基于零空间法的基坑开挖既有隧道竖向变形研究

doi:10.12454/j.jsuese.202500088

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基于零空间法的基坑开挖既有隧道竖向变形研究

更新时间：2025-05-19

- 基于零空间法的基坑开挖既有隧道竖向变形研究
- Advanced Engineering Sciences Pages: 1-11(2025)
- 作者机构：
  
  1.华东交通大学交通运输工程学院，江西南昌 330013
  2.华东交通大学江西省防灾减灾及应急管理重点实验室，江西南昌 330013
- 作者简介：
- 基金信息：
- DOI：10.12454/j.jsuese.202500088
  CLC：［U25］
- Published Online：28 April 2025，
- 稿件说明：
移动端阅览
郭文杰,杨文成,罗文俊等.基于零空间法的基坑开挖既有隧道竖向变形研究[J].工程科学与技术,

GUO Wenjie,YANG Wencheng,LUO Wenjun,et al.Study on Vertical Deformation of Existing Tunnel in Foundation Pit Excavation Based on Null Space Method[J].Advanced Engineering Sciences,XXXX,XX(XX):1‒11.
郭文杰,杨文成,罗文俊等.基于零空间法的基坑开挖既有隧道竖向变形研究[J].工程科学与技术, DOI：10.12454/j.jsuese.202500088.

GUO Wenjie,YANG Wencheng,LUO Wenjun,et al.Study on Vertical Deformation of Existing Tunnel in Foundation Pit Excavation Based on Null Space Method[J].Advanced Engineering Sciences,XXXX,XX(XX):1‒11. DOI： 10.12454/j.jsuese.202500088.

摘要

为研究上方基坑开挖对既有隧道竖向变形的影响，将隧道简化为搁置在Pasternak地基上的等效连续Euler-Bernoulli梁，先利用Mindlin解计算隧道在上方基坑开挖作用下受到的竖向附加力，再根据Euler-Bernoulli梁理论，建立隧道竖向变形微分方程，写出系统各部分功能关系式，建立系统总势能方程，而后利用变分法和零空间技术，得到基坑开挖作用下既有隧道竖向变形的理论解析，并通过与工程实测数据进行对比，验证了本文方法的准确性；对隧道轴线与基坑中心的距离

、基坑长边与隧道轴线的夹角

、隧道埋置深度

、基坑深度

展开参数分析，结果表明：

增大，隧道竖向位移值增大，

增加，隧道最大竖向位移值趋于稳定；距离

增大，隧道最大竖向位移值呈现减小趋势，

的增加能够显著减小

变化对隧道隆起的影响；

增大，隧道最大位移值增大，

的增加显著减小了

变化对隧道竖向变形的影响。

Abstract

Objective

Accurately 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.

Methods

Firstly

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 solut

ion 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

is expressed by the product of the field function

and the unknown weight coefficient

and the field function

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

and then the tunnel deformation

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 Discussions

The 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 t

he 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

between the center of the foundation pit and the tunnel axis is controlled within the range of 0-20 m. The buried depth

of the tunnel

the depth

of the foundation pit and the angle

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

is small

the maximum uplift value of the tunnel gradually decreases with the increase of the buried depth

of the tunnel. When the distance

is large

the maximum uplift value of the tunnel increases first and then decreases with the increase of the buried depth

of the tunnel. This is because when the tunnel is far from the center of the foundation pit. The additional stress applied to the tunn

el 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

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

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

significantly reduces the influence of the change of foundation pit depth

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

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

of the foundation pit

and then decreases with the increase of the angle

of the foundation pit. When

is 0 °

changing the size of the distance

the maximum vertical displacement value of the tunnel is about 9 ~ 25 mm. When

is 90 °

changing the size of the distance

the maximum vertical displacement value of the tunnel is about 15 ~ 22 mm. It can be seen that with the increase of the angle

of the foundation pit

the tunnel uplift tends to be stable

that is

the increase of the ang

le of the foundation pit reduces the influence of the distance

on the tunnel uplift.

Conclusions

Compared 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

increases

the vertical displacement value of the tunnel increases

increases

and the maximum vertical displacement value of the tunnel tends to be stable. With the increase of distance

the maximum vertical displacement of the tunnel shows a decreasing trend

and the increase of

can significantly reduce the influence of

change on the tunnel uplift. With the increase of

the maximum displacement value of the tunnel increases

and the increase of

significantly reduces the influence of

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 Method

GUO Wenjie

，

YANG Wencheng

，

LUO Wenjun

，

CHAI Tianjian

，

ZHANG Haina

，

CHEN Shunman

(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)

关键词

Keywords

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