类矩形盾构隧道纵向抗弯刚度分析
Longitudinal bending stiffness of quasi-rectangular shield tunnels
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摘要: 类矩形盾构隧道的等效抗弯刚度是分析其纵向受力变形的重要参数。基于等效连续化模型的基本原理,建立类矩形盾构隧道纵向等效连续化模型,推导得到类矩形盾构隧道的等效抗弯刚度解析解。通过参数分析,研究螺栓、管片宽度、厚度和截面形状等参数对类矩形盾构隧道纵向抗弯刚度有效率的影响。研究表明,由于类矩形盾构隧道截面的特殊性,在建立等效抗弯刚度模型时,需分别对中性轴在隧道腰部和拱底两种不同的情况进行讨论;增加螺栓数量和加大管片宽度可提高类矩形盾构隧道的等效抗弯刚度有效率,中性轴位置随着上移,环缝受拉张开区域减小;增加管片厚度可增加隧道绝对等效抗弯刚度,但是等效抗弯刚度有效率下降,中性轴位置下移;中性轴位置随着宽高比增大而快速下移,当中性轴位置角度与小圆弧圆心角相等时,中心轴下移曲线发生转折;当宽高比为1时,所得解析解退化为圆形盾构隧道等效抗弯刚度解。Abstract: The equivalent bending stiffness of the quasi-rectangular shield tunnel is a key parameter for analyzing its longitudinal deformation under external forces. A longitudinal equivalent continuous model for the quasi-rectangular shield tunnel is established, and its analytical solutions to the equivalent bending stiffness are then derived according to the principles of the longitudinal equivalent continuous model. The effects of connected bolts, width and thickness of linings and shape of cross section on the effective equivalent bending stiffness ratio are discussed and analyzed through parametric analyses. It is found that due to the cross section specificity of the quasi-rectangular shield tunnel, two neutral axis position conditions, namely, the neutral axis at tunnel waist and that at tunnel invert, should be considered, respectively, when establishing the equivalent continuous model. Increasing the connected bolt number and widening the lining width will effectively raise the effective equivalent bending stiffness ratios. Subsequently, the neutral axis then moves up and the opening zone of circumferential joint under tension decreases. Increasing the thickness of linings will increase the absolute value of the equivalent bending stiffness, yet the effective equivalent bending stiffness ratio decreases and the position of neutral axis moves down. The position of the neutral axis moves down sharply with an increase in width-height ratio. If the angle of neutral axis position is equal to the central angle of small arc, the turning point in the moving-down curve of the neutral axis occurs. The proposed analytical solutions can be degenerated into the circular shield tunnel condition when the width-to-height ratio is equal to one.