# Volume Loss Assessment with MT-InSAR during Tunnel Construction in the City of Naples (Italy)
## 1 Introduction
This allowed the separation of vertical and east-west (E-W) horizontal displacement components, induced by the excavation of two motorways tunnels. The InSAR results agree well with the conventional survey (robotic total station and automatic GPS), confirming the trend and the magnitude of displacements, in both the vertical and E-W horizontal directions. A collection of interesting works pertaining to the post-tunneling building damage assessment procedure with InSAR data is provided in [14; 15; 17; 18]. These latter papers focused on the Crossrail twin tunnels project in London, UK. A single Master MT-InSAR analysis was carried out on CSK descending SAR images. Standard Gaussian distribution or modified Gaussian distribution was used to fit the transverse profile of monitored settlements, in order to take into account the soil-structure interaction. From the traditional survey, an average value of volume loss \(\mathrm{V_{L}}=0.7\%\), with a standard deviation of 0.3%, was observed. The average inflection point distance from the tunnel axis was 0.5-z\({}_{0}\), with a standard deviation of 0.1-z\({}_{0}\) (with z\({}_{0}\) being the tunnel axis depth). InSAR data fitting with modified Gaussian reported values of volume loss in the range 0.7-1.4% for 12 out of 14 transverse sections considered by the authors, with an average value of 1.1%. The fitted inflection point was located within 1.9-z\({}_{0}\) for 12 out of 14 transverse sections, with an average value of 0.75-z\({}_{0}\). In [14], an example of a comparison between the InSAR settlement profile and the traditional survey (PLP) is provided, showing a good agreement. In general, the authors showed how InSAR can be used to detect settlements caused by tunneling, which enabled them to assess the extent of damage to over 800 buildings in London. However, two main limits were identified for the use of MT-InSAR as a tool to perform real-time monitoring [19]: the satellite revisit time and the phase ambiguity. The first limit does not allow real-time monitoring to be performed on processes that are bounded in a small temporal baseline. The second limit influences the ability of MT-InSAR to detect displacements higher than \(\lambda/4\), if the motion can change direction, or \(\lambda/2\), if the motion is monotonic, between two consecutive acquisitions and two adjacent pixels [20] (where \(\lambda\) is the sensor's wavelength). Nevertheless, the presence of an image database allows for a posteriori analyses to support the development of advanced damage assessment procedures. Therefore, the objective of this study is to show an application and validation of this satellite monitoring technique related to the excavation of twin tunnels for the metro line in the city of Naples (Italy). As far as the study area is concerned, 237 X-band images from the COSMO-SkyMed constellation in ascending geometry were selected for interferometric processing, covering the observation period from 7 March 2018 to 29 January 2022. This timeframe corresponds to the excavation of both twin tunnels. Images were analyzed with the software SARPROZ [21], using the MT-InSAR technique. The results of the analysis carried out during the excavation of the first tunnel were used to obtain tunnel-transverse settlement profiles. These were then used to calibrate established empirical methods [22; 23] and improve the prediction of subsequent excavation of the second tunnel.