## 1 Introduction  
The main goal of high-pressure vessel maintenance is to avoid leaks and ruptures that may result in substantial environmental consequences, as well as potential risks of fire of flammable gas clouds, not to mention the enormous risks of injuries and human fatalities. To reduce the failure probability and at the same time keep the system design capacity, the technical conditions of pipelines are periodically controlled by in-line inspections, which are scheduled in order to detect potential damages or defects that can endanger the system loading capacity [1, 2, 3, 4, 5]. Part-wall metal loss and defects of buried pipelines are mostly a consequence of electrochemical corrosion caused by oxidation. In these cases, repairing of damages is performed when exceeding threshold damage sizes according to the codes [6]. According to [7], more than 60% of the world's oil and gas transmission pipelines are over 40 years old. Most of these pipelines are in urgent need of rehabilitation in order to work at the desired, and continuously increasing, operating capacity. Within this scenario, the failures due to corrosion and their associated repairing techniques have recently attracted intense research interest [8, 9, 10, 11, 12, 13]. Replacements of the pipe segments are especially complicated when the pipeline maintenance operations require a pause in the fluid transport and distribution, which can generate substantial expenditures or income losses. When areas of corrosion or other damages to operating pipelines are identified, there are often significant economic and environmental incentives for repairing without removing the pipeline from service. Froman economic standpoint, a shutdown also involves revenue loss from the loss of pipeline throughput. Besides, for gas transmission pipelines, a temporary shutdown typically involves a significant quantity of gas that is lost in the atmosphere. Since methane is one of the so-called \"greenhouse gases\", there are also environmental incentives for avoiding the venting of large quantities of gas into the atmosphere. When faced with the need to repair an operating pipeline, there are often a variety of in-service repairing strategies available to pipeline operators for a given repairing situation [14]. While the use of metallic materials to repair damages is nowadays a mature technology (the use of full-encirclement steel sleeves for pipeline repair was developed in the early 1970s [15; 16]), the use of non-metallic composite for pipeline repairs has only recently attracted considerable interest [17; 18; 19; 20; 21; 22]. The first commercially available system was Clock Spring(r), which consisted of an E-glass/polyester resin-based composite material preformed into a multilayer coil installed using an adhesive. The mechanism by which composite materials reinforce the damaged areas on operating pipelines is more complicated than that of steel sleeves because the tensile properties of composite materials are much different from those of metals. Because of the reduced stiffness of composites compared to steel, composite materials must experience a considerably higher amount of strain (i.e., elongation) before a load equivalent to that of steel can be carried. For these reasons, when installed over steel, the composite is constrained by the steel and cannot carry a significant portion of the load until the steel begins to yield. For these reasons, the defect must typically plastically deform in the process of the load being transferred to the composite material and, to this aim, a high-compressive strength filler material is used to fill defect areas so that load is effectively transferred to the repairing material. Different kinds of these fibre-based reinforcements can be found in the literature [21], even though the basic idea of these reinforcement techniques is always to transfer the hoop stress, caused by the internal fluid pressure, from the defected area of the steel pipe to the reinforcing sleeve.