# The Static Frictional Behaviors of Rubber for Pipe-Laying Operation
## 1 Introduction  
Deep water pipe-laying is a standard industrial process for offshore pipeline installation or maintenance [1; 2; 3; 4]. In addition, the tensioner is one of the key pieces of equipment for the pipe-laying operation. Rubber blocks are fixed on creeper treads of tensioner against a pipe wall with normal loading. The static friction between rubber blocks and the pipe wall is used to counteract the deadweight of pipeline [5]. Therefore, the contact between the rubber blocks and the pipe wall can be seen as a soft contact of static friction during the pipe-laying operation. Rubber materials are working in great deformation due to their low elastic modulus when in contact with a rigid substrate. Tribological behaviors of rubber in soft contact is of paramountimportance and have been widely investigated in many fields. It is well known that the friction force is related to the total area of real contact [6], and friction of rubber-steel contact is proportional to normal load, due to the increase in real contact zone [7]. Adhesion force is seen as a very important factor affecting rubber friction in certain contact conditions, because the molecular interaction forces within and around the contact area add the effect of the normal load. [PERSON] et al. [8] evolved an approach (the Johnson-Kendall-Roberts (JKR) theory) from the Hertz theory to estimate the mechanics of adhesive contact of elastic materials. [PERSON] [9] observed a succession of adhesions and ruptures of the contact when rubber was sliding on a substrate plat at low velocity. These detachment waves were called Schallamach waves and they indicated that air tunnels which occurred on the interface of rubber was propagating across the contact area instead of slipping on the surface of the plat. Subsequent research, which was carried out by [PERSON] et al. [10], focused on the essence between the Schallamach waves and stick-slip motion. According to [PERSON] et al. [11], the detachment waves were also observed at the quasi-sliding stage, most of the waves vanishing during their propagation across the contact area due to the very low sliding velocity of the rubber. In addition, systematic progresses have been achieved in the studies of the static frictional behaviors of rubber contact. [PERSON] et al. [12] reported the phenomenon that the central adhesive zone and partial slipping zone appear in the apparent contact area, which is similar to the observations of [PERSON] [13]. [PERSON] et al. [14] discussed the nature of static friction and creep. [PERSON] et al. revealed the mechanisms of static and kinetic friction of different contact pairs during sliding [15]. [PERSON] et al. [16] reported the static frictions of steel-rubber contacts in the field of fishing. [PERSON] et al. [17] proposed a static contact model to predict friction between rough rubber and metal surfaces. Furthermore, the fracture mechanics that were developed by [PERSON] et al. [18], [PERSON] [19] and more recently to [PERSON] et al. [20] or [PERSON] and co-workers [21] have been used to discuss the separation of interfaces in the rubber-static frictional contact. However, despite this progress, little attention has been paid to the project of static frictional behaviors of soft contact during deep water pipe-laying operations [22]. As is schematically shown in Figure 1, at the beginning of a pipe-laying operation, the pipeline is falling into the seawater by the pipe-laying tower with a preset velocity. The rubber blocks on the tensioner contact against the pipeline with a normal load and there is no relative displacement within the rubber-pipe contact system. The dead weight of the pipeline is increasing during the pipe-laying operation, therefore the tangential load (\(F_{T}\)) in the rubber-pipe contact system increases with constant increasing rate. Little attention has been paid to the static frictional behaviors which are under different increasing rates of the tangential load.