Prediction method for stress and deformation of pipe roofs and its engineering application
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摘要: 采用管棚预先对浅埋软弱围岩进行支护时，对管棚力学响应的精确预测是保证管棚结构设计合理性的重要依据。在管棚的弹性地基梁分析模型基础上，考虑掌子面失稳段对管棚约束的弱化，建立基于Pasternak弹性地基梁理论的管棚分析模型来预测预支护段开挖时管棚的受力和变形。利用Euler-Bernoulli梁的控制方程以及Pasternak弹性地基约束反力分布方程，推导出单循环进尺下管棚受力和变形的解析表达式，并通过考虑隧道施工动态过程，提出计算管棚全长范围力学响应的方法。综合分析管径、开挖进尺长度等主要技术参数对管棚力学响应的影响，结果表明，开挖进尺长度是控制管棚变形的关键施工技术指标。通过对管棚分析模型的求解与运用，为管棚的设计和施工提供了一个较为系统的分析预测方法。Abstract: When the pipe roof is used to support the shallow soft surrounding rock in advance, the accurate prediction of the mechanical response of the pipe roof is an important basis to ensure the rationality of its structural design. Based on the elastic foundation beam analysis model for the pipe roof, considering the weakening of the pipe roof constraint caused by the instability section of the tunnel face, a pipe roof analysis model based on the Pasternak elastic foundation beam theory is established to predict the stress and deformation of the pipe roof during the excavation of the pre-support section. Using the governing equation for the Euler-Bernoulli beam and the constraint reaction distribution equation for the Pasternak elastic foundation, the analytical expressions for the force and deformation of the pipe roof under single-cycle footage are derived. By considering the dynamic process of tunnel construction, a method for calculating the mechanical response of the pipe roof in the whole length range is proposed. The influences of the main technical parameters such as the pipe diameter and excavation footage length on the mechanical response of the pipe roof are comprehensively analyzed. The results show that the excavation footage length is the key construction technical index to control the deformation of the pipe roof. Through the solution and application of the analysis model for the pipe roof, a more systematic analysis and prediction method is provided for the design and construction of the pipe roof.
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Keywords:
- tunnel /
- elastic foundation beam /
- pipe roof /
- deformation distribution /
- engineering application
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图 5 管棚预支护范围内拱顶下沉纵向分布
Figure 5. Longitudinal distribution of vault settlement within scope of pre-support of pipe roof
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图 7 环向间距对管棚变形的影响
Figure 7. Influences of circumferential spacing on deformation of pipe roof
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图 8 环向间距对管棚受力的影响
Figure 8. Influence of circumferential spacing on stress of pipe roof
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图 11 开挖进尺长度对管棚变形的影响
Figure 11. Influences of excavation footage length on deformation of pipe roof
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图 12 开挖进尺长度对管棚受力的影响
Figure 12. Influences of excavation footage length on stress of pipe roof
表 1 设计参数取值
Table 1 Values of design parameters
基床系数/(kN·m-3) 地基剪切模量/(kN·m-1) 隧道埋深/m 内摩擦角/(°) 围岩重度/(kN·m-3) 等效惯性矩/m4 等效弹性模量/kPa 开挖高度/m 管棚间距/m 进尺深度/m 30000 2800 6 45.6 24 6.68×10-6 7.89×107 2.4 0.4 0.6 
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表 2 不同管径的截面计算参数
Table 2 Cross section calculation parameters of different pipe diameters
管径/m 等效惯性矩/(10-6 m4) 等效弹性模量/(107 kPa) 0.089 3.08 9.24 0.108 6.68 7.89 0.152 26.00 5.89 0.180 51.50 5.07
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