The Use of the Spectral Element Method for Modeling Stress Wave Propagation in Non-Destructive Testing Applications for Drilled Shafts

The use of stress waves for geophysical and non-destructive testing (NDT) applications continues to grow within the geotechnical community. For example, the quality control and assurance (QC/QA) process for deep foundations often relies on NDT methods such as cross-hole sonic logging (CSL), cross-hole sonic tomography (CST), and parallel seismic (PS) that are based on the propagation of stress waves through the foundation. Although these methods are the standard techniques in the deep foundation industry, they are known to have limitations in detecting defects. Therefore, it becomes important to effectively and efficiently model the propagation of stress waves in order to advance the state of practice with respect to deep foundation NDT. For example, full waveform inversion (FWI) of stress waves is a novel technique that has shown promising performance in providing high resolution images for geophysical/NDT applications at multiple scales of interest. Unlike methods that solely rely on the first time of the arrival of the stress waves, FWI attempts to match entire recorded waveforms. Hence, it requires an accurate simulation of wave propagation through the domain. Moreover, FWI is a computationally expensive approach as it requires multiple iterations to solve the inverse problem. The spectral element method (SEM) offers an efficient solution to the forward problem of wave propagation in terms of both accuracy and computational time. This study first provides a brief overview of the spectral element method. Then the application of SEM in non-destructive testing for quality control and assurance of drilled shafts is presented through a series of numerical simulations that model stress wave propagation for FWI and compare it to a finite-difference method (FDM) approach.