Evaluating intrinsic system nonlinearities in ultrasonic scaling subtraction method for reliable rock damage monitoring

Nonlinear ultrasonic testing (NLUT) techniques have been extensively investigated for their potential to assess damage states and monitor damage evolution. Among these, the Scaling Subtraction Method (SSM) offers a state-of-the-art approach by capturing the strain-dependent nonlinear behaviour of the testing material under low- and high-voltage excitations. This study extends the application of SSM by enabling continuous monitoring and rigorously quantifying intrinsic system nonlinearity. The influence of excitation waveform, excitation frequency and excitation voltage on the nonlinearity indicator was also examined. A series of experiments were performed to isolate nonlinear contributions from waveform generators, power amplifiers, transducers and the material of interest. Results demonstrate that the proposed testing parameters and testing system result in a negligible nonlinearity compared to the substantial nonlinearity measured in an alternative nonlinear testing system and in marble. Continuous ultrasonic excitation over 900 s, conducted in the absence of external mechanical loading, revealed a time-dependent increase in the nonlinearity indicator for marble specimens, while the ultrasonic system itself remained stable throughout the prolonged excitation. These findings highlight the importance of quantifying intrinsic system nonlinearity and optimising excitation parameters for accurate nonlinearity evaluation. Continuous SSM monitoring of marble during uniaxial loading demonstrated the method's high sensitivity and resolution, clearly capturing progressive changes in nonlinearity with increasing stress. Taken together, these results establish SSM as a robust and practical tool for real-time monitoring of damage evolution in rock-like materials.