1.Introduction

Long wall and partial extraction room-and-pillar techniques are the two major mining methods employed in the US coal mines.Both systems develop 3-way and 4-way intersections during mine development and coal extraction.Thirty percent of the fatal injuries occurred at intersections,of which 68%occurred at 4-way intersections while only 32%occurred at 3-way intersections(Abbasi,2010).This increased frequency of accidents at 4-way intersections was primarily due to the greater effective roof span.Studies conducted on rock falls(fatal and non-fatal injuries)in the US by Spearing and Mueller(2008)and Chugh and Kollipara(2009)revealed that about 70-75%of rock falls occurred at intersections.

Since an intersection represents a three-dimensional(3D)problem,early closed-form solutions using plate theory for stress distribution around an intersection were simplistic(elastic,homogeneous rock mass).It is only in the last two decades,since the development of numerical modeling techniques,that researchers have attempted to develop a more Scientific understanding of stress distribution under realistic conditions such as nonhomogeneous and nonlinear rock mass behavior,sequential development of intersection(Abbasi,2010),and incorporation of turned corner on one or more pillars around an intersection.Field studies by Hanna et al.(1986)and Hanna and Conover(1988)in the Illinois Basin provided data on bed separations and displacements around intersections.However,limited research has been done on designing roof support plans that would improve the stability of intersections.

The primary hypothesis of the context is that appropriate selection of primary and/or secondary supports and their spatial distribution can improve the stability of intersections.An important associated research issue is to assess the effectiveness of a particular roof support plan.One can use a stress-based approach,as has been done by several authors(e.g.Gale et al.,2004;Esterhuizen,2012),but it suggests that using a stress-based approach in nonlinear behavior zones may not provide realistic estimates of failed zones and support requirements.Therefore,there is a need for a better understanding of stress and strain distributions around an intersection,zones of failure based on appropriate deformation-based failure criteria and its use to improve support plans around intersections.

Rock bolts have been extensively used as a primary support element in coal mines in the US for about 40 years.Typical cost of roof control constitutes about 7-20%of the production cost depending upon site-specific geo-mining conditions.The authors think that one of the primary reasons is the lack of Scientific basis in the design of roof control plans.Most of the currently practiced bolting layouts were developed based on field experience rather than on Scientific basis.Therefore,it would be a contribution to develop an approach that can identify critical areas of instability around an intersection and assess the efficiency of a roof control plan in terms of support installation time and capability.These critical zones can be supplemented with appropriate reinforcement elements to come up with Scientifically sound roof control plans that will be capable of controlling rock mass deformations around an intersection.

Recently,Chugh and Sinha(2015)suggested an approach to quantify the reinforcement effect of a roof support plan over a designated area.It employs analyzing zones of the critical tensile(ε＞ 0.5 × 10-3),compressive(ε＜ -1 × 10-3)and shear(γ＜-0.5×10-3andγ＞0.5×10-3)strains in the immediate roof before and after installation of supports.The analytical approach computes three separate reinforcement factors:reinforcement against tensile strains(RFT),compressive strains(RFC)and shear strains(RFSS)for immediate roof,coal pillar and immediate floor strata.Another study by Sinha and Chugh(2015)compared the Mine Safety and Health Administration(MSHA)approved roof support plans for 150 m and 80 m depth mines using the above approach.Since some of the previous relevant researches have been summarized in Chugh and Sinha(2015),it is not included here.

This study is a continuation of the authors’efforts to understand the stress and strain distributions around an intersection and improve its stability through cut sequence,reorienting the entries(with respect to pre-mining stress field)and bolt reinforcement.The goals of this paper are two-folds:(i)Validate the critical strain technique(CST)through comparison against published coal mine accident statistics,and(ii)Demonstrate the capability of this approach in improving the intersection stability through application to a case study.

2.Critical strain technique for assessing stability of intersections and reinforcement factors due to bolting

In Model 1,the vertical displacement at the intersection center was about 16.5 mm which corresponds well with field observations(Chugh,2011).The maximum load in the bolt also matches well with field measured values of Ray et al.(2013)(see Fig. 4).The difference in the location of the maximum load is likely due to omission of the bolt bearing plate(Abbasi,2010).Fig. 5 shows that high compressive strain of about 4×10-3existed along the pillar ribs in the N-S entry.The compressive strains are much lower along the right side of the N-S entry than that on the left side.This is because Cuts 3 and 5 relieved some of the stress before Cut 6 was made.High positive shear strains existed around the turned corner.The deformed mesh(exaggerated)of the first element in the roof,as shown in Fig. 6a,indicates that there is some distortion near Corner 2.Additionally,there is a high curvature roof deformation near Corner 3.Both of these are manifested as high compressive strains.In terms of failed zone(Fig. 6b),shear failure was observed in pillar ribs along E-W direction while the corners failed due to a combination of tension and shear.

A typical deflection curve of immediate roof over an excavation would have associated curvature and horizontal strains at each point and would be expected to be different with and without roof supports.It is further known that failure of the immediate roof stratum will initiate due to tensile,compressive,or shear strain when the critical strain values are exceeded.This analytical approach can compute three separate reinforcement factors due to roof support:RFT,RFC and RFSS.Areas of immediate roof in a specif i ed region that exceed critical tensile,compressive,or shear strain before and after bolting can be compared to compute the respective reinforcement factor.The critical value of tensile and shear strains used is 0.5×10-3although a different value could be used.The critical value of compressive strain used is 10-3(Sinha and Chugh,2015).

The following example shows how reinforcement factors can be computed from the number of critically strained elements in numerical models.Table 1 lists the critical strain areas(number of elements can be related to the area by multiplying with the dimension of model elements;here,the area is listed)for two hypothetical cases:Case I(no support)and Case II(with roof support plan)over an arbitrary region UVWX,where U,V,W and X are thevertices of the region.From the table,the following results can be computed:(i)Area of critical compressive strains in X-direction is reduced from 64 m2to 55 m2,therefore,RFC=(64-55)/64≈14%;(ii)Critical tensile strains area in X-direction is reduced from 9 m2 to 6 m2,thus RFT=(9-6)/9≈33.3%,and(iii)Critical shear strain area is reduced from 69 m2to 64 m2yielding RFSS=(69-64)/69≈7.2%.For further details on application of CST,the reader can refer to Chugh and Sinha(2015).

我以为她捞几下就不捞了，但她竟然甩了鞋子，把衣袖往上捋捋，卷起来，下了水。靠岸的麦麸捞完了，她又向水中央游去。

Table 1 Critical strain areas in an arbitrary region UVWX.

aCompressive:exceeding lower critical strain bound;Tensile:exceeding upper critical strain bound.

Case Failure typea Critical strain area(m2)εXX εYY γXY No bolt(1) Tensile 9 0 69 Compressive 64 13 74 Roof support plan(2) Tensile 6 0 64 Compressive 55 13 68

Using critical strain limits for elements in the bolted horizon,the following values were obtained:

2.1.Validation of the critical strain technique based on the US roof fall statistics

A quarter model was developed for an idealized intersection(without turning corner)following the lithological sequence and modeling procedures detailed later in Section 3.1.Three regions,as specif i ed in Fig. 1,were selected for the analysis.Each region was subdivided into volumetric elements of the size 0.25 m ×0.25 m×0.1 m.The regions extend through the entire height of the coal seam and immediate roof strata(medium gray shale).The rationale behind incorporating coal in the analysis is that the failure may occur in the coal,roof or floor strata as part of the pillar system.Since coal is the weakest link in the system,it is typically involved in the failure process.The critical strain limits used for analysis are 10-3for compressive strain,0.5×10-3for tensile strain,and 0.5×10-3for shear strain.

Within the defined 3D volume,elements exceeding critical strains were counted for coal and roof strata separately,while the fl oor layer was ignored in these preliminary analyses.Table 2 shows the values obtained through this procedure.Since the dimensions of the elements are equal in the roof and coal lithologies,additive rule can be applied.Table 3 illustrates the net possibility of failure initiation in different modes for intersection corner,entry along X-direction and entry along Y-direction.The critical strain values provide an indication of failure initiation.It must be mentioned here that the effect of stress redistribution after failure initiation is not considered.

The formulae used for determination of net failure possibility at corner and entry are:(a)Intersection corner:Four times the summation of failure initiation possibility in each failure mode,and(b)Entry:Two times the summation of failure initiation possibility in each failure mode.The factors 4 and 2 have been used since the initiation of failure can occur at four points in an intersection and at two points in an entry.The ratio of net failure initiation possibility in entries to the net failure possibility at corners was compared with US roof fall statistics.For values presented here,the calculations are as follows:

Fig. 1.Zones considered in the quarter model.

Table 2 Number of elements within each zone beyond critical strain limits.

Case Failure type Number of elements within the designated zones εXX εYY εZZ γXY γYZ γXZ Intersection(coal) Tensile 309 302 0 211 22 18 Compressive 0 0 311 297 70 66 Intersection(roof) Tensile 0 0 288 155 60 71 Compressive 7 0 0 165 0 0 Entries along Y-direction(coal)Tensile 308 0 0 0 24 117 Compressive 0 0 312 0 0 100 Entries along Y-direction(roof)Tensile 224 296 0 0 132 132 Compressive 0 0 312 0 116 39 Entries along X-direction(roof)Tensile 0 0 168 0 0 304 Compressive 121 0 87 0 0 0 Entries along X-direction(coal)Tensile 0 0 160 0 294 0 Compressive 0 16 19 2 0 0

Table 3 Number of elements beyond critical strain limits for intersection and entry in bothX-and Y-directions.

Case Failure type Number of elements within the designated zones εXX εYY εZZ γXY γYZ γXZ Intersection(coal and roof)Tensile 309 302 288 366 82 89 Compressive 7 0 311 462 70 66 Entries along Y-direction(coal and roof)Tensile 308 0 168 0 24 421 Compressive 121 0 399 0 0 100 Entries along X-direction(coal and roof)Tensile 224 296 160 0 426 132 Compressive 0 16 331 2 116 39

(1)X entry/corners:3484/9408=0.37,and

(2)Y entry/corners:3082/9408=0.33.

3.教师启发学生思考：列出比例的主要根据是什么？主要是“4个玩具汽车可以换10本小人书，假设14个玩具汽车可以换x本小人书”这两句话。

The existing database on roof falls in the US indicates that 70-75%of falls are concentrated at intersections,which corresponds well with the calculated values.Past research has revealed that coal ribs fail in a combination of shear and tension(Abbasi,2010).To further refine this approach,compressive strain areas(εXX,εYYand εZZ)in coal were subtracted from the net failure possibilities which resulted in:

青海汉话大多是将[tala]置于时间名词之后、动词之前，表示动作行为的“终止”，或者行为动作达到的“界限”，蒙古语则是将[tala]接缀在动词词干上，同样表示行为的“终止”或行为延续结束的“界限”。例如：

(1)X entry/corners:2860/8164=0.35,and

(2)Y entry/corners:2458/8164=0.3.

In this layout(Fig. 10),three 1.8 m long,#8 rebar bolts were installed vertically at each of the four intersection corners.These bolts were located 0.5 m from the pillar edge and the spacing between bolts was 1.5 m.The pre-tension loads of 50 kN and 100 kN were applied to all 12 bolts.Because these pre-tension loads did not reduce the volume of critical rock mass significantly(＜10%),the load was increased to 150 kN to stiffen the corners.The corner bolt at the turned corner assumed the maximum load of 228 kN during the course of simulation,thus,a#8 rebar was selected.Results showed a significant reduction in shear strains,especially around Corners 1 and 3.

2.2.Validation of the critical strain technique with the strength reduction technique using a case study

(1)Model 1 or base case(Fig. 3):Six cuts with the first two cuts of 9 m in length.The bolting pattern is similar to that discussed in Section 3.1,and the minimum compressive stress(σ3)is oriented along E-W.This is the excavation sequence followed by the mine under consideration.

An initial stability analysis was performed with average rock strength properties using the SRT.The analysis was repeated with incrementally decreasing strength properties until the point of collapse was satisfactorily bracketed.Adjustments in input parameters were achieved through simultaneous reduction of cohesion,tensile strength and Friction angle of the rock matrix and the bedding planes(Esterhuizen,2012).Bilinear strain softening ubiquitous joint constitutive model in FLAC3Dwas used to simulate the rock mass with properties from Esterhuizen(2012).Interfaces were also incorporated at the boundary of successive lithologies.The following checks were made after every 100 iterations to identify when the model failed or converged:

(1)Vertical displacement at the center of the roof in the excavation exceeded 30 cm.

(2)A number of points,1 m above the excavation and spaced at 1 m apart,were selected.The average velocity of two adjacent points was computed.The model was considered to collapse if after 15,000 iterations,the maximum of these average velocities exceeded 5×10-6m/step.

街坊邻里都吓了一跳，纷然向老巴打探。老巴无奈，他阻止不了阿里。这音乐是阿里每天最重要的一餐。众人便问罗爹爹何故不去东湖。罗爹爹长叹说，路被封死了，他们再去东湖会蛮难蛮难。

进而言之，程序错误在当下依法行政、依法司法等依法治国步伐的重要意义不容忽视，因而纳入错误的种类是应有之意。从某种意义上说，很多程序性错误造成的后果比实体性错误还严重，而且程序性错误容易加深老百姓对看得见的正义的深度误解。

The normal(compressive and tensile)strains are distributed along X-and Y-directions when σ3was oriented along N30°E and N60°E.This may improve intersection stability since the critical normal strains are distributed over a larger area.From that perspective,N30°E and N60°E orientations seems more stable than NS and EW orientations.A closer look at the critical normal strain areas for N30°E and N60°E cases revealed that N30°E orientation is more stable.From critical shear strains point of view,EW case is the most stable.Since a particular orientation could not be identified as the best,additional analyses were performed to simultaneously account for normal and shear strains.Since an element can fail in more than one mode,elements which have failed in any one mode(either shear or tensile)were counted(Table 7).In Table 6,it was not possible to add the number of elements since there would be an overestimation due to repeated counting of a single element failing in multiple modes.

The second case study in Esterhuizen(2012)is of a room-and pillar mine in Illinois,which was analyzed with the same model dimensions and rock mass properties.The idea was to compare the stability factor of the SRT with the reinforcement factor of the CST.

A1m thick,35.7m high model of an entry with support sin stalled under development load(loading due to the development of entries only)of 4.3 MPa was developed.The thickness of the model was chosen to be 1 m in order to simulate a plane strain condition.The initial vertical load,corresponding to the depth of mining,was increased from 2.4MP a to a development load of4.3MP a based on an extraction ratio of 43.7%.The seam thickness was 1.5 m and 0.8 m of the roof shale was extracted to provide clearance for mining instruments.Full column resin grouted bolts of 19mm in diameter and 1.8 m in length were installed 1.2 m apart across the entry width.

Fig. 2 shows high compressive strains along the entry corners which correspond to minor cutters seen in field at these locations.The load in the bolt along the edges was about 85 kN(8.6 tons)which is similar to the findings of Esterhuizen (2012).About 9 mm of vertical displacement was noted near the center of the entry in both models.

Two models were run for the purposes of comparison:bolted and unbolted.Using the above criterion for failure,it was found that the entry collapsed when the strength was reduced by a factor of 0.52(bolted)and 0.81(unbolted)giving a stability factor of 1.9 and 1.23,respectively.It is intuitive for the stability factor of the bolted case to be higher than that of the unbolted scenario.The ratio of stability factor for the bolted case to the unbolted case is 1.54(=1.9/1.23)which can be interpreted as an expression of the effect of reinforcement provided by the roof supports.

The critical strain values are related to discontinuities rather than for intact rock.Field data on critical strains in underground mines that result in rock mass failure initiation are not available.Therefore,available field data on ground deformations that result in structural damage due to mine subsidence were considered logical for use(Baker,1974).Further analyses were attempted to assess the suitability of the above values.

(1)Number of elements exceeding limits in any mode(unbolted):216,and

利用非物质文化遗产的资源优势，在保留非物质文化遗产原真性的前提下合理开发旅游产品。文旅融合背景下的商业业态需要吸收具有“个性”的商户，具有当地特色、对旅游者具有吸引力的别具一格旅游产品则更占优势。由于旅游业的季节性特征，要求旅游产品的生命周期尽可能延长，避免造成资源浪费。同时随着文旅业态的转型，商业业态也要根据旅游者产生的不同的旅游需求来提升景区的商业业态。比如从原有的观光旅游逐步向休闲、深度体验游转型，高尔夫球场、滑雪场等的建设就是对商业业态的提升和优化。

学生译文：The board shall be composed by eight directors.Each director shall beappointed or recalled by hisown side.

Fig. 2.Contours of compressive strain along the horizontal direction.

(2)Number of elements exceeding limits in any mode(bolted):154.

The ratio of the number of elements exceeding the critical strain values for the unbolted case to the bolted case is 1.4(=216/154)in comparison to the stability factor ratio of 1.54 for the SRT.Firstly,this minor discrepancy may be due to the fact that the SRT is a stress-based approach while CST is a strain-based one,and the stress and strain are nonlinearly related in Hoek-Brown criterion.Secondly,the successive reduction of the rock mass strength for all the layers in the SRT is unrealistic,since damage to the roof typically does not extend beyond 2 m in height.The mechanism of failure and the stress redistribution may also change due to strength reduction of the different layers.SRT is a macro-level approach that does not identify spatial initiation and propagation of failure.CST,on the other hand,is more mechanics-based approach and solves the last problem;however,it requires measurement of strains in the field to validate the selected critical strain values.The authors believe that the CST with its stronger Scientific foundations should be considered in conjunction with SRT for the design of excavations and roof supports.

3.Assessment of the effect of pre-mining stress field orientation on opening stability

Since conducting experiments in the field to identify the impact of pre-mining stress field orientation on opening is not feasible,3D continuum modeling using FLAC3Dwas utilized with field validation,where possible.Analyses were performed for a 4-way intersection with a cut-corner(typically,one corner is cut to facilitate turning of the continuous miner)in a southern Illinois mine operating in No.6 coal seam.Pre-mining stress can be an important factor in developing the extent of potentially unstable roof(Gercek,1982;Guo and Stankus,1997;Ellenberger and Miller,2012).Model generated outputs tend to be significantly different when excavation sequence is unaccounted(Sinha,2016).Hence,it was decided to consider the effect of cut sequence and orientation of pre-mining stress field while developing the improved roof control plans.

3.1.Model development

FLAC3Dwas used to perform nonlinear continuum analyses for a typical 4-way intersection in a mine in southern Illinois at a depth of 107 m.Generalized Hoek-Brown failure criterion with rock mass strength properties listed in Table 4 was used as the foundation foranalyses.The overall model was 30 m long,30 m wide and 50.1 m high.Three bedding planes at heights of 0.8 m,1.4 m and 2 m above the coal seam were included to simulate planes of weakness.The mechanical behavior of interfaces is represented in FLAC3Dby five parameters:normal stiffness,shear stiffness,cohesion,friction angle and tensile strength.Each of these values for coal measure rocks in southern Illinois were determined from laboratory testing(Bastola and Chugh,2015)and were selected for the purposes of this study(Table 5).The widths of openings in entries and crosscuts were 6 m and 5.8 m,respectively.

Table 4 Rock mass properties used in the model.

Note:GSI is the geological strength index(Marinos and Hoek,2000);Ermis the elastic modulus of rock mass;mband s are the Hoek-Brown parameters;Tois the tensile strength;and cois the uniaxial compressive strength.

Lithology GSI Erm(MPa) mb s To(MPa) co(MPa)Sandstone 80 5161 6.364 0.1084 1.7 51.7 Sandy shale 80 5161 6.364 0.1084 1.7 51.7 Claystone 58 4135 1.562 0.0094 0.2 10.3 Coal 76 3000 1.47 0.07 0.6 20 Medium grey shale 70 3097 3.425 0.0357 0.78 30.3 Black shale 65 3097 2.579 0.0205 0.69 32.3 Dark grey shale 65 3097 2.579 0.0205 0.69 32.3 Limestone 80 5161 6.364 0.1084 1.7 51.7 Medium brown to grey shale 70 3792 3.425 0.0357 0.78 41.4 Sandstone 95 3800 12.54 0.5738 7.83 103.4 65 3055 2.579 0.0205 0.59 41.4 Medium grey sandy shale

Pre-mining horizontal stresses of 7.58 MPa and 4.13 MPa,typical in the Illinois Basin,were applied in the E-W and N-S directions.The in situ horizontal stresses were estimated from empirical equations(Mark and Gadde,2008)and a compilation of such data within the Illinois Basin(Chugh,2011).The practiced MSHA-approved roof support plan in this mine consisted of bolts placed in 1.4 m×1.4 m grid with the first bolt 0.65 m from the pillar ribs.Short encapsulation pull test(SEPT)data,provided by bolt suppliers in the region,were used to assign bolting system stiffness and strength parameters(Chugh et al.,2016).

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Rock bolts in FLAC3Dare modeled as two-noded,straight pile structural elements of finite length which interact with the rock mass through a spring-slider system(Itasca,2009).Bolt suppliers provided SEPT data in the mining region for 8 tests using 1.8 m long,#6 rebar,grade 60 with the upper 0.3 m resin grouted(Sinha,2016).The elastic deformation of the un-grouted portion of the bolt was subtracted to compute an average bolt stiffness of 3.35×107N/m/m.The bond strength is the load at which thegrout-rock interface starts to fail.Grip factor(GF)values in the region vary from 232 N/mm to 270 N/mm.A GF value of 270 N/mm was used that is similar to the published research(Mark et al.,2002;Ray et al.,2013).

Table 5 Bedding plane interface properties used in modeling.

Note:Knand Ksare the normal and shear stiffnesses of the interfaces,respectively;c and φ are the cohesion and friction angle of the interfaces,respectively.

Bedding plane interfaces Kn(GPa/m) Ks(GPa/m) c(MPa) φ (°)Medium grey shale/black shale 8.16 3.06 0.78 22 Dark grey shale/limestone 12.88 3.31 1.99 24 Medium brown to grey shale/medium brown to grey shale 8.16 3.06 0.78 22

3.2.Effect of pre-mining stress field on intersection stability

Pre-mining horizontal principal stresses in Illinois Coal Basin are generally oriented N70°E and N20°W with typical values of 7.58 MPa(compression)and 4.13 MPa(compression),respectively.In this section,they were applied at different orientations in the horizontal plane while the vertical stress,equivalent to the depth of mining,was applied to the top of the model.In the base case(Model 1),it was assumed that entries are being driven along N-S and crosscuts along E-W to simulate north or south oriented submain or main entries.Main or sub main entries are also commonly driven along E-W and crosscuts in N-S direction.

The horizontal principal stress ratio in this region is 1:2.Where this ratio is higher or the immediate roof strata are weak,the entries are sometimes oriented at an angle to ensure that both the entries and the crosscuts are stable.Analyses have been performed for different pre-mining stress field orientations to assess intersection and mine stability.Instead of rotating the model,the in situ stress was rotated to facilitate easier modeling.The numbers in red indicate the sequence of cuts in Fig. 3.After every cut was made,bolts were installed instantaneously and the model was allowed to equilibrate.

Four models were simulated to observe the macroscopic changes caused by the rotation of the openings:

The application of strength reduction technique(SRT)to assessing the stability of mine openings was first introduced by Esterhuizen(2012).In this approach,failure is defined as the occurrence of a large roof fall that extends all the way up to or above the bolted horizon.Instead of defining a safety factor,stability factor was defined,which attempted to express the degree of safety of an excavation in its current state to a potential failed state.

(2)Model 2:This model is similar to Model 1 except that theσ3 acts along the N-S direction.

(3)Model 3:Similar to Model 1 with the minimum compressive stress aligned along N60°E.

采用CoCA分析浮游植物与浮游动物之间的关系，结果显示浮游植物与浮游动物之间的相关性显著（P=0.014）。前 4个排序轴解释了 44%共同方差，且4个排序轴相关性依次为：0.9212、0.9444、0.9194、0.9061，均超过了0.9000。较高的相关性及共同方差比例表明浮游动物与浮游植物之间存在显著的交互作用（Hanson et al.，2015）。浮游动植物名列前10的种类得分占总得分比例约为40%，因此图4仅显示了浮游植物和浮游动物拟合权重最高的前 10种类，以便更好地观察浮游动植物之间起主要作用的种类。

Fig. 3.(a)3D view,and(b)Map view along coal seam for Model 1.

(4)Model 4:Similar to Model 1 with the minimum compressive stress aligned along N30°E.

3.3.Results and discussions

The CSTis based on the assumption that immediate roof stratum over an excavation acts as a beam or a plate resting on elastic or inelastic foundations and is subjected to uniform or nonuniform loading from strata above.The loading results in a bending curve that has at each point vertical and horizontal displacements,slope,curvature and horizontal strains;the last two are mathematically correlated.

适当地选择N×M的变换矩阵H，使得随机矢量与y无关，即Rey=E[eyT]=0.设x=x1+x2，其中x1与y相关，x2与y不相关，则有

Fig. 4.Distance from bolt head versus axial load in N-S entry and intersection:Comparison of model and field data(after Ray et al.,2013).

Fig. 5.Contour of compressive strains in X-direction in the roof.

A plot of shear and compressive strains after each cut revealed that high shear strains developed only after Cut 3 was made and increased with Cuts 4 and 5.On the other hand,the distortion near Corner 3 occurred only when Cut 5 was made.Prior to Cut 6,the left portion of the E-W crosscut was solid coal and had higher stiffness,reducing the relative freedom of the rock mass to deform.Once Cut 5 was made,the roof relaxed near Corner 2 and caused the distortion.Consequently,the load in the bolt around that area increased to 142 kN.

In Model 2,high compressive strain was localized in the E-W direction.Although there was a 6%decrease in the area of critical compressive strain zone as compared to Model 1,critical shear zones increased by 48%.The magnitude of peak shear strain also increased to 2.1×10-3.High shear strains around Corner 3 may cause distortion and ultimately lead to failure.A review of the strains development after each cut revealed that Corners 3 and 4 were subjected to high shear strains after Cuts 3 and 6.Although the compressive strains can be reduced slightly by reorienting the direction of cut sequence with respect to the minimum compressive stress,it increased the shear strains significantly.It suggests that reorienting the cut sequence in relation to the minimum compressive stress direction may help to stabilize the intersection for higher ratios of the two horizontal pre-mining compressive stresses.

In Model 3,the minimum principal stress was aligned along N60°E.This was done by assigning normal stresses on the N-S and E-W faces of the model with appropriate shear stresses in the horizontal plane.A large reduction in the area of critical compressive strains was seen along the left side of the entry in comparison to Model 1.The stiffer rock mass along the left portion of the E-W crosscut reduced additional deformations with lower compressive strains.There was a large increase in positive shear strain along the turned corner(Corner 3).This may have been caused by the angular orientation of the pre-mining stress field which amplified the shear strains along the turned corner.Negative shear strains at Corners 2 and 4 were also found to increase marginally.

Finally,in Model 4,the minimum principal stress was aligned along N30°E.The compressive strains along X-and Y-directions(Fig. 7)were much smaller than those in Model 1 although there was a zone of high compression along the turned corner.High positive shear strains also existed around the turned corner(Fig. 8).Entry orientation with respect to pre-mining stress field minimized compressive strains to a large extent,but incurred additional shear strains at corners.High shear strains can result in failure of corners,which can increase the intersection roof span.Appropriate support systems must be designed to control rock mass failure around this turned corner.

“课程思政”作为一种新的思想政治工作理念，本质上是“课程承载思政，思政寓于课程”，即让所有课程都上出思政味，让所有任课教师都挑起思政担，从而形成全员育人、全方位育人的思政教育新格局。“课程思政”可以将思想政治教育渗透到一切知识的传授、应用之中，从而实现工具理性与价值理论的统一。

In order to quantify the extent of instability around the intersection for the four different models,the number of elements exceeding critical tensile,compressive and shear strains within 1.8 m(bolting horizon)of the immediate roof and over an area of the intersection plus 2 m was counted and is shown in Table 6.Each element in the bolted horizon has uniform dimensions of 0.2 m×0.2 m×0.1 m.Thus,the overall volume of rock mass susceptible to failure initiation can be computed.For simplicity,only number of elements is reported in Table 6.

(3)If the mechanical ratio was less than 10-6and the maximum of all vertical velocities was less than 5×10-7m/step,the model was considered to converge.The mechanical ratio is defined as the ratio of the maximum unbalanced force to the applied force.The FLAC calculation cycle is repeated until a steady-state solution is achieved(i.e.the maximum unbalanced force is zero).In reality,the unbalanced force never reaches zero but reduces to an acceptable low value.

Fig. 6.(a)Deformed mesh of the immediate roof,and(b)Yielded elements in the floor and the pillar around Corner 2.

Fig. 7.Contour of compressive strain in X-direction.

Fig. 8.Contours of shear strains around the intersection.

Table 6 Number of elements exceeding critical strain within the bolting horizon based on varying the pre-mining stress field.

Orientation ofσ3 Failure type Number of elements exceeding critical strains εXX εYY γXY E-W(Model 1) Tensile 548 0 598 Compressive 7019 43 1137 N60°E(Model 3) Tensile 1020 0 3423 Compressive 4760 489 702 N30°E(Model 4) Tensile 15 212 3610 Compressive 1020 2826 1727 N-S(Model 2) Tensile 0 361 2062 Compressive 54 6214 1281

Table 7 Number of elements exceeding the critical strain within the bolting horizon in any mode,encompassing the intersection and 2 m around it(37,632 elements).

Orientation ofσ3 Number of elements exceeding different critical strains Percentage of elements failure(%)EW(Model 1) 15,566 41.36 N60°E(Model 3) 10,255 27.25 N30°E(Model 4) 8285 22.01 NS(Model 2) 11,876 31.56

Results in Table 7 do not correspond with Gadde(2003)who concluded N45°E to be the most unstable orientation with EW or NS as the best.The conclusions were based on averaging the factor of safety for models with five different principal stress ratios in the immediate roof.It is also possible that the difference is due to localized stress and strain distributions caused by the cut sequence.To investigate the reason for the discrepancy in the obtained results,additional cases were simulated where all the cuts were excavated instantaneously.These results corroborated well with US National Institute for Occupational Safety and Health(NIOSH)’s Analysis of Horizontal Stresses in Mining(AHSM)software and Gadde(2003),thus attributing the discrepancy to cut-sequence.The reader can refer to Sinha(2016)for further details on this study.

4.Alternate roof control plans

Fig. 9.Deformed mesh of immediate roof around an intersection.

It was found in the previous section that orienting the entry at 30°to the direction of the minimum principal stress(Model 4)and excavating the first two cuts in 9 m length provided the maximum stability to the intersection.This section further attempts to reduce the critical strain areas through strategic installation of roof supports.Figs.8 and 9 depict the critical shear strain areas and exaggerated deformed mesh in the immediate roof whenσ3is oriented along N30°E.Corners 1 and 3 are subjected to high positive shear strains.Such high strains are likely to cause distortional failures of the corners that will increase the exposed roof span of the intersection.Since normal strains are low in this model(refer Fig. 7),it was decided to only reduce shear strains around corners.Pre-tensioned and inclined bolts were installed around areas of high critical strain to assess their effect on elements exceeding critical strain limits within the bolted horizon.

4.1.Alternate roof control plan#1

It is reasonable to expect that critical strain limits will be different for roof and coal strata.Since the Hoek-Brown parameters are used for rock mass rather than for intact rock,limiting strains will be governed to a large extent by existing discontinuities.Therefore,the authors believe that considering the same critical strain limits for these preliminary analyses will not have a dramatic effect on the entire analysis.

4.2.Alternate roof control plan#2

This layout followed the previous bolting pattern except that all 12 bolts were inclined at 45°towards the solid coal pillar.Some minor angle adjustments were made to prevent bolts from crossing each other.A pre-tension load of 100 kN was applied to these inclined bolts.There was a notable decrease in positive as well as negative shear strains at all four corners(Fig. 11).In addition,there was a 37.4%reduction in normal strains in the Y-direction compared to Model 4 of previous section.

4.3.Alternate roof control plan#3

In this case,the pre-tension load in all 45°inclined bolts was increased to 150 kN.From plots of deformed mesh(Fig. 12)and shear strain(Fig. 13),it can be concluded that the critical areas of instability have been reduced substantially.

近年贵州省骨干水源工程建设投资增长迅速，但主要依靠各级财政投入，尚未建立多元化、多层次、多渠道的投融资政策体制机制。国务院 《关于进一步促进贵州经济社会又好又快发展的若干意见》（国发〔2012〕2号文件）明确要求全面实施“三位一体”规划，到 2020年贵州省工程供水能力达到 159.4亿m3。2011—2020年，贵州骨干水源工程建设资金需求949.5亿元，需要建立骨干水源工程建设投入稳定增长机制，以确保如期完成“三位一体”综合规划提出的骨干水源工程建设目标。

4.4.Analysis of number of elements exceeding the critical strain value

Table 8 lists the number of elements the exceeding critical strains with the following observations:

(1)Inclined bolts resulted in substantial decrease in critical strains.This is due to the application of a resistive force normal to the deformation tendency of intersection corners.Since a bolt performs better in tension than in shear,identifying such orientations is crucial to the overall efficiency of a bolting plan.

Fig. 10.Plan#1 for improved support around an intersection.

Fig. 11.Contours of shear strain around an intersection with Plan#2 for alternate roof control.

Fig. 12.Deformed mesh of the immediate roof with Plan#3 for alternate roof control.

Fig. 13.Contour of shear strain around the intersection with Plan#3.

(2)Alternate bolting plan#3 reduced the critical shear strain by 79.3%as compared to Model 4 in the previous section.It also reduced the critical compressive and tensile strains in Y-direction by 64.08%and 41%,respectively.

采取有效措施，控制部分临河地段、山坡地段工程扫线和管沟开挖等施工作业带的宽度，以减轻后续水土流失治理任务，节约工程建设成本。

(3)To better understand the effect of the inclined bolts,additional analyses were conducted to count the elements exceeding any critical strain(i.e.compressive,tensile orshear).This combined the improvement in critical normal and shear strain areas and represented it using a composite value.Table 9 shows the number and percentage of elements failing in any mode.

Table 8 Number of elements exceeding the critical strain within the bolting horizon for alternate roof control plans.

Case Failure type Number of elements exceeding different critical strains εXX εYY γXY Alternate layout#1 Tensile 15 198 2803 Compressive 1015 2320 1228 Alternate layout#2 Tensile 22 175 1820 Compressive 1210 1725 827 Alternate layout#3 Tensile 26 124 624 Compressive 1255 1015 482

Table 9 Number of elements exceeding the critical strain within the bolting horizon in any mode with alternate roof control plans,encompassing the intersection and 2 m around it(37,632 elements).

Case Number of elements exceeding different critical strains Percentage of elements failing(%)N30°E orientation(Model 4) 8285 22.01 Improved layout#1 5220 13.87 Improved layout#2 3983 10.58 Improved layout#3 2415 6.42

(4)Alternate proposed roof control plans#1,#2 and#3 reduced the overall critical area by 37%,51.9%and 70.8%,respectively.It may seem that on further increasing the bolt pre-tension,the critical strain areas would reduce leading to a more stable intersection.However,it must be realized that there is an industrial limitation to the amount of pre-tension that can be applied to a bolt.Additionally,there is a cost associated with higher pre-tension and thicker bolts.Whether 150-kN pretension can be realistically applied with a precise bolt inclination is not the essence of this study.The goal is to demonstrate that such a methodology could be followed to design a more effective roof control plans.

5.Conclusions

This research has performed a 3D numerical analysis of strain distribution around a typical 4-way coal mine intersection in the Illinois Coal Basin.The goal of the study was to develop improved roof support layouts through identification of critical areas around the intersection.Since researchers have faced problems in the past in assessing the effectiveness of support systems,an alternative approach is discussed here to assess the areal reinforcement through continuum analyses of yielded zones and strain-based criteria of failure of rock mass in each zone.This approach computes three separate reinforcement factors:RFT,RFC and RFSS.

It was found that damage nucleates around intersection corners in shear mode.The distortion caused byshear strain often results in corner spalling that can in turn increase the exposed roof span.In regions where the two horizontal stresses are significantly different,compressive strains can localize along the entries and manifest as cutter roof.The high compressive strains can also increase the load in bolts causing localized roof failures.

A sound Scientific analysis is imperative to the design of roof control plans.Oftentimes,some designs are based on experience rather than an understanding of the potential failure mechanisms.A deeper insight into the critical areas can help in determining the location as well as the support capacity that is necessary for stabilization.Furthermore,the relative efficiency of different support types as a function of loading direction must be understood and utilized in this regard.

This study has shown that a sequential approach,starting with modification of the entry direction with respect to pre-mining stress field,followed by Scientific positioning of secondary supports,can prove to be extremely effective in minimizing the unstable areas around an intersection.A similar methodology should be followed when designing roof control plans for coal mines.With the advent of CST,it becomes easier to assess and compare the reinforcement effect of different roof control plans over user defined regions.A major advantage is the ability to determine whether a particular support(suited for certain loading type)is effective in reinforcing the target region/volume.Currently,endeavors are being made to use this approach in design of rib supports.

Conflict of interest

The authors wish to confirm that there are no known Conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

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