Calculation of Subsidence for Room and Pillar and Longwall Panels

Transcription

1 University of Wollongong Research Online Coal Oerators' Conference Faculty of Engineering and Information Sciences Calculation of Subsidence for Room and Pillar and Longwall Panels Anton Sroka Technische Universität Bergakademie Freiberg, Germany Krzysztof Tajdus Strata Mechanic Research Institutes, Polish Academy of Science Axel Preusse RWTH Aachen, Germany Publication Details A. Sroka, K. Tajdus and A. Preusse, Calculation of Subsidence for Room and Pillar and Longwall Panels, th Underground Coal Oerators' Conference, University of Wollongong & the Australasian Institute of Mining and Metallurgy,, Research Online is the oen access institutional reository for the University of Wollongong. For further information contact the UOW Library:

2 Underground Coal Oerators Conference The AusIMM Illawarra Branch CALCULATION OF SUBSIDENCE FOR ROOM AND PILLAR AND LONGWALL PANELS Anton Sroka,, Krzysztof Tajdus and Axel Preusse 3 ABSTRACT: A Euroean method of surface subsidence calculation for artial room and illar and longwall anel mining of coal deosit is resented. The article focuses on the Knothe method, that describes the subsidence trough by the Gauss influence function method. This method rovides calculation of tilt, curvature radius, horizontal and vertical movements, and horizontal strain of the surface subsidence trough. The method to forecast surface subsidence serves to design exloitation with resect to minimalisation of its influence so that the forecast subsidence should not exceed a limit value. INTRODUCTION The develoment of surface subsidence methods refers to a mining exloitation rocess started by Keinhorst (95). The breakthrough dissertation was ublished in 93/93 and it is called Bals Method (Kratzsch, 983). The function influencing the aforementioned method was descended from Netwon Low of Gravitation and interaction between two substances. By considering the acceted the influence function method, the segments mesh of equal imact relates to subsidence on the middle oint of the otential mesh that have been created. The subsidence of any oint on the ground caused by free shae anel excavation can be determined using the grahic integration. This grahical integration as described in the exloitation field where the middle oint of the mesh of segments will be suerimosed with the calculated oint. Reference to similar solution is reorted in Beyer (944), Sann (949) (see Kratzsch, 983), Knothe (953), Kochmanski (Collective Work, 98), Ehrhardt and Sauer (96), and Geertsma (Kratzsch, 983). The essence of surface subsidence is schematically resented in Figure. Figure - The general scheme of surface subsidence methods In general, the occurrence of surface subsidence (resent on Figure ) might be: Filling of the void caused by mining and subsequent roof caving); Gradual convergence of some cometent rock layers such as rock salt cavern; or Comaction of orous deosits during exloitation of oil and gas. CALCULATION OF SURFACE SUBSIDENCE The general formula to calculate the subsidence of a surface oint by geometrical-integration methods can be resented in the form: ( y ) = a g ( x x, y y ) dxdy w x On condition that:, ϕ () Technische Universität Bergakademie Freiberg, Germany Strata Mechanic Research Institutes, Polish Academy of Science, Poland, tajdus@img-an.krakow.l 3 RWTH Aachen, Germany February 83

3 Underground Coal Oerators Conference The AusIMM Illawarra Branch ϕ ( x, y ) dxdy = Where: a- subsidence factor, its value deends on an established system of exloitation and from a method of filling the void; g- thickness of excavated seam; φ- influences function, whose value is deendent on the method of calculation. The combination of the most imortant ast and currently alied influences function is resented in Table. Table - An influences function φ according to various authors Author An influences function φ Parameters Descrition π ln + tan ξ gr l + H Bals ( ) Beyer Knothe Kochmans l ki Ruhrkohle 3 π l r B r B ξ gr, l H tanξ gr γ B, r B =H cotγ B l r B l ex π β, r K =H cotβ rk r K ex π c( b) k π l r r l ex k r R r R b r, b b c( b) = λ ex( λ ) dλ 5.log H b( H) = +.67log H γ, k = ln. r K =H cotγ l- the horizontal distance of referenc oint from taken out element, H- deth of exloitat r- range of main influence, its value deends on alied method, γ, ξ gr, β- angles of m influence, its value deends on alied method, r - scale coefficient horizontal influence b- influences functio shae coefficient Geertsma v π H ( l + H ) 3/ v From Table, the most imortant function alicable to the Euroean mining industry includes both the Knothe and the Ruthrkohle methods (Knothe 953; Ehrhardt and Sauer 96). Knothe assumed that the influencefunction method was i adequately resented by Gauss function with roer arameters. This assumtion has a strong theoretical background e.g. dissertations written by Kolnogorow (93), Litwiniszyn (956) and Smolarski (967) (collective work, 98) which are related to stochastic medium theory and the alication of robability calculus. According to the Knothe method, the elementary subsidence trough has the Gauss function shae, on condition that an elementary mining exloitation has the Dirac s function shae (Figure ). The assumtion was achieved in at The Strata Mechanic Research Institute of the Polish Academy of Science in Cracow, where the exlorations in the loose medium (loose sand model) as a medium with a high degree of freedom have been carried out (Krzyszton, 965). The single examle of obtained results for the test are resented in Figure and Figure February

4 Underground Coal Oerators Conference The AusIMM Illawarra Branch Figure - Comarison of subsidence results for the loose sand model with the Gauss function model Figure 3 - The rofile of trough subsidence w(x), the curvature of horizontal dislacement u(x) and ratio of u(x) and w(x) for loose sand model The conformity between results of the exlorations and the Gauss curve is shown in Figure. The grah of Figure 3 shows the deendence of subsidence distribution w, horizontal dislacement distribution u, and their relation on u/w. Based on the initial results the following relationshi hold: u( x) = α x () w( x) Where: x- distance of the consider oint from the taken out element realised as dum slotted ; α- certain coefficient deendent on density of medium. Sroka (984) roosed a comutable model based on discretization (division) of the comleted exloited field on small ended surface elements. The elements are square shaed with a side of Δx. The formula of such a subsidence value is: M ( l ( ) w l, t = ex π r r (3) M ( = a V z( Where: M(- volume of elementary trough subsidence in moment t. l- distance of calculation oint from excavated element of deosit, r- radius of main influence according to Knothe theory, V- volume of excavated element ( V = Δx g ), β- angle of main influence. z t - function of time. () Radius of main influence r is calculated as: r = H cot β (4) The advantage of this solution is the fact, that each element can be described searately through a chosen thickness of excavated seam g i, deth of exloitation element H i, and time of excavated element t o. The calculation of element subsidence for the whole exloitation can be estimated by linear suerosition, i.e. trough sum u artial subsidence from single elementary field. February 85

5 Underground Coal Oerators Conference The AusIMM Illawarra Branch Figure 4 - The scheme of determination of oint subsidence P caused by taken out single deosit element Because of accuracy of the calculation, the length of square side should not be higher than Δx.r, and because of the ossibility of analysis of the influence on mining exloitation velocity and stoage of face advance on strata deformation in time the length of element side should not be higher than average face advance. The Ruhrkohle method, which is widesread in Germany, and the Knothe method are the same because of identical background of the Gauss function. The selection of time function is a key element during the sace-time continuum analysis. The collection of functions, which are used in Euroean mining industry, was resented in Table. From all functions, which were described, the Knothe function (953), the Sroka and Schober function (985), the Kwiatek function () are worthy of mentioning. In time function c(, time t is calculated from the moment of excavation of the deosit element. The time equations given by Knothe, Schober and Sroka are aroximately equal for deendences: ξ f c = (5) ξ + f For time function according to Kwiatek, the following deendences can be resented: c >> c.6 A.85 In Euroe, the rimary hazard index is an index of horizontal strain. Other indices like curvature (or curvature radius) do not have significant meaning because of increased deth of mining over m. Fundamental dynamic hazard indices, among the static one are (esecially in German mining industry), the seed of element subsidence, the growth seed of horizontal dislacement and disturbance index of subsidence arising from the stoage of longwall anel exloitation (Table 3). Both the Knothe method and the Ruthrhohle method assumes, that the horizontal dislacements need to be calculated according to the Awierszyn hyothesis (947). This hyothesis makes an assumtion on a roortionality between tilt vector T and a horizontal dislacements vector u (Formula 6). This assumtion also determines the relationshi between a tensor strains and a tensor curvature K (Formula 7). u = B T (6) ε = B K (7) Where B is the factor of roortionality, its value is located in limits of articular inequality.8r < B <. 4r. Factor B is a comutational additional arameter and it should be estimated considering in- situ measurements. The fact, that the Awierszyn hyothesis is qualitatively comatible with results of laboratory research results shown in Figure 3. The same hyothesis is also comatible with a modified method centre of gravity oint which was ublished by Keinhorst. 86 February

6 Underground Coal Oerators Conference The AusIMM Illawarra Branch Table -Time function z ( t ) based on various authors (Sroka 3) Author Time function Parameters z ( = ex( c Knothe (953) w& ( = c[ wk ( w( ] Martos (956) z( = ex( α t ) w k (- final subsidence in time t, w(- subsidence in real time t, Trojanowski (97/973) Schober, Sroka (983) Sroka (985) [ w ( w( )] w& ( = c( k t t ( ) z( = ex c λ dλ f ξ z( = ex ex f ξ f ξ ( ξ + ( f ( ) z ( = C ln Bt + for t (ex ) / B C c- the relative velocity of mining influences roagation, ξ- the relative velocity of convergence (e.g. value. year - corresond to cli assing velocity characterized by value of % annually), f- the relative velocity of transmission of mining influences by rock mass,,5 Kittlaus (986) z( = ex( μt ) Schreiner, Kamlot (99) t z ( = ex( ) t Sroka (994) z( = [ ex( ξ ] [ ex( f ] Kowalski (999) z ( = for t t ( c( t )) z( t = A ex for t > t Kwiatek () ( = ( A) ex( c A ( c z ex Sroka (3) z( = ex t t m In Euroean mining industry (excluding UK) the longwall anel exloitation is carried out without leaving illars between longwall anels. In consequences, the fact of leaving illars between longwall anels (esecially in the American and Australian mining industry) leads to irregularities of subsiding troughs characterised by huge hazards, not even on the surface but also in the overburden. Additionally, leaving the illars can lead to crums, earth tremors and other hazards in water-bearing levels. In longwall anel exloitation without leaving the illars between them, formulas to calculate the imum value of deformation indices are relatively simle, e.g. for full field (field bigger than r x r) the formulas are following: Maximum subsidence: Maximum tilt: Minimal radius of curvature: w = a g (8) w w T = tan β r H e r H R min =.66 π w w = (9) = cot β () February 87

7 Underground Coal Oerators Conference The AusIMM Illawarra Branch Maximum value of horizontal strain: ε w w = ± =.6 tan β () e r r Table 3 - Boundary values of strain factors describing a dynamic and static imact of mining exloitation on the objects Category of strength of buildings R [km] ε [mm/m] w& gr [mm/d] ε& gr [mm/d] Δ w gr [mm] 4 R ε R ε R ε R ε R ε This same method can be used for other systems of exloitation in mines and water bearing or aqueous deosits (Sroka and Tajdus, 9). In general, what is imortant to determine the convergence (comaction) of the deosit element caused by mining. Later on using the influence function method an adequate descrition of surface subsidence is achieved (Formula 3). Figure 5 shows the scheme of surface subsidence calculation when shortwall anel is alied together with leaving illars between excavations. Roof layers are influenced (deflection occurs) by taken out same art of deosit and the left illar are loaded by ressure z. The illar is artly crushed by value Δq (Figure 5). Figure 5 - Surface subsidence and convergence of illar among shortwall exloitation Emirical value Δq can be resented in form of: Δ q = z g () E f + l z = γ H (3) f Where: E- elastic modulus, f illar width with an infinite length, l excavation width with an infinite length. The scheme of stress distribution under the illar is resented in Figure 6. In this method, the calculation of otential drift (excavation) convergence and value of illar Δq deression is essential. To achieve this numerical methods of Finite Element Method (FEM) and Finite difference method, (DEM) and alike, etc. (Figure 7) can be alied in which lots of factors should be taken into consideration (i.e. faults, discontinuity, fracturing, orosity, etc.) (Tajduś, 9; Tajduś, et al., 9). 88 February

8 Underground Coal Oerators Conference The AusIMM Illawarra Branch Figure 6 - Stress distribution under the illar Figure 7 - An examle of numerical calculations of drift (excavation) convergence for shortwall anel with left illars The resented solution can also be used for continuous miner system (Sroka et al., 9). Then calculation is carried out for full exloited mining field, in addition the value of subsidence factor received form of: s ( ) aη a η = (4) Where: η- coefficient of coal deosit exhausted; a - coefficient of subsidence for full exloitation; s- coefficient deendent on tye of rocks (for weak rocks and average strength s=.5; for strong rock s=.). CONCLUSIONS Euroean comutational methods are used mostly in designing a mining exloitation over build-u areas such as: Ruhrkohle (Germany) and the Uer Silesian Coal Basin (Poland). These methods have a ositive imact on the rotection of buildings and other infrastructure e.g. heat distribution network, road nets, ower network. Moreover, the methods ositively influence on industrial infrastructures such as: storage reservoirs and water-bearing layers in a rock mass. The designing is concerned with the establishment of exloitation geometry, a run of the exloitation considering the time; imal seed of exloitation and the face advance stoing during the exloitation. Other elements, which have to be taken into consideration during the exloitation designing, are settlement of safety illars or estimation of final borders of mining exloitation. The resented comutational method allows for calculating of surface deformation, taking into account an otional shae and otional time of exloitation. This method is currently been used not only in the mining industry of hard coal, but also in metalliferous mines, such as salt and coer mines and in oile and gas fields. The comutational method, which is based on the Knothe method can be fully alied to hel in redicting subsidence and minimise its imact; this can also be in the Australian mining industry. REFERENCES Awierszyn, S G, 947. Sdwiżenije gornych orod ri odziemnych razrabotkach, Ugletiechizdat, Moskwa, Russia. Collective Work, 98. Mining surface rotection, (Śląsk, Katowice), Poland (in Polish). February 89

9 Underground Coal Oerators Conference The AusIMM Illawarra Branch Keinhorst, H, 95. Die berechnung der bodensenkungen im emschergebiet, 5 Jahre der Emschergenossenschaft Essen, Germany. Knothe, S, 953. Time influence on shaing of subsidence trough, Archives of Mining Science (), -3 (in Polish). Knothe, S, 984. Prediction of mining influence, (Śląsk, Katowice), Poland (in Polish). Kowalski, A, 999. Time function use to forecast an unsecified surfach deformation causa by underground longwall anel excavation with stoage, in Conference V Dni Miernictwa Górniczego i Ochrony Terenów Górniczych in Szczyrk, Poland, 4-5 (in Polish). Kratzsch, H, 983. Mining Subsidence Engineering, (Sringer- Verlag, Berlin Heidelberg New York). Krzysztoń, D, 965. Range of main influence in loose medium, Archives of Mining Science, (), 9-5 (in Polish). Kwiatek, J,. Buildings on mining area, (GIG, Katowice) (in Polish). Martos, F, 967. Bányakártan. Budaest, Tankönyvkiadó, Hungary. Schober, F, Sroka, A, 983. Die Berechnung von Bodenbewegungen über Kavernen unter Berücksichtigung des zeitlichen Konvergenz Und Gebirgsverhaltens, Kali und Steinsalz,, Germany. Sroka, A, 984. Abschätzung einiger zeitlicher Prozesse im Gebirge, Schriftenreihe Lagestättenerfassung und - Darstellung, Bodenbewegungen und Bergschäden, Montanuniversität Leoben, Austria. Sroka, A, 999. Dynamics of mining exloitation in terms of mining damage, (IGSMiE) (58), Habilitation thesis, AGH Kraków (in Polish). Sroka, A, 4. Time function in term of continuous and quasi- continuous survey measurements, in Conference VII Dni Miernictwa Górniczego i Ochrony Terenów Górniczych in Zakoane 4-7 czerwca 3, Geodezja, 9(/), (AGH Kraków) (in Polish). Sroka, A, Tajduś, K, 9. Determination of surface subsidence above underground oil and gas exloitation. Oil and Gas, 6(-), , (AGH), (Kraków) (in Polish). Sroka, A, Knothe, S, Tajduś, K, 9. Exloitation in safety illar for a shafts Jămy Sever in mine ČSM, Project, (unublished). (Kraków). Tajduś, K, Sroka, A, Tajduś, A, Preusse, A, 9. Three dimensional modeling of a surface dislacements as a result of an underground longwall anel extraction, in 9 th Int. Conf. on Ground Control in Mining, in Morgantown, 5-. Tajduś, K, 9. Determination of the value of strain arameters for strata rock mass in the region of underground mining influence. PhD thesis, (Verlag Glückauf GmbH, Germany, Essen) (), TU Bergakademie Freiberg, Germany. 9 February