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Bureau of Mines Information Circular/1988 
 
 MULSIM/BM-A Structural Analysis 
 Computer Program for Mine Design 
 
 By Les A. Beckett and Rudy S. Madrid 
 
 UNITED STATES DEPARTMENT OF THE INTERIOR 
 
Information Circular 9168 
 
 ft 
 
 MULSIM/BM-A Structural Analysis 
 Computer Program for Mine Design 
 
 By Les A. Beckett and Rudy S. Madrid 
 
 UNITED STATES DEPARTMENT OF THE INTERIOR 
 Donald Paul Hodel, Secretary 
 
 BUREAU OF MINES 
 
 David S. Brown, Acting Director 
 
'APR 5 1988 T\) 
 
 COPY. 
 CIP 
 
 Library of Congress Cataloging in Publication Data: 
 
 
 
 ^ y 
 
 
 Beckett, Les A. 
 
 MULSIM/BM: a structural analysis computer program for mine design. 
 
 (Information circular / United States Department of the Interior, Bureau of Mines ; 9 1 68) 
 
 Bibliography: p. 16-17. 
 
 Supt. of Docs, no.: I 28.27: 9168. 
 
 1. Mining engineering— Computer programs. 2. MULSIM/BM (Computer pro- 
 gram) I. Madrid, Rudy S. II. Title. III. Series: Information circular (United States. Bureau 
 of Mines); 9168. 
 
 TN295.U4 [TN292] 622 s [622 '.028 '55369] 87-600293 
 
CONTENTS 
 
 Page 
 
 Abstract 1 
 
 Introduction . 2 
 
 Features of MULSIM/BM 3 
 
 Material property sets 4 
 
 Inserted— material or gob model - 4 
 
 Theoretical basis 5 
 
 Linear in situ gob modulus 6 
 
 Adjusted gob modulus 7 
 
 Considerations affecting appropriate use 8 
 
 Initial elastic closure 8 
 
 Equivalent elastic modulus for supported openings 8 
 
 Equivalent rock mass modulus 9 
 
 Upper seams overlying gob zones 9 
 
 Modeling large areas 9 
 
 Coarse-mesh blocks 10 
 
 Material model definition 10 
 
 Extraction ratios 10 
 
 Boundary conditions 10 
 
 Gouge material 10 
 
 Seam limitations, sign conventions, and symmetry options 11 
 
 Maximum number of seams 11 
 
 Location of seam origins 11 
 
 Sign conventions , . 12 
 
 Symmetry options 13 
 
 Companion mesh generator program 14 
 
 Developing a plan of analysis 14 
 
 References 16 
 
 Appendix A. — MULSIM/BM user's guide 18 
 
 Appendix B. — MULSIM/BM mesh generator user's guide 25 
 
 Appendix C. — MULSIM/BM structure diagram and program listing 36 
 
 Appendix D. — MULSIM/BM mesh generator structure diagram and program listing.... 184 
 
 Appendix E. — Sample problem input 264 
 
 Appendix F. — Sample problem output 268 
 
 Appendix G. — Adaptation of program code to other computers 293 
 
 Appendix H. — Cyber job control stream to run MULSIM/BM 298 
 
 Appendix I. — Engineering symbols used in this report 301 
 
 ILLUSTRATIONS 
 
 1. Typical mine layout and displacement-discontinuity grid 2 
 
 2. Mesh generator and MULSIM/BM system flowchart 3 
 
 3. Selection of a secant elastic modulus for gob 6 
 
 4. Seam origins lie on the same normal line 11 
 
 5. Sign conventions for displacements and stresses 12 
 
 6. Symmetry options 13 
 
 7. Example mining layout 15 
 
 8. MULSIM/BM grids for the example layout 15 
 
 C-l . MULSIM/BM structure diagram , 36 
 
 D-l. MULSIM/BM mesh generator structure diagram 185 
 

 UNIT OF MEASURE 
 
 ABBREVIATIONS USED 
 
 IN 
 
 THIS REPORT 
 
 With Factors 
 
 for Conversion 
 
 to 
 
 Units 
 
 of 
 
 th 
 
 e International System of Units (SI) 
 
 ft 
 
 foot 
 
 
 
 
 
 in 2 
 
 
 square inch 
 
 GPa 
 
 gigapascal 
 
 
 
 
 
 lb 
 
 
 pound 
 
 h 
 
 hour 
 
 
 
 
 
 lb/in 3 
 
 
 pound per cubic inch 
 
 in 
 
 inch 
 
 
 
 
 
 pet 
 
 
 percent 
 
 in/in 
 
 inch per inch 
 
 
 
 
 
 psi 
 
 
 pound per square inch 
 
 Abbreviation 
 
 Unit of measure 
 
 To convert to — 
 
 Multiply by — 
 
 ft 
 
 foot 
 
 meters 
 
 0.3048 (exactly) 
 
 in 
 
 inch 
 
 centimeters 
 
 2.54 (exactly) 
 
 psi 
 
 pounds per square inch 
 
 kilopascals 
 
 6.894757 
 
MULSIM/BM— A STRUCTURAL ANALYSIS COMPUTER 
 PROGRAM FOR MINE DESIGN 
 
 By Les A. Beckett and Rudy S. Madrid 
 
 ABSTRACT 
 
 The Bureau of Mines has developed MULSIM/BM, an improved computer pro- 
 gram using the boundary-element approach for geomechanical analysis of 
 mine plans in single or multiple coal seams. This Information Circular 
 presents the improved features of the MULSIM/BM program. The four major 
 improvements are the following: (1) Ability to specify up to 26 mate- 
 rial property sets. (2) A new material model capability for gob and 
 inserted materials such as packwalls or cribs. (3) Ability to model a 
 large area with a grid of undivided blocks and to subdivide only a spec- 
 ified fine-mesh portion of these blocks into elements. (4) Specifica- 
 tion of extraction ratios for the undivided blocks. In addition, an 
 interactive graphics mesh generator program was written to accompany 
 MULSIM/BM. A complete user's guide and program listings are included 
 within the appendixes. The MULSIM/BM and mesh generator programs are 
 available on tape from the National Technical Information Service. 3 
 
 Mining engineer, Denver Research Center, Bureau of Mines, Denver, CO. 
 
 2 Systems engineer, Electronic Data Systems Corp. (now analyst III, Vanguard Tech- 
 nologies Corp., Denver, CO). 
 
 ^Accession number PB 88-129465. The nine-track computer tape is written at the 
 density of 1,600 bits per inch using unlabeled tape format. The programs are written 
 in ASCII code as 4,960 fixed length records, or card images, with 80 characters per 
 record. 
 
INTRODUCTION 
 
 One of the advances occurring in min- 
 ing technology is the increasing use of 
 computerized mine structural analysis 
 methods to analyze the stability of 
 underground coal mines. Throughout the 
 process of coal extraction from an under- 
 ground mine, the stresses formerly car- 
 ried by the newly extracted coal are 
 redistributed to unmined areas, to gob 
 zones, or to artificial structural ele- 
 ments such as packwalls or cribs. This 
 redistribution of stresses can be espe- 
 cially complicated when multiple-seam 
 raining interactions occur. Mine struc- 
 tural analysis methods can calculate the 
 redistribution of overburden stresses 
 and the resulting loadings on any given 
 portion of the underground mine, thus 
 enabling mining engineers to design coal 
 mines that are both safer and yet less 
 wasteful of coal resources. 
 
 The Bureau of Mines has conducted re- 
 search into the application and improve- 
 ment of state-of-the-art computerized 
 mine structural analysis methods. Theo- 
 retical approaches used include finite- 
 element methods, boundary-element meth- 
 ods, and discrete block methods. A 
 subvariation of the boundary-element 
 method called the three-dimensional dis- 
 placement-discontinuity approach was 
 originally incorporated in a mine struc- 
 tural analysis computer program by Crouch 
 and Fairhurst (3). In this approach, 
 the mine plan for each seam is specified 
 as a grid in plan view, as illustrated 
 in figure 1; the program then calculates 
 the resulting three-dimensional stresses 
 and ground deformations that result from 
 mining. Sinha (15) expanded upon the 
 theory of the approach in three computer 
 programs, one of which, MULSIM, was 
 designed to analyze situations of par- 
 allel multiple coal seams. During the 
 1984-85 period, the Bureau upgraded and 
 completely restructured the MULSIM pro- 
 gram into the MULSIM/BM program. 
 
 ^Underlined numbers in parentheses re- 
 fer to items in the list of reference? 
 preceding the appendixes. 
 
 The new MULSIM/BM computer program pro- 
 vides the capability to analyze many coal 
 mining situations and to determine the 
 effects of the three-dimensional stress 
 redistributions caused by mining. The 
 program can analyze problems involving 
 one or more coal seams and can incorpo- 
 rate the effects of previous mining in a 
 large surrounding area, while focusing 
 upon an area of particular interest. 
 Thus, it can be used to analyze the wide- 
 scale effects of load transfers result- 
 ing from previous mining upon the stress 
 levels experienced by particular coal 
 pillars, by unmined coal blocks, or by 
 
 Fine mesh 
 Displocement-discontinuity grid 
 
 Element 
 
 FIGURE 1.— Typical mine layout and displacement- 
 discontinuity grid. 
 
artificial structural elements such as 
 packwalls, backfill, cribs, or steel 
 frames. Recent Bureau work has shown 
 applications of a preliminary version 
 (9) and of the final version (1_) of 
 MULSIM/BM. 
 
 Some of the uses envisioned for the 
 MULSIM/BM computer program are as fol- 
 lows: The program can be used to deter- 
 mine the safe size for coal pillars or 
 artificial supports such as packwalls, 
 backfill, cribs, or steel supports used 
 for structural stability. It can be used 
 to predict the magnitude of potential 
 ground-control problems caused by stress 
 concentrations transferred from adjacent 
 mined seams. If the mine plan under con- 
 sideration is based upon a similar oper- 
 ation elsewhere, or if the in situ stress 
 field or material property conditions are 
 not fully known, the program can conve- 
 niently analyze the effects of a differ- 
 ent seam dip, different geomechanical 
 properties, and/or a different in situ 
 stress field. Such analyses can assist 
 the mine operator to maximize coal 
 extraction without compromising overall 
 mine safety. 
 
 The program is best suited to sit- 
 uations where strata properties are 
 relatively uniform and where localized 
 geological discontinuities such as rolls, 
 kettlebottoms, or faults do not strongly 
 affect the problem. If local disconti- 
 nuities or property variations are sig- 
 nificant, then a finite-element analysis 
 may be a better approach. 
 
 This Information Circular documents 
 the improvements incorporated in the 
 MULSIM/BM program and provides a complete 
 user's guide in the appendixes. It also 
 describes a companion mesh generator 
 program for use with MULSIM/BM (fig. 
 2). For detailed explanation of the 
 
 KEY 
 (32)— Unit number 
 n — Seam number 
 
 FIGURE 2.— Mesh generator and MULSIM/BM system flowchart. 
 
 mathematical theories incorporated within 
 MULSIM/BM, the reader is referred to the 
 previous literature (3-4, 11, 13-15). 
 
 FEATURES OF MULSIM/BM 
 
 The following capabilities of the 
 MULSIM/BM program were carried over from 
 the original MULSIM program (15) : 
 MULSIM/BM is designed for analysis of 
 mine designs in single coal seams or in 
 parallel multiple coal seams. The seams 
 
 can dip at any angle and lie at any 
 desired orientation to the virgin princi- 
 pal stress field. As shown in figure 1, 
 the current mining situation is specified 
 to the program in terms of a grid of 
 elements and blocks; the program then 
 
calculates the resulting seam stresses 
 and closures for each element and block. 
 By specification of "off-seam planes," 
 stresses and rock mass deformations are 
 also available for desired points in the 
 surrounding rock mass. 
 
 The rock mass itself is assumed to be a 
 homogeneous, isotropic, infinite elastic 
 body. Thus, since the effect of the 
 surface is omitted, the program is only 
 applicable to problems in which the seam 
 depth is greater than the excavation 
 width being analyzed ( 15 , p. 14). All 
 excavations are assumed to appear instan- 
 taneously in a single time step. 
 
 New features of MULSIM/BM include 
 
 1. Ability to specify up to 26 differ- 
 ent material property sets. 
 
 2. A new material model capability for 
 inserted materials such as gob, pack- 
 walls, or cribs. The inserted mate- 
 rial model (or gob model) uses a linear 
 stress-strain relationship with zero 
 stress at zero seam closure. 
 
 3. Ability to model a large raining 
 area with a grid of blocks and to sub- 
 divide a desired fine-mesh portion of 
 these blocks into elements for greater 
 accuracy. 
 
 A. Ability to specify extraction ra- 
 tios for the undivided or coarse-mesh 
 blocks. 
 
 MATERIAL PROPERTY SETS 
 
 MULSIM/BM allows definition of as many 
 as 26 different elastic material property 
 sets. A letter of the alphabet is auto- 
 matically associated with each of the 
 property sets as it is defined. Any of 
 these materials, once defined, can sub- 
 sequently be used in any portion of any 
 seam plane defined in the model. Each 
 coarse-mesh block and each fine-mesh ele- 
 ment defined for an analysis is assigned 
 the desired material property simply by 
 specifying the alphabetic designation as 
 an input for that block or element. This 
 capability is a considerable improvement 
 over the original MULSIM program, in 
 which the analysis was limited to at most 
 one elastic material property set per 
 seam. 
 
 To briefly indicate the many possibil- 
 ities opened up by this capability, con- 
 sider that in a particular analysis the 
 mining engineer might want to define only 
 six material property sets to include 
 regions of unmined coal, regions of weak- 
 ened coal in high-stress areas, gob 
 zones, and possibly artifically supported 
 areas such as backfilled openings, pack- 
 walls, and openings supported by cribs. 
 Each of these six materials could be used 
 within one or more seam levels. Clearly 
 a very detailed analysis could be con- 
 ducted using only six materials; and it 
 is therefore unlikely that any analysis 
 would be severely limited by the con- 
 straint of having no more than 26 mate- 
 rial property sets available. 
 
 The input data file is arranged so that 
 a printout of the letter codes for the 
 various blocks and elements corresponds 
 visually to the layout of the grid. This 
 feature makes it very easy to check new 
 data files visually for errors in the 
 layout. It is equally simple to deter- 
 mine the mine layout represented in an 
 old or unfamiliar data file. 
 
 INSERTED-MATERIAL OR GOB MODEL 
 
 The material behavior capability used 
 to represent fabricated structural com- 
 ponents such as gob, packwalls, cribs, 
 steel supports, or backfill is referred 
 to as the inserted-material model. In 
 contrast to the original seam materials, 
 which are in equilibrium with the virgin 
 overburden stresses at zero seam clo- 
 sure (zero roof-to-floor convergence), 
 inserted materials do not support load 
 until some degree of seam closure occurs. 
 
 Addition of this capability consid- 
 erably improved the usefulness of the 
 computer program as applied to practical 
 mine planning. The effect of large gob 
 zones upon the overall load transfer 
 across one or more mined seams can now 
 conveniently be included in an analysis. 
 Likewise the effects of adding artificial 
 support within openings, such as pack- 
 walls or cribs, can be analyzed; and the 
 expected loadings upon these supports can 
 be analyzed. 
 
 MULSIM/BM requires the program user to 
 input a linear modulus for a gob material 
 
or other inserted material. This modulus 
 is used to calculate the stress carried 
 by the material as seam closure occurs. 
 While this linear modulus may be quite 
 accurate for some materials, such as 
 cribs, for other materials, such as gob, 
 it is only an approximation. 
 
 The following subsections provide a 
 detailed discussion of the matters to be 
 considered in selecting an appropriate 
 linear modulus input value for gob. In 
 synopsis, the linear in situ elastic mod- 
 ulus is best viewed as a secant modulus, 
 selected to intercept the true stress- 
 strain curve for gob at a stress level 
 equal to the virgin stress normal to the 
 seam. Because gob stress-strain behavior 
 in situ is not well defined and is very 
 difficult to measure, selection of an 
 appropriate linear in situ elastic mod- 
 ulus value calls for exercise of engi- 
 neering judgment. In addition, once an 
 in situ elastic gob modulus is selected, 
 the elastic gob modulus input to the 
 computer program must be adjusted to 
 allow for the fact that the program 
 assumes that the gob zone height is only 
 equal to the seam thickness. Since the 
 true in situ gob zone height is neces- 
 sarily greater than the seam thickness, 
 an adjusted modulus must be used as input 
 to enable the program to calculate the 
 correct gob zone closure values. 
 
 The following discussion summarizes 
 some of the mathematical theory rele- 
 vant to gob modulus selection and also 
 points out some of the considerations 
 that affect the interpretation of results 
 computed using a gob material model. 
 
 load-bearing capacity of the gob in- 
 creases with compaction, in this mathe- 
 matical representation, towards an asymp- 
 totic limit that represents the volume of 
 the original uncaved rock. The resulting 
 stress-strain relationship is given by 
 Mozumdar (11) as follows: 
 
 p = k\w / (m - w) 
 
 where p = gob resistence, psi, 
 k' = a material constant, 
 
 (1) 
 
 and 
 
 m = extracted seam height, in, 
 
 u = amount of gob zone main-roof- 
 to-floor convergence, in. 
 
 Salamon (14) gave a value of 133 psi for 
 the constant, k', as a representative 
 value for European coal measure rocks. 
 
 Finite-element analyses conducted by 
 the Bureau using this equation to repre- 
 sent gob behavior have shown that struc- 
 tural analysis using this theory can give 
 useful results for gob behavior. The 
 value of k' given by Salamon is, however, 
 thought to be too low for Western U.S. 
 conditions, and recent Bureau analysis 
 (1_, 9) has pointed to a higher value, 
 approximately 1,700 psi, corresponding to 
 use of a secant Young's modulus of 20,000 
 psi. 
 
 To convert equation 1 into a form using 
 stresses and strains, substitute o"nl f° r 
 p, and divide both the numerator and the 
 denominator by the gob zone height, g, 
 which results in the following equation: 
 
 Theoretical Basis 
 
 a NL = k' e g /(e max - e g ), 
 
 (2) 
 
 A mathematical theoretical model of gob where 
 zone behavior was first developed by 
 Salamon (1_4_). Mozumdar (1_1_) demonstrated 
 the application of this theoretical model 
 in mine structural analysis using the 
 finite-element method. 
 
 The Salamon model of gob behavior 
 is that of a rubblized mass, formed by 
 caving of the immediate roof layers 
 overlying an excavation, that bears no and 
 load until it is compacted by the weight 
 of the main, uncaved, rock mass. The 
 
 e q = overall normal strain in 
 
 the gob zone, between the 
 main roof and the floor, 
 
 : max = maximum possible overall 
 normal strain in the gob 
 zone, between the main 
 roof and the floor, 
 
 Onl = stress carried by the gob 
 zone (nonlinear equation) 
 
Linear In Situ Gob Modulus 
 
 MULSIM/BM requires the program user to 
 input a linear approximation to the non- 
 linear curve of equations 1 and 2. This 
 linear approximation corresponds to use 
 of a secant elastic (Young's) modulus 
 for the in situ stress-strain response 
 of a gob zone. The linear approximation 
 was chosen to simplify program execu- 
 tion with resulting savings in execution 
 time and also in computer core storage 
 requirements. 
 
 Figure 3 shows the recommended method 
 of selecting a secant modulus to corre- 
 spond to the Salamon curve as applied to 
 a particular virgin overburden stress 
 level. In figure 3, 0q is the virgin 
 overburden stress level and E max is the 
 amount of compressive strain that would 
 correspond to a gob-zone convergence 
 equal to the extracted seam height, m. 
 eo is the strain corresponding to an 
 
 A 
 
 -D 
 O 
 
 
 
 cr„ 
 
 Eq--CT /€o 
 
 CO 
 
 to 
 
 Q. 
 
 o 
 a 
 
 Og = Eg €q 
 
 €■0 ^max 
 
 COMPRESSIVE STRAIN (€), arbitrary scale 
 
 <!> 
 
 k' 
 
 eg 
 
 £max 
 
 Nonlinear curve for in 
 situ gob behavior 
 
 Stress sustoined by gob 
 (nonlinear equation) 
 
 Gob material constant 
 
 Strain sustained by gob 
 
 Moximum possible gob 
 strain 
 
 Equilibrium point 
 for gob 
 
 -(2)- Linear approximation 
 
 O~ Overburden stress 
 
 €0 Equilibrium strain 
 for gob 
 
 0~g Stress sustained by 
 gob (linear equation) 
 
 Eg Secant elastic gob mod- 
 ulus (linear modulus) 
 
 amount of gob convergence, w, that just 
 enables the gob to sustain the overburden 
 stress, Oq. The resulting secant in situ 
 gob modulus, E q , is then given by 
 
 Eg = o /e Q . 
 
 (3) 
 
 FIGURE 3.— Selection of a secant elastic modulus for gob. 
 
 When using this method, the extracted 
 seam height, m, must be taken as equal to 
 the full seam thickness, t, that is input 
 to the computer program, since the pro- 
 gram assumes that full seam extraction 
 occurs. 
 
 In the implementation of this linear 
 gob model in MULSIM/BM, the program 
 begins with a working assumption that all 
 elements of the grid are initially at 
 equilibrium with the virgin overburden 
 stress field. While for an original seam 
 material (coal) this working assumption 
 corresponds to a condition of zero roof- 
 to-floor closure across the seam, for 
 a gob zone it corresponds to an initial 
 closure, c, equal to the product of eo 
 multiplied by the gob zone height, g. 
 This initial working assumption is nor- 
 mally considerably different from the 
 final solution for a particular mining 
 situation. 
 
 In the process of iteratively solving 
 for a balanced set of closures, the pro- 
 gram normally ends up reducing the clo- 
 sures of gob elements, thus reducing the 
 calculated stress carried by those ele- 
 ments, and increasing the closures of 
 coal elements near the gob zones, thus 
 increasing the stress carried by those 
 elements. In the coal elements, this 
 process results in calculation of stress 
 abutments. In the gob, this process 
 results in calculation of stress-relieved 
 areas near adjacent unmined coal pillars 
 or blocks. 
 
 In calculating the precise stresses 
 carried by the gob elements or blocks, 
 the program uses the secant modulus; 
 and in the destressed gob regions the 
 stresses calculated by the secant modulus 
 are slightly higher than the stresses 
 that would be calculated by use of the 
 nonlinear equations 1 and 2. The total 
 stress levels calculated by either method 
 are, however, sufficiently low compared 
 with the overburden stresses that the 
 resulting disparity should in most cases 
 
have little impact on the stresses calcu- 
 lated for other areas of an analysis. 
 
 Gob zones are rarely located in such a 
 way that the calculated equilibrium 
 stresses would be greater than the over- 
 burden stress. One plausible way for 
 such a condition to occur would be for 
 a gob zone to be located within the 
 influence zone of a remnant pillar in an 
 adjacent seam, which might then cause a 
 considerable stress concentration. Even 
 so, such a condition would rarely cause 
 the calculated loads in a gob zone to 
 exceed the overburden stress unless there 
 were no stiff er load-bearing structures, 
 such as coal pillars or unmined coal 
 blocks, nearby. Because the focus of 
 analytical interest is usually directed 
 towards areas that contain working faces, 
 entries, coal pillars, and the like, the 
 conditions that might cause gob stresses 
 greater than 0*0 were judged unlikely to 
 be of interest; and therefore no provi- 
 sion was made in MULSIM/BM to track the 
 stiffer gob behavior in the region of 
 stresses greater than oq. 
 
 Recent Bureau analyses have used the 
 MULSIM/BM gob material model successfully 
 to analyze the stress transfers around 
 longwall panel gob zones (1_, $0. These 
 analyses have used an assumed in situ 
 elastic gob modulus of 20,000 psi, a 
 number that lies within the middle of 
 a range of 1,000 to 47,000 psi reported 
 by Peng ( 12 , p. 222) for rubblized rock 
 material or gob. 
 
 Adjusted Gob Modulus 
 
 Reason for Adjustment ( 1_) 
 
 The load transfers away from a gob zone 
 can be adequately calculated by the pro- 
 gram provided that a properly adjusted 
 gob modulus is used. The total closure 
 of the gob zone corresponds to the flex- 
 ing of the main rock mass. This rock 
 mass response to mining determines the 
 amount and the lateral extent of the load 
 transfer. A complication arises, now- 
 ever, because the program considers all 
 elements in the grid for a particular 
 seam to have the height of the original 
 seam thickness. In reality, of course, 
 the height of a gob zone is higher: 
 
 typically, about three to four times the 
 seam height, depending on the bulking 
 factor of the immediate roof that caves 
 to fill the excavation. The resulting 
 discontinuity in height does not per se 
 cause great difficulties, since an under- 
 lying assumption of the program is that 
 the element thicknesses are negligible 
 in calculating the response of the rock 
 mass. Because of the discrepancy between 
 the real gob height and the modeled gob 
 height, however, a modified gob modulus 
 must be used in order to calculate the 
 correct gob-zone closures (1_, 9_) . 
 
 Derivation of Adjusted Gob Modulus 
 
 The derivation of the modified gob mod- 
 ulus is straightforward. For any ele- 
 ment, the closure, C, is determined by 
 the equation (1): 
 
 C = (F/A)/S, 
 
 (4) 
 
 where F = the normal force acting upon 
 the element, 
 
 A = the area of the element, 
 
 and S = the area stiffness of the 
 
 element (or, stiffness per 
 unit area). 
 
 The area stiffness, S, has units of force 
 per cubic inch and is given by the fol- 
 lowing equation (1): 
 
 S = M/h, 
 
 (5) 
 
 where M = the elastic modulus that is 
 specified as the input to 
 the computer program for the 
 material type used by that 
 element 
 
 and h = the element height used by the 
 program (equal to the seam 
 thickness, t). 
 
 From equations 4 and 5, calculation of 
 the correct element closure requires 
 maintaining an area stiffness that corre- 
 sponds to the correct area stiffness of 
 the in situ area represented by that ele- 
 ment. It also follows from equation 5 
 
that the in situ effective area stiffness 
 of a gob zone, S g , can be given by the 
 following equation: 
 
 s g - E g/g> 
 
 (6) 
 
 where E g = the effective in situ elastic 
 (Young's) modulus of the gob 
 
 and 
 
 g = the in situ gob zone height. 
 
 As noted, the in situ gob zone height 
 is always greater than the seam thick- 
 ness, t, and typically is three to four 
 times greater. MULSIM/BM, however, 
 assumes that gob elements also have the 
 height of the original seam thickness, t. 
 Therefore, in order for the program to 
 calculate the correct gob closure, or 
 closure between the main roof and the 
 floor of the gob zone, it is essential to 
 maintain the condition that 
 
 S = S 
 
 9* 
 
 (7) 
 
 Thus, the right hand sides of equations 5 
 and 6 must be maintained equal to each 
 other: 
 
 M/h = E g /g, 
 
 (8) 
 
 Setting h equal to t and rearranging 
 terms in equation 8 gives the following 
 equation which should be used to calcu- 
 late the adjusted gob modulus that is 
 needed as input to the computer program 
 (1): 
 
 M = Eg t/g, 
 
 (9) 
 
 where 
 
 and 
 
 Eg = effective in situ elastic 
 (Young's) modulus of the 
 gob, 
 
 t = the seam thickness as input 
 to the program, 
 
 g = the in situ gob zone height. 
 
 Use of a gob modulus adjusted in this 
 manner has been shown (J_, _9) to give 
 results for the overall load transfers 
 that are in reasonable agreement with 
 field experience. As a linear approxi- 
 mation of the in situ modulus of a gob, 
 a number in the range of 1,000 psi to 
 
 47,000 psi is consistent with data re- 
 ported by Peng ( 12 , p. 222). Recent 
 analyses using MULSIM/BM have used an 
 assumed in situ gob modulus of 20,000 psi 
 and an adjusted gob modulus of 5,000 psi 
 
 (I. 2>- 
 
 Considerations Affecting Appropriate Use 
 
 The following considerations affect the 
 use of the inserted-material model. 
 
 Initial Elastic Closure U_) 
 
 The program does not account for the 
 elastic closure that occurs in an open- 
 ing before the new material is inserted, 
 because all excavations are assumed to 
 occur at the same instant; thus, slightly 
 more load may be calculated on the 
 inserted material than would actually 
 occur. For many mining problems, this 
 approximation is acceptable. 
 
 For example, if a packwall having an 
 elastic modulus of 25,000 psi is inserted 
 in a 10-ft seam after 1 in of roof clo- 
 sure has occurred, then the additional 
 packwall stress calculated by MULSIM/BM 
 will be approximately 1/120 times 25,000 
 psi, or about 200 psi of additional 
 stress. The magnitude of this effect may 
 be as much as 5 to 10 pet of the calcu- 
 lated stress in a packwall, a crib, or a 
 gob zone. If the focus of interest is 
 the magnitude of the stress abutment in 
 a pillar or a rib side, then this level 
 of inaccuracy is negligible and is an 
 acceptable tradeoff for the convenient 
 calculation of the overall load transfer 
 effects. 
 
 Equivalent Elastic Modulus for 
 Supported Openings (1_) 
 
 For modeling openings that contain 
 structural supporting members, an ad- 
 justed elastic modulus should be used. 
 For example, consider a 20-ft-wide open- 
 ing supported by steel arches whose legs 
 occupy 3 in of that width, or 1.25 pet 
 of the opening width. This opening is 
 best modeled as an inserted material 
 whose elastic modulus is 1.25 pet of the 
 elastic modulus of the steel in the 
 arches. Another example is the modeling 
 
of packwalls in the gate road system of 
 an advancing longwall. If the packwalls 
 occupy 40 pet of the cross section of the 
 gate road system, then the system can 
 be modeled as an inserted material whose 
 modulus is 40 pet of the effective elas- 
 tic modulus of the packwalls. 
 
 When interpreting the output for an 
 element or block treated in this manner, 
 one must remember that the load carried 
 by the load-bearing member will be aver- 
 aged across the entire element or block. 
 Thus, the stress output from the program 
 for the two example situations will be as 
 follows: For the 3-in steel legs occupy- 
 ing 1.25 pet of a 20-ft opening width, 
 the normal stress printed out for the 
 element or block will be only 1.25 pet of 
 the actual average normal stress in the 
 steel legs. For the packwalls occupying 
 40 pet of an opening cross section, the 
 normal stress printed out for the element 
 or block will be 40 pet of the average 
 normal stress in the packwall. 
 
 Equivalent Rock Mass Modulus (J_) 
 
 The program does not account for the 
 disruptive effects of caving upon the 
 rock mass elastic behavior and upon over- 
 lying seams. In reality, as the rock 
 mass deflects and descends upon a gob 
 zone, nonelastic effects such as cracking 
 open of joints occur; and the effective 
 modulus of the rock in this region may 
 be considerably lowered. This in situ 
 situation calls for some engineering 
 judgment in the selection of an effective 
 rock mass modulus for the program. If 
 an approximate overall rock mass rating 
 (RMR) can be inferred for the overburden, 
 taking into account that the overburden 
 above a gob zone will be weakened and 
 thus will have a low RMR, then an over- 
 all overburden modulus may be estimated 
 from the following equation given by 
 Bieniawski (2): 
 
 E M = 2 * RMR - 100, 
 
 (10) 
 
 where Em is the overall modulus of defor- 
 mation of the rock mass, in gigapascals. 5 
 Recent Bureau works have used values of 
 
 5 1 GPa equals 145,040 psi. 
 
 400,000 psi (9) and 384,000 psi (1_) for 
 the effective in situ rock mass elastic 
 modulus. 
 
 Upper Seams Overlying Gob Zones 
 
 The program cannot accurately calculate 
 what would happen to a second seam over- 
 lying a gob zone unless the interburden 
 is considerably greater than the expected 
 caving height (O* Major damage will 
 occur to a coal seam overlying a gob zone 
 if the interburden distance is less than 
 a critical distance of 6.3 times the 
 extraction height in the lower seam ( 6_) ; 
 and if the interburden distance is less 
 than about 3.5 times the lower seam 
 extraction height, the upper seam will be 
 completely destroyed by caving (6^). 
 
 Therefore, MULSIM/BM should not be used 
 if an overlying coal seam is within 3. 5 
 seam heights of a lower seam gob zone. 
 If the interburden distance is between 
 3.5 and 6.3 seam heights, the program 
 should be used, if at all, with caution. 
 In such a situation, the elastic prop- 
 erties of coal elements or blocks that 
 overlay the lower seam gob should be 
 reduced according to some estimate of the 
 amount of in situ softening caused by the 
 lower seam extraction. The amount of 
 reduction needed would vary from little 
 or none for 6.3 seam heights of inter- 
 burden to almost 100 pet reduction for 
 only 3.5 seam heights of interburden. 
 
 MODELING LARGE AREAS (1_) 
 
 The ability to represent a large area 
 is especially useful. In many coal min- 
 ing situations, the overburden load 
 transfer caused by mining can extend over 
 a very wide area; thus, any given portion 
 of the mine can potentially be affected 
 by extraction at a considerable distance 
 in the same or a neighboring seam. 
 
 Nonetheless, the mining engineer often 
 wishes to determine the effect of the 
 total system upon only one or a few of 
 its components, such as a given chain 
 pillar or row of pillars. 
 
 MULSIM/BM permits a distinction between 
 coarse-mesh blocks (undivided blocks) and 
 fine-mesh blocks (divided into 25 ele- 
 ments each). The coarse-mesh blocks are 
 
10 
 
 each assigned a material property; and if 
 this is an original seam material (coal), 
 an extraction ratio can also be speci- 
 fied. Coarse-mesh blocks can also be 
 defined as gob or other inserted mate- 
 rials, such as backfill or a packwall 
 system. The area of interest can be 
 included in a fine-mesh area for which 
 the resulting overburden load distribu- 
 tions are calculated on an eleraent-by- 
 element basis. 
 
 Coarse-Mesh Blocks 
 
 By use of coarse-mesh blocks, the 
 structural characteristics of the mine 
 structure remote from the area of inter- 
 est can be accurately represented and the 
 resulting effects included in the cal- 
 culated results; yet the computer calcu- 
 lation time and costs are considerably 
 decreased. 
 
 Material Model Definition 
 
 Coarse-mesh blocks may use any of the 
 material property sets defined for a par- 
 ticular analysis. The appropriate mate- 
 rial property set is specified simply by 
 providing the property set letter, A 
 through Z, as an input associated with 
 the particular coarse block. 
 
 Extraction Ratios 
 
 For coarse-mesh blocks that represent 
 an original seam material (coal), an 
 extraction ratio is specified in addi- 
 tion to the material property set assign- 
 ment. This feature allows an analysis 
 to include the effects of previous or 
 current mining activity adjacent to an 
 area of interest without defining all the 
 details of the adjacent raining layout. 
 The program internally reduces the stiff- 
 ness of a partially extracted coarse-mesh 
 block in accordance with the extraction 
 ratio. 
 
 The extraction-ratio feature is appro- 
 priate only for mining regions where no 
 roof caving has occurred. If roof caving 
 has occurred in a mined-out region, then 
 this region should be modeled using the 
 gob material model. 
 
 Boundary Conditions 
 
 Computer programs using the three- 
 dimensional displacement -discontinuity 
 approach normally consider that the 
 region outside the modeled area Is at 
 equilibrium with the overburden stress 
 and therefore is implicitly unmined and 
 incompressible. In applications of this 
 method, it has been a matter of concern 
 how best to avoid distortion of results 
 due to the influence of an incompressible 
 model boundary (for example, reference 5, 
 p. 15). 
 
 MULSIM/BM deals with this problem fair- 
 ly easily, through the mechanism of the 
 undivided coarse-mesh blocks. If the 
 coarse-mesh area includes the entire area 
 of interaction that affects the fine-mesh 
 area of interest, as described in the 
 preceding subsection, then the unmodeled 
 regions outside this area of interaction 
 are in a sense irrelevant, since they 
 do not in any case affect the area of 
 interest. 
 
 A further refinement of the boundary 
 effect exists in MULSIM/BM because of the 
 potential use of different material prop- 
 erty types near the model boundaries. In 
 effect, each individual element or block 
 in the model grid considers that the 
 unmodeled area consists of the same mate- 
 rial type that was used for that indi- 
 vidual element or block. The result is 
 that any material type, for example a gob 
 zone, can be carried right to the coarse- 
 mesh model boundary. If the blocks close 
 to the boundary are under a stress that 
 is close to the overburden stress, then 
 regardless of material type they will not 
 be significantly affected by the presence 
 of the model boundary. 
 
 GOUGE MATERIAL 
 
 The MULSIM/BM gouge material capability 
 is taken from the original MULSIM program 
 ( 15 , pp. 140-144). This material model 
 capability allows the use of a seam plane 
 to model a fault plane filled with a 
 gouge material. The resulting capabil- 
 ity is very similar to a slip or joint 
 element. 
 
11 
 
 The gouge material uses a Mohr-Coulomb 
 shear strength criterion for calculation 
 of rides (differential horizontal dis- 
 placements across the material). Besides 
 the Young's modulus and shear modulus, 
 the material model makes use of values of 
 cohesion and internal friction angles. 
 Two sets of these values for cohesion and 
 internal friction angle are used: The 
 first set gives the normal values for an 
 intact material; the second set gives 
 residual values for a material that has 
 cracked open (i.e., with negative clo- 
 sure) and then closed back up again. 
 
 In the solution using this material 
 model, the difference between horizontal 
 stresses in the roof and floor of the 
 seam is compared to the maximum allowable 
 shear stresses that are obtained from the 
 operative (intact or residual) strength 
 properties, using the normal compres- 
 sive stress as a confining stress. If 
 the difference between the horizontal 
 stresses is within the allowable limits, 
 then the rides are determined by using 
 the shear modulus in the normal manner. 
 If, however, the difference between the 
 horizontal stresses exceeds the allowable 
 limits, then the amount of excess stress 
 is used to introduce horizontal slip into 
 the ride components for the next iter- 
 ation, until the excess horizontal 
 stresses are relieved. 
 
 SEAM LIMITATIONS, SIGN CONVENTIONS, 
 AND SYMMETRY OPTIONS 
 
 Maximum Number of Seams 
 
 In general, the maximum number of seams 
 that can be analyzed depends on the 
 dimension statements within a particular 
 program version being used. The program 
 dimension statements must be fitted to 
 the total computer core memory available, 
 unless the program is to run on a virtual 
 memory machine, in which case the memory 
 limitation effectively disappears. 
 
 The original MULSIM program ( 15 ) was 
 dimensioned for a maximum of four par- 
 allel tabular seams. The MULSIM/BM pro- 
 gram, as listed in appendix C, is limited 
 to a maximum of two seams with a maximum 
 grid of 40 by 40 blocks per seam, in 
 
 order to meet the memory limitations of 
 the computer used for program develop- 
 ment. To remain within the same core 
 memory limits, a three-seam maximum would 
 require reducing the maximum grid size 
 to about 30 by 30 blocks per seam, and a 
 four-seam maximum would require a maximum 
 total grid of about 20 by 20 blocks per 
 seam. The mesh-generating program listed 
 in appendix D is compatible with any max- 
 imum number of seams and with maximum 
 grid sizes up to 40 by 40 blocks per 
 seam. Appendix G shows how MULSIM/BM can 
 be modified to run on a virtual memory 
 computer. 
 
 Location of Seam Origins 
 
 As shown in figure 4, the grids for the 
 
 MULSIM/BM seam planes must be located 
 
 with the grid origins all lying on the 
 
 same normal line. This limitation arises 
 
 Surface 
 
 X 3 (Z) 
 
 /7 X 2 
 
 FIGURE 4.— Seam origins lie on the same normal line. 
 
12 
 
 because the programmed calculation of 
 influence coefficients does not allow for 
 relative displacement of the seam grids. 
 Thus, for level seams, the Xi and X2 
 coordinates of all seam origins must be 
 the same. For dipping seams, the X1, X2, 
 and X3 coordinate inputs must be calcu- 
 lated to meet the constraint imposed on 
 the seam origin location. 
 
 Sign Conventions 
 
 The global coordinate system of MULSIM/ 
 BM is a standard set of three orthogonal 
 axes, Xi, X2, and X3, that follow the 
 standard right-hand rule: If the thumb 
 of the right hand points in the X3 direc- 
 tion, then an outstretched finger points 
 in the Xi direction while a finger curved 
 to 90° points in the X2 direction. The 
 global origin lies at the surface. For 
 dipping seams, as shown in figure 4, the 
 
 local XJ and X2 axes remain in the plane 
 of the seam, and X3 is normal to the seam 
 plane. 
 
 The sign conventions for displacements 
 and stresses are the same as in the orig- 
 inal MULSIM program (1_5, pp. 33-34) and 
 are shown in figure 5. Positive dis- 
 placements, ui, U2> and M3, are in the 
 direction of the corresponding global 
 axes, as shown in figure 5A. Figure 55 
 shows the positive sense of closure and 
 rides. Seam closure (vertical movement 
 between roof and floor) is positive in 
 the direction that compresses a seam 
 material. Rides (differential horizontal 
 movement between roof and floor) are 
 positive when the floor undergoes a posi- 
 tive relative displacement. Figure 5C 
 shows the positive sense of the stress 
 components, oij. a j j has a positive 
 sense if it points in the positive xj 
 direction while acting on a plane whose 
 
 X2,^2 
 
 * X I'^I 
 
 A. Positive displacements, fJL } 
 
 - n+n - 
 
 ,.x 3 =o:o 
 
 if 0- ^ 
 ^Ride 
 B. Positive rides and closures 
 
 '2 1 
 
 1 
 
 I 
 
 
 \ 
 
 '22 
 
 '23 
 
 C. Positive normal and shear stresses 
 
 FIGURE 5.— Sign conventions for displacements and stresses. 
 
13 
 
 outward normal points in the negative 
 Xi direction. Therefore, compressive 
 stresses are positive; and the positive 
 senses of the shear stresses are as shown 
 in figure 5C . 
 
 Symmetry Options 
 
 MULSIM/BM includes the same symmetry 
 options as in the original MULSIM pro- 
 gram (15). Figure 6 illustrates the four 
 
 symmetry options available. As shown in 
 the figure, option 1 specifies no sym- 
 metry. Options 2 and 3 allow a line of 
 symmetry through the center of the model 
 grid, and option 4 combines options 2 and 
 3 so that two lines of symmetry exist. 
 
 The effect of specifying symmetry op- 
 tion 2, 3, or 4 is to reduce the solution 
 time and, to a small extent, the input 
 data requirements. Only the nonsymmetri- 
 cal portion of the grid Is specified as 
 
 X- 
 
 t 
 
 40 
 
 20 
 
 □ 
 
 20 40 
 
 (0,0) 
 
 A. Symmetry code 
 (no symmetry) 
 
 ->X_ 
 
 I 
 m 
 a 
 
 g 
 e 
 
 I 
 
 ■> X- 
 
 B. Symmetry code 2 
 
 (0,0) 
 
 > X- 
 
 X- 
 
 r 
 
 (0,0) 
 
 X 
 
 _J 
 
 J 
 
 -> x^ 
 
 C. Symmetry code 3 
 
 D. Symmetry code 4 
 
 FIGURE 6— Symmetry options. 
 
14 
 
 input. For example, for the program as 
 listed in appendix C, the maximum grid 
 size is 40 by 40 blocks, including a max- 
 imum 20- by 20-block fine-mesh grid; but 
 if symmetry code 4 is used, only a 20- 
 by 20-block grid with a maximum 10- by 
 10-block fine-mesh grid can be input. 
 The fine-mesh area must be located so 
 that the lines of symmetry also bisect 
 the fine-mesh grid. For symmetry codes 2 
 and 3, the fine-mesh area can lie any- 
 where along the line of symmetry, so 
 long as the line of symmetry bisects the 
 
 fine-mesh grid; for symmetry code 4, the 
 fine-mesh grid must necessarily occupy 
 the center of the coarse-mesh grid. 
 
 The savings in solution time occurs 
 because the program needs only to find 
 solutions for the nonsymmetric portion 
 (half or quadrant) of the grid. During 
 the iteration process, the current solu- 
 tions for each element and block are also 
 stored for the corresponding imaged ele- 
 ments and blocks. Total solution time in 
 the iteration phase is thus reduced by a 
 factor of either 2 or 4. 
 
 COMPANION MESH GENERATOR PROGRAM 
 
 The companion interactive-graphics mesh 
 generator program is quick and conve- 
 nient. The different material types are 
 each assigned elastic property values 
 (Young's modulus and shear modulus) and 
 an identifying letter (A through Z); each 
 element or undivided block is then 
 assigned the desired material type by 
 specifying the appropriate identifying 
 letter. For the undivided coarse-mesh 
 blocks, a table of extraction ratios can 
 be defined; each undivided block that 
 uses an original seam material can then 
 be assigned one of the extraction ratios. 
 
 Figure 7 shows an example mining lay- 
 out that was defined to illustrate 
 use of MULSIM/BM and of the companion 
 
 mesh-generator program. Example grids 
 for analysis of this layout are shown in 
 figure 8. A mining engineer can easily 
 generate a data file to analyze this 
 example problem in a 1-h session using 
 the mesh-generator program. 
 
 Appendix B shows a sample terminal ses- 
 sion using the mesh generator to create a 
 MULSIM/BM input file for this example. 
 Appendix E shows the resulting MULSIM/BM 
 input data file. Appendix F shows the 
 output that results from MULSIM/BM for 
 the same example. The job control lan- 
 guage needed to run the program on the 
 computer system used at the Bureau's 
 Denver (CO) Research Center is shown in 
 appendix H. 
 
 DEVELOPING A PLAN OF ANALYSIS 
 
 The following procedure is recommended 
 as a general approach to analyzing a 
 problem using MULSIM/BM. The procedure 
 presented here expands upon a general 
 approach recommended previously U_)» 
 While some of the recommended steps may 
 appear obvious, it is worth taking note 
 that none of them should, in general, be 
 omitted. 
 
 1. Define the problem. This means 
 explicitly asking one or more questions 
 that one expects can be answered on the 
 basis of analysis. Examples of such 
 questions might be, "What is the safe 
 size for a particular coal pillar?" or 
 "How much steel support is needed in a 
 certain area to limit opening closure to 
 desired limits?" 
 
 2. Identify the appropriate theoreti- 
 cal approach to analyze the problem. For 
 some problems a finite-element approach 
 or perhaps a discrete block analysis 
 will be indicated. This selection of 
 approach must be made on the basis of the 
 analyst's experience and familiarity with 
 the capabilities and limitations of dif- 
 ferent available methods. The following 
 steps assume that MULSIM/BM has been 
 selected as the vehicle of the analysis. 
 
 3. Define the area of interest. This 
 area should be included within the fine- 
 mesh zone of the grid. 
 
 4. Identify the relevant area of in- 
 teraction. This will be the maximum area 
 from which load transfer effects will 
 
15 
 
 Upper seam 
 
 Upper seam 
 
 Lower seam 
 
 100 200 
 i . I 
 
 Scale, ft 
 
 FIGURE 7.— Example mining layout 
 
 KEY 
 * t i i 1 1 Mine entryway 
 
 Lower seam 
 
 KEY 
 Coal block, 
 zero extraction 
 
 ZT\ Coal block, 
 -J 0.2 extraction 
 
 r , o o 
 
 Gob block 
 
 ■ 
 
 u 2 ' 7& 2 
 
 l'2 u 
 
 
 'jl ai? 
 
 
 
 
 
 
 
 
 Coal 
 elements 
 
 Gob 
 
 elements 
 
 Open 
 elements 
 
 FIGURE 8.— MULSIM/BM grids for the example layout. 
 
16 
 
 be felt within the area of interest. If 
 possible, this entire area should be 
 included within the MULSIM/BM grid. 
 
 5. Identify reasonable initial values 
 for effective material properties and 
 for the virgin stress conditions. True 
 stress values can only be determined by 
 in situ measurements. Material proper- 
 ties are sometimes available from labora- 
 tory or in situ testing; in other cases, 
 representative properties can be used 
 with reasonable accuracy. As discussed 
 previously in this report, recent Bureau 
 work (J_, 9_) has used rock mass modulus 
 values in the range of 400,000 psi, cor- 
 responding to relatively low values of 
 the rock mass rating (2), and an effec- 
 tive in situ gob modulus of 20,000 psi, 
 adjusted to 5,000 psi in accordance with 
 equation 9 of this report. 
 
 The initial values used for the coal 
 seam or for other materials such as pack- 
 walls may need to be reduced in highly 
 stressed areas such as those adjacent to 
 a large gob zone or within the influence 
 zone of a stress concentration emanating 
 from an adjacent seam. Previous Bureau 
 work (1, 7-10) has shown that a procedure 
 
 of reducing the effective modulus value 
 until the resulting stresses become 
 allowable can adequately represent the 
 transfers of stresses that result from 
 in situ weakening and softening of highly 
 stressed materials. 
 
 6. Identify cases to be analyzed. 
 
 7. Generate MULSIM/BM input files for 
 the desired cases using the mesh genera- 
 tor program. 
 
 8. Run MULSIM/BM to obtain results 
 for the desired cases. 
 
 9. Analyze the results using postpro- 
 cessing graphics or other methods. 
 
 10. Determine whether the problem has 
 been satisfactorily solved. If not, it 
 may frequently be desirable to redefine 
 the problem on the basis of the analysis 
 conducted so far. At this stage, all 
 the parameters of the analysis should be 
 reexamined; even the selection of theo- 
 retical approach may be subject to 
 change. Therefore the analyst should at 
 this point return to step 1 of this sug- 
 gested analysis procedure. 
 
 REFERENCES 
 
 1. Beckett, L. A., and R. S. Madrid. 
 Practical Application of MULSIM/BM for 
 Improved Mine Design. Paper in Use of 
 Computers in the Coal Industry (Third 
 Conf., WV Univ., Morgantown, WV, July 
 28-30, 1986). A. A. Balkema, Rotterdam, 
 Netherlands, 1986, pp. 209-219. 
 
 2. Bieniawski, Z. T. Determining Rock 
 Mass Def ormability: Experience From Case 
 Histories. Int. J. Rock Mech. , Min. Sci. 
 & Geomech. Abstr. , v. 15, 1978, pp. 237- 
 247. 
 
 3. Crouch, S. L. , and C. Fairhurst. 
 The Mechanics of Coal Mine Bumps and the 
 Interaction Between Coal Pillars, Mine 
 Roof, and Floor (contract H0101778, Univ. 
 MN). BuMines OFR 53-73, 1973, 88 pp.; 
 NTIS PB 222 898. 
 
 4. Crouch, S. L. , and A. M. Star- 
 field. Boundary Element Methods in Solid 
 Mechanics. Allen & Unwin, 1983, 322 pp. 
 
 5. Hardy, M. P., H. N. Maleki, and 
 S. J. Mitchell. Application of Dis- 
 placement of Discontinuity Methods in 
 Underground Mine Design. Paper in Rock 
 Masses: Modeling of Underground Open- 
 ings/Probability of Slope Failure/Frac- 
 ture of Intact Rock, ed. by C. H. Dowding 
 (Proc. Symp. sponsored by ASCE Geotech. 
 Eng. Div. in conjunction with ASCE Conv. , 
 Denver, CO, Apr. 29-30, 1985). ASCE, 
 1985, pp. 14-20. 
 
 6. Hladysz, Z. Analysis of Risk in 
 Multiple Seam Mining. Soc. Min. Eng. 
 AIME preprint 85-357, 11 pp. 
 
17 
 
 7. Kidybinski, A., and C. 0. Babcock. 
 Stress Distribution and Rock Fracture 
 Zones in the Roof of Longwall Face in 
 a Coal Mine. Rock Mech. , v. 5, No. 1, 
 1973, pp. 1-19. 
 
 8. Kripakov, N. P. Analysis of Pil- 
 lar Stability on Steeply Pitching Seam 
 Using the Finite Element Method. BuMines 
 RI 8579, 1981, 33 pp. 
 
 9. Kripakov, N. P., L. A. Beckett, 
 and D. A. Donato. Loading on Underground 
 Mine Structures Influenced by Multiple 
 Seam Interaction. Paper in International 
 Symposium on Application of Rock Char- 
 acterization Techniques in Mine Design 
 (SME-AIME Ann. Meeting, New Orleans, LA, 
 Mar. 1986). Soc. Min. Eng. AIME, Little- 
 ton, CO, 1986, pp. 225-236. 
 
 10. Kripakov, N. P. , and M. T. Mel- 
 vin. A Computer Program To Simulate Pro- 
 gressive Rock Failure Around Coal Mine 
 Entries. Paper in Proceedings of the 
 First Conference on Use of Computers in 
 the Coal Industry (WV Univ., Morgantown, 
 WV, Aug. 1-3, 1983). Soc. Min. Eng. 
 AIME, New York, 1983, pp. 487-502. 
 
 11. Mozumdar, B. J. A Mathematical 
 Model of Ground Movement Due to 
 
 Underground Mining. Ph.D. Thesis, PA 
 State Univ. , 1974, 134 pp. Xerox Univ. 
 Microfilms, Ann Arbor, MI, fac. 75-9815, 
 1978. 
 
 12. Peng, S. S. Coal Mine Ground Con- 
 trol. Wiley, 1978, 450 pp. 
 
 13. Salamon, M. D. G. Elastic Analy- 
 sis of Displacements and Stresses Induced 
 by the Mining of Seam or Reef Deposits. 
 J. South African Inst. Min. & Metall. , 
 Part I, v. 64, No. 4, 1963, pp. 128-149; 
 Part II, v. 64, No. 6, 1964, pp. 197- 
 218; Part III, v. 64, No. 10, 1964, 
 pp. 468-500; Part IV, v. 65, No. 5, 1964, 
 pp. 319-338. 
 
 14. . Reconsolidation of Caved 
 
 Areas. Coll. Res. Lab. Transvaal and 
 Orange Free State Chamber of Mines Res. 
 Org., Republic of South Africa, Res. Rep. 
 58/66, July 1966, 25 pp. 
 
 15. Sinha, K. P. Displacement Discon- 
 tinuity Technique for Analyzing Stresses 
 and Displacements Due to Mining in Seam 
 Deposits. Ph.D. Thesis, Univ. MN, 1979, 
 311 pp.; Univ. Microfilms Int., Ann 
 Arbor, MI, fac. 7918390, 1982. 
 
18 
 
 APPENDIX A.— MULSIM/BM USER'S GUIDE 
 
 This appendix explains to the user of MULSIM/BM how to create the input data file. 
 
 The coarse mesh features and the method of assigning material properties to ele- 
 ments are new within this program. Many of the remaining data definition require- 
 ments are the same as the original MULSIM program as documented by Sinha (15). ' 
 
 The input data file may be created by using any available text editor, or by run- 
 ning the companion mesh generator program. If the user's computer system has Tek- 
 tronix graphics software Plot-10, and the appropriate terminals (Tektronix 4010, 
 4014, etc.), then the best way to generate the input data file is to use the mesh 
 generator program. 
 
 The mesh generator program is described fully in appendix B. 
 
 The maximum grid size and maximum number of seams allowed depend on the particular 
 MULSIM/BM version. The version listed in appendix D allows a maximum grid of 40 by 
 40 blocks and a maximum of two seams. 
 
 Underlined numbers in parentheses refer to items in the list of references preced- 
 ing this appendix. 
 
19 
 
 INPUT DATA INSTRUCTIONS 
 
 THE INPUT FILE CONSISTS OF SEVERAL DIFFERENT CARD TYPES, 
 THE FILE MUST BE IN CARD TYPE SEQUENCE. 
 
 THE INPUT DATA MUST BE IN CONSISTENT UNITS FOR 
 DIMENSIONS, STRESSES, AND MODULI. 
 FOR EXAMPLE: 
 
 METERS KILOPASCALS KILOPASCALS 
 
 METERS MEGAPASCALS MEGAPASCALS 
 
 CARD TYPE 1 - TITLE 
 DATUM 
 TITLE (ANY TEXT) 
 
 CARD TYPE 2 - HOST ROCK MATERIAL PROPERTIES 
 DATUM 
 
 POISSON'S RATIO OF ROCK MASS 
 MODULUS OF ELASTICITY OF ROCK MASS 
 NUMBER OF SEAMS (1-N) 
 
 N - THE CURRENT VERSION WILL ACCEPT UP TO 2 
 
 SEAMS. THIS IS BECAUSE OF THE MAXIMUM 40X40 
 BLOCK MODEL. OTHER VERSIONS WITH SMALLER 
 BLOCK MODELS WILL ACCEPT UP TO 4 SEAMS. 
 
 COLUMNS FORMAT 
 1-80 20A4 
 
 COLUMNS FORMAT 
 1-8 F8.2 
 9-20 E12.6 
 21-28 18 
 
 CARD TYPE 3 - NUMBER OF MATERIAL PROPERTIES 
 
 DATUM 
 
 NUMBER OF MATERIAL TYPES (1-26) 
 
 COLUMNS FORMAT 
 1-80 * 
 
 CARD TYPE 4 - SEAM MATERIAL PROPERTIES 
 
 (ONE CARD FOR EACH MATERIAL TYPE INPUT IN CARD TYPE 3) 
 DATUM COLUMNS FORMAT 
 
 MODULUS OF ELASTICITY 1-16 E16.10 
 
 SHEAR MODULUS (MODULUS OF RIGIDITY) 17-32 E16.10 
 
 THE FOLLOWING DATA MAY BE IGNORED IF THE SHEAR FAILURE OF 
 SEAM MATERIAL IS NOT TO BE CONSIDERED. (STATUS CODE IS 3) 
 
 COHESION 
 
 FRICTION ANGLE 
 
 RESIDUAL VALUE OF COHESION 
 
 RESIDUAL VALUE OF FRICTION ANGLE 
 
 33-40 E8.2 
 
 41-48 E8.2 
 
 49-56 E8.2 
 
 57-64 E8.2 
 
 AN '*' FORMAT IS FREE FORMAT( NUMBERS SEPARATED BY COMMAS) 
 GOB MATERIAL INDICATOR(l=YES,0=NO) 
 
 65-72 18 
 
20 
 
 CARD TYPE 5 - PRIMITIVE STRESS PARAMETERS 
 
 THE STRESS TENSOR THAT DESCRIBES A STRESS STATE THAT EXISTS 
 PRIOR TO MINING IS DEFINED AS LINEAR FUNCTIONS OF GLOBAL DIRECTION. 
 WITH COMPRESSION BEING POSITIVE; THE EQUATIONS ARE OF THE FORM: 
 STRESS(1,1) = All - Bll * X3 
 
 (1,2) = A12 - B12 * X3 AND SO ON. 
 
 AXX MUST BE >= -.9999 AND <= 99999. 
 BXX MUST BE >= -.9999 AND <= 9.9999 
 X3 MUST BE NEGATIVE. 
 
 REFER TO SINHA (15) FOR MORE DETAILS. 
 
 DATUM 
 
 All 
 
 CONSTANT 
 
 Bll 
 
 CONSTANT 
 
 A12 
 
 CONSTANT 
 
 B12 
 
 CONSTANT 
 
 A13 
 
 CONSTANT 
 
 B13 
 
 CONSTANT 
 
 A22 
 
 CONSTANT 
 
 B22 
 
 CONSTANT 
 
 A23 
 
 CONSTANT 
 
 B23 
 
 CONSTANT 
 
 A3 3 
 
 CONSTANT 
 
 B33 
 
 CONSTANT 
 
 COLUMNS 
 
 FORMAT 
 
 1-6 
 
 F6.0 
 
 7-12 
 
 F6.4 
 
 13-18 
 
 F6.0 
 
 19-24 
 
 F6.4 
 
 25-30 
 
 F6.0 
 
 31-36 
 
 F6.4 
 
 37-42 
 
 F6.0 
 
 43-48 
 
 F6.4 
 
 49-54 
 
 F6.0 
 
 55-60 
 
 F6.4 
 
 61-66 
 
 F6.0 
 
 67-72 
 
 F6.4 
 
 CARD TYPE 6 - MODEL DATA 
 
 DATUM 
 
 BLOCK WIDTH 
 
 NUMBER OF BLOCKS IN X-AXIS (1 TO 40) 
 THIS IS THE NUMBER OF BLOCKS ALONG THE 
 LOCAL X-AXIS IN EACH SEAM. 
 (TOTAL COARSE GRID PLUS FINE GRID). 
 IF SYMMETRY IS SPECIFIED, THEN THIS SHOULD 
 BE THE UNIQUE PORTION (QUADRANT OR HALF) 
 OF THE MESH. 
 
 COLUMNS FORMAT 
 1-8 F8.2 
 9-16 18 
 
 NUMBER OF BLOCKS IN Y-AXIS (1 TO 40) 
 SAME AS ABOVE EXCEPT FOR THE Y-AXIS. 
 
 17-24 18 
 
 SYMMETRY FLAG(1 , 2, 3, 4) 
 IF SYMMETRY IS SPECIFIED, THE LINES OF 
 SYMMETRY PASS THROUGH THE CENTER OF THE MODEL. 
 
 1 - NO SYMMETRY 
 
 2 - VERTICAL LINE OF SYMMETRY 
 
 3 - HORIZONTAL LINE OF SYMMETRY 
 
 4 - VERTICAL AND HORIZONTAL LINES OF SYMMETRY 
 
 25-32 18 
 
21 
 
 NUMBER OF OFF-SEAM PLANES 
 AT WHICH DISPLACEMENTS AND 
 STRESSES ARE TO BE COMPUTED. 
 
 33-40 18 
 
 THE FINE MESH BLOCKS ARE SUBDIVIDED INTO 25 ELEMENTS. THIS 
 CONSISTS OF 5 ROWS OF 5 ELEMENTS PER ROW. 
 
 STARTING BLOCK IN FINE MESH 
 
 X-AXIS 
 ENDING BLOCK IN FINE MESH 
 
 X-AXIS 
 STARTING BLOCK IN FINE MESH 
 
 Y-AXIS 
 ENDING BLOCK IN FINE MESH 
 
 Y-AXIS 
 
 NOTE: ENDING BLOCK - STARTING BLOCK MUST BE LESS THAN 20 
 
 CARD TYPE 7 - EXTRACTION DATA FOR COARSE MESH BLOCKS 
 
 EXTRACTION CODE '0' IS THE DEFAULT FOR ZERO EXTRACTION. 
 THIS CODE IS IRRELEVANT FOR GOB OR OPENINGS. 
 
 41-48 18 
 
 49-56 18 
 
 57-64 18 
 
 65-72 18 
 
 DATUM 
 
 NUMBER OF EXTRACTION RATIOS 
 NUMBER OF ADDITIONAL EXTRACTION RATIO 
 CODES. (ADDITIONAL TO ZERO). VALID VALUES 
 ARE 1 THROUGH 9. 
 
 COLUMNS FORMAT 
 1-8 18 
 
 EXTRACTION RATIO 1 
 ALL EXTRACTION RATIOS MUST BE A FRACTIONAL 
 NUMBER GREATER THAN AND LESS THAN 1. 
 
 9-16 F8.3 
 
 EXTRACTION 
 EXTRACTION 
 EXTRACTION 
 EXTRACTION 
 EXTRACTION 
 EXTRACTION 
 EXTRACTION 
 EXTRACTION 
 
 RATIO 
 RATIO 
 RATIO 
 RATIO 
 RATIO 
 RATIO 
 RATIO 8 
 RATIO 9 
 
 CARD TYPE 8 - GLOBAL COORDINATES OF GRID ORIGIN 
 
 (ONE CARD FOR EACH SEAM AS INPUT IN CARD TYPE 2) 
 ( THE SEAM ORIGINS ARE AT THE ROOF OF THE SEAM ) 
 
 DATUM 
 
 X-COORDINATE FOR SEAM ORIGIN 
 
 Y-COORDINATE FOR SEAM ORIGIN 
 
 Z-COORDINATE FOR SEAM ORIGIN(MUST BE NEGATIVE) 
 
 SEAM THICKNESS 
 
 17-24 
 
 F8.3 
 
 25-32 
 
 F8.3 
 
 33-40 
 
 F8.3 
 
 41-48 
 
 F8.3 
 
 49-56 
 
 F8.3 
 
 57-64 
 
 F8.3 
 
 65-72 
 
 F8.3 
 
 73-80 
 
 F8.3 
 
 COLUMNS FORMAT 
 
 1-8 F8.1 
 
 9-16 F8.1 
 
 17-24 F8.1 
 
 25-32 F8.1 
 
22 
 
 CARD TYPE 9 - GRID ORIENTATION FOR SEAM 
 
 (DIRECTION COSINES BETWEEN SEAM GRID AND GLOBAL COORDINATE SYSTEM) 
 EN(I,J) IS THE DIRECTION COSINE OF LOCAL AXIS X(I) AT THE 
 SEAMS WITH RESPECT TO THE GLOBAL AXIS X(J). 
 
 DATUM 
 
 EN(1,1) 
 
 EN(2,1) 
 
 EN(3,1) 
 
 EN(1,2) 
 
 EN(2,2) 
 
 EN(3,2) 
 
 EN(1,3) 
 
 EN(2,3) 
 
 EN(3,3) 
 
 COLUMNS 
 
 FORMAT 
 
 1-8 
 
 F8.5 
 
 9-16 
 
 F8.5 
 
 17-24 
 
 F8.5 
 
 25-32 
 
 F8.5 
 
 33-40 
 
 F8.5 
 
 41-48 
 
 F8.5 
 
 49-56 
 
 F8.5 
 
 57-64 
 
 F8.5 
 
 65-72 
 
 F8.5 
 
 CARD TYPE 10 - MODEL RUN AND RESTART CONTROL PARAMETERS 
 
 DATUM 
 
 OVER RELAXATION FACTOR 
 VALID VALUES 1.0 THROUGH 1.99 
 (1.35 IS OFTEN BEST) 
 
 COLUMNS FORMAT 
 1-8 F8.2 
 
 MAXIMUM ITERATIONS FOR THIS RUN 
 COMPUTER RUN NUMBER (SEE NOTE 1.) 
 COMPLETED ITERATIONS (SEE NOTE 2.) 
 
 IN PREVIOUS RUNS 
 USE PREVIOUS GRID FLAG ( 1 =Y, 0=N) (SEE NOTE 3.) 
 
 9-16 
 
 18 
 
 17-24 
 
 18 
 
 25-32 
 
 18 
 
 33-40 18 
 
 NOTES: 1. COMPUTER RUN NUMBER GREATER THAN 1 IMPLIES THAT DESIRED 
 ACCURACY WAS NOT ACHIEVED IN PREVIOUS RUN. 
 
 2. COMPLETED ITERATIONS GREATER THAN ZERO IMPLIES THAT 
 THE RIDE AND CLOSURE VALUES OBTAINED AND SAVED IN 
 PREVIOUS RUNS ARE TO BE USED AS THE INITIAL APPROXIMATIONS 
 FOR THIS RUN. 
 
 3. IF THE PREVIOUS GRID FLAG IS SET TO '1', THEN THE INFLUENCE 
 COEFFICIENTS ARE TO BE RETRIEVED FROM A PREVIOUSLY 
 
 SAVED FILE. ALSO THE MODEL GRID IS TO REMAIN THE SAME AS 
 IN A PREVIOUS RUN. 
 
 CARD TYPE 11 - FINE MESH MATERIAL PROPERTY CODES 
 
 (ONE CARD FOR EACH ROW OF ELEMENTS IN THE FINE MESH GRID 
 OF EACH SEAM) 
 
 EACH CARD CONTAINS THE MATERIAL PROPERTY CODES FOR 
 ALL ELEMENTS IN THE ROW. 
 (THE NUMBER OF ELEMENTS PER ROW IS 5 TIMES THE NUMBER OF 
 FINE MESH BLOCKS IN THE X-DIRECTION. THE TOTAL NUMBER 
 OF ELEMENT ROWS IS 5 TIMES THE NUMBER OF FINE MESH BLOCKS 
 IN THE Y-DIRECTION, TIMES THE NUMBER OF SEAMS.) 
 
23 
 
 DATUM COLUMNS FORMAT 
 
 MATERIAL PROPERTY CODES 1-100 100A1 
 
 EACH CODE ENTERED SPECIFIES THE MATERIAL 
 
 PROPERTY SET FOR A PARTICULAR ELEMENT. 
 
 THE CODES MUST CORRESPOND TO THE NUMBER OF 
 
 MATERIAL TYPES ENTERED IN CARD TYPE 3, PLUS THE VALUES 1 AND 2. 
 
 I. E. IF 2 MATERIAL TYPES ENTERED, THEN 
 
 VALID VALUES ARE (A,B, 1, 2). 
 
 IF 3 MATERIAL TYPES ENTERED, THEN 
 
 VALID VALUES ARE (A,B,C, 1, 2) ETC. 
 
 CODE 1 INDICATES AN OPENING, CODE 2 INDICATES A COMPLETELY RIGID MATERIAL. 
 
 CARD TYPE 12 - FINE MESH MINING STATUS CODES 
 
 (ONE CARD FOR EACH ROW OF ELEMENTS IN THE FINE MESH GRID 
 OF EACH SEAM) 
 
 EACH CARD CONTAINS THE MINING STATUS CODES FOR 
 ALL ELEMENTS IN THE ROW. 
 (THE NUMBER OF ELEMENTS PER ROW IS 5 TIMES THE NUMBER OF 
 FINE MESH BLOCKS IN THE X-DIRECTION. THE TOTAL NUMBER 
 OF ELEMENT ROWS IS 5 TIMES THE NUMBER OF FINE MESH BLOCKS 
 IN THE Y-DIRECTION TIMES THE NUMBER OF SEAMS.) 
 
 DATUM COLUMNS FORMAT 
 
 MINING STATUS CODES 1-100 100A1 
 
 EACH CODE ENTERED SPECIFIES THE 
 MINING STATUS CODE SET FORA 
 PARTICULAR ELEMENT. 
 VALID VALUES ARE: 
 
 3 - NORMAL PROPERTIES 
 (SEAM MATERIAL, GOB 
 
 INSERTED MATERIAL) 
 
 4 - GOUGE MATERIAL 
 (MOHR-COULOMB MODEL) 
 
 CARD TYPES 13 AND 14 MUST BE INCLUDED IF A COARSE MESH AREA HAS 
 BEEN DEFINED. THEY MUST NOT BE INCLUDED IF THE MODEL DOES NOT CONTAIN 
 ANY COARSE MESH BLOCKS. 
 
 CARD TYPE 13 - COARSE MESH MATERIAL PROPERTY CODES 
 
 (ONE CARD FOR EACH ROW OF BLOCKS IN THE TOTAL GRID MODEL) 
 (EACH CARD CONTAINS THE MATERIAL PROPERTY CODES FOR ALL 
 BLOCKS IN THE ROW) 
 
 DATUM - COLUMNS FORMAT 
 
 MATERIAL PROPERTY CODES 1-40 40A1 
 
 THE VALID CODES ARE THE SAME AS THE 
 FINE MESH AREA WITH THE ADDITIONAL 
 SPECIAL CODE '*' WHICH IS USED TO 
 DESIGNATE A FINE MESH BLOCK. 
 
24 
 
 CARD TYPE 14 - COARSE MESH EXTRACTION RATIO CODES 
 
 (ONE CARD FOR EACH ROW OF BLOCKS IN THE TOTAL GRID MODEL) 
 EACH CARD CONTAINS THE EXTRACTION CODE FOR EVERY BLOCK 
 IN THE ROW. 
 
 DATUM 
 
 EXTRACTION RATIO CODES 
 
 EACH CODE ENTERED SPECIFIES THE 
 
 EXTRACTION RATIO FOR A PARTICULAR 
 
 BLOCK IN THE ROW. VALID CODES 
 
 (1 TO 9) ARE SET UP IN CARD TYPE 7. 
 
 I.E. IF 2 ENTERED, THEN THE VALID 
 
 VALUES ARE (0,1,2). 
 
 IF 3 ENTERED, THEN THE VALID 
 
 VALUES ARE (0,1,2,3) ETC. 
 
 AGAIN, THE SPECIAL CODE »*» IS 
 
 USED TO DESIGNATE A FINE MESH BLOCK. 
 
 COLUMNS FORMAT 
 1-40 40A1 
 
 CARD TYPE 15 - OFF SEAM GRID DETAILS 
 
 THE OFF-SEAM PLANE IS AN ARBITRARY PLANE IN THE ROCK 
 MASS. STRESSES AND DISPLACEMENTS ARE CALCULATED AT THE 
 CENTER OF EACH BLOCK WITHIN THE OFF-SEAM PLANE. 
 
 DATUM 
 
 X-COORDINATE OF OFF-SEAM ORIGIN 
 Y-COORDINATE OF OFF-SEAM ORIGIN 
 Z-COORDINATE OF OFF-SEAM ORIGIN 
 BLOCK WIDTH ALONG X-AXIS 
 BLOCK WIDTH ALONG Y-AXIS 
 NUMBER OF BLOCKS ALONG X-AXIS 
 NUMBER OF BLOCKS ALONG Y-AXIS 
 
 COLUMNS 
 
 FORMAT 
 
 1-12 
 
 F12.3 
 
 13-24 
 
 F12.3 
 
 25-36 
 
 F12.3 
 
 37-48 
 
 F12.3 
 
 49-60 
 
 F12.3 
 
 61-68 
 
 18 
 
 69-76 
 
 18 
 
 CARD TYPE 15A - OFF SEAM PLANE ORIENTATION 
 (DIRECTION COSINES) 
 
 DATUM 
 
 EN1X 
 
 EN2X 
 
 EN3X 
 
 EN1Y 
 
 EN2Y 
 
 EN3Y 
 
 EN1Z 
 
 EN2Z 
 
 EN3Z 
 
 COLUMNS 
 
 FORMAT 
 
 1-8 
 
 F8.5 
 
 9-16 
 
 F8.5 
 
 17-24 
 
 F8.5 
 
 25-32 
 
 F8.5 
 
 33-40 
 
 F8.5 
 
 41-48 
 
 F8.5 
 
 49-56 
 
 F8.5 
 
 57-64 
 
 F8.5 
 
 65-72 
 
 F8.5 
 
 NOTE: CARD TYPE PAIRS(15, 15A) ARE REPEATED FOR EACH OFF-SEAM PLANE 
 
25 
 
 APPENDIX B.~ MULSIM/BM MESH GENERATOR USER'S GUIDE 
 
 This user's guide is in the form of a sample terminal session. The MULSIM/BM input 
 file created by this sample session is listed in appendix E. 
 
 As installed on the computer system used by the Bureau, the mesh generator is 
 started by entering the following commands following the "ready" prompt from the 
 computer: 
 
 GET , PRGENM/UN=BM000 1L 
 BEGIN, PRGENM 
 
 These commands will start up a procedure file that calls the mesh generator pro- 
 gram. A listing of the procedure file follows the sample terminal session. Anyone 
 using a different computer system will need to implement an equivalent procedure. 
 
 The user will make the selection as to whether or not the mesh generator will con- 
 vert depth and distance entered in feet to inches. 
 
 All card type data will be requested as outlined in the input data instructions in 
 appendix A, except for the orientation of the grid or the orientation of any off-seam 
 planes. The orientation will be supplied in terms of strike, dip, and offset angles, 
 and the mesh generator program will then calculate the appropriate direction cosines. 
 
 The maximum grid size and maximum number of seams depend on the MULSIM/BM version 
 to be used. 
 
26 
 
 SAMPLE TERMINAL SESSION 
 
 READY 
 
 GET,PRGENM/UN=BM0001L USER 
 
 BEGIN, PRGENM USER 
 
 THIS PROGRAM GENERATES INPUT-DATA FOR MULSIM 
 
 WHAT DO YOU WANT TO DO NOW 
 
 TYPE TO END THIS PROGRAM NOW 
 
 TYPE 1 TO GENERATE A DATA FILE 
 
 ? 1 USER 
 
 PREPARATION OF INPUT-DATA FOR —ENHANCED MULSIM 
 
 YOU MUST USE CONSISTENT UNITS FOR: 
 
 DIMENSION, STRESSES, AND MODULI 
 (FOR EXAMPLE: METERS, KILOPASCALS, KILOPASCALS 
 METERS, MEGAPASCALS, MEGAPASCALS 
 INCHES, PSI, PSI 
 
 DO YOU WANT AUTOMATIC CONVERSION OF DEPTH AND 
 DISTANCE ENTERED IN FEET TO INCHES(Y OR N) 
 ? Y USER 
 
 DEPTH AND DISTANCE VALUES WILL BE CONVERTED 
 FROM FEET TO INCHES. 
 
 (MODULUS VALUES WILL NOT BE CONVERTED) 
 CARD TYPE 1 —TITLE 
 WHAT IS THE TITLE 
 ? MULSIM/BM SAMPLE PROBLEM — THIS IS LINE 1 OF THE FILE USER 
 TITLE ENTERED IS: 
 MULSIM/BM SAMPLE PROBLEM — THIS IS LINE 1 OF THE FILE 
 IS THIS OK(Y/N) 
 ? Y USER 
 
 CARD TYPE 2 
 
 POISSON'S RATIO OF THE ROCK MASS = 
 ? .15 USER 
 
 MODULUS OF ELASTICITY OF THE ROCK MASS = 
 ? 400000 USER 
 
 THE MAXIMUM GRID AND THE MAXIMUM 
 NUMBER OF SEAMS ALLOWED DEPEND 
 ON THE MULSIM/BM VERSION TO BE USED 
 1-2 40 X 40 
 
 3 30 X 30 
 
 4 20 X 20 
 NUMBER OF SEAMS = 
 
 ? 2 USER 
 
 HOST MATERIAL PROPERTIES ENTERED ARE: 
 
 POISSON'S RATIO: .15 
 
 MODULUS OF ELASTICITY: 400000. 
 
 NUMBER OF SEAMS: 2 
 IS THIS OK(Y/N) 
 ? Y USER 
 
27 
 
 CARD TYPE 3 
 
 SEAM MATERIALS ARE SPECIFIED BY A LETTER CODE 
 
 (A,B,C,....Z) 
 HOW MANY OF THESE MATERIALS ARE THERE 
 ? 2 
 CARD TYPE 4 
 
 MATERIAL NUMBER: 1 
 
 MATERIAL CODE: A 
 
 IS THIS A 
 GOUGE MATERIAL(MOHR-COULOMB MODEL)? 
 
 3 = "NORMAL MATERIALS" 
 
 (SEAM MATERIALS, GOB, OR "INSERTED" MATERIALS) 
 
 4 = GOUGE METERIAL (MOHR-COULOMB MODEL) 
 (ENTER 3 OR 4) 
 
 ? 3 
 
 INPUT MATERIAL PROPERTIES: 
 (COHESION AND FRICTION ANGLE CAN BE ASSIGNED 0.0) 
 IF THEY ARE UNNECESSARY. ) 
 YOUNGS MODULUS = 
 ? 200000 
 
 SHEAR MODULUS = 
 ? 76923 
 
 COHESION OF SOLID MATERIAL = 
 ? 
 
 INTERNAL FRICTION ANGLE OF SOLID MATERIAL = 
 ? 
 
 COHESION OF BROKEN MATERIAL = 
 ? 
 
 INTERNAL FRICTION ANGLE OF BROKEN MATERIAL = 
 ? 
 
 IS THIS A GOB/INSERTED MATERIAL TYPE (Y/N) 
 ? N 
 
 DATA ENTERED FOR MATERIAL NUMBER: 1 
 YOUNGS MODULUS: 200000 
 SHEAR MODULUS: 76923 
 COHESION : 0. 
 INTERNAL ANGLE: 0. 
 COHESION BROKEN: 0. 
 INTERNAL ANG BROKEN: 0. 
 GOB MATERIAL: N 
 IS THIS OK(Y/N) 
 ? Y 
 CARD TYPE 4 
 
 MATERIAL NUMBER: 2 
 
 MATERIAL CODE: B 
 
 IS THIS A 
 
 GOUGE MATERIAL (MOHR-COULOMB MODEL)? 
 3 = "NORMAL MATERIALS" 
 
 <SEAM MATERIALS, GOB, OR "INSERTED" MATERIALS) 
 
 USER 
 
 USER 
 
 USER 
 USER 
 USER 
 USER 
 USER 
 USER 
 USER 
 
 USER 
 
28 
 
 4 = GOUGE MATERIAL (MOHR-COULOMB MODEL) 
 (ENTER 3 OR 4) 
 ? 3 
 
 INPUT MATERIAL PROPERTIES: 
 (COHESION AND FRICTION ANGEL CAN BE ASSIGNED 0.0 
 IF THEY ARE UNNECESSARY. ) 
 YOUNG'S MODULUS = 
 ? 5000 
 
 SHEAR MODULUS = 
 ? 1786 
 
 COHESION OF SOLID MATERIAL = 
 ? 
 
 INTERNAL FRICTION ANGLE OF SOLID MATERIAL = 
 ? 
 
 COHESION OF BROKEN MATERIAL = 
 ? 
 
 INTERNAL FRICTION ANGLE OF BROKEN MATERIAL = 
 ? 
 
 IS THIS A GOB/INSERTED MATERIAL TYPE(Y/N) 
 ? Y 
 
 DATA ENTERED FOR MATERIAL NUMBER: 2 
 YOUNG'S MODULUS: 5000. 
 SHEAR MODULUS: 1786 
 COHESION : 0. 
 INTERNAL ANGLE: 0. 
 COHESION BROKEN: 0. 
 INTERNAL ANG BROKEN: 0. 
 IS THIS OK(Y/N) 
 ? Y 
 
 CARD TYPE 5 
 
 INPUT THE PRIMITIVE STRESS DATA 
 
 THE STRESS TENSOR THAT DESCRIBES A STRESS STATE 
 THAT EXISTS PRIOR TO MINING IS DEFINED AS LINEAR 
 FUNCTIONS OF GLOBAL X3 DIRECTION. WITH COMPRESSION 
 BEING POSITIVE, THE EQUATIONS ARE OF THE FORM: 
 STRESS(1,1) = A11-B11*X3 
 STRESS(1,2) = A12-B12*X3 ETC. 
 (X3 IS NEGATIVE) 
 AFTER CONVERSION(IF ANY) 
 
 AXX MUST BE >= -.9999 AND <= 99999. 
 BXX MUST BE >= -.9999 AND <= 9.9999 
 INPUT STRESS DATA IN PSI ASSUMING X3 IS IN FEET; 
 THE MESH GENERATOR WILL DIVIDE YOUR BXX VALUES BY 12 
 TO MAINTAIN CONSISTENT UNITS SINCE COORDINATES 
 HAVE BEEN CONVERTED TO INCHES 
 
 INPUT All: 
 ? 
 
 INPUT Bll: 
 ? 0.55 
 
 INPUT A12: 
 ? 
 
 USER 
 
 USER 
 USER 
 USER 
 USER 
 USER 
 USER 
 USER 
 
 USER 
 
 USER 
 USER 
 USER 
 
29 
 
 INPUT B12: 
 ? 
 
 INPUT A13 
 ? 
 
 INPUT B13 
 ? 
 
 INPUT A22: 
 ? 
 
 INPUT B22 
 ? 0.55 
 
 INPUT A23: 
 ? 
 
 INPUT B23: 
 ? 
 
 INPUT A33 
 ? 
 
 INPUT B33: 
 ? 1.1 
 
 PRIMITIVE STRESS DATA ENTERED 
 
 A11,B11, B33 
 
 0. 0.55 0. 0. 0. 0. 0. 0.55 0. 0. 0. 1.1 
 IS THIS OK(Y/N) 
 ? Y 
 
 CARD TYPE 6 
 
 MODEL DATA 
 IF SYMMETRY IS SPECIFIED. THE AXES OF SYMMETRY 
 PASS THROUGH THE CENTER OF THE MODEL 
 WHAT IS THE SYMMETRY CODE 
 
 1 - NO SYMMETRY 
 
 2 - COLUMN SYMMETRY (VERTICAL AXIS OF SYMMETRY) 
 
 3 - ROW SYMMETRY (HORIZONTAL AXIS OF SYMMETRY) 
 
 4 - COLUMN AND ROW SYMMETRY 
 ENTER 1,2,3, OR 4 
 
 ? 1 
 
 WHAT IS THE BLOCK WIDTH 
 
 (INPUT WIDTH IN FEET: YOUR DATA WILL BE CONVERTED 
 TO INCHES.) 
 
 ? 100 
 
 HOW MANY BLOCKS LIE ALONG THE LOCAL X AXIS IN 
 EACH SEAM(TOTAL GRID-COARSE + FINE) 
 IF SYMMETRY WAS SPECIFIED. INPUT ONLY THE UNIQUE 
 PORTION (QUADRANT OR HALF) OF THE MESH. 
 
 ? 8 
 
 HOW MANY BLOCKS LIE ALONG THE LOCAL Y-AXIS 
 
 IN EACH SEAM(TOTAL GRID-COARSE + FINE) 
 
 IF SYMMETRY WAS SPECIFIED. INPUT ONLY THE UNIQUE 
 
 PORTION (QUADRANT OR HALF) OF THE MESH. 
 
 ? 8 
 
 FINE MESH STARTING BLOCK X AXIS 
 
 USER 
 USER 
 USER 
 USER 
 USER 
 USER 
 USER 
 USER 
 USER 
 
 USER 
 
 USER 
 
 USER 
 
 USER 
 
 USER 
 
30 
 
 ? 4 USER 
 
 FINE MESH ENDING BLOCK X AXIS 
 ? 5 USER 
 
 FINE MESH STARTING BLOCK Y AXIS 
 ? 2 USER 
 
 FINE MESH ENDING BLOCK Y AXIS 
 ? 7 USER 
 
 AT THIS POINT THE MODEL WILL BE PLOTTED OUT ON THE TEKTRONIX 
 SCREEN. THE USER WILL SEE A PROMPT AT THE TOP LEFT HAND CORNER 
 OF THE SCREEN. 
 
 IF THE USERS RESPONSE TO THE QUESTION "IS THE MODEL OK" IS NO 
 THEN THE PROMPTS FOR CARD TYPE 6 ARE REPEATED AND THEN THE 
 MODEL IS PRESENTED ON THE SCREEN AGAIN. 
 
 IS MODEL OK(Y/N) 
 ? Y USER 
 
 DO YOU WANT A HARD COPY(Y/N) 
 ? N USER 
 
 HOW MANY OFF-SEAM PLANES WILL BE USED TO 
 OBTAIN ADDITIONAL STRESS AND DISPLACEMENT DATA 
 
 ? 1 
 
 USER 
 
 MODEL DATA ENTERED IS 
 BLOCK WIDTH: 100. 
 
 X-AXIS BLOCKS 
 
 : 8. 
 
 Y-AXIS BLOCKS 
 
 : 8. 
 
 FINE MESH X 
 
 : 4 
 
 
 5 
 
 FINE MESH Y 
 
 : 2 
 7 
 1 
 
 SYMMETRY CODE 
 
 NUM OFFSEAM 
 
 1 
 
 IS THIS OK(Y/N) 
 ? Y 
 
 CARD TYPE 7 
 
 EXTRACTION CODE "0" IS ZERO EXTRACTION 
 (THIS CODE IS IRRELEVANT FOR GOB OR OPENINGS) 
 ENTER NUMBER OF ADDITIONAL 
 EXTRACTION RATIO CODES (0 TO 9) 
 ? 1 
 
 ENTER EXTRACTION RATIO FOR CODE 1 
 (FRACTIONAL NUMBER > AND < 1) 
 ? .2 
 
 EXTRACTION DATA ENTERED IS: 
 NUMBER OF NON-ZERO EXTRACTION CODES: 1 
 EXTRACTION RATIOS:. 2 
 IS THIS OK(Y/N) 
 ? Y 
 
 CARD TYPE 8 
 
 SEAM NUMBER: 1 
 
 WHAT ARE THE GLOBAL COORDINATES OF THE GRID 
 
 USER 
 
 USER 
 
 USER 
 
 USER 
 
 ; 
 
31 
 
 ORIGIN 
 
 (INPUT IN FEET; YOUR DATA WILL BE CONVERTED 
 
 TO INCHES. 
 
 XO = 
 ? USER 
 
 YO = 
 ? USER 
 
 ZO = 
 ? -1080 USER 
 
 THICKNESS = 
 ? 10 USER 
 
 GLOBAL COORDINATES FOR SEAM 1 
 XO: 0. 
 YO: 0. 
 ZO: -1080. 
 THICKNESS: 10. 
 IS THIS OK(Y/N) 
 ? Y USER 
 
 CARD TYPE 8 
 
 SEAM NUMBER: 2 
 
 WHAT ARE THE GLOBAL COORDINATES OF THE GRID 
 ORIGIN 
 
 (INPUT IN FEET; YOUR DATA WILL BE CONVERTED 
 TO INCHES. 
 XO = 
 ? USER 
 
 YO = 
 ? USER 
 
 ZO = 
 ? 1000 USER 
 
 MUST BE A NEGATIVE NUMBER 
 ZO = 
 ? -1000 
 
 THICKNESS = 
 ? 8 USER 
 
 GLOBAL COORDINATES FOR SEAM 2 
 XO: 0. 
 YO: 0. 
 ZO: -1000. 
 THICKNESS: 8. 
 IS THIS OK(Y/N) 
 ? Y USER 
 
 CARD TYPE 9 
 
 GRID ORIENTATION 
 SPECIFY STRIKE, DIP AND OFFSET ANGLE 
 STRIKE ANGLE IS IN DEGREES COUNTERCLOCKWISE FROM 
 GLOBAL Y 
 
 (COUNTERCLOCKWISE IS MEASURED LOOKING DOWN FROM THE 
 SURFACE) 
 
32 
 
 WHAT IS THE STRIKE ANGLE 
 
 ? USER 
 
 POSITIVE DIP IS TOWARD THE ROTATED X DIRECTION 
 WHAT IS THE ANGLE OF DIP 
 ? USER 
 
 IN THE PLANE OF THE SEAM, THE OFFSET ANGLE 
 IS MEASURED COUNTERCLOCKWISE FROM THE DIP DIRECTION. 
 TO THE ENTRY LINE ( THE LOCAL X-AXIS OF YOUR MESH 
 WHAT IS THE OFFSET ANGLE? 
 
 ? USER 
 
 ANGLES ENTERED ARE: 
 STRIKE: 0. 
 DIP: 0. 
 OFFSET: 0. 
 IS THIS OK(Y/N) 
 ? Y USER 
 
 CARD TYPE 10 
 
 PROGRAM FLOW PARAMETERS 
 
 THE OVER-RELAXATION FACTOR CAN BE ANY NUMBER 
 FROM 1.0 TO 1.99 (1.35 IS OFTEN BEST). 
 OVER-RELAXATION FACTOR = 
 ? 1.35 USER 
 
 WHAT RUN NUMBER IS THIS 
 ? 1 USER 
 
 HOW MANY ITERATIONS WERE COMPLETED IN PREVIOUS RUNS 
 ? USER 
 
 MAXIMUM NUMBER OF NEW ITERATIONS FOR THIS RUN = 
 ? 100 USER 
 
 IS A PREVIOUS COEFFICIENT MAXRIX TO BE USED 
 ENTER (1 = YES, = NO) 
 ? USER 
 
 FLOW PARAMETERS ENTERED ARE: 
 RELAXATION FACTOR: 1.35 
 RUN NUMBER: 1 
 PREV ITERATIONS: 0. 
 MAX NEW ITERATIONS: 100. 
 PREV COFFICIENTS: 0. 
 IS THIS OK(Y/N) 
 ? Y USER 
 
 CARD TYPE 15 
 
 OFFSEAM GRID DETAILS: PLANE NO. 1 
 INPUT COORDINATES AND WIDTH IN FEET: 
 AND THEY WILL BE CONVERTED TO INCHES 
 LOCAL ORIGIN 
 XO = 
 ? 300 USER 
 
 YO = 
 ? 400 USER 
 
 ZO = 
 
 
33 
 
 ? -1089 USER 
 
 BLOCK WIDTH ALONG THE LOCAL X AXIS= 
 ? 20 USER 
 
 BLOCK WIDTH ALONG THE LOCAL Y AXIS= 
 ? 20 USER 
 
 NUMBER OF BLOCKS IN LOCAL X DIRECTION= 
 ? 10 USER 
 
 NUMBER OF BLOCKS IN LOCAL Y DIRECTION= 
 ? 1 USER 
 
 OFFSEAM GRID DETAILS FOR PLANE NO: 1 
 XO = 300. 
 YO = 400. 
 ZO = -1089. 
 
 X-AXIS BLOCK WIDTH: 20. 
 Y-AXIS BLOCK WIDTH: 20. 
 X-AXIS NUM OF BLOCKS: 10. 
 Y-AXIS NUM OF BLOCKS: 1. 
 IS THIS OK(Y/N) 
 ? Y USER 
 
 CARD TYPE 15A 
 
 INPUT PLANE ORIENTATION 
 SPECIFY STRIKE, DIP AND OFFSET ANGLE 
 STRIKE ANGLE IS IN DEGREES COUNTERCLOCKWISE FROM 
 GLOBAL Y 
 
 (COUNTERCLOCKWISE IS MEASURED LOOKING DOWN FROM THE 
 SURFACE 
 
 WHAT IS THE STRIKE ANGLE 
 
 ? USER 
 
 POSITIVE DIP IS TOWARD THE ROTATED X DIRECTION 
 WHAT IS THE ANGLE OF DIP 
 ? USER 
 
 IN THE PLANE OF THE SEAM, THE OFFSET ANGLE 
 IS MEASURED COUNTERCLOCKWISE FROM THE DIP DIRECTION. 
 TO THE ENTRY LINE ( THE LOCAL X-AXIS OF YOUR MESH 
 WHAT IS THE OFFSET ANGLE? 
 
 ? USER 
 
 ANGLES ENTERED ARE: 
 STRIKE: 0. 
 DIP: 0. 
 OFFSET: 0. 
 IS THIS OK(Y/N) 
 ? Y USER 
 
 THE MESH GENERATOR WILL NOW DISPLAY THE FINE MESH AREA ON THE 
 SCREEN AND ALLOW THE USER TO INSERT IN EACH ELEMENT THE APPROPRIATE 
 MATERIAL PROPERTY CODE. THE USER IS FIRST PROMPTED FOR THE DEFAULT 
 MATERIAL PROPERTY CODE WHICH WILL FILL THE FINE MESH AREA. 
 THE FINE MESH AREA WILL BE MODELED FIRST 
 FOLLOWED BY THE COARSE MESH AREA 
 ENTER THE DEFAULT PROPERTY FOR SEAM 1 
 
34 
 
 ? A USER 
 
 1 = OPENING 
 
 2 = RIGID; 
 
 A-Z = MATERIALS; 
 ENTER LETTER 
 OR NUMBER 
 TO SUBSTITUTE 
 ? 1 USER 
 
 MOVE CURSOR TO 
 THE TWO OPPOSITE 
 CORNERS OF THE 
 ZONE TO CHANGE 
 ENTER "X"<RETURN> 
 AT EACH CORNER 
 ENTER "E"<RETURN> 
 WHEN DONE 
 IF USING A 4054 
 TERMINAL, DO NOT 
 PRESS <RETURN> AFTER 
 ENTERING "X" OR "E" 
 
 THE USER WILL NOW CHANGE THE MODEL BY USING THE GRAPHIC INPUT 
 CURSOR AS PER THE ABOVE INSTRUCTIONS. WHEN THE USER ENTERS AN 
 "E" INDICATING THAT THE CHANGES ARE COMPLETED, THE PROGRAM WILL 
 PROMPT AS FOLLOWS: 
 CHANGES (Y/N) 
 ? N USER 
 
 DO YOU WANT 
 A HARD COPY(Y/N) 
 ? N USER 
 
 THE SAME PROCEDURE IS FOLLOWED IN MODELING THE COARSE 
 
 MESH AREA AND THEN IN MODELING THE EXTRACTION RATIOS FOR 
 
 THE COARSE MESH BLOCKS. 
 
 WHEN THE ENTIRE SEAM HAS BEEN MODELED, THE PROGRAM WILL 
 
 PROMPT THE USER AGAIN. 
 
 IF SEAM 1 
 
 IS NOT O.K. 
 
 YOU MAY REMODEL 
 
 THE ENTIRE MESH 
 
 FOR THIS SEAM. 
 
 IS SEAM 1 O.K. (Y/N) 
 ? Y USER 
 
 SEAM 2 WILL BE MODELED IN THE SAME MANNER AS SEAM 1. 
 
 THE USER WILL BE PROMPTED AS TO WHETHER SEAM 2 IS 
 
 ALLRIGHT. IF NOT THEN SEAM 2 WILL BE COMPLETELY 
 
 REMODELED AGAIN. 
 ENTER FILE NAME (FOR FILE TO BE CREATED) 
 ? SAMPLE USER 
 
 . . .NOW WRITING CONTROL CARDS 
 ...NOW WRITING MATERIAL CODES FOR SEAM 1 
 
35 
 
 ..NOW WRITING MATERIAL CODES FOR SEAM 2 
 ..NOW WRITING STATUS CODES FOR SEAM 1 
 ..NOW WRITING STATUS CODES FOR SEAM 2 
 . .NOW WRITING COARSE MESH MATERIAL CODES FOR SEAM 1 
 ..NOW WRITING COARSE MESH MATERIAL CODES FOR SEAM 2 
 ..NOW WRITING COARSE MESH EXTRACTION CODES FOR SEAM 1 
 . .NOW WRITING COARSE MESH EXTRACTION CODES FOR SEAM 2 
 ..NOW WRITING OFF-SEAM CONTROL CARDS 
 WHAT DO YOU WANT TO DO NOW 
 
 TYPE TO END THIS PROGRAM NOW 
 
 TYPE 1 TO GENERATE A DATA FILE 
 
 USER 
 
 READY 
 
 END OF SAMPLE TERMINAL SESSION 
 
 - LISTING OF PROCEDURE FILE PRGENM 
 
 .PROC,PRGENM*I. 
 
 CLEAR(*, PRGENM) 
 
 RFL, 77000. 
 
 GET , BGNMLBM/UN=BM000 1L. 
 
 ATTACH, PLOT 10/UN=GRAFLIB. 
 
 LDSET,LIB=PLOT10. 
 
 BGNMLBM. 
 
 REVERT,NOLIST. 
 
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 APPENDIX E. --SAMPLE PROBLEM INPUT 
 
 This is the file generated by the sample session of appendix B. 
 
 MULSIM/BM SAMPLE PROBLEM — THIS IS LINE ONE OF THE FILE 
 
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 APPENDIX G.— ADAPTATION OF PROGRAM CODE TO OTHER COMPUTERS 
 
 The most complex changes to the MULSIM/BM code for implementation on 
 any other computer system would involve the replacement of the CDC mass 
 storage routines (OPENMS, READMS, WRITMS , CLOSMS) with the equivalent 10 
 routines on the user's computer. 
 
 Because the CDC Cyber allows up to 10 characters per computer word, 
 any manipulations involving the packing of material property codes 
 and mining status codes would have to be looked at closely and possibly 
 reprogrammed. 
 
 The definition of the array MKOD to a character variable type of 
 length 10 would be the easiest way to take care of the 10 characters per 
 word code. 
 
 The CDC format editing character for literals is "*". This would have 
 to be changed to the ANSI standard of 
 
 M t ii 
 
 The CDC routine to get the elapsed CPU time (second) would have to be 
 replaced with the equivalent routine on the user's computer. 
 
 The following routines illustrate how to replace the Cyber mass stor- 
 age routines: 
 
 c============================================= _ ===================c 
 
 C c 
 
 C CLOSMS C 
 
 C C 
 
 SUBROUTINE CLOSMS(IUNIT) 
 C 
 
 C CLOSMS - SIMULATES CDC ROUTINE OF SAME NAME 
 C 
 
 C ARGUMENTS 
 
 C IUNIT - FILE UNIT NUMBER OF FILE TO BE CLOSED 
 C 
 
 INTEGER IUNIT 
 C 
 
 CLOSE (UNIT=IUNIT) 
 
 RETURN 
 
 END 
 
294 
 
 c c 
 
 C OPENMS C 
 
 C C 
 
 SUBROUTINE OPENMS(IUNIT, INDEXF ,MXREC, IKTYP) 
 C 
 
 C OPENMS - SIMULATES CDC ROUTINE OF SAME NAME 
 C WITH SOME RESTRICTIONS 
 
 C ARGUMENTS 
 
 C IUNIT - FILE UNIT TO BE OPENED 
 C INDEXF - FILE INDEX ARRAY(NOT USED) 
 
 C MXREC - MAX. NO. OF RECORDS TO BE WRITTEN TO FILE 
 C (NOT USED) 
 
 C IKTYP - INDEX TYPE FLAG(NOT USED) 
 C 
 
 C RESTRICTIONS - 
 
 C 1. IF UNIT NOS. ARE THOSE DEFINED FOR RE ST ART, HI STORY 
 C OR GEOMETRY FILES - FILENAME IS SET UP ACCORDINGLY 
 
 C 2. IF UNIT NO. IS NOT DEFINED AS IN 1. THEN A UNIQUE 
 C FILENAME IS GIVEN AS RANF$$%% WHERE $$ AND %% ARE 
 
 C CHOSEN AS FOLLOWS 
 
 C $$ IS A CHARACTER BETWEEN A - Z , AND 
 
 C %% IS THE VALUE IUNIT SUCH THAT A UNIQUE FILENAME 
 
 C IS PRODUCED 
 
 C 3. THE RECORD LENGTH IN BYTES NNREC IS DEFINED 
 C ACCORDINGLY 
 
 C 
 
 INTEGER IUNIT, I NDEXF(l), MXREC, IKTYP 
 C 
 
 CHARACTER*20 RSTFIL,HSTFIL,GEOFIL 
 
 COMMON/RFILEC/ RSTFIL,HSTFIL,GEOFIL 
 
 INTEGER NRCRST , NRCHST , NRCGEO , NRCFIL , NBYTRL , NBYTIN 
 
 COMMON/RF ILEI/ NRCRST , NRCHST , NRCGEO , NRCFIL , NBYTRL , NBYTIN 
 C 
 
 C LOCAL VARIABLES 
 C 
 
 CHARACTER*20 FILNAM 
 
 CHARACTERS CHAR(26) ,ICHN(2) , ICH 
 
 LOGICAL IEXIST 
 
 INTEGER I,J,INO(2),IDIG,IDIV,NUM,IPOS,NNREC 
 C 
 
 C INITIALIZE VARIABLES 
 C 
 
 data char/' a', 'b ' , 'c ' , 'd ' , 'e ' , *f ' , 'g » , 'h' , 'i • , ' j' , 'k' , ? l' , »m' 
 i/nvovpvqvrvsvtvuvvvwvxvyvzV 
 
 FILNAM = ' ' 
 C 
 C CHECK FOR UNALLOWABLE FILE UNIT 
 
295 
 
 IF (IUNIT.LT.0.OR.IUNIT.GT.99) GO TO 10430 
 C 
 
 C FOR ANY OTHER VALUES OPEN FILE WITH A UNIQUE NAME 
 C TRANSFORM TWO DIGIT NO. TO CHARACTERS 
 C 
 
 IDIG = 1 
 
 IDIV = IUNIT/10 
 
 IF (IDIV.EQ.O) THEN 
 
 INO(l) = IUNIT 
 ELSE 
 
 INO(l) = IDIV 
 INO(2) = IUNIT-10*IDIV 
 IDIG = 2 
 ENDIF 
 C 
 
 DO 1011, J = 1,IDIG 
 NUM = INO(J) 
 WRITE(ICH, '(II) ')NUM 
 ICHN(J) = ICH 
 1011 CONTINUE 
 C 
 
 DO 1032, I = 1,26 
 
 FILNAM(1:4) = 'RANF' 
 FILNAM(5:5) = CHAR(I) 
 C 
 
 C INSERT NUMERIC PART TO FILENAME 
 C 
 
 1021 
 C 
 C 
 C 
 
 IPOS = 5 
 
 DO 1021, J = 1,IDIG 
 
 IPOS = IPOS + 1 
 
 FILNAM( IPOS: IPOS) = ICHN(J) 
 CONTINUE 
 
 DOES FILENAME ALREADY EXIST 
 
 INQUIRE (FILE=FILNAM,EXIST=IEXIST) 
 
 IF (IEXIST) GOTO 1032 
 C 
 
 NNREC = NRCFIL 
 
 IF (NNREC. LE.O) GOTO 10430 
 
 GOTO 10510 
 1032 CONTINUE 
 C 
 
 10510 CONTINUE 
 C 
 
 C CONVERT RECORD LENGTH TO BYTES 
 C 
 
 NNREC = NNREC*NBYTRL 
 
296 
 
 OPEN (UNIT=IUNIT , FILE=FILNAM , STATUS= 'UNKNOWN ' , ACCESS= 'DIRECT ' 
 1 ,FORM=' UNFORMATTED' ,RECL=NNREC,ERR=10430) 
 C 
 10430 CONTINUE 
 
 WRITE(6,80110)IUNIT,NNREC 
 
 STOP 
 C 
 
 80110 FORMAT( IX, 'SUBROUTINE OPENMS - CANNOT OPEN FILE'/ 
 11X, 'FILE UNIT NO. =' ,15, ' REC. LENGTH= ' ,15/) 
 
 END 
 
 C C 
 
 C READMS C 
 
 C C 
 
 SUBROUTINE READMS (IUNIT,ARR, NOW, JREC) 
 C 
 
 C READMS - SIMULATES CDC ROUTINE OF SAME NAME 
 C 
 
 C ARGUMENTS 
 
 C IUNIT - OUTPUT FILE UNIT 
 C ARR - ARRAY TO BE READ 
 C NOW - NUMBER OF ITEMS OF 'A' TO READ 
 C JREC - RECORD NUMBER 
 C 
 
 INTEGER IUNIT, NOW, JREC 
 
 REAL ARR(NOW) 
 C 
 
 INTEGER MSTORT 
 
 COMMON/CDCDAT/LARRTP 
 
 INTEGER LARRTP 
 
 PARAMETER (MSTORT=1000) 
 
 COMMON/TMSTOR/XTRRW(MSTORT ) , NTRRW(MSTORT ) 
 
 DOUBLE PRECISION XTRRW 
 
 INTEGER NTRRW 
 C 
 
 C LOCAL VARIABLES 
 C 
 
 INTEGER NOV, I 
 C 
 
 C SET UP NO. OF VARIABLES TO BE TRANSFERRED FOR REALS OR INTEGERS 
 C ** ASSUME 2 INTEGERS = 1 REAL ** 
 C LARRTP .EQ. - FOR AN INTEGER ARRAY 
 C LARRTP .NE. - FOR A REAL ARRAY 
 C 
 
 NOV = NOW 
 
 IF ( LARRTP .EQ. 0) NOV = (NOW+l)/2 
 
 READ (IUNIT, REC=JREC)(ARR(I), 1=1, NOV) 
 C 
 
 RETURN 
 
 END 
 
297 
 
 C C 
 
 C WRITMS C 
 
 C C 
 
 SUBROUTINE WRITMS ( IUNIT , ARR , NOW , JREC ) 
 C 
 
 C WRITMS - SIMULATES CDC ROUTINE OF SAME NAME 
 C 
 
 C ARGUMENTS 
 
 C IUNIT - OUTPUT FILE UNIT 
 
 C ARR - ARRAY OF VARIABLES TO BE WRITTEN 
 C NOW - NUMBER OF VARIABLES TO BE WRITTEN 
 C JREC - RECORD NUMBER 
 C 
 
 INTEGER IUNIT, NOW, JREC 
 
 REAL ARR(NOW) 
 C 
 
 INTEGER MSTORT 
 
 COMMON/CDCDAT/LARRTP 
 
 INTEGER LARRTP 
 
 PARAMETER (MSTORT=1000) 
 
 COMMON/TMSTOR/XTRRW(MSTORT ) , NTRRW(MSTORT ) 
 
 DOUBLE PRECISION XTRRW 
 
 INTEGER NTRRW 
 C 
 
 C LOCAL VARIABLES 
 C 
 
 INTEGER NOV, I 
 C 
 
 C SET UP NO. OF VARIABLES TO BE TRANSFERRED FOR REALS OR INTEGERS 
 C ** ASSUME 2 INTEGERS = 1 REAL ** 
 C LARRTP .EQ. - FOR AN INTEGER ARRAY 
 C LARRTP .NE. - FOR A REAL ARRAY 
 C 
 
 NOV = NOW 
 
 IF (LARRTP .EQ. 0) NOV = (NOW+l)/2 
 
 WRITE(IUNIT,REC=JREC)(ARR(I),I=l,NOW) 
 C 
 
 RETURN 
 
 END 
 
298 
 
 APPENDIX H. — CYBER JOB CONTROL STREAM TO RUN MOLSIM/BM 
 
 A CDC Cyber procedure file has been written that allows the user to 
 respond to questions about the input files and output files necessary to 
 submit a MULSIM/BM job to the computer. 
 
 A sample session using the procedure file follows. The listing of the 
 procedure file itself is included after the sample session. 
 
 SAMPLE SESSION 
 
 READY 
 
 GET,PRSUBM/UN=BM0001L 
 
 -,PRSUBM 
 
 ENTER PRIORTY JOB PRIORITY( 1 , 3, 5) ? 5 
 
 THE JOB PRIORITY ON THE CDC CYBER IS DEFINED AS FOLLOWS: 
 1 = DAYTIME PROCESSING AT 10 TIMES 
 
 THE COST OF WEEKEND PROCESSING. 
 3 OVERNIGHT PROCESSING AT 2.5 TIMES 
 
 THE COST OF WEEKEND PROCESSING. 
 5 = WEEKEND PROCESSING. 
 
 ENTER USRNAM USER NAME ? USER1 
 
 ENTER USREXT USER EXTENSION ? 1234 
 
 ENTER DISCFIL DISPLACEMENTS FILE NAME ? DFILE 
 
 ENTER COFFSFL COEFFICIENTS FILE NAME ? CFILE 
 
 ENTER COFFSDF C0EFFICIENTS2 FILE NAME ? CFILE2 
 
 ENTER MLSINPT MULSIM/BM INPUT FILE NAME ? MFILE 
 
 ENTER SEAM10T SEAM 1 OUTPUT FILE NAME ? SFILE 
 
 ENTER CSEAM10 SEAM 1 COARSE MESH OUTPUT FILE NAME ? CFILE 
 
 ENTER TIMLIMT JOB TIME LIMIT ? 100 
 
 ENTER PRTLIMT JOB PRINT FILE LIMIT ? 1000 
 
 ENTER PRTNAME JOB PRINT OUTPUT FILE NAME ? OFILE 
 
 ENTER DAYNAME JOB DAYFILE FILE NAME ? DFILE 
 
 ENTER JOBDISP JOB OUTPUT DISPOSITION^, B ,E ,T0) ? N 
 
 14.33.30. SUBMIT COMPLETE. JSN IS AKVZ. 
 
^ 
 
 299 
 
 After the submit message is displayed, the user may monitor the job 
 execution by entering "ENQ,UJN". The operating system will respond with 
 the status of all jobs submitted by the user. 
 
 LISTING OF PROCEDURE FILE PRSUBM 
 
 .PROC,PRSUBM*I, 
 
 PRIORTY" JOB PRIORITY(l,3,5)"=(l,3,5), 
 
 USRNAME" USER NAME", 
 
 USREXTN" USER EXTENSION", 
 
 DISCFIL" DISPLACEMENTS FILE NAME"=(*F), 
 
 COFFSFL" COEFFICIENTS FILE NAME"=(*F), 
 
 COFFSDF" C0EFFICIENTS2 FILE NAME"=(*F), 
 
 MLSINPT" MULSIM/BM INPUT FILE NAME"=(*F), 
 
 SEAM10T" SEAM 1 OUTPUT FILE NAME"=(*F), 
 
 CSEAM10" SEAM 1 COARSE MESH OUTPUT FILE NAME"=(*F), 
 
 TIMLIMT" JOB TIME LIMIT", 
 
 PRTLIMT" JOB PRINT FILE LIMIT", 
 
 PRTNAME" JOB PRINT OUTPUT FILE NAME"=(*F), 
 
 DAYNAME" JOB DAYFILE FILE NAME"=(*F), 
 
 JOBDISP" JOB OUTPUT DISPOSITION^, B,E ,TO)"=(N,B ,E,TO). 
 
 IF,. NOT. NUM (TIMLIMT), PASS. 
 
 REVERT. TIME LIMIT NOT NUMERIC. 
 
 ENDIF,PASS. 
 
 IF, .NOT. NUM (PRTLIMT) ,PASS2. 
 
 REVERT. PRINT LIMIT NOT NUMERIC. 
 
 ENDIF.PASS2. 
 
 SUBMIT , FILE , JOBDISP. 
 
 .DATA, FILE 
 
 /JOB 
 
 MULSI,T3600,P=PRIORTY. 
 
 /USER 
 
 CHARGE,*. 
 
 HEADING. $1MINES-DRC 
 
 HEADING. $ USRNAME 
 
 HEADING. $ USREXTN 
 
 GET,BMLBM. 
 
 GET,INPUT=MLSINPT. 
 
 PURGE, SEAMIOT/NA. 
 
 RETURN, SE AMI. 
 
 DEFINE , SEAM1=SEAM10T. 
 
 PURGE, CSEAMIO/NA. 
 
 RETURN, CSEAM1. 
 
 DEFINE , CSEAM1=CSEAM10. 
 
 SETTL(TIMLIMT) 
 
300 
 
 BMLBM(PL=PRTLIMT). 
 
 SKIP.L40. 
 
 EXIT. 
 
 ENDIF,L40. 
 
 REPLACE ,DISC=DISCFIL. 
 
 SKIP,L41. 
 
 EXIT. 
 
 PURGE, DISCFIL/NA. 
 
 DEFINE, DISCFIL. 
 
 REWIND, DISC. 
 
 COPYEI, DISC, DISCFIL. 
 
 ENDIF,L41. 
 
 REPLACE , C0FFS=C0FFSFL. 
 
 SKIP,L42. 
 
 EXIT. 
 
 PURGE, COFFSFL/NA. 
 
 DEFINE, COFFSFL. 
 
 REWIND, COFFS. 
 
 COPYEI, COFFS, COFFSFL. 
 
 ENDIF,L42. 
 
 REPLACE , COFFSD=COFFSDF , 
 
 SKIP,L50. 
 
 EXIT. 
 
 PURGE, COFFSDF/NA. 
 
 DEFINE, COFFSDF. 
 
 REWIND, COFFSD. 
 
 COPYEI , COFFSD, COFFSDF . 
 
 SKIP,L50. 
 
 EXIT. 
 
 ENDIF,L50. 
 
 PURGE, PRTNAME/NA. 
 
 DEFINE, PRTNAME. 
 
 REWIND, OUTPUT. 
 
 SKIPR, OUTPUT, 4. 
 
 COPYEI , OUTPUT , PRTNAME . 
 
 RETURN, PRTNAME. 
 
 SKIP,L60. 
 
 EXIT. 
 
 ENDIF,L60. 
 
 DAYFILE,DAYNAME. 
 
 REPLACE,DAYNAME. 
 
 /EOF 
 
 REVERT, NOLIST. 
 
301 
 
 APPENDIX I. —ENGINEERING SYMBOLS USED IN THIS REPORT 
 2 
 
 A element area, in 
 
 C element closure, in 
 
 c initial gob-zone closure, in 
 
 Eg secant elastic gob modulus (linear modulus), psi 
 
 Em modulus of deformation, GPa 
 
 F normal force acting on an element, lb 
 
 g gob-zone height, in 
 
 ■ 
 
 h element height, in 
 
 k ' gob material parameter, psi 
 
 M linear elastic gob modulus (input to program), psi 
 
 m extracted seam height, in 
 
 P equilibrium point 
 
 p gob resistance, psi 
 
 S area stiffness (stiffness per unit area), lb/in 
 
 Sg area stiffness of gob, lb/in 
 
 t seam thickness (input to program), in 
 
 e strain, in/in 
 
 £q strain sustained by gob, in/in 
 
 £max maximum possible gob strain, in/in 
 
 Eo equilibrium gob strain (at virgin overburden normal stress), in/in 
 
302 
 
 o stress, psi 
 
 Og stress sustained by gob (linear equation), psi 
 
 ' ] 
 
 o"nl stress sustained by gob (nonlinear equation), psi 
 
 o virgin overburden normal stress, psi 
 
 a i j stress acting in the positive Xj direction on a plane whose outward 
 normal points in the negative X] direction 
 
 to gob zone convergence, main roof to floor, in 
 
 y l displacement in the positive X[ direction 
 
 Xj global axis in the i-direction 
 
 Xy local axis, or rotated axis, in the i-direction 
 
 X Xi or XJ, as appropriate 
 
 Y X2 or XJ, as appropriate 
 
 Z X3 (depth below surface; numerically negative) 
 
 C 3£ 5 
 
 U.S. GOVERNMENT PRINTING OFFICE: 1988 - 505016/80,007 INT.-BU.0F Ml NES,PGH. ,PA. 28612 
 
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