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Sensitivity and Linear Correlation Analysis of Secondary Lining Structures in Highway Tunnels
DOI: 10.12677/HJCE.2022.115075, PDF, HTML, XML, 下载: 116  浏览: 207  科研立项经费支持

Abstract: In order to study the influence of highway tunnel lining thickness on the secondary lining, a highway tunnel is used as an example to construct a structural finite element calculation model by using the “load-structure method”, and the sensitivity and linear correlation analysis of the secondary lining is achieved by using PDS technology and combining with Monte Carlo analysis. This leads to the influencing factors and laws of action for the random variables of secondary lining. The study concluded that: the influence of lining thickness on the maximum displacement, maximum axial force and maximum bending moment of the lining structure accounted for more than 40%, indicating that the lining thickness has a greater influence on the safety of the tunnel secondary lining structure and is the main influencing factor of the secondary lining safety; the linear correlation coefficients of thickness and its maximum displacement, maximum axial force and maximum bending moment are greater than 0.73, while the slope of the trend line has a larger value, indicating that the linear correlation between lining thickness and tunnel secondary lining safety is obvious, and the influence rate is relatively large. By analyzing the sensitivity and linear correlation of secondary lining in highway tunnels, the research results are proposed to draw reference to the structural design and safe construction of highway tunnels.

1. 引言

2. 隧道模型建立与参数选取

2.1. PDS技术

2.2. 依托工程概况

2.3. 建立有限元模型

Figure 1. “Load-structure” model diagram

2.4. 随机变量取值

Table 1. Summary table of features of random variables

3. 衬砌结构随机变量分布特征分析

Figure 2. Lining thickness distribution curve

Figure 3. Lining elastic modulus distribution curve

Figure 4. Lining elastic coefficient distribution curve

Figure 5. Lining density distribution curve

Figure 6. Vertical load distribution curve

Figure 7. Curve of horizontal load distribution

4. 衬砌结构灵敏度分析

Figure 8. Maximum displacement sensitivity diagram

Figure 9. Maximum shear sensitivity diagram

Figure 10. Maximum axial force sensitivity graph

Figure 11. Maximum bending moment sensitivity diagram

5. 衬砌结构输出变量关于厚度的线性相关性分析

Table 2. Table of lining thickness, trend line slope of random variables and linear orrelation coefficient

Figure 12. Scatter plot of lining thickness and maximum displacement

Figure 13. Scatter diagram of lining thickness and maximum shear force

Figure 14. Scatter diagram of lining thickness and maximum axial force

Figure 15. Scatter diagram of lining thickness and maximum bending moment

6. 结论

1) 通过ANSYS计算程序，利用蒙特卡罗法对随机变量采取循环2000次分析，得到收敛数据，并对随机变量变量分布曲线图进行分析，验证抽样次数满足研究需求及其数据分布与数值的合理性，保证灵敏度分析结果的正确性。

2) 针对衬砌结构最大弯矩、最大位移以及最大剪力进行灵敏度数据分析，分析结构衬砌关于随机输入变量因素比例，得出影响隧道二次衬砌结构最大因素为衬砌厚度，其中衬砌厚度作为衬砌结构的最大位移、最大轴力、最大弯矩方面影响占比均大于40%，影响效果显著，在隧道施工过程中应当对其厚度重点控制。

3) 通过对衬砌结构散点图进行线性相关分析，得知衬砌厚度与相关输出变量指标线性相关程度大，影响速率大，二次衬砌厚度与二次衬砌结构的最大位移、最大轴力、最大弯矩得相关系数均大于0.73，线性相关性大，其中二衬厚度对最大剪力、最大轴力、最大弯矩的趋势线斜率数值较大，其影响速率较大，研究结果对隧道衬砌结构设计和施工提供经验参考。

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