深埋圆截面隧道弹—粘—塑—脆性应力—位移及任意截面隧道塑性区的解析计算

发布时间：2018-01-11 05:19

本文关键词：深埋圆截面隧道弹—粘—塑—脆性应力—位移及任意截面隧道塑性区的解析计算　出处：《北京交通大学》2014年硕士论文　论文类型：学位论文

【摘要】：隧道围岩应力-位移解析解能够清晰准确地反映应力、位移的变化规律,并可以通过分析不同参数的计算结果获得规律性的认识。但是目前还没有针对现有深埋隧道围岩应力-位移解析解的系统计算验证以及与数值解的对比分析,同时现有解析解原文中一些不清楚甚至不合理的地方也需要进一步说明与纠正。本文针对深埋圆截面隧道弹-粘-塑-脆性应力-位移解析解进行解析计算并和数值解对比分析,利用分段光滑截面弹性解来预测塑性区。主要研究内容及成果如下： (1)针对均匀轴对称初始应力场内深埋圆截面隧道,对隧道围岩服从四种不同的屈服准则和弹塑性模型的组合,包括：摩尔-库伦屈服准则和理想弹塑性零塑性体积应变模型、摩尔-库伦屈服准则和弹-脆塑性非相关流动模型、无量纲霍克-布朗屈服准则和理想弹塑性非相关流动模型、霍克-布朗屈服准则和弹-脆塑性非相关流动模型,进行解析计算并和数值解对比分析。其中,当解析解服从零塑性体积应变模型和弹-脆塑性模型时,数值模拟软件FLAC中没有内置这些模型,此时数值解采用FLAC内置的理想弹塑性模型和上述解析解对比,以分析围岩脆性等差异产生的影响。与采用理想弹塑性零塑性体积应变模型相比,采用理想弹塑性模型的围岩应力完全相同而相对径向位移较大,故采用理想弹塑性模型是偏于安全的。与理想弹塑性模型不同,当采用弹-脆塑性模型时,屈服准则中的强度参数会降低为其残余值。因此无论是服从摩尔-库伦屈服准则还是服从霍克-布朗屈服准则,与采用理想弹塑性模型相比,采用弹-脆塑性模型的(脆)塑性区半径、相对径向位移均较大,而(脆)塑性区的径向应力和环向应力均较小。 (2)针对均匀轴对称初始应力场内深埋圆截面隧道弹-脆-粘塑性模型的解析解,首先,通过差分计算求解关于初始塑性区待定函数的超越方程,求得待定函数的近似解；然后,求解并分析塑性区半径随时间变化情况、围岩任意点的应力和相对位移随时间变化情况、任意时刻围岩的应力和相对位移随距离变化情况；最后,把服从宾海姆弹-粘脆塑性模型的解析解与数值解对比分析,由于数值模拟软件FLAC中没有内置这种模型,故此处数值解采用FLAC内置的马克斯威尔粘弹塑性模型和上述解析解对比,以分析围岩脆性等差异产生的影响。弹-脆-粘塑性模型动态塑性区围岩任意点的环向应力随时间的变化是不连续的,在瞬态塑性区半径扩张到该点瞬时发生跳跃；任意时刻围岩环向应力随距离变化是不连续的,在初始塑性区半径和瞬态塑性区半径两处发生跳跃。 (3)针对均匀初始应力场内深埋边界分段光滑截面隧道复势函数弹性解,首先,以椭圆隧道为例证明当映射函数的系数取值使隧道截面竖向对称轴和坐标纵轴夹角为π/4时,把隧道顺时针旋转π/4后隧道截面的竖向对称轴和坐标纵轴重合,此时求得的应力、位移,与映射函数的系数取值使得隧道截面的竖向对称轴和坐标纵轴重合时求得的应力、位移相差π/4。然后,进行解析计算分析并和数值解对比分析。 (4)把均匀初始应力场内深埋边界分段光滑截面隧道弹性解的解析计算结果带入屈服准则来预测塑性区,并对不同截面隧道的预测解和解析解、数值解以及不同初始应力条件下的预测解进行对比分析。通过计算对比可见,这种预测隧道塑性区范围的方法有一定局限性,当粘聚力和内摩擦角取值相对较大时,塑性区的理论预测较为准确。
[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.

【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：U451

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