# Multi-Temporal InSAR Structural Damage Assessment: The London Crossrail Case Study
## 1 Introduction  
MT-InSAR is a well-established monitoring technique capable of extracting time-series of LOS surface displacements. It was born around the end of the 1990s in order to overcome traditional InSAR limitations such as atmospheric artifacts, and temporal and geometrical decorrelation when long ERS interferometric stacks of data started being available [1; 2]. Since then several improvements have been made on both the algorithms and the quality of the data. In particular, the availability of high resolution and short repeat time satellite constellations lead to more effective near real-time disaster monitoring, assessment response and greater ability to constrain dynamically changing physical processes [3; 4]. Although many studies have been carried out using InSAR in the field of structural monitoring looking at urban areas [5; 6; 7], bridges [8; 9], railways [10; 11], tunneling [12; 13; 14; 15], and dams [16; 17; 18; 19], state of the art scientific literature sees only few papers coupling MT-InSAR and structural modeling as a building damage assessment tool [6; 20; 21; 22].  
Several procedures have been proposed in civil engineering to predict the structural damage caused by underground excavations to adjacent structures (e.g., [23; 24]). One of the key factors for anaccurate damage assessment is the quantification of the soil-structure interaction, which influences the settlement profile originated by the excavation [25; 26; 27; 28]. Attempts have been made to include this effect in simplified procedures for the damage assessment of large scale urban projects, by connecting the building-induced variation of the settlement profile with the relative stiffness between the structure and the soil [29; 30; 31; 32]. Structural engineering literature compared the outcome of these methods with experimental [26; 33] and numerical [27; 29; 30; 31] data, but their potentials and limitations need to be assessed against large datasets of field measurements to further validate their practical application [34].  
In this paper we propose a new integrated damage assessment methodology that aims to bridge the gaps between InSAR time-series analysis and the relative stiffness method for the assessment of tunneling-induced structural damage [32]. Our dataset includes 72 images acquired from April 2011 to December 2015 combined to produce time-series of cumulative deformation over the city of London (UK), where the Crossrail twin tunnels were excavated starting in 2012 [35]. We compare our InSAR dataset to a dense set of ground based measurements acquired over 14 buildings, showing how the MT-InSAR time-series product can overcome the lack of ground based monitoring of building displacements and thus facilitate the application of damage assessment procedures which take the soil-structure interaction mechanism into account [34].  
The paper is organized as follows: Section 2 describes the data and the area of interest together with the Crossrail project. Section 3 describes briefly the MT-InSAR methodologies and the relative stiffness method. Section 4 presents and discusses the results and the modeling. Conclusions are provided in Section 5.