# Detection and Localization of Multiple Damages through Entropy in Information Theory
## 3 Buried Oil & Gas Pipelines
### Typical Damages and Defects  
A geometry-based classification of main damage typologies frequently encountered in buried pipelines can be found in [29]. These include several crack shapes (circumferential, longitudinal, spiral, or others), plus blowout holes. Some examples are represented in Figure 1.  
The most commonly occurring types of damage can be further classified according to the different failure mechanisms from which they originate. These typically include pitting corrosion, pipeline thinning, and pipe bursts. These latter ones are caused by sudden transient pressures of the carried liquid (e.g., the \"water hammer\" phenomenon). The pipeline thinning, generally, derives from steel corrosion, graphitization, or other material-related degradation phenomena which result in metal loss. These are all time-dependent and intensified by the exposition to a chemically aggressive environment, both externally (i.e., in the surrounding soil) and/or internally (i.e., in the transported fluid).  
Apart from mechanical fatigue and corrosion, other damaging factors include manufacturing-related defects, which are known to cause internal cavities which coalesce into larger cracks under mechanical stress [30], and defective welding. This latter case may result in localized damages or larger coupling failures. Rapid (e.g., landslides) or slow (e.g., long-term subsidence) large land movements of the nearby and underneath soil are two other frequent issues, as well as weather-related and natural phenomena. Due to their long extension, pipelines are also strongly vulnerable to seismic events and other large natural disasters (this aspect is analyzed in-depth in [31]).  
Finally, mechanical damages (voluntary or involuntary, such as vandalism, impacts, incorrect operations) constitute a significant cause of instantaneous, immediate failure. Mechanical damages caused by third-party excavation are widely considered as the main cause of pipeline failure.  
In their less severe form, these generally result in dent and gouge defects. More rarely, these may cause latent weak points, very difficult to detect due to their limited area and severity, until they lead to rapid collapse even after years.  
Plain dents, which may occur due to small ground movements, rock impingement, poor installation, or limited buckling phenomena, are not of great interest here since they usually are not harmful, provided they are not excessively large [32]. Thus, they have not been considered for this study.  
Figure 1: Some examples of typical damages in SPs (modified from [[https://www.linkedin.com/in/daniellukebeesford/?originalSubdomain=uk](https://www.linkedin.com/in/daniellukebeesford/?originalSubdomain=uk)]([https://www.linkedin.com/in/daniellukebeesford/?originalSubdomain=uk](https://www.linkedin.com/in/daniellukebeesford/?originalSubdomain=uk)), Accessed on 14 June 2021).  
For the sake of this study, two different typologies of damage have been considered and numerically modeled. In the first case, localized reductions in the material stiffness are representative of dents or manufacturing defects (for low damage severity), pitting corrosion (at intermediate/high damage level), or any through-thickness crack (for higher damage intensity). In the second case, the stiffness is uniformly reduced over a narrow ring-like cross-section of the pipe. This is intended to replicate, e.g., the loosening of bolts at joints. More details about the modelling of these two damage cases will be provided throughout Section 4.