Ultrasonic prediction of crack density using machine learning: A numerical investigation

Cracks are accounted as the most destructive discontinuity in the rock, soil, and concrete. Enhancing our knowledge from their properties such as crack distribution, density, and/or aspect ratio is crucial in geo-systems. The most well-known mechanical parameter for such an evaluation is wave velocity through which one can qualitatively or quantitatively characterize the porous media. In small scales, such information is obtained using the ultrasonic pulse velocity (UPV) technique as a non-destructive test. In large-scale geo-systems, however, it is inverted from seismic data. In this paper, we take advantage of the recent advancements in machine learning (ML) for analyzing wave signals and predict rock properties such as crack density (CD)- the number of cracks per unit volume. To this end, we designed numerical models with different CDs and, using the rotated staggered finite-difference grid (RSG) technique, simulated wave propagation. Two ML networks, namely Convolutional Neural Networks (CNN) and Long Short-Term Memory (LSTM), are then used to predict CD values. Results show that, by selecting an optimum value for wavelength to crack length ratio, the accuracy of predictions of test data can reach R2 > 96% with mean square error (MSE) < 25e-4 (normalized values). Overall, we found that: (i) performance of both CNN and LSTM is highly promising, (ii) accuracy of the transmitted signals is slightly higher than the reflected signals, (iii) accuracy of 2D signals is marginally higher than 1D signals, (iv) accuracy of horizontal and vertical component signals are comparable, (v) accuracy of coda signals is less when the whole signals are used. Our results, thus, reveal that the ML methods can provide rapid solutions and estimations for crack density, without the necessity of further modeling.