Numerical modeling for karst cavity sonar detection beneath bored cast in situ pile using 3D staggered grid finite difference method

Abstract Karst cavities beneath bored cast in situ piles constitute substantial dangers to the stability and quality of underground construction projects. Therefore, it is important to detect and image these karst cavities before the construction of piles for such projects. New sonar detection methods, which have advantages such as low cost and high efficiency, can ensure the quality of the bedrock for underground construction projects. In this study, a three-dimensional (3D) hole-bedrock-cave model for the sonar detection of karst cavities was developed using the finite difference time domain (FDTD) method. The modeling parameters were calibrated with measured data, and the numerical results were then compared with measured field detection data to validate the reliability of the proposed method. The numerical results revealed the following findings. (1) The waves transmitted to the center of the pile hole bottom can be divided into three types: the waves traveling upward into the slurry that are absorbed by a perfectly matched layer (PML) and can be ignored, the waves traveling horizontally along the hole bottom that constitute the primary interference during the detection process, and the waves traveling downward into the bedrock that represent the effective detection signal. To minimize the negative effects of multiple reflections from the pile hole wall, we deployed a receiver at the midpoint between the transmission point and the hole wall, at which location the signals from the multiple reflections are symmetrical and easy to identify. (2) The reflected signals generated from different depths, sizes and directions of cavities have different travel time features that make it possible to estimate the depth, size and direction of a cavity beneath a pile. (3) The velocities of multiple surface wave reflections can be predicted in the frequency spectrum of a test signal and then used to predict the arrival times of multiple surface wave reflections and identify reflected P-waves. (4) Cavities have a focusing effect on waves when they are completely filled with a low-velocity medium. The energy of a wave reflected from the floor of a karst cavity after focusing is theoretically stronger than that reflected from the roof of a karst cavity. (5) PMLs can effectively absorb waves reflected from artificial boundaries to avoid false interference. High-order FDTD methods can eliminate numerical dispersion and reduce the computational costs. In general, the sonar detection of karst cavities beneath bored piles can be simulated using a 3D high-order staggered grid finite difference method and PMLs. This numerical modeling scheme is reliable and can improve the accuracy and feasibility of practical detection experiments.