## 8 Conclusions  
This study investigated a system for monitoring displacements of underground pipelines in regions prone to landslides. It consists of a real time measurement of the axial strain through FBG sensors located at three points of some cross-sections of the pipe. The displacement field along the pipeline is reconstructed from the strain field by means of a nonlinear finite element model exploiting, as boundary conditions, the assumption of negligible displacement at the end-points of the model external to the affected area. The finite element analysis is based on a geometrically exact 3D beam model and a variational formulation that makes it possible to find the finite displacement and rotation fields corresponding to the measured strains and satisfy the boundary conditions. The nonlinear discrete problem is solved efficiently by a high-performing mixed iterative scheme. Some theoretical assessments were firstly carried out on large deformation benchmarks found in the literature. Subsequently, experimental results were produced on an underground monitored pipeline subject to an artificially induced landslide. A satisfactory agreement was found between predicted and actual displacements. Specifically, a mean displacement error of about 18% was obtained with just three effective monitored sections in the pipe stretch of 18 m affected by the landslide. Finally, a web application was developed for real-time monitoring and alarm management.  
In a future work, it would be interesting to optimize the distribution of the sensors along the pipeline using, for example, direct finite element simulations to estimate the strain distribution caused by assumed landslides [29, 30].  
Finally, although the finite element model application was validated on a pipeline subjected to landslide movements, it is important to specify that this model is applicable to underground pipelines subjected to the movement produced by different causes (for example seismic movement) and also for sub-sea pipelines. In this last case, a different model of sensors with waterproof properties has to be selected.  
Conceptualization, D.M., G.G. ([PERSON]) and E.M.; Data curation, M.M.; Formal analysis, D.M.; Funding acquisition, A.C. and E.M.; Investigation, M.M., G.G. ([PERSON]) and R.C.; Methodology, D.M. and G.G. ([PERSON]); Project administration, A.C. and E.M.; Resources, G.G. ([PERSON]) and A.C.; Software, D.M., L.L. and G.G. ([PERSON]); Supervision, G.G. ([PERSON]), A.C. and E.M.; Validation, M.M., A.M., G.V., F., A.P. and R.C.; Writing--original draft, D.M. and G.G. ([PERSON]); Writing--review & editing, M.M., G.G. ([PERSON]), G.V., F.F., A.P. and R.C. All authors have read and agreed to the published version of the manuscript.  
This research was funded by R&D project 38C17000130006, entitled _Allestimento nuovo condute con smart technology per industria 4.0_, granted by the Calabria Region within the POR CALABRIA FESR-FSE 2014-2020 Asse I, Obiettivo Specifico 1.2.  
Not applicable.  
Figure 17: Web application-Pipeline monitoring page.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Acknowledgments:** We thank for the support the project partner Azienda Agricola Fangiano by [PERSON] and Engineer [PERSON]. They have provided valuable help in the construction of the prototype test bench.  
**Conflicts of Interest:** The authors declare no conflict of interest.