To test our full waveform inversion technology in a real-world setting, we conducted a pilot study together with IMP Bautest on a concrete retaining wall. To ensure sufficient tieback of the retaining wall, new rock anchors had to be installed in a precise location in the vicinity of existing anchors and vertical counterorts. As existing plans did not correspond with observable features of the wall, the location of the hidden counterforts and embedded anchors had to be determined. Measurements were performed on the structure using a Proceq Pundit PD8050 ultrasonic inspection device.
In addition to conventional imaging, we applied our full waveform inversion technology to the acquired data. Full waveform inversion relies on repeated simulations of ultrasonic wave propagation in the retaining wall. Starting from an initial guess of the elastic material properties of the structure, we created a digital twin of the ultrasonic inspection experiment. Salvus comes with an automated calibration procedure that allows one to estimate the average velocity and the temporal signature of the pulse that is emitted by the testing device with no input from the user. As part of our Salvus software suite, we also offer a digital twin library that includes a wide range of commercially available ultrasonic inspection devices to easily simulate and image ultrasonic NDT data. The video below shows an example of such a simulation in a segment of the retaining wall with a counterfort.
We ran repeated simulations of the experiment in the digital twin and compared the simulated ultrasonic data with the measurement data. Our full waveform inversion software leverages a powerful optimization algorithm to minimize a goodness of fit measure between the simulated digital twin data and the actually recorded data. After each simulation, our guess of the distribution of elastic material properties inside the digital twin are updated to yield an increasingly better match between the simulations and reality.
This iterative procedure is illustrated on the data of the retaining wall in the animation below. Note how the simulated data matches the measurement data more closely after each added iteration.
A major advantage of full waveform inversion is that it yields quantitative images of the elastic material properties (in this case shear-wave velocity and density),which can significantly facilitate the interpretation of the retrieved images.Additionally, the method leverages information from the full signal, including multiply scattered waves and different wave types (compressional and shear), to yield a high-resolution image of the material properties.
A comparison of the default images provided by the Proceq device and the images obtained after 15 iterations of full waveform inversion are shown in the figure below for two measurement profiles. The first measurement profile (on the left) was recorded over a counterfort without anchored reinforcement. The second profile (on the right) was recorded over a counterfort that includes an anchor.
The location of the backwall is clearly visible in both results at a depth of about 40 cm. The counterfort position can be accurately determined by evaluating where the backwall disappears from the images. Note that full waveform inversion also uses multiply scattered waves (waves that bounce multiple times between the surface and the backwall) to reconstruct an image. As a result, the multiple of the backwall echo appears weaker in the full waveform inversion images. The feature marked with the letter a corresponds to the echo of the anchor head. This feature appears to be imaged more continuously by full waveform inversion. The features marked with the letter b only appears in the full waveform inversion results and marks two almost circularly shaped high-density and high-shear-wave velocity anomalies right above the rib. These features likely represent steel reinforcements that are not imaged with conventional techniques. Since full waveform inversion includes information from both transmitted and reflected waves, the technique provides better images of features that are located close to the surface.
