o " o <£ 
 
 v^ 
 
 o 
 
 -?■ 
 
 
 ♦♦*% 
 
 
 
 , ♦* \-w<\^ V«>^ V-^V 
 
 \ G °^fe> /^k^ c°\>^% 
 
 • ***** 
 
 •lo. 
 
 
 v, 
 
 V«* 
 
 \ v c. 
 
 A 
 
 ** % °. , 
 
 A 
 
 .6* *V-» 
 
 ■^ 6* °mjmy!^ * *b v 
 
 " • - ^ o* • ' ' " 
 
 ^ 
 
 ^ 
 
 ^ 
 
 .<? 
 
 S V *V 
 
 
 -?■ 
 
 
 ^ 
 
 <j 
 
 
 
 
 
 .K* 
 
 .1°. 
 
 :•/%/' 
 .♦♦*% 
 
 
 V %*^>° \^^\/ %^^-/ \/^?\/ %-^v 
 
 
 
 <r. , :>' .a. 
 
A v ' 
 
 V .. •*• "°"° f 
 
 
 
 A 9 ** 
 
 .7* A 
 
 
 <, 
 
 ^ > *v§»f° ^ a* 
 
 ^ A •YSH^'". ^ A 
 
 ~i * _ < • o _ ^ 
 
 
 "oV u 
 
 
 
 ^ y^ 
 
 
 J"* AT *^ 
 
 
 
 ^ 
 
 ^ 
 
 
 
 
 '■•^ ^sjmk°» J^y^kS ^*$tok°» / v - 0< 
 
 
 
 8.°"^ 
 
 /,. 
 
 
 
 
 
 
 
 
 e, 
 
IC 
 
 9042 
 
 Bureau of Mines Information Circular/1985 
 
 Mine Subsidence Control 
 
 Proceedings: Bureau of Mines Technology 
 Transfer Seminar, Pittsburgh, PA, 
 September 19, 1985 
 
 Compiled by Staff, Bureau of Mines 
 
 UNITED STATES DEPARTMENT OF THE INTERIOR 
 
 75 
 
 'W/NES 75TH AV*^ 
 

 Information Circular 9042 
 
 Mine Subsidence Control 
 
 Proceedings: Bureau of Mines Technology 
 Transfer Seminar, Pittsburgh, PA, 
 September 19, 1985 
 
 Compiled by Staff, Bureau of Mines 
 
 l cCf j g5-(oOOZ[t 
 
 UNITED STATES DEPARTMENT OF THE INTERIOR 
 Donald Paul Hodel, Secretary 
 
 BUREAU OF MINES 
 Robert C. Horton, Director 
 
run 
 
 X 
 
 ^ 
 
 ^ 
 
 'J 
 
 * 
 
Go 
 
 <5> 
 
 Q. 
 
 
 PREFACE 
 
 $( This Information Circular summarizes recent Bureau of Mines research 
 
 aimed at improving technology for predicting and controlling mine sub- 
 sidence. The four papers contained in this publication constitute a 
 large portion, but not all, of the research being performed by the Bu- 
 reau in this area. 
 
 The papers were presented at a technology transfer seminar on mine 
 subsidence control in September 1985. Technology transfer seminars are 
 sponsored frequently by the Bureau of Mines to direct the mineral in- 
 dustry's attention to research results that may be useful and helpful 
 in solving problems. Those desiring more information about Bureau re- 
 search programs should contact the Bureau of Mines, Branch of Technol- 
 ogy Transfer, 2401 E St., NW, Washington, DC 20241. 
 
CONTENTS 
 
 111 
 
 Page 
 
 Preface i 
 
 Abstract 1 
 
 Introduction 1 
 
 Longwall mine subsidence surveying — an engineering technology comparison, 
 
 by Gary W. Krantz and John C. LaScola 2 
 
 Short-term effects of longwall mining on shallow water sources, by Noel N. 
 
 Moebs and Timothy M. Barton 13 
 
 Comparison of the subsidence over two different longwall panels, by Paul W. 
 
 Jeran and Timothy M. Barton 25 
 
 Precalculation of subsidence over longwall panels in the northern Appalachian 
 
 coal region, by Vladimir Adamek and Paul W. Jeran 34 
 

 UNIT OF 
 
 MEASURE 
 
 ABBREVIATIONS USED 
 
 IN THIS REPORT 
 
 cm 
 
 centimeter 
 
 
 mm 
 
 millimeter 
 
 deg 
 
 degree 
 
 
 mm/m 
 
 millimeter per meter 
 
 ft 
 
 foot 
 
 
 ym 
 
 micrometer 
 
 ft/d 
 
 foot per day 
 
 
 pmho/cm 
 
 micrometer per centimeter 
 
 gpm 
 
 gallon per minute 
 
 pet 
 
 percent 
 
 h 
 
 hour 
 
 
 ppm 
 
 part per million 
 
 in 
 
 inch 
 
 
 V ac 
 
 volt, alternating current 
 
 km 
 
 kilometer 
 
 
 V dc 
 
 volt, direct current 
 
 min 
 
 minute (time) 
 
 
 W 
 
 watt 
 
MINE SUBSIDENCE CONTROL 
 
 Proceedings: Bureau of Mines Technology Transfer Seminar, 
 Pittsburgh, PA, September 19, 1985 
 
 Compiled by Staff, Bureau of Mines 
 
 ABSTRACT 
 
 This publication contains four papers presented at a seminar on mine 
 subsidence control held in Pittsburgh, PA, on September 19, 1985. The 
 seminar was designed to keep the mineral industry informed of new tech- 
 nology developed by the Bureau of Mines that permits reliable and accu- 
 rate prediction of mine subsidence. The papers describe actual field 
 studies undertaken by the Bureau to monitor surface subsidence over 
 longwall panels. Topics discussed include the efects of subsidence on 
 water table levels, the development of subsidence precalculation meth- 
 odology suitable for use with the specific lithological conditions of 
 the Pittsburgh coalbed, an engineering comparison of technologies used 
 in surveying for longwall mine subsidence, and a comparison of the pro- 
 cess of subsidence over two different longwall panels. 
 
 INTRODUCTION 
 
 To minimize damage caused by mining-related subsidence, a better un- 
 derstanding of the relationship between underground mining and subse- 
 quent surface movement is needed. Such an understanding, coupled with 
 information gathered while researching this relationship, can be used 
 advantageously by mine operators to predict when and where subsidence 
 will occur. Mine subsidence prediction methods have been developed by 
 European countries, but these methods are tailored to the mining and 
 geologic conditions of those countries — conditions that often differ 
 greatly from those of the United States. To fill the existing subsi- 
 dence information and technology voids, the Bureau of Mines conducted 
 in-depth research to develop techniques that permit accurate prediction 
 of surface ground movements over underground mines. The investigation 
 entailed an extensive data gathering effort to properly characterize 
 the extent and nature of subsidence under various geologic conditions. 
 Results of this research are presented in this Information Circular 
 through four papers presented at a Technology Transfer Seminar on Mine 
 Subsidence Control on September 19, 1985, in Pittsburgh, PA. 
 
LONGWALL MINE SUBSIDENCE SURVEYING—AN ENGINEERING TECHNOLOGY COMPARISON 
 By Gary W. Krantz 1 and John C. LaScola^ 
 
 ABSTRACT 
 
 A typical longwall mine subsidence sur- 
 vey monitoring grid was installed at the 
 Bureau of Mines. Conventional and high- 
 technology surveying systems, including 
 an electronic distance meter-theodolite- 
 level, (EDM-theodolite) , an automatic 
 recording infrared laser tacheometer, a 
 global positioning system satellite 
 
 surveyor, aerial photography (photogram- 
 metry) , and a prototype inertial surveyor 
 were developed over the grid during a 
 1-month period. A statistical analysis 
 indicates that the average three-dimen- 
 sional displacements from the base (EDM- 
 theodolite) for both the tacheometer and 
 photogrammetry were almost identical. 
 
 INTRODUCTION 
 
 This investigation evaluates and com- 
 pares five surveying methodologies 
 available for use in surface longwall 
 subsidence monitoring. They include EDM- 
 theodolite, tacheometer, and photogram- 
 metry surveying. Inertial surveying 
 systems are discussed, but an in-depth 
 evaluation was impossible owing to on- 
 site system failure. 
 
 Geodetic survey work is conducted to 
 establish time-based def ormational char- 
 acteristics of the ground surface as the 
 longwall mine face advances beneath. 
 Surface monuments installed above the 
 mine panel must be accurately and repeti- 
 tively measured to determine the dynamic 
 vertical and horizontal movements. 
 
 ACKNOWLEDGMENTS 
 
 The authors would like to acknowledge 
 the assistance provided by the U.S. Army, 
 Corps of Engineers, Huntington, WV , Dis- 
 trict and Ft. Belvoir, VA, Engineering 
 Topographic Laboratory; Jan Stenstroem 
 of Carl Zeiss, Inc., Thornwood, NY; 
 
 Geo-Hydro Inc., of Rockville, MD; the 
 Tennessee Valley Authority, Chattannooga, 
 TN; John W. Antalovich of Kucera & Asso- 
 ciates, Inc.; Mentor, OH; 
 Keddal of R. M. Keddal 
 Inc., Library, PA. 
 
 and Robert M. 
 & Associates, 
 
 APPROACH 
 
 The purpose of this investigation was 
 to compare conventional and high-tech- 
 nology geodetic surveying systems using a 
 survey grid with physical characteristics 
 typical of current longwall mine subsi- 
 dence study sites. Since continued aber- 
 rant surface movement during the study 
 would have masked the comparative mea- 
 surements, the grid, as shown in fig- 
 ure 1, was installed on the Bureau of 
 Mines Pittsburgh Research Center (PRC) 
 grounds over a stable surface. 
 
 ^Engineering geologist. 
 ^Physical scientist. 
 Pittsburgh Research Center, Bureau of 
 Mines, Pittsburgh, PA. 
 
 The grid was developed over gently 
 rolling, well-drained topography with 
 slopes approaching 30 pet and a maximum 
 relief of approximately 150 ft (45 m) . 
 Figure 2 shows the grid layout on a 
 topographic base map. The grid base- 
 line, 1,750 ft (533.4 m) long, was ori- 
 ented with two perpendicular cross pro- 
 files intersecting it at monuments 4+50 
 and 14+50. The profile at monument 4+50 
 is 1,200 ft (365.8 m) long; the other 
 profile is 650 ft (198.1 m) long. This 
 configuration is typical of actual subsi- 
 dence grids since it allows cross-section 
 capability both parallel and perpendicu- 
 lar to the direction of mining. The mon- 
 uments were spaced every 25 ft (7.62 m) 
 
1& . "'-?> 
 
 ! SW contro 
 ,, monument 
 
 FIGURE 1. - Aerial photograph of survey grid. 
 
 and consisted of 2-ft (0.6-m) sections of 
 No. 5 reinforcement bars driven into the 
 ground. Although the center of the grid 
 was located in an open field, the ends of 
 the baseline and profiles encountered 
 thick vegetation. 
 
 Property boundaries forced control mon- 
 ument locations much closer to the grid 
 than normal, but since the site was not 
 being undermined, there was no danger of 
 
 subsidence alteration. The control monu- 
 ment coordinates were determined to a 
 first-order accuracy horizontally, and to 
 a second-order accuracy vertically. 
 
 The results and conclusions of this 
 report should be interpreted in light 
 of the prerequisites and requirements 
 of surveying for this particular 
 application. 
 
MCELHANL^^- 
 
 Scale, ft 
 
 LEGEND 
 Surface monument 
 
 — -Il50 — -Topographical contour 
 lines, 5-ft intervals 
 
 Paved road 
 
 zr~.z^rAccess road 
 
 Property boundary line 
 
 — Intermittent stream 
 □ Surface structures 
 
 FIGURE 2. - Survey grid on topographic base map. 
 
SURVEY STUDY 
 
 ELECTRONIC DISTANCE 
 METER-THEODOLITE-LEVEL SURVEY 
 
 The grid was installed using conven- 
 tional optical alignment procedures and 
 two different EDM-theodolite systems, a 
 Wild Tl-A 3 and a Topcon GTS-2 semitotal 
 station, plus a steel tape. All control 
 and grid monuments were then surveyed 
 with a precision (second-order) Zeiss 
 NI-1 level. The field data were hand- 
 tabulated. Computations were performed 
 on a Radio Shack TRS-80 model 1000 micro- 
 computer. The data were later trans- 
 formed using global positioning values, 
 a Hewlett-Packard HP41CX calculator, and 
 a Stevenson Transformation software 
 program. 
 
 The EDM-theodolite surveying system and 
 equipment are extremely portable, rugged, 
 and relatively simple to operate when 
 used by a trained engineering surveyor. 
 Strict field procedures and data tabu- 
 lation (compilation) are required for 
 precise work. Since the data are hand- 
 tabulated and compiled, the human factor 
 can result in error. In fact, an analy- 
 sis of the grid data indicates that such 
 an error may have occurred. 
 
 The grid was resurveyed with the EDM- 
 theodolite after all other survey systems 
 had been developed to detect any possible 
 monument movements. 
 
 Environmental constraints imposed on 
 the EDM-theodolite system are customary 
 and standard. Windy, rainy conditions 
 cause a variety of problems including 
 lens fogging, survey rod movement, and 
 hand tabulation errors. The EDM-theodo- 
 lite is particularly susceptible to wet 
 weather downtime, primarily in an effort 
 to protect the system, and to heat turbu- 
 lence on bright, clear sunny days. 
 
 SATELLITE-BASED GLOBAL 
 POSITIONING SYSTEM (GPS) 
 
 The NAVSTAR GPS is a space-based, 
 worldwide, all-weather system designed to 
 
 ^Reference to specific products does 
 not imply endorsement by the Bureau of 
 Mines . 
 
 provide extremely accurate three-dimen- 
 sional navigational and/or positioning 
 capability. Present plans call for the 
 system to be fully operational in 1989 
 (J_). 4 The system, at that time, will 
 consist of a constellation of 18 active 
 space satellites, plus 3 or more passive 
 satellites, orbiting approximately 20,000 
 km above the earth in 6 different orbital 
 planes. When the entire constellation is 
 in place, an observer any place on the 
 earth will be able to receive signals 
 from a minimum of four satellites at any 
 time and determine his position instanta- 
 neously (2^ . At present , only 6 of the 
 18 satellites have been successfully 
 placed in orbit. 
 
 The GPS receiver system demonstrated on 
 the grid was the Macrometer interferomet- 
 ric surveying system, which is capable of 
 receiving NAVSTAR satellite signals but 
 is not capable of decoding the special 
 military "P" and "S" codes. The system 
 is advertised as having three-dimensional 
 relative positioning capability to 5 mm 
 over a 1-km baseline and 5 cm capabil- 
 ity over a 10-km baseline with 2 h of re- 
 corded data. The system requires two 
 or more receivers, one of which must be 
 located over a precisely known survey 
 control monument, and the other(s) lo- 
 cated on unknown monuments or point(s). 
 Survey points can be separated by consid- 
 erable distances (miles) and do not have 
 to be intervisible. 
 
 The GPS survey was performed on July 9 
 and 10, 1984. The survey was designed to 
 accomplish three objectives: 
 
 1. Establish first-order horizontal 
 and vertical control on the grid datum 
 and four control monuments. 
 
 2. Establish coordinates on at least 
 two randomly selected grid monuments for 
 comparison with other survey data. 
 
 3. Perform repeat observations on a 
 minimum of three monuments for comparison 
 purposes. 
 
 ^Underlined numbers in parentheses re- 
 fer to items in the list of references at 
 the end of this paper. 
 
Unfortunately, repeat observation data 
 were not provided by the contractor, al- 
 though four monuments were occupied in 
 more than one session. 
 
 The Macrometer Interferometric Survey 
 System includes the field unit V-1000 re- 
 ceiver, a remote control-display unit, a 
 DEC TU-58 tape drive, and an antenna as- 
 sembly. The office-based equipment in- 
 cludes a P-1000 data processor, computer 
 terminal (monitor), disk drive unit, and 
 line printer. A unique, proprietary 
 software package is provided with the 
 system for data analysis. The field sys- 
 tem requires power both from a 115-V-ac 
 inverter and from high-amperage 12-V-dc 
 batteries. The battery system must 
 
 provide constant power to the precision 
 clock system and other systems. The en- 
 tire system requires 350 W of power. 
 
 Approximately 2-1/2 h of observation 
 time is required to secure first-order- 
 accuracy data. The observation window, 
 therefore, permitted each survey instru- 
 ment to occupy two monuments per day 
 since they were close enough to permit 
 relocation of the receiver "and antennae 
 system within 15 to 20 min. The layout 
 of the GPS survey is showh^tn figure 3. 
 
 A tripod is centered over the monument 
 to be measured, and an optical plummet 
 is used to precisely align and level the 
 center of the antenna coupler over the 
 center of the monument. An acrylic dome 
 
 Castle Shannon 
 
 Coast and Geodetic Survey 
 
 bench mark 
 
 Pittsburgh Research 
 Center 
 
 Not to scale 
 
 Bureau of Mines 
 
 Pittsburgh Research 
 
 Center 
 
 LEGEND 
 @U.S. route ©State route 
 a Bench mark Not to scale 
 
 LEGEND 
 
 — Main traverse 
 
 — Check line 
 
 Datum 
 FIGURE 3. - Layout of the GPS survey. 
 
protects the antennae from rain, dew, or 
 frost without affecting the reception 
 performance significantly. 
 
 Although the GPS survey control monu- 
 ment sites were very carefully selected 
 so as to have open sky above a 20° zenith 
 angle and within the azimuth range of the 
 known satellite observation sectors, a 
 loss of data on one control monument was 
 reported by the contractor. The data 
 loss also reportedly prevented the com- 
 putation of individual survey session 
 results from which repeat-reading com- 
 parisons could have been documented. 
 Accordingly, the survey site selection 
 process may be the system's primary envi- 
 ronmental constraint. If the stystem can 
 only be used in open fields, as was the 
 case for three of the four subsidence 
 grid control monuments, the constraint 
 would seriously limit the use of the 
 system for establishing subsidence survey 
 control. 
 
 The GPS equipment apparently functions 
 satisfactorily in rainy weather. Al- 
 though light showers occurred during the 
 survey, high winds, thundershowers , and 
 lightning were not observed. 
 
 The high-amperage requirement of the 
 GPS equipment and its sensitivity to tem- 
 perature variations may impose a mea- 
 sure of environmental constraint. The 
 system requires a stable ac power sys- 
 tem plus massive batteries for the dc 
 requirements. 
 
 AUTOMATIC RECORDING TACHEOMETER SURVEY 
 
 The automatic recording survey instru- 
 ment used in measuring the PRC subsid- 
 ence grid was a Zeiss Elta 2 electronic 
 tacheometer with digital precision theo- 
 dolite, electro-optical range finder, mi- 
 crocomputer, program module, and record- 
 ing unit. The tacheometer was capable of 
 computing, processing, and storing the x, 
 y, and z coordinates of the monuments 
 instantaneously as they were being mea- 
 sured, either in metric, feet, or survey 
 "chains" format. Additionally, the ze- 
 nith angle, slope distance, and hori- 
 zontal azimuth could be recorded or com- 
 puted into horizontal distance, direc- 
 tion, and difference in elevation and 
 
 then recorded. The smallest range finder 
 display unit is 1 mm. Distances of up to 
 5 km can reportedly be measured in one 
 shot . 
 
 Data acquired and computed in the field 
 over the grid during the daytime were 
 printed out in easting, northing, and 
 elevation format within 1 h after col- 
 lection. The tacheometer survey was per- 
 formed July 24 and 25, 1984. 
 
 All of the raw data acquired during the 
 survey were collected in an arbitrary 
 "relative" positioning format. Since 
 horizontal and vertical controls were not 
 available at the time of the tacheometer 
 survey, angular and vertical assumptions 
 had to be made. Survey data transforma- 
 tion was later performed on the collected 
 data using first-order GPS-acquired co- 
 ordinates for two control monuments. 
 
 The data were transformed using a sur- 
 vey data transformation software package 
 on a Hewlett Packard 9845B computer sys- 
 tem, HP9885 flexible disk drives, and an 
 HP2631B printer. 
 
 Owing to scheduling obligations, the 
 tacheometer survey had to be terminated 
 abruptly on the second day before a sur- 
 vey closure could be completed back to 
 the point of origin. Had closure been 
 completed, errors could have been spread 
 out through the data points using compu- 
 tational procedures, rendering the final 
 data slightly more precise than those 
 contained in this comparative analysis. 
 Another control monument was surveyed by 
 the tacheometer as the last point mea- 
 sured in the lengthy traverse. 
 
 For a short period at the beginning of 
 the survey, there were two reflector rod- 
 men. Using two rodraen, the instrument 
 operator was able to survey seven or 
 eight monuments every 3 min. This rate 
 includes instrument positioning on the 
 reflectors and a rodman positioning on 
 monuments in an open field. 
 
 The tacheometer system used had essen- 
 tially the same environmental constraints 
 as the EDM-theodolite, discussed previ- 
 ously. The system was repeatable and 
 easy to operate when used by an experi- 
 enced surveyor trained on the system. 
 Since the system contains a sophisticated 
 computer system, function setting, system 
 
programming, and calibration are more in- 
 volved than for conventional systems. 
 The basic operational procedures, how- 
 ever, were straightforward, easily under- 
 stood, and well labeled on the instru- 
 ment. A person with basic surveying 
 knowledge could produce accurate data 
 with a minimum of instruction and train- 
 ing. The time required to survey the en- 
 tire subsidence grid, consisting of 145 
 monuments plus the instrument traverse 
 points, with 1 instrument operator and 
 1 rodman was approximately 14 h. Since 
 each instrument move and/or setup in 
 traverse mode requires precise leveling 
 and adjustment, the selection of traverse 
 instrument station locations is very im- 
 portant. Good selection of traverse sta- 
 tions for maximum grid monument visibil- 
 ity can result in rapid advancement of 
 the survey. Poor traverse station selec- 
 tion can result in survey time increases. 
 Data processing was performed immediately 
 after data collection. 
 
 The important factor to consider when 
 using the tacheometer is that human error 
 involved in the computation is reduced 
 essentially to zero. Hand tabulations or 
 computations are not performed. Field 
 errors can only be made if the instrument 
 operator incorrectly sets a function or 
 incorrectly tags a data point; in this 
 case compiled data will be printed cor- 
 rectly but will be incorrectly labeled. 
 One such error was made and easily 
 detected. 
 
 On extremely clear, bright, hot, sunny 
 days, the process of setting up, adjust- 
 ing, leveling the instrument, and making 
 readings across bright reflective sur- 
 faces was considerably more difficult and 
 time consuming than on overcast cool 
 days. These factors may be the most ser- 
 ious environmental constraints and are 
 characteristic of laser surveying equip- 
 ment. Other constraints that customarily 
 apply to surveying equipment relate to 
 the use of the system in windy, rainy 
 weather. 
 
 AERIAL PHOTOGRAMMETRY SURVEY 
 
 Photogrammetry is frequently employed 
 as a precise, noncontact measuring method 
 
 in geotechnical engineering and mining, 
 particularly for measuring ground dis- 
 placements such as subsidence. 
 
 Conventional survey methods commonly 
 take days to gather data. Since subsi- 
 dence is a dynamic phenomenon, during 
 active periods it is possible to miss 
 significant pieces of information by mon- 
 itoring the surface as if it were static. 
 Photogrammetric surveying eliminates this 
 problem because all data are simultane- 
 ously recorded on photographs. The ac- 
 tual measurement process takes a certain 
 amount of time, but since all the work is 
 done on photographs, the surface condi- 
 tions are frozen in time and the monument 
 positions are computed for the instant of 
 the photograph. 
 
 Photogrammetry offers two other advan- 
 tages over conventional surveys under 
 certain conditions. First, a survey can 
 be conducted in remote, inaccessible 
 areas without significant additional 
 cost. However, a ground survey might be 
 required to establish a few control 
 points outside the subsidence area if no 
 existing control data are available. 
 
 Second, the survey will provide much 
 greater detail of the visible surface 
 area. This offers two valuable options: 
 the interpreter may use any visible, dis- 
 crete natural object as a monitoring 
 point whether originally planned or not; 
 and the interpreter may utilize the tech- 
 niques of remote sensing to determine the 
 effects of subsidence on vegetation or 
 other facets of the surface environment. 
 This is possible because once the pho- 
 tographs exist, they can be reevalu- 
 ated, remeasured, and checked for new 
 information (3) . 
 
 The survey was conducted on July 31, 
 1984. The plane was equipped with a Wild 
 model RC-8 camera fitted with a 6-in- 
 focal-length lens. To make the 1/2-in- 
 diam rebar grid monuments visible from 
 the air, reflective 13-in-diam disposable 
 aluminum pans were installed over each 
 monument. To make the photogrammetric 
 analysis more accurate, the distance be- 
 tween the top of the rebar monument and 
 its marker was measured and recorded for 
 adjusting the elevations. 
 
Aerial photographs were taken at 1,200, 
 3,000, and 6,000 ft. Photogrammetric 
 analysis, however, was performed only 
 on the 1,200-f t-elevation stereo photo- 
 graphs. The targets were observable on 
 the 3,000- and 6, 000-f t-elevation photo- 
 graphs but could not be measured to the 
 same accuracy. 
 
 The analysis of the aerial photography 
 was performed on a first-order-accuracy 
 Matra Traster stereo plotter. The in- 
 strument has a reported 1-ym interpreta- 
 tion accuracy in both horizontal and 
 vertical directions. The system was in- 
 terfaced with a Data General model 5/130 
 Eclipse computer. Coordinates for each 
 target were read three distinct times 
 using the system floating mark. The 
 computer converts the Traster machine 
 stage coordinates into precise ground 
 coordinates. 
 
 Photo point coordinates can be read off 
 stereo (60-pct overlay) photographs using 
 a space coordinate system and either me- 
 chanically or mathematically intersect- 
 ing the coordinate lines. Although me- 
 chanical intersection is performed in 
 conventional mapping (stereoplotting) , 
 mathematical intersection or analytical 
 aerotriangulation and/or stereocompila- 
 tion can be performed. The analytical 
 technique permits data refinement and 
 statistical adjustment for extremely ac- 
 curate photo point identification. Addi- 
 tionally the procedure permits error 
 correction in camera calibration, film 
 emulsion deformation, camera platen flat- 
 ness, tangential lens distortion, atmos- 
 pheric refraction, and earth curvature 
 (3). 
 
 The primary environmental constraint in 
 photogrammetric surveying is the ground 
 visibility requirement. Obviously a 
 point must be seen in the photograph if 
 it is to be surveyed and its position 
 computed. This necessitates clearing 
 away any ground cover that might obscure 
 the target from the air and making the 
 target visible. Photogrammetric surveys 
 must generally be conducted in early 
 spring and late fall when ground cover is 
 at a minimum. However, normal subsidence 
 monitoring continues through all seasons. 
 
 In addition, photographs must be taken in 
 a clear atmosphere and with a proper sun 
 angle for exposure. The problem of tar- 
 get visibility is probably the limiting 
 factor when deciding whether or not pho- 
 togrammetry can be used (3) . 
 
 INERTIAL SYSTEM SURVEY 
 
 The technology began in the early 
 1970' s when the Department of Defense de- 
 classified an older version of an iner- 
 tial navigation system used in early 
 space ventures and in high-technology 
 aircraft. Prototype inertial surveying 
 equipment has been greatly improved and 
 is now reportedly accurate enough for 
 geodetic survey work over large traverses 
 in rough terrain. The equipment is nor- 
 mally placed in four-wheel-drive surface 
 vehicles; however, it can be flown in 
 fixed wing or helicopter-type aircraft. 
 The system is moved from established con- 
 trol points to unknown monuments and re- 
 turned to the original control point or 
 to a known second control point. The 
 electrostatic gyro inertial system used 
 was built by Litton. The system had been 
 retrofitted with high-precision acceler- 
 ometers for use in research and develop- 
 ment by the U.S. Army Corps of Engineers 
 Topographic Laboratories. The equipment 
 permits survey data accumulation with 
 only one operator. 
 
 The sources of noise or error can 
 be assigned to three major categories: 
 
 (1) accelerometer measurement error, 
 
 (2) platform drift rate, or (3) environ- 
 mental effects. Measurement errors asso- 
 ciated with the accelerometer are induced 
 by thermal or vibration effects during a 
 survey traverse. Platform drift rate oc- 
 curs because of vibration variations and 
 thermal transients. Environmental noise 
 includes variations in the earth's grav- 
 ity field, temperature variations, and 
 other causes (4^ . 
 
 The inertial surveying was conducted 
 on October 3 and 4, 1984. Data obtained 
 during the survey were erroneous, how- 
 ever, owing to system computer malfunc- 
 tions. The system could not be repaired 
 and was returned. 
 
10 
 
 System accuracies have been reported to 
 be in the range of 0.33 to 0.82 ft for 
 horizontal components. Vertical accuracy 
 has been reported to range from 0.03 to 
 0.39 ft (_5). 
 
 OTHER HIGH-TECHNOLOGY SURVEY METHODS 
 
 A variety of other remote-sensing tech- 
 nologies have been used to detect and 
 delineate mine subsidence (6). Studies 
 conducted in the Northern Anthracite 
 Coalfields of Pennsylvania included Earth 
 Resources Technology Satellite imagery 
 (ERTS-1), side-looking airborne radar 
 
 (SLAR) imagery, and multispectral scanner 
 imagery for 11 spectral bands including 
 thermal infrared, color, color infrared, 
 and black and white photography. The 
 multispectral scanning work was conducted 
 to observe subsidence-related moisture 
 patterns in bare soil areas. The air- 
 craft imagery was used in the detection 
 of faults, fractures, and other features 
 related to subsidence. Since these tech- 
 niques are not of sufficient accuracy or 
 resolution to be useful for subsidence 
 surveys, they will not be discussed fur- 
 ther in this report. 
 
 SURVEY DATA ANALYSIS 
 
 Statistical analyses were performed for 
 the EDM-theodolite, tacheometer, and pho- 
 togrammetric surveys since the values of 
 northing, easting, and height data were 
 available for a majority of the monu- 
 ments. The GPS system data, however, 
 were not used because survey data were 
 available for only a few select monu- 
 ments. The EDM-theodolite data were used 
 as the base for comparison because this 
 is a most commonly used method for making 
 subsidence measurements. 
 
 Since only a limited number of surveys 
 were made using each type of system, the 
 ultimate question of accuracy cannot be 
 addressed as part of this study. How- 
 ever, the difference in monument posi- 
 tions can be examined. The statistical 
 analyses were therefore performed on the 
 difference in individual monument posi- 
 tions as identified by a survey method as 
 compared to the base (EDM-theodolite). 
 All statistical parameters were calcu- 
 lated using the absolute value of the 
 differences. This approach was used be- 
 cause the sign of the difference in monu- 
 ment position relative to the base were 
 
 not nearly as important as the magnitude 
 of the number. Furthermore, if the ac- 
 tual difference values are used, they 
 tend to mask the real variation in monu- 
 ment position. 
 
 Various statistical parameters are 
 shown in table 1. For the tacheometer 
 survey comparison, the mean and its stan- 
 dard deviation of the northing values are 
 approximately twice those of the easting 
 values. However, for the photogrammetric 
 comparison, the mean and its standard 
 deviation of the northing and easting 
 values are almost identical. While the 
 tacheometer ' s mean elevation is 1/4 to 
 1/2 that of its horizontal values, the 
 photogrammetric mean elevation is approx- 
 imately 2 times its horizontal values. 
 Furthermore, the photogrammetric eleva- 
 tion shows the largest mean and dis- 
 persion observed, approximately 4 times 
 those of the tacheometer values. The 
 total three-dimensional displacement from 
 the base for both the tacheometer (0.25 
 ft) and photogrammetry (0.24 ft) is al- 
 most identical. 
 
 SUMMARY AND DISCUSSION 
 
 A typical longwall mine subsidence sur- 
 vey grid was installed over stable ground 
 to compare conventional and high-tech- 
 nology survey systems. Five systems were 
 employed: inertial, GPS, EDM-theodolite, 
 tacheometer, and photogrammetry. High- 
 lights of the systems follow: 
 
 Inertial - Extremely portable in that 
 it can be placed in surface vehicles and 
 aircraft. Sources of error include ac- 
 celerometer measurement caused by thermal 
 effects, platform drift rate caused by 
 vibration variations and thermal tran- 
 sients, and environmental effects such as 
 
TABLE 1. - Statistics on the absolute value of the difference 
 in measurements 
 
 11 
 
 Statistic 
 
 Northing Easting Vertical 
 
 TACHEOMETER-THEODOLITE 
 
 
 
 
 138.00 
 
 31.58 
 
 .23 
 
 .01 
 
 .22 
 
 .01 
 
 .09 
 
 .51 
 
 .08 
 
 .43 
 
 1.08 
 
 1.00 
 
 138.00 
 
 12.12 
 
 .09 
 
 .01 
 
 .08 
 
 .00 
 
 .06 
 
 .34 
 
 .00 
 
 .34 
 
 1.24 
 
 2.44 
 
 138.00 
 6.53 
 
 
 .05 
 
 
 .00 
 
 
 .05 
 
 
 .00 
 
 
 .04 
 
 
 .44 
 
 
 .00 
 
 
 .44 
 5.83 
 
 
 52.66 
 
 
 
 PHOTOGRAMMETRY-THEODOLITE 
 
 
 127.00 
 12.22 
 .10 
 .01 
 .09 
 .00 
 .07 
 .25 
 .00 
 .25 
 .32 
 -.98 
 
 127.00 
 10.97 
 .09 
 .00 
 .07 
 .00 
 .05 
 .26 
 .00 
 .26 
 .55 
 -.26 
 
 127.00 
 25.64 
 
 
 .20 
 
 
 .01 
 
 
 .17 
 
 
 .03 
 
 
 .16 
 
 
 .67 
 
 
 .00 
 
 
 .67 
 
 
 .94 
 
 
 .22 
 
 variations in the earth's gravitational 
 field and temperature variations. Survey 
 data could not be used in this study ow- 
 ing to computer malfunction. 
 
 GPS - When completed, will be able to 
 determine receiver position instantane- 
 ously. Constraints are the high amperage 
 required to power the field system and 
 sensitivity to temperature variations and 
 site selection. This system was used to 
 accurately determine the position of the 
 control monuments, but the expense and 
 time required to survey precluded its use 
 over the entire grid. 
 
 EDM-theodolite - Portable, rugged, and 
 relatively simple to operate. Sensitive 
 to windy and/or rainy conditions and sub- 
 ject to errors due to hand tabulations 
 and computations. Utilized as the base 
 for this comparison because it is the 
 
 most commonly used method for making sub- 
 sidence measurements. 
 
 Tacheometer - Completely automated for 
 rapid recording, computing, and data gen- 
 eration. Subject to the same environmen- 
 tal constraints as the theodolite system. 
 
 Photogrammetry - Can be used for inac- 
 cessible areas. All data are gathered 
 simultaneously, providing a permanent 
 photographic record that can be reevalu- 
 ated. Surveys cannot be conducted dur- 
 ing inclement weather, data for control 
 points must be available, and targets 
 must be visible on the photographs. 
 
 A statistical analysis indicates that 
 the three-dimensional displacements from 
 the base (EDM-theodolite) were almost 
 identical for the tacheometer and 
 photogrammetry . 
 
12 
 
 REFERENCES 
 
 1. Hothem, L. D. , and C. J. Fronczek. 
 Report on Test and Demonstration of Mac- 
 rometer Model V-1000 Interferometric Sur- 
 veyor. Fed. Geod. Control Comm. , Rep. 
 15-83-2, May 1983, 36 pp. 
 
 2. Collins, J. A Satellite Solution 
 to Surveying. Prof. Surv. , Nov. -Dec. 
 1982, pp. 13-17. 
 
 3. Sendlein, L. V., Y. Hasan, C. L. 
 Carlson, and K. R. Herbert (eds.). Sur- 
 face Mining Environmental Monitoring and 
 Reclamation Handbook (U.S. Dep. Energy, 
 Asst. Sec. Energy Tech., Off. Coal Min- 
 ing, contract DE-AC-2280-ET-14146) . El- 
 sevier, 1980, 750 pp. 
 
 4. Huddle, J. R. Theory and Perform- 
 ance for Position and Gravity Survey 
 With an Inertial System. J. Guidance and 
 Control, v. 1, No. 3, May- June 1978, 
 pp. 183-188. 
 
 5. Roof, E. F. Inertial Survey Appli- 
 cations to Civil Works. U.S. Army Corps 
 Eng., Eng. Topog. Lab., ETL-0309, Jan. 
 1983, 63 pp. 
 
 6. Earth Satellite Corp. (Washington, 
 DC) . Use of Photo Interpretation and 
 Geological Data in the Identification of 
 Surface Damage and Subsidence. Appalach- 
 ian Reg. Comm. Rep. ARC-73-1 1 1-2554, 1973 
 (final rep. 1975), 113 pp. 
 
13 
 
 SHORT-TERM EFFECTS OF LONGWALL MINING ON SHALLOW WATER SOURCES 
 By Noel N. Moebs 1 and Timothy M. Barton 2 
 
 ABSTRACT 
 
 The Bureau of Mines monitored surface 
 subsidence, water table levels, and 
 stream flow above a longwall panel in 
 southwestern Pennsylvania, for about 
 6 months prior to mining and 12 months 
 afterward. Only water levels within 
 the boundary of the longwall showed a 
 
 precipitous decline as a result of min- 
 ing. Water levels 500 ft or more outside 
 the panel rib line were unaffected. No 
 evidence of mining effects on the small 
 streams or springs located within 1,200 
 ft of the panel was detected. 
 
 INTRODUCTION 
 
 Federal regulations controlling sub- 
 sidence are intended to ensure that un- 
 derground raining is conducted so as to 
 protect the health and safety of the pub- 
 lic, minimize damage to the environment, 
 and protect the rights of landowners 
 (1_). 3 These regulations furthermore re- 
 quire the applicant for a mining permit 
 to "...identify the extent to which the 
 proposed underground mining activities 
 may proximately result in contamination, 
 diminution, or interruption of an under- 
 ground or surface source of water within 
 the proposed mine plan or adjacent area 
 for domestic, agricultural, industrial, 
 or other legitimate use" (2^). 
 
 This is not easily accomplished because 
 of the lack of documented quantitative 
 information regarding the effects of un- 
 derground mining on surface or under- 
 ground sources of water. Throughout the 
 northern Appalachian bituminous coal re- 
 gion, numerous instances of springs, 
 streams, or domestic wells going dry be- 
 cause of underground coal mining have 
 been reported, but without documentation 
 or allowances for the effect of seasonal 
 changes or precipitation. 
 
 Two recent studies, however, have pro- 
 vided some urgently needed information on 
 the relation between mining and ground 
 
 1 Geologist. 
 
 ^Mining engineer. 
 Pittsburgh Research Center, Bureau of 
 Mines, Pittsburgh, PA. 
 
 •^Underlined numbers in parentheses re- 
 fer to items in the list of references at 
 the end of this paper. 
 
 water resources. The first study, by 
 Owili-Eger (3), was conducted in the 
 Dunkard Basin of the northern Appalachian 
 bituminous coal region. The effects of 
 longwall mining on well yields and water 
 quality were assessed, and conclusions 
 were reached as follows: 
 
 1. Water levels in aquifers located at 
 least 330 ft above the mine horizon usu- 
 ally recovered after mining. 
 
 2. There was a general lowering of the 
 piezometric levels. 
 
 3. There was no major lasting deteri- 
 oration in the quality of ground water 
 systems studied. 
 
 In a second study, Hill, Burgdorf, and 
 Price (4) monitored the short-term ef- 
 fects of longwall mining on ground wa- 
 ter aquifers in western Pennsylvania. 
 Eleven wells ranging in depth from 75 to 
 250 ft were monitored. Some of the gen- 
 eral conclusions resulting from this 
 study follow: 
 
 1. Only minor water level declines of 
 12 to 31 ft occurred in shallow wells 
 less than 100 ft in depth. Water levels 
 rebounded to near premining levels within 
 2 months after the face had passed be- 
 neath a well. 
 
 2. Water level declines of 20 to 211 
 ft occurred in wells 160 to 250 ft deep. 
 The most precipitous water level declines 
 occurred during the 2- to 3-week period 
 of maximum surface subsidence, when the 
 face still was less than 200 ft beyond a 
 well. 
 
 3. Water level declines were greater 
 over the center of the longwall panel 
 than near the edge or bey«ad. 
 
14 
 
 The diminution or interruption of water 
 sources, especially of shallow domestic 
 wells, springs, and small streams, has 
 occurred largely as a result of room-and- 
 pillar mining, which accounts for about 
 93 pet of all underground coal produc- 
 tion in the Appalachian region. However, 
 longwall mining, a more uniform method of 
 extraction, is providing an increasing 
 portion of underground coal production, 
 and interest in environmental effects and 
 damage prevention is shifting toward this 
 method. 
 
 In rural areas , such as much of the 
 northern Appalachian coal region, the de- 
 gree of subsidence damage to frame struc- 
 tures generally is not as devastating as 
 even a temporary loss of water sources, 
 especially in farming. While a certain 
 amount of water can be hauled for house- 
 hold use, the requirements for watering 
 farm animals or washing are substantial 
 and heavily dependent on a local supply. 
 Therefore, it is essential that the ef- 
 fects of mining on local water supplies 
 can be assessed and general predictive 
 guidelines developed. 
 
 Cautions must be exercised, however, in 
 applying general conclusions drawn from 
 disparate results to specific mining sit- 
 uations, for as Waite (_5) admonishes 
 "...there really is no such thing as a 
 'typical 1 underground coal mine. Indi- 
 vidual mines, even in close proximity to 
 one another, often exhibit dramatic dif- 
 ferences in relation to ground water." 
 It is highly probable, also, that no two 
 individual water wells, even in close 
 proximity, will respond identically to 
 mining and subsidence. 
 
 The Bureau of Mines currently is moni- 
 toring surface deformations over longwall 
 panels as part of a long-range program to 
 improve the prediction of longwall sub- 
 sidence and ultimately to control damage 
 to surface structures. At one longwall 
 
 monitoring site in southwestern Pennsyl- 
 vania (fig. 1), where the first longwall 
 panel in the area was mined, the Bureau 
 also arranged for the measuring of water 
 levels in five 6-in-diam wells, each 
 drilled to a depth of 150 ft. These 
 wells were located along a survey moni- 
 toring profile which extends from the 
 centerline of the longwall panel, where 
 the first well is located (fig. 2), to 
 a distance of 1,270 ft outside the rib 
 line, where the outermost hole was 
 located. 
 
 The purpose of this study was to deter- 
 mine the short-term effects of mining the 
 longwall panel on the water levels in the 
 five wells, which were intended to simu- 
 late a fairly typical domestic water well 
 in the region. Wells of this depth (150 
 ft) penetrate the shallow water table 
 aquifer but do not reach any of the deep- 
 er confined aquifers. The term "water 
 table" is used here to designate the sur- 
 face below which the overburden is sat- 
 urated. The water table aquifer extends 
 from the water table down through the 
 saturated zone to the first layer of rel- 
 atively impermeable rock that does not 
 transmit ground water rapidly enough to 
 supply a well or spring. In the Appa- 
 lachian region water wells rarely are 
 drilled to the several-hundred-foot 
 depths where the deeper aquifers occur 
 because these aquifers commonly are of 
 very low yield and may be highly saline 
 in character. 
 
 Weekly measurements were made of water 
 levels in the five wells, and weirs were 
 installed on three small streams and one 
 spring in the vicinity of the longwall 
 panel for measuring flow rates. 
 
 The long-term effects of mining, such 
 as the postmining recovery of water lev- 
 els, will be reported later, along with 
 an assessment of the effects of mining an 
 adjacent longwall panel. 
 
 ACKNOWLEDGMENTS 
 
 The author is grateful for the coopera- 
 tion of EMway Resources Inc., operators 
 
 of the mine, and to landowners 
 Tustin and John T. Gaskill. 
 
 Carl E. 
 
 SITE DESCRIPTION 
 
 The study site at which the water 
 sources and subsidence were monitored is 
 
 is near Waynesburg, Greene County, PA, 
 in the hilly terrain typical of the 
 
15 
 
 Pittsbur 
 
 gh I 
 
 ^^Uniontown 
 
 WEST VIRGINIA 
 
 FIGURE 1. 
 
 20 
 
 _l 
 
 Scale, miles 
 Index map. 
 
 1,000 
 
 LEGEND 
 
 { ) Surface contou 
 
 O Water well 
 
 I Outline of longwall panel 
 
 J Outline of proposed panel 
 
 ▼ V- notch weir 
 /* Spring 
 
 FIGURE 2. - Surface features and longwall panel. 
 
 Appalachian Plateau province. Land use 
 is chiefly for grazing and hay crops; 
 very little is wooded. Bedrock at the 
 site is overlain by 7 to 11 ft of resid- 
 ual soil consisting of clay and weathered 
 shale fragments. There is evidence of 
 
 200 
 
 LU 
 
 o 
 < 
 
 rr 
 
 CO 
 
 o 
 a: 
 
 bJ 
 
 o 
 
 CO 
 Q 
 
 400 
 
 600 
 
 800 
 
 i i 
 
 1 [ 
 
 1 T 
 
 OJ 
 
 I 
 
 rn 
 
 SE 
 
 Clay 
 
 Weathered shale 
 
 Clay shale, silt shale 
 Claystone 
 
 Clay shale, silt shale 
 
 Sandstone 
 
 Clay shale, silt shale 
 
 Limestone 
 
 Clay shale, silt shale 
 
 Limestone 
 
 Clay shale, silt shale 
 
 Sandstone 
 Argillaceous limestone 
 
 Clay shale, silt shale 
 
 Limestone 
 
 Clay shale, silt shale 
 
 Limestone 
 
 Clay shale, silt shale 
 
 Argillaceous limestone 
 
 Sandstone 
 
 Shale 
 
 Sewickley Coalbed 
 
 Limestone 
 Pittsburgh Coalbed 
 
 1,000 
 FIGURE 3. - Generalized columnar section. 
 
 weathering 
 about 50 ft. 
 The geolog 
 the overbur 
 consists of 
 shale, clay 
 and coal. 
 Pittsburgh 
 1,000 ft th: 
 1° SE. 
 
 in the bedrock to a depth of 
 
 ic character of the strata in 
 den is shown in figure 3 and 
 interbedded clay shale, silt 
 stone, limestone, sandstone, 
 Mine overburden above the 
 coalbed ranges from 750 to 
 ck, and the strata dip about 
 
16 
 
 SITE MONITORING 
 
 All measurements of surface deforma- 
 tions above the longwall panel were con- 
 ducted by a local commercial firm fa- 
 miliar with the site. These surface 
 deformations are summarized in transverse 
 
 profiles (fig. 4), in longitudinal pro- 
 files (fig. 5), and as the final sub- 
 sidence contours in the vicinity of water 
 wells 1-4 (fig. 6). 
 
 800 700 
 
 600 
 
 500 400 
 
 300 
 
 200 100 100 200 300 400 500 600 700 800 900 
 
 DISTANCE FROM CENTERLINE, ft 
 
 FIGURE 4. - Transverse subsidence profiles. 
 
 _ 1,400 
 O 1,300 
 > 1,200 
 
 1,100 
 
 -Water well profile 
 
 ^m&m&mmm&®$2®s&$&m &n 
 
 ipoo 
 
 DATE OF LONGWALL PANEL FACE POSITION 
 
 1983 
 
 800 600 400 200 200 400 600 800 1,000 
 
 DISTANCE FROM WATER WELL PROFILE, ft 
 
 1,200 1,400 1,600 1,800 2,000 
 
 FIGURE 5. - Longitudinal subsidence profiles. 
 
17 
 
 0.2 
 
 0.5 
 
 -2.0- 
 
 Panel 
 
 -3.0- 
 
 centerline 
 
 Proposed longwall panel~^y 
 
 LEGEND 
 ®3 Water well 
 
 -2.5 
 
 Subsidence contour, ft 
 
 200 400 
 
 Scale, ft 
 
 FIGURE 6. - Subsidence contours. 
 
 Measurements of water levels in the 
 five water wells and flow rates at the 
 three weirs and one spring were conducted 
 by the Bureau on a weekly schedule as 
 nearly as possible. It is recognized 
 that, ideally, observations to establish 
 premining hydrologic conditions should be 
 conducted for a full year to determine 
 seasonal variations. This, however, was 
 impossible to accomplish at this site, 
 and hence observation water well records 
 in the vicinity were examined for sea- 
 sonal variations. The wells on the site 
 
 were completed as soon as possible, in 
 the second quarter of 1982, the water 
 levels were allowed to stabilize for sev- 
 eral weeks , and regular measurements were 
 begun in July 1982. 
 
 Weirs A and B were installed in May 
 1982, and weir C in January 1983. Mea- 
 surements of the spring overflow were 
 initiated in May 1982. This information 
 on surface water sources was compiled 
 to supplement that obtained from the wa- 
 ter wells. 
 
 WELL WATER QUALITY 
 
 Water samples were bailed from each of 
 the five water wells at the study site 
 prior to mining of the longwall panel. 
 These samples were analyzed, and the re- 
 sults are shown in table 1. 
 
 The analysis of well water samples col- 
 lected about 12 months after mining had 
 reached the profile is shown in table 2. 
 
 It is apparent 
 and 2 that there 
 in overall water 
 ing and 1 year 
 passed the wate 
 well the pH has 
 the alkalinity 
 amount . The d 
 
 from comparing tables 1 
 is no pronounced change 
 quality between premin- 
 after the longwall face 
 
 r well profile. In each 
 
 increased slightly and 
 
 has decreased a small 
 
 issolved solids changed 
 
18 
 
 very little; some increased and some de- 
 creased slightly. These minor changes 
 could be natural variations, or could be 
 attributed to a lowered water table, the 
 effects of cascading 4 and a fluctua- 
 tion in water level, or possibly altered 
 channels of flow in the overburden as a 
 result of the subsidence process. No 
 
 correlation could be made between water 
 quality and the water levels in the 
 wells. 
 
 ^Cascading is ground water entering a 
 water well above the water level in the 
 well, indicating a hydraulically unstable 
 condition. 
 
 TABLE 1. - Well water analyses, premining 
 
 
 Well 1 
 
 Well 2 
 
 Well 3 
 
 Well 4 
 
 Well 5 
 
 Analysis, ppm: 
 
 Alkalinity as CaC03 
 
 211 
 245 
 
 17 
 0.2 
 502 
 0.4 
 0.1 
 
 80 
 
 ND 
 
 1.0 
 
 2 
 
 13 
 101 
 0.4 
 0.5 
 
 6.8 
 
 410 
 
 207 
 
 184 
 
 17 
 
 0.2 
 
 207 
 
 1.2 
 
 0.2 
 
 94 
 
 ND 
 
 1.6 
 
 2 
 
 11 
 
 57 
 
 1.2 
 
 0.2 
 
 7.0 
 600 
 
 252 
 
 197 
 
 23 
 
 0.2 
 
 252 
 
 ND 
 
 0.2 
 
 80 
 
 ND 
 
 2.4 
 
 2 
 
 12 
 
 48 
 
 0.4 
 
 0.1 
 
 7.0 
 600 
 
 176 
 
 157 
 
 12 
 
 0.2 
 
 176 
 
 ND 
 
 0.1 
 
 43 
 
 ND 
 
 2.5 
 
 2 
 
 21 
 
 62 
 
 0.7 
 
 0.1 
 
 7.4 
 350 
 
 218 
 
 
 101 
 
 Chloride as NaCl 
 
 29 
 
 
 0.2 
 
 
 218 
 
 
 0.7 
 
 
 0.1 
 
 
 38 
 
 
 ND 
 
 
 4.4 
 
 
 2 
 
 
 53 
 
 Sulfate as SO4 
 
 12 
 
 
 0.7 
 
 
 0.2 
 
 PH..... 
 
 7.3 
 
 560 
 
 TABLE 2. - Well water analyses, postmining 
 
 
 Well 1 
 
 Well 2 
 
 Well 3 
 
 Well 4 
 
 Well 5 
 
 Analysis, ppm: 
 
 Alkalinity as CaC03 
 
 161 
 
 195 
 20 
 ND 
 
 386 
 ND 
 ND 
 88 
 ND 
 
 2.1 
 
 ND 
 
 9 
 
 89 
 
 1.3 
 ND 
 
 7.9 
 
 440 
 
 164 
 
 155 
 25 
 ND 
 
 236 
 ND 
 ND 
 62 
 ND 
 
 2.2 
 
 ND 
 
 8 
 
 41 
 
 0.2 
 ND 
 
 7.4 
 440 
 
 162 
 
 155 
 25 
 ND 
 
 210 
 ND 
 ND 
 50 
 ND 
 
 1.7 
 
 ND 
 
 7 
 
 36 
 
 0.2 
 ND 
 
 7.4 
 390 
 
 166 
 
 176 
 33 
 ND 
 
 250 
 ND 
 ND 
 36 
 ND 
 
 2.5 
 ND 
 17 
 48 
 
 0.2 
 ND 
 
 7.5 
 
 440 
 
 193 
 
 
 117 
 
 Chloride as NaCl 
 
 45 
 
 
 ND 
 
 
 256 
 
 
 ND 
 
 
 ND 
 
 
 38 
 
 
 ND 
 
 
 1.8 
 
 
 ND 
 
 
 41 
 
 Sulfate as SO4 
 
 29 
 
 
 0.3 
 
 
 ND 
 
 PH..... 
 
 7.7 
 450 
 
ANALYSIS OF RESULTS 
 
 mat 
 
 19 
 
 Figure 7 illustrates the general situa- 
 tion along profile A-A' of figure 2, in- 
 cluding the amount of surface subsidence 
 and the depression of the water levels 
 (water table) that occurred after the 
 longwall panel had been completely ex- 
 tracted. Figure 8 illustrates the rela- 
 tion of well water levels with respect to 
 longwall face advance. 
 
 The most pronounced surface effect from 
 the mining is the formation of the sub- 
 sidence trough with a maximum subsidence 
 of 3.4 ft. Analysis of survey data indi- 
 cates a 15° angle of major surface defor- 
 mation and a 24° angle to the limit of 
 detectable surface deformation (commonly 
 referred to as the angle of draw) . 
 
 The most pronounced effect of mining 
 on the water table aquifer was indi- 
 cated by well 1, which went dry, and by 
 wells 2 and 3, in which the water levels 
 dropped 10 and 25 ft, respectively. It 
 is noteworthy that water levels in wells 
 
 4 and 5, located beyond the 24° limit of 
 surface deformation, were unaffected by 
 the mining. 
 
 The effects of mining, if any, on the 
 streams and spring in the vicinity of 
 the longwall panel (fig. 2) were not 
 detectable over the short term of this 
 study, partly because of normal seasonal 
 variations. 
 
 Further details on the results of moni- 
 toring the wells , streams , and spring are 
 discussed in the following sections. 
 
 WATER WELLS 
 
 Well 1 
 
 After remaining fairly stable for a 
 month after monitoring began, the water 
 level in well 1, located near the center- 
 line of the longwall panel (fig. 2), 
 began an unexplained rise in late August 
 1982 (fig. 9), when the longwall face was 
 
 1,400 
 
 1,200 
 
 1,000 
 
 800 
 
 < 
 
 > 
 
 600- 
 
 400- 
 
 200 
 
 \ I 
 \ \ 
 
 V 
 
 \ 
 
 \ 
 
 Surface 
 
 Panel centerline 
 
 "1 1 
 
 Water level prior to 
 panel extraction 
 
 Water level after complete^ 
 extraction of panel 
 
 // 
 
 Creek 
 
 5 
 
 »>~\\f c* 
 
 i 
 
 I5°angle to limit of major 
 surface deformation 
 
 Mined-out 
 longwall panel 
 
 •/A 
 
 25°angle to limit of detectable 
 surface deformation 
 
 Proposed 
 
 longwall panel 
 
 1,000 
 
 800 r 
 co 
 
 600 o 
 
 LLl 
 
 400 g 
 
 ■=> 
 ao 
 or 
 
 LlI 
 
 200 o 
 
 800 600 400 200 200 400 600 800 1,000 1,200 1,400 1,600 1,800 
 
 DISTANCE FROM CENTERLINE, ft 
 
 FIGURE 7. - Subsidence and water well profiles. 
 
20 
 
 DISTANCE OF FACE FROM 
 WATER WELL SECTION, ft 
 
 1,000 
 2,000 
 3,000 
 
 Surface 
 
 15° angle to limit of 
 major surface deformation 
 
 / / 
 / / 
 / / 
 / / 
 / / 
 
 / 
 
 -Longwall panel" 
 
 / 
 
 if 
 
 II 
 1/ 
 
 -25° angle to limit of 
 
 detectable surface 
 
 deformation 
 
 500 
 
 Scale, ft 
 
 If 
 
 FIGURE 8. - Relation of water levels to longwall face advance. 
 
21 
 
 10 20 10 20 10 20 
 
 JULY AUG. SEPT. 
 
 3.77 3.52 2.33 
 
 MONTHLY RAINFALL, in 
 
 1982 
 
 1983 
 
 FIGURE 9. - Graph of water well levels. Significant precipitation during the winter months 
 nated as either rain (R) or snow (S). 
 
 1984 
 
 is desig- 
 
 over 1,450 ft away and mining had not yet 
 begun. This rise continued for 3 months. 
 A similar but less pronounced rise was 
 detected in well 3. The rise cannot be 
 explained by precipitation, which was be- 
 low average for the 3-month period, nor 
 can it be attributed to seasonal effects 
 because in this region stream and wa- 
 ter table levels generally continue to 
 decline through October and sometimes 
 November. This is because of the high 
 evapotranspiration rates prevailing in 
 the summer and fall. 
 
 A declining trend began about December 
 2, 1982, when the longwall face was 500 
 ft from the well. This trend continued 
 for 3 months to February 24, when the 
 well went dry. At this time the longwall 
 face had progressed to 400 ft past the 
 well. 
 
 It is worth noting at this point that 
 at this study site the first detectable 
 surface subsidence commonly occurs when 
 the face has approached to within 500 to 
 700 ft of a survey monument, and the 
 first major surface subsidence, defined 
 here as 10 pet of maximum subsidence, oc- 
 curred when the face was about 200 ft 
 from the monument (fig. 10). These rela- 
 tions are a function of the character and 
 thickness of the overburden and the 
 thickness of the coalbed and vary from 
 site to site. 
 
 10-pct 
 subsidence 
 
 z.une ui nisi 
 
 r detectable — -\ 
 subsidence 
 
 ■" 1 
 
 Direction of mining 
 
 200 400 
 
 DISTANCE TO FACE, ft 
 
 600 
 
 800 
 
 FIGURE 10. - Longitudinal subsidence profile. 
 
 At this site, then, both the land sur- 
 face and the water table showed the first 
 detectable effects of mining when the 
 longwall face had approached to within 
 500 ft. At 200 ft, 10 pet of maximum 
 subsidence had occurred and the water 
 level in the well was falling at a rate 
 of 1.6 ft/d. 
 
 Well 1 went completely dry on February 
 24, 1983, and remained dry for 3 weeks. 
 Cascading then occurred, and water lev- 
 els rebounded for about 2-1/2 months, 
 finally dropping below the well bottom 
 and remaining there for the remainder of 
 1983. 
 
22 
 
 Well 2 
 
 The water in well 2, located over the 
 chain pillars 440 ft from the longwall 
 panel centerline (fig. 2), remained at a 
 relatively constant level throughout most 
 of the monitoring. Some minor fluctua- 
 tions occurred for an interval of 4 
 months from January 6, 1983, when the 
 longwall face was directly even with the 
 well profile, to May 10, 1983, when the 
 face had progressed 1,250 ft past the 
 well profile (fig. 5). These fluctua- 
 tions probably can be attributed to min- 
 ing because wells 4 and 5, located much 
 farther away from the panel (fig. 7), re- 
 mained unchanged for the same interval 
 (fig. 8). Also, well 2 lies within the 
 15° angle of major deformation where some 
 effects were anticipated. 
 
 Well 3 
 
 The water level in well 3, located 320 
 ft beyond the rib line of the longwall 
 panel (fig. 7) , was unstable throughout 
 most of the 17-month interval of monitor- 
 ing from July 1982 to December 1983 (fig. 
 9). Water levels varied up to 33 ft. 
 While no pronounced effects could be at- 
 tributed with certainty to mining, 
 water levels during the interval of Janu- 
 ary 6 to May 10, 1983, were somewhat more 
 unstable than at other times. Also, well 
 3 was within the 24° angle of detectable 
 surface deformation, so that some effects 
 were anticipated. 
 
 The low level of June 8 to October 25, 
 averaging 110 ft below the surface, can 
 be attributed to the summer season ef- 
 fects of high evapotranspiration, after 
 which the levels recovered to premining 
 levels of about 90 ft. 
 
 Wells 4 and 5 
 
 Wells 4 and 5 are located 580 ft and 
 1,270 ft, respectively, outside the rib 
 line of the longwall panel and 230 ft and 
 920 ft, respectively, beyond the 24° lim- 
 it of detectable surface subsidence (fig. 
 7). 
 
 Neither well showed any detectable sea- 
 sonal or mining effects. Water levels 
 
 remained stable 
 of monitoring (f 
 Precise compar 
 study with those 
 such as that des 
 and Price (4) , s 
 theless, general 
 ter level depres 
 wall mining were 
 each site, as fo 
 
 throughout the 17 months 
 
 ig. 9). 
 
 isons of results of this 
 of a similar test site, 
 
 cribed by Hill, Burgdorf, 
 
 hould be avoided. None- 
 similarities in the wa- 
 
 sion resulting from long- 
 noted in three wells at 
 
 Hows: 
 
 Well location 
 
 Water level 
 depression, ft 
 
 
 Bureau 
 site 
 
 Other 
 site 
 
 Near panel centerline 
 Outside panel: 
 
 350 ft 
 
 -150 (dry) 
 
 -21 
 
 
 
 NAp 
 
 108-211 
 -14 
 
 4,000 ft 
 
 NAp 
 
 
 
 
 NAp Not applicable. 
 
 The comparison of wells near the mar- 
 gins of the panels at these sites yielded 
 only erratic results. 
 
 STREAMS 
 
 One very small perennial stream flows 
 across the longwall panel about 450 ft 
 southeast of the monitoring profile A-A 1 
 (fig. 2). The stream flow rate was mea- 
 sured at two points, weir A and weir B, 
 to establish flow rate characteristics 
 and to detect the effects of mining. 
 
 The most outstanding features of the 
 hydrograph for weir A (fig. 11) are the 
 sharp peak flows of February through May 
 and November through December 1983, char- 
 acteristic of winter and early spring 
 seasons when evapotranspiration is low 
 and infiltration rates are high. Between 
 peak flows a base flow of about 1 gpm was 
 measured for mid- June to mid-November 
 1983 due to high evapotranspiration. 
 While the peak flows of February through 
 May 1982 might have obscured any effects 
 from mining activity, which brackets that 
 interval (fig. 11), similar peaks recur 
 in November through December 1983, indi- 
 cating the response of the stream to sim- 
 ilar episodes of precipitation is about 
 the same and the effects of mining must 
 be minimal. 
 
23 
 
 150 - 
 
 -i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — r 
 
 l.ilJiu.1 
 
 Jl, t,J J,l ML Jti IvlfflJ ,« iJifflLll 
 
 u 
 
 A 
 
 LlUlAlhiiil 
 
 jM 
 
 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 
 
 MAY JUNE JULY AUG SEPT OCT. NOV DEC JAN. FEB. MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC JAN FEB 
 
 342 3.34 3.77 3 52 2.33 0.63 3.11 2.58 1.33 1.68 3.47 5.55 6.40 1.98 3.09 4.26 2.51 3.74 3.68 3.95 1.16 1.81 
 
 MONTHLY RAINFALL, in 
 1982 1983 1984 
 
 FIGURE 11. - Hydrograph at weirs A and B. R = rain; S = snow. 
 
 -i — i — i — i — i — r 
 
 n — i — i — i — i — i — i — r 
 
 i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — r 
 
 Weir C 
 
 -B-tS i i S r Sr _3? 
 
 j 1 
 
 r, t,J JJ MTtit it! kllLi ,«, id it 111 
 
 .► It i 1 
 
 i.lilLAlU . JjiiLiJ 
 
 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 
 
 MAY JUNE JULY AUG SEPT OCT NOV DEC JAN. FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC JAN FEB 
 
 342 334 3.77 3.52 2.33 0.63 3.11 2.58 1.33 1.68 3.47 5.55 6.40 1.98 3.09 4.26 2.51 3.74 3.68 3.95 1.16 1.81 
 
 MONTHLY RAINFALL, in 
 
 1982 1983 1984 
 
 FIGURE 12. - Hydrograph at weir C and spring. R = rain; S = sno 
 
 w. 
 
 Weir B was located 1,450 ft downstream 
 from weir A (fig. 2) and 1,100 ft outside 
 the longwall panel rib line. The hydro- 
 graph for weir B is similar to that for 
 weir A except that the peak flows are 
 higher owing to minor augmentation along 
 the 1,450-ft course between the two weirs 
 and to more extended premining measure- 
 ments. As with weir A, it was antici- 
 pated that some change in flow rates due 
 to mining might be detected; however, the 
 
 only apparent changes are those easily 
 attributed to seasonal effects. Thus, to 
 date, no loss of flow rate due to mining 
 in the source area can be determined at 
 either weir A or B. 
 
 Another very small perennial stream 
 located 600 ft off the monitoring pro- 
 file A-A' and well outside the panel was 
 monitored by weir C (fig. 2) for flow 
 rate background data. The source area 
 seepages that feed this stream probably 
 
24 
 
 are far enough outside the panel to be 
 free from any pronounced subsidence ef- 
 fects. This seams to be confirmed by the 
 hydrograph (fig. 12), which shows the 
 well-established cycle of peak flows dur- 
 ing the winter-spring season of high in- 
 filtration and the low flow rates of the 
 summer-fall season of high evapotranspi- 
 ration. No effects of the mining and 
 subsidence in the source area could be 
 detected. 
 
 SUMMARY AND 
 
 This report has described the short- 
 term effects of mining a longwall panel 
 on water resources in the immediate 
 vicinity. Monitoring of these effects 
 continued for about a year after the 
 longwall face had passed the profile 
 along which surface deformations and the 
 water levels in five observation wells 
 were measured. Two very small streams 
 and a spring located in the vicinity were 
 monitored to establish flow rate charac- 
 teristics. This study was conducted un- 
 der specific conditions existing at the 
 site. The findings are not applicable to 
 areas having different topography, geol- 
 ogy, and hydrology. 
 
 The results of this study, while 
 short term only, support the following 
 conclusions : 
 
 1. Water levels in a 150-ft-deep well 
 located near the centerline of the panel 
 began to decline when the longwall face 
 had approached within 500 ft of the well. 
 The water levels continued to fall, and 
 
 A spring located about 400 ft north- 
 east of weir C (fig. 2) was monitored 
 to determine the flow rate charac- 
 teristics. The hydrograph for this 
 spring (fig. 12) is similar to that for 
 weir C, but shows somewhat higher peak 
 flows and a higher flow during the sum- 
 mer season. No subsidence effects were 
 detected. 
 
 CONCLUSIONS 
 
 the well went dry about 2 months after 
 the face had passed beneath it, at which 
 time the face was 550 ft beyond the well. 
 A temporary recovery of the water level 
 was attributed to cascading, after which 
 the well remained dry. 
 
 2. Water levels in two wells, located 
 100 and 300 ft outside the rib line of 
 the panel, declined some 15 to 30 ft as a 
 result of mining but recovered to near 
 premining levels about 10 months after 
 the longwall face had passed by. 
 
 3. Water wells located more than 500 
 ft outside the longwall panel rib line 
 showed no detectable change in water lev- 
 els as a result of mining. These wells 
 also lie beyond the distance at the 
 surface subtended by the 24° angle to the 
 limit of detectable surface deformation. 
 
 4. No evidence of mining effects on 
 the small streams or spring located 
 within 1,200 ft of the panel could be 
 detected. 
 
 REFERENCES 
 
 1. U.S. Code of Federal Regulations. 
 Title 30 — Mineral Resources; Chapter 
 VII — Office of Surface Mining Reclamation 
 and Enforcement, Department of the In- 
 terior; Subchapter K — Permanent Program 
 Performance Standards; Part 817 — Under- 
 ground Mining Activities; July 1, 1984. 
 
 2. . Title 30 — Mineral Re- 
 sources; Chapter VII — Office of Surface 
 Mining Reclamation and Enforcement, De- 
 partment of the Interior; Subchapter G — 
 Permanent Program Performance Standards; 
 Part 783 — Underground Mining Permit Ap- 
 plications — Minimum Requirements for 
 Information on Environmental Resources; 
 July 1, 1984. 
 
 3. Owili-Eger, A. S. C. Geohydrologic 
 and Hydrogeochemical Impacts of Longwall 
 Coal Mining on Local Aquifers. Soc. Min. 
 Eng. AIME preprint 83-376, 1983, 16 pp. 
 
 4. Hill, J. C, G. J. Burgdorf, and 
 D. R. Price. Effects of Coal Mine Sub- 
 sidence on Ground Water Aquifers in 
 Northern Appalachia (contract J0199063, 
 SMC Martin Inc.). BuMines OFR 142-84, 
 1984, 149 pp., NTIS PB 84-236710. 
 
 5. Waite, B. A. Ground Water Monitor- 
 ing of Underground Coal Mines. Min. Eng. 
 (Littleton, CO), v. 34, 1982, pp. 170- 
 171. 
 
25 
 
 COMPARISON OF THE SUBSIDENCE OVER TWO DIFFERENT LONGWALL PANELS 
 By Paul W. Jeran 1 and Timothy M. Barton 2 
 
 ABSTRACT 
 
 The subsidences over two longwall sec- 
 tions operating in the northern Appalach- 
 ian coal region were monitored. The 
 panels differed in dimensions, overburden 
 thickness, and coalbed mined. Although 
 
 the final subsidence profiles differed, 
 analysis of the data indicates that the 
 same process of subsidence operated at 
 each panel. 
 
 INTRODUCTION 
 
 Since 1960, when the first longwall 
 with powered supports was installed in 
 the United States, the use of the long- 
 wall system of mining by the coal indus- 
 try has grown. In 1984, 21 U.S. coal 
 companies were operating 112 longwalls.3 
 Eighty-four of these panels were in the 
 northern Appalachian coal region, and the 
 majority of these were 500 to 600 ft 
 wide. In recent years, the trend has 
 been to wider panels because of greater 
 productivity allowed by changes in 
 equipment. 
 
 One consequence of longwall mining is 
 the subsidence of the ground surface 
 above the panel. The Bureau has for sev- 
 eral years monitored selected mining 
 sites to obtain reliable and useful data 
 on the reaction of the surface to mining. 
 The ultimate goal of this work is to de- 
 velop a surface subsidence predictive 
 methodology based upon mining and geolog- 
 ic parameters. 
 
 The magnitude of subsidence of a point 
 on the ground surface is proportional to 
 the area of influence coincident with the 
 zone of total extraction. In relatively 
 flat-lying coalbeds the area of influence 
 is typically circular in plan view. If 
 the area of influence is entirely within 
 the zone of extraction, then the maximum 
 
 Geologist. 
 
 ^Mining engineer. 
 Pittsburgh Research Center, Bureau of 
 Mines, Pittsburgh, PA. 
 
 3 Sprouls, M. W. Longwall Census 1984. 
 Coal Min. , v. 21, Dec. 1984, pp. 39-53. 
 
 possible subsidence will occur. If less, 
 then the subsidence will be some fraction 
 of the maximum subsidence. Figure 1 il- 
 lustrates in cross-section the three typ- 
 ical geometries using a constant angle of 
 draw and constant width of panel. The 
 radius of the area of influence is depen- 
 dent upon the thickness (H) of the over- 
 burden. Traditionally, the terms used to 
 describe the three geometries are super- 
 critical, where the radius of influence 
 (RI) is less than half the width (w) of 
 
 FIGURE 1. - Supercritical, critical, and sub- 
 critical geometries. 
 
26 
 
 the panel; critical, where the radius of 
 influence is equal to half the width of 
 the panel; and subcritical, where the 
 half width of the panel exceeds the ra- 
 dius of influence. 
 
 The resulting subsidence curves for 
 each of these geometries are shown in 
 figure 1. The supercritical geometry re- 
 sults in a subsidence curve with multiple 
 points of maximum subsidence. The criti- 
 cal case has one point of maximum subsid- 
 ence. The subcritical case has a maximum 
 point at the center, but this is less 
 than the maximum possible subsidence. By 
 inspection only the supercritical subsid- 
 ence trough can be identified by its 
 
 multiple points of maximum subsidence. 
 The remaining two cannot be differenti- 
 ated without additional information be- 
 cause we cannot know if the maximum ob- 
 served subsidence is the maximum possible 
 subsidence. 
 
 Recently a very wide panel (950 ft 
 wide) was monitored. The resultant sub- 
 sidence exhibited multiple points of max- 
 imum subsidence. This differed from the 
 subsidence troughs monitored over typical 
 width (450 to 600 ft wide) panels which 
 have but a single point of maximum sub- 
 sidence. This report compares the data 
 from this wide panel with data recently 
 obtained from a typical width panel. 
 
 DISCUSSION 
 
 The two longwall panels used in this 
 report are in the northern Appalachian 
 coal region. The typical width panel, 
 designated "E," is in southwestern Penn- 
 sylvania. It is 630 ft wide by 4,700 ft 
 long. It was chosen because the average 
 extracted thickness was the same as that 
 at the wide panel, the subsidence was 
 typical of the standard width panels we 
 have monitored, and the data were ob- 
 tained in the same manner as at the wide 
 panel. The wide panel, designated "K," 
 is in north-central West Virginia. This 
 panel is 950 ft wide by 2,100 ft long. 
 
 At both panels, surface survey points 
 were installed on 25-ft centers across 
 two profiles and a centerline. The ini- 
 tial surveys were taken prior to mining, 
 and the final surveys were taken a month 
 after each panel was finished mining. 
 Each panel was surveyed several times 
 during mining. Figure 2 is a sketch of 
 the survey lines relative to the panels. 
 
 Aside from their dimensions, the panels 
 differed in coalbed mined and overburden. 
 Panel E operated in the Pittsburgh Coal- 
 bed and extracted an average thickness of 
 6 ft. Panel K removed the same average 
 thickness from the Lower Kittanning Coal- 
 bed. Figures 3 and 4 show the variation 
 in overburden thickness for the center- 
 lines and profiles at each of the 
 panels. 
 
 Based upon drillers' logs of the core- 
 holes drilled in the vicinity of each 
 
 panel, the overburden at each site aver- 
 aged about 30 pet resistant strata (i.e., 
 sandstones and limestones). Typical of 
 Pennsylvanian age sediments, there is 
 lateral variation and the range of re- 
 sistant rock content is from 10 to 40 pet 
 of the total thickness. 
 
 Profile A 
 
 ■^\r- 
 
 h 
 
 570' 475' 
 
 Profile B — 
 
 825' 
 
 ♦ b Panel E 
 <o Centerline 
 
 1,425' 
 
 Profile A 
 
 Panel K 
 Centerline - 
 
 200' 
 
 Profile B 
 
 400' 
 
 o 
 
 400' 
 
 o 
 o 
 
 GO 
 
 ^1 
 
 ■-V- 
 
 FIGURE 2. - Subsidence survey lines at panels 
 E and K. 
 
27 
 
 950- — 
 
 900-- 
 
 850-- 
 
 800-- 
 
 750-- 
 
 «- 700-- 
 
 g 650 -- 
 Q 
 
 3 600-- 
 
 CD 
 
 UJ 550-- 
 O 
 
 500-- 
 
 450-- 
 
 400-- 
 
 350-- 
 
 300-- 
 
 250' 
 
 H r- 
 
 ***^^ 
 
 + 
 
 H h 
 
 1 ■ !****£ 
 
 V. Panel E centerline 
 
 Panel K centerline 
 
 + 
 
 400 600 800 1,000 1,200 1,400 1,600 1,800 2,000 2,200,2,400 2,600 2,800 3,000 3,200 3,400 
 
 LOCATION, ft 
 
 FIGURE 3. - Overburden thickness at centerlines. 
 
 1,000 
 900 
 800-- 
 700-- 
 £ 600-- 
 
 W 500 
 CD 400 
 
 rr 
 
 LU 
 > 
 
 O 300 
 
 200-- 
 
 1 oo-- 
 
 {vixvA 
 
 •100 
 
 cm 
 
 Width of panel E 
 
 , Panel K, profile A 
 
 IIIIIIIIIITT7 
 
 Panel K, profile B 
 
 Width of panel K 
 
 ■1,000 -800 -600 -400 
 
 -200 200 
 
 LOCATION, ft 
 
 400 600 
 
 800 
 
 1.000 
 
 FIGURE 4. - Overburden thickness at profile lines. 
 
28 
 
 The final subsidence of the centerline 
 for each panel is shown in figure 5. 
 Subsidence along each centerline was not 
 uniform. Part of this variance may be 
 attributed to one or more of the follow- 
 ing: variation in overburden thickness, 
 variation in extracted thickness, or var- 
 iation in the lithologic composition of 
 the overburden. 
 
 As the position of the face was re- 
 corded for each survey date, its position 
 relative to each survey point during each 
 survey is easily obtained. If the sub- 
 sidence of a point at each survey is 
 divided by the final measured subsidence 
 of that point and these ratios are plot- 
 ted against the relative face position, 
 then a curve is obtained that shows the 
 movement of the point relative to the 
 movement of the face. By plotting these 
 ratios from all points along the center- 
 line for each panel, figure 6 and 7 re- 
 sult. These show that, at both panels, 
 the surface exhibited some upheaval as 
 the face approached some, but not all, of 
 the survey points. Downard movement be- 
 gan as the face passed beneath each 
 point. If the relative position of the 
 face is divided by the overburden thick- 
 ness at each point, then the response of 
 the surface to the face position in terms 
 of overburden thickness may be readily 
 compared between the two sites. Figures 
 8 and 9 clearly show that, at both sites, 
 the subsidence process was over 90 pet 
 complete when the face had advanced the 
 thickness of the overburden beyond the 
 corresponding surface point. 
 
 The final subsidence profiles are shown 
 in figure 10. Those from panel K exhibit 
 
 a broad flattish trough, indicating 
 supercritical geometry. Profiles from 
 panel E show the single point of maximum 
 subsidence, which does not indicate the 
 degree of criticality. Comparing pro- 
 files A and B at panel E, profile B, 
 having the greater subsidence and thinner 
 overburden, is closer to critical geome- 
 try than profile A, assuming all other 
 factors are equal. At panel K, profile B 
 exhibited a lesser magnitude of subsid- 
 ence than did profile A. This may have 
 resulted from the thinner overburden not 
 compacting the gob as much as the thicker 
 overburden. Differences in lithology and 
 extracted thickness may also have played 
 a part. 
 
 Inclinations between survey points were 
 computed from the final profile survey 
 data (fig. 11). At each panel, the 
 greater inclination was created at the 
 profile with the thinner overburden. 
 Plotting the inclinations from the cen- 
 terline data relative to face position as 
 a function of overburden thickness (figs. 
 12-13) shows that for each panel, the 
 maximum inclination occurred when the 
 face was about a third the thickness of 
 the overburden past the corresponding 
 surface point. The maximum inclination 
 over panel K exceeded that over panel E, 
 which indicates that the potential for 
 damage to surface structures is greater 
 over thinner overburden. However, it 
 should be noted that at both panels the 
 maximum inclinations exceeded the limit 
 of 15 mm/m established for protection of 
 lowest priority surface structures in the 
 Silesian coal basin. 
 
 
 SUMMARY 
 
 Subsidence over two longwall panels of 
 different widths (630 and 950 ft) was 
 monitored, and the data were compared. 
 The subsidence profiles at the wider pan- 
 el show the geometry to be supercritical. 
 Those at the narrower panel indicate it 
 is most likely subcritical. At both pan- 
 els, the subsidence process relative to 
 face position can be correlated to over- 
 
 burden thickness. Inclinations at both 
 panels were in excess of 15 mm/m, and the 
 thinner overburden exhibited the greater 
 inclinations. In general, the similarity 
 of the response of the overburdens to 
 mining at each panel indicates that 
 though the final subsidence troughs were 
 differently shaped, the process of sub- 
 sidence at each site was the same. 
 
29 
 
 -2.4 
 
 -2.6 
 
 -2.8-- 
 
 H -3.0-- 
 
 ul -3.2 
 
 % -3.4 
 
 3.6 + 
 
 UJ 
 Q 
 
 to "3.8 
 
 CD 
 
 •4.0 
 
 3 
 
 co _ 4#2 „ 
 
 -4.4-- 
 -4.6-- 
 
 •4.8 
 
 Panel E centerline 
 
 A a AAA 
 
 A AAA A aA A 
 
 AAA> 
 
 Panel K centerline 
 
 400 600 800 1,000 1,200 1,400 1,600 1,800 2,000 2,200 2,400 2,600 2,800 3,000 3,200 3,400 
 
 LOCATION, ft 
 FIGURE 5. - Final subsidence for centerlines. 
 
 10- 
 
 0- 
 
 -10- 
 
 -20- 
 
 o 
 
 -30 
 
 CL 
 
 
 „ 
 
 
 UJ 
 O 
 
 -40 
 
 z 
 
 
 UJ 
 
 
 n 
 
 
 CO 
 
 -bO 
 
 CO 
 
 
 z> 
 
 
 CO 
 
 -60 
 
 •70 
 
 -80 
 
 •90 
 
 100 
 
 fttfA-YWWAVfl; 
 
 AAAIAAAAAAAAAA 
 
 1,000 
 
 -500 
 
 1,500 
 
 500 
 
 FACE POSITION, ft 
 FIGURE 6. - Percent of final subsidence versus face position at panel E. 
 
 2p00 
 
30 
 
 ■Jt -30 
 
 O 
 
 z 
 
 Ld 
 Q 
 
 CO 
 
 00 
 
 CO 
 
 -100 
 
 -1,000 -800 -600 -400 -200 200 400 600 800 1,000 1,200 
 
 FACE POSITION, ft 
 
 FIGURE 7. - Percent of final subsidence versus face position at panel K. 
 
 -100 
 
 AA A A |A A A A A. 
 
 ■1 -0 
 
 2-5 
 
 -0-5 0.0 0.5 1-0 1-5 2-0 
 
 FACE POSITION -OVERBURDEN RATIO 
 FIGURE 8. - Percent of final subsidence versus face position as a function of over 
 burden thickness at panel E. 
 
 3.0 
 
31 
 
 Ui 
 
 o 
 
 LU 
 
 Q 
 
 Mw^WiffiS^; 
 
 77 "50 
 
 ■100 
 
 -1 .0 
 
 -0.5 
 
 2.5 
 
 0.0 0.5 1-0 1.5 2.0 
 
 FACE POSITION-OVERBURDEN RATIO 
 FIGURE 9. - Percent of final subsidence versus face position as a function of over- 
 burden thickness at panel K. 
 
 3.0 
 
 
 0.5- 
 
 o.o- 
 
 i 
 i 
 
 cm- 
 
 h 
 
 1 1 1 1 1 1 
 
 1 
 
 *♦- 
 
 -0.5- 
 -1 .0- 
 -1 .5-J 
 -2.0- 
 
 ■ 
 
 u^m 
 
 * %V AA A ■ 
 D A A A A O 
 
 ■4a a ■ 
 
 D \ A A D 
 H * A * # 
 
 BM^^_A 
 
 III 
 o 
 
 z 
 w 
 
 Q 
 0> 
 
 00 
 
 => 
 </> 
 
 -2.5- 
 -3.0- 
 -3.5- 
 -4.0- 
 
 
 
 A A m 
 i ^ ^ 
 
 ^iT^iiiiiijHig' 
 
 -- 
 
 
 -4-5- 
 
 i 
 
 KEY 
 3 rofile A 
 
 Profile B ^Ur^" 
 
 -- 
 
 
 -5.0- 
 
 _ Panel E 
 Panel K 
 
 A 
 
 a 
 
 A 
 ■ 
 
 -- 
 
 
 -5.5- 
 -6.0- 
 -6.5- 
 
 1- 
 
 1- 
 
 Width of panel E 
 
 —1 1 h- 
 
 
 Width of panel K 
 
 
 1 1 1 1 1 1 
 
 -1,000 -800 
 
 -600 
 
 -400 -200 200 
 
 LOCATION, ft 
 
 400 
 
 600 
 
 800 
 
 1.000 
 
 FIGURE 10. - Final subsidence profiles. 
 
32 
 
 34 
 
 32+ 
 
 30 
 
 28-- 
 
 26-- 
 
 24-- 
 
 22-- 
 
 20-- 
 
 18-- 
 
 16 
 
 . 14-- 
 
 Z 
 
 O 12-- 
 
 I- 
 
 < 10-- 
 
 z 
 
 3 8- 
 o 
 
 Z 6-- 
 
 4-- 
 
 2-- 
 
 0- 
 
 -2- 
 
 -4-- 
 
 -6-- 
 
 -8-- 
 
 KEY 
 
 
 Profile A 
 
 Profile B 
 
 Panel E A 
 
 A / 
 
 Panel K D 
 
 ■/- 
 
 •10 
 
 -1,000 
 
 % 
 
 A 
 A A 
 
 H A 
 
 A A 
 
 AA. 
 
 A 
 A*. 
 
 D 
 
 J" 
 
 A 
 AB 
 A 
 
 A 
 
 
 
 ZA 
 
 cP 
 
 Width of panel E 
 Width of panel K 
 
 + 
 
 + 
 
 ■800 
 
 -600 
 
 -400 
 
 400 
 
 -200 200 
 
 LOCATION, ft 
 
 FIGURE 11. - Inclination across profiles. 
 
 600 
 
 800 
 
 1,000 
 
 16- 
 15- 
 
 14-- 
 
 13- 
 
 12- 
 
 1 1-- 
 
 10- 
 9-- 
 8-- 
 7-- 
 6- 
 5- 
 4- 
 3- 
 2- 
 
 A 
 AA 
 A 
 A A 
 A 
 AA 
 A 
 A 
 
 AAA 
 
 A 
 
 AAiWSA 
 
 
 AA 
 
 AA A 
 
 AA AA 
 
 ■HftA^^A AAA 
 
 A_ 
 AA A AAA. 
 
 AA AAA 
 
 •1 -0 
 
 -0.5 
 
 -r 
 
 0.0 
 
 2.5 
 
 0.5 1.0 1.5 2.0 
 
 FACE POSITION-OVERBURDEN RATIO 
 FIGURE 12. - Inclination versus face position as a function of overburden thick 
 ness, centerline panel E. 
 
 3.0 
 
33 
 
 1 .0 
 
 •0.5 
 
 0.0 
 
 2.5 
 
 0.5 1.0 1.5 2.0 
 
 FACE POSITION-OVERBURDEN RATIO 
 FIGURE 13. - Inclination versus face position as a function of overburden thickness, centerline 
 panel K. 
 
 3.0 
 
34 
 
 PRECALCULATION OF SUBSIDENCE OVER LONGWALL PANELS 
 IN THE NORTHERN APPALACHIAN COAL REGION 
 
 By Vladimir Adamek 1 and Paul W. Jeran 2 
 
 ABSTRACT 
 
 The specific lithological conditions 
 over the Pittsburgh Coalbed, highly re- 
 sistive limestone and sandstone units 
 with relatively shallow overburden, pre- 
 vent the use of any predictive method as 
 developed for European conditions. 
 
 This paper describes the development of 
 a subsidence precalculation methodology 
 suitable to the raining and geological 
 conditions in the northern Appalachian 
 coal region. 
 
 It has been found that owing to litho- 
 logical conditions over the Pittsburgh 
 Coalbed, the subsidence coefficient var- 
 ies within the area of the subsidence 
 trough. This is different from the Euro- 
 pean conditions, where the subsidence 
 coefficient is considered to be a 
 constant. 
 
 The effects of lithology, in the form 
 of a variable subsidence coefficient, 
 
 have been separated for each test site 
 by introducing a correlation between 
 hypothetically homogeneous overburden and 
 existing lithological conditions, while 
 providing for different mining 
 conditions. 
 
 Field data from 11 Bureau longwall pan- 
 el studies were used in the regression 
 analysis. For each panel the character- 
 istics of the variability of the subsid- 
 ence coefficient along individual profile 
 lines were defined. Regression analysis 
 of the subsidence coefficients from all 
 test sites on the location relative to 
 the edge of the panel has yielded a 
 third-degree polynomial equation with a 
 coefficient of correlation of 0.9999. 
 
 All sensitivity tests have shown good 
 results. 
 
 INTRODUCTION 
 
 The enactments of Surface Mining Con- 
 trol and Reclamation Act of 1977 and Pub- 
 lic Law 95-87 made it mandatory that mine 
 operators, prior to mining, define — 
 
 1. The aerial extent of surface 
 movement. 
 
 2. The surface deformations resulting 
 from both vertical and horizontal 
 movements. 
 
 3. The time dependency of surface 
 movements that will be caused by the pro- 
 posed mining. 
 
 Since little or no experience in sub- 
 sidence prediction existed in this coun- 
 try, the methods developed in Europe were 
 applied to meet these requirements. It 
 
 T — '• — : '• 
 
 Mining engineer. 
 
 Geologist. 
 
 Pittsburgh Research 
 
 Mines, Pittsburgh, PA. 
 
 Center, Bureau of 
 
 quickly became apparent that none of the 
 methods yielded acceptable results. 
 
 The Bureau of Mines began work on a 
 project to develop a predictive model for 
 subsidence caused by coal mining in this 
 country. To date, field subsidence data 
 have been collected from 11 longwall test 
 sites via in-house monitoring programs. 
 Analysis of these data verified the non- 
 applicability of the existing methods to 
 U.S. conditions. 
 
 The model presented in this paper is 
 limited to predicting vertical movements 
 over longwall panels and thus far has 
 been investigated only for applications 
 in the northern Appalachian coal region. 
 It requires the operator only to input 
 the geometry of the proposed mining and 
 therefore can be used without prior 
 knowledge or understanding of the sub- 
 sidence process. 
 
■ - IV, 
 
 35 
 
 DEVELOPMENT OF SUBSIDENCE PRECOMPUTATION METHODOLOGY 
 
 Since the coefficient of subsidence and 
 the angle of draw are important to the 
 understanding of this model, a discussion 
 of these follows. 
 
 COEFFICIENT OF SUBSIDENCE 
 
 For critical and supercirtical situa- 
 tions, the coefficient of subsidence is 
 defined as a ratio 
 
 smax 
 
 a = » 
 
 m 
 
 where smax = maximum subsidence measured 
 
 and m = extracted coal seam 
 thickness , 
 
 For subcritial situations 
 
 a = 
 
 smax 
 me 
 
 where 
 
 e = the efficiency coefficient of 
 the partial area of 
 influence. 
 
 Practically, for all existing predic- 
 tive methods, subsidence coefficient a is 
 considered to be constant within the 
 whole area of the subsidence trough. 
 
 The average coefficient of subsidence a 
 can be defined as 
 
 - _ VE 
 a VS 
 
 VS = volume of the subsidence trough 
 VE = volume of the coal extracted. 
 
 For homogeneous overburden, or overbur- 
 den behaving homogeneously from the point 
 of view of subsidence, the values of a 
 and a should be about equal. 
 
 Moderate discrepancies between the val- 
 ues of a and a can be caused by insuffi- 
 cient compaction of the gob area at the 
 edges of the longwall panel, due to the 
 resistance of chain pillars. 
 
 ANGLE OF DRAW 
 
 By definition, the angle of draw is 
 identified as an angle between the line 
 
 connecting the top edge of a longwall 
 panel with the nearest zero-movement 
 point on the surface, and a vertical 
 dropped from this point. The angle of 
 draw serves at leaste two purposes as de- 
 scribed below: 
 
 1. The angle of draw serves to delin- 
 eate the surface area influenced by un- 
 derground mining. The identification of 
 a zero-movement point is a rather dif- 
 ficult task, depending on overall circum- 
 stances. For relatively shallow overbur- 
 den and a smooth surface, good results 
 are more probable. 
 
 In reality, in many cases, small sur- 
 face subsidences (up to 0.2 to 0.3 ft) 
 occur far beyond the edge of the panel, 
 suggesting an unrealistically large angle 
 of draw. These movements may not even be 
 directly connected with underground min- 
 ing activities, but can be caused by 
 ground water movement, sliding, tempera- 
 ture changes, etc. 
 
 Therefore, it would be realistic to de- 
 fine the limit angle of draw as the angle 
 between a vertical line and the line con- 
 necting the upper edge of the panel with 
 the place on the surface where surface 
 deformations do not exceed a certain lim- 
 it. An example follows: 
 
 Vertical movement 
 
 S < 0.1 ft 
 
 Inclination I < 2 mm/m 
 Horizontal strains E < 1 mm/m 
 
 2. The angle of draw serves as a 
 functional parameter for predictive 
 methodologies . 
 
 For a majority of predictive methods 
 based on influence functions, the angle 
 of draw is the functional parameter that, 
 together with the underground geometry 
 and overburden thickness, defines the 
 characteristics of surface deformations. 
 
 For homogeneous overburden or overbur- 
 den behaving homogeneously, the concep- 
 tion of the angle of draw as a functional 
 parameter for predictive methodologies 
 based on the principle of the area of the 
 influence has been proven valid. 
 
 Individual theories developed on this 
 conception (Keinhorst, Bals, Niemczyk, 
 
36 
 
 Beyer, etc.) differ from each other very 
 little, the differences being caused by 
 assigning different values of influence 
 to individual zones within the whole area 
 of influence. Bals ' theory has achieved 
 the widest recognition and practical use 
 in Europe. Its substance is the defini- 
 tion of the efficiency coefficient e. 
 (See appendix. ) 
 
 In accordance with Newton's law govern- 
 ing the attraction of masses, Bals 
 
 assumes that each differential part of 
 mined-out area within the area of influ- 
 ence exerts an influence on the surface 
 point inversely proportional to its dis- 
 tance from it. 
 
 Using the computer algorithm developed 
 by the Bureau, it was possible to compute 
 and tabulate the values of e for differ- 
 ent mining conditions, i.e., underground 
 geometry and overburden thickness (table 
 1). 
 
 TABLE 1. - Efficiency coefficients (e) for y = 25' 
 
 w/H 
 
 
 Distance inward from 
 
 edge of 
 
 panel 
 
 as fraction of 
 
 panel 
 
 width 
 
 
 
 0.50 
 
 0.45 
 
 0.40 
 
 0.35 
 
 0.30 
 
 0.25 
 
 0.20 
 
 0.15 
 
 0.10 
 
 0.05 
 
 0.00 
 
 0.1 
 
 0.289 
 
 0.289 
 
 0.289 
 
 0.286 
 
 0.286 
 
 0.280 
 
 0.277 
 
 0.268 
 
 0.258 
 
 0.250 
 
 0.237 
 
 
 .473 
 
 .471 
 
 .468 
 
 .466 
 
 .460 
 
 .449 
 
 .440 
 
 .428 
 
 .415 
 
 .389 
 
 .361 
 
 0.3 
 
 .609 
 
 .609 
 
 .606 
 
 .599 
 
 .590 
 
 .577 
 
 .563 
 
 .542 
 
 .520 
 
 .487 
 
 .439 
 
 0.4 
 
 .722 
 
 .719 
 
 .714 
 
 .706 
 
 .692 
 
 .676 
 
 .654 
 
 .629 
 
 .594 
 
 .554 
 
 .487 
 
 0.5 
 
 .811 
 
 .808 
 
 .801 
 
 .788 
 
 .772 
 
 .749 
 
 .723 
 
 .686 
 
 .643 
 
 .588 
 
 .500 
 
 
 .879 
 
 .877 
 
 .868 
 
 .853 
 
 .833 
 
 .803 
 
 .765 
 
 .720 
 
 .667 
 
 .600 
 
 .500 
 
 0.7 
 
 .934 
 
 .931 
 
 .919 
 
 .899 
 
 .870 
 
 .833 
 
 .793 
 
 .744 
 
 .686 
 
 .609 
 
 .500 
 
 0.8 
 
 .973 
 
 .969 
 
 .952 
 
 .927 
 
 .896 
 
 .858 
 
 .818 
 
 .765 
 
 .703 
 
 .622 
 
 .500 
 
 0.9 
 
 .998 
 
 .988 
 
 .972 
 
 .949 
 
 .920 
 
 .882 
 
 .841 
 
 .786 
 
 .720 
 
 .633 
 
 .500 
 
 1.0 
 
 1.000 
 
 .999 
 
 .987 
 
 .967 
 
 .939 
 
 .903 
 
 .861 
 
 .804 
 
 .737 
 
 .644 
 
 .500 
 
 
 1.000 
 
 1.000 
 
 .977 
 
 .982 
 
 .957 
 
 .921 
 
 .879 
 
 .823 
 
 .751 
 
 .656 
 
 .500 
 
 1.2 
 
 1.000 
 
 1.000 
 
 1.000 
 
 .992 
 
 .972 
 
 .939 
 
 .896 
 
 .841 
 
 .765 
 
 .667 
 
 .500 
 
 1.3 
 
 1.000 
 
 1.000 
 
 1.000 
 
 .999 
 
 .983 
 
 .953 
 
 .913 
 
 .855 
 
 .780 
 
 .677 
 
 .500 
 
 1.4 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 .992 
 
 .966 
 
 .927 
 
 .870 
 
 .793 
 
 .686 
 
 .500 
 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 .999 
 
 .977 
 
 .939 
 
 .884 
 
 .804 
 
 .692 
 
 .500 
 
 1.6 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 .986 
 
 .952 
 
 .896 
 
 .818 
 
 .703 
 
 .500 
 
 1.7 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 .987 
 
 .963 
 
 .909 
 
 .828 
 
 .711 
 
 .500 
 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 .993 
 
 .972 
 
 .920 
 
 .841 
 
 .720 
 
 .500 
 
 1.9 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 .999 
 
 .979 
 
 .929 
 
 .851 
 
 .728 
 
 .500 
 
 2.0 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 .987 
 
 .939 
 
 .861 
 
 .737 
 
 .500 
 
 2.1 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 .992 
 
 .949 
 
 .870 
 
 .744 
 
 .500 
 
 2.2 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 .997 
 
 .957 
 
 .879 
 
 .751 
 
 .500 
 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 .964 
 
 .888 
 
 .758 
 
 .500 
 
 2.4 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 .972 
 
 .896 
 
 .765 
 
 .500 
 
 2.5 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 .978 
 
 .906 
 
 .772 
 
 .500 
 
 2.6 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 .983 
 
 .913 
 
 .780 
 
 .500 
 
 2.7 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 .988 
 
 .920 
 
 .786 
 
 .500 
 
 2.8 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 .992 
 
 .927 
 
 .793 
 
 .500 
 
 2.9 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 .996 
 
 .934 
 
 .799 
 
 .500 
 
 3.0 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 .999 
 
 .939 
 
 .804 
 
 .500 
 
 
 
 Distanc 
 
 e outwa 
 
 rd fron 
 
 i edge o 
 
 f panel 
 
 as f ra 
 
 ction o 
 
 f panel 
 
 width 
 
 
 
 0.00 
 
 -0.50 
 
 -0.10 
 
 -0.15 
 
 -0.20 
 
 -0.25 
 
 -0.30 
 
 -0.35 
 
 -0.40 
 
 -0.45 
 
 -0.50 
 
 0.1 
 
 0.237 
 
 0.222 
 
 0.213 
 
 0.201 
 
 0.191 
 
 0.184 
 
 0.180 
 
 0.177 
 
 0.171 
 
 0.166 
 
 0.160 
 
 
 .361 
 
 .332 
 
 .304 
 
 .288 
 
 .274 
 
 .261 
 
 .246 
 
 .234 
 
 .224 
 
 .214 
 
 .203 
 
 0.3 
 
 .439 
 
 .392 
 
 .357 
 
 .331 
 
 .305 
 
 .286 
 
 .263 
 
 .244 
 
 .227 
 
 .209 
 
 .194 
 
 0.4 
 
 .487 
 
 .418 
 
 .375 
 
 .333 
 
 .297 
 
 .263 
 
 .235 
 
 .207 
 
 .182 
 
 .159 
 
 .139 
 
 
 .500 
 
 .412 
 
 .356 
 
 .308 
 
 .263 
 
 .228 
 
 .196 
 
 .166 
 
 .139 
 
 .116 
 
 .094 
 
 0.6 
 
 .500 
 
 .400 
 
 .333 
 
 .280 
 
 .235 
 
 .196 
 
 .159 
 
 .130 
 
 .104 
 
 .080 
 
 .061 
 
37 
 
 TABLE 1. - Efficiency coefficients (e) for y = 25° — Continued 
 
 w/H 
 
 Distance outward from edge 
 
 of panel as fraction 
 
 of panel width — Continued 
 
 
 0.00 
 
 0.05 
 
 0.10 
 
 0.15 
 
 0.20 
 
 0.25 
 
 0.30 
 
 0.35 
 
 0.40 
 
 0.45 
 
 0.50 
 
 0.7 
 
 0.500 
 
 0.391 
 
 0.314 
 
 0.256 
 
 0.207 
 
 0.166 
 
 0.130 
 
 0.099 
 
 0.073 
 
 0.051 
 
 0.033 
 
 0.8 
 
 .500 
 
 .378 
 
 .297 
 
 .235 
 
 .182 
 
 .139 
 
 .104 
 
 .073 
 
 .048 
 
 .028 
 
 .013 
 
 0.9 
 
 .500 
 
 .367 
 
 .280 
 
 .214 
 
 .159 
 
 .116 
 
 .080 
 
 .051 
 
 .028 
 
 .012 
 
 .001 
 
 
 .500 
 
 .356 
 
 .263 
 
 .196 
 
 .139 
 
 .094 
 
 .061 
 
 .033 
 
 .013 
 
 .001 
 
 .000 
 
 1.1 
 
 .500 
 
 .344 
 
 .249 
 
 .177 
 
 .121 
 
 .077 
 
 .043 
 
 .018 
 
 .003 
 
 .000 
 
 .000 
 
 1.2 
 
 .500 
 
 .333 
 
 .235 
 
 .159 
 
 .104 
 
 .061 
 
 .028 
 
 .008 
 
 .000 
 
 .000 
 
 .000 
 
 1.3 
 
 .500 
 
 .323 
 
 .220 
 
 .145 
 
 .087 
 
 .046 
 
 .017 
 
 .001 
 
 .000 
 
 .000 
 
 .000 
 
 1.4 
 
 .500 
 
 .314 
 
 .207 
 
 .130 
 
 .073 
 
 .033 
 
 .008 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 1.5 
 
 .500 
 
 .308 
 
 .196 
 
 .116 
 
 .061 
 
 .022 
 
 .001 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 
 .500 
 
 .297 
 
 .182 
 
 .104 
 
 .048 
 
 .013 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 1.7 
 
 .500 
 
 .289 
 
 .172 
 
 .091 
 
 .037 
 
 .007 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 1.8 
 
 .500 
 
 .280 
 
 .159 
 
 .080 
 
 .028 
 
 .001 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 1.9 
 
 .500 
 
 .272 
 
 .149 
 
 .071 
 
 .021 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 2.0 
 
 .500 
 
 .263 
 
 .139 
 
 .061 
 
 .013 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 2.1 
 
 .500 
 
 .256 
 
 .130 
 
 .051 
 
 .008 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 2.2 
 
 .500 
 
 .249 
 
 .121 
 
 .043 
 
 .003 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 2.3 
 
 .500 
 
 .242 
 
 .112 
 
 .036 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 2.4 
 
 .500 
 
 .235 
 
 .104 
 
 .028 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 2.5 
 
 .500 
 
 .228 
 
 .094 
 
 .022 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 2.6 
 
 .500 
 
 .220 
 
 .087 
 
 .017 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 2.7 
 
 .500 
 
 .214 
 
 .080 
 
 .012 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 
 .500 
 
 .207 
 
 .073 
 
 .008 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 2.9 
 
 .500 
 
 .201 
 
 .066 
 
 .004 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 3.0 
 
 .500 
 
 .196 
 
 .061 
 
 .001 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 In general, subisdence of any surface 
 point above a longwall panel can be ex- 
 pressed as 
 
 s = smax f(x) = m a f(x). 
 
 The function f(x) is a mathematical ex- 
 pression that relates to the physical 
 setting and depends mainly on the under- 
 ground geometry, overburden thickness, 
 overburden properties, and relative posi- 
 tion of the surface point toward the 
 mined-out area. 
 
 The equation s = m a f(x) is theoreti- 
 cally valid for any mining and geological 
 conditions because of the broad meaning 
 and flexibility of f(x). 
 
 In this equation, there are three un- 
 known: s, a, and f(x). After acquiring 
 a sufficient amount of field data (s), 
 there still remain two unknown members in 
 the equation, a and f(x). 
 
 By alternately substituting a as a con- 
 stant with computed values from field 
 measurements 
 
 a = 
 
 smax 
 m 
 
 or 
 
 a = 
 
 smax 
 me 
 
 and substituting f(x) with different ex- 
 isting predictive methodologies, one may 
 verify the validity of individual method- 
 ologies for U.S. mining and geological 
 conditions. 
 
 After analyzing data from 11 test 
 sites, it has been found that none of the 
 existing predictive methodologies based 
 either on influence or profile function 
 is applicable to U.S. mining geological 
 conditions. The main reason is the ex- 
 treme effect of lithology on the subsid- 
 ence characteristics, namely highly re- 
 sistant layers of limestone and sandstone 
 with relatively shallow overburden. Fig- 
 ure 1 shows a typical subsidence profile 
 as measured over the Pittsburgh Coalbed 
 compared with precalculated profiles 
 using the above-mentioned methods. 
 
 As a first step in developing a predic- 
 tive model, the problem was approached 
 by trying to establish the effect of 
 
38 
 
 
 
 """*^r-=*J— . 1 
 
 .____ 1 1 
 
 1 1 1 1 
 
 
 ^SS^ --^ s 
 
 
 
 
 ^KCn^ 
 
 ^^ s ~~~~. 
 
 
 10 
 
 ^T 
 
 "Beyer s ~ 
 
 S 
 
 
 _ Keinhorst — -»>\ 
 
 
 \^^ Typical subsidence 
 *C profile, 
 
 20 
 
 
 *$X 
 
 *. Pittsburgh Coalbed ~~ 
 
 30 
 
 Bals--" 
 
 \v /Niemczyk *. 
 
 
 
 %. 
 
 \ 
 
 u 
 
 
 
 ■t 
 
 o- 40 
 
 — 
 
 \\ 
 
 \ - 
 
 LU 
 O 
 
 
 \i 
 
 \ 
 
 § 50 
 
 — 
 
 
 \ 
 
 Q 
 
 
 
 t, » 
 
 CO 
 
 CO 
 
 
 
 V \ 
 
 13 60 
 
 co 
 
 — 
 
 
 \ \ 
 
 
 
 
 70 
 
 
 
 
 
 
 80 
 
 
 
 
 
 
 
 90 
 
 — 
 
 
 100 
 
 1 1 1 
 
 1 1 
 
 i i r^-3^ 
 
 1 ^=F 
 S ^'"^-Bals forr=25' 
 
 10 20 30 40 50 60 70 80 90 I00 
 
 WIDTH, pet 
 
 FIGURE 1. - Comparison of measured profile 
 with some precalculated profiles for Pittsburgh 
 Coalbed. 
 
 lithology on subsidence characteristics 
 for each test site and also to define 
 relative differences of this effect be- 
 tween individual test sites. This cannot 
 be done by simple comparison of sub- 
 sidence profiles. Different mining con- 
 ditions and underground geometry in- 
 cluding depth of cover must be taken into 
 account. 
 
 The principle of this idea is to es- 
 tablish the difference in subsidence 
 characteristics between hypothetically 
 homogeneous overburden, i.e. , overburden 
 without the presence of resistive hard 
 rock units, and existing lithological 
 conditions. At the same time, one must 
 provide for given mining conditions. 
 
 For computation of subsidences for ho- 
 mogeneous overburden, Bals ' theory was 
 used. Since one cannot define the exact 
 value of the angle of draw, the whole 
 process of computation for three concepts 
 was repeated, namely, for y = 25°, for y 
 = 15° , and also for a constant value of 
 efficiency coefficient e = 1 for all 
 points. 
 
 According to Bals , the subsidence of 
 any surface point for homogeneous over- 
 burden is 
 
 p-Edge of panel | <™g 
 
 700 
 
 100 200 300 400 500 600 
 DISTANCE FROM THE CENTERLINE, ft 
 FIGURE 2. - Comparison of measured profile 
 with Bals' predictive method. 
 
 si = m a e 5 
 
 with predetermined or estimated constant 
 subsidence coefficient a. 
 
 Figure 2 shows precalculated profiles 
 by Bals, using the values of the angle of 
 draw y = 15° and y = 25° in comparison 
 with measured profile. It is evident 
 that there is no possibility of obtaining 
 reasonable congruency between precalcu- 
 lated and measured profiles for any value 
 of y as a functional parameter. This 
 leads to the conclusion that the concep- 
 tion of using the angle of draw as a 
 funtional parameter for direct precompu- 
 tation of surface deformations is unsat- 
 isfactory for conditions where effect of 
 lithology is as overwhelming as it is 
 over the Pittsburgh Coalbed. 
 
 The specific lithological conditions 
 over the Pittsburgh Coalbed, namely high- 
 ly resistive limestone and sandstone 
 units with relatively shallow overburden, 
 prevent the use of any predictive method 
 as developed for European conditions. 
 Further, it is also justifiable to assume 
 that the resistance of interbedded hard 
 rock layers is strongest at the edge of 
 the panel and diminishes toward the 
 centerline. 
 
 Such a situation must lead to variabil- 
 ity of the subsidence coefficient along 
 the profile, otherwise considered to be 
 constant for homogeneous overburden. 
 This assumption is further supported by 
 the discrepancy between the subsidence 
 coefficient 
 
asaaffi 
 
 39 
 
 a = 
 
 smax 
 m 
 
 or 
 
 a = 
 
 smax 
 me 
 
 and the average subsidence coefficient 
 
 VS 
 a = VE 
 
 As mentioned before, for homogeneous 
 overburden these two values should be 
 about equal. 
 
 As shown in table 2, the values of a at 
 the centerline of the panel, at each test 
 site, are close to 0.6 and a is about 
 0.35. Such discrepancy must have a de- 
 cisive effect on the subsidence charac- 
 teristics. 
 
 To obtain the congruency between pre- 
 computed and measured data, the subsid- 
 
 ence coefficient 
 variable: 
 
 a w was introduced as a 
 
 sF 
 me 
 
 I, 
 
 where SF. = measured subsidence. 
 
 For each surface point at all test 
 sites the value of a v ; has been defined. 
 Figures 3-8 show the characteristics of 
 a v for y = 25° and y = 15° and for con- 
 stant e = 1 along all profiles. 
 
 If the assumption about the validity of 
 Bals ' theory for homogeneous overburden 
 is correct — and no reason has been found 
 to doubt it — then each of these curves 
 represents a lithological effect on sub- 
 sidence characteristics, expressed in the 
 form of the variable subsidence coeffi- 
 cient. The dispersion of individual 
 curves shows the differences of litholog- 
 ical effect between individual test 
 sites. 
 
 The usefulness of this approach for 
 subsidence precalculation depends on two 
 possibilities: 
 
 1. The lithological effect on subsid- 
 ence characteristics differs at each site 
 beyond acceptable limits, as would be 
 demonstrated by a large dispersion of in- 
 dividual curves. 
 
 2. The lithological effect at each 
 site is acceptably similar. Then the 
 
 TABLE 2. - Overview of basic parameters at various test sites 
 
 
 H 
 
 , ft 
 
 m, ft 
 
 w, ft 
 
 s F at 
 centerline, 
 
 a at 
 centerline 
 
 a 
 (VS/VE) 
 
 w 
 
 Mine 
 
 Range 
 
 At 
 
 H 
 
 
 
 centerline 
 
 
 
 ft 
 
 for y = 25° 
 
 
 
 1 
 
 520-706 
 
 650 
 
 5.5 
 
 460 
 
 -2.62 
 
 0.513 
 
 0.30 
 
 0.71 
 
 2 
 
 677-700 
 
 700 
 
 5.5 
 
 600 
 
 -3.25 
 
 .597 
 
 .35 
 
 .86 
 
 3 
 
 645-700 
 
 700 
 
 5.5 
 
 600 
 
 -3.25 
 
 .597 
 
 .32 
 
 .86 
 
 4 
 
 509-624 
 
 615 
 
 5.5 
 
 605 
 
 -3.65 
 
 .664 
 
 .44 
 
 .98 
 
 5 
 
 652-781 
 
 652 
 
 5.5 
 
 605 
 
 -3.55 
 
 .645 
 
 .39 
 
 .93 
 
 6 
 
 740-795 
 
 795 
 
 5.5 
 
 600 
 
 -3.09 
 
 .587 
 
 .32 
 
 .75 
 
 7 
 
 732-795 
 
 795 
 
 5.5 
 
 600 
 
 -3.09 
 
 .587 
 
 .32 
 
 .75 
 
 8 
 
 913-995 
 
 913 
 
 6.0 
 
 630 
 
 -3.42 
 
 .614 
 
 .40 
 
 .69 
 
 9 
 
 803-913 
 
 913 
 
 6.0 
 
 630 
 
 -3.42 
 
 .614 
 
 .38 
 
 .69 
 
 10 
 
 802-855 
 
 855 
 
 6.0 
 
 630 
 
 -3.12 
 
 .547 
 
 .34 
 
 .74 
 
 11 
 
 717-780 
 
 717 
 
 6.0 
 
 630 
 
 -3.72 
 
 .623 
 
 .34 
 
 .88 
 
 12 
 
 702-719 
 
 717 
 
 6.0 
 
 630 
 
 -3.72 
 
 .623 
 
 .34 
 
 .88 
 
 13 
 
 368-402 
 
 402 
 
 6.0 
 
 940 
 
 -4.04 
 
 .673 
 
 .37 
 
 2.34 
 
 14 
 
 345-40Z 
 
 402 
 
 6.0 
 
 940 
 
 -4.04 
 
 .673 
 
 .39 
 
 2.34 
 
 15 
 
 700-845 
 
 845 
 
 5.5 
 
 600 
 
 -2.95 
 
 .571 
 
 .31 
 
 .71 
 
 16 
 
 747-866 
 
 747 
 
 5.5 
 
 510 
 
 -2.79 
 
 .547 
 
 .34 
 
 .68 
 
 H = Height of th 
 m = Effective co 
 w = Width of the 
 Sr = Subsidences 
 
 e overburden. 
 
 al seam thickness, 
 
 panel, 
 measured. 
 
 a = 
 a = 
 VS = 
 VE = 
 
 Subside 
 Average 
 Volume 
 Volume 
 
 nee coeffic 
 
 subsidence 
 
 of the subs 
 
 of the coal 
 
 lent smax/me. 
 
 coefficient, 
 idence trough. 
 
 extracted. 
 
40 
 
 0.7 
 
 i.s 
 
 h- 
 y 
 
 u. 
 u. 
 
 UJ 
 
 O 4 
 
 UJ 
 
 o 
 
 UJ 
 
 Q 
 
 CO 
 00 
 
 CO • 
 
 GO 
 < 
 
 a: 
 
 0L_ 
 400 
 
 For r = 25° right 
 
 30 m 
 _l 
 
 100 ft 
 
 300 
 
 200 100 
 
 DISTANCE FROM EDGE OF PANEL, ft 
 
 FIGURE 3. - Variable subsidence coefficient for y = 25° right 
 
 -100 
 
 -200 
 
41 
 
 0.7 
 
 o .5 
 
 UJ 
 
 y 
 
 u. 
 
 o .4 
 
 o 
 
 UJ 
 
 •z. 
 
 UJ 
 
 9 
 
 00 _ 
 => .3 
 
 (J) 
 
 UJ 
 
 _J 
 
 DO 
 
 < 
 
 sr 
 
 §.2 
 
 oi — 
 
 400 
 
 For r=25° left 
 
 /^ 
 
 100 ft 
 
 Scale 
 
 Edge of 
 panel 
 
 300 200 100 
 
 DISTANCE FROM EDGE OF PANEL, ft 
 
 FIGURE 4. - Variable subsidence coefficient for y = 25° left. 
 
 -100 
 
 -200 
 
42 
 
 0.7 
 
 3 .5 
 
 \- 
 
 o 
 
 L_ 
 U_ 
 UJ 
 O 4 
 
 UJ 
 
 o 
 
 LU 
 
 Q 
 
 CD 
 00 
 
 3 3 
 C/) ° 
 
 LU 
 _J 
 0Q 
 < 
 
 S .2 
 
 
 400 
 
 200 100 
 
 DISTANCE FROM EDGE OF PANEL, ft 
 
 FIGURE 5. - Variable subsidence coefficient for y = 15° right. 
 
 -200 
 
BsaasHaja 
 
 »™" 
 
 43 
 
 0.7 
 
 3 5 
 
 h- 
 z 
 
 UJ 
 
 y 
 u. 
 
 UJ 
 
 o .4 
 
 o 
 
 UJ 
 
 o 
 
 z 
 
 UJ 
 
 q 
 
 CO 
 
 CD 
 
 3 .3 
 
 CO 
 
 UJ 
 
 _J 
 
 CD 
 < 
 
 cr 
 §.2 
 
 0l_ 
 400 
 
 30 m 
 
 100 ft 
 
 Scale 
 
 300 200 100 
 
 DISTANCE FROM EDGE OF PANEL, ft 
 
 FIGURE 6. - Variable subsidence coefficient for y = 15° left. 
 
 -100 -200 
 
44 
 
 0.7 
 
 For constant e=l right 
 
 > 
 
 LU 
 
 o 
 
 LU 
 L_ 
 
 LU 
 O 
 
 o 
 
 LU 
 O 
 
 -z. 
 
 LU 
 Q 
 
 CO 
 DQ 
 
 Z> 
 CO 
 
 LU 
 
 _l 
 CO 
 
 < 
 
 or 
 
 0l— 
 400 
 
 300 
 
 200 100 
 
 DISTANCE FROM EDGE OF PANEL, ft 
 
 FIGURE 7. - Variable subsidence coefficient for e = 1 right. 
 
 -100 
 
 -200 
 
i* bi 
 
 Htwmii i nw t mm i 
 
 45 
 
 300 200 100 -100 
 
 DISTANCE FROM EDGE OF PANEL, ft 
 
 FIGURE 8. - Variable subsidence coefficient for e = 1 left. 
 
 -200 
 
46 
 
 0.7 
 
 6 V 
 
 100 ft 
 
 Scale 
 
 
 
 300 
 
 200 
 
 200 100 -100 
 
 DISTANCE FROM EDGE OF PANEL, ft 
 
 FIGURE 9. - Averaged values of variable sub- 
 sidence coefficients. 
 
 standard deviations to the averaged val- 
 ues of subsidence coefficients would be 
 satisfactory. 
 
 Figure 9 shows averaged values of the 
 subsidence coefficient a v for y = 25° and 
 y = 15° and for constant value of effi- 
 ciency coefficient e = 1 for all points. 
 
 Regression analysis of the subsidence 
 coefficients from all sites on the loca- 
 tion relative to the edge of the panel 
 has yielded a third-degree polynomial 
 equation with a coefficient of correla- 
 tion of 0.9999. 
 
 For y = 25° 
 
 a u = -3.587 x 1CT 8 X 3 + 1.628 
 
 10-5 X 2 _ 9.io5 x 10 -5 X 
 
 + 1.359 
 
 10 
 
 -1 
 
 For the points located outwards of the 
 edge of the panel, X = 0. 
 
 Then, the subsidence of any point to- 
 ward the centerline will be 
 
 s j = me j x a v j 
 
 and outwards si = mej x 0.1359. 
 
 Efficiency coefficients ej are tabu- 
 lated in table 1 for different mining 
 conditions. Interpolation will be nec- 
 cesary, where the ratios 
 
 W _ width of the panel 
 
 where X is the distance in feet from the 
 edge of the panel toward the centerline. 
 
 H thickness of the overburden 
 
 distance in feet from 
 X = the edge of the panel 
 
 W width of the panel 
 
 do not match the values in the table. 
 
 As an example, given a point located 
 100 ft inside the edge of a 600-ft-wide 
 panel, calculate the subsidence if the 
 overburden is 684 ft thick and extracted 
 thickness is 5.5 ft. 
 
 Using table 1, first determine the val- 
 ues of w/H and X/W where 
 
 w = width of panel, 
 
 H = thickness of overburden, 
 
 and X = distance inside edge of panel. 
 
 w/H = 600/684 = 0.88 X/w = 100/600 = 0.17 
 
 The closest values in the table are 
 
 x/w 
 
 w/h 
 
 By interpolation, the efficiency coeffi- 
 cients for X/w = 0.17 at w/H = 0.8 and 
 w/H = 0.9 are calculated: 
 
 ((0.818 - 0.765)/5) x 2 + 0.765 = 0.786; 
 
 ((0.841 - 0.786)/5) x 2 + 0.786 = 0.808. 
 
 
 0.20 
 
 0.15 
 
 0.8 
 
 0.818 
 
 0.765 
 
 0.9 
 
 0.841 
 
 0.786 
 
47 
 
 From these, the efficiency coefficient 
 for w/H = 0.88 and X/w = 0.17 can be 
 interpolated: 
 
 ((0.808 - 0.786)/10) x 8 + 0.786 = 0.803. 
 
 Using the Bals algorithm to compute the 
 precise efficiency coefficient for the 
 above point, a value of 0.8017 is ob- 
 tained. The use of either value in the 
 regression equation yields a predicted 
 subsidence of 1.12 ft. 
 
 Coefficient a u can be 
 
 defined directly 
 point identified 
 edge of 
 
 from figure 10 for any 
 
 by the distance in feet from the 
 
 the panel. 
 
 As shown in table 2, the majority of 
 the field data on which the analyses are 
 based comes from longwall panels with a 
 width of about 600 ft or less. Only one 
 panel is 940 ft wide. 
 
 To avoid any guesswork, the polynomial 
 equation has been developed for points 
 with maximum distance 300 ft from the 
 edge of the panel or up to the center- 
 line, whichever comes first. Only for 
 panels much wider than 600 ft and over- 
 burdens in excess of 800 ft would subsid- 
 ences around the centerline have to be 
 adjusted to the shape of the precomputed 
 partial profile. 
 
 0.7 
 
 300 
 
 200 1 00 
 
 DISTANCE FROM EDGE OF PANEL, ft 
 FIGURE 10. - Variable subsidence coefficient 
 for y = 25°. 
 
 
 
 The equation s ; = m e f a v for subsid- 
 ence precomputation is a combination of 
 principles on which both influence and 
 profile functions are based. 
 
 Efficiency coefficient e represents the 
 principles of influence functions, and a v 
 represents the principles of profile 
 functions. Such a combination seems to 
 be justified by at least two logical 
 reasons: 
 
 1. Whatever mining geological condi- 
 tions are involved, only a certain mined- 
 out area influences the movement of a 
 surface point. Coefficient e provides 
 for that and also for variable mining 
 
 conditions, namely for — ratio. 
 
 rl 
 
 2. At the same time, geological condi- 
 tions vary for different mining areas. 
 The introduction of a variable subsidence 
 coefficient seems to be the only logical 
 solution to the problem for mining areas 
 where lithological effect on subsidence 
 characteristics is so overwhelming. 
 
 As previously stated, the regression 
 analysis of the variable coefficient a v 
 has been performed for the angles of draw 
 y = 25° and y = 15° and for constant e = 
 1. The reason is as follows: 
 
 One cannot define the exact value of 
 the angle of draw for hypothetically ho- 
 mogeneous overburden, i.e., overburden 
 without the presence of highly resistive 
 hard rock units. Only by comparing re- 
 sults from several conceptions can the 
 most appropriate be chosen. 
 
 Table 3 contains the computed values of 
 a v along each profile with averaged val- 
 ues of a v and standard deviations. 
 
 It must be emphasized that the magni- 
 tude of standard deviations to a v only 
 cannot determine which conception is the 
 best. They are influenced by correspond- 
 ing efficiency coefficients, which differ 
 for each point and different mining 
 conditions. 
 
 For a better understanding, a practical 
 case was analyzed, namely the profile for 
 No. 2 Mine. The width of the panel is w 
 = 600 ft, and the coal seam thickness is 
 m = 5.5 ft. 
 
 Table 4 shows, for all three concep- 
 tions , the comparison between measured 
 and precomputed subsidences and compari- 
 son of standard deviations ± a j in feet 
 
48 
 
 TABLE 3. - Variable subsidence coefficients (a v ) along individual profiles with 
 averaged values (a v ) and standard deviations (±0;) 
 
 Mine 
 
 Distance inward, 1 ft 
 
 300 
 
 250 
 
 200 
 
 150 
 
 100 
 
 50 
 
 Edge of 
 
 panel 
 
 (0) 
 
 Distance outward, ' ft 
 
 -50 
 
 -100 
 
 -150 
 
 Y ■ 25- 
 
 1 
 
 NA 
 
 NA 
 
 0.480 
 
 0.410 
 
 0.275 
 
 0.182 
 
 0.135 
 
 0.170 
 
 0.210 
 
 0.240 
 
 2 
 
 0.597 
 
 0.590 
 
 .515 
 
 .370 
 
 .235 
 
 .207 
 
 .068 
 
 .053 
 
 .055 
 
 .075 
 
 3 
 
 .597 
 
 .571 
 
 .475 
 
 .335 
 
 .186 
 
 .106 
 
 .098 
 
 .105 
 
 .110 
 
 .150 
 
 4 
 
 .662 
 
 .655 
 
 .565 
 
 .435 
 
 .308 
 
 .205 
 
 .175 
 
 .295 
 
 .230 
 
 .230 
 
 5 
 
 .645 
 
 .627 
 
 .565 
 
 .440 
 
 .318 
 
 .200 
 
 .135 
 
 .120 
 
 .112 
 
 .124 
 
 6 
 
 .587 
 
 .530 
 
 .445 
 
 .335 
 
 .230 
 
 .155 
 
 .100 
 
 .105 
 
 .112 
 
 .115 
 
 7 
 
 .586 
 
 .564 
 
 .502 
 
 .405 
 
 .315 
 
 .235 
 
 .167 
 
 .190 
 
 .170 
 
 .150 
 
 8 
 
 .600 
 
 .530 
 
 .425 
 
 .335 
 
 .270 
 
 .234 
 
 .245 
 
 .265 
 
 .295 
 
 .320 
 
 9 
 
 .610 
 
 .571 
 
 .487 
 
 .380 
 
 .267 
 
 .200 
 
 .180 
 
 .196 
 
 .225 
 
 .225 
 
 10 
 
 .542 
 
 .505 
 
 .430 
 
 .340 
 
 .245 
 
 .175 
 
 .145 
 
 .153 
 
 .165 
 
 .190 
 
 11 
 
 .610 
 
 .545 
 
 .410 
 
 .285 
 
 .193 
 
 .152 
 
 .145 
 
 .145 
 
 .200 
 
 .300 
 
 12 
 
 .622 
 
 .571 
 
 .445 
 
 .250 
 
 .154 
 
 .150 
 
 .180 
 
 .210 
 
 .248 
 
 .248 
 
 13 
 
 .635 
 
 .600 
 
 .535 
 
 .405 
 
 .255 
 
 .130 
 
 .042 
 
 .015 
 
 NA 
 
 NA 
 
 14 
 
 .660 
 
 .621 
 
 .572 
 
 .432 
 
 .250 
 
 .128 
 
 .100 
 
 .122 
 
 .137 
 
 .300 
 
 15 
 
 .575 
 
 .525 
 
 .450 
 
 .350 
 
 .255 
 
 .152 
 
 .098 
 
 .065 
 
 .065 
 
 .055 
 
 16 
 
 NA 
 
 .540 
 
 .460 
 
 .375 
 
 .265 
 
 .192 
 
 .157 
 
 .135 
 
 .110 
 
 .135 
 
 a v . . . . 
 
 .609 
 
 .570 
 
 .485 
 
 .368 
 
 .251 
 
 .169 
 
 .136 
 
 .147 
 
 .163 
 
 .191 
 
 ±0;... 
 
 .033 
 
 .043 
 
 .053 
 
 .054 
 
 .045 
 
 .041 
 
 .050 
 
 .074 
 
 .070 
 
 .083 
 
 
 Y = 15° 
 
 1 
 
 NA 
 
 NA 
 
 0.438 
 
 0.365 
 
 0.225 
 
 0.128 
 
 0.065 
 
 0.039 
 
 0.021 
 
 0.006 
 
 2 
 
 0.591 
 
 0.576 
 
 .482 
 
 .327 
 
 .189 
 
 .075 
 
 .035 
 
 .016 
 
 .011 
 
 .009 
 
 3 
 
 .591 
 
 .555 
 
 .442 
 
 .293 
 
 .149 
 
 .075 
 
 .049 
 
 .033 
 
 .022 
 
 .018 
 
 4 
 
 .662 
 
 .633 
 
 .547 
 
 .398 
 
 .260 
 
 .128 
 
 .088 
 
 .081 
 
 .043 
 
 .018 
 
 5 
 
 .645 
 
 .613 
 
 .529 
 
 .387 
 
 .253 
 
 .138 
 
 .069 
 
 .039 
 
 .025 
 
 .018 
 
 6 
 
 .562 
 
 .529 
 
 .455 
 
 .344 
 
 .245 
 
 .158 
 
 .084 
 
 .062 
 
 .042 
 
 .020 
 
 7 
 
 .562 
 
 .501 
 
 .407 
 
 .287 
 
 .185 
 
 .108 
 
 .051 
 
 .039 
 
 .027 
 
 .015 
 
 8 
 
 .558 
 
 .487 
 
 .378 
 
 .275 
 
 .203 
 
 .151 
 
 .120 
 
 .093 
 
 .078 
 
 .062 
 
 9 
 
 .566 
 
 .523 
 
 .430 
 
 .315 
 
 .203 
 
 .133 
 
 .089 
 
 .066 
 
 .052 
 
 .045 
 
 10 
 
 .513 
 
 .473 
 
 .387 
 
 .288 
 
 .192 
 
 .117 
 
 .074 
 
 .048 
 
 .037 
 
 .030 
 
 11 
 
 .603 
 
 .529 
 
 .382 
 
 .242 
 
 .153 
 
 .104 
 
 .073 
 
 .046 
 
 .044 
 
 .045 
 
 12 
 
 .617 
 
 .548 
 
 .410 
 
 .213 
 
 .121 
 
 .056 
 
 .049 
 
 .049 
 
 .041 
 
 .040 
 
 13 
 
 .635 
 
 .603 
 
 .537 
 
 .400 
 
 .234 
 
 .101 
 
 .022 
 
 .013 
 
 .006 
 
 .005 
 
 14 
 
 .658 
 
 .620 
 
 .570 
 
 .437 
 
 .253 
 
 .102 
 
 .049 
 
 .025 
 
 .009 
 
 .006 
 
 15 
 
 .537 
 
 .489 
 
 .404 
 
 .296 
 
 .198 
 
 .102 
 
 .048 
 
 .023 
 
 .008 
 
 .005 
 
 16 
 
 NA 
 
 .501 
 
 .440 
 
 .340 
 
 .209 
 
 .126 
 
 .079 
 
 .044 
 
 .025 
 
 .022 
 
 a v . . . . 
 
 .593 
 
 .545 
 
 .452 
 
 .325 
 
 .205 
 
 .113 
 
 .065 
 
 .045 
 
 .031 
 
 .023 
 
 ±Oj... 
 
 .046 
 
 .053 
 
 .063 
 
 .061 
 
 .040 
 
 .028 
 
 .024 
 
 .022 
 
 .019 
 
 .017 
 
 
 
 Di 
 
 stance ii 
 
 ward, 1 i 
 
 :t 
 
 
 Edge of 
 panel 
 
 Distance outwai 
 
 rd, 1 ft 
 
 
 300 
 
 250 
 
 200 
 
 150 
 
 100 
 
 50 
 
 -50 
 
 -1( 
 
 )0 
 
 
 
 
 
 
 
 
 (0) 
 
 
 
 
 CONSTANT e = 1 
 
 NA 
 
 0.590 
 
 .590 
 
 .665 
 
 .645 
 
 NA 
 
 0.575 
 
 .555 
 
 .640 
 
 .612 
 
 0.435 
 .480 
 .445 
 .555 
 .526 
 
 0.365 
 .330 
 .300 
 .405 
 .393 
 
 0.240 
 .210 
 .166 
 .285 
 .281 
 
 0.165 
 .095 
 .096 
 .170 
 .180 
 
 0.120 
 .068 
 .098 
 .169 
 .131 
 
 0.400 
 .070 
 .145 
 .525 
 .152 
 
 0.690 
 .110 
 .235 
 .700 
 .190 
 
 NA Not applicable. 
 
 From edge of panel. 
 
49 
 
 TABLE 3. - Variable subsidence coefficients (a v ) along individual profiles with 
 averaged values (a v ) and standard deviations (±aj ) — Continued 
 
 
 Distance inward, 1 ft 
 
 Edge of 
 
 panel 
 
 (0) 
 
 Distance outward, 1 ft 
 
 Mine 
 
 300 
 
 250 
 
 200 
 
 150 
 
 100 
 
 50 
 
 -50 
 
 -100 
 
 
 
 
 CONSTANT 
 
 e = 1 — Continued 
 
 
 
 6 
 
 0.562 
 
 0.500 
 
 0.410 
 
 0.298 
 
 0.207 
 
 0.142 
 
 0.103 
 
 0.195 
 
 0.285 
 
 7 
 
 .565 
 
 .530 
 
 .465 
 
 .365 
 
 .280 
 
 .216 
 
 .168 
 
 .310 
 
 .430 
 
 8 
 
 .560 
 
 .486 
 
 .385 
 
 .300 
 
 .245 
 
 .213 
 
 .247 
 
 .320 
 
 .440 
 
 9 
 
 .570 
 
 .525 
 
 .440 
 
 .340 
 
 .240 
 
 .185 
 
 .185 
 
 .250 
 
 .325 
 
 10 
 
 .505 
 
 .445 
 
 .365 
 
 .277 
 
 .200 
 
 .150 
 
 .163 
 
 .215 
 
 .360 
 
 11 
 
 .607 
 
 .535 
 
 .385 
 
 .256 
 
 .175 
 
 .140 
 
 .153 
 
 .189 
 
 .400 
 
 12 
 
 .620 
 
 .550 
 
 .415 
 
 .220 
 
 .135 
 
 .140 
 
 .180 
 
 .325 
 
 .480 
 
 13 
 
 .632 
 
 .600 
 
 .535 
 
 .400 
 
 .232 
 
 .112 
 
 .038 
 
 .030 
 
 .030 
 
 14 
 
 .660 
 
 .620 
 
 .575 
 
 .440 
 
 .255 
 
 .135 
 
 .100 
 
 .120 
 
 .140 
 
 15 
 
 .535 
 
 .481 
 
 .396 
 
 .305 
 
 .220 
 
 .135 
 
 .098 
 
 .083 
 
 .067 
 
 16 
 
 NA 
 
 .500 
 
 .430 
 
 .335 
 
 .238 
 
 .170 
 
 .155 
 
 .165 
 
 .180 
 
 a v 
 
 .593 
 
 .544 
 
 .453 
 
 .333 
 
 .226 
 
 .153 
 
 .136 
 
 .218 
 
 .316 
 
 ±0;... 
 
 .047 
 
 .057 
 
 .065 
 
 .059 
 
 .042 
 
 .036 
 
 .052 
 
 .131 
 
 .202 
 
 NA Not applicable. 
 
 'From edge of panel. 
 
 for a given case. The distribution of 0\ 
 (ft) = mejOj for each conception is the 
 decisive factor for their evaluation. It 
 shows which conception reflects best the 
 reality in situ. Despite the relatively 
 small differences between a (ft) , the 
 conception for y = 25° clearly shows the 
 best results. 
 
 Small differences between individual 
 conceptions are due to the nature of the 
 data from which they were derived. As 
 shown on table 2, the range of differ- 
 ences between mining conditions (width of 
 the panels, overburden thickness) at in- 
 dividual test sites is relatively small. 
 It means that for mining conditions simi- 
 lar to those at the test sites, all three 
 conceptions could be used for subsidence 
 precomputation with good results. The 
 question remains, which one would yield 
 the best results, should it be used for 
 precomputation at a site with substan- 
 tially different mining conditions? For 
 example, let us assume that we have to 
 precompute subsidences over a longwall 
 panel 350 ft wide with 1,800 ft of over- 
 burden and coal seam thickness of 6 ft. 
 The results are shown on figure 11. The 
 difference between individual conceptions 
 is obvious. 
 
 From the logical point of view, the 
 conception for constant e = 1 is out of 
 
 competition, since it virtually neglects 
 different mining conditions and the mag- 
 nitude of maximum subsidence becomes only 
 a function of the width of the panel. 
 More difficult is the choice between the 
 conceptions y = 15° and y = 25°. The 
 question can be answered only after 
 having sufficient field data. 
 
 From available data the conception of y 
 = 25° shows the best results. Therefore, 
 this conception is considered as the most 
 applicable. 
 
 ■200 
 
 DISTANCE FROM EDGE OF PANEL, ft 
 -100 100 175 100 -100 -200 
 
 Longwall panel 
 
 FIGURE 11. - Precompiled subsidence profiles 
 for y = 25° and y = 15° for e = 1. (H = 1,800 ft, 
 w = 350 ft). 
 
50 
 
 TABLE 4. - Comparison of precomputed values for y = 25°, y = 15°, and e = 1 
 
 
 
 Distance inwards, 2 
 
 ft 
 
 
 Edge of 
 
 panel 
 
 (0) 
 
 Distance outward, 2 
 
 Values ' 
 
 300 
 
 250 
 
 200 
 
 150 
 
 100 
 
 50 
 
 ft 
 
 
 -50 -100 -150 
 
 
 
 
 
 
 y = 
 
 25° 
 
 
 
 
 
 
 a v . • • • < 
 
 • ••••• 
 
 0.606 
 
 0.567 
 
 0.485 
 
 0.368 
 
 0.251 
 
 0.169 
 
 0.136 
 
 0.146 
 
 0.163 
 
 0.190 
 
 ±0,... 
 
 »•••••• 
 
 .032 
 
 .042 
 
 .053 
 
 .054 
 
 .045 
 
 .041 
 
 .055 
 
 .074 
 
 .070 
 
 .083 
 
 e i 
 
 • ••••• 
 
 .990 
 
 .971 
 
 .933 
 
 .878 
 
 .802 
 
 .692 
 
 .500 
 
 .309 
 
 .198 
 
 .121 
 
 a,ej.. 
 
 >•••••• 
 
 .032 
 
 .041 
 
 .049 
 
 .047 
 
 .036 
 
 .028 
 
 .027 
 
 .022 
 
 .014 
 
 .010 
 
 ±o,... 
 
 ...ft.. 
 
 .18 
 
 .22 
 
 .27 
 
 .26 
 
 .20 
 
 .16 
 
 .15 
 
 .13 
 
 .08 
 
 .060 
 
 sF 
 
 ...ft.. 
 
 3.25 
 
 3.17 
 
 2.65 
 
 1.80 
 
 1.04 
 
 .41 
 
 .19 
 
 .09 
 
 .06 
 
 .050 
 
 sP 
 
 ...ft.. 
 
 3.30 
 
 3.04 
 
 2.47 
 
 1.77 
 
 1.12 
 
 .64 
 
 .37 
 
 .23 
 
 .15 
 
 .090 
 
 ±Aj... 
 
 ...ft.. 
 
 .05 
 
 -.13 
 
 -.18 
 
 -.03 
 
 .08 
 
 .23 
 
 .18 
 
 .14 
 
 .09 
 
 .040 
 
 
 
 
 
 
 Y = 
 
 15° 
 
 
 
 
 
 
 a^. ..•••) 
 
 • • • • 
 
 0.588 
 
 0.540 
 
 0.453 
 
 0.333 
 
 0.226 
 
 0.153 
 
 0.136 
 
 0.218 
 
 0.316 
 
 NA 
 
 ±°i 
 
 • • • • 
 
 .046 
 
 .057 
 
 .065 
 
 .059 
 
 .042 
 
 .036 
 
 .052 
 
 .131 
 
 .202 
 
 NA 
 
 fc- j • •»••*> 4 
 
 • • • • 
 
 1.0 
 
 1.0 
 
 1.0 
 
 .976 
 
 .899 
 
 .766 
 
 .5 
 
 .235 
 
 .101 
 
 NA 
 
 tfiej 
 
 • • • • 
 
 .046 
 
 .057 
 
 .065 
 
 .058 
 
 .038 
 
 .038 
 
 .026 
 
 .03 
 
 .02 
 
 NA 
 
 **! 
 
 ft.. 
 
 .25 
 
 .31 
 
 .36 
 
 .32 
 
 .21 
 
 .16 
 
 .14 
 
 .17 
 
 .11 
 
 NA 
 
 sF 
 
 .ft.. 
 
 3.25 
 
 3.17 
 
 2.65 
 
 1.80 
 
 1.04 
 
 .41 
 
 .19 
 
 .09 
 
 .06 
 
 NA 
 
 sP 
 
 ft.. 
 
 3.24 
 
 2.97 
 
 2.49 
 
 1.78 
 
 1.11 
 
 .64 
 
 .37 
 
 .28 
 
 .18 
 
 NA 
 
 ±Ai 
 
 ft.. 
 
 -.01 
 
 -.20 
 
 -.16 
 
 -.02 
 
 .05 
 
 .17 
 
 .18 
 
 .19 
 
 .12 
 
 NA 
 
 
 
 CONSTANT e = 1 
 
 a v ..... al 
 
 • • • • 
 
 0.587 
 
 0.545 
 
 0.452 
 
 0.325 
 
 0.205 
 
 0.113 
 
 0.065 
 
 0.045 
 
 0.031 
 
 0.023 
 
 ±*l 
 
 t m m • ■ 
 
 .05 
 
 .053 
 
 .063 
 
 .061 
 
 .04 
 
 .028 
 
 .024 
 
 .022 
 
 .019 
 
 .017 
 
 ±<7j 
 
 .ft.. 
 
 .28 
 
 .29 
 
 .35 
 
 .34 
 
 .22 
 
 .15 
 
 .13 
 
 .12 
 
 .1 
 
 .09 
 
 sF 
 
 .ft.. 
 
 3.25 
 
 3.17 
 
 2.65 
 
 1.80 
 
 1.04 
 
 .41 
 
 .19 
 
 .09 
 
 .06 
 
 .05 
 
 sP 
 
 .ft.. 
 
 3.23 
 
 3. 
 
 2.49 
 
 1.79 
 
 1.13 
 
 .62 
 
 .36 
 
 .25 
 
 .17 
 
 .13 
 
 ±Aj 
 
 .ft.. 
 
 -.02 
 
 -.17 
 
 -.16 
 
 -.01 
 
 .09 
 
 .21 
 
 .17 
 
 .16 
 
 .11 
 
 .08 
 
 NA Not applicable. 
 Nomenclature explanations: 
 
 a v = averaged variable subsidence coefficient as computed for individual con- 
 ceptions (y = 25°, 15°, e = 1). 
 
 Oj = standard deviations to the averaged values of the subsidence coefficient 
 a v for individual conceptions. 
 
 ei = efficiency coefficients. 
 
 Oj (ft) = me j a j . 
 
 sF (ft) = subsidences as measured in the field. 
 
 sP (ft) = precomputed subsidences SP = m.ei avi (inwards) 
 
 SP = m.ei 0.1359 (outwards). 
 
 Ai (ft) = differences between measured and precomputed subsidences. 
 
 From edge of panel. 
 
51 
 
 SENSITIVITY TESTS 
 
 The subsidences of all 16 half profiles 
 from 11 test sites with the total of 189 
 surface points involved in the regression 
 analysis have been computed using 
 the polynomial equation developed for y 
 = 25°. 
 
 Figure 12 shows the distribution of de- 
 viations between computed and directly 
 measured subsidences with regard to the 
 distance from the edge of the panel. 
 Table 5 shows that for 89 pet of all 
 points the deviation is between 0.00 and 
 0.29 ft, and for 74 pet it is between 
 0.00 and 0.19 ft. 
 
 Such results must be considered sat- 
 isfactory, especially if the possible 
 sources of these deviations are 
 considered: 
 
 1. The effect of lithology on subsid- 
 ence characteristics is not absolutely 
 the same at all investigated sites. 
 
 TABLE 5. - Summary of the distribution of 
 deviations 
 
 Deviations 
 
 Number of 
 
 Pet of 
 
 ft 
 
 points 
 
 total 
 
 
 81 
 
 43 
 
 
 57 
 
 31 
 
 .20- .29 
 
 29 
 
 15 
 
 
 14 
 
 7 
 
 
 4 
 
 2 
 
 .50- .59 
 
 4 
 
 2 
 
 Total 
 
 189 
 
 100 
 
 
 
 2. If the estimate of the extracted 
 coalbed thickness is inaccurate, the 
 full value of the error affects the 
 precalculation. 
 
 TIME COEFFICIENT 
 
 Figures 13 and 14 show characteristics 
 of time coefficient, involving the sub- 
 sidence process. Ninety-five pet of 
 total subsidence ususally occurs within 2 
 
 months of passing of the longwall face. 
 Residual subsidences may occur during 
 several more months. In no case have 
 they lasted for more than 1 year. 
 
 0.6 
 
 3 .4 
 
 < .2 
 > 
 
 Ld 
 Q 
 
 300 
 
 
 
 
 
 • 
 
 • 
 
 • 
 • 
 
 1 1 
 
 • 
 • 
 
 • • 
 • 
 
 • 
 
 • • 
 
 # • • • • 
 
 • 
 • 
 
 1 
 
 • 
 • 
 
 • 
 • # 
 
 • 
 • 
 
 • 
 
 • 
 
 • • 
 • 
 • 
 
 • • 
 
 • • 
 
 1 1 
 
 Toward the centerline 
 
 1 1 
 
 Outward 
 
 • 
 
 • 
 • • 
 •• • 
 
 • 
 
 : • •' ! - • ; 
 
 .. . . 
 
 . • . • . •; 
 
 -•—Edge of panel 
 
 • 
 
 : 
 
 • • 
 
 • ' •• •• .' " - 
 
 :: 
 
 • • 
 
 ...» •• • • 
 
 • • .i • •♦• •• 
 
 250 200 
 
 50 
 
 00 
 
 50 
 
 -50 -100 -150 
 
 DISTANCE FROM EDGE OF PANEL, ft 
 
 30 m 
 
 100 ft 
 
 Scale 
 
 FIGURE 12. - Distribution of deviations between computed and measured subsidences. 
 
52 
 
 LlI 
 
 Q 
 
 CO 
 CO 
 
 CO 
 
 
 
 1 00 200 
 
 LONGWALL FACE POSITION, ft 
 300 400 500 600 
 
 i-l 
 
 T 
 
 T 
 
 700 3.500 3,600 
 
 — i ^n 
 
 30 m 
 
 100 ft 
 
 V 
 
 15 23 28 
 Feb. 1 
 
 1982 1983 
 
 FIGURE 13. - Characteristics of time coefficient. 
 
 1 00 
 
 60 
 
 40 
 
 23 
 Nov. 
 
 o 
 
 a. 
 
 x 
 
 o 
 E 
 co 
 
 80 Z 
 
 UJ 
 CJ 
 
 UJ 
 
 a 
 co 
 
 CO 
 00 
 
 X 
 
 20 < 
 
 CO 
 CD 
 
 3 
 CO 
 
 100 
 
 - 2 h 
 
 ul 
 a 
 
 
 
 23 28 
 
 — »-] Nov.f-«— 
 
 LONGWALL FACE POSITION, ft 
 200 300 400 500 600 700 
 
 800 
 
 
 1 1 1 
 
 pi 
 
 1 1 
 
 
 -I — - — r 
 
 
 40- 
 
 
 
 
 
 
 ~~60^ 
 
 -2 
 
 
 
 
 
 80- 
 
 
 
 
 
 
 cm 
 
 ^3 / 
 
 
 
 
 — 
 
 _ Scale / 
 
 
 1 
 
 
 30 m 
 
 i 
 
 1 
 
 
 1 1 
 
 1 
 
 
 1 1 
 
 Scale 
 
 1 
 
 1 
 100 ft 
 
 1 1 
 
 17 
 
 20 
 
 27 
 
 Dec- 
 
 FIGURE 14. 
 
 1984 
 
 Characteristics of time coefficient. 
 
 900 
 100 
 
 - 80 
 
 o 
 a. 
 
 o 
 
 E 
 
 CO 
 
 UJ 
 
 60 ^ 
 
 LlI 
 O 
 
 CO 
 
 m 
 
 z> 
 
 CO 
 
 - 40 
 
 - 20 
 
 x 
 
 < 
 
 3 i 
 Jan 
 1985 
 
53 
 
 The extremely low average subsidence coefficient 
 
 a = 
 
 VS 
 
 VE 
 
 Volume of subsidence trough „ 
 Volume of the coal extracted 
 
 in comparison with a = 0.6 to 0.8 in Eu- 
 ropean conditions may be a cause for some 
 concern. It means that about 65 pet of 
 the volume of extracted coal has been 
 left as underground voids. This is due 
 to high resistance of hard rock units, 
 decreasing toward the centerline of the 
 panel. 
 
 At this time, it is difficult to pre- 
 dict whether such a new equilibrium with- 
 in the overburden is permanent or not. 
 On the test sites that were remeasured 2 
 years after mining activities had fin- 
 ished, no additional subsidences had 
 occurred. 
 
 CONCLUSION 
 
 Good results for subsidence precomputa- 
 tion by the developed formula have been 
 proven by the sensitivity tests. 
 
 Despite this fact, the methodology must 
 be considered to be a preliminary one. 
 The regression analysis is based on a 
 still limited amount of field data with 
 relatively similar mining conditions. 
 Its applicability in other mining areas 
 has to be tested. The advantages of the 
 developed methodology are — 
 
 1. It can be used by persons without 
 any previous knowledge of the theory of 
 subsidence. 
 
 2. It is relatively simple and fast 
 in comparison with existing predictive 
 methods. 
 
 3. It eliminates the use of inaccu- 
 rately estimated functional parameters 
 (maximum subsidence, location of the in- 
 flection point, etc.), necessary for ex- 
 isting predictive methods. 
 
 BIBLIOGRAPHY 
 
 Adamek, V., and P. W. Jeran. Evalua- 
 tion of Existing Predictive Methods for 
 Mine Subsidence in the U.S. Paper in 
 Proceedings First Conference on Ground 
 Control in Mining, ed. by S. S. Peng. 
 West Virginia University, July 1981, 
 pp. 209-219. 
 
 . Evaluation of Surface Deforma- 
 tion Characteristics Over Longwall Panels 
 in the Northern Appalachian Coal Field. 
 Paper in Proceedings International Sympo- 
 sium on Ground Control in Longwall Coal 
 
 Mining and Mining Subsidence - State of 
 the Art (Honolulu, Hawaii, 1982). AIME, 
 1982, pp. 183-197. 
 
 Bals, R. Beitrag zur Frage der 
 Vorausberechnung Bergbaulicher Senkungen 
 (Contribution to the Problem of Precalcu- 
 lating Mining Subsidence). Mitt, 
 aus dem Markscheidewesen 1931/1932, 
 pp. 98-111 (in German). 
 
 Niemczyk, 0. Bergschadenkunde (Study 
 of Mine Damages). Verlag Gluckauf, 
 G.m.b.H., 1949, p. 107 (in German). 
 
54 
 
 APPENDIX 
 
 To facilitate the use of this precal- 
 culation methodology, a basic computer 
 program was written for use on a per- 
 sonal computer. The program prompts the 
 user for the values of point location 
 (distance from the edge of the panel in 
 feet), overburden thickness, extracted 
 coalbed thickness, and width of the 
 panel. It then computes the efficiency 
 coefficient, e, using an algorithm based 
 on Bals 1 theory. This value is used in 
 the developed regression equation to cal- 
 culate the subsidence of the input point. 
 The result is output to the screen. 
 
 Values of the efficiency coefficients e 
 cannot be tabulated within the area of H 
 tan 25° from the beginning and the end of 
 the panel, since within this area there 
 are irregular partial areas of influence. 
 Therefore, the values of coefficient e 
 for surface points within this area have 
 to be individually calculated. 
 
 As previously stated, the definition of 
 efficiency coefficient e is based on an 
 assumption that the extracted area con- 
 sists of an infinitely large number of 
 small particles i, each of them influ- 
 encing the movement of a surface point by 
 a force inversely proportional to the 
 square of its distance f from it. The 
 full area of influence is defined by a 
 conical section with its base at the top 
 of the coal seam and the apex at surface 
 reference point P (fig. A-l). The angle 
 of draw y is equal to one half of the in- 
 terior angle of the cone. For flat seams, 
 the area of influence is a circle. 
 
 Only that part of the full area of in- 
 fluence that overlaps the extracted area 
 influences the magnitude of displacement 
 of investigated point P. 
 
 Based on previously expressed assump- 
 tions, the acting force on point P for 
 the full area of influence is 
 
 Yl i 
 
 K- / fJTfl. 
 YO 
 
 Since f = 
 
 H 
 
 cos y 
 
 (H = overburden thickness) 
 
 Yl 
 
 K=^J cos Yi d Yl . 
 Yo 
 
 Surface 
 
 w=600' 
 
 FIGURE A-l. - Graphic definition of subsidence 
 by Bals' theory. 
 
55 
 
 After neglecting — for flat coal seams 
 H 2 
 
 and for Yo = to Yi 
 
 K = 1/2 [(sin y cos Y + Y)] ] 
 
 
 
 = 1/4 (sin 2yi + 2yi). 
 
 The expression 2y i in the equation is in 
 radians. 
 
 Example: For y = 25° and after neglect- 
 ing constant factors 1/4 
 
 2.5 
 
 2.0 
 
 K = sin 50° + 50° = 0.766 + 
 = 0.766 + 0.872 = 1.638 
 
 50° TT 
 360° 
 
 Figure A-2 shows the curve sin 2y + 2y 
 for K from y = 0° to 35°. 
 
 To define the coefficient of efficiency e 
 for an area that is only a part of the 
 full area of influence, Bals' theory di- 
 vides the full area into a certain (the- 
 oretically unlimited) number of areas of 
 equal influence, by annular circles and 
 diameters. 
 
 For better understanding and practical 
 use, this is demonstrated in the follow- 
 ing example (fig. A-l): 
 
 Efficiency coefficient e has to be 
 defined for point P. 
 
 Width of the panel w = 600 ft. 
 
 Thickness of the overburden H = 700 ft. 
 
 Angle of draw y = 25°. 
 
 By experience, reasonable accuracy can 
 be obtained by dividing the full area of 
 influence into 40 sections, by 4 diame- 
 ters and 5 concentric circles. Then each 
 section bears 2.5 pet of the total influ- 
 ence. The influence of section B is 
 equal to the influence of the larger but 
 more distant section A. 
 
 5 10 15 20 25 30 35 
 ANGLE OF DRAW (y), deg 
 FIGURE A-2. - The curve sin 2y + ly by Bals. 
 
 First, one must define values of radii 
 of single-zone areas: 
 
 For y =25°, the radius of the full 
 area is 
 
 r = r 5 = 700' x tan 25° - 700» 
 
 x 0.466 = 326' 
 
 and K = 1.638. 
 
 To obtain single-zone areas of equal 
 influence, a particular k must be as- 
 signed to each of them. 
 
 For five zones, 
 
 kj = -=- x 1; k2 = 7 x 2; etc. 
 
 For each k, , the corresponding zone 
 angle Yj is determined from the curve 
 sin 2y + 2y (fig. A-2) : 
 
 Zone 
 
 ki 
 
 Yj, deg 
 
 r j = H tan y 
 ft 
 
 » 
 
 1 
 
 0.3276 
 
 .6552 
 
 .9828 
 
 1.3104 
 
 1.6380 
 
 4.6 
 
 9.5 
 
 14.4 
 
 19.5 
 
 25 
 
 56.3 
 117.1 
 179.7 
 247.9 
 326 
 
 
 2 
 
 
 3 
 
 4 
 
 
56 
 
 Each zone area is divided by diame- 
 ters into eight sections for better esti- 
 mation of extracted area. Parts of sec- 
 tions can be measured by planimeter or 
 simply estimated: 
 
 Zone 
 
 Sections 
 
 
 1 
 
 2 
 3 
 4 
 5 
 
 NA 0.3+0.3 NA = 
 0.4 + 1.0 + 1.0 + 0.4 = 
 .6 + 1.0 + 1.0 + .6 = 
 .7 + 1.0 + 1.0 + .7 = 
 .8 + 1.0 + 1.0 + .8 = 
 Total = 
 
 13.6 x 2.5% = 34% 
 
 0.6 
 2.8 
 3.2 
 3.4 
 3.6 
 13.6 
 
 Efficiency coefficient e for point P 
 is 0.34. For cases that do not require 
 high accuracy, single radii of concen- 
 tric circles can be determined by divid- 
 ing radius of the influence area into 
 five equal parts. This method is not 
 limited as to the shape of the extraction 
 area. 
 
 NA Not applicable. 
 
 #U.S. CPO: 1985-505-019/20,094 
 
 INT.-BU.OF MIN ES,PGH.,P A. 28 129 
 
' 
 
H 71 86 
 

 "oV° 
 
 "fet? 
 
 
 
 v- ,^r^L% ^ 
 
 
 ^4 
 
 „<°* 
 
 .7* A <v ^TTJ* A v "o *•.":* A <\. ^T^* -0*" *o, -<TA>> A 
 
 iV 
 
 
 
 > ^ 
 
 
 
 **0< 
 
 A r 
 
 ^O 1 
 
 "A ^ **T.«* A v 
 
 .0' 
 
 ^ 
 
 5°J 
 
 " c « ^^ -A „ <■ ' ' . *£u <"* f ° " ° « <? 
 
 •^ ^ 
 
 c v 
 
 
 ^q. 
 
 
 & 
 
 
 
 i0 
 
 f 
 
 
 
 -,v- 
 
 
 .0 
 
 .o- 
 
 
 ■^ v 
 
 
 ^, 
 
 
 .0^ \5 *o . » * A 
 
 y"^ 
 
 

 
 
 
 * ' •-"- > v s * VL/* cv sy 
 
 *« 
 
 
 
 
 
 
 A 
 
 ... # o *^ r ° A 
 
 V-^ 
 
 
 ^ A^ 
 
 
 ^o< 
 
 &" 
 
 N. MANCHESTER /