7/29/2019 A 3-D Semi-Analytical Method for Subsidence Prediction and Stress Analysis in Coal Mining

1/6

21* International Conference on Ground Control in Mining

A 3-D Semi-Analytical Method for Subsidence Prediction and StressAnalysis in Coal MiningLi-min Liu, Associate ProfessorHan-long Liu, ProfessorChuan-jle L ian, ProfessorZhen-de Zhu, Associate ProfessorHehai UniversityResearch lnstitute of Geotechnical EngineeringNanjing, Jiangsu Province, P .R. China

Abstract The Semi-Analytical method can be used tosolve a variety of prablems in geom echanics and civilengineering. When it comes to layered rock strata androck masses, it is superior to all o t k analytical methods.This paper presents the application of a 3-D semi-analytical method to 3-D surface subsidence and stressanalysis caused by mining. In this semi-analytical methodthe layered elements and triangular elements ate usedalternatively. Their displacement pattern, strain mahix,elastic matrix, stiffiness matrix, load matrix and stressmatrix are presented. A numerical simulation programbased on the semi-analytical method bas been developedusing Fortran 90. This program is suitable for subsidenceprediction and stress analysis of mom and pillar mining,strip longwall and m echanized longwall mining methods.It is applicable to all geological conditions and miningmethods. Comparing with the finite method, this methodreduces significantly the number of simultaneousequations to be solved and the amount of data preparation.It not only reduces the computer memory, but also runsfaster and cost less.

Key Words Semi-analytical method, surface subsidence,stres s analysis, layered elernenL triangular prism elem ent

Bing Gu, Economic EngineerShandong Costume Profession lnstituteTai'an. Shandong Province, P.R . ChinaJian Chen, Graduate StudentHehai UniversityResearch Institute of Geotechnical EngineeringNanjing, Jiangsu Province, P.R. China

does not require 3-D analysis and saves considerably indatapreparation, computing time and cost.

Surface subsidence due to underground coal miningmay cause damages to surface st tuctures and f d a n d andchange surface and surface damage patterns. During thepast few decades, a number of subsidence predictiontechniques have been proposed Currently the InfluenceFunction method is the most widely used method forprediction of longwall mining subsidence. But this methodcan only be used for subsidence prediction. It cannot beused for stress analysis in the affected strata. The finiteelement method can be used to analyze the shrcss anddisplacement in the strata affected by miqig. But due tocomputer memory size and com puter time requid, it hasbeen used mostly to solve2-D ngineering problems.

The 3-D problems discussed in this paper involvesusing the semi-analytical method to predict surfacesubsidence and analyze, through microcomputer, thecomplicated stress fieid induced by mining. This methodnot only overcomes the difficulties encountered whenusing mathematical analysis and its limited applicability,but also bas the following advantages based on the totaldiscrete principle: Greatly reduce the amount andcomplication of calculation work and the demand forinternal memory, and faste r calculation speed.

1. Introduction2. The 3-D Model of Sem i-analytical MethodWith the recent rapid development of computertechnology, the numerical analysis of engineeringproblems has become very popular and been used in many Figure 1 shows the 3-D model for this research.enginee ring fields. The fmite element method has proven Figure 2 is a cross-sectional view. The upper block A is a

to be a powerful tool for analyzing 3-D problems with horizontal strata of transversely isotropic material which iscomplicated geometry, material property and boundary under'ain by an triangular block B.Thecondition. However there exists one type of problem that block C includes the inclined seam excavated with tunnels

7/29/2019 A 3-D Semi-Analytical Method for Subsidence Prediction and Stress Analysis in Coal Mining

2/6

21" International Con fer en ce o n Ground Control in Mining

Fig. 1The 3-D emi-anslyeP 1 modelFi. The triangu lar prism element

Fig. ZThe cross-section view of the 3-DmodelIn the model, A and C are represented by 2-D layeredelements. The local coordinates for Block A coincide withthe global coordinates while that forBlock C intersects theglobal coordinates with an angle a. Under the localcoordinates equations are similar for both blocks. If

openings are made within tbe layer, its effect can beeliminated thmugh integration. A typical layered elementis shown in Figure 3.

Flg. 3 The layer element

Th e surface strata of transversely isotropic materialare divided into discrete layered elements in the zdirection with analysis in the x and y directions Thetriangular block ABC can be divided into many elementssimilar to Figure 4, with the discrete direction in they andz directions and analysis in the x direction. Th e inclinedblock C (including coal seam) is discrete in the z irectionwith analysis in the x and y directions.

Boundary conditions: four sides of the model are freein the z direction, but fured in the x and y directions. Theupper bounw of the model is fm hile the lowerboundary is fixed.As shown by Figure 1, tbrough various combinationsof layered and triangular elements, the model can easilydeal with the 3-D roblems of surface subsidence andstress analysis in the strata affected by mining. Thereforeit is very flexible and suitable for wide ranging conditions.

3. Theory of3-D Semi-analytical MethodThe key step in using the 3-D Semi-analytical method

to analyze and solve engineering problems is how to selectsuitable displacement models for layered and triangularelements. The displacement models should meet thecompa tibility conditions.1The layer element1.1 Thedisplacementmodel

As for the triangular block B, it can be automaticallydivided into many discrete triangular elements of 1-D. 1 } I = I 1-1 [Figure4 shows a typical triangular element. whereIn the model, the left, right, front, rear, and bottomboundaries are fixed boundaries and the upper boundary is 0 C,s,

7/29/2019 A 3-D Semi-Analytical Method for Subsidence Prediction and Stress Analysis in Coal Mining

3/6

21" International Conference on Ground Control in Mining

1.2The strain m a r k

where

1.3 The elasticmafruThe elastic matrix o f mafenal is expressed by [D].

1.4 Thc slffnnesl matr ix ofrhe element

1 5 The loadmetnx of the elementThe gravitational body force:

m m X I nw Y ,~ l ~ l ~ w sTlX2@'The concentrated force on the surface:

1.6Th e stress mafru

I dm = D X B ~ { ~ ) " , " = [sl{4""b s,l(fiI,.2The triangular prism element2.1 The d~splocementmodel

If I= = E I N L ( J I U . ~ Jn- lwhere

I mxr \

[NL1 a /

cos- 0a 0mm0 sin- oa0 m m0 sm-

x

7/29/2019 A 3-D Semi-Analytical Method for Subsidence Prediction and Stress Analysis in Coal Mining

4/6

21" International Conference on Ground Control in Mining2.4 The loadmat& ofthe dement

1.5 Thestressmahix

iff], =[sl(s24. Examples

Based on the above analysis, a computer programusing Forvan 90 has been developed for 3-D surface

subsidence prediction and stress analysis. In comparisonwith f h t e element analysis, this method drasticallyreduces the number of simultaneous equations to besolved and the amount of data preparation required. It notonly saves the internal memory an d increases computingspeed, but also reduces computer cost.1.Example No. 1

Elastic Modulus of the material, E=500MPa;Poisson's Ratio, ~ 0 . 2 6 ;nit weight ~ 2 7N/m3. Underthe pvi ta tio na l forow, the stresses at surface points A & Band points of interest C & D are shown in Tables 1 and 2,respectively (me Figure 5).

Flg 5. Example No.] modelTable 1. Subsidence of surface min t

I I Subsidence value w(mm) Ipoint F=l F=5 P=9Theoretical Computed I Enor(%) ComputGd 1 Enor(%) Computed I Em"(%)

A 221 255 15.4 232.3 5.1 223 0.9B 22 1 327 48.0 238.4 7.9 224 1.4

Table 2. Stress at points of interest

2. Exam ple No. 2 of matenal which is transversely isotmpic. Its elasticmodulus is E,=0.30 MPa, &=I7 MPa,b=p=0.23, y=This example involves 7 different materials in 12 27 KN/m3. AU other layers from the 3 layer on arelayers (Figure 6).Th e tophw layers consist of the 1' type inclined at 20fm m the horizontal. The types of materials

7/29/2019 A 3-D Semi-Analytical Method for Subsidence Prediction and Stress Analysis in Coal Mining

5/6

21" International Conference on Ground Control in Miningfor these layers are in descending order 2 ,3 ,2 ,3 ,4 ,5 ,6 ,7 ,7 & 7. The elastic constants for those types of materialsand their respective thickness arc shown in Tables 3 and 4,respectively.

Table3. MPterW propertyElastic I Type of materials

Table 4. Thickness of layerI 2 3 4 5 6 7 8 9 10 11 12number

Layerthislmess 50 50 . . 40 30 20 10 10 10 20 30

Fig. 7The computed surface subsidencebash

n monumentFigure 7 shows the computed surface subsidencebasin after m ining under self-weight Surfact subsidence Fig. 8 Comparison between the computed surface subsidenceprofile in the major cross-section along the dip direction is and measured valueshown in Figure 8 along with the measured surfacesubsidence values. Stress distribution at major mininglocationsis shown inFigure9. iIt can be seen from Figure 9 that the maximumcompre9sive stress occurred at point A with stressconcentration=2.8. Along the bottom boundary, ththe islocalized tensile stress which means this cross-section i s inthe tensile yield zone.

i z Fig.6 Exam ple vertical profile

Flg. 9 Stnudistribution

5.ConclusionThrough systematic research, the 3-D semi-analyticalmethod has been successfully applied to surfacesubsidence prediction and stress analysis due to minmg.Many ca se studies have shown that this method is a very

efticient alternative to solve a variety of geameohanicsproblems. It is feasible to deal with the 3-D groundsubsidence problems due to mining with the semi-analytical method. The results generated by this methodsatisfy the needs for engineering prediction It provides aneffective numerical method for mining engineering designand geomechnnics research.

7/29/2019 A 3-D Semi-Analytical Method for Subsidence Prediction and Stress Analysis in Coal Mining

6/6

21'' International Conference on Ground Control in Mining6. References

[I] Y. K. Cheung, FiniteSh ip Method in Structural Mechanics, [4]L.M.Liu. Study o n Miming Subsidence Using Sem i-AnalyticalF'cople's Traffic Ress, 1976 Method, International Conference on Computation Methods[2] 2.Y. Cao and Y. K. Cheung, the Semi-snalytio Numerical in Sm ctural and Geotechnical Engineering, CopyrighmMethcd, Defmse Industry Ress . 1992 1994 by the Dep artment of Civil and Structural Engineering,[3] J. R Bwker and J. C. Small, The Application of Finite Layer the University of Hong KongMethod to T i m Dependent problems. Copyright0 1994 bytheDepartment of Civil and Structural Engineering,the University of Hong Kong