基于零空间法的基坑开挖既有隧道竖向变形研究

• Published in: 工程科学与技术 pp. 1 - 11
• Main Authors: 郭文杰, 杨文成, 罗文俊, 柴天建, 张海娜, 陈顺满
• Format: Journal Article
• Language: English
• Published: Editorial Department of Journal of Sichuan University (Engineering Science Edition) 01.01.2025
• Subjects: Euler-Bernoulli beam; foundation pit excavation; null space method; tunnel uplift
• ISSN: 2096-3246

ObjectiveAccurately evaluating the influence of foundation pit excavation on the vertical deformation of existing tunnels is very important to ensure the safe operation of existing tunnels. However, the traditional energy method is often difficult to construct a displacement field function that satisfies the boundary conditions when calculating the vertical deformation of tunnels under the action of foundation pit excavation. In this paper, based on the total potential energy equation of the system established by using the functional relationship, the vertical deformation of the tunnel is solved by using the variational method and the null space technology. The purpose is to better evaluate the influence of foundation pit excavation on the vertical deformation of the existing tunnel.MethodsFirstly, the tunnel is simplified as an equivalent continuous Euler-Bernoulli beam placed on the Pasternak foundation. The Mindlin solution is used to calculate the vertical additional force of the tunnel under the excavation of the foundation pit above. According to the Euler-Bernoulli beam theory, the differential equation of the vertical deformation of the tunnel is established. Because the solution process of the fourth-order differential equation is more complicated, in order to simplify the calculation, this paper chooses to use the null space method to solve it. Firstly, the tunnel deformation w is expressed by the product of the field function f and the unknown weight coefficient a, and the field function f is expressed by the improved Fourier series. According to the functional relationship, the functional relationship of each part of the system is written, and the total potential energy equation of the system is established. Then, the variational method is used to simplify the equation. Further, the null space technology is used to solve the constraint matrix to obtain the weight coefficient a, and then the tunnel deformation w is obtained. The theoretical analysis of the vertical deformation of the existing tunnel under the excavation of the foundation pit is obtained, and the accuracy of the method in this paper is verified by comparing with the measured data, the finite element calculation results and the existing Winkler foundation method.Results and DiscussionsThe vertical displacement value of the tunnel calculated by the method in this paper is compared with the field measured data, the finite element calculation results and the results obtained by the Winkler foundation method in the existing research. Through comparison, it is found that the maximum vertical displacement value of the tunnel calculated by the method in this paper and the measured maximum displacement value occur at about 4 m from the projection point of the tunnel axis to the center of the foundation pit. The maximum value calculated by the method in this paper is 6.54 mm, and the maximum value measured in the field is about 6.4 mm. The two are almost equal, and the distribution trend of the displacement value obtained by the method in this paper and the measured value in the direction of the tunnel axis is also consistent. The displacement value near the center of the foundation pit is the largest, and the two sides gradually decrease until it is zero. By comparison, it is not difficult to see that compared with the finite element method and the Winkler foundation method, the vertical displacement value of the tunnel calculated by the method in this paper is closer to the measured data value. It can be further concluded that the Pasternak foundation considering the continuity of the soil has more advantages than the Winkler foundation in calculating the vertical displacement value of the tunnel under the influence of foundation pit excavation. Therefore, this method can effectively calculate the vertical displacement value of the tunnel under the influence of foundation pit excavation, evaluate the influence of foundation pit excavation on the vertical deformation of the existing tunnel, and provide reference for practical engineering. On the basis of the verification, the actual engineering conditions are taken as an example for parameter analysis. The distance d between the center of the foundation pit and the tunnel axis is controlled within the range of 0-20 m. The buried depth z0 of the tunnel, the depth h of the foundation pit and the angle α between the foundation pit and the tunnel are changed. It can be seen from the relationship curve between each parameter and the maximum vertical displacement value that when the distance d is small, the maximum uplift value of the tunnel gradually decreases with the increase of the buried depth z0 of the tunnel. When the distance d is large, the maximum uplift value of the tunnel increases first and then decreases with the increase of the buried depth z0 of the tunnel. This is because when the tunnel is far from the center of the foundation pit. The additional stress applied to the tunnel by the equivalent unloading of the foundation pit increases first and then decreases with the increase of the buried depth of the tunnel. When the center of the foundation pit is far away from the tunnel axis, the influence of the buried depth z0 on the tunnel uplift is significantly reduced. Therefore, in the actual project, the excavation of the foundation pit should be avoided as far as possible above the tunnel axis. The maximum vertical displacement of the tunnel increases with the increase of the depth h of the foundation pit. The reason for this phenomenon is that the vertical deformation of the tunnel is mainly affected by the excavation load at the bottom of the pit. The increase of distance d significantly reduces the influence of the change of foundation pit depth h on the vertical deformation of the tunnel. It can be seen that in the actual project, the excavation of the foundation pit should be kept away from the position directly above the tunnel axis as much as possible or the excavation operation directly above the tunnel axis cannot be avoided. The reinforcement and monitoring of the tunnel should be strengthened. Increasing the distance d between the center of the foundation pit and the axis of the tunnel, the maximum uplift value of the tunnel decreases first with the increase of the angle α of the foundation pit, and then decreases with the increase of the angle α of the foundation pit. When α is 0 °, changing the size of the distance d, the maximum vertical displacement value of the tunnel is about 9 ~ 25 mm. When α is 90 °, changing the size of the distance d, the maximum vertical displacement value of the tunnel is about 15 ~ 22 mm. It can be seen that with the increase of the angle α of the foundation pit, the tunnel uplift tends to be stable, that is, the increase of the angle of the foundation pit reduces the influence of the distance d on the tunnel uplift.ConclusionsCompared with the actual engineering case, the vertical displacement distribution of the tunnel calculated by the method in this paper is in good agreement with the measured data, which indicates that the method in this paper can effectively calculate the vertical displacement value of the tunnel under the excavation of the foundation pit. On the basis of verification, the parameters are analyzed. The results show that as d increases, the vertical displacement value of the tunnel increases, α increases, and the maximum vertical displacement value of the tunnel tends to be stable. With the increase of distance d, the maximum vertical displacement of the tunnel shows a decreasing trend, and the increase of d can significantly reduce the influence of z0 change on the tunnel uplift. With the increase of h, the maximum displacement value of the tunnel increases, and the increase of d significantly reduces the influence of h change on the vertical deformation of the tunnel. The variation trend of tunnel displacement obtained by analysis can provide reference for proposing deformation control measures, which is of great significance to practical engineering.Study on Vertical Deformation of Existing Tunnel in Foundation Pit Excavation Based on Null Space MethodGUO Wenjie1，YANG Wencheng1，LUO Wenjun1,2*，CHAI Tianjian2，ZHANG Haina2，CHEN Shunman2(1.School of Transportation Engineering, East China Jiaotong University, Nanchang 330013, China;2.Jiangxi Provincial Key Laboratory of Disaster Prevention, Mitigation and Emergency Management, East China Jiaotong University, Nanchang 330013, China)