Drilled Shafts Imaging with 2D Ultrasonic Waveform Tomography

Drilled shafts are the foundation of choice for heavily loaded structures, particularly in urban areas. However, their in-situ concrete casting process is vulnerable to the formation of foundation defects, requiring full-volume imaging of as-built drilled shafts for quality assurance. This study presents a novel two-dimensional (2D) acoustic full-waveform inversion (AFWI) method for high-resolution ultrasonic imaging of drilled shafts, capturing details both inside and outside the rebar cage at centimeter-scale resolution. The method is formulated using 2D acoustic wave equations and adjoint-state optimization, integrating Tikhonov and Total Variation (TV) regularizations to enhance solution stability and preserve sharp structural boundaries. Additionally, an approximate Hessian matrix is incorporated in the regularization gradient, significantly improving inversion accuracy, particularly in regions beyond the rebar cage. Validated through synthetic experiments, the method successfully reconstructs shaft boundaries and detects defects without requiring prior knowledge of design diameter. The mean radial boundary errors of 2.4 m diameter shafts without and with defect are 1.2 cm and 4.4 cm, respectively. To further evaluate its real-world performance, the method is applied to a full-scale drilled shaft measuring 2.4 m in diameter and 21.3 m in length. Experimental ultrasonic data are collected by the standard cross-hole sonic logging (CSL) at depths along the shaft length and inverted to obtain a 2D image of P-wave velocity (V_p) at each depth. Individual 2D V_p images are then combined into a 3D image of the whole drilled shaft. Results confirm that the AFWI approach effectively characterizes the entire shaft, providing high-fidelity imaging and precise boundary delineation with the mean radial error of about 3 cm. To our knowledge, this is the first reported application of full-waveform inversion on an actual drilled shaft, marking a significant advancement in quality assurance of cast-in-place foundations.