[go: up one dir, main page]

CN108222937A - Secondary top board structure quantitative analysis and its evaluation method based on inclined seam exploitation - Google Patents

Secondary top board structure quantitative analysis and its evaluation method based on inclined seam exploitation Download PDF

Info

Publication number
CN108222937A
CN108222937A CN201810087055.9A CN201810087055A CN108222937A CN 108222937 A CN108222937 A CN 108222937A CN 201810087055 A CN201810087055 A CN 201810087055A CN 108222937 A CN108222937 A CN 108222937A
Authority
CN
China
Prior art keywords
stress
formula
rock
zone
mining
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN201810087055.9A
Other languages
Chinese (zh)
Other versions
CN108222937B (en
Inventor
邢鲁义
杨永杰
薛彦超
吕嘉锟
宁杉
张琰岽
纪海玉
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Shandong University of Science and Technology
Original Assignee
Shandong University of Science and Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Shandong University of Science and Technology filed Critical Shandong University of Science and Technology
Priority to CN201810087055.9A priority Critical patent/CN108222937B/en
Publication of CN108222937A publication Critical patent/CN108222937A/en
Application granted granted Critical
Publication of CN108222937B publication Critical patent/CN108222937B/en
Expired - Fee Related legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • EFIXED CONSTRUCTIONS
    • E21EARTH OR ROCK DRILLING; MINING
    • E21CMINING OR QUARRYING
    • E21C41/00Methods of underground or surface mining; Layouts therefor
    • E21C41/16Methods of underground mining; Layouts therefor
    • E21C41/18Methods of underground mining; Layouts therefor for brown or hard coal

Landscapes

  • Engineering & Computer Science (AREA)
  • Mining & Mineral Resources (AREA)
  • Remote Sensing (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • General Life Sciences & Earth Sciences (AREA)
  • Geochemistry & Mineralogy (AREA)
  • Geology (AREA)
  • Lining And Supports For Tunnels (AREA)

Abstract

本发明公开了一种基于倾斜煤层开采的次生顶板结构定量分析及其评判方法,属于煤矿煤层开采技术领域。其解决了现有技术中倾斜煤层开采过程中所面临的诸多生产难题。本发明评判方法包括:首先确定上部煤层采动对底板的破坏程度,然后确定下方采动对顶板的破坏程度,即下方采动对顶板的破坏高度,利用巷道围岩松动圈理论来展开分析等;接着对巷道围岩松动圈进行实测、分析,进一步依据松动圈的大小将围岩分为小松动圈、中松动圈和大松动圈;最后,通过双重采动的影响综合确定动压次生顶板结构分类指标。本发明对于采空区下近距离倾斜煤层巷道围岩控制、保证矿井安全高效生产具有极其重要的指导意义。

The invention discloses a secondary roof structure quantitative analysis and evaluation method based on inclined coal seam mining, and belongs to the technical field of coal seam mining in coal mines. It solves many production problems faced in the mining process of the inclined coal seam in the prior art. The evaluation method of the present invention includes: first determining the degree of damage to the bottom plate caused by mining in the upper coal seam, and then determining the degree of damage to the roof caused by mining in the lower part, that is, the damage height of the roof caused by mining in the lower part, and performing analysis by using the loose circle theory of surrounding rock in the roadway, etc. ; Then carry out actual measurement and analysis on the loosening circle of surrounding rock in the roadway, and further divide the surrounding rock into small loosening circle, medium loosening circle and large loosening circle according to the size of the loosening circle; finally, through the influence of double mining, the dynamic pressure secondary Roof structure classification index. The invention has extremely important guiding significance for controlling the surrounding rock of the roadway in the near-distance inclined coal seam under the goaf and ensuring the safe and efficient production of the mine.

Description

基于倾斜煤层开采的次生顶板结构定量分析及其评判方法Quantitative analysis and evaluation method of secondary roof structure based on inclined coal seam mining

技术领域technical field

本发明涉及煤矿煤层开采技术领域,具体涉及一种基于倾斜煤层开采的次生顶板结构定量分析及其评判方法。The invention relates to the technical field of coal seam mining in coal mines, in particular to a quantitative analysis and evaluation method of a secondary roof structure based on inclined coal seam mining.

背景技术Background technique

近距离煤层下行开采期间,下部煤层巷道在重复采动的剧烈影响下,形成了动压巷道以及上部煤层开采后采空区矸石形成的次生顶板结构。与单一煤层开采相比,其顶板覆岩结构及力学机理发生了明显的改变。具体表现为:巷道围岩移近量增加,变形明显,围岩裂隙发育,塑性区范围扩大,矿压显现剧烈,甚至诱发巷道整体失稳垮落或者冲击地压。倾斜煤层开采过程中面临的生产难题必然更多。During the downward mining of short-distance coal seams, under the severe influence of repeated mining, the roadway in the lower coal seam forms a dynamic pressure roadway and a secondary roof structure formed by gangue in the goaf after mining in the upper coal seam. Compared with single coal seam mining, the roof overlying rock structure and mechanical mechanism have changed significantly. The specific manifestations are: the approaching amount of the surrounding rock of the roadway increases, the deformation is obvious, the cracks in the surrounding rock develop, the plastic zone expands, the mine pressure appears intense, and even induces the overall instability and collapse of the roadway or rock burst. There are bound to be more production difficulties faced in the mining process of inclined coal seams.

发明内容Contents of the invention

基于上述现有技术中倾斜煤层在开采过程中所面临的诸多难题,本发明提出了一种基于倾斜煤层开采的次生顶板结构定量分析及其评判方法,该方法对于采空区下近距离倾斜煤层巷道围岩控制、保证矿井安全高效生产具有极其重要的指导意义。Based on the many difficulties faced in the mining process of inclined coal seams in the above-mentioned prior art, the present invention proposes a quantitative analysis and evaluation method for secondary roof structure based on inclined coal seam mining. It is of great guiding significance to control the surrounding rock of coal seam roadway and ensure the safe and efficient production of mines.

为实现上述目的所需要解决的技术问题为:The technical problems that need to be solved for realizing above-mentioned purpose are:

针对近距离倾斜煤层下行开采过程中带来的诸多技术难题,首次提出了下部煤层巷道在重复采动影响下形成的一种“次生顶板结构”。如何重点分析巷道顶板距上方采空区的层间距与动压次生顶板结构之间的内在联系;如何实现对次生顶板结构的定量预测及判断,动压次生顶板结构判断标准如何来确定。Aiming at many technical problems brought about by the downward mining of close-distance inclined coal seams, a "secondary roof structure" formed by the lower coal seam roadway under the influence of repeated mining was proposed for the first time. How to focus on the analysis of the internal relationship between the roadway roof and the goaf above the floor space and the dynamic pressure secondary roof structure; how to realize the quantitative prediction and judgment of the secondary roof structure, and how to determine the judgment standard of the dynamic pressure secondary roof structure .

为解决上述技术问题,本发明提出了以下技术方案:In order to solve the problems of the technologies described above, the present invention proposes the following technical solutions:

基于倾斜煤层开采的次生顶板结构定量分析及其评判方法,其特征在于,依次包括以下步骤:The quantitative analysis and evaluation method of the secondary roof structure based on inclined coal seam mining is characterized in that it includes the following steps in sequence:

a、确定上部煤层采动对底板的破坏程度,即采空区底板岩层最大塑性破坏深度hmax,通过式(1)计算:a. Determine the degree of damage to the floor caused by the mining of the upper coal seam, that is, the maximum plastic failure depth h max of the floor rock layer in the goaf, and calculate it by formula (1):

式(1)中,M—采高,m;k—应力集中系数,k=2;γ—上覆岩层平均容重,kN/m3;H—煤层埋深,m;c—煤层内聚力,MPa;φ—煤层内摩擦角,°;f—煤层与顶底板摩擦系数,ξ—三轴应力系数,φf—底板岩层内摩擦角,°;In formula (1), M—mining height, m; k—stress concentration factor, k=2; γ—average bulk density of overlying strata, kN/m 3 ; H—coal seam burial depth, m; c—cohesive force of coal seam, MPa ; φ—coal seam internal friction angle, °; f—coal seam and roof-floor friction coefficient, ξ—triaxial stress coefficient, φ f — internal friction angle of floor rock formation, °;

b、确定下方采动对顶板的破坏程度,即下方采动对顶板的破坏高度,利用巷道围岩松动圈理论来确定,分为以下子步骤:b. Determine the degree of damage to the roof caused by mining below, that is, the damage height of the roof caused by mining below, which is determined by using the loose circle theory of surrounding rock in the roadway, which is divided into the following sub-steps:

b1、将巷道开挖后的围岩分为松动圈、塑性区及弹性区;b1. The surrounding rock after roadway excavation is divided into loose circle, plastic zone and elastic zone;

b2、进行巷道围岩松动圈的理论分析:b2. Carry out theoretical analysis of the loose circle of surrounding rock in the roadway:

岩体经开挖应力重新分布后,使得二次应力出现弹塑性并存的应力分布特点。为了简化理论分析,认为圆形巷道开掘在连续、均质、各向同性、处于原岩应力为P0的均匀应力场中,当洞壁的二次应力超出岩体的屈服应力,则洞壁岩体产生塑性区,塑性区是一种极限平衡状态,根据弹性力学,各点应力所满足的平衡微分方程如式2所示:After the rock mass is excavated, the stress is redistributed, which makes the secondary stress present the stress distribution characteristics of elastic and plastic coexistence. In order to simplify the theoretical analysis, it is considered that the circular roadway is excavated in a continuous, homogeneous, isotropic, and uniform stress field where the original rock stress is P 0. When the secondary stress of the tunnel wall exceeds the yield stress of the rock mass, the tunnel wall The rock mass produces a plastic zone, which is a limit equilibrium state. According to elastic mechanics, the balance differential equation satisfied by the stress at each point is shown in Equation 2:

式(2)中,σθ—环向应力,kg/cm2;σr—径向应力,kg/cm2;r—塑性区内所考察的任意一点的半径,cm;In the formula (2), σ θ — hoop stress, kg/cm 2 ; σ r — radial stress, kg/cm 2 ; r — radius of any point examined in the plastic zone, cm;

b3、在塑性区内,由于岩体刚开始破坏,处于极限平衡状态,各点应力都应满足莫尔-库仑强度准则,如式(3)所示:b3. In the plastic zone, since the rock mass has just begun to fail and is in a state of limit equilibrium, the stress at each point should satisfy the Mohr-Coulomb strength criterion, as shown in formula (3):

式中:c—围岩的粘结力,kg/cm2—内摩擦角,°;σθ—环向应力,kg/cm2;σr—径向应力,kg/cm2;r—塑性区内所考察的任意一点的半径,cm。In the formula: c—the cohesive force of the surrounding rock, kg/cm 2 ; —internal friction angle, °; σ θ —circumferential stress, kg/cm 2 ; σ r —radial stress, kg/cm 2 ; r—radius of any point examined in the plastic zone, cm.

将式(3)代入式(2)得该方程通解如式(4)所示:Substituting formula (3) into formula (2), the general solution of the equation is shown in formula (4):

c1为待定常数,根据边界条件来确定:在巷道周边上,r=r0,σr=Pi;Pi是支架对围岩的反力;c 1 is an undetermined constant, determined according to the boundary conditions: on the periphery of the roadway, r = r 0 , σ r =P i ; P i is the reaction force of the support to the surrounding rock;

将r0和Pi代入式(4)得式(5):Substitute r 0 and P i into formula (4) to get formula (5):

b4、将式(5)代入式(3)、(4)得塑性区应力如式(6)所示:b4. Substituting formula (5) into formulas (3) and (4), the stress in the plastic zone is shown in formula (6):

b5、将式(6)代入弹性应力满足的条件σrθ=2P0得式(7):b5. Substituting formula (6) into the condition that the elastic stress satisfies σ rθ = 2P 0 to get formula (7):

c、对巷道围岩松动圈进行实测、分析,进一步依据松动圈的大小L将围岩分为小松动圈、中松动圈和大松动圈;c. Carry out actual measurement and analysis on the loosening circle of surrounding rock in the roadway, and further divide the surrounding rock into small loosening circle, medium loosening circle and large loosening circle according to the size L of the loosening circle;

所述的小松动圈是指0≤L≤40cm;所述的中松动圈是指40<L≤150cm,所述的大松动圈是指L>150cm。The small loose circle refers to 0≤L≤40cm; the medium loose circle refers to 40<L≤150cm; the large loose circle refers to L>150cm.

d、基于步骤a所述的上部煤层采动对底板的破坏程度和步骤b所述的下方采动对顶板的破坏程度,即通过双重采动的影响综合确定动压次生顶板结构分类指标HG,其根据式(8)计算获得:d. Based on the degree of damage to the floor caused by mining in the upper coal seam described in step a and the degree of damage to the roof caused by mining in the lower part described in step b, that is, to comprehensively determine the classification index H of the dynamic pressure secondary roof structure through the influence of double mining G , which is calculated according to formula (8):

HG=hmax+L (8);H G = h max + L (8);

即当煤层间距hc≤HG时,巷道顶板视为次生顶板力学结构;当hc>HG时,则视为原生顶板力学结构。That is to say, when the coal seam spacing h c ≤ H G , the roadway roof is regarded as the secondary roof mechanical structure; when h c > H G , it is regarded as the primary roof mechanical structure.

作为本发明的一个优选方案,上部煤层采动对底板的破坏,是由被动应力区在主动应力区和过渡应力区的作用下向采空区移动形成的。As a preferred solution of the present invention, the damage to the floor caused by the mining of the upper coal seam is formed by the movement of the passive stress zone to the goaf under the action of the active stress zone and the transition stress zone.

优选的,当围岩为小松动圈时,采用喷混凝土支护或裸体;当围岩为中松动圈时,采用喷层局部支护或喷层金属网局部支护;当围岩为大松动圈时,采用喷层金属网局部支护或综合治理。Preferably, when the surrounding rock is a small loose circle, use shotcrete support or bare; when the surrounding rock is a medium loose circle, use sprayed layer local support or sprayed metal mesh partial support; when the surrounding rock is large loose When the circle is closed, the sprayed metal mesh is used for partial support or comprehensive treatment.

本发明所带来的有益技术效果:Beneficial technical effects brought by the present invention:

(1)针对近距离倾斜煤层下行开采带来的技术难题,首次提出了一种用于多煤层开采的次生顶板覆岩结构的定量分析及评判方法;(1) Aiming at the technical difficulties brought about by the down mining of close-distance inclined coal seams, a quantitative analysis and evaluation method for the secondary roof overlying rock structure used in multi-coal seam mining is proposed for the first time;

(2)基于巷道围岩松动圈理论,探测动压巷道围岩的塑性区范围并对其加以分类,客观评价巷道的整体稳定性,为围岩控制、支护优化等提供理论指导和科学依据。(2) Based on the loose circle theory of roadway surrounding rock, detect the plastic zone range of dynamic pressure roadway surrounding rock and classify it, objectively evaluate the overall stability of the roadway, and provide theoretical guidance and scientific basis for surrounding rock control and support optimization .

附图说明Description of drawings

下面结合附图对本发明做进一步说明:The present invention will be further described below in conjunction with accompanying drawing:

图1为本发明动压巷道次生顶板力学结构图;Fig. 1 is the mechanical structure diagram of secondary roof of dynamic pressure roadway of the present invention;

图2为采动对煤层底板破坏的力学形态图;Fig. 2 is the mechanical morphology diagram of mining damage to the coal seam floor;

图3为巷道围岩松动圈示意图;Fig. 3 is a schematic diagram of the loose circle of the roadway surrounding rock;

图4为巷道周围应力分布状态图;Figure 4 is a diagram of stress distribution around the roadway;

图5为力学模型图。Figure 5 is a mechanical model diagram.

图中,1、上部煤层顶板,2、上部煤层采空区,3、隔离岩层,4、下部煤层,5、松动圈,6、塑性区,7、弹性区。In the figure, 1. roof of upper coal seam, 2. goaf of upper coal seam, 3. isolated rock formation, 4. lower coal seam, 5. loose circle, 6. plastic zone, 7. elastic zone.

图1中,l、动压巷道与次生顶板之间的距离;α、两层煤的倾角;hc、煤层间距。In Fig. 1, l, the distance between the dynamic pressure roadway and the secondary roof; α, the inclination angle of the two coal layers; h c , the distance between the coal seams.

具体实施方式Detailed ways

本发明提出了一种基于倾斜煤层开采的次生顶板结构定量分析及其评判方法,为了使本发明的优点、技术方案更加清楚、明确,下面结合具体实施例对本发明做详细说明。The present invention proposes a quantitative analysis and evaluation method of secondary roof structure based on inclined coal seam mining. In order to make the advantages and technical solutions of the present invention clearer and clearer, the present invention will be described in detail below in conjunction with specific examples.

针对近距离倾斜煤层下行开采过程中带来的诸多技术难题,首次提出了下部煤层巷道在重复采动影响下形成的一种“次生顶板结构”。基于此,分析动压巷道次生顶板对围岩稳定性的不利影响,进而为科学选取合理的支护方案提供充分的技术指导和理论依据。Aiming at many technical problems brought about by the downward mining of close-distance inclined coal seams, a "secondary roof structure" formed by the lower coal seam roadway under the influence of repeated mining was proposed for the first time. Based on this, the adverse effect of the secondary roof of the dynamic pressure roadway on the stability of the surrounding rock is analyzed, and then sufficient technical guidance and theoretical basis are provided for the scientific selection of a reasonable support scheme.

一、如图1所示,两层煤的倾角为α,间距为hc,次生顶板结构是指动压巷道上方一定距离l存在上部煤层开采后引发岩梁断裂形成的上部煤层顶板1以及遗留的上部煤层采空区2,上部煤层采空区2的存在对下方巷道矿压显现影响极大。其主要特点是上部煤层采空区2与下部煤层4巷道顶板之间距离较小,两者之间隔离岩层3受双重采动的影响,节理裂隙较为发育,隔离岩层3基本处于塑性状态;加之采空区的存在使得岩层的完整性、水平力传递的潜在性及自然平衡结构等遭到严重破坏,上方采空区内矸石、部分基本顶岩梁和煤柱对下方巷道矿压显现影响比较剧烈,巷道的稳定性较差,一般发生明显变形,极易发生失稳破坏。1. As shown in Figure 1, the inclination angle of the two coal seams is α, and the distance is h c . The secondary roof structure refers to the upper coal seam roof 1 formed by rock beam fracture after the mining of the upper coal seam at a certain distance l above the dynamic pressure roadway. The remaining upper coal seam goaf 2, the existence of the upper coal seam goaf 2 has a great impact on the mine pressure of the lower roadway. Its main feature is that the distance between the upper coal seam goaf 2 and the lower coal seam 4 roadway roof is small, and the isolation rock layer 3 between them is affected by double mining, the joints and fissures are relatively developed, and the isolation rock layer 3 is basically in a plastic state; The existence of the goaf has severely damaged the integrity of the rock formation, the potential for horizontal force transmission, and the natural balance structure. The influence of gangue, some basic roof beams and coal pillars in the upper goaf on the mine pressure of the lower roadway is compared. severe, the stability of the roadway is poor, and generally there is obvious deformation, and it is very easy to cause instability and damage.

二、动压次生顶板结构判断标准“HG”的确定2. Determination of the judgment standard " HG " of the dynamic pressure secondary roof structure

顶板结构分类指标“HG”是基于上方采动对底板的破坏和下方采动(掘巷)对顶板的破坏程度,即通过双重采动的影响综合确定。The roof structure classification index " HG " is based on the damage to the floor by upper mining and the damage to the roof by lower mining (entrying), that is, it is determined comprehensively through the impact of double mining.

(1)上部煤层采动对底板的破坏(1) The damage to the bottom plate caused by the mining of the upper coal seam

根据已有的研究:在开采过程中,底板岩体在支承压力的作用下,根据所处位置、受力特点及移动路径形成三个区,Ⅰ为主动应力区,Ⅱ为过渡应力区,Ⅲ为被动应力区,如图2所示。被动应力区在主动应力区和过渡应力区的作用下向采空区移动,形成底板岩层破坏。According to the existing research: during the mining process, under the action of supporting pressure, the floor rock mass forms three zones according to its location, force characteristics and moving path, Ⅰ is the active stress zone, Ⅱ is the transition stress zone, and Ⅲ It is the passive stress zone, as shown in Figure 2. The passive stress zone moves to the goaf under the action of the active stress zone and the transitional stress zone, resulting in floor rock formation failure.

采空区底板岩层最大塑性破坏深度hmax为:The maximum plastic failure depth h max of the floor rock layer in the goaf is:

式中:M—采高,m;k—应力集中系数,k=2;γ—上覆岩层平均容重,kN/m3;H—煤层埋深,m;c—煤层内聚力,MPa;φ—煤层内摩擦角,°;f—煤层与顶底板摩擦系数,ξ—三轴应力系数,φf—底板岩层内摩擦角,°。In the formula: M—mining height, m; k—stress concentration factor, k=2; γ—average bulk density of overlying strata, kN/m 3 ; H—coal seam burial depth, m; c—cohesive force of coal seam, MPa; φ— Coal seam internal friction angle, °; f—coal seam and roof and floor friction coefficient, ξ—triaxial stress coefficient, φ f — internal friction angle of floor rock formation, °.

(2)下方采动(掘巷)对顶板的破坏(2) Damage to the roof caused by mining (digging) below

近距离倾斜煤层巷道顶板岩层受双重采动的影响比较大,岩层强度降低,节理裂隙发育严重,故可近似为松散岩层。下方采动(掘巷)对顶板的破坏高度可利用巷道围岩松动圈理论加以确定。The roof strata of roadways with near-distance inclined coal seams are greatly affected by double mining, the strength of the strata is reduced, and the joints and fissures are seriously developed, so it can be approximated as a loose strata. The damage height of the roof caused by mining (entrying) below can be determined by using the loose circle theory of the surrounding rock of the roadway.

围岩松动圈是进行巷道围岩稳定性评价和进行合理支护设计的重要依据。巷道围岩松动圈支护理论是由中国矿业大学董方庭教授对巷道围岩状态进行深入研究后提出的。研究发现,围岩松动圈的存在是巷道固有的特性,它的范围(厚度值L)目前可利用钻孔成像仪(围岩裂隙探测仪)、声波仪或多点位移计等仪器进行测定。巷道支护的主要对象是围岩松动圈产生、发展过程中产生的碎胀变形力,锚杆承受拉力的来源在于松动圈的发生、发展;并根据围岩松动圈厚度值L的大小,将其分为小、中、大3类,进而得出相应的支护机理及优化方案。The loose circle of surrounding rock is an important basis for evaluating the stability of roadway surrounding rock and making reasonable support design. The loose ring support theory of roadway surrounding rock was proposed by Professor Dong Fangting of China University of Mining and Technology after in-depth research on the state of roadway surrounding rock. The study found that the existence of the surrounding rock loose circle is an inherent characteristic of the roadway, and its range (thickness value L) can currently be measured by drilling imagers (surrounding rock fissure detectors), acoustic wave meters or multi-point displacement meters. The main object of the roadway support is the crushing and deformation force generated during the generation and development of the surrounding rock loose circle. The source of the tensile force of the bolt is the occurrence and development of the loose circle; It is divided into three categories: small, medium and large, and then the corresponding support mechanism and optimization scheme are obtained.

①巷道开挖后的应力状态① Stress state after roadway excavation

在巷道开挖之前,岩体处于原始应力状态,巷道开挖后引起岩体内部应力的重新分布,围岩受力由三向变成了两向和单向受力状态,造成岩石强度出现不同程度的降低,破坏了原来的应力平衡状态,并产生应力集中。如果围岩集中应力值小于下降后的岩石表征强度,则围岩处于弹塑性状态,围岩稳定,反之围岩将发生破坏,这种破坏逐渐向深部扩展,直至达到新的三向应力平衡状态为止,此时围岩中出现了一个松弛破裂带,把这个由于应力作用产生的松弛破裂带称为围岩松动圈,其力学特征表现为应力降低。巷道开挖后的围岩可分为松弛破裂区(松动圈5)、塑性区6及弹性区7,如图3所示。Before the excavation of the roadway, the rock mass was in the original stress state. After the excavation of the roadway, the internal stress of the rock mass was redistributed, and the stress on the surrounding rock changed from three directions to two directions and one direction, resulting in different rock strengths. The degree of reduction destroys the original state of stress balance and produces stress concentration. If the concentrated stress value of the surrounding rock is less than the characteristic strength of the rock after falling, the surrounding rock is in an elastic-plastic state, and the surrounding rock is stable; otherwise, the surrounding rock will be damaged, and this damage will gradually expand to the deep, until it reaches a new three-dimensional stress balance state So far, a relaxation and fracture zone has appeared in the surrounding rock at this time, and this relaxation and fracture zone due to stress is called the surrounding rock loose zone, and its mechanical characteristics are characterized by stress reduction. The surrounding rock after roadway excavation can be divided into loose and cracked zone (loose circle 5), plastic zone 6 and elastic zone 7, as shown in Figure 3.

松动圈越大,围岩破坏越严重,支护越困难,影响巷道围岩松动圈大小的因素主要有:围岩应力、岩石强度、地质构造、巷道跨度、巷道形状、开掘时间、地下水作用,施工方法、支护方式及支护强度等,松动圈是上述多种影响因素共同作用下的一个综合指标。合理确定巷道围岩松动圈的大小对于评价巷道围岩稳定性及支护效果、优化巷道支护方式与支护参数、保证巷道支护安全等具有重要指导意义。The larger the loose circle, the more serious the surrounding rock damage and the more difficult the support. The main factors affecting the size of the roadway surrounding rock loose circle are: surrounding rock stress, rock strength, geological structure, roadway span, roadway shape, excavation time, groundwater effect, Construction methods, support methods and support strength, etc., the loose circle is a comprehensive index under the joint action of the above-mentioned various influencing factors. Reasonable determination of the size of the surrounding rock loose circle of the roadway has important guiding significance for evaluating the stability of the surrounding rock of the roadway and the support effect, optimizing the roadway support method and support parameters, and ensuring the safety of the roadway support.

②巷道围岩松动圈的理论分析②Theoretical analysis of the loose circle of surrounding rock in the roadway

岩体经开挖应力重新分布后,使得二次应力出现弹塑性并存的应力分布特点。为了简化理论分析,近似认为圆形巷道开掘在连续、均质、各向同性、处于原岩应力为P0的均匀应力场中,其力学模型如图4、图5所示。After the rock mass is excavated, the stress is redistributed, which makes the secondary stress present the stress distribution characteristics of elastic and plastic coexistence. In order to simplify the theoretical analysis, it is approximately considered that the excavation of the circular roadway is continuous, homogeneous, isotropic, and in a uniform stress field where the original rock stress is P 0 , and its mechanical model is shown in Figure 4 and Figure 5.

当洞壁的二次应力超出岩体的屈服应力,则洞壁岩体产生塑性区,塑性区是一种极限平衡状态,根据弹性力学,各点应力所满足的平衡微分方程为:When the secondary stress of the cave wall exceeds the yield stress of the rock mass, the cave wall rock mass produces a plastic zone, which is a limit equilibrium state. According to elastic mechanics, the equilibrium differential equation satisfied by the stress at each point is:

在塑性区内,由于岩体刚开始破坏,处于极限平衡状态,各点应力都应满足莫尔-库仑强度准则:In the plastic zone, since the rock mass has just begun to fail and is in a state of limit equilibrium, the stress at each point should satisfy the Mohr-Coulomb strength criterion:

式中:c—围岩的粘结力,kg/cm2—内摩擦角,°;σθ—环向应力,kg/cm2;σr—径向应力,kg/cm2;r—塑性区内所考察的任意一点的半径,cm。In the formula: c—the cohesive force of the surrounding rock, kg/cm 2 ; —internal friction angle, °; σ θ —circumferential stress, kg/cm 2 ; σ r —radial stress, kg/cm 2 ; r—radius of any point under consideration in the plastic zone, cm.

将式(2)代入式(1)得该方程通解为:Substituting formula (2) into formula (1), the general solution of this equation is:

c1为待定常数,可根据边界条件来确定:在巷道周边上,r=r0,σr=Pi(Pi是支架对围岩的反力)。将r0和Pi代入式(3)得:c 1 is an undetermined constant, which can be determined according to the boundary conditions: on the periphery of the roadway, r = r 0 , σ r =P i (P i is the reaction force of the support to the surrounding rock). Substitute r 0 and Pi into formula (3) to get:

把式(4)代入式(2)、式(3)得塑性区应力为:Substituting formula (4) into formula (2) and formula (3), the stress in the plastic zone is:

在弹性区和塑性区的交界处(r=R0),应力是连续的,所以σr和σθ既应满足弹性区的应力分布规律,又应满足塑性区的应力分布规律,通常将此弹性分界点到洞轴线的距离称作塑性圈半径r。将(5)式代入弹性应力满足的条件σrθ=2P0得:At the junction of the elastic zone and the plastic zone (r=R 0 ), the stress is continuous, so σ r and σ θ should not only satisfy the stress distribution law of the elastic zone, but also satisfy the stress distribution law of the plastic zone. Usually, this The distance from the elastic boundary point to the axis of the hole is called the radius r of the plastic ring. Substituting equation (5) into the condition σ rθ = 2P 0 satisfied by the elastic stress, we get:

由式(6)可以得出,巷道所在处的原岩应力愈大,非弹性变形区就愈大;支架对围岩的反力愈大,非弹性变形区的半径就愈小,如不用支架,则非弹性变形区的半径为最大值;岩石强度愈小,非弹性变形区就愈大;反映到巷道面积上就是巷道半径愈大,非弹性变形区也愈大。说明巷道围岩松动圈与围岩强度,受力大小及支护状况密切相关。From formula (6), it can be concluded that the greater the stress of the original rock where the roadway is located, the larger the inelastic deformation zone; the greater the reaction force of the support to the surrounding rock, the smaller the radius of the inelastic deformation zone. , the radius of the inelastic deformation zone is the maximum value; the smaller the rock strength, the larger the inelastic deformation zone; reflected in the area of the roadway, the larger the radius of the roadway, the larger the inelastic deformation zone. It shows that the surrounding rock loose circle of the roadway is closely related to the strength of the surrounding rock, the magnitude of the force and the support condition.

③巷道围岩松动圈的实测及分析③ Actual measurement and analysis of the loose circle of surrounding rock in the roadway

本次测试采用CXK6型矿用本安型钻孔成像仪(借鉴现有技术即可)实时记录围岩破裂图像来确定动压巷道围岩松动圈的大小。CXK6型矿用本安型钻孔成像仪适用于煤矿井下恶劣条件下的各类钻孔检测,如观测锚杆锚索孔、瓦斯排放孔、超前探测孔、煤层岩层勘探孔、地质勘探孔和围岩松动圈等,可准确揭示地下工程围岩状态,结合相关分析软件可较准确地推测岩层产状、裂隙发育扩展情况及松动破坏范围等,探测结果可用于煤矿工作面顶板离层垮冒、巷道围岩破裂失稳、矿井井筒破裂变形等地下灾害工程预警预报;也可用于地下工程锚杆支护、围岩注浆加固、巷道修复等参数设计和地下工程施工质量、支护方案评估分析等,为煤矿及岩土工程提供可靠、真实有效的实测资料和分析。In this test, the CXK6 mining intrinsically safe borehole imager (using existing technology) is used to record the surrounding rock rupture image in real time to determine the size of the surrounding rock loosening circle in the dynamic pressure roadway. CXK6 Mine Intrinsically Safe Borehole Imager is suitable for all kinds of borehole detection under harsh conditions in coal mines, such as observing bolt and cable holes, gas discharge holes, advanced detection holes, coal seam exploration holes, geological exploration holes and The loose circle of surrounding rock can accurately reveal the state of surrounding rock in underground engineering. Combined with relevant analysis software, it can more accurately predict the occurrence of rock formations, the development and expansion of cracks, and the scope of loosening and damage. It can also be used for parameter design of underground engineering bolt support, surrounding rock grouting reinforcement, roadway repair, etc., and evaluation of underground engineering construction quality and support schemes Provide reliable, true and effective measured data and analysis for coal mines and geotechnical engineering.

④巷道围岩松动圈分类④ Classification of loose circles of surrounding rock in roadways

表1巷道围岩松动圈分类表Table 1 Classification table of roadway surrounding rock loose circle

围岩分类的目的在于正确评价支护难度,判明主要支护对象,以便合理地确定支护参数和施工工艺,为同类巷道支护设计提供依据。围岩松动圈大小既包括影响围岩稳定性的诸多因素,又反映出诸多因素的相互作用结果,是一个综合性的分类指标。用围岩松动圈分类围岩有以下几个突出优点:The purpose of surrounding rock classification is to correctly evaluate the support difficulty and identify the main support objects, so as to reasonably determine the support parameters and construction technology, and provide a basis for the design of similar roadway support. The size of the surrounding rock loose circle not only includes many factors that affect the stability of the surrounding rock, but also reflects the interaction results of many factors. It is a comprehensive classification index. Classifying surrounding rocks with surrounding rock loose circles has the following outstanding advantages:

a.绕过了原岩应力、围岩强度、结构面性质测定等困难问题,但又着重抓住了它们的影响结果,即松动圈是一个包含多因素影响的综合指标;a. Bypassing the difficult problems such as original rock stress, surrounding rock strength, structural surface properties measurement, etc., but focusing on their influence results, that is, the loose circle is a comprehensive index including the influence of multiple factors;

b.松动圈系现场实测所得,未在重要方面作任何假设;b. The loose ring is measured on site, without any assumptions in important aspects;

c.松动圈大小通过实测获得后,确定支护参数时直观简单,现场应用方便;c. After the size of the loose circle is obtained through actual measurement, it is intuitive and simple to determine the support parameters, and it is convenient for on-site application;

d.采用单一综合指标分类,分类的重复性、可靠性不以人们的经验不同而异;d. Use a single comprehensive index to classify, and the repeatability and reliability of the classification do not vary with people's experience;

e.松动圈分类方法的理论及实践基础较为坚实,与锚杆支护设计形成了技术系列。e. The theoretical and practical basis of the loose circle classification method is relatively solid, and it forms a technical series with the design of bolt support.

结合锚喷支护机理,根据巷道围岩松动圈支护理论,依据松动圈的大小L将围岩分为小松动圈(0~40cm,包括端点值)、中松动圈(40~150cm,不包括40,包括150)和大松动圈(大于150cm)三大类六个小类,见表1。Combined with the support mechanism of bolting and spraying, according to the support theory of the roadway surrounding rock loose circle, according to the size L of the loose circle, the surrounding rock is divided into a small loose circle (0-40cm, including the endpoint value), a medium loose circle (40-150cm, no Including 40, including 150) and large loose circle (greater than 150cm) three categories and six subcategories, see Table 1.

综合以上分析可知,次生顶板覆岩结构的预测标准为HG=hmax+L。即当煤层间距hc≤HG时,巷道顶板视为次生顶板力学结构;当hc>HG时,则视为原生顶板力学结构。Based on the above analysis, it can be seen that the prediction standard for the overlying rock structure of the secondary roof is H G =h max +L. That is to say, when the coal seam spacing h c ≤ H G , the roadway roof is regarded as the secondary roof mechanical structure; when h c > H G , it is regarded as the primary roof mechanical structure.

需要说明的是:本领域技术人员在本发明的启示下对这些术语所做的简单替换,均应在本发明的保护范围之内。It should be noted that any simple replacement of these terms by those skilled in the art under the inspiration of the present invention shall fall within the protection scope of the present invention.

Claims (3)

1. a kind of secondary top board structure quantitative analysis and its evaluation method based on inclined seam exploitation, which is characterized in that successively Include the following steps:
A, determine that superjacent adopts the extent of the destruction to bottom plate, i.e. gob floor rock stratum maximum plastic failure depth hmax, lead to Cross formula (1) calculating:
In formula (1), M-mining height, m;K-the factor of stress concentration, k=2;γ-overlying rock volume-weighted average, kN/m3;H-coal seam Buried depth, m;C-coal seam cohesive force, MPa;φ-coal seam internal friction angle, °;F-coal seam and roof and floor friction coefficient, ξ-triaxial stress coefficient,φf- floor strata internal friction angle, °;
B, determine that the extent of the destruction to top plate is adopted in lower section, i.e. the destruction height to top plate is adopted in lower section, utilizes roadway surrounding rock pine Moving-coil theory determines, is divided into following sub-step:
B1, the country rock after roadway excavation is divided into relaxation zone, plastic zone and elastic region;
B2, the theory analysis for carrying out Exploring Loose Rock Country in Tunnels:
Rock mass is after excavating stress redistribution so that the stress distribution feature that secondary stress elastoplasticity occurs and deposits, for letter Change theory analysis, it is believed that circular tunnel digging is P in continuous, homogeneous, isotropism, in the stress of primary rock0Uniform stress field In, when the secondary stress of hole wall exceeds the yield stress of rock mass, then wall rock mass in hole generates plastic zone, and plastic zone is that a kind of limit is put down Weighing apparatus state, according to Elasticity, shown in the balance differential equation such as formula (2) that each point stress is met:
In formula (2), σθ- circumference stress, kg/cm2;σr- radial stress, kg/cm2;Any point investigated in r-plastic zone Radius, cm;
B3, in plastic zone, since rock mass just starts to destroy, in state of limit equilibrium, each point stress should all meet More- Coulomb strength criterion, as shown in formula (3):
In formula:The cohesive force of c-country rock, kg/cm2- internal friction angle, °;σθ- circumference stress, kg/cm2;σr- radially should Power, kg/cm2;The radius at any point investigated in r-plastic zone, cm;
Formula (3) is substituted into formula (2) to obtain shown in equation general solution such as formula (4):
c1For undetermined constant, determined according to boundary condition:On tunnel-surrounding, r=r0, σr=Pi;PiIt is stent to country rock Counter-force;
By r0And PiSubstitution formula (4) obtains formula (5):
B4, formula (5) substitution formula (3), (4) are obtained shown in plastic zone stress such as formula (6):
B5, formula (6) is substituted into the condition σ that elastic stress meetsrθ=2P0Obtain formula (7):
C, Exploring Loose Rock Country in Tunnels surveyed, analyzed, country rock is divided into small loosening according further to the size L of relaxation zone Circle, middle relaxation zone and big relaxation zone;
The small relaxation zone refers to 0≤L≤40cm;The middle relaxation zone refers to 40 < L≤150cm, the big loosening Circle refers to L > 150cm;
D, it is adopted based on the superjacent described in step a and the lower section described in the extent of the destruction of bottom plate and step b is adopted to top plate Extent of the destruction, that is, pass through the dual influence synthesis adopted and determine dynamic pressure secondary top board structure classification indicators HG, according to formula (8) It calculates and obtains:
HG=hmax+L (8);
I.e. as coal seam spacing hc≤HGWhen, back is considered as secondary top plate mechanical structure;Work as hc> HGWhen, then it is considered as primary top plate Mechanical structure.
2. secondary top board structure quantitative analysis and its evaluation method according to claim 1 based on inclined seam exploitation, It is characterized in that:Superjacent adopts the destruction to bottom plate, is in active stressed zone and unfair stress area by passive stressed zone Move what is formed to goaf under effect.
3. secondary top board structure quantitative analysis and its evaluation method according to claim 1 based on inclined seam exploitation, It is characterized in that:When country rock is small relaxation zone, using shotcrete support or nude;When country rock is middle relaxation zone, use The supporting of spray-up part or the part supporting of spray-up metal mesh;When country rock is big relaxation zone, using the part supporting of spray-up metal mesh or Comprehensive treatment.
CN201810087055.9A 2018-01-30 2018-01-30 Secondary top board structure quantitative analysis and its evaluation method based on inclined seam exploitation Expired - Fee Related CN108222937B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201810087055.9A CN108222937B (en) 2018-01-30 2018-01-30 Secondary top board structure quantitative analysis and its evaluation method based on inclined seam exploitation

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201810087055.9A CN108222937B (en) 2018-01-30 2018-01-30 Secondary top board structure quantitative analysis and its evaluation method based on inclined seam exploitation

Publications (2)

Publication Number Publication Date
CN108222937A true CN108222937A (en) 2018-06-29
CN108222937B CN108222937B (en) 2019-03-12

Family

ID=62669562

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201810087055.9A Expired - Fee Related CN108222937B (en) 2018-01-30 2018-01-30 Secondary top board structure quantitative analysis and its evaluation method based on inclined seam exploitation

Country Status (1)

Country Link
CN (1) CN108222937B (en)

Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110610043A (en) * 2019-09-10 2019-12-24 辽宁工程技术大学 A Calculation Method for the Destruction Depth of the Floor in the Mined-Out Zone of the Inclined Coal Seam
CN111608663A (en) * 2020-04-29 2020-09-01 临沂矿业集团菏泽煤电有限公司 Omnibearing pressure relief method for rock burst dangerous roadway of thick coal seam working face
CN111608707A (en) * 2020-04-29 2020-09-01 临沂矿业集团菏泽煤电有限公司 Rock burst dangerous roadway support method based on double-cylinder protection theory
CN112267879A (en) * 2020-10-22 2021-01-26 山西工程技术学院 Method for determining grouting pressure of gas drilling and sealing
CN113449414A (en) * 2021-06-07 2021-09-28 西安科技大学 Three-layer structure-based bottom plate slippage failure depth calculation method
CN114357692A (en) * 2021-11-15 2022-04-15 常州工学院 A Calculation Method of Surrounding Rock Plastic Zone Range in Roof Roadway of Steeply Inclined Extra-thick Coal Seam
CN115146713A (en) * 2022-06-16 2022-10-04 天地科技股份有限公司 Coal mine tunnel surrounding rock classification method

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
SU836364A1 (en) * 1979-07-26 1981-06-07 Институт Горной Механики Им. Г.А.Цулукидзе Ah Грузинской Ccp Method of preventing dynamic phenomena at working of coal beds
US8113763B2 (en) * 1999-06-15 2012-02-14 Philippi-Hagenbuch, Inc. Process for three-dimensional modeling and design of off-highway dump bodies
CN103197041A (en) * 2012-01-05 2013-07-10 贵州省煤矿设计研究院 A technique for evaluating the risk degree of outburst in short-distance coal seam groups
CN104181611A (en) * 2014-08-28 2014-12-03 山东科技大学 Mine working face top board and bottom board mining breaking fracture development dynamic monitoring method
CN104794315A (en) * 2015-05-18 2015-07-22 辽宁工程技术大学 Coal seam floor damaged zone depth determination method based on improved rupture mechanical model
CN105160174A (en) * 2015-08-31 2015-12-16 安徽理工大学 Computing method of stope floor damage depth capable of considering artesian pressure action
CN107503795A (en) * 2017-08-29 2017-12-22 西安科技大学 A kind of stope drift active workings coal seam floor failure method of determining range

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
SU836364A1 (en) * 1979-07-26 1981-06-07 Институт Горной Механики Им. Г.А.Цулукидзе Ah Грузинской Ccp Method of preventing dynamic phenomena at working of coal beds
US8113763B2 (en) * 1999-06-15 2012-02-14 Philippi-Hagenbuch, Inc. Process for three-dimensional modeling and design of off-highway dump bodies
CN103197041A (en) * 2012-01-05 2013-07-10 贵州省煤矿设计研究院 A technique for evaluating the risk degree of outburst in short-distance coal seam groups
CN104181611A (en) * 2014-08-28 2014-12-03 山东科技大学 Mine working face top board and bottom board mining breaking fracture development dynamic monitoring method
CN104794315A (en) * 2015-05-18 2015-07-22 辽宁工程技术大学 Coal seam floor damaged zone depth determination method based on improved rupture mechanical model
CN105160174A (en) * 2015-08-31 2015-12-16 安徽理工大学 Computing method of stope floor damage depth capable of considering artesian pressure action
CN107503795A (en) * 2017-08-29 2017-12-22 西安科技大学 A kind of stope drift active workings coal seam floor failure method of determining range

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
刘亮: "《上煤层采动影响下煤层底板破坏特征试验研究》", 《煤炭与化工》 *
赵春波: "《采动底板岩体应力分布与破坏特征模拟研究》", 《内蒙古煤炭经济》 *

Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110610043A (en) * 2019-09-10 2019-12-24 辽宁工程技术大学 A Calculation Method for the Destruction Depth of the Floor in the Mined-Out Zone of the Inclined Coal Seam
CN111608663A (en) * 2020-04-29 2020-09-01 临沂矿业集团菏泽煤电有限公司 Omnibearing pressure relief method for rock burst dangerous roadway of thick coal seam working face
CN111608707A (en) * 2020-04-29 2020-09-01 临沂矿业集团菏泽煤电有限公司 Rock burst dangerous roadway support method based on double-cylinder protection theory
CN112267879A (en) * 2020-10-22 2021-01-26 山西工程技术学院 Method for determining grouting pressure of gas drilling and sealing
CN113449414A (en) * 2021-06-07 2021-09-28 西安科技大学 Three-layer structure-based bottom plate slippage failure depth calculation method
CN114357692A (en) * 2021-11-15 2022-04-15 常州工学院 A Calculation Method of Surrounding Rock Plastic Zone Range in Roof Roadway of Steeply Inclined Extra-thick Coal Seam
CN115146713A (en) * 2022-06-16 2022-10-04 天地科技股份有限公司 Coal mine tunnel surrounding rock classification method

Also Published As

Publication number Publication date
CN108222937B (en) 2019-03-12

Similar Documents

Publication Publication Date Title
CN108222937A (en) Secondary top board structure quantitative analysis and its evaluation method based on inclined seam exploitation
Zhao et al. Mechanism analysis and control technology of surrounding rock failure in deep soft rock roadway
Cheng et al. A zoning model for coal mining-induced strata movement based on microseismic monitoring
Cheng et al. Microseismic investigation of mining-induced brittle fault activation in a Chinese coal mine
Wang et al. Application of a combined supporting technology with U-shaped steel support and anchor-grouting to surrounding soft rock reinforcement in roadway
Xu et al. Investigation of key techniques on floor roadway support under the impacts of superimposed mining: theoretical analysis and field study
Fan et al. An innovative approach for gob‐side entry retaining in deep coal mines: a case study
CN103063335B (en) Three-dimensional geological survey testing method of deep portion crustal stress based on loading monitoring data
Xue et al. The influence of magmatic rock thickness on fracture and instability law of mining surrounding rock
Wu et al. Failure mechanism and stability control of surrounding rock in mining roadway with gentle slope and close distance
Tian et al. Experimental study of deformations and failures of the coal wall in a longwall working face
CN102852524B (en) Method for utilizing hydraulic support to improve bauxite recovery rate
Guo et al. A three-dimensional supporting technology, optimization and inspiration from a deep coal mine in China
Xiao et al. An effective control method of rock burst induced by shear instability of fault structure under complicated geological conditions
Zang et al. Research on deformation characteristics and control technology of soft rock roadway under dynamic disturbance
Fan et al. Improvement to the calculating model of the pressure arch’s height considering the confining pressure in the excavation of shallow tunnels
Huang et al. Parameter determination and effect evaluation of gob-side entry retaining by directional roof cutting and pressure releasing
Sun et al. Model test and numerical verification of surrounding rock stability of super-large-span and variable-section tunnels
Lai et al. Study on the prediction of the height of two zones in the overlying strata under a strong shock
Kong et al. The characteristics of roof breaking and the law of ground pressure behavior in fully mechanized top-coal caving face with large mining height
Xue et al. Numerical investigation on overburden migration behaviors in stope under thick magmatic rocks
CN108509746A (en) A kind of Exploring Loose Rock Country in Tunnels method of determining range
Zhou et al. Study on the mechanism of tunnel catastrophe in Xigeda formation considering the interbed effect
Yang et al. Geomechanical model test investigation of roof cutting and roadway maintenance technology under fault structures
Zhang et al. Stability of a roadway below a coal seam under dynamic pressure: a case study of the 11123 floor gas drainage roadway of a mine in huainan, China

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant
CF01 Termination of patent right due to non-payment of annual fee

Granted publication date: 20190312

CF01 Termination of patent right due to non-payment of annual fee