本文關鍵詞：深埋圓截面隧道彈—粘—塑—脆性應力—位移及任意截面隧道塑性區(qū)的解析計算　出處：《北京交通大學》2014年碩士論文　論文類型：學位論文

  更多相關文章： 隧道圍巖 應力-位移 解析解 數(shù)值計算 塑性區(qū)

【摘要】：隧道圍巖應力-位移解析解能夠清晰準確地反映應力、位移的變化規(guī)律,并可以通過分析不同參數(shù)的計算結果獲得規(guī)律性的認識。但是目前還沒有針對現(xiàn)有深埋隧道圍巖應力-位移解析解的系統(tǒng)計算驗證以及與數(shù)值解的對比分析,同時現(xiàn)有解析解原文中一些不清楚甚至不合理的地方也需要進一步說明與糾正。本文針對深埋圓截面隧道彈-粘-塑-脆性應力-位移解析解進行解析計算并和數(shù)值解對比分析,利用分段光滑截面彈性解來預測塑性區(qū)。主要研究內容及成果如下： (1)針對均勻軸對稱初始應力場內深埋圓截面隧道,對隧道圍巖服從四種不同的屈服準則和彈塑性模型的組合,包括：摩爾-庫倫屈服準則和理想彈塑性零塑性體積應變模型、摩爾-庫倫屈服準則和彈-脆塑性非相關流動模型、無量綱霍克-布朗屈服準則和理想彈塑性非相關流動模型、霍克-布朗屈服準則和彈-脆塑性非相關流動模型,進行解析計算并和數(shù)值解對比分析。其中,當解析解服從零塑性體積應變模型和彈-脆塑性模型時,數(shù)值模擬軟件FLAC中沒有內置這些模型,此時數(shù)值解采用FLAC內置的理想彈塑性模型和上述解析解對比,以分析圍巖脆性等差異產生的影響。 與采用理想彈塑性零塑性體積應變模型相比,采用理想彈塑性模型的圍巖應力完全相同而相對徑向位移較大,故采用理想彈塑性模型是偏于安全的。 與理想彈塑性模型不同,當采用彈-脆塑性模型時,屈服準則中的強度參數(shù)會降低為其殘余值。因此無論是服從摩爾-庫倫屈服準則還是服從霍克-布朗屈服準則,與采用理想彈塑性模型相比,采用彈-脆塑性模型的(脆)塑性區(qū)半徑、相對徑向位移均較大,而(脆)塑性區(qū)的徑向應力和環(huán)向應力均較小。 (2)針對均勻軸對稱初始應力場內深埋圓截面隧道彈-脆-粘塑性模型的解析解,首先,通過差分計算求解關于初始塑性區(qū)待定函數(shù)的超越方程,求得待定函數(shù)的近似解；然后,求解并分析塑性區(qū)半徑隨時間變化情況、圍巖任意點的應力和相對位移隨時間變化情況、任意時刻圍巖的應力和相對位移隨距離變化情況；最后,把服從賓海姆彈-粘脆塑性模型的解析解與數(shù)值解對比分析,由于數(shù)值模擬軟件FLAC中沒有內置這種模型,故此處數(shù)值解采用FLAC內置的馬克斯威爾粘彈塑性模型和上述解析解對比,以分析圍巖脆性等差異產生的影響。 彈-脆-粘塑性模型動態(tài)塑性區(qū)圍巖任意點的環(huán)向應力隨時間的變化是不連續(xù)的,在瞬態(tài)塑性區(qū)半徑擴張到該點瞬時發(fā)生跳躍；任意時刻圍巖環(huán)向應力隨距離變化是不連續(xù)的,在初始塑性區(qū)半徑和瞬態(tài)塑性區(qū)半徑兩處發(fā)生跳躍。 (3)針對均勻初始應力場內深埋邊界分段光滑截面隧道復勢函數(shù)彈性解,首先,以橢圓隧道為例證明當映射函數(shù)的系數(shù)取值使隧道截面豎向對稱軸和坐標縱軸夾角為π/4時,把隧道順時針旋轉π/4后隧道截面的豎向對稱軸和坐標縱軸重合,此時求得的應力、位移,與映射函數(shù)的系數(shù)取值使得隧道截面的豎向對稱軸和坐標縱軸重合時求得的應力、位移相差π/4。然后,進行解析計算分析并和數(shù)值解對比分析。 (4)把均勻初始應力場內深埋邊界分段光滑截面隧道彈性解的解析計算結果帶入屈服準則來預測塑性區(qū),并對不同截面隧道的預測解和解析解、數(shù)值解以及不同初始應力條件下的預測解進行對比分析。通過計算對比可見,這種預測隧道塑性區(qū)范圍的方法有一定局限性,當粘聚力和內摩擦角取值相對較大時,塑性區(qū)的理論預測較為準確。
[Abstract]:The tunnel surrounding rock stress displacement analytical solution can clearly and accurately reflect the stress, displacement variation, and can be calculated through the analysis of different parameters regularities. But there is no existing deep tunnel system for stress displacement analytic solution calculation verification and comparison with numerical analysis. At the same time, existing analytical solutions are not clear or even unreasonable places also need further explanation and correction. According to the deep buried circular tunnel elastic visco plastic brittle stress displacement analytic solution and numerical solution of analytical calculation and analysis, the use of piecewise smooth section elastic method to predict the plastic zone. The main research contents and results are as follows:
(1) according to the uniform axisymmetric deep buried circular tunnel initial stress field, the surrounding rock of the tunnel to four kinds of yield criterion and elastic-plastic model of different combinations, including: Moore - Kulun yield criterion and ideal elastic-plastic Zero plastic volumetric strain model, Mohr yield criterion and Kulun elasto brittle plastic non associated flow model, the dimensionless Hawke Brown yield criterion and ideal elastic-plastic non associated flow model, Hawke - Brown yield criterion and elasto brittle plastic non associated flow model, analytical calculation and numerical solution of comparative analysis. The analytical solution when the assumption of Zero plastic volumetric strain and elastic model the brittle plastic model, numerical simulation of the model has no built-in software FLAC, the numerical solution using FLAC's built-in ideal elastic-plastic model and the analytical solution compared to influence analysis of surrounding rock brittleness differences.
Compared with the ideal elastoplastic Zero plastic volumetric strain model, the ideal elasto-plastic model has the same stress and larger radial displacement. Therefore, the ideal elastoplastic model is safe.
Different from the ideal elastic-plastic model, when using the elasto brittle plastic model, strength parameter yield criterion will reduce its residual value. So whether Kulun follows the Mohr yield criterion or obeys Hawke Brown yield criterion, and the ideal elastic-plastic model compared with the elasto brittle plastic model the (brittle) plastic zone radius, radial displacement are larger, and the plastic zone (brittle) radial stress and circumferential stress are small.
(2) according to the uniform axisymmetric initial analyses of stress field of deep buried circular tunnel elastic brittle viscoplastic model, firstly, calculate the transcendental equation of initial plastic zone of undetermined function through the differential, obtain an approximate solution of undetermined function; then, solve and analyze the plastic zone radius with time the changes of arbitrary point of rock stress and relative displacement variation with time, stress and displacement of surrounding rock with the change of distance any time; finally, the solution and numerical solution of comparative analysis to analysis of Bingham visco brittle plastic model, because this model has no built-in numerical simulation software FLAC. For numerical solution using FLAC built-in Marx weir viscoplastic model and the analytical solution compared to influence analysis of surrounding rock brittleness differences.
Elasto Viscoplastic Dynamic Model of brittle rock plastic zone of arbitrary point of circumferential stress variation with time is not continuous, transient in the radius of plastic zone expansion to the point of instantaneous jump; any time surrounding the circumferential stress changes with the distance is not continuous, the initial radius of plastic zone the transient and the radius of plastic zone occurs at the two jump.
(3) according to the uniform initial stress field of deep buried tunnel section of piecewise smooth boundary complex potential elastic solution, first of all, the elliptical tunnel for example prove coefficient when the mapping function of the tunnel cross section vertical symmetry axis and coordinate axis angle for PI /4, the vertical axis of symmetry tunnel clockwise PI /4 tunnel section the coordinate axis and overlap, at this time the stress, displacement, and the coefficient of the mapping function makes the vertical symmetry axis and longitudinal axis coordinates overlap tunnel cross section stress according to the displacement difference PI and /4., analytical calculation and numerical solution analysis and comparative analysis.
(4) the calculation results into the yield criterion to predict the plastic zone should be uniform initial analytical solution of deep buried tunnel section smooth piecewise elastic boundary force field, and the prediction of the different sections of the tunnel solution and analytic solution, numerical solution and different initial stress is predicted under the condition of the solution were analyzed by comparing the visible. This prediction method, the plastic zone of the tunnel has certain limitations, when the cohesion and internal friction angle is relatively large, the theoretical prediction of the plastic zone is more accurate.

【學位授予單位】：北京交通大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：U451

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