全波形反演方法在复合地基承载力检测中的应用

Full Waveform Inversion Method and Its Application in the Quantitative Detection for the Bearing Capacity of Composite Foundation

弹性波全波形反演方法是岩土工程领域中一种较新的无损检测手段,它综合运用响应波场的振幅、旅时、相位和频谱特种等波形信息,通过一定的数学反演方法,获取目标介质的物理力学参数,具有对介质模型精确刻画的潜力。将时域有限差分法结合完全匹配层吸收边界条件技术实现对弹性波波动方程数值模拟求解。然后将拟线性最优化法与随机搜索法相结合,发展了一种稳定、高效且适用于尺度较小(0.1~10 m)的时间域弹性波全波形反演方法,具有对初始模型依赖少,易收敛于全局最优解等优点。将弹性波全波形反演方法应用我国北方某住宅楼已建结构实体的复合地基承载力检测复核中,根据在该楼混凝土地下室底板上采集到响应波场,全波形反演方法计算获得地下室底板下部复合地基剪切波速剖面,进而通过经验公式获得复合地基综合承载力值,取得了良好的应用效果。

Elastic full waveform inversion( FWI) is used as a kind of new nondestructive testing( NDT) method in geotechnical engineering. It attempts to extract the information of target medium from the received waveform data comprehensively utilizing the amplitude,travel time,phase and frequency spectrum dispersed by various inversion approaches. FWI method is competent for quantitative estimates of physical and mechanical parameters and offers the potential to produce more detailed resolution of target medium. The framework of FWI method mainly contained two critical issues: the forward calculation and the inversion approach. In the forward calculation,the elastic wave equations are well solved by Finite Difference Time Domain( FDTD) method coupled with the absorbing boundary condition of Perfectly Matched Layer( PML). The inversion method adopts quasi-linearization method coupled with random search algorithm. Numerical results indicate that it is a stable and efficient FWI algorithm and suitable for small scale model( 0.1 ~ 10 m). Also,it has advantages of less dependence on initial model and good convergence.Based on numerical results,the FWI method is used in the bearing capacity test for the composite foundation of a halfbaked building in north China. According to the response wave field collected on the concrete basement floor,the shear wave velocity profile of the composite foundation under basement floor is well revealed by FWI method.Furthermore,the bearing capacity of composite foundation is achieved by empirical equation.