类矩形盾构隧道纵向等效抗弯刚度解析解

Analytical solution for longitudinal equivalent bending stiffness of quasi-rectangular shield tunnels

结合类矩形盾构隧道截面特点,分别对中性轴位于截面上部边缘(环缝完全闭合)、截面上拱部、截面腰部和截面下拱部4种情况进行分析,并进一步考虑螺栓预紧力和环缝影响范围,推导得到类矩形盾构隧道的纵向等效抗弯刚度解析解,并对影响纵向等效刚度的相关因素进行探究。研究表明:当施加弯矩小于环缝启动弯矩时,环缝全部闭合,等效纵向抗弯刚度有效率为1,中性轴位于截面上部外缘;随着弯矩进一步增加,环缝逐渐张开,同时中性轴位置逐步下移,等效纵向抗弯刚度减小;纵向等效抗弯刚度有效率随环缝作用区系数增大呈现先迅速下降而后缓慢减小的趋势;螺栓预紧力越大,纵向等效刚度越大,中性轴位置随之上移;随宽高比增大,等效纵向抗弯刚度有效率逐渐下降,中性轴位置随之下移,并在中性轴位置角与小圆弧圆心角相等时出现转折点。

According to the sectional characteristics of quasi-rectangular shield tunnels,the neutral axes located at four different positions,the upper section edge(the ring joint is completely closed),the section vault,the section waist and the section invert,are analyzed,respectively.The analytical solution for the equivalent longitudinal bending stiffness of quasi-rectangular shield tunnels is then derived by further considering the pretightening force of bolts and the influence range of circumferential joints.The relative influencing factors on the longitudinal equivalent stiffness are also investigated.It is shown that when the applied bending moment is smaller than the activating one,the circumferential joint is completely closed,the effective efficiency of equivalent bending stiffness is 1,and the neutral axis is located at the upper edge of the section.By further increasing the applied bending moment,the circumferential joint starts to partially separate.Simultaneously,the position of the neutral axis moves down gradually.The equivalent longitudinal bending stiffness decreases with the increase of the applied bending moment.The effective efficiency of the equivalent longitudinal bending stiffness decreases first rapidly and then slowly with the increase of the coefficient of circumferential seam action zone.The greater the pretightening force of bolts is,the larger the equivalent longitudinal bending stiffness is.Subsequently,the position of the neutral axis moves up.With the increase of width-height ratio,the effective efficiency of the equivalent bending stiffness decreases gradually,the position of the neutral axis moves down subsequently,and a turning point appears when the position angle of the neutral axis is equal to the center angle of small arc.