关 键 词：

煤矿 1.8 Mta 设计 CAD 版本

资源描述：

恒源煤矿1.8Mta新井设计含5张CAD图-版本1.zip,煤矿,1.8,Mta,设计,CAD,版本

内容简介：

英文原文Numerical modelling of longwall mining and stability analysis of the gates in a coal mineMahdi Shabanimashcool *, CharlieC.LiDepartment of Geology and Mineral Resources Engineer ing, Norwegian University of Science and Technology (NTNU), Trondheim, NorwayAbstract: This paper presents a novel numerical approach to simulate the longwall mining in detail, aiming to investigate the stability of gates and the loading process to rock bolts. The study site is the Svea Nord coalmine in Svalbard. In the proposed approach, progressive cave-in and fracturing of the roof strata, consolidation of the cave-in materials and stress changes are simulated in detail. The results of the simulations are used to analyse the loading process of the rock bolts in the gates. The numerical model is calibrated with the measurement data. The simulations reveal that the stability of the gates and the loading to the rock bolts are closely related to the width of the chain pillars. With slender pillars, shear displacements along weak inter layers and bedding planes results in heavy loading to the rock bolts. Therefore, the locations of weakness zones should be taken into account for rock bolt design. The proposed numerical approach can be used to find an optimal combination of the dimension of the chain pillars and the rock reinforcement in the gates.Keywords : Longwall mining; Numerical modeling;Coalmine Cave-in of the roof strata;Rockbolt ;Chainpillar1. IntroductionThe stability of gates is essential to ensure the safety of longwall mines. In longwall mines, stope voids are filled by cave- in roof rocks. Roof cave- in causes rock fracturing and yielding as well as stress concentrations in the surrounding ro ck mass. Gates and chain pillars between longwall mining panels are subjected to a complex loading process throughout their service life. Roof bolting is one of the major measures for stabilising gates. Obviously, loading to the rock bolts is caused by the longwall mining. Therefore, analysis of the bolt load can be a proper method for studying the stability of gates. Generally, there are four methods to estimate the bolt load and roof bolting design: empirical, analytical, a hybrid numerical and empirical and numerical method. In empirical methods, design charts are constructed by statistical analyses of the data collected in industrial practices. The bolt load is estimated based on the data collected in a limited number of sites. Such a chart is limited in its ability to take into account the variety of rock conditions and mining sequences. Analytical methods are mainly developed based on elasticity theory. They are appropriate for low-stress conditions in hard rocks. In such a site, it can be assumed that the rock behaves elastically.Lawrance developed a hybrid numerical and empirical method to design rock bolting ingates. A number of datasets regarding rock bolting in Australian coalmines were collected to develop design charts. In that method, simple elastic numerical simulations were used to account for the stress concentrations in gates caused by longwall mining. Numerical modelling can be used to investigate the stability of gates. However, the constitutive models and parameters used to simulate the behaviour of rock masses need to be carefully considered. In addition, it requiresan appropriate algorithm to simulate longwall mining. Many attempted to numerically model longwall mining in the past years. In those attempts, empirical methods, the parameter of bulking factor and field measurements were employed to estimate the height of the cave-in zone. Whittles et al. employed an empirical method to estimate the height of the cave-in zone above a mined-out panel. The empirical method was developed by Bai et al.based on data collected in coal mines in China and USA regarding changes in the hydraulic conductivity in the rocks surrounding the mined-out panels. Trueman and Thin et al. used the bulking factor concept to find the height of the cave- in zone. The bulking factor is implemented to find out a boundary in the roof under which the cave- in rocks fully fill the stope voids. Wardle reported a trial to measure the height of the cave- in zone by borehole drilling from the mine surface to the goaf. Roof cave-in is a progressive process which starts at a critical distance behind the stope face and develops upward in the roof strata with face advance. Cave- in ceases when the volume of the cave- in materials is large enough to fully fill the stope void. All the me thods mentioned above, i.e., empirical method, bulking factor method and drilling method, can be used to find out the maximum height of the cave- in zone. However, numerical modelling is an appropriate approach to assess the dynamic stress state around a lo ngwall face. Moreover, roof strata cave- in not only depends on the geomechcnical characteristics of the roof strata, but also is associated with the height of the stope and the location of the bedding planes at the roof. In other words, it is strongly site dependent.Another issue in modelling of longwall mining is the constitutive model for consolidation ofthe cave- in materials under the weight of the overburden rocks. Trueman implemented a modified stressstrain relationship of a stone-built pack and assumed a maximum volumetric strain of 0.33 for consolidation. Thin et al. used the double- yield constitutive model of FLAC(2D) code to simulate the consolidation of the cave- in materials. They applied the stressstrain relationship by Trueman to calculate the parameters of the double-yield model. The double-yield constitutive model was also used for cave- in materials in the study reported in this paper. In this study a back- calculation approach was applied to assess the parameters of the double-yield model for cave- in materials.This paper presents a novel numerical simulation algorithm to model the longwall mining in the Svea Nord mine. A finite difference numerical code, FLAC（3D）,is used for simulations. A strain-softening constitutive model is used to simu late the nonlinear behaviour of the rock masses. In the simulations, the progressive cave-in and fracturing process of the roof strata and the consolidation of the cave- in materials are modelled. The stability of the gates under different thicknesses of overburden is also studied.Three-dimensional (3D) simulations of the gates with all the rock support devices require a huge computational capacity. For the sake of simplicity, a two-dimensional (2D) model was constructed to simulate the loading process of rock bolts. The boundary conditions of the 2D model were taken from the results of the 3D modelling.2. Study siteSvea Nord is one of the large coalmines in the arctic area. The longwall mining method is used with an annual production of 3 million tonnes o f coal. Longwall panels are approximately 250 wide and 2500 m long. The overburden of the panels varies from 10 to 400 m. In addition, most of the ground surface is covered by glaciers, with an ice thickness of up to 250 m in the mine area. Fig. 1 shows the mine map.Two gates are parallel excavated for every panel. For instance, gates A and B are excavated for panel 1 (see Fig. 1). The rock party between the two gates is the so-called chain pillar, which is 40 m wide. Crosscuts are excavated in the chain pillar about every 75 m between the two gates.In-situ rock stresses were measured in six locations in the mine using the overcoring relief method. The measurements show that both the major and the moderate principal stresses arehorizontal. The major principal stresss 1 is approximately parallel to the longwall panels, whilethe moderate stress s 2is perpendicular. The minor principal stress s 3is vertical and equal tothe weight of the overburden.The horizontal-to- vertical-stress ratios are kmax=2 and kmin=1.7.Fig. 2 shows the vertical geological column in the study site, which is constructed based on core logging. The roof stratum is composed of siltstone and finely grained sandstone .A bentonite seam is 23 m above the coal seam. The roof rocks may be roughly divided into three units. Unit 1 contains the rock party from 0 to 2.5 m in the roof and is composed of siltstone with thin coal interlayers. A layer of bentonite is the upper limit of this unit. Unit 2 refers to the party from 2.5 to 10 m in the roof and is composed of sandstone and siltstone with coal interlayers. This unit is capped by a thin coal layer. Unit 3 is the rock party above 10 m and is mainly composed of sandstone and siltstone.The ground subsidence was measured along the line drawn in Fig. 1. The measurement was started when the fist southern panel of the mine had been mined out and it was continued during mining of the second southern panel of the mine. The maximum subsidence was 1.8 m at the northern end of the line.3. In-situ measurements in the gateA measurement station was set up about 30 m from crosscut 7 in gate B (Fig. 1). Strain- gauge instrumented rock bolts were installed in the roof of the gate. The bolts were 2.5 m long. The strain gauges on all the instrumented bolts except on bolts 5 and 6 became damaged shortly after installation. Thus, only measurement data for bolts 5 and 6 are available for analysis. The instrumented bolts were installed when the excavation face of gate B was about 10 m from the station. Measurements started immediately after the bolt installation and lasted throughout the excavation of gate B and mining of the entire panel 1 until the longwall front of panel 2 reached the measurement statio n. Figs. 3 and 4 show the axial loads and bending moments measured in the two bolts at different excavation stages.It is seen in the figures that the bolt load and the bending moment are mainly built up duringexcavation of the gate. Afterwards, they did not change much over the course of the mining in panel 1. They started to change only when the longwall front reached a distance of about 300 m to the measurement station. However, the changes were not considerable until the distance was shorter than 20 m. The bolt load refers to the pull load subjected by the bolt, while the bending moment is a measure of the shear load laterally applied to the bolt. The measurement data show that the bolts were generally loaded both axially and laterally along their lengt hs. This fact implies that both rock dilation and shear moments between bedding planes occurred in the rock mass.Fig. 1. Mine map:(a) plan view of the longwall panels and close-up of the marked rectangle.Fig. 2. Geological column of the stud ysite.Fig. 3. Distribution of the axial load and the bending moment along rock bolt 5: (a)axial load,(b)bending moment.Fig. 4. Distribution oftheaxialloadandbendingmomentalongrockbolt6:(a) axialload,(b)bendingmoment.4. Numerical simulations(a) Algorithm for simulation of longwall miningIn longwall mining, the roof strata of the panel cave in and fill the stope voids. The cave- in of the roof rock is a complex process that involves not only a large volume of cave-in materials but also fracturing and deformation in the rock stratum above. The cave-in materials are compacted and consolidated afterward, and the stress concentration in the chain pillar is reduced. The roof strata above the longwall panel can be divided into three zones: the cave- in zone, the fracture zone and the continuous deformation zone. In accordance with Duplancic and Brady, the cave- in zone refers to the region in which rock blocks are separated from the host rock strata and fall into the panel void. The fracture zone refers to the region in which rocks are fractured and lose some or all of their cohesion on the fracture planes. The deformation continuous zone consists of two regions: a seismic active zone and an elastic deformation zone. The seismic zone is located immediately above the fracture zone, where micro seismic activities occur on bedding planes and other types of discontinuities. The elastic deformation zone refers to the rest of the rocks above the seismic active zone, which behave elastically.Cave- in is different from yield in a mechanical sense. Yield means that the rock is subjectedeto failure because the stress exceeds the rock strength. Cave-in refers to the disintegration of failed rock pieces, which then move downward because of gravity. Singh and Singh numerically studied the ground pressure on the hydraulic shields next to the longwall face. The criterion for identifying the cave- in rocks in their study is a shear strain of 0.25 or a downward displacement of 1 m. In reality, it is not necessary that rock fails in shear in the case of cave- in. In reality, rock is more than often subjected to tensile failure when cave- in occurs. In addition, the vertical displacement of the cave- in body is associated with the size of the stope void. Therefore, neither shear strain nor the downward displacement is appropriate as a cave- in criterion. In the cave- in area, rock slabs separate from the host rock and move downward. The maximum principal1plastic strainp (in tension) should be an appropriate parameter to o utline the boundary of thee1cave- in zone. In the plasticity theory, the total maximum principal straint is defined ase t = e e + e p（1）111Wheree is the maximum principal elastic strain andp is the maximum principalee11plastic strain. In the cave-in zone, the rock mass yields in tension. The tension strength of the coal rock is very small. The plastic strain is usually much larger than the elastic strain in the cave- in zone, Therefore, it can be said that the total principal strain is approximately equal to the plastic strain, The maximum tensile strain in the roof strata before they cave in is denoted as thecritical cave- in strain（ e e ）.This critical value is used to identify the cave- in boundary. The roofstrata is said to be caving in ife1t e e（2）The bulking factor (BF) is a parameter that represents the dilation of the rock after cave- in. Site investigations in coalmines show that the bulking factor of coal rocks is in a range of 1.11.5. Several studies have proved that the porosity of cave- in materials is approximately 0.3. This porosity corresponds to a bulking factor of 1.43. In this study, the bulking factor is used to determine whether the stope voids are fully filled by cave-in materials. A bulking factor of 1.43 refers to the stope being fully filled. The bulking factor can be estimated by taking into account the change in the size of the cave- in zone with respect to the height of the stope:BF = h c + h crh crWhere hc is the stope height, and hcr is the thickness of the cave- in zone in the roof.（3）Knowledge of the consolidation behaviour of the cave- in material is limited owing to the inaccessibility of the goaf. Pappas and Mark conducted laboratory compressive tests to study the consolidation of loose materials. They claimed that Salamons formula is valid for cave- in materials:o =E0e v（4）1 - e v / evvmWhere s is the applied compressive stress to the loose material while the material isrigidly conned laterally,E0 is the initial tangential modulus of the material, e vis thevolumetric strain and bulking factor :m is the maximum volumetric strain;eve m = BF -1m can be obtained from theev(5)vBFA strain-softening constitutive law is assigned to the rock mass in the simulations. The rock experiences a path of unloading reloading in the fracture zone. The stresses in the fracture zone decrease during cave-in. After cave- in ceases, consolidation of the cave- in materials starts. The stresses at the fracture zone increase again in the consolidation period. The deformation modulus of the rock mass is reduced in the post-failure stage because of the created fractures. In this study, fracturing of the rock above the cave- in zone is taken into account by using a residual strength and a reduced deformation modulus in the models.The double-yield constitutive model is used to simulate the consolidation of the cave- in materials. The mechanical properties of the rock in the cave- in and fracture zones are calculated by back-calculating the subsidence data measured on the ground surface above the mine. Salamons formula, Eq. (4), is used to calculate the cap pressure parameters. The back calculation method is presented in the next section.An algorithm was developed for the numerical simulation of the cave- in and mining process in accordance with the scenario proposed by Peng and Chiang (Fig. 5). The height of thelongwall stope is denoted ashc .The rst cave- in event occurs when the length of the open stopereachesl p . The cave-in rock has a constant thickness of b in the middle of the cave- in zone,while the thickness decreases approaching the longwall front, which results in a concave roof formed by cantilever beams of laminated rock behind the longwall front. With a critical advanceof ls , the cantilever beams break and fall down. Caving in occurs repeatedly with every advanceof lsuntil the panel is completed. The calculation results show that the thickness of the cave- inroof is constant regardless of whether the cave- in occurs for the rst time or during the sequential excavations.Fig. 5. A cave-in scenario in longwall mining.In the proposed algorithm, it is assumed that the roof convergence ceases when the roof of the stope meets the oor. The upper boundary of the cave- in zone is then determined with the criterion described above in Eq. (2). Until this moment, the cave- in materials are loose and do not bear any stress. The volume of the cave- in rocks is checked whether it is large enough to fully ll the stope voids. Caving in ceases when BF1.43. Afterward, the loose materials are compacted and consolidated in the cave- in zone due to the inward deformation of the surrounding rock mass.Fig. 6 is a owchart for the simulation of the mining and cave- in processes. The longwall mining starts with advance of 5 m every time in the beginning. The calculation steps 100 cycles after every excavation round. The unbalanced force in the model is then checked to see whether equilibrium has been reached. A further 100 calculation cycles are run if the unbalanced force islarger than10-5and the maximum vertical roof displacement is smaller than the stope height.This iteration continues until the unbalanced force becomes le ss than10-5, and then, a furtherexcavation advance is performed. The iteration ceases when the maximum vertical displacementof the stope roof, d max , is equal to the height of the stope void, h . The roof of the stope void hasmet the oor whenzdmaxz hcc.The boundary of the cave- in zone is then identied by the criterione1oft= e e .Fig. 6. The owchart for modelling the longwall mining process by FLAC (3D) .Bulking factor is calculated by Eq.（3）. The BF is innitive before cave- in occurs and gradually declines with the upward extension of the cave- in zone. In the numerical modelling, calculation iterations are carried out and the bulking factor is checked. Excavation advances until the bulking factor reaches 1.43, which indicates that the cave- in materials have fully lled the mined-out void underneath and the cave- in process stops. From now on the cave- in materials will be consolidated under the pressure of the strata above. A double-yield material model is used for simulating the consolidation of the cave-in materials. Accordingly, the mechanical properties of the nulled mesh elements of the model in the stope voids with BF1.43 are changed to the double-yield model. The elastic properties, i.e., the Youngs modulus and Poissons ratio, of the rock mass in the fracture zone are then reduced for a certain amount from their originalvalues. At this moment, the critical cave- in length l pand the thickness,b, of the cave- in strataare determined. After that, a similar excavation process is done to nd the critical advance lengthls . Finally, the longwall face advances a length of lssevery time and calculation iterations arecarried out to update the boundary of the cave- in zone and the bulking factor. This process continues until the entire panel is mined out.(b) Determination of the critical cave -in strain and the mechanical prope rties for the cave-in and fracture d materialsThe critical cave- in strain, e e , was used in the algorithm to outline the border of the cave- inzone. It represents the maximum value of the extension strain the roof strata could sustain beforecave- in. The critical strain e edepends on the quality of the roof strata, the thickness of the eachstratum andthe stress state.There areno straightforwardmethods toobtaine e .Back-calculation of measurement data is the most reliable way to do it. In the study site, the ground subsidence was once measured in the location marked in Fig. 1. The subsidence dataalong the measurement prole there was adopted to back-calculate the critical strain e emechanical properties for the cave- in and fracture zones.and theIt is recommended that the acceptable range of the critical strain should be pre-dened for back-calculations. Coal rocks have low ultimate tensile strains. Therefore, it was assumed that the critical strain of the rock strata in question is less than 10% in Table 1 the back-calculations.The consolidation of the cave- in materials is simulated by using the double-yield constitutive model. The cohesion of the cave-in materials is assumed zero and their inherent basic friction angle is about 30 degrees. The cap pressure and the maximum volumetric strain were calculated with Eqs. (4) and (5), respectively. The initial tangential mod ulus of the cave- in materials Eo was obtained by back-calculation. Laboratory compressive tests of the cave- in materials revealed that the initial tangential modulus of the cave- in materials with considering the compressive strength of the roof strata is about 80 MPa. In the back calculations it wasassumed60MPa E0 100MPa .The E modulus of fractured rocks above a cave- in zone is assumed about 500 MPa. In our back-calculations the E modulus was limited to a range larger than the initial tangential modulus of the cave- in rocks and smaller than 500 MPa i.e., 即 E0 E 500MPa . The Poissons ratio of the fractured rocks was assumed 0.3.The numerical simulation code of FLAC 3D was used in the back-calculations. The shape and the boundary conditions of the model is similar to the one shown in Fig. 7. However, t hemodel has a dimension of100 300 400 m (lengthwidthheight). The mechanical propertiesof the rock masses and the discontinuities assigned to the model are presented in Tables 1 and 2, respectively. The longwall mining process was simulated according to the algorithm shown in Fig. 6.In the simulations, three E-modulus values were assumed for each of the cave- in zone andthe fracture zone. For the cave- in rock, they areE0 =50, 80 and 100 MPa and for the fracturedrock E =100, 200 or 400 MPa. The critical strains for the trials are e e =2%, 5% and 10%, respectively. It was found in the simulations that use of 10% for the critical strain resulted in unrealistic subsidence data so that only it was disregarded in the subsequent simulations. Thesubsidence obtained forE0 =80 MPa are presented along the measurement line in Fig. 8. In thegure the measurement data are also plotted for comparison. It is seen that the simulatio n result by usinge e e = 5% and E =150 MPa matches very well the measurement data.The approved mechanical properties of the cave- in materials and fractured rocks arepresented in Table 3 and cave- in zone.e e = 5% was chosen for the criterion to outline the border of theFig. 7. (a) The three-dimensional model.(b)Vertical cross section in the yz plane.Fig. 8.Ground subsidence prole for the group of the simulations with Eo=80 MPa and E=120 and 150 MPa.Table 1 Mechanical and physical parameters of the rock mass.Rock massCoalSandstoneSiltstoneK (GPa)2.336.85.3G (GPa)0.55.13.2c (MPa)1.062.81.9f (deg.)294937o t (MPa)0.0330.280.42cr (MPa)0.01060.280.19fr (deg.)293030ep (%)0.50.050.05K is the bulk modulus,G the shear modulus,c the cohesion, f the internal friction, s tthetensilestrength,cr the residual cohesion,fr the residual friction and ep the plastic strainparameter at the residual strengthTable 2 Mechanical properties of the discontinuities used in the numerical modelsDiscontinuityCohesion(MPa)Frictio(deg.)Tensile strength (MPa)Bedding0.3300.03Thin coal interlayer0.3300.1Bentonite inter layer0.5250.4Table 3 Mechanical properties of the cave-in and fracture zones.Note:e v the volumetric strain;e m the maximum volumetric strain, P the cap pressure,Eo the initialvtangential modulus,C the cohesion,E the Youngs modulus and v the Poissons ratio.(c) Simulation of longwall miningThe proposed algorithm was implemented for the study site in the Svea Nord mine. The 3DFLAC model has dimensions of100 300 400 m (lengthwidthheight). The geometry andthe boundary condition of the model are sketched in Fig. 7. The pro le of the eld measurement station is included in the model. The o verburden in the position of the measurement station is 110 m with a glacier of 250 m. A nonlinear strain-softening constitutive law was used for the rock mass. The mechanical and physical properties of the rock mass are presented in Table 1. Bedding planes and bentonite and coal interlayers are modelled as discontinuities in the model. The mechanical properties of the discontinuities are presented in Table 2.Fig. 9. Height of the cave-in/fracture zone above the longwall panel.In the Svea-Nord mine, the longwall stopes usually start to cave in when the mined out distance reaches about 36 m. This gure is used to validate the model. The model is then used for the simulation of the entire mining process. Fig. 9 shows the simulation results on the dimensions of the cave- in and fracture zones above the mining panel. It is seen that the rstcave- in distance ( l p ) is about 36 m in the 4-m- high longwall stope. The height of the cave- in zone increases from zero at the longwall front to about 16 m when the distance to the longwall front is beyond the cave- in distance (36 m). The fracture zone has a height of about 110 m in thecave- in area. It shows that the fracturing of the rocks would propagate to the ground surface in the shallow parts of the mine.(d) Modelling of the bolt loadWe desired to compare the numerical modelling results of the bolt load with the in-situ measurement data obtained for gate B. The 3D model was too large for such detailed modelling. Therefore, a 2D model was estab lished for this purpose. The 2D model was constructed in a vertical cross section in the YZ plane in the middle of the model where the in-situ measurement station was located (Fig. 7). A plain strain condition must remain valid for 2D models. Three-dimensional modelling was conducted to check how the plain strain condition could be achieved when the 3D problem was simplied to a 2D problem. The modelling showed that the plain strain condition remains valid in the vertical cross section prole until the longwall front reaches about 20 m from the prole. The boundary conditions of the 2D model were identical to the 3D model except on the upper boundary, where a distribution of the vertical stress and in-plane shear stress is applied. The vertical and shear stress on the upper boundary change with the advance of the longwall front. It is determined in the 3D model and then applied to the 2D model.Fig. 10 shows the 2D model. The normal and shear stresses applied on the upper boundaryof the model are different at different mining stages and are determined in the 3D model. They are presented in detail in Fig. 11 for different mining stages. It is seen that the vertical stress is very low close to the chain pillar in panel 1, which is lled by cave-in materials. The stress approaches its original state at long distances from the chain pillar. A large stress elevation occurs in the chain pillar. The vertical stress increases gradually in panel 2 when the longwall front approaches the prole. The shear stress has its maximum above gate A and decreases with the distance apart from the gate.The computer program Phase 2 was used to run the 2D model. The physical and mechanical properties of the rock mass and discontinuities are identical to those in the 3D model (Tables 1, 2 and 3).The bolts are simulated by fully bonded elements of the software. Their mechanical parameters are presented in Table 4. The modelling results of the axial load for bolts 5 and 6 are presented in Fig. 12. In comparison to Figs. 3 and 4, the modelling results are generally consistent with the measurement data. The modelling results deviate from the measurement results in the position close to the roof surface. The reason for this deviation may be that themodel used a continuum material, while the real roof strata contain bedding planes. The discrete separations of the bedding planes may induce local high loads in the rock bolts. It is also observed in the numerical modelling that the axial load in the rock bolts is mainly built upFig. 10. Geometry and boundary conditions of the two-dimensional model.Fig. 11 .Stress distributions applied to the upper boundary of the two-dimensional modelat different stages. (a) The vertical stress. Negative values indicat e compressive stresses. (b) The horizontal in-plane shear stress.Table 4 Mechanical parameters of the rock bolts in the two-dimensional modelE(GPa)d(mm)Ultimate axial strength(kN)Out of plane spacing20021.73000.5E is the Youngs modulus of the bolt material and d is the diameter of the bolt.5. DiscussionSensitivity analysis was conducted to study the effects of the chain pillars and the disturbed zones (i.e., the cave- in and fracture zones) to the loading of rock bolts in the gate.(a) On the cave-in zoneFig. 13 illustrates the height of the cave- in and fracture zones with respect to different overburdens. The nal height of the cave- in zone is a constant regardless of the overburden. It is mainly related to the strength of the roof strata and the locations of the weakness planes in thehanging wall. The major cave- in distance ( l p ), however, is affected by overburden. It becomes shorter when the overburden increases. This change is because of higher tension stresses induce in the roof under a large overb urden. The height of the fracture zone increases slightly with an increase in the overburden.Fig. 12. The numerical results of the bolt load in two rock bolts:(a)bolt5, (b) bolt6.(b) Influence of the chain pillarThe influence of the pillar width on the load on rock bolts was studied numerically. Three pillar widths, 30, 40 and 50 m, were used for the simulations. Fig. 14 shows the modelling results of the load distribution in bolt 5 in gate B. The bolt load changes abruptly at a depth of1.5 m because of the existence of a weak coal seam. The maximum bolt load increases with a decrease in the width of the chain pillar. The bolt load was further studied by varying the thickness of the overburden (Fig. 15). Under an overburden thicker than 400 m (300 m rock+100 m ice), the bolts are subject to failure when the chain pillar is less than 40 m wide.Shear displacement occurred along the coal seam located at a depth of 1.5 m in the roof of the gate B. The relative shear displacement between the upper and low er limits of the seam is presented in Fig. 16 with respect to three different pillar widths. The shear displacement will load rock bolts laterally and induce bending moments in the bolts. The shear displacement increases with a decrease in the pillar width. Therefore, rock bolts are more highly shear loaded in the case of a thin chain pillar than a wide pillar.Fig. 13. Height of the cave-in and fracture zones under different overburdensFig. 14. Numerical results of the axial load in bolt 5 under an overburden of 110 m of rock and 250 m of ice.Fig. 15. Influence of the width of the chain pillar. Maximum axial load of the rock bolts in gate B versus the width of the chain pillar for different overburden conditionsFig. 16. Relative shear displacement along the coal seam at a depth of 1.5 m in the roof of gate B after completion of mining in panel 1.(c) Stress changes in the mining regionThe stress changes in the rock and the cave- in materials obtained from the 3D model are shown on a horizontal plane located 2 m above the stope roof. It is assumed in the model thatpanel 1 has been completely mined out and panel 2 is half mined out. The width of the chain pillar is 30 m, and the overburden of the model consists of 110 m of rock plus 250 m of ice. The distribution of the vertical stress on the horizontal plane is shown in Fig. 17(a). The vertical stress on the plane is quite low in areas close to the chain pillars in the mined-out regions. The vertical stress returns to its original state in the central areas of the mined-out regions. Stress concentration occurs also in the un- mined party of rock in panels in front of the longwall front and along gate B. The vertical stress is elevated in the position of the chain pillar, particularly in the completely mined-out region. It is worth pointing out that the vertical stress in the chain pillars is highly elevated for about 50 m ahead of the longwall front.Fig. 17(b) shows the horizontal stress parallel to the longwall front. It is obvious that low horizontal stresses occur in the mine- out regions because the cave- in materials are loaded mainly vertically. The horizontal stress increases ahead of the panel face along gate B for 30 m.Fig. 17.Vertical and horizontal stresses on a horizontal plane located 2 m above the stope roof in thethree-dimensional model. (a) Vertical stress. (b) Horizontal stress s yy is parallel to the longwallface.6. ConclusionComprehensive numerical simulations were carried out to study the stability of the ga tes and the loading to rock bolts installed in the gates in the Svea Nord Coalmine. A numerical algorithm was developed to simulate the longwall mining process. The simulations involved rock fracturing, cave- in and consolidation of cave- in materials. The numerical results of bolt load were consistent with the eld measurement data.Both the eld measurement data and the numerical results show that the loading to the rock bolts installed in gates occurs mainly during excavation of the gate. Mining in panels does not cause signicant load increments in the bolts. The current width of the chain pillars, 40 m, is wide enough to provide protection to the gates from disturbance of the panel mining under an overburden of 110 m of rock plus 250 m of ice. Under larger overburdens, panel mining would cause signicant load increments in bolts.The dimension of the chain pillar has a signicant inuence on the stability of the gates and the loading to rock bolts. In the case of thin chain pillars, shear displacements o n weakness zones would cause stability problems in the gates. Therefore the locations of weakness zones should be taken into account for support design.AcknowledgmentsThe authors would like to thank the Svea Nord Coal Mine for their permission of using t he in-situ measurements. Particular thanks are given to David Hovland for his assistance in the course of the study中文译文煤矿长壁开采面和回采巷道稳定性数值模拟研究Mahdi Shabanimashcool *, CharlieC.Li挪威，特隆赫姆市，科技大学(NTNU)，地质与矿产资源工程部摘要：本文提出了一种新的数值模拟方法，通过详细地模拟长壁开采,旨在研究巷道的稳定性和巷道锚杆的负载过程。研究地点选在斯瓦尔巴群岛 Svea Nord 煤矿，在研究中详细模拟了顶板跨落和压裂过程以及跨落岩石的压实和应力变化过程，并将模拟结果用于分析巷道中锚杆的负载情况，经过数值模型与测量数据的校准，结果表明巷道的稳定性和锚杆的负载情况与护巷煤柱宽度密切相关。留设较窄护巷煤柱情况下，沿着软弱夹层和层理面发展的剪切位移会增加锚杆的负荷，因此,在锚杆设计中，应考虑软弱岩层区域的位置，并通过数值模拟方法寻找到最合适的保护煤柱尺寸，从而加固巷道围岩。关键词：长壁开采；数值模拟；煤层顶板跨落；锚杆；护巷煤柱1 引言巷道的稳定性是确保长壁工作面开采安全至关重要的因素。在长壁开采过程中，采用自然跨落处理采空区，跨落是由上覆岩层断裂和变形引起巷道围岩应力集中所造成的，巷道和护巷煤柱在其服务年限内还会受到复杂的应力变化过程。锚杆支护是维护巷道稳定性的重要措施之一，显然,采动引起了锚杆负载增加，因此,分析锚杆负载是一种研究巷道稳定性的可靠方法。一般而言,有四种方法可估计锚杆负载和设计顶板支护:经验法,分析法， 数值经验结合法以及数值模拟法。经验法中，图表的数据来源于有限的工业实践中，锚杆负载就是基于有限的煤矿数据，所以这种图表的适用性也是有限的；分析法的设计开发主要基于弹性理论，适用于坚硬岩石中压力较小的条件，并往往假设岩石呈弹性表现。Lawrance 开发了数值经验结合法用于设计巷道锚杆支护。他从澳大利亚煤矿收集了有关锚杆的大量数据用于设计图表，用简单的弹性数值模拟来解释由开采造成的应力集中， 通过数值模拟观察巷道的稳定性。该方法除需要认真考虑模拟岩体活动的本构模型和参数之外，还需要一个合适的算法来模拟长壁开采，在过去几年有很多人试图对长壁开采进行数值模拟，因此可通过经验法，用那些试验中的体积膨胀系数和实地测量数据来估计跨落带的高度范围。例如：Whittles et al.曾采用经验法估计出了采空区上方跨落带高度；Bai et al.依据中美煤矿采空区围岩水力传导性变化中收集的数据扩展了经验法；Trueman and Thin etal.使用体积膨胀系数的概念找到跨落带高度范围，并计算出了顶板跨落岩石完全填充采空区时的临界值；Wardle 还发表了一个通过打地面钻孔到采空区来测量跨落带高度的实验。顶板跨落是一个循序渐进的过程，随着工作面推进逐渐向采场上覆岩层发展，到跨落岩石足以完全填充采空区时停止。上面提到的所有方法,即经验法、体积膨胀计算法和钻探方法都可以用来找出跨落带的最大高度。数值模拟是在长壁工作面动态应力状态评估的一种适宜方法。此外,还应注意到顶板岩层跨落不仅取决于顶板岩层的特性,也与采场的高度和顶板层理位置密切相关，换句话说,它具有强烈的矿点依赖性。长壁开采的模型是在上覆岩层的重量下压实跨落岩块的本构模型。Trueman 通过一个改进砌体的应力-应变关系,得出了最大体积应变率为 0.33，Thin et al.使用 FLA（2D）程序中双面屈服本构模型来模拟压实塌落岩石的过程，并通过 Trueman 得出的应力应变关系来计算双面屈服模型的参数。在本文中也使用双面屈服本构模型研究跨落石块，并使用反算法来评估双面模型的参数。本文提出了一种新的数值模拟算法来模拟 Svea Nord 煤矿的长壁开采，通过有限差分数值代码和 FLAC（3D）软件，用应变软化本构模型来模拟岩体的不规则运动，建立了顶板跨落、顶板岩层断裂和跨落岩石压实过程的模型，同时也研究了不同厚度覆岩下巷道的稳定性情况。巷道支护的三维(3 D)模拟需要很大的计算能力，为了方便起见,用二维(2 D)模型模拟锚杆的负载过程，用 3 D 模型决定 2 D 模型的边界条件。2 矿区概况Svea Nord 是北极地区的一个大型煤矿，年产 3 Mt 吨，使用长壁开采方法，工作面宽约 250，长约 2500 m，覆岩厚度从 10 到 400 m 不等,地面大部分有冰川覆盖,冰层厚度达 250m，图 1 是矿区地图。煤矿采用双巷掘进，例如,采面 1 的巷道 A 和 B(参见图 1)，两巷之间即是保护煤柱,宽40m，两巷之间每隔 75m 掘进一条联络巷。在该矿六个地点使用套孔解除法测量原岩应力，测量结果表明,最大主应力和中等主应力均为水平应力，最大主应力s 1 近乎平行于工作面长边,而中等主应力s 2 是垂直于工作面长边，最小主应力s 3 是垂直与工作面平面且等于上覆岩层的重量，水平应力与垂直应力的最大最小比值是 kmax = 2 和 kmin = 1.7。图 2 是该矿基于钻孔绘制的综合地质柱状图。顶板岩层由沙质泥岩和细砂岩组成，粘土层距离煤层是 23m，顶板岩石大致可以分为三个部分，第一部分包括顶板中 0 到 2.5m的岩层，由含薄煤夹层的砂质泥岩组成，粘土层是这部分的上限；第二部分是 2.5 到 10m 的岩层，由砂岩和含煤夹层的沙质泥岩组成，这个部分是上限是上层的薄煤；第三单元范围在 10m 之上的岩层,主要是由砂岩和沙质泥岩组成。地面沉降是沿着图 1 所示直线进行测量的。测量从南边第一个采面开采完毕开始，持续到南边第二个采面采出为止，最大下沉量为 1.8m 位于测量线北部端头。图 1 矿图：长壁开采平面图和标记矩形区放大图3 巷道中地应力测量图 2 综合地质柱状图在巷道 B 中建立一个离联络巷 7 约 30m 远的测量站 (图 1)，在巷道顶板上安装上带有应变计和仪表的测量锚杆，锚杆长 2.5m。除了锚杆 5 和 6，所有电阻应变计安装后不久就损坏了，因此,仅锚杆 5 和 6 的测量数据可供分析。测量锚杆是在巷道 B 掘进到远离测量站10 之后开始安装的，锚杆安装后即开始测量,巷道 B 的掘进和采面 1 的开采完成后，到采面 2 推进到测量站位置为止，图 3 和 4 显示了两根锚杆不同时期的轴向载荷和弯矩。可以看到，锚杆负载和弯矩主要是在巷道掘进过程中开始出现，随后在工作面 1 开采过程中并没有太多变化，当工作面推进到距离测量站约 300m 的位置才开始变化，但改变量也比较小，直到工作面推进距离测量站小于 20m 时才发生较大的改变。锚杆载荷是指在加载在锚杆之上的应力,而弯矩是用于衡量作用于锚杆之上的横向剪切应力。测量数据表明, 锚杆受力一般都在沿其长度的轴向和切向方向，这意味着岩体结构面之间出现了膨胀扩容和剪切滑移现象。图 3 锚杆 5 的轴向载荷和弯矩分布：（a）轴向载荷，（b）弯矩图 4 锚杆 6 的轴向载荷和弯矩分布：（a）轴向载荷，（b）弯矩4 数值模拟4.1 长壁开采仿真模拟长壁开采过程中，工作面顶板岩层跨落填充采空区一个复杂的过程,不仅涉及大量跨落岩石,还有上部岩层的压裂和变形，跨落岩石后将被压实合并,减少了集中在保护煤柱上的应力。采场上覆岩层可以分为三个带:跨落带,裂隙带和弯曲下沉带。按照 Duplancic and Brady 的定义,跨落带是指与主岩体分离并向采空区跨落的区域；裂隙带是指岩体破碎并失去部分或者全部粘聚力的区域；弯曲下沉带分两个区域：震动活跃区和弹性变形区，震动活跃区紧靠于裂隙带上方，该区微震活动多发生在层理面和其他类型的不连续区域；弹性变形区是指保持其弹性且位于震动活跃区之上的其余部分。1顶板跨落不同于机械意义上的屈服，屈服意味着岩石所受到的压力超过其强度而遭到破坏，而跨落是指岩石解体在重力的作用下向下移动。Singh 定量地研究了综采工作面液压支架上的压力，研究中定义跨落带的标准是剪应变值达 0.25 或向下位移达 1m，事实上, 就顶板跨落来说，围岩受到剪切破坏的可能性是较小的，而多是受到拉伸破坏，此外,冒落岩体的垂直位移是与采场的空间大小有关的,因此,无论是剪应变还是垂直位移都不适合作为跨落带的衡量标准。最大主塑性应变(张力) e p 是描述跨落带边界的一个适当参数，根据1塑性理论,总最大主应变e t 被定义为：e t = e e + e p（1）111其中e e 是最大主弹性应变， e p 是最大主塑性应变。跨落带岩体在张力下逐渐屈服，11岩体中张力是非常小的，跨落带的塑性应变的通常是远远大于弹性应变,因此,可以说总主应变约等于塑性应变, 顶板岩层的最大拉应变可用来表示临界跨落应变值（ e e ）, 这个临界值用来确定跨落的边界条件，当满足e1t e e（2）采场上覆岩层发生跨落。体积膨胀系数是一个表示跨落岩石体积扩张程度的参数，煤矿现场调查表明,煤岩体体 积膨胀系数范围在 1.1 - -1.5 之间，研究表明跨落石块的孔隙度大约是 0.3，这个孔隙度对应于体积膨胀系数 1.43。在该研究中,用体积膨胀系数决定采空区能否被跨落岩石完全填充， 当体积膨胀系数为 1.43 时即可认为采空区能被完全填充，通过一定的采场高度，考虑跨落带高度，就可估算出体积膨胀系数：BF = h c + h crh cr其中 hc 是采高；hcr 是顶板跨落带高度（3）由于采空区的未知性局限了对跨落带压实过程的了解。Pappas and Mark 进行了松散材料的受压实验，证明 Salamon 的公式对跨落岩石有效:o =E0e v（4）1 - e v / evvm其中s 加载在松散材料上的横向刚性压力；Eo 是材料的初始切向模量； 变； e m 是最大体积应变； e m 是可由体积膨胀系数得出:e v 是体积应vve m = BF -1(5)vBF岩体的模拟使用了应变软化本构关系。裂隙带的岩体经历了从卸载到重新加载的过程， 在跨落过程中，裂隙带的压力减小，跨落停止后,开始压实岩块，压实过程中裂隙带所受压力又重新升高，到峰后阶段再生裂隙使岩体的变形模量降低。在这项研究中,跨落带上方的 岩石的破裂强度可由模型中的剩余强度和减少的变形模量推出。通过双面屈服本构模型模拟跨落岩石的压实过程，裂隙带和跨落带岩石的力学性能由地面测量的下沉值经过反算得出，可用 Salamon 的公式(4)来计算上限压力，反算法是在下一小节中介绍。依据 Peng and Chiang 提出的方案，建立了顶板跨落和开采过程数值模拟的算法 (图 5), 采场采高记作hc ，当工作面推进长度达到l p 时，顶板初次跨落。跨落带中部的高度基本恒为b ,当靠近工作面时其高度减小,中间的岩层悬臂梁导致形成凹形顶板，当达到临界距离ls 时，悬臂梁断裂跨落，此后每次推进达到临界 ls ，顶板就重复一次跨落直到工作面开采完成。计算结果表明,跨落带的厚度与第一次跨落还是在开采过程中跨落无关。在方案算法中,假定当回采工作面顶板与底板接触后顶板即停止下沉，跨落带的上界由前述式(2)中描述的准则所决定，跨落石块的体积可检验其是否能够完全填充采空区，当BF1.43 顶板停止跨落，随后由于围岩变形使跨落带松散岩石压实合并。图 6 是采矿和顶板跨落的模拟流程图。长壁工作面每次开始以进尺 5m 推进,每个开采循环需进行 100 次循环计算，然后检验模型中的不平衡力是否达到平衡，若不平衡力大于10-5 ，模型将另外进行 100 次循环计算，保证顶板的最大垂直位移小于采场的高度的前提下，迭代计算将持续进行直到不平衡力小于10-5 ,然后,使用更大的开采进尺进行计算。当最大的垂直位移采场顶板 d max 等于采空区高度h 时迭代停止，当d max h时，顶板和地板zczc1相接触。由准则e t = e e，可确定跨落带边界，膨胀系数由公式（3）计算，体