隧洞围岩应力复变函数分析法中的解析函数求解

利用复变函数理论进行地下任意开挖断面隧洞围岩应力分析的前提,是根据围岩应力边界条件方程推导出两个解析函数．从Harnack定理出发,将隧洞围岩应力边界条件方程转化成积分方程;把Laurent级数有限项表示的映射函数引入积分方程中,将以任意开挖断面为边界条件的解析函数求解转化成以单位圆周线为边界条件的求解问题．对积分方程中各被积函数在讨论域内的解析性进行了分析,在此基础上利用留数理论求解了方程中各项积分值,并获得了用来表示任意开挖断面隧道围岩应力的两个解析函数通式．给出了圆形和椭圆形隧道的两个解析函数求解算例,所获得的结果与文献中的结果一致．利用留数理论推导出的两个解析函数通式,适用于任意开挖断面隧洞的围岩应力解析解的计算,且计算过程更为简单,计算结果更为精确．     

单位圆外域-洞室外域共形映射下任意开挖断面隧洞围岩应力解析解

以地下任意开挖断面隧洞为研究对象,将原岩应力场归化为无穷远处与水平轴呈一角度的均匀应力场,引入单位圆外域-洞室外域的共形映射函数,把目标域中以变量z表示的围岩应力函数转化为映射域中的变量ζ表示.将洞壁的应力边界条件方程转化成Cauchy积分方程,利用被积函数的解析性和留数理论,获得了任意开挖断面隧洞围岩应力函数解析通式和围岩应力解析解.将椭圆形隧洞应力边界条件代入应力函数解析通式,求得的φ(z)和ψ(z)与文献结果一致;以公路两车道隧道为研究对象,利用围岩应力解析解开展围岩应力计算和分析,所获结果符合工程规律;利用ABAQUS软件对隧道洞壁应力进行对比分析,分布规律与解析解结果一致.研究表明,只要给出任意开挖断面隧洞的单位圆外-洞室外域共形映射函数,利用研究成果可方便地开展围岩应力解析计算分析.     

基于系统识别方法的围岩弹性模量及水平地应力反演分析

利用有限元软件建立隧道开挖正演模型,基于新奥法隧道施工现场实测围岩收敛数据,采用灵敏度分析建立了参数调整算法,利用系统识别方法对隧道围岩弹性模量及水平地应力进行了反演分析,并讨论了初始值的影响.结果表明,系统识别反演分析法具有自适应能力强、反演分析过程收敛计算稳定性好和计算速度快等优点,在隧道及地下工程领域具有广阔的应用前景.     

考虑浅埋破坏的拖曳锚在黏土中安装运动特性分析

拖曳锚是海洋工程中一种常见的系泊基础,因造价低廉和高承载特性而得到广泛应用.其在海床中的安装轨迹和运动特性受到锚与土体之间复杂相互作用的影响,使得精确定位仍存在挑战.目前已有的塑性屈服面方法被广泛用于计算拖曳锚的运动特性,即假设整个拖曳过程为深埋板在不同深度的破坏过程.实际上,拖曳锚的安装是从浅埋到深埋的连续贯入,因此该方法不能考虑浅埋破坏对拖曳锚运动特性的影响,从而可能导致预测的轨迹不准确.通过有限元分析研究了锚板方位角及埋深比对单向承载和复合荷载下屈服面的影响,确定了锚板浅埋破坏时的屈服面,补充了塑性屈服面法对浅埋破坏效应的考虑;进一步地,考察了锚板方位角、承载系数、浅埋区域大小对拖曳锚轨迹预测和运动特性的影响,并与传统仅假设深埋破坏情况对比分析.结果表明:浅埋破坏时锚板方位角与浅埋区域大小决定了锚板的运动特性和轨迹;合理考虑浅埋破坏后,与纯假设深埋破坏情况比,锚板在达到稳定状态之前的预测埋深和锚链力要小,但极限嵌入深度一致.     

深埋公路隧洞围岩应力和位移分布的复变函数解

为了优化公路隧道的设计和确保施工安全,必须明确公路隧洞开挖时围岩的力学行为.利用复变函数方法,通过保角映射函数把隧洞外域变换为单位圆外域.利用Cauchy(柯西)积分和留数定理求出两个应力函数,从而得到围岩的应力与位移的平面应变问题的解析解.结合曲墙马蹄形断面,通过数学软件MATLAB编程计算,分别给出了应力和仅考虑开挖引起的位移沿隧洞边和坐标轴方向的分布.利用有限元软件ANSYS建立二维平面应变模型,对理论推导得到的应力和位移的分布进行验证,数值解结果与近似解析解结果吻合性很好.研究结果表明:最大的环向应力发生在隧洞拱脚处,最大水平位移发生在拱腰处,最大的沉降和隆起分别发生在拱顶和仰拱中心处.沿坐标轴的正应力在隧洞附近变化较大,不一定在洞边取得最大值,离洞边不到10 m的距离,便分别趋于所加外荷载.位移值在洞边最大,随着离洞边距离的增大,逐渐单调趋于0.     

公路隧道围岩稳定性评价的改进人工神经网络方法

本文运用改进的人工神经网络方法 ,研究了公路隧道围岩稳定性的评价定级问题 .首先讨论了模型建立和算法选择与分析 ,并对实际的工程问题进行了计算和模拟 .所得的评价定级结果接近于实际 ,计算方法可靠 ,计算时间适中 ,方法稳定性良好 .本文的研究结果表明 ,利用人工神经网络方法评价隧道围岩的稳定性具有广阔应用前景 .     

基于Schwarz-Christoffel变换的圆形隧道围岩应力分布特征研究

隧道围岩应力还原到实际区域的变换方法被越来越多地应用到工程实践中,对复杂形状围岩体内的隧道围岩应力计算方法和隧道围岩稳定性的研究具有重要的实践指导意义.该文建立了不规则岩体中开挖圆形隧道的力学模型,运用复变函数理论,通过映射函数Schwarz-Christoffel变换,得到复平面单位圆到隧道所处多边形岩体的映射函数,在复变函数数域内分析了多边形岩体应力的求解步骤,运用弹性力学理论等推导了不规则岩体中圆形隧道的复变应力函数Φ(ξ)和φ(ξ)的表达式,并得出围岩体任一点应力分量σρ和σθ的解析通式.通过具体算例分析可知,岩体形状对圆形隧道的稳定性有较大的影响,隧道所处4种形状下的围岩体最大应力值分布规律为:顶底板的最大应力值从六边形、五边形、四边形、圆形围岩体依次减小,帮部的最大应力值从圆形、四边形、五边形、六边形围岩体依次减小.     

双重孔隙渗流作用井眼围岩损伤力学模型研究

考虑双重介质建立了井眼围岩力学模型,考虑井眼围岩岩体为孔隙、裂缝双重介质,将围岩区域分为破坏区、损伤区和弹性区,建立双重介质渗流作用下的井壁围岩不同区域的损伤力学计算模型和井眼损伤区域的计算方法,计算结果表明理论计算模型与有限元模拟结果吻合较好.     

基于模糊灰色新陈代谢FGM(1,1)模型预测及应用探讨

巷道围岩变形是煤矿开采普遍存在的问题,巷道开挖过程中围岩会出现破裂现象.主要探讨模糊灰色系统的深部巷道围岩变形预测模型及应用,通过分析模糊数学理论、灰色理论,给出模糊灰色系统预测新陈代谢模型.     

基于层次分析-可拓模型的公路隧道施工风险评估

公路隧道施工存在的风险因素较多、较为复杂,运用科学的方法对公路隧道施工风险进行评估,具有一定的现实意义.首先,从地质条件、开挖断面等四个方面对风险进行划分,建立公路隧道施工风险评估指标体系.其次,运用层次分析法确定各评估指标权重,基于该权重建立层次分析-可拓模型,综合考虑公路隧道施工风险发生的概率及带来的损失,将风险定级.最后,结合湖南地区某公路隧道工程进行实例分析,得出地质条件风险、开挖断面风险、隧洞施工风险、洞口工程风险分别为高、较高、中等、较高,总体风险为较高的结论.在项目实施过程中,风险的现场调研情况与评估结果较为接近,证明了方法可行.运用层次分析-可拓模型对公路隧道施工风险评估是一种新的尝试,能够为同类问题的研究提供借鉴.     

Analytical stress and displacement around non-circular tunnels in semi-infinite ground

The construction of non-circular tunnels at shallow depths is becoming increasingly common to efficiently use excavation space. However, the stress concentration and ground movement are probably much greater around shallow non-circular tunnels than around deep ones; the greater stress and ground movement have significant negative effects on tunnel stability and the safety of nearby structures. This study provides a methodology for obtaining the analytical solutions of ground response induced by non-circular tunnel excavation. The surcharge loadings and gravity induced initial stresses, as well as the internal forces due to liners, are considered in the derivation.Using the Schwartz alternating method combined with complex variable theory, a series of two types of problems on simply connected domain, i.e., a non-circular hole in an infinite plane and a half-plane without holes, is in turn successfully solved. Convergent and accurate analytical solutions are finally achieved by superposing the solutions in all the alternating iterations. The analytical solutions exhibit a close agreement with the numerical results, except for the horizontal displacement along the line near the ground surface. Finally, a parametric study is performed for the elliptical/square tunnel subjected to infinite surcharge loadings.The proposed analytical solutions have great value for the conceptual understanding of the mechanical behavior of non-circular tunnels and for verifying the numerical models. Moreover, an alternative approach is provided for the preliminary designs of future shallow tunnels excavated in rock or medium/stiff clay.     

非圆形水工衬砌隧洞与横观各向同性岩体在光滑接触下的解析分析

提出了横观各向同性岩体中的非圆形水工衬砌隧洞在各向同性衬砌与岩体处于光滑接触条件下的解析方法.基于复变函数理论,通过建立两种介质在光滑接触边界上的力和位移连续关系以及衬砌自由边界的水压力边界条件,考虑衬砌支护滞后效应并使用幂级数解法获得解析解.针对倾斜结构面岩体中的马蹄形水工衬砌隧洞,使用解析和数值方法验证了解析解的正确性,获得了岩体各向异性和不同洞内水压力对衬砌和围岩接触边界,以及衬砌自由边界上应力和位移分布的影响规律.     

A semi-analytical solution for shallow tunnels with radius-iterative-approach in semi-infinite space

This study presents a semi-analytical elastic-plastic solution for a shallow tunnel subjected to ground loss in the strain-softening surrounding rock. The most important contribution is the radius-iterative-approach in which the initial plastic radius is first determined by the strain continuity boundary condition on the elastic-plastic interface and then corrected to the precise one. The corrected approach follows three steps: (1) Applying the radius increment technique to semi-infinite space (2) Carrying out the plastic radius correction by using iteration method from the elastic-plastic interface to the tunnel wall. (3) If the calculated convergence value is equal to the convergence value on the tunnel wall, the accurate determination of the plastic region, stresses, and displacements, of the whole half plane, can be derived consequently. All the results compare favorably with numerical simulation results. The study completes the theoretical framework for addressing the fundamental problem of shallow tunnels excavated in the semi-infinite space and also provides a useful theoretical tool for potential application on the tunnel and underground engineering problems.     

基于线性涡模型的风洞孔壁干扰特性分析

发展了一种适用于二元翼型试验洞壁干扰特性的评估和修正方法.基于Prandtl-Glauert速度势方程和布置在模型及洞壁表面的线性涡,采用迭代方法计算了风洞孔壁对翼型表面压力分布特性的影响,分析了不同孔壁透气特性参数的影响规律和量值,利用与国外参考结果及风洞试验结果的对比确定了该方法的准确性.结果表明,孔壁对翼型绕流的影响主要反映在上翼面吸力峰和最大厚度位置之间,使压力系数减小,积分后的升力系数降低,且随着孔壁透气特性参数的增大,洞壁干扰由实壁特性向开口特性发展,洞壁干扰、影响量急剧增大.与传统方法相比,该方法计算快速,结果可靠,同时具备试验前评估的能力,可用于亚临界范围内翼型表面压力的快速估算,以及翼型试验的洞壁干扰修正.     

深埋隧洞围岩应力的精确解与近似解的对比分析

对不同断面形状的深埋隧洞进行了分析,比较了隧洞围岩应力解析解与通过当量半径方法得到的近似解之间的差别.首先,应用复变函数的基本理论,给出圆形、椭圆、矩形、直墙拱形等几种常见深埋隧洞围岩应力的解析表达式.其次,应用当量半径的折算形式,将其任意形状的边界转化为标准圆形断面,利用Lamé解答得到了各围岩应力分量.最后,考虑隧洞断面形状参数的变化,通过数值算例对精确解和近似解进行了比较,分析了当量半径折算形式的精确度.在此基础上,应用有限元方法验证了复变函数解析解的精确性,以椭圆、矩形和直墙拱形的复变函数解验证当量半径精确度.结果表明,当量半径的折算形式解答与精确解答之间相似程度与隧洞的断面形状和几何参数之间有着密切的关系.     

Analytical prediction of tunneling-induced ground movements and liner deformation in saturated soils considering influences of shield air pressure

Complex underground constructions in urban areas require strict predictions for ground movements and liner deformation induced by shield-driven tunneling, in which the complex interaction mechanics between ground and liner play a substantial role. Previous studies, however, provided little information on the ground-liner interaction and less attention to the effects of groundwater and compressed air during the shield operation. This paper presents a closed-form analytical solution for predicting long- and short-term ground deformation and liner internal forces induced by tunneling in saturated soils in which shield excavation effects with and without air pressure are both considered. The oval-shaped convergence deformation pattern is incorporated as the boundary condition of displacements around the tunnel section. This paper also investigates the difference between uniform radial and oval-shaped convergence deformation patterns on the ground and tunnel responses. Generally, the predicted ground movements by the oval-shaped deformation pattern aligns well with measured data of actual tunnels with and without considering the shield air pressure. It is comparatively observed that the shield excavation under air pressure obtains larger ground deformation than the non-pressure condition, and the long-term ground settlements induced by tunneling in saturated soils are confidently larger than the short-term. Moreover, the effects of sensitive parameters, including the shield air pressure, the long- and short-term effects on the tunneling-induced ground movements are assessed based on the oval-shaped deformation pattern. Furthermore, parametric analyses are conducted to measure the influences of concerned tunneling coefficients on the liner displacements and internal forces, namely, soil Young's modulus, soil unit weight, coefficient of lateral soil pressure, tunnel radius, tunnel buried depth and gap parameter. In summary, the analytical approach proposed in this research provides an effective insight into the ground-liner interaction mechanics related with the shield air pressure, which can serve as an alternative approach in the preliminary design for conservatively estimating the excavation influences caused by tunneling in saturated soils.