基于2.5维有限元-完全匹配层技术的隧道振动建模研究

为解决隧道受周围区域复杂影响的三维隧道动力模拟问题,基于有限单元法,采用2.5D技术,应用完全匹配层（PML）处理由有限单元网格截断的边界,提出一种针对超长隧道结构动态性能模拟的高效、精确解法。结合2.5D技术、有限单元法（FEM）及完全匹配层（PML）的方法并不常见,推导2.5D技术和有限单元法（FEM）结合法的方程,着重说明其与2.5D技术和完全匹配层（PML）结合法的兼容性。通过与常用数值模型（MEF-MEC）和半解析解（PIP）法的结果验证,证明了模型的准确性,并进行了参数研究,以评估隧道和土体性质对土体振动的影响。结果表明：提出的2.5D MEF-PML方法能够解决有限元法不能处理无限域的缺点,与常规PML法相比,精度更高,在隧道动力分析时,能准确考虑隧道周围区域因素的影响。

Modeling and vibration analysis of tunnel based on 2.5-dimensional finite element-perfectly matched layer method

In order to solve the difficulty and complexity for three-dimensional dynamic uncertainty problem of tunnel surrounding area. Based on the finite element method (FEM), this paper presents an efficient and accurate method for dynamic performance simulation of super long tunnel structure by using 2.5-dimension technique and PML to deal with the boundary truncated by FEM mesh. Since the combination of 2.5-dimension method, finite element method (FEM) and perfectly matched layer (PML) is not common, we derive the equations of the combination of 2.5D technique and FEM, and emphasize its compatibility with 2.5D technique and PML. After a brief introduction of the model, a series of verification examples are provided to prove the accuracy of the model. Finally, parametric studies are carried out to evaluate the influence of tunnel and soil properties on soil vibration. The results show that the proposed 2.5D MEF-PML method can solve the problem that the finite element method can not deal with the infinite domain, and has high accuracy, making it possible to accurately consider the influence of the factors around the tunnel in the dynamic analysis of the tunnel.