Coal Bumps (after Newman, 2008)
Initially, the recovery of pillars was implemented using the “Close In 3” (CI3) plan, which involved retreating from the outside toward the belt entry This approach led to significant stress on the last cuts, particularly the half pillars adjacent to the belt entry, resulting in four out of eight bump occurrences To mitigate the concentrated stress, the recovery strategy was revised to the “Close In 5” (CI5) plan, where pillars are retreated sequentially from left to right While this modification reduced stress on the previous cuts, bumps still occurred during the initial cuts into the last full pillar, and access for the haulage system to these final cuts became restricted, necessitating the use of a shuttle car.
The "Close In 4" (CI4) plan, also known as the mirror-image close in 2, was implemented to optimize mining operations In this strategy, the fifth entry is initially retreated, followed by the mining of entries 1 to 4, concluding with the extraction of the final two half pillars near entry 4 Notably, bumps were observed during the cutting of these last two half pillars, which occurred in step 36 This approach facilitates access for the haulage system to all cuts, but it also introduces stress from mining activities on both sides of the panel.
Figure 5.1: Close In 3 (Middle) retreat plan (hatching indicates bump location) (after Newman,
Figure 5.2: Close In 5 retreat plan (hatching indicates bump location) (after Newman, 2008)
Figure 5.3: Close In 4 (mirror of close in 2) retreat plan (hatching indicates bump location)
Newman decided to utilize the LaModel program for numerical modeling of both previous and new retreat mining plans, focusing on a cut-by-cut analysis to identify highly stressed cuts The models were calibrated using field data, incorporating physical information from 389 samples collected since 1986 Key inputs included physical samples, cut sequence geometry, and thick overburden, while additional inputs were based on field conditions A significant lamination thickness was employed to represent the stiff massive layers of overburden, alongside a hanging gob scenario to simulate the cantilevering of the main roof over the gob.
The implementation of "bump cuts"—strategically made cuts in the center of the pillar during the outby crosscut—serves as an effective method for destressing pillars before extraction The Close in 4 with bump cuts (CI4 BC) sequence closely resembles the standard CI4 sequence, with the key difference being the execution of bump cuts in the outby pillar row during the mining process (cuts 19-22) Similarly, the Close in 5 with bump cuts (CI5 BC) sequence mirrors the CI5 approach, but incorporates bump cuts in the active pillar row prior to mining each entry from left to right (cuts 1-4).
A single bump event was recorded during the mining of a bump cut under 1950 feet of cover
Figure 5.4: Close In 4 retreat plan with bump cut taken prior to retreat mining (after Newman,
Figure 5.5: Close In 5 retreat plan with bump cut taken prior to retreat mining (after Newman,
Modeling with LaModel was conducted on the CI3, CI5, and CI4, considering scenarios both with and without bump cuts Two approaches for implementing bump cuts were analyzed: one in the outby pillar row and the other in the active pillar row, prior to further retreat mining All scenarios were assessed under high average overburden conditions of 1,784 feet and 2,000 feet, incorporating both hanging and non-hanging gob models.
Numerical modeling results indicate that the CI3 and CI4 plans concentrate front and side abutment pressures on the remaining pillars near the panel center, leading to larger, highly stressed cuts, as confirmed by the mine's bump history (refer to Table 5.1) In contrast, the CI5 plan emerged as the optimal choice for bump control, although it necessitates the use of a shuttle car.
Numerical modeling indicates that bump cuts are effective only when executed before retreat mining; if applied during the retreat process, they fail to relieve stress and may trigger bumps in highly stressed areas While both the CI5 and CI4 alternatives show effectiveness in pre-retreat models, their implementation underground poses challenges, necessitating the movement of the miner and bridge system to create cuts prior to mining However, the company found this method to be unproductive and economically unviable.
The company has chosen to cease retreat mining in sections where the overburden exceeds 1,700 feet and sandstone thickness surpasses 50 feet To mitigate side abutment pressures from neighboring panels, larger barrier pillars have been implemented between adjacent mining areas.
Practical Application
To effectively apply energy calculations in the LaModel 3.0 program, users must successfully utilize the LamPre 3.0 and LamPlt 3.0 programs While these new programs share similarities with their LaModel 2.1 predecessors, they offer several additional options for enhanced user experience.
The Program Control Parameters form in the LamPre 3.0 program includes both control and solution options for the model While the control options have not changed from LamPre 2.1, the solution options now feature an additional checkbox By selecting the “Include Energy Calculations” checkbox, users instruct the LaModel 3.0 program to execute energy calculations as outlined in Chapter 3.
Figure 5.6: The Program Control Parameters form in LamPre 3.0
After running the input file in LaModel 3.0, which retains the same user interface as LaModel 2.1, users must utilize the LamPlt 3.0 program to process the generated output file The key enhancement in LamPlt is the expanded list of stress items, increasing from 12 to 18 across all plot types, including colored square, cross section, history, and fishnet plots For instance, Figure 5.7 illustrates a colored square plot featuring the Dissipated Energy stress item.
Figure 5.7: LamPlt 3.0 Colored Square Plot Options
Figure 5.8: LamPlt 3.0 Dissipated Energy colored square plot
While a colored square plot effectively visualizes energy quantities in LaModel, it is less suitable for detailed model analysis and comparison In the case study by Newman (2008) using LaModel 3.0, the history plot proved to be more beneficial Figure 5.9 illustrates the History Plot dialog box with the Total Energy Released stress option selected, displaying the same coordinate range utilized in the case study, along with the selected total stress value.
Figure 5.9: LamPlt 3.0 History Plot Options
Selecting this stress item reveals a history plot of the Total Energy Release (see Figure 5.10) This plot facilitates the comparison of stress items across different steps, serving as a valuable tool for the detailed analysis conducted in the case study.
Figure 5.10: LamPlt 3.0 Total Energy Released History Plot
For enhanced analysis, these plots can be exported as ASCII files, which can then be opened in Microsoft Excel to generate the charts referenced in section 5.3 This practical application is suitable for comparing different steps, such as various cut sequences.
Application of the LaModel ERR Calculations to the Case Study
In LaModel 3.0, the new ERR calculations are applied to the Darby Seam mine, building on Newman’s 2008 analysis that examined five variations of stressed cuts likely to cause bumps during extraction The study quantitatively compared vertical stresses in each cut to identify the highest pre-extraction stresses, with the cuts exhibiting the greatest stresses deemed most prone to bumps.
Before analyzing the cut sequences using energy calculations, it was essential to calibrate the critical input parameters for the LaModel program Specifically, the lamination thickness was adjusted to ensure that 90% of the abutment load was effectively distributed within the gob load extent (D), with a depth (h) of 2000 feet (Heasley, 2008).
The lamination thickness achieved was 1200 feet, and the final gob modulus was calibrated to ensure an average gob stress of approximately 293 psi, based on a 21° abutment angle (Heasley, 2008) Consequently, the final gob modulus reached 750,000 psi.
To accurately calculate energy values, the final critical parameter to calibrate is coal strength, utilizing strain-softening coal properties as outlined by Karabin and Evanto (2001) The peak coal strength is determined using the Mark-Bieniawski stress gradient, ensuring precise analysis alongside established lamination thickness and final gob modulus.
Where: σe-s = peak stress of the element
SI = in situ coal strength x = distance from the element center to the free face h = seam height
For determining the residual coal strength (SR) and residual coal strain (εr), the equations developed by Karabin and Evanto (2001) were used:
Where: εr = the residual strain of the element εp = the peak strain of the element
Once the insitu coal strength and modulus are established, the complete behavior of coal pillars can be determined A model based on the Close In 3 cut sequence was developed to calibrate the optimum insitu coal strength, adjusting it to align the calculated total energy release values with observed underground conditions, particularly in the highly stressed final cuts (cuts 35-42) noted by Newman (2008) The Total Energy Release was calculated using LaModel's history plot over the active pillar line (x = 94-157 and y = 126-146) and normalized per element removed during each cut Initially, a strain-softening coal strength of 1550 psi was applied, leading to the highest energy releases occurring in the second-to-last entry/last full pillar (cuts 26-31).
As coal strength increased, the energy release transitioned from the second-to-last entry to the last entry, aligning with field observations A strain-softening coal strength of 1700 psi was found to best match the conditions observed in the field.
The calibration model revealed that the highest energy releases, particularly from cuts 39, 41, and cut 36, were linked to mining highly stressed pillars, with cut 36 noted for bump-prone activity Despite this, field observations indicated that most bump incidents were related to mining the last entry, with only one bump occurring during the second-to-last entry Adjusting coal strength alone did not significantly affect the energy release patterns, nor did it elevate cut 36 to the maximum energy release level Future research should explore additional input parameters beyond coal strength to enhance the optimization of calculated energy values.
This calibration analysis focuses solely on the normalized total energy released across the active pillar row The findings illustrate the total energy release along with its components, specifically kinetic and stored energy To enhance the understanding of input parameters, it is crucial to examine static energy quantities and variations in released energy, which will contribute to a deeper insight into bump potential.
Figure 5.11: Energy release as a function of coal strength
After calibrating the coal strength using the Close In 3 (CI3) cut sequence, the calibrated properties were utilized in models for Close In 3, Close In 4, Close In 5, and their respective bump cuts retreat sequences The energy results for the CI3 cut sequence are illustrated in Figure 5.12, showcasing the kinetic, stored, dissipated, and total energy released, all derived from the same area of the model as the calibration case.
Most energy release is derived from stored energy, with all components of total energy release exhibiting similar trends across different steps.
Figure 5.12: Close in 3 (CI3) normalized energy release versus cut
In the CI3 cut sequence, most bumps were recorded in the #36 cut, which was the initial cut into the last half pillar (the #3 entry) These bumps were primarily caused by mining stress directed toward the panel's center, and this sequence was utilized for a longer duration than the others Energy results for the CI4 cut sequence are illustrated in Figure 5.13.
Figure 5.13: Close in 4 (CI4) normalized energy release versus cut
For the CI4 cut sequence, two bumps occurred in the field while mining cut 36 (Newman,
In the LaModel energy calculations for CI4, the mining of the second-to-last entry (cuts 26-31) reveals the highest energy releases, aligning with the findings from CI3 Notably, cut 36 also exhibits significant energy release The peak observed at cut 27, which is the first cut into the last full pillar, was anticipated due to the high stress in that area, consistent with the CI3 sequence, despite the absence of a recorded bump at this location Figure 5.14 illustrates the calculated energy results for the CI5 cut sequence.
Figure 5.14: Close in 5 (CI5) normalized energy release versus cut
The CI5 cut sequence analysis reveals that the LaModel energy calculations indicate the highest energy releases at cut 28 and the second-to-last entry (#4) This finding aligns with field observations, which recorded a significant bump during cut 28 Additionally, the CI5 sequence exhibits less variability in energy release over both space and time compared to the CI3 and CI4 sequences.
The analysis of the #36 cut reveals that the highest energy releases are linked to mining activities in the middle and last side entries, showing consistent patterns across three sequences Notably, the LaModel analysis indicates that there is no significant difference (within 10%) in energy release or bump potential among the first three models, all of which experienced coal bumps in the field.
The final sequences analyzed are the Close In 4 with Bump Cuts (CI4 BC) and Close In 5 with Bump Cuts (CI5 BC) retreat sequences Energy results for the CI4 BC cut sequence are presented in Figure 5.15.
Figure 5.15: Close in 4 Bump Cut (CI4 BC) normalized energy release versus cut
Summary and Conclusions
This thesis presents the development and practical application of new energy calculations in LaModel 3.0, enhancing the program with features derived from previous research by Salamon (1984) and Zipf and Heasley (1990) Verification of these calculations was achieved by replicating prior studies using MULSIM/NL, yielding similar results when analyzing retreat mining cut sequences The application of energy release calculations revealed that accurate calibration of critical input parameters is essential for reliable outcomes, though achieving a precise match with field results on a cut-by-cut basis remains challenging Factors such as roof stiffness, gob loading, and coal residual stress may require improved calibration, alongside considerations of local mine and post-failure pillar stiffness Despite these challenges, the energy calculations effectively identified areas more susceptible to bumps and demonstrated that bump cuts can strategically manage energy release timing When designed correctly, bump cuts hold potential for mitigating hazards associated with bumps.
The exploration of coal bump potential through energy calculations is in its early stages By integrating these calculations into the LaModel 3.0 program, researchers aim to enhance mine design in areas susceptible to bumps Additionally, applying energy analysis to diverse bump scenarios will facilitate improved parameter calibration and protocols, leading to more precise energy assessments and safer retreat mining practices.
Suggestions for Future Research
The ERR research serves as a valuable resource for researchers and engineers involved in designing mines in bump-prone environments This study not only provides insights but also raises further questions, indicating potential areas for future research.
This research investigates the time dependencies of the ERR, the behavior of post-failure pillars, gob loading and its final modulus, as well as local mine stiffness.
When evaluating the uniformity of the ERR, it is essential to consider both its magnitude and the specific cut sequences, as some exhibit greater uniformity than others While time intervals for each cut are challenging to define in coal mining, grouping rapid succession cuts within a single entry and distinguishing them from other entries that require miner relocation could enhance the analysis This approach would enable a more comprehensive examination by factoring in both spatial and temporal elements.
To fully comprehend pillar failure and coal bump behavior, it is essential to investigate the post-failure behavior of coal pillars, as current understanding is limited While laboratory studies have been conducted, there is a notable lack of field data on post-failure pillars Key parameters that require exploration include the post-failure softening modulus and residual strength, as well as the impact of the width-to-height ratio on these values Conducting extensive research in this area could yield valuable insights into the post-failure behavior of coal pillars.
A crucial yet often misunderstood aspect of the ERR models is the overburden loading present in the gob Numerous field stress measurements have aimed to assess the abutment and gob loading following complete coal extraction While the abutment angle concept effectively represents "average" gob loading, it tends to falter in deeper cover scenarios.
2008) Also, the gob loading is certainly affected by geology, seam thickness, panel width, panel depth, etc., but these relationships have never been adequately determined
Historically, Local Mine Stiffness (LMS) has been linked to bump incidents akin to the Energy Release Rate (ERR), demonstrating its relevance in the 1980s and 1990s LMS assesses the relative stiffness of support pillars post-failure and compares it to the surrounding rock mass's loading stiffness; if the latter is softer, dynamic failures may ensue This relationship mirrors the rock mass modulus paradox, where weaker overburden increases bump likelihood Assuming a constant rock mass modulus facilitates meaningful comparisons between mining parameters By adjusting mining geometries and pillar dimensions, these dynamic LMS issues can be mitigated Previous LMS calculations were utilized in the MULSIM/NL program and could serve as valuable analytical tools if integrated into the modern LaModel program.
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Heasley, K A., 1998, “Numerical Modeling of Coal Mines with a Laminated Displacement- Discontinuity Code,” Ph.D Dissertation, Colorado School of Mines, 179 pp
Heasley, K A., 1991, "An Examination of Energy Calculations Applied to Coal Bump
Prediction," Proc 32nd U.S Symp on Rock Mech p 481-490
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Damage, and Seismicity in Deep Mines,” Proc 8th U.S Symp on Rock Mech., p 194-203 Iannacchione, A T and J C Zelanko, 1995, “Occurrence and Remediation of Coal Mine
Bumps: A Historical Review,” Proc Mechanics and Mitigation of Violent Failure in Coal and Hard-Rock Mines, BuMines SP 01-95, p 27-67
Karabin G J and M A Evanto (2001) presented their findings on the Boundary-Element Method for numerical modeling, addressing complex ground control issues in their paper at the 2nd International Workshop on Coal Pillar Mechanics and Design Their research, published in NIOSH IC 9448, spans pages 89 to 113, highlighting innovative approaches to enhance safety and efficiency in mining operations.
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Appendix A Derivation of the Energy for the Strain Hardening Gob Model
The gob model is derived from the premise that the tangent modulus increases linearly with stress, transitioning from an initial modulus of EI to a final modulus of EF within the stress range of zero to the ultimate stress σu Consequently, the tangent modulus (E) at any given stress value (σ) can be expressed accordingly.
From the theory of elasticity, we know that the differential relation between stress (σ) and strain (ε) is:
By substituting equation A.1 into the second part of equation A.2 the following integral can be written obtained with limits of integration between zero and ε or σ respectively: ε 0 σ 0
By solving the integral in equation A.3, the solution can be expressed as:
After evaluation of equation A.4 with respect to the limits of integration, the following solution for strain as a function of stress and the material properties is obtained:
By solving equation A.5 for stress, the solution for stress in terms of strain and the material properties is determined:
In the formulation of previous equations, the effective modulus (EE) has been utilized instead of the true modulus (ET) To enhance Zipf’s analysis, it is essential to incorporate a factor that considers the thickness of the gob (caved zone) in relation to the mined coal seam The gob height factor (n), defined as the ratio of the caved zone height to the seam thickness, serves to adjust the true modulus for the gob—accounting for its greater thickness compared to the coal seam—resulting in an effective modulus that reflects an equivalent gob material with the same thickness as the seam.
In terms of the true modulus, the stress equation A.6 can be modified with the gob height factor (n) and used in the following form
To accurately calculate the energy release, it is essential to integrate the stress-strain curve, specifically using equation A.8 with respect to strain (ε) This integration is performed with the lower limit set at zero, representing the starting point on the curve, and the upper limit at S P, which indicates the current position on the curve.
We know that the derivative of the strain term is equation A.10 nσ ε
Then by inspection and integration of equation A.10, the solution can be expressed as follows:
The integration of the stress-strain curve for the strain hardening gob material in LaModel, evaluated between the specified limits, yields a solution that accurately represents the area under the curve from a strain of 0 to Sp.
Appendix B Verification of the ERR Programming Using Manual Calculations
The initial validation of energy calculations in the LaModel 3.0 program involved manual calculations to compare against the program's results, ensuring accuracy and identifying any potential programming errors This section outlines the methods employed in this validation process, beginning with the creation of a generic model using the input file in LamPre 2.1.
The General Model Information form enables users to define essential parameters for the model, including one seam, twenty in-seam materials, and three steps, with program units set to feet and psi The subsequent form (Figure B.2) outlines the specifications for overburden and rock mass parameters.
Figure B.2: Overburden / Rock Mass Parameters
The Overburden/Rock Mass Parameters form allows users to input essential parameters such as Poisson’s ratio, elastic modulus, lamination thickness, and vertical stress gradient In this test model, we utilized LaModel’s default parameters without aiming to replicate specific real-world conditions The seam geometry and boundary conditions are subsequently detailed in the following form (refer to Figure B.3).
Figure B.3: Seam Geometry and Boundary Conditions
In this form the seam geometry, seam location, and boundary condition are specified In this test, 10 ft elements are used in a 100 x 100 grid The overburden depth and seam thickness are