【作者】 赵龙宾；

【导师】 刘齐建；

【作者基本信息】 湖南大学 ， 岩土工程， 2010， 硕士

【摘要】 中国地域辽阔,地形复杂多样,高等级公路建设中遇到大量的隧道工程问题。受地形的限制和影响,越来越多的隧道出现偏压问题,其理论解析还存在很多难点。本文基于平面弹性复变理论,对地形引起的圆形偏压隧道二次应力场进行了理论解析。主要研究内容和成果包括：(1)将偏压隧道问题应力场的求解分解为三部分。第一部分为偏压隧道的初始应力场；第二部分为体力为零的半平面内作用一个集中力时的应力场,该集中力大小等于开挖洞室部分材料的重力；第三部分为隧道洞周作用一应力张量时的应力场,该应力张量是为了平衡前两部分求解结果以满足应力边界条件。(2)采用平面弹性复变理论和Fourier变换,首次得到了圆形偏压隧道的应力场解析解。引入Mobius保角映射,将所求域映射到一圆环内,分别求出三部分情况下的应力场。最后将三部分结果叠加,得到该问题的闭合形式解。(3)采用本文介绍的方法,对圆形偏压隧道应力场进行参数分析。编写计算程序,实现对问题求解的程序化。对势函数的收敛性进行了探讨。系数的可根据边界条件求得,根据洞周和上边界的应力边界条件,结合无穷远处的位移边界条件可知,在变量k值趋近于无穷大时,系数的ak值应为零,根据这个条件可对系数进行迭代求解出ak,然后根据边界条件求得其他系数,即求出了势函数。由于应力场必须收敛,则要求势函数必须收敛,势函数的系数必须收敛。通过系数的求解,发现势函数的系数随着变量k值的增大急剧收敛,在k=6时,系数的实部和虚部都已经收敛,且大小趋近于零。(4)采用本文介绍的方法,对圆形偏压隧道应力场进行参数分析。探讨了材料和几何参数对计算结果的影响,其中重点分析了泊松比、自由半平面的倾角及隧道埋深等因素的影响。计算结果表明,随着倾角的增大,隧道洞周应力越大,但是最大值一般都出现在洞顶的两侧附近区域；随着埋深的减小,应力在地面处受影响的范围越小；泊松比对偏压隧道应力场的影响较小。更多还原

【Abstract】 China has a vast territory, and a complex and diverse topography, high-grade roads construction engineering encountered in a large number of problems in tunnels. Subject to the restrictions and effects of topography, more and more tunnels appears the problems of unsymmetrical pressure problem, the theoretical analysis of this problem still has a lot of difficulties. Based on plane elastic complex variable theory,this Article theoretically analysised the secondary stress distribution caused by topography in circular unsymmetrical tunnel. The main contents and results include:(1) In this study, the integral stress distribution is divided into three sub-distributions. The first one is the initial stress distribution in the unsymmetrical tunnels; and the second is that of a concentrates stress, which is equal to the weight of materials dug out, in a half plane excluding the field of body forces. The third is that caused by stresses weighting on the tunnel’s periphery. This stress tension is used to balance the previous two segments and to adaptive the whole distribution to satisfy the initial boundary conditions.(2) Using plane elastic complex variable method and of Fourior transform, the stress distribution in round unsymmetrical tunnels is obtained at the first time. And the Mobius conformal mapping is adopted. The solution domain is represented by a circle and the three sub-distributions are obtained. The closed form is gained by summing them.(3) Using the methods this article describes, the parameters of the circular bias tunnel’s stress field can be got. Writing programs and procedures to achieve the solution of the problem. The convergence of the potential function is discussed. Coefficients can be obtained under the boundary conditions, according to tunnel on the border weeks and the stress boundary conditions, combined infinite and known boundary conditions, the value of the variable k approaches infinity, the coefficient of ak value should be zero, according to the conditions of the coefficients can be solved out of iterative ak, and then obtained the boundary conditions of other factors, to derive the potential function. As the stress field must be convergence, requires the potential function must converge, the coefficient of the potential function must converge. Through coefficient is found that the potential function of the coefficient of variable k with the rapid increase of the value of convergence, in the k= 6, the coefficient of the real and imaginary parts have convergence, and the size of the near zero.(4)Last, apply the methods this article describes to analysis stress field parameters of the circular unsymmetrical tunnel. Investigate the influence of material and geometric parameters on the calculation results, which focus on analysis of Poisson’s ratio, free half-plane angle and tunnel depth and some other factors. The results show that with increasing inclination, the greater the tunnel on stress, but the maximum generally appears in the top of the cave near the region on both sides; as the depth decreases, the stress get smaller infuence area in the surface; Poisson’s ratio has little effect on the stress distribution of unsymmetrical tunnel.更多还原