A Study of Angle of Draw in Mining Subsidence Using Numerical Modeling Techniques

Transcription

1 A Study of Angle of Draw in Mining Subsidence Using Numerical Modeling Techniques G. Ren*, J. Li School of Civil, Environmental and Chemical Engineering, RMIT University, GPO Box 2476V, Melbourne 3001, Australia *Corresponding author; ABSTRACT Mining subsidence is a well recognized problem in many countries. Particularly in the recent years with increasing demand for energy and resources, mining activities have been extended to a limit where previously being regarded as no-mining zones. It is important to understand the mechanism involved in the substratum movement induced by underground mining. One of the key parameters in subsidence analysis and prediction has been the angle of draw which defines the limit of the subsidence affecting the surface. Most of the traditional empirical subsidence models are reliant on the value of angle of draw. In this paper numerical modeling techniques were used to study the mechanism of substratum movements and the associated subsidence limit at ground surface. Particular emphasis is placed on the effects of overburden stiffness and the extraction seam dip angle on the values of angle of draw. The analytical results are discussed in the context of observational data worldwide. KEYWORDS: Subsidence; finite element; ground movement; overburden stratum; angle of draw; limit angle; numerical analysis INTRODUCTION Subsidence analysis and prediction rely heavily on, inter alia, the input of subsidence limit angles. It is particularly significant at mine planning and approval stage when the extent of the subsidence is required to be fully assessed. Safe and economical design of modern mines calls for reliable and accurate evaluation of the limit angles at a given mine field. The sub-stratum movement above mining horizon plays an important role in the subsidence limit characteristics. The subsidence mechanism has been well established since 1965 following the publication of the Subsidence Engineer s Handbook (SHE) [1] by the UK National Coal Board. Whittaker [2] described in detail a number of possible subsidence mechanism above a mining goaf using physical modeling techniques and numerical analysis. Various subsidence analysis techniques have been introduced based on empirical and numerical models [1, 2, 3 & 4], including the SEH model established on observations of approximately 200 sites in the UK coal fields, and the influence function based computer models. The subsidence analysis

2 Vol. 13, Bund. F 2 models have been employed worldwide with various degrees of success. Of all the techniques used in subsidence analysis and perditions, the most important parameter, yet often been overlooked is the angle of draw (also called limited angle), which determines the extent of subsidence influence at surface level. The angle of draw is defined as the angle at which the subsidence spreads out from the edge of underground extraction panel towards the limit of subsidence at the surface (see Figure 1). There has been limited publication studying the effect of the subsidence mechanism on the value of the angle of draw. It is intended in this study that the angle of draw is looked at from both statistical point of view and analytical point of view. Max. horizontal movement Tensile strain Original ground surface Subsidence profile Cover depth Smax Seam Roof Overburden Compressive strain Angle of draw (limit angle) ζ Panel width Figure 1: Mining Subsidence terminology THEORETICAL ASPECT OF ANGLE OF DRAW Rock strata at mining horizon are considered to be in a state of equilibrium before mining activities taking place. The removal of minerals will create an initial imbalance of stresses around the opening and this leads to stress redistribution. The redistribution of the stresses causes the deformation of the overburden strata. In a longwall coal mining face, the immediate roof strata above the goaf area is normally unsupported and allowed to break and cave into the void. The caving process propagates upwards to the surface thus subsidence occurs. The subsidence mechanism is highly complex in practice, because it involves many factors including geological structure of the overburden strata, mining method and geometry, groundwater conditions, strength of the overburden rocks [2]. The overburden strata are rarely homogeneous and normally consist of a series of sedimentary rocks of different origin, thickness and strength properties. When an excavation is not sufficiently wide, and the roof stratum is adequately strong, the roof may not collapse and hence very little subsidence is reflected on the surface. On the other hand, when an excavation is wide enough and the immediate roof could not support the overburden pressure, the roof will cave in and ground movement is transferred from the mining level to the ground surface. The observed subsidence and ground movement at surface is the product of combined reaction of the overburden strata and soils to the influence of underground mining excavation. The angle of draw defines the extent of such effect of underground extraction at surface.

3 Vol. 13, Bund. F 3 Elementary trough at surface r R Kz P Limit line H ξ Angle of draw seam Extraction element Figure 2: Effect of infinitesimal extraction element on surface On a micro-scale the angle of draw can be understood using the sketch shown in Figure 2, where the extraction of an infinitesimal element at mining horizon creates an elementary trough at the surface within the limit angle. The underground extraction element is assumed to have no influence at the surface beyond the limit line. The overall subsidence profile could be determined by the combined effect of all extraction elements at the mining horizon. This influence of the infinitesimal extraction element can be mathematically defined by a function, referred to as influence function [2]: Where K z is the effect of an infinitesimal extraction element. γ is the zone angle in the range 0 γ ξ (angle of draw) K z = f(γ) (1) Different influence functions were proposed by researchers [2], among them the stochastic influence function was one of the most successful solutions that have been employed for subsidence modeling and perdition: K z = 1 πr 2 / e R 2 R 2 (2) Where R is the distance between centre of the elementary trough and the edge of the trough, and r is the radial distance from centre of the elementary trough to a point P. From the influence function Eq. 2, it can be seen that the value of R is a predefined parameter that is dependent of the angle of draw (see Figure 2). Where H is the depth of extraction, and ξ is the angle of draw. R = H tan ξ (3) From overall modeling point of view, the overburden strata can be simplified as a massive continuous beam under gravitational load and it is supported by un-mined seam at the rib sides. The beam deflects under

4 Vol. 13, Bund. F 4 gravity load when the mineral is removed at mining level. The deflection of the beam as reflected at the surface represents the subsidence profile. The affected area at the surface usually exceeds the area of the underground excavation. The angle of draw can be readily observed from the output of the finite element model. In determining the value of the limit angle for a particular subsidence profile, a value of subsidence limit would have to be assumed. In some countries, e.g. Australia, an arbitrary value of 20mm settlement is used to define this limit and it is generally accepted that subsidence of less than 20mm will have negligible effect on surface. In other countries, a value in the order of 2 to10mm was used as the limit. This fixed value of subsidence as a cut-off point for determination of the angle of draw has caused some confusion in comparing the values of limit angle from different countries, as it is not usually stated in the publications as to how the angle of draw as defined. The Subsidence Engineers Handbook [1] uses a limit value of 2mm in the interpretation of subsidence limit angles. Yao [9] found this fixed limit approach is unsatisfactory and he proposed that the limit value should be expressed as a function of the seam thickness. He suggested the use of 2-5% the maximum subsidence to define the subsidence limit. It is generally accepted that the subsidence limit at the surface can be regarded as the limit beyond which the effect of subsidence is insignificant and negligible. OBSERVATIONAL VALUES OF ANGLE OF DRAW The angle of draw depends on the strength and composition of the overburden strata as well as mining configurations. It is reported that the depth of cover to the coal seam also influence the angle of draw. A number of researchers observed subsidence troughs from different coal fields in the world and reported the values of angle of draw and made remarks on the nature of the overburden strata (see Table 1). After comparing the data obtained from Kamptee coalfield India with that of South Africa, Singh [5] suggested that weak and soft overburden was associated with high value of angle of draw, and the strong massive overburden would tend to result in a small angle of draw. This observation is not consistent with data obtained from some of the Australian coalfields. Table 1: Reported subsidence values of angle of draw in different countries (main source of data based on Singh [5] and Li [6] and Waddington [7]) Country Value of angle of draw Overburden strata Reference Austria Weak and saturated strata Singh [5] - Perz (1957) Netherlands Mainly saturated sands and other unconsolidated materials Singh [5] -Dernt (1957) Czechoslovakia Singh [5]- Zilavy (1968) Japan Singh [5] -Hiramatsu st al. (1979) USA Singh [5] -Moebs et al. (1985) Hood et al. (1983) South Africa 11 Massive dolerite sill Singh [5] -Schumann (1984) UK Mostly weak, argillaceous overburden strata Yao [9] India 40 >62% clays in overburden Singh [5] China Cui [11] Australia Mainly strong overburden strata; sandstone and massive conglomerate Li [6] Waddington [7] Holla [10]

5 Vol. 13, Bund. F 5 Table 2: Reported subsidence angle of draw in Australian coal fields Australian Coal Value of angle of draw Overburden strata Reference fields Newcastle 35 Strong overburden strata Holla (1986) coalfield Mainly saturated sands and other unconsolidated materials Waddington (1995) Liddell Colliery Fine to medium grained Li (2007) sedimentary rock, typically strong sandstone conglomerate Hiramatsu (1979) Table 2 lists some collected values from published and unpublished sources showing the values of angle of draw from Australian coalfields. It should be recognized that there may have been some discrepancies in the definition of the subsidence limit in various data bases, e.g. in some countries a limit value of 20mm was adopted in the interpretation of the angle of draw from the surveyed subsidence troughs, whereas in other countries, the subsidence engineers might have assumed different limit values. For this reason, it is difficult to cross compare the available observed data from different mining fields and countries. It is also noted that some of the reported data on angle of draw did not make any differentiation between continuous and discontinuous subsidence. Ideally, angle of draw should be taken from continuous subsidence profiles obtained by precision survey. The discontinuous subsidence trough is heavily influenced by geological features and may involve a range of complex failure mechanisms which may have been time related and manifest itself erratically on the ground surface. It is fairly difficult to derive an angle of draw with practical meaning from a discontinuous subsidence profiles. Figure 3: Limit angles for inclined seam (after Ren et al and Whittaker 1989)

6 Vol. 13, Bund. F 6 The matter becomes even more complicated when inclined seams are involved. According to observation for seams pitching at different angle, the limit angle at the dip-side of the panel is generally greater than that at rise-side. Ren [4] and Whittaker [2] compiled a graphical representation based on data obtained from China, UK, Japan and Germany (see Figure 3), showing that the limit angle at dip-side is generally between 25 º to 50º and at rise-side 10º to 35º. The following observations are made after comparing the data sets: (1) The values of limit angle show marked scattering in respect of seam gradient. (2) The limit angle values at the rise-side show less scattering of data than that of dip-side. The maximum limit angle of approximately 50º at the dip-side corresponds to 20 º seam gradient on Ren s curve; while on the Zilavy s curve, the maximum limit angle of 40º corresponds to a seam gradient of 60º. (3) The center angle ξ 2 which determines the maximum subsidence position, generally varies between 5º to 15º. Little data is available beyond 40º dip. Zilavy did not report on the center angle. INVESTIGATION OF SUBSTRATUM MOVEMENT USING NUMERICAL MODELING TECHNIQUES The overburden strata can be simplified as a beam spanning over the width of extracted coal seam. The excavation can be modeled by removal of elements at the mining horizon in an idealized finite element mesh. The problem is then becomes one of determining the stresses around the opening via a stress-strain constitutive relationship, and the displacement induced by the removal of elements in a previously gravity stressed semi-infinite body. A series of two-dimensional numerical models, using the commercial finite element package Plaxis version 8, were constructed to investigate the overburden stratum movements as the consequence of coal mining extraction. The finite element model shown in Figure 4 represents a vertical section perpendicular to the longwall face with various extraction widths. The boundary conditions at the roof in the goaf area were prescribed by assuming that the roof is in contact with the floor after the extraction. A generalized elasto-plastic material using a Mohr-Coulomb failure criterion was assumed for the rock strata in the numerical analysis. A range of internal frictional angles and apparent cohesion values as the equivalent strength of the overburden strata were used to ensure that the models would not prematurely fail before reaching the prescribed boundary conditions. The model adopted for the study is a longwall mining configuration with 5m thick seam at 200m depth using the adopted parameters shown in Table 3. The extraction width was gradually increased from subcritical width to super-critical width. Figure 5 shows the subsidence profiles and movement contours for a sub-critical and a supercritical extraction widths generated by a finite element model. In this particular example, the subsidence factor (defined as the ratio between maximum subsidence over the seam thickness) is approximately 0.9 which is consistent with the empirical SHE model [1]. Table 3: Material parameters adopted in finite element model Material Parameters Overburden stratum Coal seam Unit Weight (kn/m 3 ) Young s Modulus (kn/m 2 ) 1.2E6 0.8E6 Poisson s Ratio

7 Vol. 13, Bund. F m Sub-critical width 200 m Overburden Deformation Modulus 1.2E6 (kn/m 2 ) Super-critical width 100 m 5 m Various width from 120m to 300 m Figure 4: Basic subsidence mesh and model dimensions From Figure 5 it is obvious that the most of the movement taken place directly above the roof and the movement magnitude gradually decreases towards the surface. The lateral extent of the subsurface movement contours in relation to the limit angle is also clearly shown. It demonstrates that using finite element modeling techniques, the limit angle can be readily derived using a predefined subsidence limit, e.g. 2% of the maximum subsidence (S max ). Figure 5: Sub-critical and super-critical subsidence profiles by finite element modeling

8 Vol. 13, Bund. F 8 EFFECT OF OVERBURDEN STIFFNESS ON THE ANGLE OF DRAW One of the objectives of this study is to examine the effect of overburden stiffness on the angle of draw which defines the subsidence profile. The observed data from different parts of the world does not appear to be consistent: some observers [5] reported that the weak and soft overburden strata would be associated with a high value of limit angle, whereas others recorded higher value of limit angle over strong overburden layers [6]. The numerical modeling would serve to provide a theoretical basis for the study of the effect of overburden stiffness on the subsidence profile. A series of different Young s modulus values were used in the models while all other input were kept unchanged. For comparison, the Young s modulus of 10 and 100 times of the general overburden was assigned to the beam layer respectively. Again, for simplicity and clarity, elastic material model was adopted for the study, although it was recognized that yielding of material in the model would affect the subsidence characteristics. Figure 6 shows the subsidence profile derived from varied values of Young s modulus. It clearly demonstrated that the angle of draw would extend further away from the edge of extraction under stratum with high Young s modulus, i.e. the stiffer overburden would result in higher value of angle of draw. Based on the model study, it would appear that the stronger overburden stratum would tend to bridge itself over the extraction and extend the movement further laterally on the surface, hence results in higher angle of draw. Vertical Subsidence (m) E 0.1E 0.01E 100E 50E E Figure 6: Effect of overburden stiffness on the subsidence profiles for a super-critical case In real world the geological conditions are far more complex than the simplified model studied above. The angle of draw at surface level is the product of many factors including stiffness and strength of overburden strata, geological setting, mining methods and mining configurations. The subsequent numerical model is focused on the presence of a relatively stronger layer between the mining horizon and the ground surface. The general model geometry and input parameters are essentially the same as the previous model, but with a stronger beam layer added to the model (see Figure 7). From the output of the finite element analysis presented in Figure 7, the following findings are observed: A sub-critical subsidence profile can develop over a longwall panel of supercritical width when there is a stiffer/stronger beam layer present in the overburden. The value of angle of draw would be significantly greater when a stiffer beam layer is present in the over overburden strata. The maximum subsidence at centre of the subsidence trough is significantly reduced as a result of the presence of stiff beam layer.

9 Vol. 13, Bund. F 9 The magnitude of movement in the overburden decreases progressively towards the surface and the beam would act as a barrier preventing the migration of movement upwards depending on the stiffness of the beam. With increased stiffness of the beam, the bridging effect becomes more profound with relatively little movement in the overburden passing the beam up to the surface. Substratum movements take place predominantly in the area directly above the panel and below the beam. In practice, this is the area where most of the collapsing and beds separation would occur. The above findings are in reasonably good agreement with the observed subsidence data at Newcastle Coalfield, Australia. Creech [12] reported a number of cases where numerous thick conglomerate units existed in the overburden, the bridging effect was considered to be the reason of low recorded subsidence on the surface. It must be emphasized that the above observations were made under the assumption that the stiff bed or beam is adequately strong and no break up or failure taking place during and after the mining extraction. If the beam is broken, the observations and conclusions would be rather different. When the beam is broken the stratum movement would be more confined and concentrated to the failed zones in the overburden, thus less movement transmitted to the surrounding areas. As such, the subsidence at the surface would extend laterally to less extent, resulting in lower value of limit angle. This would be consistent with the observation made by Singh [5] in Kamptee coalfield India and South Africa. In Australia, some subsidence data showed that high value of limit angle occurred over massive overburden rocks (Table 2), which is in general agreement with the elastic model. It may well be that the roof stratum was adequately strong and competent and did not break during and after the mining operation. In such case, the stratum would behave in the similar way as demonstrated in the finite element model. EFFECT OF OVERBURDEN STRENGTH ON THE ANGLE OF DRAW The effect of overburden strength on subsidence limit characteristics has been reported by Yao et al [9]. Yao carried out comparative analysis using a series of uniaxial compressive strength (UCS) as index of strength for a bed or a beam in the overburden in a finite element model. The results showed that increasing the strength of the overburden stratum would reduce the value of limit angle, i.e. one would expect less extent of subsidence effect at surface over a strong overburden rock mass. Conversely the subsidence limit angle would be greater over a weak bed in the overburden than over a strong bed. Table 4 shows the relationship of overburden strength and the angle of draw based a finite element study by Yau [9]. It should be noted that Yau s numerical model utilized an UCS based failure criterion, which was a non-linear material model. With weak overburden rock masses above the extraction, the stressed elements in the model would tend to yield at early stage of loading and failed zones would propagate over a larger area, thus showed significant extent of subsidence at the surface. Table 4: Relationship between UCS and angle of draw using 2% maximum subsidence as limit data based on Yau et al [9] UCS of Overburden stratum (MPa) Angle of Draw (degree)

10 Vol. 13, Bund. F 10 Movement Contours E=E 0 (a) No beam Beam E=10E 0 Movement Contours (b) Presence of beam with E=10E 0 Beam E=100E 0 Movement Contours (c) Presence of beam with E=100E 0 Beam Beam (d) Sub-strata movement patterns Vertical Subsidence (m) No Beam Overburden E=2.2E12 Pa E=2.2E14 Pa E=2.2E15 Pa Figure 7: Effect of presence of overburden beam on subsidence profile

11 Vol. 13, Bund. F 11 On the other hand, if the overburden rock is strong and stiff, when roof did collapse the strong bed would break and reached failure limit in the model. As a result, most of the movements would tend to concentrate in the failed areas and is likely just above the centre of the panel. Little movement would be transmitted over the remaining un-yielded strong bed elements. Consequently, the subsidence profile as it appears at the surface would have a lower value of limit angle. It is interesting to note that as discussed in above (p. 6), if the rock mass in the roof stratum does not reach failure limit and it would deform like an elastic beam. In such case, the subsidence profile would extend further away from the rib of excavation with a reduced maximum vertical subsidence (Figure 6 and Figure 7) and increased limit angle. This is because the strong and competent roof would behave as a beam which bends under gravity and settle into the excavation, and the movement is extended well beyond the rib of the excavation. Effect of Seam inclination on the angle of draw As discussed in Section 3, the inclination of seams has significant influence on the angle of draw both at the dip-side and the rise-side of the panel. Observational data suggested that the value of limit angle at the dip-side is often more than 35 and the value at rise-side normally less than 35. Based on subsidence observations from many reported cases, the following generally equation for estimating the limited angle for inclined seams is postulated: ξ 1 = f 1 (α) (4) ξ 3 = f 2 (α) (5) Where ξ 1 is the angle of draw (in degree) at dip-side of panel and ξ 3 is the angle of draw at rise-side. α is the inclination angle (in degree) of the seam. f 1 (α) and f 2 (α) are functions depending on local geological condition and can be obtained from experience and observational data sets. For example, based on Rom s data [4] the following relationships can be defined: ξ 1 = f 1 (α) = ( α 45) (6) ξ 3 = f 3 (α) = ( α 45) (7) Similarly, from SEH data set, using curve fitting, the following mathematical representation of the limit angles can be defined for the UK coal fields: ξ 1 = f 1 (α) = 2 + α (8) α 2 ξ 3 = f 3 (α) = ( α 45) / 2809 (9) When there is sufficient observed data for the limit angle at centre (ξ 2 ), similar process can be adopted to derive the empirical relationship between ξ 2 and the seam inclination angle.

12 Vol. 13, Bund. F 12 For inclined seams, the subsidence profile is determined by the three limit angles (ξ 1, ξ 2, and ξ 3 ) and the maximum subsidence (S max ) at the centre of the subsidence trough. The three limit angles are ultimately dependent on geological conditions and mining configurations. All available observational data suggest that the inclination of seam would tend to increase the limit angle at the dip-side and reduce the limit angle at the rise-side, i.e. ξ 1 > ξ 3 when α>0. To investigate the mechanism of the inclination effect on the limit angles, a further finite element model is established using the identical input parameters as previous model and the results relevant to subsidence profile and limit angles are shown in Figure 8. The model shows the general movement pattern over an inclined seam (α = 20 ) and ground movement vectors at surface. The two limit angles are clearly shown in the movement contour diagram, ξ 1 = 48 and ξ 3 = 33. The results from the numerical analysis are in reasonable good agreement with general observed data. From Figure 8 it is clear that the ground movements at surface are directed towards the excavation, which is consistent with the assumption of influence function method. The surface horizontal strains can be readily calculated from the movement vectors. CONCLUSIONS The extent of mining subsidence affected area is defined by the limit angles, which is predominantly controlled by geological conditions of the overburden strata and the mining configurations, including seam inclination angle. From observational data worldwide and numerical modeling analysis the following conclusions are drawn: The stiffness, strength and failure of the overburden play an important role in the characteristics of subsidence limit. When overburden rocks are sufficiently strong and no major failure or break up taking place in the roof, the limit angle would tend to be greater in roof rocks with higher stiffness. However, if the roof collapses, stronger strata would produce lower limit angle at the surface and weak roof strata would result in greater limit angle. When there is an adequately strong and stiff rock bed in the overburden, it is possible for a sub-critical subsidence profile to be developed over a panel of super-critical width. The rock strength and stiffness also affect the magnitude of the maximum subsidence. Generally the maximum subsidence over a strong overburden is less than that over a weak overburden. Numerical model has demonstrated that the effect of seam inclination is such that it increases the limit angle at the dip-side of the panel and reduces the limit angle at the rise-side. The values of limit angles over inclined seams may be established from observed data set. Empirical relationship between the limit angles and the seam inclination angle may be derived either using numerical modeling techniques or observed data set in a specific mining field.

13 Vol. 13, Bund. F 13 Movement vectors at surface Finite element model: α = 20 ξ 1 = 48 ξ 3 = Figure 8: Finite element model showing the limit angles at dip-side and rise side of inclined seam REFERENCES 1. National Coal Board (NCB). Subsidence engineer s handbook. NCB Mining Department; London, 1965 & Whittaker B N and Reddish D J. Subsidence occurrence, prediction and control. Elsevier, Amsterdam G. Ren, D.J. Reddish, and B.N. Whittaker. Mining subsidence and displacement prediction using influence function methods. Mining Science and Technology, 5(1987) G. Ren, D.J. Reddish, and B.N. Whittaker. Mining subsidence and displacement prediction for inclined seams. Mining Science and Technology, 8(1989) Singh K. B., and Singh T. N Ground movement over longwall workings in the Kamptee coalfield, India, Engineering Geology 50 (1998) Li G., Stewart P., and Paquet R A case study on multi-seam subsidence with specific reference to longwall mining under existing longwall goaf. In 7th Triennial Conference Proceedings: Mine Subsidence: A Community Issue, Nov. 2007,

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