Analytical solution for equivalent stiffness of shield tunnels under combined action of longitudinal channel steel and axial force
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摘要: 为准确快速地预测纵向槽钢加固技术对盾构隧道等效刚度的影响，开展了纵向槽钢加固技术的理论研究。解析地提出了纵向槽钢和纵向轴力耦合作用的盾构隧道等效刚度理论解，并与经典理论、模型试验和数值模拟对比验证了本方法的可靠性。结果表明盾构隧道的中性轴φ随槽钢、纵向轴压力的增加而减小，其大小直接改变了隧道管片间的接触状态，从而影响了隧道的等效刚度；盾构隧道的等效刚度与纵向轴压力呈S曲线正相关，与弯矩呈非线性反相关，与隧道管片宽度、槽钢截面面积、数量、弹性模量呈线性正比关系；盾构隧道的等效刚度贡献大小顺序依次为纵向槽钢数量、截面面积、弹性模量。从理论上诠释了纵向槽钢等敏感性参数对隧道等效刚度的影响机理，可准确快速地预测纵向槽钢加固效果。Abstract: To accurately and quickly predict the effects of longitudinal channel steel reinforcement technology on the equivalent stiffness of a shield tunnel, the theoretical researches are conducted on the longitudinal channel steel reinforcement technology. A new analytical solution is proposed for the equivalent bending stiffness of the shield tunnel under the combined action of longitudinal channel steel and axial force. The solution can be degenerateed into a special case without longitudinal channel steel, and it is validated those the classical theory, model tests and numerical simulation. The results show that the neutral axial φ of the shield tunnel decreases with the increasing longitudinal channel steel and longitudinal axial force, directly affecting the contact state between tunnel segments, which will impact the equivalent stiffness of the shield tunnel. The equivalent stiffness of the shield tunnel increases nonlinearly in an S-curve with the longitudinal axial force and decreases with the increasing bending moment, which is directly proportional to the width of tunnel segment, the number, elastic modulus and sectional area of channel steel. The influential order on the equivalent stiffness of the shield tunnel is the number, sectional area and elastic modulus of longitudinal channel steel. The influence mechanism of sensitivity parameters of longitudinal channel steel on the equivalent stiffness of tunnels is theoretically explained, which enables accurate and quick prediction of the reinforcement effects of longitudinal channel steel.
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图 1 等效线刚度及槽钢连接示意图
Figure 1. Diagram of equivalent linear stiffness and connection of channel steel
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图 3 等效刚度有效率与荷载关系图
Figure 3. Relationship between effective ratio of equivalent stiffness and load
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图 4 等效刚度有效率与螺栓数量
Figure 4. Relationship between effective ratio of equivalent stiffness and number of bolts
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图 5 纵向轴力对等效刚度和中性轴的影响
Figure 5. Effects of longitudinal axial force on equivalent stiffness and neutral axis of tunnel
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图 6 弯矩和纵向轴力对等效刚度的影响
Figure 6. Effects of bending moment and longitudinal axial force on equivalent stiffness of tunnel
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图 7 管片宽度对等效刚度的影响
Figure 7. Effects of width of tunnel segment on equivalent stiffness of tunnel
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图 8 槽钢数量对等效刚度的影响
Figure 8. Effect of the number of channel steel on the equivalent stiffness of tunnel
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图 9 槽钢面积对等效刚度的影响
Figure 9. Effects of sectional area of channel steel on equivalent stiffness of tunnel
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图 10 槽钢模量对等效刚度的影响
Figure 10. Effects of elastic modulus of longitudinal channel steel on equivalent stiffness of tunnel
原型隧道 模型隧道 R t n lt Et Eb lb Rb R t n lt Et Eb lb Rb 3.1
m350
mm17 1.0
m34.5
GPa206
GPa400 mm 15
mm200 mm 23 mm 6 65 mm 2.06 GPa 2.41 GPa 34 mm 8
mm
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R t n lt Et Eb lb Rb 3.0
m300 mm 16 1.0
m34.5 GPa 206 GPa 400 mm 15 mm
下载: 导出CSV
表 3 纵向槽钢设计参数（C14b）
Table 3 Design parameters of longitudinal channel steel
槽钢厚度b 槽钢数量ng 槽钢模量Ecg 槽钢面积Ag 60 mm 7根 206 GPa 21.316 cm2
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