多次爆炸载荷作用下浅埋隧道破坏过程的持续同调特征分析

Analysis on Persistent Homology Characteristics of Failure Processes of Shallow Buried Tunnels Under Multi-Time Explosions

浅埋隧道在多次爆炸载荷作用下的破坏特征是防护工程设计和评估的重要研究问题,发展适应浅埋特征安全预警方法具有重要意义.采用离散元法建立浅埋隧道力学模型,运用Saint-Venant载荷等效原理将爆炸载荷看作一系列均匀作用在地表的动力,基于离散元法得到各次爆炸载荷作用后的动力响应和隧道围岩损伤演化过程,利用强度折减法得出隧道围岩的安全系数.引入持续同调理论,采用持续同调的数学方法对离散元模型在多次爆炸载荷作用下的破坏特征进行定量与定性分析.结果表明,持续同调的方法能准确反映隧道围岩的拓扑特征,其中1维条形码连通半径最大值能对隧道失稳进行有效预警.这为隧道安全设计与灾害预报研究提供了一种全新的数学方法.

The failure characteristics of shallow buried tunnels under multi-time explosions make an important research issue in the design and evaluation of protection engineering.It is of great significance to develop a method for early warning of the safety for shallow buried features.The discrete element method was used to establish the mechanical model for the shallow buried tunnel.With the Saint-Venant principle the blast loads were treated as a series of dynamic forces acting uniformly on the surface.Based on the discrete element method,the dynamic response under each blast load and the damage evolution process of the tunnel surrounding rock were obtained.The strength reduction method was used to calculate the safety factor of the surrounding rock.The persistent homology theory was introduced to quantitatively and qualitatively analyze the failure characteristics of the discrete element model under multi-time explosive loads.The results show that,the method of persistent homology can accurately reflect the topological characteristics of the surrounding rock.The maximum 1D barcode connection radius can effectively predict tunnel instability.The work provides a new mathematical method for tunnel safety design and disaster prediction research.