翻译部分英文原文Finite element analysis of three-way roadway junctions inlongwall miningR.N. Singh, I. Porter, J. HematianFaculty of Engineering, UniÍersity of Wollongong, Northfields Avenue,Wollongong, NSW 2522, AustraliaAbstract:This paper presents a three-dimensional finite element analysis of three-way roadway intersections in longwall mining, and assesses the stable/unstable behaviour of three-way intersections under a range of loading conditions. Loads were applied to the model by means of uniform stresses on the internal free faces. This method of loading the model from the inside helped to reduce its size and to eliminate the boundary effects. Stress concentrations and displacement results on the mid-height of the pillars, roof and floor strata adjacent to the three-way intersections and cut-throughs were calculated.Based on this study, guidelines for designing the support system for three-way intersections are suggested. The results were validated by a case study of a three-way intersection in an underground coal mine in the southern coal fields of the Sydney Basin.Keywords:underground coal mining; gate roadway; intersections; stability; finite element method1. IntroductionA trend exists in Australia for installing high productivity longwall faces producing 3.0~4.0 milliontonne raw coal per annum per face. The mainconcern for the success of the high-production longwallfaces is to achieve high rates of developmentand to maintain stability of access roadways andtheir intersections during the life span of the face.Intersections are formed when the pillars betweenthe two roadways are intersected by driving a crosscut. Roadway intersections in underground mines areparticularly susceptible to ground control problemsdue to inherently wide roof spans used and the difficulty in installing roof supports promptly inhighly mechanised headings. Stresses induced duringintersection formation may result inhigh incidenceof roof and rib failures. Despite many investigationsinto the stability of gate roadways intersectionsadverse conditionssuch as high horizontal stress and unsteady state ofabutment pressure from moving longwall faces maycause instability of gate roadway intersections.For example in 1985; major strata control problems inthe main gate of no. 6 longwall panel at WestcliffColliery resulted in roof fall, which stopped coalproduction for a period of 6 weeks. Similarly, a rooffailure incident at Pacific Colliery caused the longwallequipment to be buried resulting in stoppage ofthe longwall operations for a period of 3 months.Thus, unprecedented stratacontrol problems may have significant effects onoverall production from high-productivity longwallsystems even over a short duration.This paper containsan investigation of the application of a three-dimensionalfinite element method to calculate stressesand displacement around three-way roadway intersections.The effects of individual parameters such as depth of cover, the ratio of horizontal to verticalstress (K) and the width of opening on the stability of the three-way intersections are examined. Theresults are compared with the field observations at anunderground coal mine in the southern coal field ofthe Sydney Basin.2. Stability analysis of three-way intersections using three-dimensional finite element modelsThe procedure used in the stability analysis of thethree-way intersections comprised of defining themechanical properties of the rocks surrounding theintersection, the geometry of the intersection and thevirgin state of stress. The stresses and displacements induced around the intersections were computed usinga three-dimensional finite element method. Ifunstable conditions existed, either the design of supportsystem was changed or the geometry of thestructure was modified.Important input data forthese models were vertical stress and the ratio ofhorizontal to vertical stress K for a given lithologyand dimensions of the roadway intersection .Assuming symmetrical conditions around a threewayintersection, only half of the structure wasmodelled using eight-node solid elements comprisinga total of 7190 elements and the 11 597 grid points.The computer running time was 17 h using around 1Gb of memory. The rock mass properties assigned tothe intersection model are presented in Table 1.The loads were applied to the model by means ofuniform pressures on the internal free faces. Thistechnique of applying load from the inside helped to reduce the size of the model and to eliminate boundaryeffects. For all the loading configurations depictedin Table 2, a linear solution method was used.Preliminary computer analysis was carried out tocompute the induced vertical stress distributionthroughout the three-dimensional model for a litho-staticcondition. In order to gain better understandingon the behaviour of the structure, the vertical stressconcentration on various horizontal and verticalplanes was shown for different loading conditions byplotting stress concentration contour lines for variousratios of induced virgin stresses. These results are discussed in the subsequent sections.3. Pillar behaviour at three-way intersectionFig. 2 indicates vertical stress concentration at themid-height of the pillar for various loading configurations.For the litho-static stress condition at K=K x=K y=1, the stress concentration at the midheight of the pillar has a symmetrical pattern (see Fig. 2a). The stress concentration zone on the ribside of the intersection has a width of 2.5 m, equal tohalf the roadway span. The maximum stress concentrationis about 1.4 times the virgin stress for theloading configuration K y>1 for a limited zone at the corner of the pillar.When K y >1, the vertical stress pattern at the mid-height of the pillar is no longer symmetrical;thestress is more pronounced along the roadway perpendicularto the direction of maximum horizontal stress(see Fig. 2b).No tensile zone along the rib side wasdetected. The maximum stress concentration zone islocated close to the edge of the pillar and extends along the roadway perpendicular to the major horizontal stress.4. Roof behaviour at three-way intersectionThe vertical stress distribution on a plane 1.5-mabove the roof line is shown inFig. 3, which indicatesthat the stress is 0.8z σ over the edge of pillar increasing to 1.0z σ at a distance of 6 m within the edge of the pillar. The stress distribution lines abovethe individual roadways show the contour lines atintervals of 0.2z σ.This stress distribution pattern indicates a semi-dome shaped destressed zone overthe three-way intersection. When the ratio of horizontalto vertical stress, K x or K y increases, the stress contour line 0.2 z σ moves towards the centre of the roadway while 1.0z σ line moves further into the pillar indicating that the height of the semi-domeshaped destressed zone becomes shallower in thefield of high horizontal stress.When K x ≠K y , as shown in Fig. 3b, the stresspattern varies over the individualroadways and 0.2z σpartly disappears in the roadway perpendicular to themajor horizontal stress. In this case, the boundary ofthe roof fall in this roadway will be controlled by thestress contour lines of 0.4z σ .However, the rate of changes in stress distribution across the roof line ofthe roadway parallel to high horizontal stress is moresignificant. The height of the roof fall in the roadwayintersection might be evaluated by using appropriatedestressed contour lines on the vertical plane at themid-span of the main roadways and the cut-throughs,respectively, as presented in Figs. 4 and 5. Thejustification of using 0.4z σ contour line to delineate the boundary of roof fall is presented in a subsequentsection.Fig. 5 Vertical stress concentration on the vertical plane at the mid-span of thecut-through.Fig. 5 also indicates that the radius of influence ofthe intersection over theindividual roadways with respect to the stress distribution in the roof is estimatedto be one span from the centre of the intersection.Fig. 6 shows the vertical displacement on the roofline under various loadingconfigurations at the roadwayintersection. The maximum sag occurs at the centre of the intersection and its maximum value is12 mm. It can also be seen that the roadway parallelto the major horizontal stress will show more roofsag than the roadwayperpendicular to the horizontalstress.Behaviour of the floor at the T-junction of athree-way intersection is given in Fig.7 on the floorline for loading configuration K x=1 and K y=2. The floor lift patterns are similar to that of the roofsag except that the amount of the maximum floorheave is much less than the corresponding value forsag.5. Case history of three-way intersectionsAn investigation into the mechanism of instabilityat roadway intersections was carried out at tail gatesof a longwall panel in an underground coal mine inthe southern coal fields of the Sydney Basin. Thefield measurements included roof sag, floor heaveand rib deformation monitoring ahead and behind thelongwall face. The overall objective of this studywas to validate the results of three-dimensional finiteelement modelling of the three-way junction by comparingthe results with the field measurements.5.1. Site location and the description of the site-specific ModelFig. 8 presents the details of the longwall panel, gate roadways and intersections at the site beinginvestigated. The panels were 200-m wide and 2000-m long with a double entry gate roadway system.Each roadway was 5 m wide, 3 m high, with 55×40 m pillars centre-to-centre. The height of extractionvaried between 2.4 and 2.6 m.The actual sites ofmonitoring were 35, 36 and 9 intersections of 24longwall’s tail gate and 35 and 36 cut-throughs. Thevertical stress at the site was 10 MPa at the depth of420 m, the major horizontal stress 25 MPa orientedparallel to the gate roadways andthe minor horizontalstressThe mechanicalproperties of the strata units are shown in Table3. Based on the above information, a number ofthree-dimensional finite element models were constructedand analysed to simulate the existing conditionsaround the sites of investigation. Both inducedstresses and displacements around the roadways andintersections were computed for each site of investigation. The results of the finite element analyses arepresented together with the values obtained from thefield displacement measurements.A series of roof, rib and floor extensometers were installed at and in between 35,36 and 9 cut-throughsahead of 23 longwall panel. The objective of thisstudy was to determine the pattern of deformationaround the area of investigation and provide a measureof ground control. The extensometers site andlocation for principle modes of failure are also presentedin Fig. 8.The roof sag measurements have been carried outat different locations and compared with values predicted by the finite element model.In all cases,Table 3 Mechanical properties of rock at the site of investigationThe differences between the measured and predicted values are very small. Fig.10 indicates typical results of roof sag measurements, together with the predictedvalues of displacements at 9 cut-through, before andafter the longwall face has passed through the monitoringsite.Monitoring continued when the longwallface approached and passed 9 cut-through andreached the end of the panel. Readings were regularlytaken over a period of 45 days, but for the sakeof simplicity, only the initial and final readings areshown.It can be noted that the difference betweenthe initial and final readings was very little. Therefore, it can be concluded that the time dependentdeformation of the roof was very little. In addition,visual examinations indicated that good roof conditionsprevailed throughout the investigation without displaying any strata softening and roof paring the results of deformation at 9cut-through before and after longwall no. 23 passedthe site, it can be seen that tailgate behaviour issignificantly affected by the retreat of the adjacent face.5.2. Rib behaviourThe results of rib extensometers and those predicted by the finite element analysis are presented in Fig. 11. The results indicate a timedependent deformation of 0.4 mm dayy1. As thetime dependent behaviour of the coal seam could notbe modelled in the finite element analysis of thestructure, the predicted values are only the totaldeformation after complete relaxation and thereforeless than the measured values.The important aspect of the chain pillar between35 and 36 cut-throughs is the nature of the ribmovement. The extensometer readings indicate thatthe softening has occurred to a depth of 5 m. This isin contrast to rib behaviour observed at 9 cut-throughwhere the deformation into the pillar rapidly abatesfrom the rib line.5.3. Floor behaviourThe floor extensometers results and the displacementvalues predicted by the finite element method at 35 cut-through are presented in Fig. 12. The plotindicates that although the deformation initiated 5 mbelow the floor surface, the majority of deformationtook place between 1.0 and 1.5 m into the floor.Thus, floor heave takesplace in the broken shale andthe laminated shale units as referred to in the lithologyprofile presented in Fig. 9. Although the shaleunit is surrounded by the laminated sandstone/shale,it can generate an uplift stress in the immediate floorwhen failure occurs within it. The significant floorheave at 9 cut-through is mainly attributed to thehigh horizontal stress and the side abutment stress ofthe longwall face.It has been previously demonstrated in an earlierpublication by the present authors that roadways parallel to the major horizontalstress, where K (K x or K y ) > 1, will have greaterfloor heave and roof sag when compared to road-ways parallel to minor horizontal stress.6. Guidelines for designing the support system at three-way intersectionsThe results of investigation of three-way intersectionsshowed that the maximum vertical stress at themid-height of the coal seam occurs at the corner ofthe pillar and increases with the roadway width andthe depth below surface. The destressed zone overthe pillar extends along the roadway perpendicular to the major horizontal stress.A uniform pattern ofhorizontal dowels in conjunction with wire meshwould be necessary to ensure the integrity of thepillars. A minimum dowel length equal to 50% ofthe entry width at 1.0-m spacing is suggested. Thispattern should be implemented on the edge of thepillar extending along the roadways for a distanceequal to one roadway span. The rest of the pillars inthe individual roadways should be reinforced if necessaryaccording to single roadway conditions.The four potential modes of failure should betaken into account when designing the optimum roofbolt pattern at three-way intersections.The first zoneof instability may manifest itself as a semi-domeshaped failure over the T-intersection. One side ofthe zone is parallel to the left of the main roadwaywith the base being a semi-circle. When K x ≠K y the base of the zone will have a different length ineach roadway, with the longer length perpendicularto the major principle horizontal stress. Although theproperties of the roof strata have significant effect onthe stability of the roof, the stress contour lines 0.1z σand 0.3z σ have been used to define the boundary of the roof failure zone above the three-way intersectionfor K x or K y <2 and K x or K y > 2, respectively However, observations at two field sites in theSouthern Coalfield and Hunter Valley have indicatedthat the height of roof falls is generally governed bythe regional stresses, in particular, the ratio of horizontalto vertical stress, the width of the openingsand mechanical properties of the overlying strata.Previous observations at site 2 in Hunter ValleyCoalfield by one of the authors have indicated thatthe height of roof falls matched very well with thearea under stress contours of 0.3z σ. Therefore, in order to be on a conservative side, a stress contour of 0.4z σwas adopted as a criterion for roof fall height in the present study.The second mode of failure is due to shearingalong the bedding planes, which occurs when theshear stress exceeds the frictional strength of thebedding planes.The most probable location for slidingof bedding planes occurs closer to the rib sidethan to the roadway centre. The required length ofthe fully grouted bolts depends upon the cohesion, the coefficient of internal friction and the location ofthe bedding planes. Thus, a general roof bolt pattern cannot be devised for all conditions and an accurateanalysis of site-specific models based on the accuratefield data is necessary.The third potential mode of failure is gutteringalong and over the rib sides and corners of theintersection. This is more likely to happen when thehorizontal stress is greater than the vertical stress.Inclined roof bolts passing through this zone andanchored over the pillars are a possible solution.The fourth mode of failure is controlled by thepresence of a geological feature in the intersection.When a major geologically weak zone is present inthe area of the intersection, the roof instability ishighly influenced by the structural feature. In thatcase, the prediction of the roof fall would be governedby the orientation and inclination of the geologicalfeature, internal angle of friction and dimensionsof the intersection. In that case, a specialsupport measure will be required to ensure stability.The three-way intersections cause specific stratadisturbances in the vicinity and can be convenientlydivided into two zones as indicated in Fig. 13. Inregion I, which is outside the zone of intersection, the roof condition is the same as in main roadways.Therefore, roof support is carried out based on theprocedure for individual roadways. Region II, whichis within the roadway intersection, experiences increasedstrata loading and therefore special adjustmentto roof bolt length and location must be considered.The roof bolt length must be increased by 50%and the spacing reduced by 25% in comparison tothe bolts in region I. The load carrying capacity ofthe bolt must be calculated according to height of thedestressed zone. It is suggested that in high horizontal stress fields, the roadways running parallel to thehigh horizontal stress must be driven first and thesupport for the completed intersection must be installedbefore the other roadway is inter-connected.Itis also suggested that the installation of inclined roofbolts near the rib and use of w-straps parallel to thepillar edge would help in maintaining structural stabilityof the three-way intersection.7. General discussion and conclusionsDrivage conditions can be significantly influencedby the orientation of roadways with respect to themajor horizontal stress, the effect of side abutmentpressure due to longwall extraction and the presenceof soft strata in the floor. Field investigation indicatedthat the drivage conditions parallel to the majorhorizontal stress were goodwith minimum roof shearfailure.In contrast, the drivage perpendicular to themajor horizontal stress displayed considerable shearzones particularly at locations close to the intersections.An increase in the stress magnitude due to thepresence of geological structures accentuated theshear failure.These situations were well illustratedand predicted during the finite element analysis ofroadways and intersections undervarious configurations and stress regimes.Due to a number of reasons, there are still somedifference between the field measurements and thefinite element model results.Uncertainty regardingthe in situ properties of the strata units, stress regime, the presence of geological discontinues and geologicalstructures may be some of the reasons for thisdiscrepancy. Moreover, lack of consideration to thetime dependent properties of the rock mass anddynamic loading resulting from an approaching longwallface may further contribute to the lack ofaccuracy.This paper contains a successful demonstration ofthe application of the finite element method to thestability analysis of three-way intersections.In general,the significant agreement achieved between thefield measurements and the FE results have provedthat the FEM can be successfully used for the stabilityanalysis of underground structures.Results of investigations on the stability of threewayintersections showed that the general stress and displacement patterns around the three-way intersectionsare the same as in four-way intersections butpresenting less severe instability problems 。