外圆内椭管片结构内力计算模型

为了使地铁隧道适应地层荷载的不均匀性，参考异形管片结构形式，同时兼顾制作与施工等因素，提出外圆内椭管片结构，以保证管片结构最不利位置的刚度满足安全要求，并适当降低管片其他位置的刚度，充分利用材料特性；采用刚度阶梯折算法求解外圆内椭管片的柔度系数与自由项，建立外圆内椭管片的计算模型；参照实际工程地质条件，研究外圆内椭管片的内力分布特点；利用《铁路隧道设计规范》(TB 1003—2016)对外圆内椭管片的安全性进行评价。计算结果表明:相比于等刚度管片，在相同的荷载条件下，外圆内椭管片减小了管片结构拱顶与拱底的弯矩，将最大弯矩与最大轴力转移至拱腰，在验算时重点分析管片结构拱腰处的内力能否满足安全条件即可，简化了安全验算内容；在稳定性方面，等刚度管片在拱顶、拱肩与拱腰处的安全系数分别为3.07、18.05和2.45，外圆内椭管片在拱顶、拱肩与拱腰处的安全系数分别为2.79、14.86和2.21，虽然较之等刚度管片略有降低，但仍然大于安全验算要求规定的最小值2.0，可充分发挥混凝土的材料特性；在内部空间方面，外圆内椭管片在外径与等刚度管片一致的情况下，等刚度管片的内部空间面积为22.9m2，而外圆内椭管片的内部空间面积为23.76 m2，明显大于等刚度管片面积，因此，可在不扩大外径的条件下，增加了内部空间面积，提高了内部空间利用率。 

Computational model of outer-circle and inner-ellipse shield tunnel lining structure

In order to adapt the metro tunnel to the inhomogeneity of stratum load, referring to the structural form of special-shaped shield tunnel lining and taking into account the factors such as production and construction, the outer-circle and inner-elliptic shield tunnel lining structure was proposed, ensuring that the stiffness of the most unfavorable position of the lining structure meets the safety requirement, appropriately reducing the stiffness of the rest of the lining structure, and taking advantage of material properties. The flexibility coefficient and free term of outer-circle and inner-elliptic shield tunnel lining were solved by the stiffness step discounting method, and the calculation model of the lining was established. Referring to the actual engineering geological condition, the internal force distribution characteristics of outer-circle and inner-elliptic shield tunnel lining were studied. The safety of outer-circle and inner-elliptic shield tunnel lining was evaluated by the Code for Design of Railway Tunnel (TB 1003—2016). Calculation results show that compared with the equal stiffness shield tunnel lining, under the same loading condition, the outer-circle and inner-elliptic shield tunnel lining reduces the bending moments at the top and bottom of the lining structure, and transfers the maximum bending moment and maximum axial force to the arch waist, which simplifies the safety test by focusing on whether the internal force at the arch waist of the lining structure can meet the safety condition during the test. In terms of stability, the safety factors of equal stiffness shield tunnel lining are 3.07, 18.05 and 2.45 at the vault, arch shoulder and arch waist, respectively. The safety factors of outer-circle and inner-elliptic shield tunnel lining are 2.79, 14.86 and 2.21 at the vault, arch shoulder and arch waist, respectively, and slightly lower than those of the equal stiffness shield tunnel lining, but still greater than the minimum value 2.0 stipulated by the safety checking requirement, giving full play to the material characteristics of concrete. In terms of internal space, when the outer-circle and inner-elliptic shield tunnel lining and the equal stiffness shield tunnel lining have the same outer radius, the internal space area of the equal stiffness shield tunnel lining is 22.9 m2, and the value of the outer-circle and inner-elliptic shield tunnel lining is 23.76 m2 and significantly larger than that of the equal stiffness shield tunnel lining. Therefore, the area and utilization rate of internal space of the proposed lining increase without expanding the outer radius. 8 tabs, 11 figs, 31 refs.