The 2.5D approach is an efficient tool for the dynamic analysis of half-space with longitudinally invariant properties. In this paper, a newly formulated 2.5D version of the NURBS-based isogeometric analysis (IGA) and the scaled boundary IGA (SBIGA) is proposed for analyzing the bounded and unbounded domains, respectively, of a soil-tunnel system subjected to moving railway loads. The bounded domain is discretized by IGA, since the NURBS used can exactly represent the variations in geometry and materials with negligible errors. The unbounded domain is discretized by SBIGA, which automatically satisfies the Sommerfeld radiation condition and can be easily connected with the bounded IGA domain. The 2.5D approach differs from the 2D approach in that both the in-plane and out-of-plane displacements of the profile of the soil-tunnel system are included in analysis. By applying the Fourier transformation, the IGA and SBIGA equations of the 2.5D version in the frequency-wavenumber domain are derived individually and then assembled at the interface of the bounded and unbounded domains. Two examples are prepared for the ground and underground trains moving at subsonic and transonic speeds. Both single and multi moving loads are considered. It was demonstrated that the wave propagation characteristics including the Mach cones at transonic speeds can be precisely predicted. The results in time and frequency domains have been compared with existing ones. It was shown that the proposed method is accurate and reliable for application to a wide range of soil-tunnel systems.

2.5D 方法是动态分析具有纵向不变属性的半空间的有效工具。在本文中，提出了一种新制定的基于 NURBS 的等几何分析 (IGA) 和比例边界 IGA (SBIGA) 的 2.5D 版本，分别用于分析受移动铁路影响的土隧道系统的有界和无界域。负载。有界域由 IGA 离散化，因为使用的 NURBS 可以准确地表示几何和材料的变化，误差可以忽略不计。无界域由 SBIGA 离散化，自动满足 Sommerfeld 辐射条件，可以方便地与有界 IGA 域连接。2. 5D 方法与 2D 方法的不同之处在于，土-隧道系统剖面的平面内和平面外位移都包含在分析中。通过应用傅里叶变换，分别导出频波数域中2.5D版本的IGA和SBIGA方程，然后在有界域和无界域的界面处组装。为以亚音速和跨音速移动的地面和地下列车准备了两个示例。考虑单个和多个移动载荷。结果表明，可以精确预测包括跨音速下的马赫锥在内的波传播特性。时域和频域的结果已与现有结果进行了比较。