盾构隧道管片环纵向接头抗弯刚度值的不动点迭代确定方法

METHOD FOR DETERMINING BENDING STIFFNESS OF SHIELD TUNNEL SEGMENT RINGS LONGITUDINAL JOINT BASED ON FIX-POINT ITERATION

盾构隧道管片环纵向接头构造复杂,偏压荷载作用下,其变形具有明显的非线性特征,合理的接头抗弯刚度值是运用梁–弹簧模型进行盾构隧道管片环断面设计、计算的前提,而该抗弯刚度值与接头截面处内力组合情况密切相关。针对双衬垫式管片环纵向接头,利用已有简化力学模型,提出一定轴压作用下,接头各变形模式及各模式下的抗弯刚度解析式,并将已有管片接头各工况加载试验的转角实测值与对应变形模式的理论计算值进行对比,验证了其工程设计适用性。根据接头各变形模式下抗弯刚度解析式,结合基于梁–弹簧模型考虑接头刚度差异性的管片环内各纵向接头处截面内力解析式,构造关于管片环内各纵向接头抗弯刚度值的非线性方程组,由数值计算软件Maple编写该接头刚度非线性方程组的不动点迭代求解程序,多次试算最终得到合理的管片环内各纵向接头抗弯刚度值。

The deformation of the longitudinal joint with a complex structure in shield tunnel is closely related to its internal force and highly nonlinear under eccentric compression. A reasonable value of the bending stiffness of joint is vital for the design of the segment ring of shield tunnels with the beam-spring model. The analytical formulas of calculating the deformations at different deforming modes based on the existed model were presented for the double-padded longitudinal joints under a constant axial force. The angles of rotations measured in the joint bending tests were compared with the calculated results with a good agreement. A non-linear equation system for the joints stiffness was derived considering the stiffness difference between the joints and the segment and using the formulas for the internal force of the segment ring and the one for different deformation modes of the joints. The non-linear equation system was solved with the fix-point iteration programme utilizing the software Maple. Reasonable stiffness values of the joints were obtained after several trial calculations with the iteration programme.