隧道衬砌病害探地雷达三维正演模拟及工程验证

GPR Three-Dimensional Forward Modeling of Defects in Tunnel Lining and Engineering Verification

从Maxwell旋度方程出发,通过引入复介电常数和复磁导率,推导导电介质UPML吸收边界在考虑和不考虑磁损耗情况下各区的电场和磁场分量的时域差分公式。通过选取各区不同的匹配参数,建立模型区与UPML吸收边界电场和磁场分量的统一离散差分公式。用MATLAB语言编制基于UPML吸收边界的图像可视化的探地雷达三维正演模拟程序。正演模拟衬砌内方形空洞三维地电模型,揭示方形空洞在不同显示剖面上的图谱特征。单剖面的响应特征类似"平锅盖形",z方向切片图定出空洞的形状;反射界面呈强负相反射异常,在立体剖视图中,空洞角点位置产生了2个交叉的双曲线绕射波。将该方法应用于现场隧道衬砌质量的检测,并开孔验证。结果表明:不密实区反射界面多且不规则,同相轴错断、零乱、不连续的较强反射能量团块状异常;在z方向切片图上能清楚反映隧道衬砌密实程度,并且判译直观、准确。

Starting from the Maxwell curl equations, by introducing the complex permittivity and permea- bility, the FDTD electric field component formula and magnetic field component when magnetic loss was considered or not about UPML absorbing boundary of conducting medium was derived. Discrete difference formula which unified the simulation area and UPML absorbing boundary field links was established by selecting different matching parameters in each region. The 3-D image visual processing and the GPR 3-D forward simulation program based on UPML absorbing boundary were compiled with MATLAB. The square-cavity 3-D geoelectric model in the lining was forward modeled and the image features of square-cavity under different display profiles were revealed. The response characteristics correspond to single profile was similar to ＂flat pot form＂. The square-cavity shape was confirmed by the section graph in z-direction. Reflection interface showed strong negative phase anomaly. In stereoscopic cutaway view, there were two crossed hyperbola diffracted waves at cavity＇s corner. The 3D radar detection was used for the quality inspection of tunnel lining and verified by the opening. The result shows that the reflection interface in lacuna is abundant and irregular, event leap, scattered and disconnected stronger reflection energy mass is abnormal. The dense degree of tunnel lining is reflected on section graph in z-direction, and it is proved to be accurate and visual.