MSFP’s structure, the extra pressure armor layer is added in its inner reinforcement cross-section design, regarded as Case 2. As previously shown, the contribution to the overall radial stiffness induced by the pressure armor allows the possibility of neglecting the innermost and outermost HDPE layers. The tensile armor layers, existing in Case 3, are substituted by four steel strip reinforced layers accounting for thickness h = 0.5 mm. The detailed longitudinal profile of Case 2 is illustrated in Figure 4.28. For this numerical campaign, the inner diameter and the loading condition are the same as the previous case. The theoretical model is extended to the new geometry, for which the coefficients expressed in Eqs. (4.11) and (4.12) should be modified by considering the variation in terms of number of layers and thickness, which can be expressed as
(4.15)
(4.16)
Figure 4.28 MSFP-based reinforced longitudinal profile.
Tensile forces comparison for those pipes with three different configurations is shown in Figure 4.29. As expected, the strength provided by MSFP is the lowest. In fact, for the same inner diameter, the MSFP shows a decrement in axial resistance equal to 81.07% compared to the case which includes two tensile armor layers. At the same time, it is possible to see the improvement in terms of tensile capacity when the pressure armor is included in the MSFP design equal to 81.53%, which results from the comparison between Case 1 and Case 2. When both the pressure and tensile armor layers are included in the design, the high strength in radial direction is not only provided by the pressure armor but also by the tensile armor due to its relevant thickness. Thus, reducing the thickness of the wires not only affects the tensile capacity itself but also the loss of the external capacity.
Figure 4.29 Tensile force comparison.
Being the elongation of the pipe strictly related to its weight, which mostly depends on the amount of the reinforcement needed as well as the water depth, it is possible to assert that the steel strip reinforcements in terms of axial strength of the pipe are suitable for shallow waters. On the other hand, the contribution of thick steel wires is suitable for extreme loading conditions such as for deep water design. It is noteworthythat for both Cases 2 and 3, the contribution of the radial stiffness induced by pressure armor plays an important role in terms of axial capacity of the pipe.
4.6 Conclusions
In this chapter, an easy theoretical method for estimating the tensile stiffness of the unbonded flexible pipe is verified by numerical simulations. Secant modulus is employed in order to carry out the plastic behavior of the material, and this theoretical model is suitable for high loading conditions, which can provide relatively accurate tensile strength for pipeline engineers. The following conclusions could be drawn.
When considering both pressure and tensile armor layers in the pipe’s profile, the external pressure will not have very big impact on its tensile capacity as the radial stiffness of the pressure armor are large enough to resist the radial deformation induced by external pressure.
MSFP is only suitable for shallow water application. Adding a certain profile of pressure armor into MSFP leads to a significant increase in terms of resistance capacity (about eight times). In order to avoid material waste, the profile of the pressure armor could be adjusted according to the water depth, and this can make MSFP exploitable for deeper water depth.
Tangent modulus should be used for next works in order to obtain more accurate results. The contribution of the interlocked carcass should also be taken into account in future works, to verify whether its radial stiffness leads to a remarkable increasing tensile capacity of the pipe.
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