【正文】 中 國 礦 業(yè) 大 學(xué) 本科生畢業(yè)論文 姓 名： 金紅全 學(xué) 號 ： 10094715 學(xué) 院： 力學(xué)與建筑工程學(xué)院 專 業(yè)： 工程力學(xué) 論文題目： 基于邊界元的煤巖體穩(wěn)定性分析 指導(dǎo)教師： 高亞楠 職 稱： 講師 二○一三 年 六 月 徐 州 摘 要 在數(shù)學(xué)模擬方法中，以往只有“有限元方法”可以靈活的處理煤巖體復(fù)雜的非線性性狀及地質(zhì)的不連續(xù)性。近十余年來，邊界元法已有很大發(fā)展，提供了求解煤巖體力學(xué)問題的另一種數(shù)值方法，無論是處理復(fù)雜的非線性因素，邊界元法都具有它的特色，是一種簡單而效率高的數(shù)值方法。 煤層巷道的穩(wěn)定性受地應(yīng)力影響極大，分析不同地應(yīng)力分布情況下煤巖巷道的穩(wěn)定性對煤炭開采具有較大的工程意義和指導(dǎo)作用。 本文首先介紹了邊界元的發(fā)展及基本原理，隨后采用邊界元算法，計(jì)算了不同地應(yīng)力分布情況下煤巖巷道的位移場、應(yīng)力場分布及其演化規(guī)律 。計(jì)算表明 在地應(yīng)力與水平方向呈 45176。時(shí)，巷道變形較為明顯，容易失穩(wěn)，因此，在實(shí)際開挖時(shí)，應(yīng)盡量避免 45176。角方向開挖深部煤巖層巷道。 關(guān)鍵字： 邊界元法； 煤巖體穩(wěn)定性；二維彈性問題； 間接邊界元法； 直接邊界元法； ABSTRACT The finite element method was the only way to well solve the plex nonlinear behavior of coal and rock mass and geological discontinuity among all the mathematical simulation methods. During recent ten years, as a simple and highefficient numerical method, boundary element method has been developed greatly, which provides an alternative method to deal with coal and rock mass mechanics and shows its specialty in dealing with the plex nonlinear element. The stability of coal roadway influenced by crustal stress is great. Analysis the stability of the coal rock under different crustal stress distribution of coal mining has great engineering significance and guiding role. This paper first introduces the development of the boundary element and the basic principle. Then it uses the boundary element method. Coal rock is calculated under the different insitu stress distribution of displacement field, stress field distribution and its evolution regularity. Calculation shows that in crustal stress and the 45176。to the horizontal direction. The roadway deformation is relatively obvious. The roadway is easy to lose stability. Therefore, the actual excavation should avoid a 45 176。 angle direction roadway excavation of deep coal strata. Key words: boundary element method。 stability of coal and rock mass。 twodimensional elastic problems。 indirect boundary element method。 direct boundary element method 目 錄 1 邊界元發(fā)展概況 ............................................................................................................................. 1 發(fā)展歷史 ............................................................................................................................. 1 ( 1950— 1978 ) ................................................................................ 2 ( 1978— 1990 ) .................................................................... 3 (1990至今 ) ............................................................................ 5 我國邊界元法研究概況 ........................................................................................................ 5 巖體工程中邊界元的發(fā)展 ..................................................................................................... 6 2 邊界元法基礎(chǔ) ................................................................................................................................. 8 概述 .................................................................................................................................... 8 .................................................................................................. 8 ................................................................................................ 10 Betti 定理、 Kelvin解及 Somigliana 等式 ............................................................11 本章小結(jié) ........................................................................................................................... 13 3 幾種常見的邊界元方法 ............................................................................................................... 14 ................................................................................................................. 14 .............................................................................................................. 14 Flamant 問題 .......................................................................................................... 16 ................................................................................................................. 18 ......................................................................................... 18 .............................................................................. 19 .................................................................................. 21 .............................................................................. 22 ............................................................................................................................ 23 4 案例分析 ...................................................................................................................................... 24 案例 設(shè)計(jì)及軟件介紹 .......................................................................................................... 24 ............................................................................................................................ 25 .......................................................................................................... 25 ................................................................................................................. 28 ............................................................................................................................ 35 5 結(jié)論與展望 .................................................................................................................................. 36 ......................................................................................................... 錯誤 !未定義書簽。 ..............................................................................................