# Analyzing effect of fluid flow on surface subsidence

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1 Analyzing effect of fluid flow on surface subsidence in mining area Y. Abousleiman", M. Bai\ H. Zhang', T. Liu" and J.-C. Roegiers* a. School of Engineering and Architecture, The Lebanese American University, Byblos, Lebanon b. Rock Mechanics Institute, The University of Oklahoma, Norman, OK, U.S.A. c. China Coal Research Institute, Beijing, China Abstract This paper presents an analysis of the mechanisms related to surface subsidence over a longwall mining region where ground water inflow into the mining panel occurs concurrently with the overburden deformation. The finite element analysis is based on the theory of poroelasticity for dual-porosity media in which natural fractures embedded in the porous formation provide significant flow paths and deformability as well as the interaction with the host rock mass, that renders in the subsidence simulation substantially different from the traditional singleporosity approach or sole rock mechanics approach. 1 Introduction Surface subsidence is a common phenomenon in mining industry. Accurate prediction of surface subsidence is crucial to protect surface structures vulnerable to mining activities. In mining industry, the subsidence has been primarily considered due to the mining-induced destruction of overlying strata. Other factors of influence are rarely investigated. The present study is aimed at providing numerical evidences that fluid inflow into mining panel, as a result of the discharge from the overlying aquifers through mining induced fractures, may also contribute significantly to the surface subsidence. This is especially important where the measured surface subsidence shows the magnitudes unproportional to the mined seam thickness, and where the related overburden groundwater flow is substantial. The subsidence due to mining and fluid flow is a coupled phenomenon, in which the poroelastic behavior of overlying strata indicates the typical response to the external disturbance. For the naturally fractured overburden,

2 236 Computer Methods in Water Resources IV the dual-porosity poroelastic approach appears to be more suitable because the fluid flow and rock deformation are more realistically characterized in accordance with the interactive behavior between highly conductible fractures and high storage porous matrix blocks. The behavior of naturally fractured media is considerably different from that of conventional media comprised solely of intergranular porosity. In comparison with the conventional single-porosity media, dual-porosity media appear to produce greater displacement due to larger compliance, which is demonstrated by more substantial surface subsidence over the mined area. However, the response of fluid pressure to the external disturbance appears to be slower for the dual-porosity media due to the initial fluid interchange between matrix blocks and fractures. For a mining case in the fractured porous media,fluiddrainage into a mined void can be sudden and disruptive as a result of this interporosity flow. The detailed description about the dual-porosity poroelasticity can be referred to Elsworth and Bai* and Bai et al.^ In addition to conducting parametric analysis, the objectives of present investigation are to provide some quantified results showing the differences in terms of subsidence magnitudes between the traditional rock mechanics approach and the poroelastic approach. The dual-porosity concept is implied in the analysis, in which more parameters than the single-porosity concept are applied to provide additional modelingflexibility.the analysis of interporosity flow between fractures and matrix blocks is omitted because the primary focus is on the identification of the difference in subsidence between pure rock deformation and flow-dependent rock deformation. 2 Model description The finite element model used in this study was introduced by Elsworth and Bai.* The horizontal symmetry is applied in the finite element mesh design, as shown in Figure 1, where half of the domain is depicted. The simulated mining conditions are: (a) mining depth 400 m, (b) extracted thickness 2 m, (c) mining width 140 m (70 m shown in the mesh). The 2- D model represents the plane strain configuration. The external force and inflow boundary conditions, as a result of gravitational loading and excavation, are shown in Figure 2, respectively. In the initial calculation, three types of materials are assumed, i.e.: (1) overburden and under bur den, (2) coal seam, and (3) gob. The porous media is fully saturated. The fluid flowing into the panel is simultaneously pumped out, resulting in the dissipation of overburden pore pressure, thus causing strata compaction. This flow activity is accompanied by the narrowing of original panel height under the equivalent overburden load, while the latter also induces subsidence. Since there is no additional fluid recharge outside the domain, the domain boundary is impermeable except on the surface which is free from any fluid sources.

3 Computer Methods in Water Resources IV ' J I I I 1 I" 1 ' I I I ( Distance from centcriine (m) ' Figure 1: Finite element mesh layout. 3 Sensitivity study There are basically nine independent parameters for each designated material in the dual-porosity poroelastic analysis,* as illustrated in Table 1, which lists the average values, corresponding to medium fractured porous rocks for underburden, where the subscripts 1 and 2 represents matrix and fracture, respectively. For a general analysis in which the interest focuses on the profile rather than on the magnitude, most displacements and pressures are normalized against maximum possible values. The normalized subsidence versus elastic modulus for different time frames after the initial loading is given in Figure 2. The subsidence changes are more significant at smaller modulii, showing nonlinear relationship in general. The previous evidence indicates that the rocks embedded in the fluid saturated formations usually yield lower elastic modulii than those measured from the dry sites (Liu, 1984). As an inference from Figure 2, the lower modulii may imply more significant flow-deformation impacts. The distributions of the normalized subsidence over and under the centerline of the panel at various times are shown in Figure 3. Several observations can be made as: (a) larger subsidence occurs at later times; (b) positive subsidence in the overburden indicates compaction; (c) ground heave occurs in the underburden; (d) subsidence is in general uniformly distributed except at the earlier time; and (e) the largest subsidence appears at the panel

4 238 Computer Methods in Water Resources IV 0.00 i Maximum subsidence is the subsidence t=le+08 days J I 1 I I I I I I I I I I I I I I 1EH 1E+5 Elastic Modulus El (MPa) 1E+6 Figure 2: Subsidence versus elastic modulus. roof. In contrast, the normalized pore pressure distributions at various times along the centerline are depicted in Figure 4. It may be observed that: (a) relatively higher pressures are developed near the panel where ground water is drained into the panel, which occur at earlier time; and (b) pore pressure decreases significantly with the elapse of time. Final time indicates that the pore pressure completely dissipates when the subsidence reaches the maximum value, signifying the end of a transient consolidation process. By modifying over- and underburden elastic modulus, temporal subsidences are shown in Figure 5. It is seen that the magnitude of subsidence is nonlinearily proportional to that of time. During the evaluated period, the subsidence increases about four times with the reduction of the elastic modulus being only two and half times. The temporal pore pressure distributions subjected to different elastic modulii are depicted in Figure 6, while the difference in the maximum pressures is smaller than that in elastic modulii. This relatively smaller influence is expected since the mechanical properties has an indirect and therefore lesser impact on the changes in fluid pressure. One interesting observation is the slight pressure increase over the original magnitudes at earlier time, a well known Mandel effect. ^ Figure 7 compares the temporal development of normalized surface subsidence at the trough center for the domain with three types of dual-porosity

5 Computer Methods in Water Resources IV Time=10day Time = 100day Normalized subsidence Figure 3: Subsidence along centerline of the panel i iii t iii. \ i\ i \ / Legend Time =1 day Time=10day Time = 100 day Time = 1000 day Normalized pore pressure 1.00 Figure 4: Pore pressure along centerline of the panel.

6 240 Computer Methods in Water Resources IV 0.00 i Legend E = 5e+04MPa E = 2e+04MPa I I '"'""I '"'""I ' i"im -r-mmi '"'""I '"'""I '"'""I '"'""I '"'""I E+1 1E+2 1E+3 1E-+4 1E+5 1E46 1E+7 1E+8 Time (day) Figure 5: Temporal subsidence i J I n linn) i i mini ' ' Him; i i nun; i i mm; i i nun; i i nun; i i mm; E+1 1E+2 1E+3 1E44 1E+5 1E+6 1E+7 Time (day) Figure 6: Temporal pore pressure.

7 Computer Methods in Water Resources IV 241 permeabilities. With similar subsidence profiles at initial stage, the differences are observed only during the late period. Then it is noted that the subsidence slope changes occur when the fracture and matrix permeabilities are smaller. These slope changes resemble the pressure gradient changes reported by Warren and Root* in their dual-porosity model, a consequence of the interporosity flow between these two interacting media. Similar observation can be made to the normalized pressure distributions, as shown in Figure 8. For smaller fracture and matrix permeabilities, Mandel effect appears to be more apparent, and pressure slope changes are more radical, indicating larger interporosity flow. Because the porosity is in general proportional to the permeability for the porous media, the less porous strata appears also to lead to the delayed subsidence i I J I '"'""I M"ini{ iihmi * M.IIII iiinm] i iiiini MIIIIII IMIIIII iiiimi E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 1E+8 Time (day) Figure 7: Subsidence for various permeabilities. The relationship between the normalized subsidence and the fracture spacing at various times is depicted in Figure 9. In general, the smaller the spacing is, the greater the subsidence will be, especially at earlier times. A smaller fracture spacing implies a more densely fractured medium, where larger fracture compressibility results in greater displacement. The influence of fluid flow on the magnitude of surface subsidence can be assessed by the evaluation of Biot's coefficient af which is proportional to pore pressure contribution over the change of rock displacement. Figure 10 indicates that the maximum subsidence will result when a reach one. a

8 Normalized subsidence I _J I L_ Normalized pore pressin s o s- O CO I cr

9 Computer Methods in Water Resources IV 243 is a function of bulk modulus of rock masses as well as that of solid grains. For sedimentary rocks, a usually is within the range of 0.5 to 0.9. Legend Alpha = Alpha = 0.1 Alpha = 03 Alpha =1.0 (Alpha = Boifs coefficient) 400 Distance from centedine (m) 800 Figure 10: Subsidence for various Biot's coefficients. 4 Concluding remarks The results of numerical analysis presented in the previous can be summarized as follows: (a) The transient dual porosity model shows a strong coupling between strata deformation and fluid flow. The changes in the regional pore pressure mainly occur in the vicinity of the mining panel where excessive strains due to mining are expected. (b) The dual-porosity models analyzed may generate larger displacements in comparison with the single-porosity models. This may correspond, in large part, to the inherent compliance of the dual-porosity medium as a result of fracture compressibility. (c) It is found from this study that the induced surface subsidence may be maximized if: (a) long time has elapsed since the mining is over; (b) pore pressure completely dissipates; (c) mechanical properties of overburden and gob are the softest, (d) fracture spacing of the overburden is the smallest, (e) Biot's coefficient becomes one, and (f) fracture and matrix permeabilities are the largest. The maximum possible surface subsidence would result if all the above features are combined.

10 244 Computer Methods in Water Resources IV (d) The most important finding of this research is perhaps attributed to the identification of the influence of fluid flow on the surface subsidence. This impact can become so significant that mining induced surface subsidence might be overshadowed. As a result, where mining under the aquifers and the groundwater is diverted either into the mining panel or to other places, it is crucial to be able to assess the subsidence magnitude through separate calculations of the contribution from the fluid flow and from the underground mining. Under such conditions, the maximum surface subsidence may not be proportional to the thickness of the extracted seam alone, and the subsidence due to fluid drainage must be taken into account. In most cases, the subsidence will be larger under this coupled phenomenon than that subjected to mining only. Acknowledgments Support of the National Science Foundation/State/Industry under the S/IUCRC program and under the contract EEC , and support of China Coal Research Institute under the collaborative contract, are gratefully acknowledged. References 1. Els worth, D. and Bai, M., Flow-deformation response of dual-porosity media, Journal of Geotechnical Engineering, ASCE, 1992, Bai, M., Els worth, D. and Roegiers, J-C., Modeling of naturally fractured reservoirs using deformation dependent flow mechanism, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 1993, Mandel, J., Consolidation des sols, Geotechnique, 1953, 3, Warren, J.E. and Root, P.J., The behavior of naturally fractured reservoirs, 5oc. PeZ. E%#. J., 1963, 3, Biot, M.A., General theory of three dimensional consolidation, J. s., 12, 1941,

11 Computer Methods in Water Resources IV 245 Parameter E V I<n Kf HI %2 k\ln ^2//^ 5 Table 1 Selected parameters in modeling Definition elasticity modulus Poisson's ratio fracture stiffness fluid bulk modulus matrix porosity fracture porosity matrix permeability fracture permeability fracture spacing Magnitude 10* 0.2 2xlO< 10* * Unit MN/nf MN/m^/m MN/nf rn*/(mn s) m</(mn s) m

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