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Structural analysis of mine pillars using finiteelement method- case studyD.H.Y. Tang and S.S. Peng

Abstract- hree-dimen sional finite element m odeling( 3 - 0 FEM ) was performed to analyze the safety facto rs ofstump pillars, 5 .5 m x 5 .5 m , under a co ver of 63 m using theModified D rucker-Prag er Th eory. The results showed thatt h ~ yere safe. This wa s substantiated b y underground obser -vations. But the safety factors predicted by three comm onlyused pillar desig n formulae showed othe rwise . This paperdiscusses the modeling details and analyzes the differencebetween 3 - 0 FEM method and traditional pillar designformulae.Introduction

The major objective of this study was to evaluate thepillaring plan fo r preventing p illar failure in a northern W estVirginia coal mine.The study was carried out by both mine visits and finiteelement analysis. The mine visit consisted of undergroundinvestigation of the pillaring area an d the collection of rocksamples for rock property de termination. Th e finite elementmethod w as employed to model the configurations of m ineworkings in the same pillaring sequence as that practicedunderground. By applying appropriate failure criteria to thefinite element results, the stability conditions of all mem bersof underground structure and surface zones were evaluated.The results of finite element analyses confirmed the fieldobservations w hile the traditional strength formulae were tooconservative. T he finite elemen t results also indicated that thehorizontal stress (confinement) in the coal pillars played avery im portant role in pillar stability.Mine description an d pillaring plan

The mine was located in northern West Virginia andextracted coal from the U pper Freeport seam, which had anaverage thickness of 1.2 m. The sea m depth ranged from 44m to 87.5 m with the majority being about 63 m. Th eimmediate roof was gray shale, which was overlain by san d-stone. The floor rock was fireclay an d shale.The room-and-pillar mining method was used to extract thecoal. During the first mining (or deve lopment), both entry andcrosscut were 5.5 m wide w hereas pillars were squa re and at21 m center. During the second mining (or pillaring), the 16m x 16 m coa l pillar was split into four stump pillars at thecom ers, the size of which w as 5.5 m x 5.5 m. In other words,a 5-m wide cut was m ade along the center of the pillar in twoperpendicular directions.In order to protect the residential houses and w ater wells onthe surface, a solid coal pillar, 36.5 m x 36.5 m, with eachresidential house at its center was left unmined. A lso, one ortwo row s of coal pillars surrounding the four sides of the largesolid pillar were left unsplit. Fig. I shows the plan view of atypical mine pillaring layout with a big solid pillar at thecenter. Th e mine visits confirmed tha t in spite of its small size(5.5 m x 5.5 m), the stump pillars remained intact as thepillaring proceeded and that no ground control problems e veroccurred.

a SOLID PILLARPARTIPL PILLIRING

Fig. 1- lan view of mine pillaring layout at the study area.Preliminary study of pillar stability

In order to estim ate pillar stability in the pillaring area, apreliminary study was conducted by using the pillar strengthformulae. T he tributary area theory was used to calculate theaverage pillar stress whereas the pillar strength was deter-mined by the laboratory compression tests on small coalsamples that considered the size and shape effects of thepillars.The re are many pillar strength formulae. In this study, onlythree strength formulae that are commonly used in US room-and-pillar mining are employed (Peng, 1986):Obert-Duvall Formulag 0,0.778+0.mwlh) (1)

Holland Formula1Rq,=4 (wlh)

Bieniawski Formulag =0,0.64+0.36wlh)

where ap is the in situ strength of coa l pillar, 0, s the strengthof a cubical pillar at the critical specimen size, w is pillarwidth, and h is pillar height.

D.H.Y. Tang, member SME, is design engineer with Morrison-Knudsen Inc., Boise, ID. S.S. Peng, member SME, is professor,depa rtment of mining engine ering, West Virginia University, Morga n-town, WV. SME prep rint 87-81, SME-AIM E Annual Meeting, Denver,CO, February 1987. Manuscript Novembe r 1986. Discussion of thispaper mu st be submitted, in duplicate, prior to No v. 30, 1988.

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Based on the results of laboratory tests on coal samples and wherethe above mentioned formulae, the safety factors of stumpcoal pillar were determined and listed in Table 1. Clearly, all 1 2 2J =-[(CT,-Or' + (0 2 -0 3 )the safety factors of coal stump pillars from three formulae 2 6 2were less than 1O. In other words, the stump pillars were not (03 0,)safe (or stable), which were not supported by undergroundobservations. J , = 0,+o2+o3=ox+5 oz

~~

Table 1 - afety factors of coal stump pillars determined byvarious strength formulae--nvestigator Overburden depth, m45.1 63.4 87.8Obert 0.630 0.447 0.324Holland 0.750 0.533 0.385Bieniaws ki 0.800 0.565 0.41 1

Note: 1 . The size of coal stump pillar is 5.5 m x 5.5 m and the width of entryis 5 m on one side and 5.5 m on the other.2. The overburden stress is calculated using an average unit weight of2.6 t1m3.

Finite element analysisIn order to clarify the pillar stability at the study area, the

stability analysis using the finite element method is recom-mended. In finite element analysis, not only the structuralbehavior of all underground members, such as roof, coal, andfloor are simulated, but the interaction among them and themine layout are also taken into consideration.

In this study, finite element analysis using NASTRANcomputerprogram (McCormick, 198 1) wasemployed. Three-dimensional models with hexahedron elements were usedthroughout the analyses. The mechanical and physical prop-erties of coal and rocks (Table 2) were obtained by laboratorytests on the samples secured from the mine. In order toaccount for the in situ rock mass conditions, a scale factormust be used for the strength values obtained in the labora-tory. Based on numerous case studies conducted by theauthors (Su andPeng, 1986; Hsiung andPeng, 1987) n whichcorrelation of finite element modeling results and field con-ditions was available, a scale factor of 115 was adopted.

All strata were assumed to be homogeneous, isotropic, andlinearly elastic. In order to evaluate the stability conditions ofall the members of the underground structures, the modifiedDrucker-Prager failure criterion (Drucker and Prager, 1952)was used in the analysis:

where a,.,,and 0,are principal stresses, q, ,nd 4 arenormal stress inx-,y- , and z- direction, respectively, @ is theinternal angle of friction, Co is the uniaxial compressivestrength, q is the triaxial stress factor, and T is the tensilestrength.Results and discussions

Fig. 2 shows the average pillar stress from both tributaryarea theory and finite element analysis for stump pillars andbarrier pillars. It can be seen that for stump pillar the verticalstress from the mbutary area theory is greater than that fromthe finite element analysis. But for the barrier pillar the resultis reverse. This means that for stump pillars the averageloading from the tributary area theory is generally more thanthe real situation, which, in turn, will result in either over-design or prediction of failure and yet it is safe in reality. Butif the immediate roof is made of very weak rock, the pillarstress determined from the finite element analysis may begreater than that determined from the tributary area theory.

Fig.3shows the safety factors of coal pillars along the crosssectionE-E' (Fig. 1). It is clear that safety factors of all coalpillars aregreater than 1O. The closer the stump pillars to thelarge pillar, the greater is the safety factor. It is apparent thatthe large pillar carries part of the load that is originallysustained by the stump pillars. Therefore, the finite elementresults confirm the underground observations.

The tributary area theory, on the other hand, usually over-estimates the average stress n the pillar. In addition to this, thetraditional method does not consider the effects of the inter-action of the roof, coal, and floor (i.e. the structural behaviorof the roof and floor of different material properties cannot beconsidered).In order to find out the effects of the interaction of the roofand floor as well as the effects of the change of their proper-ties, a series of finite eIement analyses was done by assumingvarious models of differentmaterial properties of the roof andfloor. Fig. 4 shows the safety factors of coal pillars for fourdifferent models in which the coal strength for all four models

Table 2 - hysical and mechanical properties of coa l and rocks- --

oung's Poisson's Uniaxial Triaxiai* Tensile Unlt WelghtMalerlal modulus ratlo compressive stress strength (llm3)strength factor (MPa)(MPa)Sandy shale 23718 0.22 78.13 4.0 3.12 2.60Sandstone 38218 0.16 100.80 4.8 3.56 2.69Gray shale 13086 0.18 74.22 4.0 2.98 2.71(Immediate roof)Coal 2020 0.30 5.60 3.3 2.26 1.33(Upper Ffeeport seam)Fireclaylshale 8101 0.20 34 67 3.8 3.09 2.57(Immediate floor)--Data, belng unavailable, are taken from the representative values in the Handbook.

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Fig. 2- illar stressat the mid-height of coal pillars determinedfrom both tributary area theory and finite elementanalysis (overburden depth is 63 m ).

Overburdon b p th , 83.4 m

is the same. Model A is the original model for this case,Model B has a weak roof, ModelC has the same material forall strata (i.e. homogeneous) while for Model D, the Young'smodulus of coal is two times of its original value.It canbe seen that four models have different safety factors,with Model C having the largest and Model B having thelowest one. Fig. 5 shows the vertical stress of coal pillars forModels A, B, and D. By comparing Fig. 5 and Fig. 4, it isfound that although Model B has the smallest vertical pillarstress, it has the smallest safety factor. This indicates that thevertical pillar stress, which is usually used in the determina-tion of the safety factor by the traditional method, is not theonly controlling factor for the evaluation of pillar stability.There must be some other controlling factors involved in thestructural behavior of the coal pillar.In reality, each coal pillar is not only subjected to thevertical stress, it is also subjected to the horizontal stresses inboth x and y directions (i.e., it is triaxially confined by the

7A!!- 8-a-a6 5-5? 4-PI

3-mnf 2-a-h 1-PI 0

stresses acting on it). Thus, the horizontal stress confinementmust play a very important role in pillar stability. As shownin Fig. 2, the horizontal stress, with its magnitude larger thanone-third of the vertical stress, is acting on both x and ydirections. As a result, the confinement of the coal pillar dueto horizontal stress increases the coal pillar strength to someextent.Fig.6 shows the pillar stress and safety factor of coal pillarsfor two different models. One model is the same as model Adescribedbefore while the other one is made of weak roof andfloor with everything else the same. It can be seen that thevertical stress from the original model is larger than that of theweak one. But the safety factor of the coal pillar of the formeris also greater than that of the latter. The main reason is thatthe horizontal stress confinement for the former case is alsogreater than that of the latter one. Therefore, due to horizontalconfinement, the real coal pillar strength is usually greaterthan that determined from the strength formulae.

Vertical StrnaTributary Area Thory

-8-$-=* *Flnite El-t kulys lr

Ckl~alt s t r w0-8-0- -/-0 I l- lnStr~r&.el_mPe --- --- -

Fig. 3- afely factors for coal pillars (along cross section E-E').MINING ENGINEERING

1.675

1672 ____: 1.6692>: .658 ISEPTEMBER 1988 895

aI

1.663-

1.660-

7 - S T R A T A MODEL63 4 m. DEEP

9 I I I30 40 50 60 70

DISTANCE FROM EDGE OF LARGE SOLID PILLAR. M


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DISTANCE FROM EDGE OF LARGE SOLID PILLAR. M

1 . 6 -L

1 . w -u 1.62-t

f 1.60-un 1.58-

- - - - - - - - - - ppFig. 4- afety factor of coal pillars for four different models (along cross section E-E').

A-ORIG INALQ 0 *... 0

D- STIFF FOAL 0 4 0

Fig. 5 - ertical stress of coal pillar for different models along E-E'cross section.

6.4 -

P6.2 -6.0 -C) 5.8 -5. 6 -

5.4 -5 2 -

0-STIFF COAL0 #

B-WEAK ROOF ;00

0 0

I I I

Fig. 6- illar stress and safety factor for the original model and the modified model with weak roof and floor.896 SEPTEMBER 1988 MINING ENGINEERING

30 40 50 60 70

DISTANCE FROM EDGE OF LARGE SO L ID PILLAR, M

SOLID LINE, PILLAR STRESSWTTED LINE: SAFETY FACTOR0 ORIGINAL MODEL

WEAK ROOF AND FLOOR MODEL

7 - 2 0b VERTICAL STRESS6 -

4 .----.----.---.--HORIZONTAL STRESS

0-" 2-a

1 -etm = = - - 1


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Fig. 7- ve rage pillar stress determined by tributary area t heo ry and FEM f o r ditferent models.

7"4j 6 --a-- 5 -DeP 4 -IEs 3 -?-" 2 -.P

b 1 -D:0

There is another factor that usually cannot be considered inthe traditional method, the effect of strata sequence. Fig. 7shows the average pillar stress from both the tributary areatheory and finite element analysis. The average pillar stressby the tributary area theory is the same for both the originaland the modified models with different roof strata sequence.However, the average pillar stress from the finite elementanalysis is smaller for the modified strata sequence than theoriginal model.

a MODIFIED ROOF STRATA SEQUENCEo- ORlGlNU STRATA SEQUENCE0- TRIBUTARY AREA THEORY

ConclusionsThe traditional pillar design method usually overestimates

the pillar size. For smaller coal pillars, the average pillar stressdetermined from the tributary area theory is usually largerthan the real pillar stress in underground. In other words, thepillar loading from the tributary area theory is a little overes-timated.

The three-dimensionalfinite element analysis not only canmodel the mine layout and mining sequence, but also cansimulate the interaction of the roof, coal, and floor. The pillardesign based on this method considered the pillar, roof andfloor as an integrated structure, which generally yields moreaccurate results.

For this mine, the traditional design methods predicted thatstump pillars would fail whereas the finite element analysisindicated that they would be stable. The field observationsduring and one-and-a-half years after mining confirmed theresults of the finite element analyses.

The horizontal stress confinement within the pillars playsan important role in the underground pillar behavior. Itincreases the pillar strength to varying extent depending onthe overburden depth, strata sequence, and the material prop-erties of the roof and floor. 4

ReferencesDrucker, D.C.. and Prager, W.J., 1982,'Soil MechanicsandPlastic Analysis of Limit Design."Applied Mathematic Quarterly, Vol. 10, No. 2, pp. 157-165.Hsiung. S.M. and Peng, S.S.. 1987, "Controlof Floor HeavewithProper Mine Design-ThreeCase Studies." MiningScienceand Technology, Vol. 4, No. 3, pp.257-272.McCormick.C.W.. 1981. The NASTRAN User's Manual (Level 17.5). National Aeronauticsand Space Administration. Washington, DC.Peng, S.S., 1986, Coal Mine Ground Control, 2nded.,Wiley, New Yolk, 491 pp

Su, W.H.. and Peng, S.S., 1986, 'Investigation of me Causes of Roof Falls in a DeepUnderground Coal Mine," Trans., SME, Vol.. 280, pp.2019-2023.

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