工程科学学报，第37卷，第5期：543550,2015年5月 Chinese Journal of Engineering,Vol.37,No.5:543-550,May 2015 DOI:10.13374/j.issn2095-9389.2015.05.001:http://journals.ustb.edu.cn 地下煤火燃空区冒落岩体孔隙率随机分布规律 王少锋12)四，李夕兵”，王德明，曹凯2》 1)中南大学资源与安全工程学院，长沙4100832)中国矿业大学煤矿瓦斯与火灾防治教有部重点实验室，徐州221116 ☒通信作者，E-mail:wsfcumt(@163.com 摘要本文经随机实验统计分析得出孔隙率函数(3lng-2ln(1-p)近似服从正态分布，在实验的粒径范围内(30~ 180m),其期望值和方差都随着岩块粒径的增大而增大.在推导出岩层二维下沉曲面方程的基础上，先后推演出燃空区冒 落岩体孔隙率的连续非均质分布模型和随机离散化非均质分布模型.依据模型计算矩形煤火空间得出以下结果：燃空区浅 部及边缘侧冒落岩体的孔隙率大，而中间区域孔隙率小：孔隙率等值线在x一y平面上的投影呈侧躺的“U”形分布：沿x轴，随 着深入燃空区距离的增加，孔隙率呈类负指数形式衰减.此外，孔隙率连续分布和随机离散化分布，在整体的变化趋势上是 相同的，区别之处在于后者所表示的孔隙率具有一定的随机波动性.将上述随机离散化模型应用在某火区温度场的数值模 拟中，并经现场红外测温验证了模拟的准确性和孔隙率模型的适用性. 关键词地下煤燃烧：燃空区：孔隙率：离散化：非均质 分类号TD75 Random distribution of porosity in the combustion space area of underground coal fire WANG Shao-feng,LI Xi-bing,WANG De-ming),CAO Kai2) 1)School of Resources and Safety Engineering,Central South University,Changsha 410083,China 2)Key Laboratory of Gas and Fire Control for Coal Mines,China University of Mining&Technology,Xuzhou 21116,China Corresponding author,E-mail:wsfcumt@163.com ABSTRACT Through statistical analysis of random experiments,there is a function of porosity 3no-2In(1)that approximately follows a normal distribution.In the test particle size range of 30 to 180 mm,the expectation and variance of this function value increase with an increase in grain size of rock blocks.On the basis of deriving the subsidence hypersurface equation of a basic roof,a continuous inhomogeneous distribution model and a random inhomogeneous distribution model of porosity in the combustion space area (CSA)are deduced.For a rectangular coal fire space,the porosity in the shallow and edge side of CSA is large,but in the middle region is small.In the xy plane,the porosity contour appears a side lying U-shaped distribution,and the porosity presents negative exponent attenuation with an increase in distance entering CSA along the x axis.In addition,the overall trend of the porosity of contin- uous distribution and random distribution is the same,but the difference is that the porosity described by the random distribution model has a certain stochastic volatility.The random distribution model of porosity has been used in a numerical simulation of the temperature field in a fire zone,and the accuracy of simulation and the applicability of this porosity model are verified by infrared temperature measurements. KEY WORDS underground coal combustion:combustion space area:porosity:discretization:inhomogeneous 地下煤火是指在赋存于地下的煤体与空气接触一定的规模，并对环境产生一定影响的煤自燃现 后，发生煤氧复合作用，从氧化自燃到剧烈燃烧后形成 象-习.世界上所有产煤国家都不同程度地存在着地 收稿日期：2014-02-08 基金项目：国家自然科学基金资助项目(51134020,11472311)工程科学学报，第 37 卷，第 5 期: 543--550，2015 年 5 月 Chinese Journal of Engineering，Vol． 37，No． 5: 543--550，May 2015 DOI: 10． 13374 /j． issn2095--9389． 2015． 05． 001; http: / /journals． ustb． edu． cn 地下煤火燃空区冒落岩体孔隙率随机分布规律 王少锋1，2) ，李夕兵1) ，王德明2) ，曹 凯2) 1) 中南大学资源与安全工程学院，长沙 410083 2) 中国矿业大学煤矿瓦斯与火灾防治教育部重点实验室，徐州 221116  通信作者，E-mail: wsfcumt@ 163． com 摘 要 本文经随机实验统计分析得出孔隙率函数( 3lnφ － 2ln( 1 － φ) ) 近似服从正态分布，在实验的粒径范围内( 30 ～ 180 mm) ，其期望值和方差都随着岩块粒径的增大而增大． 在推导出岩层二维下沉曲面方程的基础上，先后推演出燃空区冒 落岩体孔隙率的连续非均质分布模型和随机离散化非均质分布模型． 依据模型计算矩形煤火空间得出以下结果: 燃空区浅 部及边缘侧冒落岩体的孔隙率大，而中间区域孔隙率小; 孔隙率等值线在 x--y 平面上的投影呈侧躺的“U”形分布; 沿 x 轴，随 着深入燃空区距离的增加，孔隙率呈类负指数形式衰减． 此外，孔隙率连续分布和随机离散化分布，在整体的变化趋势上是 相同的，区别之处在于后者所表示的孔隙率具有一定的随机波动性． 将上述随机离散化模型应用在某火区温度场的数值模 拟中，并经现场红外测温验证了模拟的准确性和孔隙率模型的适用性． 关键词 地下煤燃烧; 燃空区; 孔隙率; 离散化; 非均质 分类号 TD75 Ｒandom distribution of porosity in the combustion space area of underground coal fire WANG Shao-feng1，2)  ，LI Xi-bing1) ，WANG De-ming2) ，CAO Kai2) 1) School of Ｒesources and Safety Engineering，Central South University，Changsha 410083，China 2) Key Laboratory of Gas and Fire Control for Coal Mines，China University of Mining ＆ Technology，Xuzhou 21116，China  Corresponding author，E-mail: wsfcumt@ 163． com ABSTＲACT Through statistical analysis of random experiments，there is a function of porosity 3lnφ － 2ln( 1 － φ) that approximately follows a normal distribution． In the test particle size range of 30 to 180 mm，the expectation and variance of this function value increase with an increase in grain size of rock blocks． On the basis of deriving the subsidence hypersurface equation of a basic roof，a continuous inhomogeneous distribution model and a random inhomogeneous distribution model of porosity in the combustion space area ( CSA) are deduced． For a rectangular coal fire space，the porosity in the shallow and edge side of CSA is large，but in the middle region is small． In the x － y plane，the porosity contour appears a side lying U-shaped distribution，and the porosity presents negative exponent attenuation with an increase in distance entering CSA along the x axis． In addition，the overall trend of the porosity of contin￾uous distribution and random distribution is the same，but the difference is that the porosity described by the random distribution model has a certain stochastic volatility． The random distribution model of porosity has been used in a numerical simulation of the temperature field in a fire zone，and the accuracy of simulation and the applicability of this porosity model are verified by infrared temperature measurements． KEY WOＲDS underground coal combustion; combustion space area; porosity; discretization; inhomogeneous 收稿日期: 2014--02--08 基金项目: 国家自然科学基金资助项目( 51134020，11472311) 地下煤火是指在赋存于地下的煤体与空气接触 后，发生煤氧复合作用，从氧化自燃到剧烈燃烧后形成 一定的 规 模，并 对 环 境 产 生 一 定 影 响 的 煤 自 燃 现 象［1--3］． 世界上所有产煤国家都不同程度地存在着地