Quantification of the effect of pump wave amplitude on crack breathing for the Nonlinear Coda Wave Interferometry

In civil engineering, an emerging ultrasonic approach based on Code Wave Interferometry (CWI), called Nonlinear Coda Wave Interferometry (NCWI) has been developed to detect microcracks in cementitious materials that cannot be detectedby conventional ultrasonic methods. NCWI uses a high amplitude low frequency (LF) nonlinear pump wave to generate a nonlinear clapping effect at microcracks that can be detected by a high frequency (HF) probe wave. The imaging of cracks inside heterougeneous materials using NCWI requires the inversion technique, which is constitued by model space and data space, in which conatains model parameters and data parameters respectively. In the frame of inversion with NCWI, the model parameter used is the scatetring cross section of a crack sigmaD, and the experimental parameter is the decorrelation coefficient Kd. Knowing that sigmaD depends on the pump wave amplitude. Therefore, in order to introduce NCWI in inversion, the relationship between the pump wave and sigmaD is needed, which is the goal of this study. The dynamic pump wave generates clapping effect at crack tips, the probe wave frequencies are higher than the pump waves’ by an order of magnitude, hence the effect of pump wave on the coda wave is rather averaged. Previous study showed that this clapping effect is equivalent to a single crack length change dL, dL can be related to an equivalent static stress sigma0 which produces the same dL in quasi-static regime, which is equivalent to the dynamic pump wave. Therefore, a relation can be established between sigma0 and sigmaD. This introduces NCWI into the inverison. Then, the theoretical estimation of Kd can be achieved by the simulation of NCWI using 2D Spectral Element Method (SEM2D), combining with the relationship between sigma0 and sigmaD, which can be used later on in the inversion for the crack imaging.