Investigating different methods used for approximating pillar loads in longwall coal mines

Deniz Tuncy,Ihsn Berk Tulu,Ted Klemetti

a Department of Mining Engineering,West Virginia University,Morgantown 26501,USA

b NIOSH Pittsburgh Mining Research Division,Pittsburgh 15236,USA

Keywords:Abutment loads Numerical modeling LaModel FLAC3D Longwall coal mines

ABSTRACT Accurately estimating load distributions and ground responses around underground openings play a significant role in the safety of the operations in underground mines.Adequately designing pillars and other support measures relies highly on the accurate assessment of the loads that will be carried by them,as well as the load-bearing capacities of the supports.There are various methods that can be used to approximate mining-induced loads in stratified rock masses to be used in pillar design.The empirical methods are based on equations derived from large databases of various case studies.They are implemented in government approved design tools and are widely used.There are also analytical and numerical techniques used for more detailed analysis of the induced loads.In this study,two different longwall mines with different panel width-to-depth ratios are analyzed using different methods.The empirical method used in the analysis is the square-decay stress function that uses the abutment angle concept,implemented in pillar design software developed by the National Institute for Occupational Safety and Health (NIOSH).The first numerical method used in the analysis is a displacement-discontinuity (DD)variation of the boundary element method,LaModel,which utilizes the laminated overburden model.The second numerical method used in the analysis is Fast Lagrangian Analysis of Continua (FLAC) with the numerical modeling approach recently developed at West Virginia University which is based on the approach developed by NIOSH.The model includes the 2D slice of a cross-section along the width of the panel with the chain pillar system that also includes the different stratigraphic layers of the overburden.All three methods gave similar results for the shallow mine,both in terms of load percentages and distribution where the variation was more obvious for the deep cover mine.The FLAC3D model was observed to better capture the stress changes observed during the field measurements for both the shallow and deep cover cases.This study allowed us to see the shortcomings of each of these different methods.It was concluded that a numerical model which incorporates the site-specific geology would provide the most precise estimate for complex loading conditions.

1.Introduction

According to the 2019 U.S.Longwall Census,there are 40 longwall faces being operated by 35 longwall mines in the United States.West Virginia is the leading state in terms of longwall faces with 11 in operation followed by Pennsylvania(6),Illinois(5),and Alabama(5).Collectively,these 35 longwall mines produced 168.6 million tons of coal in 2019,increasing their total production by 800,000 tons from 2017,while the total coal production of the United States decreased by 22 million tons[1].In longwall coal mines,since 2011,fall of ground accounts for more than 25%of the occupational fatalities [2].Ground-fall incidents are the result of changes in stress conditions around openings induced by the mining operation,and the site-specific geology is one of the most important factors governing whether a ground fall is expected to occur due to the induced stresses.

The Analysis of Longwall Pillar Stability (ALPS) software is the most widely accepted and federal government mandated pillar design software program for longwall mines in the United States[3].ALPS uses empirical equations derived from a database of case studies and focuses on the stability of the pillars.

In cases where more complex stress changes are expected,calibrated numerical models can be used [4,5].LaModel is a widely used software in the United States for modeling the stresses and displacements on thin tabular deposits by utilizing the laminated overburden model;it uses a displacement-discontinuity variation of the boundary-element method[6].Another widely used numerical modeling software is FLAC3D which uses the finite difference method and can be used to model different stratifications of the overburden and their behavior[7].The numerical models are based on fundamental laws of physics and approximates the geomechanical behavior of coal and overburden strata.Since geologic material rarely follows theoretical behavior,models must be carefully calibrated,and model outputs are as reliable as the model input.This study aims to compare the mining induced loading approximations of ALPS,an empirical method,LaModel,a boundary element method,and FLAC3D,a finite volume method.Ultimately,all methods are compared to available field measurements from two different mines in this study.

2.Empirical method

In the early 1990 s,the Analysis of Longwall Pillar Stability(ALPS) was introduced by Mark as a chain pillar design software and was generally accepted and used by the United States coal mining industry [8].Following the success of ALPS,NIOSH developed the Analysis of Retreat Mining Pillar Stability (ARMPS) program for designing retreat mining pillars using a similar approach as ALPS[9].The ARMPS overburden load prediction algorithm was improved to more accurately predict the loading of narrow panels with high overburden depths by implementing the pressure arch concept,and this new version is called ARMPS2010[10].

These programs utilize the abutment angle concept for the abutment stress calculations.The abutment angle β is used to calculate the magnitude of abutment loading adjacent to a gob area.It considers an angle between the vertical plane and the panel roof in order to calculate the transferred load to the abutments when the panel is mined(Fig.1).If the total area above the mined-out panel is considered as the total load to be transferred,the hatched areas in Fig.1 constitute the load that is transferred to the side abutment and the remaining load is carried by the gob.The total load to be transferred is calculated as the dead weight of the overburden directly above the mined-out panel.

In 1990,Mark analyzed the abutment stress measurements collected from five different mines.All measurements were conducted using vibrating wire stressmeters (VWS).The U.S.Bureau of Mines conducted three of the studies,all of which were conducted in the Pittsburgh seam.The fourth study was conducted by the Pennsylvania State University in the Lower Kittanning seam,and the U.S.Steel conducted the fifth study at a mine operating in the Harlan seam.Mark back-calculated the measured side abutment load by multiplying the load-bearing area of the pillars by the average pillar stresses determined from the array of stress cells inside each pillar [3,11].A summary of the panel widths and depths from the case histories that were used by Mark to backcalculate the abutment angles from the case histories is shown in Table 1 [8].

Fig.1.Abutment angle concept [3].

Originally,a total of 16 stressmeter arrays were installed in five different mines,but side abutment measurements were available only from six arrays due to some of the stressmeters being destroyed once the longwall had passed an array.Therefore Table 1 only has data from four different mines.Mark concluded that an average abutment angle of 21°would yield a conservative estimate of the side abutment load,but there was a wide range (10.7° to 25.2°) in the measured values as seen in Table 1 [3].

Peng and Chiang summarized the abutment stress measurements performed prior to the mid-1980 s,and they developed Eq.(1)for calculating the maximum extent(influence)of the abutment load (D) as a function of the depth (H) [12].

From the stress measurements at those five mines (Table 1),Mark found that a square-decay function Eq.(2) fits the measured stress distributions best.

where σais the abutment stress level;x the distance from the panel edge;LSthe total side abutment load;and D the extent of the abutment stress from Eq.(1).

The side abutment loads(LSand LSS)can be calculated according to the appropriate subcritical or supercritical panel formulas using the 21° abutment angle [13].

where H is the overburden depth;PW the panel width;and γ the average unit weight of the overburden.

3.Boundary element method-Laminated model

Salamon proposed the mathematical basis for the laminated model,which would be more suitable for describing the behavior of stratified coal measure rocks,and later updated it in 1991[14,15].The model considers the media as a stack of thin plates with cohesionless and frictionless interfaces and calculates the basic displacements and stresses for thin tabular deposits.The model uses ‘‘homogeneous stratifications”,meaning the plates have the same elastic modulus E,Poisson’s ratio ν,and thickness t.

The fundamental behavior of the laminated model was investigated across a two-dimensional slot where the slot can be considered as a longwall panel with rigid ribs without any support from gob.The panel convergence,abutment stresses,remote displacements,and surface subsidence were investigated [6].The induced vertical stress in the side abutment as a function of the distance(x) from the panel rib is given in Eq.(5).

where m is the abutment load/total panel load ratio;q the in-situ stress;P the width of the panel;Esthe elastic modulus of the seam;E the elastic modulus of the overburden;λ a stiffness parameter of the laminated model;and h the seam thickness.

In this equation,the laminated model parameter λ is defined as:

where t is the lamination thickness;and ν the Poisson’s ratio of the rock mass.

Table 1.ummary of the stress measurement sites used by Mark [8]

The distance Dnfrom the panel rib where a certain percentage of the total abutment load n is carried can be calculated using Eq.(7).This equation can also be used to determine the lamination thickness t for a given abutment distance that is expected for given overburden and seam characteristics.

4.Continuum method-FLAC3D

The finite difference software FLAC3D can model the mining induced stresses and the related overburden behavior in terms of deformations and displacements.It can model the strength anisotropy of the bedded coal measure rocks and the weakening of the failed rocks.In addition,the built-in FISH coding language allows the user to control the loads and the displacements in the model[16].

The basis of the modeling methodology used in this study was developed in 2010 [16].The model includes the 2D slice of a cross-section along the width of the panel including the chain pillar system.The 2D model employs actual stratigraphy,using all the geological layers as thin as 0.25 m.The overburden layers are modeled as strain-softening ubiquitous joint material,which simulates the bedding weaknesses in a strongly bedded strata as well as the vertical joints in massive rock types.

In addition to the model developed by Esterhuizen et al.,interface elements are used to model the interfaces between the geological layers in the overburden.As described by Su,the coefficient of friction of interfaces was set to 0.25 [17,18].Joint shear stiffness was set to 50 GPa/m,and normal stiffness was set to 100 GPa/m.The friction angle of the interfaces was selected as 15°between the overburden layers and 20°on the coal-rock interfaces to be able to simulate appropriate stress gradient at the edge of the pillar[16].

The coal is modeled with a Hoek-Brown coal model based on the model developed at NIOSH with the updated input parameters in Table 2 [16].These parameters were selected to give matching pillar strength values with the Bieniawski pillar strength formula.

In 2010,Esterhuizen et al.published suggested overburden rock parameters to be used in large-scale models [16].Those parameters were later modified by Tulu et al.and are presented in Table 3[4].The uniaxial compressive strength (UCS) values in Table 3 are laboratory scale values,and the field UCS values are estimated by reducing the laboratory-scale value to 58% [16,19].Other parameters listed in Table 3 (elastic modulus-E,friction angle,cohesion,and tensile strength) are field-scale values,and their calculations are presented in detail by Tulu et al.[4].

Table 2.oek-Brown coal model and related interface properties.

Using the rock parameters in Table 3,bedding strength parameters were derived by Esterhuizen et al.[16].Bedding tensile strengths were calculated as the 10% of field-scale UCS values(0.58 × UCSlab).The suggested peak bedding strength properties are also presented in Table 3.The bedding cohesion and tensile strength are decreased to residual values,that are 10%of their peak values over 5mε of plastic strain [20].The bedding planes are assumed to be elastic perfectly plastic in terms of their stressstrain behavior.

Accurately simulating the gob response is critical to approximate the mining-induced load distribution along the chain pillars,gob,and gate-road entries.According to the study conducted by Pappas and Mark,the stress-strain response of the caved material they tested followed a strain-hardening curve [21].The strainhardening gob response was found to fit the hyperbolic function derived by Salamon [22]:

where σ is vertical gob stress,MPa;ε the vertical gob strain;b the maximum strain parameter (related to void ratio);and a the gob stress when ε=b/2,MPa.

The FISH option of the FLAC3D software is used to simulate the strain-hardening gob behavior.It is achieved by updating the elastic modulus of each zone inside the gob with the expected tangent modulus,which can be calculated by taking the derivative of the hyperbolic function with respect to vertical strain [23].

Esterhuizen et al.examined the gob parameters,a and b,by matching the model results with subsidence profiles obtained from the Surface Deformation Prediction Software (SDPS) [16,24].The maximum strain parameter b was determined as 0.44,and parameter a was found to be dependent on the type of rock material in the gob ranging from 5.9 MPa for weak gob up to 25.2 MPa for very strong gob.

Su assumed an initial bulking factor of 1.5 for the formation of the gob[17].This suggests a maximum strain of 0.33 and a caving height of three times the mining height.Su applied this approach successfully to various longwall mine cases for estimating subsidence and pillar stresses.Compared to the results obtained by Esterhuizen et al.,the stress-strain values obtained from the parameters that Su used give similar results to weak/moderate gob [4,16,17].In this study,the gob parameters a and b were selected as 3 MPa and 0.33,respectively.

5.Case study mines

Two different longwall mines were selected for the investigation in this study.The main difference between these mines is thatone is in supercritical and the other is in subcritical loading condition.These mines were selected to examine the different loading mechanisms caused by the different panel width-to-depth ratios.One of the mines (Mine A) is a shallow cover mine with a wide panel from the Northern Appalachian Coal Basin and the other mine(Mine B)is a deep cover mine with a relatively narrow panel width from the Central Appalachian Coal Basin(Fig.2).Both mines were instrumented,and in-situ stress change measurements were obtained from the headgate chain pillars during the period the panel was being mined.

Table 3.uggested intact rock properties [4].

5.1.Mine A (supercritical)

The first mine (Mine A) studied is in Northern West Virginia.The mine operates in the Pittsburgh seam and the depth of cover around the study area is about 213 m.The mine area (Eastern U.S.coalfields) was identified by the World Stress Map (WSM) as a stable mid-plate region with a consistent NE horizontal stress orientation [26,27].

The studied longwall panel is roughly 357 m wide,and the gateroad system is a three-entry system with approximately 30 m wide,center-to-center chain pillars (Fig.3a).The entries are approximately 5 m wide and the mining height is 2.1 m.The immediate roof generally consists of shale,rider coal,claystone,and sandstone or limestone,and the floor is claystone or shale.Fig.3b shows the stratigraphic column generated from a core log near the area where field measurements were taken.

Fig.2.Locations of the studied mines [25].

5.2.Mine B (subcritical)

The second mine (Mine B) is located in Southwestern Virginia.The mine has been operating in the Pocahontas No.3 coal bed that is typically 1.5 to 2.4 m thick,with an average thickness of 1.8 m.The coal bed within the mine area is under overburden ranging from 400 to 700 m in thickness,averaging around 530 m.The coal bed is overlain by shales,followed by sandstone,and then the Pocahontas No.4 seam.

Fig.4b shows the stratigraphic column generated from a core log near the area where field measurements were taken.The sandstones are generally more developed in the Central Appalachian region compared to other regional coalfields,and they are usually massive,thick,well cemented,and strong within the Pocahontas formation [28].The horizontal stress orientation is again NE according to WSM as the mine area falls inside the same region as Mine A.

The analyzed panel is 214 m wide and the depth of cover is 627 m near the instrumentation site from where vertical stress change data was collected.The panel width-to-depth ratio is 0.34,which is subcritical.The instrumented chain pillar system consists of 10 m wide yield pillars on both sides of 45 m wide chain pillars (rib-to-rib),and the gate-roads are 5.5 m wide (Fig.4a).

6.Load analysis

6.1.Mine A

6.1.1.Empirical model

Mine A utilizes a 3-entry chain pillar system with pillar widths of 24 and 26 m,rib to rib.Using Eq.(1),the abutment extent D was calculated as 65 m,substituting 158 m overburden depth.Substituting the parameters into the supercritical abutment load formula Eq.(5),the total load to be transferred to the side abutment(LS)is calculated as 243617 kN/m of gate entry.The total load above the panel is calculated as 1446759 kN/m of entry,considering 360 m of panel width.These calculations indicate that the 16.8%of the total load is transferred to the side abutments,and the remaining 83.2%load is carried by the gob.

Fig.3.General information about Mine A.

Fig.4.General information about Mine B.

The square decay function Eq.(2) is used to determine the distribution of the abutment load,starting from the edge of the abutment pillar closest to the gob.The highest stress change is calculated as 5.66 MPa,resulting in a total vertical stress of 9.61 MPa(3.95 MPa in-situ stress).The total load on the individual pillars can be determined by integrating Eq.(2) over the required distance x1and x1+x2from the gob side edge of the abutment pillar Eq.(9).The total load on each abutment pillar is determined by substituting LS,D,x1,and x2values into Eqs.(9) and (10).For this case,the distances x1and x2are 26.5 and 31 m,respectively(Fig.5).Substituting LSand D,we calculated the pillar loads as 81% and 19% of the side abutment load,LS.Since the abutment extent D does not reach the solid coal of the next panel,no stress change is expected there.

Fig.5.Load distribution following the square decay function for Mine A.

6.1.2.Laminated model

The laminated model was a 2D slice with a single panel mined.Each element was selected to be 1 m,and the model was created 2,000 elements wide,with 10 elements in the y direction.The gridding of the 3-entry chain pillar system can be seen in Fig.6.

For the overburden rock mass parameters,mostly the default values suggested by LaModel were selected.The default values for the Poisson’s ratio and the elastic modulus of the overburden were selected as 0.25 and 20.7 GPa,respectively.The vertical stress gradient was selected as 0.025 MPa/m,which is also the default.The lamination thickness parameter to be used in the model is determined by the lamination thickness wizard offered by LaModel software,and it is determined as 40 m.

Default values for the in-seam material properties are used,with coal strength and coal modulus being 6.2 MPa and 2.07 GPa,respectively.LaModel uses a strain-hardening gob model.In order to calculate the final gob modulus,the program initially calculates a suggested value for the percentage of load,that would be carried by the gob.This value is calculated considering the width of the gob area,which is entered as 357 m.The corresponding final gob modulus was calculated as 12.7 GPa.

The total vertical stress distribution obtained after the LaModel analysis is presented in Fig.7.The maximum vertical stress observed was on the abutment pillar,around 1.5 m into the pillar,and it was found to be around 14 MPa.The stress increase at that point after development was found to be 9 MPa.The average pillar stresses were calculated as 8.95 and 5.2 MPa after the panel was mined,the higher being the pillar closer to the gob.

Fig.6.LaModel grid of chain pillar system for Mine A.

Fig.7.Vertical stress distribution by LaModel on the headgate side of the panel for Mine A.

The gob load is found to be 85.1% of the total transferred load and 16.4%of the load is transferred to the chain pillars on the headgate and tailgate sides.This results in a 20.8°abutment angle when back-calculated,which is in agreement with the 21° default abutment angle.This is expected considering that the calibration of the lamination thickness and gob parameters were done using the wizards implemented in LaModel,and those wizards follow the empirical methods as the basis.

6.1.3.FLAC3D model

A two-panel configuration with headgate and tailgate chain pillar systems was modeled for Mine A.The model was 3072-elements wide and each element was 1 m wide in the x and y direction.The overburden stratification obtained from a core log is modeled with layers as thin as 25 cm.There were 95 overburden layers above the coal seam,with ranging thicknesses between 0.25 and 8.2 m.The overburden layers include shale,coal,fireclay,and sandstone.The shale layers are mostly dark gray and sandy,and the sandstone layers are generally gray.Laboratory scale UCS values for the sandstone were selected from 50 to 100 MPa,softer ones being closer to the seam level.From 40 to 60 MPa laboratory-scale UCS values are assigned for shales,and the fireclays were assigned 20 MPa.

A total of 100 layers were modeled including the seam level and the bottom filler layers,resulting in a total of approximately 860000 total number of elements.Fig.8 shows the model of Mine A with the highlighted portion showing the area of interest.

Vertical stress distributions along the center of the coal seam are plotted for both the development and panel retreat stages in Fig.9.The highest vertical stress was observed as 17.9 MPa,2.5 m into the first abutment pillar.The stress change at that point after development was calculated as 12.2 MPa.After the panel retreat,the average vertical stresses on the pillars were calculated as 9.6 and 5.9 MPa,with the higher one being closer to the gob.

Fig.8.FLAC3D model of Mine A (cropped for convenience).

Fig.9.Vertical stress distribution on the headgate obtained from FLAC3D Model for Mine A.

The panel load was carried mostly by the gob with 77.3%,while the abutments carried the remaining 22.7%of the total panel load.Although not that significant,some amount of load is transferred to the solid coal at the adjacent panel (approximately 3%).Using Eq.(3),the abutment angle β is calculated as 27.4°,which is higher than the default 21°.This suggests more load is expected to be transferred onto the chain pillars,compared to empirical calculations.

6.1.4.Comparison of methods with monitoring results

Stress change measurements were obtained for Mine A from six hollow inclusion(HI)cells,three installed over the abutment pillar and three over the solid coal on the next panel.Each hole was 9 m deep,and from outby to inby,they were installed at 30°,45°,and 60°angles from the horizontal.The instrumentation study in Mine A was conducted by the Pittsburgh Mining Research Division(PMRD) of NIOSH and is explained in detail in a publication by Gearhart et al.[29].

The measured stress values after first-panel mining are plotted in Fig.10 together with the vertical stress profiles obtained using different methods.Although both FLAC3D and LaModel show some inconsistencies compared with the measurements,both approximates the general trend and stresses reasonably accurate.The FLAC3D stress profile shows higher peeks near the ribs and lower stresses in the middle of the large abutment pillar.LaModel shows lower peaks near the ribs compared to FLAC3D,but larger stresses in the middle of abutment pillar.These differences are due to the different assumptions used during the derivation of the governing equations of pillar material-models for FLAC3D and LaModel.In LaModel,seam elements are modelled as one-dimensional springs,and the stress-strain behavior of each element is the function of vertical stress,and replicates the linear Mark-Bieniawski pillar strength formula.The FLAC3D model input parameters are also calibrated to replicate the Bieniawski pillar strength formula,but the stress-strain behavior of each element is the function of threedimensional stress tensor;nonetheless,the failure criterion is only the function of maximum and minimum principal stresses.

Fig.10.Measured stress data compared with stress profiles from different methods for Mine A.

Table 4 shows the load percentages on the gob and the abutments.The empirical method and LaModel both resulted in more load transferred to the gob,compared to the FLAC3D model.In terms of load percentages,the empirical method and LaModel gave almost identical results.The only difference was the load extent,resulting in some load carried by the solid coal for LaModel,where the empirical method showed no load there.The FLAC3D model transferred more load on to the abutments and less on to the gob compared to the other methods,resulting in a higher abutment angle.Aside from the different material-models used,the overburden stratigraphy also plays a role in the FLAC3D model.The limestone layer near the coal seam (Fig.3b) also influences the load carried by the gob,transferring more load on to the abutments.

6.2.Mine B

6.2.1.Empirical model

The loads were initially analyzed using the empirical method.Mine B utilizes yield pillars,so it is logical to assume the yield pillars adjacent to the gob will not contribute substantially to the load-bearing capacity of the support system.Using Eq.(1),the abutment extent is calculated as 129 m considering the overburden depth as 627 m.Substituting the parameters into the subcritical abutment load formula Eq.(4),the total load to be transferred to the side abutment is calculated as 1458535 kN/m of gate entry.The total load above the panel is calculated as 3413956 kN/m of entry,considering the yield pillars on both sides of the panel would yield,resulting in an 805 m effective panel width.The load calculations indicate that 85.4%of the total load is transferred to the side abutments,and the remaining 14.6% load is carried by the gob.

The square decay function Eq.(2) is used to determine the distribution of the abutment load,starting from the edge of the abutment pillar.The highest stress was calculated as 49.7 MPa,including the in-situ stress of 15.7 MPa,located at the gob side edge of the abutment pillar.The distances x1and x2to be used in Eqs.(9) and (10) can be seen in Fig.11.Substituting Lss=1458535 kN/m of gate entry and D=129 m,we can calculate the total load carried by the abutment Eq.(9) and the yield pillar Eq.(10).

Percentage wise,75%of the side abutment load was found to be carried by the abutment pillar and 12% is carried by the adjacent yield pillar.The remaining 13% is carried by the solid coal on the next panel.From the load calculations,we can also calculate the average pillar stresses.The average abutment pillar stress was calculated as 40.1 MPa (24.5 MPa increase) and it was 26.6 MPa(10.9 MPa increase) for the yield pillar.One shortcoming of this method is that it does not consider load transfer due to pillar yielding.We assumed the first yield pillar would completely yield and did the calculations accordingly.However,the second yield pillar would also yield to some extent and would transfer some of its load to both the abutment pillar and the solid coal on the next panel.

6.2.2.Laminated model

The laminated model was carried out using the LaModel software.The mine is modeled as a 2D slice with two consecutive panels,one mined in each step.Each element is selected to be 1 m,and the model was created 2000-elements wide,with 10 elements in the y direction.The gridding of the yield-abutment-yield chain pillar system can be seen in Fig.12.

For the overburden rock mass parameters,mostly the default values suggested by LaModel are selected.The default values for the Poisson’s ratio and the elastic modulus of the overburden were selected as 0.25 and 20.7 GPa,respectively.The vertical stress gradient was selected as the default 0.025 MPa/m.The lamination thickness parameter to be used in the model is determined by the lamination thickness wizard offered by LaModel software as 211 m.Default values for the coal strength and coal modulus were used,and the final gob modulus was calculated as 2.17 GPa.

The total vertical stress distribution obtained after the LaModel analysis is presented in Fig.13.The maximum vertical stress observed was on the abutment pillar,around 8 m into the pillar,and it was found to be around 60.9 MPa.The stress increase at that point after development was found to be 40.9 MPa.

The gob load was found to be 35.9%of the total transferred load;64.1% of the load is transferred to both sides of the panel,carried by the chain pillar systems and the adjacent solid coal.This results in a 13.37°abutment angle when back-calculated,which is considerably less than the 21°abutment angle used as the default for the empirical methods.

6.2.3.FLAC3D model

For the numerical analysis,a single-panel configuration with headgate and tailgate chain pillar systems was modeled.The model was 4,096-elements wide to eliminate the boundary effect.Each element was 1 m wide in the x and y direction.Each layer of the overburden strata is also modeled separately,and they are connected with interface elements.The overburden stratification was obtained from a core log,and each layer as thin as 1 m is modeled on top of the seam layer.Floor layers were also modeled accordingto the extent of the core log,and more layers are added to extend the floor as much as the overburden thickness.Larger elements are used for the bottom layers to reduce the total number of elements,consequently the run times.

Table 4.omparison of transferred load percentages for Mine A determined using different methods.

Fig.11.Load distribution following the square decay function for Mine B.

There were 136 overburden layers above the coal seam,with ranging thicknesses from 1 to 32 m.The layers include various coal measure rocks,mostly shale,sandy shale,and sandstone.The shale layers are mostly shales with sandstone streaks or sandy shales,and the sandstone layers usually have shale streaks.Laboratoryscale UCS values for the sandstone were selected from 120 to 200 MPa,which are reduced with a factor of 0.58 for the field values.Up to 80 MPa laboratory-scale UCS values were selected for massive sandy shales,going as low as 40 MPa for coalinterbedded shale.

A total of 142 layers were modeled,including the seam level and the bottom filler layers,resulting in a total of almost 1 million elements.Fig.14 shows the model of Mine B,cropped at the sides and bottom,and the highlighted box shows the area of interest.

Vertical stress profiles are plotted for both the development and panel retreat stages (Fig.15).The highest vertical stress was observed as 74.0 MPa,5 m into the abutment pillar.The stress change at that point after development was calculated as 52.0 MPa.After the panel retreat,the average vertical stresses on the pillars were calculated as 21.0,32.9,and 28.3 MPa,the highest one being the abutment pillar and the lowest one is the yield pillar closer to the gob.

The adjacent solid coal was found to be carrying the majority of the total panel load with 42.4%,where 39.7%is carried by the abutment pillar.Only 3.7%of the total panel load is carried by the yield pillars,and the remaining 14.2% is on the gob.Using Eq.(4),the abutment angle β was calculated as 31.4°,which is considerably higher than the default 21°.This suggests more load is expected to be transferred on to the abutments,compared to the empirical calculations.

Fig.12.LaModel grid of chain pillar system for Mine B.

Fig.13.Vertical stress distribution by LaModel on the headgate side of the panel for Mine B.

Fig.14.FLAC3D model of Mine B (cropped for convenience).

6.3.Comparison of methods with monitoring results

Mine B had 22 borehole pressure cells (BPC) installed in two sites into the abutment and yield pillars.The instrumentation and monitoring were done by researchers from the Pittsburgh Mining Research Division (PMRD) of NIOSH.The stress change data used for this study was obtained when the instrumentation site had a completely mined panel on one side,before the consecutive panel retreat was started.

Each instrumentation site had 11 BPCs installed.For both sites,the abutment pillars were instrumented with seven BPCs that were 3,4.6,6.1,7.6,9.1,10.7,and 12.2 m into the pillar,nominally.The other four BPCs were installed 3,4.6,6.1,and 4.6 m into the yield pillars that are farther away from the mined-out panel [30].

Table 5.omparison of transferred load percentages for Mine B determined using different methods.

Fig.15.Vertical stress distribution on the headgate obtained from the FLAC3D model for Mine B.

Fig.16.Measured stress data compared for Mine B with stress profiles from different methods.

The measured stress values for sites 1 and 2 are averaged and plotted in Fig.16 together with the vertical stress profiles obtained using different methods.Fig.16 shows the total vertical stresses after the first panel is completely mined.It is observed that the FLAC3D model was able to better capture the stress peaks observed during the field measurements.

Table 5 shows the percentages of the total transferred load on the gob and the abutments for Mine B.If abutments (pillars and solid coal) are considered as whole,the FLAC3D numerical model gives the highest abutment loads at around 86%,and the rest on gob.LaModel resulted in higher loads carried by the gob,compared to other methods.If pillars are considered separately,the empirical method and LaModel show that most of the load is transferred on to the abutment pillar,whereas the FLAC3D model transferred a significant portion of the load onto the solid coal on the adjacent panel.

Another thing to take into account is strong and stiff layers in the stratigraphic column results in higher abutment load extents than determined by Eq.(1).In this study,we utilized material property wizards implemented in LaModel which are calibrated to fit the abutment extent to Eq.(1).When using LaModel in cases where competent layers are present,observations and measurements should be considered to determine the load transfer distance [31].

7.Conclusions

Accurate assessment of mining-induced loads is essential for adequately designing pillars and other support measures which play a significant role in the safety of the operations in longwall mines.There are different methods that can be used to assess load transfer that takes place during panel retreat.In this study,three of these methods are tested on two different mines,and the results are compared and verified against collected field measurements.

All three methods gave similar results for Mine A,which is a shallow mine that has a wide panel(supercritical).In terms of load percentages,the empirical method and LaModel showed more load carried by the gob,compared to the FLAC3D model.For Mine B,in terms of both load percentages and the load distribution,the difference between methods was significant.However,considering individual pillars and the adjacent solid coal,both the empirical method and the LaModel method show most of the load is carried by the abutment pillar,whereas the FLAC3D model showed a lot of load transfer onto the solid coal.For the empirical method,this can be explained by the fact that this method does not consider the load transfer due to pillar yielding.The pillars yield to some extent and the load they originally support is shed further.LaModel showed much more load on the gob,resulting in a relatively lower load transferred to the abutments with a lower abutment extent.Also,the load transferred to the abutments was higher for the FLAC3D model,and LaModel showed the highest gob load among the three methods.

Field measurements were conducted in both mines and were compared with the estimated results for each method.For both Mine A and Mine B,the FLAC3D model was observed to better capture the higher stresses seen near the pillar edges.This can be explained by the confinement that occurs in the FLAC3D model,where other methods do not simulate that phenomenon.Higher stresses closer to the ribs were observed due to the confinement of those zones,which was comparable to the instrumentation data.Some of the variation between the field measurements and the modeling results can be due to the instrumentation installation as well as the local composition and strength of the material surrounding the cells.

Disclaimers

This study was sponsored by the Alpha Foundation for the Improvement of Mine Safety and Health,Inc.(Alpha Foundation).The views,opinions and recommendations expressed herein are solely those of the authors and do not imply any endorsement by the Alpha Foundation,its directors,and staff.

The findings and conclusions in this report are those of the author(s) and do not necessarily represent the official position of the National Institute for Occupational Safety and Health,Centers for Disease Control and Prevention.Mention of any company or product does not constitute endorsement by NIOSH.