articulated concrete mattress for submarine pipeline ...

ARTICULATED CONCRETE MATTRESS FOR SUBMARINE PIPELINE PROTECTION: EVALUATION OF THE WAVE-INDUCED FORCES AND STABILITY ANALYSIS. Maria Gabriella Gaeta1, Alberto Lamberti1, Fabio Ricchieri2, Michela Zurlo2 Submarine pipelines are commonly used along coastlines for wastewater draining or for gas/fluid transportation from platforms at deep waters. Depending on the installation area, they are subject to waves and currents and the common solution to improve the pipe stability is to cover them with bitumen or articulated concrete block mattresses. The aim of the present study is to investigate the wave-induced forces on the articulated concrete block mattress covering a submarine pipe, laid on sea bed, by using a RANS numerical model in order to evaluate its global stability.

INTRODUCTION

Submarine pipelines are widely used for wastewater draining along coastlines or for fluid transportation across seas or from platforms at deep waters to shore. For instance, the first and main pipeline crossing the Mediterranean Sea is the Transmed, transporting with the 156 km long submarine conduit 30.8% of the total gas imported by Italy from Algeria and Tunisia (IEA, 2011). Depending on the where they are laid, pipelines are subject to breaker impact, to pulsating flow and currents, anchor drag and similar, inducing bed scour and potentially pipe free span (Sumer & Fredsöe, 2002). Table 1 summarizes most common hazards for submarine pipelines, induced by environmental factors and by human activities. Table 1. Hazards for subsea pipeline stability. Environmental Hazards Hydrodynamic forces (wave, currents) Sand waves, scour, pipe spanning Earthquakes, liquefaction, slope instability, submarine debris flows

Human Hazards Fishing operation Dredging operation Ship impact or anchor drag Construction works, platforms

Figure 1. Mattress for the protection of pipes: bitumen mattress on site (left) and articulated concrete block mattress during lay down test (right). 1 2

University of Bologna, DICAM, viale Risorgimento 2, Bologna, Italy Officine Maccaferri spa, via Kennedy, Zola Predosa (Bologna), Italy

2 In shallow waters, where current and waves are significant at seabed, where ships and swimmer are present, environmental and local restrictions usually force to bury the pipe. At greater depth, a solution to improve submarine pipe stability is to cover them with a rubble mound or a mattress. In deep waters and for important pipelines bitumen mattresses are commonly installed (Figure 1, left); in some cases, the cheaper articulated concrete block mattresses are preferred (Figure 1, right). The last type of protection is the object of this study. The mattress is usually assembled nearby the installation place and is laid down on the pipe suspended with steel cables and possibly with the help of a diver; when they are installed they assume a particular shape, named “omega” (Figure 2). This configuration gives a more hydrodynamic shape to the mattress-pipe system, eventually reducing the wave loads on it. At the same time, the added mass increases the inertia of the system.

Figure 2. “Omega” configuration for a pipe laid on the seabed and protected by a mattress.

Although experimental evidence shows that loads induced by regular sinusoidal wave are more irregular than Eq. 1 do represent (especially for the lift force, that strongly depends on flow history effects, Sarpkaya & Rajabi, 1979), the hydrodynamic load acting on unprotected pipes is usually estimated using expressions proposed by Morison et al. (1950). The drag force FD and the lift force FL, per unit length, are given by:

(1) FL (t) = "CL D#

2 x

u (t) 2

(2)

where CD, CM and CD are the drag, the added mass and the lift coefficients; D the pipe diameter, ! is the water density, ux the horizontal velocity component and ax the horizontal ! acceleration component, both orthogonal to pipeline and evaluated for an undisturbed flow at pipe center position, A the pipe cross sectional area. The choice of the appropriate values for the coefficients CD, CM and CL is essential for an accurate analysis of the global stability of the protected or

3 unprotected pipeline. These coefficients depend on the Reynolds number Re, the Keulegan-Carpenter number KC, the relative roughness and the relative trench depth (Sumer & Fredsöe, 1997). For Re>106, coefficients do not depend on flow regime and for a smooth pipe laid on the bed (neither trenched nor spanning), the relation given by Det Norske Veritas (DNV) recommendations (1988) and valid in the KC range 7-50 is commonly adopted: (3) (4) In case of trenching or soil penetration a reduction coefficient is suggested. In any case, the recent recommendations by DNV (2009) only define requirements to concrete coating in terms of minimum thickness, minimum density and reinforcement. Since neither flow velocity nor pipe diameter do influence the requirement, the authors evaluated it was worth to define their influence and found lack of scientific documentation on the hydrodynamic processes developing around these protected pipelines, motivating to investigate the wave-induced forces on the articulated concrete mattress using a 2DV numerical model and to evaluate its global stability. NUMERICAL MODEL

The used numerical model, originally developed by Lin & Liu (1998) and recently implemented and validated by Lara et al. (2006), solves the 2DV Reynolds Average Navier-Stokes (RANS) equations. The k-! closure (Launder et al., 1972) is adopted to model the Reynolds stress tensor. More model details can be found in Lin & Liu (1998), Lara et al. (2006) and Gaeta et al. (2009). In the present study, the wave generation occurs at the left boundary of the numerical domain, imposing free surface elevation and velocity profile according to linear wave theory; the right boundary allows open flow; no-slip and Neumann conditions are imposed at the bottom and at the obstacle surface. The model allows obtaining detailed information on velocity, pressure and turbulence field around the structure. The hydrodynamic forces acting on mattress and pipe are calculated by integrating the pressure distribution around all the exposed parts of the obstacle cells. Model validation

Wave-induced loads acting on an unprotected pipe laid over a horizontal bed are

4 evaluated order to validate numerical results by comparison with a case that is well documented in literature. Regular waves are generated and 3 tests are performed with increasing KC number. Table 2 lists the wave height (H), wave period (T), water depth (d), pipe diameter (D) and corresponding KC and Re values for each test. Table 2. Characteristics of validation tests. Test H (m) T (s) d (m) C01 2 6 10 C02 2 6 10 C03 4 6 8

D (m) 0.9 0.5 0.5

KC 4 7 12

Re O(105) O(105) O(106)

Figure 3 shows the calculated streamlines during the wake development at the lee side of the pipe. The computed flow and vortex patterns qualitatively agree with experimental and numerical results shown in literature (among others, Zhao et al., 2006). In the first half period, a vortex develops on the leeside of the pipe; as the wave crest passes over the cylinder, the vortex size increases until velocity changes direction. Then, when the wave trough passes over the pipe, this vortex is partially dissipated while another smaller one develops in the seaside of the cylinder.

Figure 3. Computed streamlines during the wake development in the lee side of the pipe (Test C02): regular wave propagates from left to right.

The computed drag and lift forces are compared to results by using the Morison’s expression and using velocity and acceleration information by numerical results. The drag, added mass and lift coefficients are estimated using the least mean square method and are found similar to the values proposed in literature by Sumer & Fredsöe (1997) for similar conditions. In particular, Figure 4 shows an example of the comparison between numerical (pressure resultant on the obstacle, dotted line) and analytical (Morison equation, solid line) results in terms of drag force FD for one validation test: the maximum and the minimum values are well reproduced. It results also that the lift force signal shows two peaks in one wave period due to vortex shedding development at the leeside of the pipe.

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Figure 4. Drag force (kN/m) for unprotected pipe: comparison between computed results (dotted line) and Morison’s equation (solid line), evaluated using literature coefficients.

Further analysis is carried out on the evolution in time of CD and CL coefficients (Gaeta & Lamberti, 2011) during the wave propagation, and an oscillatory pattern is found correlated to the irregular vortex dynamics around the pipe. Finally, achieving good agreement in validation tests, allows the following considerations on the protected pipeline configuration. ARTICULATED CONCRETE BLOCK PROTECTION ON PIPE Numerical set-up

The studied mattress is a concrete blanket composed by 12 hexagonal cross sectional blocks linked together (in the two directions) with a cable net (Figure 2, right), forming a flexible mattress, capable to form a highly resistant protection and stabilization system. Mattresses with two different block thicknesses are simulated (20 cm -s20- and 30 cm -s30-), while a pipe with a constant 90 cm diameter is chosen.

Figure 5. Numerical discretization of the studied articulated concrete block mattress: block thickness equal to 20 cm (left) and equal to 30 cm (right).

After a grid accuracy analysis, a very fine resolution (grid size =5 cm) is chosen to discretize the area close to the pipeline in order to well determine velocity and pressure over each block and over the pipe, while wider cells define the generation and propagation zones of the numerical channel. Figure 5 shows the numerical discretization for the simulated mattress s20 (left) and s30 (right). The analysis is carried out simulating: - regular waves propagating in deep waters, with H=8 m, T=12 s, d=24 m, KC= 25 (Test A); - solitary wave propagating in shallow waters, with H=5 m, d=8 m (Test B).

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Figure 6. Evolution of streamlines around the mattress (Test As20): regular wave propagates in deep water from left to right.

Figure 7. Streamlines around the mattress (Test Bs20): solitary wave propagates in shallow water from left to right.

7 Hydrodynamics

Figure 6 represents the streamline evolution in 10 different instants during the regular wave (Test As20) propagation over the mattress-pipe structure. In the first half period (t/T=0-0.5), the wave crest passes over the cylinder and the previous generated vortex dissipates in upward direction while a clockwise vortex develops at the leeside of the protected pipe, grows and is convected upstream, until flow reverses at t/T=0.5. This vortex is dissipated as the velocity is reduced. In the interval t/T=0.5-1, the wave trough passes over the pipe and another smaller counter-clockwise vortex is generated at the cylinder seaside, potentially compromising the stability of the edge block. Two small recirculating cells are observed between the mattress and the pipe, generated by the flux through gaps between the blocks. In case of solitary wave, the flow structure is slightly different due to the flow patterns generated by the positive water displacement above the mean water level. The generation of clockwise vortex at the leeward side of the mattress is clearly shown in Figure 7: its size increases as the wave passes and the vortex is convected further shoreward than in the previous case. The effects induced by turbulence field generated by previous pulsating waves are here not evident, and the vortex shedding effects induced on the mattress-pipe are eventually greater. The analysis of hydrodynamics is also performed for the other block thickness (s30). A thicker concrete block does not substantially influence the flow pattern developing around the protected pipe, but a larger weight of the coat increases the pipe stability. The analysis of the block edge stability is influenced by block shape and dimension and requires deeper and dedicated laboratory investigation, with movable bed. Force evaluation

The drag and the lift forces induced by oscillatory flow on the mattress-pipe system are evaluated by integrating the computed dynamic pressure along each block contour and along the pipe diameter. Figure 8 shows the pressure time evolution at 3 significant points on the pipe for Test As20.

t (s)

Figure 8. Pressure at 3 significant points on the pipe (Test As20).

8 Differences between the seaside (blue line) and the leeside (red line) points of the pipe are shown, probably induced by turbulent fluxes through the block gaps. In order to evaluate the global stability, the force is evaluated for each block, revealing that the inner and outer edge blocks as well as the suspended blocks (not laid on bed or pipe) are subject to the greater loads. Finally, the forces are calculated as summation of force on mattress and force acting on the pipe (i.e. F-,M + F-,P). Figures 9 and 10 show the evolution in time of the surface oscillation (") and of the drag force on the mattress (FD,M), respectively induced by regular waves (Test As20) and by solitary wave (Test Bs20).

t (s)

Figure 9. Numerical results for drag force FD,M on the mattress for Test As20.

t (s)

Figure 10. Numerical results for drag force FD,M on the mattress for Test Bs20.

The signal shape appears irregular, especially in case of regular wave train tests. The computed global forces are compared to Morison’s expressions (Eqs. 1 and 2), using numerical velocity and acceleration fields in an undisturbed position. A first estimation for the constant coefficients CD, CM and CL are obtained by applying the least mean square method and, since no suggestions are found in case of protected pipeline, they are compared to the values CD0, CM0 and CL0, evaluated in case of a unprotected pipe over the seabed, in accordance with the

9 DNV’s recommendations (1988). The results of the comparison are summarized in Table 3. The effect of the mattress installation over a submarine pipe is expressed in terms of reduction of the drag (CD/CD0), added mass (CM/CM0) and lift coefficients (CL/CL0) in comparison with unprotected pipes, that are found to be different for Tests A and Tests B Table 3. Drag CD, added mass CM and lift CL coefficients for protected pipe. Tests A Tests B

CD 0.50 CD0 0.85 CD0

CM 0.25CM0 0.25 CM0

CL 0.50 CL0 0.85 CL0

In case of deep water and regular wave attack, turbulence induced by wave train propagation around mattress leads to disturbances on vortex development and in terms of loads on the structure, while in case of solitary wave propagating in shallow waters, this effect is less pronounced. Once the forces are determined, the global stability analysis is performed evaluating the safety factor fs as:

(5) where Ptot’ is the total (mattress and pipe) submerged weight, FL and FD are the total lift and drag forces (evaluated according Table 3), kg is the seabed friction coefficient, chosen following DNV suggestions (0.2 for sand and 0.4 for clay). CONCLUSIONS AND FUTURE WORKS

In the present study, numerical simulations, solving 2DV RANS equations, have been carried out to investigate the interaction between waves and protected pipe laid on horizontal and impermeable seabed. The model has been validated for unprotected pipes, showing a good agreement with literature in terms of force values. The influence of the concrete block mattress on flow and vortex patterns and on the hydrodynamic forces on the pipe have been investigated for two hydraulic conditions (regular waves in deep waters and breaking wave in shallow water), revealing the development of complex recirculating flow structure, also through the gaps between the mattress blocks and the pipe. The drag, added mass and lift coefficients are found to be smaller than the corresponding values computed for unprotected pipe. Further analysis to evaluate the dependence of hydrodynamic force on wave and current characteristics are ongoing, extending the present results to a wider KC number range. Laboratory investigation of wave-induced loads on protected pipelines is also

10 suitable in order to extend numerical result validity and research sediment transport and 3D effects. REFERENCES Det Norske Veritas, 1988. On bottom stability design for submarine pipelines, Recommended Practise DNV-E305, Oslo, pp. 42. Det Norske Veritas, 2007. Rules for submarine pipeline system, On bottom stability design for submarine pipelines, Recommended practice DNV-RP-F109, Oslo, pp. 28. Gaeta, M.G., Lamberti, A., and Liu, P. L.-F., 2009. A two-phase numerical model for incompressible fluids: air influence in wave propagation and applications. Proc. 31st Int. Conf. Coast. Eng., 144-156. Gaeta, M.G. and Lamberti, A., 2011. A numerical study for the stability analysis of articulated concrete mattress for submarine pipeline protection, Proc. of 5th SCACR, Aachen (Germany), June 2011, pp.8, in press. International Energy Agency, 2011. Oil and Gas Emergency Policy - Italy 2010 update, Oil Supply Security: Emergency Response of IEA Countries, pp.16. Lara, J. L., Garcia, N. & Losada, I. J., 2006. RANS modelling applied to random wave interaction with submerged permeable structures, Coastal Engineering, 53, 395-417. Launder, B.E., Morse, A., Rodi, W. and Spalding, D.B., 1972. Prediction of free shear flows: a comparison of the performance of six turbulence models, Free Shear Flow, 361-426. Lin, P., and Liu, P. L.-F., 1998. A numerical study of breaking waves in the surf zone, J. Fluid Mech., 359: 239-264. Morison, J.R, O’Brien JP et al., 1950. The forces exerted by surface waves on piles. J. Petrol. Technology, AIME, 189: 149-154. Sarpkaya, T. and Rajabi, F., 1979. Hydrodynamic drag on bottom-mounted smooth and rough cylinders in periodic flow, OTC 3761, Houston, Texas, 219-226. Sumer, M. and Fredsöe, J., 1997. Hydrodynamics around Cylindrical Structures, Adv. Series on Ocean Eng., Vol. 12. Sumer, M. and Fredsöe J., 2002. The mechanics of scour in the marine environment, Adv. Series on Ocean Engineering, Vol. 17. Zhao, M., Cheng L., and Hongwei, A.H., 2006. A finite element solution of wave forces on a horizontal circular cylinder close to the sea-bed, J. of Hydrodynamics, Proc. of the Conference of Global Chinese Scholars on Hydrodynamics, 18 (3): 139-145.

KEYWORDS – CSt2011 Abstract n. 0206 ARTICULATED CONCRETE MATTRESS FOR SUBMARINE PIPELINE PROTECTION: EVALUATION OF THE WAVE-INDUCED FORCES AND STABILITY ANALYSIS. 1st Author: Gaeta, Maria Gabriella 2nd Author: Lamberti, Alberto 3rd Author: Ricchieri, Fabio 4th Author: Zurlo, Michela Subsea pipeline Articulated concrete mattress Dynamic force Stability analysis Numerical modeling

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