Keywords: Submarine pipeline; Well graded soil; High hydraulic conductivity; Horizontal and vertical wave forces; Minimum safe burial depth.

Transcription

1 225 Minimum Safe Burial Depth of Submarine Pipelines in Well Graded and High Hydraulic Conductivity Sand *S. Neelamani Senior Research Scientist K. Al-Banaa Associate Research Scientist Coastal and Air Pollution Dept., Environmental and Urban Development Division, Kuwait Institute for Scientific Research, P.O. Box: 24885, SAFAT, KUWAIT. * Phone: , Fax: Abstract An important unknown while burying a submarine pipeline is What is it s minimum safe burial depth?. It is a function of wave climate, water depth, engineering and hydraulic properties of the seabed soil, etc. To solve this problem, physical model investigations were carried out in a wave flume to assess the change in the horizontal and vertical hydrodynamic forces on a submarine pipeline for different depth of burial. The marine sand is well graded and has hydraulic conductivity of 1.84 mm/s. It is found that the horizontal force reduces non-linearly with increase in depth of burial. 75% of the magnitude of the horizontal force reduces by just burying the pipe, when compared to the one placed on the seabed. The vertical hydrodynamic force is smaller for half buried pipe and increases for just fully buried case due to the significant change in the magnitude as well as the phase difference between the pore water dynamic pressures. For any burial depth and for a constant wave height, increase in wave period has noticeable increase in the vertical wave force than the horizontal wave force. The horizontal wave force dictates the stability of the submarine pipeline, when it is placed on the sea floor. For buried pipeline, the upward wave force dictates. Workout example is presented as a ready reference. Keywords: Submarine pipeline; Well graded soil; High hydraulic conductivity; Horizontal and vertical wave forces; Minimum safe burial depth. 1. INTRODUCTION Submarine pipelines are used extensively for transporting liquid hydrocarbons and gas, seawater intake and sewage disposal, subsea tunnel, natural marine life observation structure, cable for power transport etc. These submarine pipelines encounter significant dynamic forces due to the action of waves and currents. In order to reduce such forces and associated risk of failures, they are recommended to be buried below the seabed. How deep a pipeline needs to be buried for the prevailing marine conditions is a million dollar question. The minimum safe depth of burial of the submarine pipeline depends on design marine environment (especially waves and currents), type of seabed soil (engineering and hydraulic properties), pipeline material, liquid to be transported by using the pipeline etc. It is safe to bury submarine pipes which are used for transporting hazardous and inflammable cargo like hydrocarbons, acids/bases as well as power transmission cables. Published literatures, standard codes and guidance to help the engineers to select the minimum safe burial depth are scarce. Some of the available literatures related to the buried submarine pipeline topic are listed below: Mac Pherson (1978) derived an analytical solution from the potential theory for the wave induced pressure distribution in the sandy soil bed surrounding a buried pipeline. The dynamic seepage force

2 226 Minimum Safe Burial Depth of Submarine Pipelines in Well Graded and High Hydraulic Conductivity Sand exerted on the pipeline is computed. It is a linear theory based approach and its application for the design extreme wave condition is limited. Lennon (1985) reported three dimensional wave-induced seepage pressures on a buried pipeline in sandy marine soil of finite depth using Boundary Integral Element Method. The soil structure and fluid were assumed as incompressible; seabed was horizontal and extended infinitely in both horizontal and vertical directions. The force on pipeline was found to be a function of relative pipe size, location of wave crest and soil properties. The effect of angle of incidence on the wave-induced pressure on the buried pipeline was studied. Spierenburg (1986) derived analytical solution for the hydrodynamic force on a submarine pipeline. A comparison was also made with numerical solution based on the finite element method. It was concluded that the hydrodynamic force acting upon a submarine pipeline is about 10-30% of the buoyancy of the pipe depending on the maximum wave load and the burial depth. McDougal et al. (1988) developed an analytical model for estimating the pore water pressure in the sandy soil and the resulting hydrodynamic force on the submarine pipelines. The analytical solutions were compared with the results of both small- and large-scale tests. Reasonable agreement was obtained for the small-scale tests. Magda (1999) studied the behavior of hydrodynamic uplift force acting on a submarine pipeline in sandy soil and concluded that the uplift force increased with increase in wavelength and degree of saturation of soil. Formula to estimate the force on the buried pipeline was given. Vijayakumar et al., (2001; 2002; 2003; 2005a; 2005b) carried out the physical model studies to estimate the forces and scour around pipeline for few samples of Indian marine clay of different consistency index. The reduction of dynamic pressure on the pipeline due to burial was studied. The investigations were carried out with 3 pressure sensors only and for limited wave heights and period combinations. Madhu Shudan et al. (2002) have carried out experimental investigations to analyze wave induced pressures on a pipeline buried in a permeable seabed. The model tests were performed on a 200 mm dia pipeline buried in the soil test bed. The soil used in the formation of the test bed is a poorly graded medium to fine sand with d 50 =0.57 mm. The average density of the soil bed was kn/m 3 and the average hydraulic conductivity of the soil was m/s. 96 number of tests were conducted with waves generated for different wave heights. The pipeline was buried in the sandy bed at different burial depth ratios. The pipeline was laid perpendicular to the wave direction. Dynamic pressures were measured with 12 transducers along the outer circumference of the pipeline. The results shows that wave induced pressures are significantly controlled by the wave period analyzed in terms of the scattering parameter (ka). Higher pressures were recorded at the top and the lower pressures were recorded at the bottom. It was found that the normalized horizontal force increased with depth of burial, which is very much unexpected. The test was carried out for one soil condition and very limited wave parameters. The variation of vertical force with different depth of burial was provided in figures but nothing is described on why the trend of vertical wave force was different from the horizontal force variation due to different burial of the pipeline. Xu et al. (2010) has carried out studies on bed form evolution around a submarine pipeline and its effects on wave-induced forces under regular waves. The aim of the study was to investigate the scour formation around a submarine pipeline initially either resting on or half buried in the seabed under regular wave action by means of a series of wave tank experiments, and to evaluate the influence of the scour on the hydrodynamic forces exerted on the pipeline. The evolving bed profile and wave pressure on the pipeline were recorded simultaneously, from which the horizontal and vertical force components were determined by integrating the measured pressure numerically on the circumference of the pipeline. The scour processes and the influence of scour on the hydrodynamic forces on the pipeline were discussed. From the literature review, it is clear that the answer for the question What is the minimum safe burial depth of a submarine pipeline for a given marine environmental condition? remains an unsolved question. The results obtained from the present R&D work will help in understanding and answering International Journal of Ocean and Climate Systems

3 S. Neelamani & K. Al-Banaa 227 this question. It can be imagined that the hydrodynamic forces on buried pipeline is dictated by the type of marine environment (Wave height, wave period, water depth etc), engineering properties of seabed soil (soil size distribution, porosity, submerged density, hydraulic conductivity etc), pipe diameter and depth of burial of the pipeline. A lack of knowledge to select minimum safe burial depth compel the designers to select extra burial depth to reduce the risk of exposure of the pipeline for direct action of waves and currents. The consequence of this decision is the excavation of deeper trenches than required during pipeline laying in the dynamic environment and hence wastage of resources. The results from the present investigation will be helpful for submarine pipeline designers to select the minimum safe burial depth in order to take care of safety as well as costs for burying the subsea pipelines in the marine environment. The study is carried out with soil, which is well graded and has high hydraulic conductivity. Soil with high hydraulic conductivity is preferred as covering material around the buried pipeline to reduce the liquefaction effect of the soil during wave action. 2. METHODOLOGY The present problem is investigated using physical model investigations. Froude scale model is used. Wide range of wave height, wave periods and depth of burial of the pipeline is selected to cover realistic field conditions. The main mission of the physical model study is to obtain the wave induced forces (both in the horizontal and vertical direction) on the submarine pipeline for different burial depths in the selected soil for different combinations of wave height and wave period. The wave force on a buried pipeline cannot be measured using conventional strain gauge type force sensors. Hence, the hydrodynamic pore water pressures (at 12 points equally distributed around the pipeline model) were measured. The in-line and uplift forces were estimated from the dynamic pressure measurements. Once the hydrodynamic forces at any burial depth are known, then it is possible to assess the stability of the pipeline. Detailed physical model investigations were carried out in the wave flume of Kuwait Institute for Scientific Research (Figure 1). The wave flume is 54.5 m long, 1.2 m high and 0.6 m wide. The details of the dimensions of the flume, location of test section etc are as shown in Figure 2. The model pipeline is 0.20 m dia, water depth near the wave maker is 0.90 m and it is 0.45 m at the test section. A mild sloped false bottom (1:35) is fixed in between the wave maker and soil pit. The soil pit Figure 1. Pipeline model with instruments in the wave flume of Kuwait Institute for Scientific Research

4 228 Minimum Safe Burial Depth of Submarine Pipelines in Well Graded and High Hydraulic Conductivity Sand Wave Probe Wave Probe 2 Force balance False Bottom Pressure Sensor 1:35 Submarine pipeline 1: Soil Wave maker Wave absorber Drawing Not to Scale. All dimensions are in m Figure 2. The experimental set-up for measuring forces and dynamic pressures on the submarine pipeline. is 0.45 m deep. The pipeline width is m. 12 Nos. of diaphragm type pressure sensors (RTC28R0.5BV1 by KISTLER, Switzerland), each of capacity of 0.5 bar are used. The linearity, hysteresis and repeatability of the pressure sensors at 25 C are ±0.25% of full scale. A strain gauge type force balance (DHI Denmark) with rated horizontal force, Fx of 500 N and vertical force Fz of 1000 N is used only for measuring the wave force on the pipeline, when it is just resting on the seabed (with a miniature gap between the pipe bottom and seabed for accurate transfer of force to the force balance). The linearity and hysteresis are less than ±0.05% full-scale. The temperature influence on sensitivity is less than ±0.05% full-scale/degree C. Two capacitance type wave gauges of 0.6 m range (DHI Denmark) is used for measuring the incident wave history and are placed as shown in Figure 2. The instruments are periodically calibrated and the repeatability of the calibration constants within ±0.1% of the average calibration constants was assured. The wave maker is piston type and is capable of actively absorbing any wave reflection from the model or beach. It generates wave up to breaking steepness for periods from 1.0 to 2.4 sec. A 12 bit A/D conversion card is used for the conversion of analog data into digital form during data acquisition. The duration and speed of data collection for each combination of regular wave height and period was for 30 sec and 40 sample/s respectively. The pressure sensor location on the pipeline with respect to wave direction is revealed in Figure 3. In this figure, the depth of burial of the submarine pipeline, e is indicated, which is the vertical distance between the sea floor and the bottom of the pipeline. The angle between the successive pressure sensors along the circumference is 30. The horizontal wave force, F x and the vertical wave force, F z acting on the submarine pipeline is estimated using the following formula: F x = [P 1 cos P 2 cos P 3 cos P 4 cos 90 + P 5 cos 60 + P 6 cos 30 + P 7 cos 0 + P 8 cos P 9 cos P 10 cos P 11 cos P 12 cos 210] da (1) F z = [P 1 sin P 2 sin P 3 sin P 4 sin 90 + P 5 sin 60 + P 6 sin 30 + P 7 sin 0 + P 8 sin P 9 sin P 10 sin P 11 sin P 12 sin 210] da (2) International Journal of Ocean and Climate Systems

5 S. Neelamani & K. Al-Banaa 229 Wave Direction θ P7 P6 P5 P4 P3 P2 P1 e P8 P12 P9 P10 P11 Soil Bed Figure 3. Pressure sensor s location on the pipeline with respect to wave direction Where da is the segmental outer surface area of the pipeline and is estimated as da = [(πd)/12] W (3) where, D = Outer dia of the pipe (0.20 m), W = Width of the pipe (0.597 m) and hence da= m 2. In the above equations, the dynamic pressures and hydrodynamic forces are functions of time. After simplification, the formula become F x = [(P 7 P 1 ) (P 2 P 6 P 8 + P 12 ) 0.5 ( P 3 P 5 P 9 + P 11 )] (4) F z = [(P 4 P 10 ) 0.5 ( P 2 P 6 + P 8 + P 12 ) ( P 3 P 5 + P 9 + P 11 )] (5) The experiments were carried out for a wide range of regular wave conditions. The range of input parameters used and the range of normalized hydrodynamic parameters are listed in Table 1. In the above table, H i is the Incident wave height T is the Wave period d is the Water depth at the test section D is the Pipeline diameter L is the Wave length at the test section and is estimated using the dispersion equation (L=1.56 T 2 tanh (2πd/L) H i /d is the Relative wave height H i /L is the Incident wave steepness d/l or kd is the Relative water depth (where k is the wave number, k =2π/L) ka or D/L is the Scattering parameter (where a is the radius of the pipe) U r is the Ursell parameter (U r = HL 2 /d 3 ) KC is the Keulegan Carpenter No., (KC=U max T/D; where U max is the maximum horizontal water particle velocity at the seabed level) R e is the Reynolds No., (R e = U max D/γ; where γ is the kinematic viscosity of water, 1x10-6 m 2 /sec.)

6 230 Minimum Safe Burial Depth of Submarine Pipelines in Well Graded and High Hydraulic Conductivity Sand Table 1. The Range of input and normalized hydrodynamic parameters Hydrodynamic parameter Range Unit Wave period, T (0.2 s increment) s Wave height, H i for T=1.0 s for T=1.2 s for T=1.4 to 3.0 s (0.05 m increment) m Water depth at the test section, d 0.45 m m Pipeline burial depth, e 0.0, 0.1, 0.2, 0.3 and 0.4 m Pipe dia, D 0.2 m Wave length at the test section, L m Relative depth of burial, e/d 0.0, 0.5, 1.0, 1.5 and 2.0 Unitless H i /d Unitless H i /L Unitless d/l Unitless kd Unitless D/L Unitless ka Unitless Ur Unitless U max. SWL m/s U max. Bed m/s KC Unitless R e Unitless The variation of hydrodynamic force on the submarine pipeline is functions of the engineering and hydraulic properties of the soil and are provided in Table 2. It is clear from this table that the hydraulic conductivity of the soil is high. Table 2. Engineering and hydraulic properties of the soil used Soil Property Value Unit D mm D mm D mm D mm C u Unitless C c Unitless Bulk density t/m 3 Saturated density t/m 3 Submerged density t/m 3 Porosity Unitless Hydraulic Conductivity, k mm/s Angle of shearing resistance, Φ Degree Coefficient of friction, tan Φ Unitless Passive earth pressure coefficient of the soil, K p Unitless Remarks Almost well graded soil International Journal of Ocean and Climate Systems

7 S. Neelamani & K. Al-Banaa 231 In the table D10, D30, D50, D60 are the diameter of the soil particle at 10%, 30%, 50% and 60% finer on the grain size distribution curve respectively. Cu is the uniformity coefficient (Cu = D60 / D10) and Cc is the coefficient of curvature of the soil. The physical appearance of the soil is as shown in Figure 4. The soil contains significant quantity of marine shells, sand and gravel and no clay and silt. The particle size distribution of this soil is given in Figure 5. The minimum size of the particle is 0.05 mm and the maximum size is 5 mm. The hydraulic conductivity is estimated using the standing procedure for falling head permeability test (Murthy, 2003). During the experiment, the soil was poured gently around the installed pipe and water is sprayed to make it fully saturated. Before actual data collection, long Figure 4. The physical appearance of the Soil. Figure 5. Particle size distribution curve for the soil.

8 232 Minimum Safe Burial Depth of Submarine Pipelines in Well Graded and High Hydraulic Conductivity Sand waves of high amplitudes were generated for 30 minutes for inducing dynamic vibrations of the soil so that it reaches a condition similar to the field condition. 3. RESULTS AND DISCUSSIONS The results pertaining to regular waves are produced. However it is found that the results based on the random waves are also similar in magnitude as well as in trend due to variation of any of the input parameters. 3.1 Effect of pipeline burial on horizontal and vertical wave forces in high hydraulic conductivity soil It is important to understand how the horizontal and vertical wave force on the submarine pipeline vary when it is changed from e/d=0.0 to e/d=2.0. The locus of F x and F z for e/d=0.0, H i =0.15 m and T=3.0 s is given in Figure 6. The shape of the loop in this figure indicates the variation of the resultant wave force for one wave cycle. The data points for 10 wave cycles (30 sec) is superimposed. It can be seen from this plot that when the submarine pipeline is resting on the seabed, the horizontal force dominates than the vertical force. One can understand why the horizontal wave force dominates the submarine pipeline resting on the seafloor by visualizing the magnitude and phase differenence of main dynamic pressures, which are responsible for the horizontal and vertical wave force. It is to be noted from eqn. 4 that the main dynamic pressure responsible for the horizontal wave force on the pipe is due to the pressure sensors P1, P2, P6, P7, P8 and P9 (Refer Figure 3), the magnitude and phase lag between them is shown in Figure 7. The difference in magnitude between the pressure sensors at the leading and trailing end is small but the phase lag is significant, which is responsible for the high magnitude of the horizontal force. Similarly, the main dynamic pressures causing vertical force on the pipe is due to the pressure sensors P3, P4, P5, P9, P10 and P11 (Refer Figure 3 and eqn. 5), the magnitude and phase lag between them for the same input condition (e/d=0.0, H i =0.15 m and T=3.0 s) is shown in Figure 8. The difference in magnitude and phase lag is not at all significant. This is the reason for smaller magnitude of vertical force in Figure 6 when compared to the magnitude of horizontal force. For half burial case (Figure 9), the magnitude of the horizontal wave force has reduced appreciably due to reduction in the exposure. The shape of the locus of the total wave force has changed significantly. Figure 6. The locus of the resultant wave force on the submarine pipeline for e/d=0.0, Hi=0.15 m and T=3.0 s in a soil with high hydraulic conductivity International Journal of Ocean and Climate Systems

9 S. Neelamani & K. Al-Banaa 233 Figure 7. Magnitude and phase lag between dynamic pressures from sensors, which contributes significantly for the horizontal wave force on the submarine pipeline for e/d=0.0, H i =0.15 m and T=3.0 s in a soil with high hydraulic conductivity Figure 8. Magnitude and phase lag between dynamic pressures from sensors, which contributes significantly for the vertical wave force on the submarine pipeline for e/d=0.0, H i =0.15 m and T=3.0 s in a soil with high hydraulic conductivity For just buried case (Figure 10), the shape of the locus of total wave force has completely changed when compared to Figure 6 and 9 for e/d=0.0 and 0.5. The vertical component of the force is much larger than the horizontal force component. The reason is that when the pipeline is fully buried, the magnitude and phase lag between the pressure sensors, which cause the horizontal wave force, has less variation (Figure 11) when compared to the pressure sensors, which are responsible for vertical wave forces (Figure 12). From Figure 12, one

10 234 Minimum Safe Burial Depth of Submarine Pipelines in Well Graded and High Hydraulic Conductivity Sand Figure 9. The locus of the resultant wave force on the submarine pipeline for e/d=0.5, H i =0.15 m and T=3.0 s in a soil with high hydraulic conductivity Figure 10. The locus of the resultant wave force on the submarine pipeline for e/d=1.0, H i =0.15 m and T=3.0 s in a soil with high hydraulic conductivity can viualize the change in the magnitude of pressures between the upper (P3, P4, P5) and lower (P9, P10 and P11) part of the pipe due to elevation difference with respect to still water level and also the difference in phase of the peak pressure values (P3, P4, and P5 leads P9, P10 and P11). Similar trend is also observed for further burial of the pipeline with e/d=1.5 (Figure 13) and hence the vertical wave force is much larger than the horizontal force. The persistence of high vertical force is due to the high hydraulic conductivity of the soil. For e/d=1.5, it is observed with a similar study in International Journal of Ocean and Climate Systems

11 S. Neelamani & K. Al-Banaa 235 Figure 11. Magnitude and phase lag between dynamic pressures from sensors, which contributes significantly for the horizontal wave force on the submarine pipeline for e/d=1.0, Hi=0.15 m and T=3.0 s in a soil with high hydraulic conductivity Figure 12. Magnitude and phase lag between dynamic pressures from sensors, which contributes significantly for the vertical wave force on the submarine pipeline for e/d=1.0, Hi=0.15 m and T=3.0 s in a soil with high hydraulic conductivity soils of low hydraulic conductivity that both horizontal and vertical force reduce more than 80% of that measured on the pipeline when it is resting on the seabed (Neelamani et al. 2010). Further increase in burial (e/d=2.0) results in the reduction of the magnitude of dynamic pressures and hence reduction of both horizontal and vertical forces (Figure 14). From Figure 6, 9, 10 and 13 one can record that burial of submarine pipeline in a soil with high hydraulic conductivity results in consistant reduction of horizontal wave force with increase in burial depth of the pipeline, whereas the vertical wave force increases with burial upto certain depth, beyond which the it reduces.

12 236 Minimum Safe Burial Depth of Submarine Pipelines in Well Graded and High Hydraulic Conductivity Sand Figure 13. The locus of the resultant wave force on the submarine pipeline for e/d=1.5, H i =0.15 m and T=3.0 s in a soil with high hydraulic conductivity Figure 14. The locus of the resultant wave force on the submarine pipeline for e/d=2.0, H i =0.15 m and T=3.0 s in a soil with high hydraulic conductivity 3.2 Effect of relative depth of burial, e/d and relative water depth, d/l on horizontal and vertical wave forces on the submarine pipeline The variation of normalized in-line (Shoreward and Seaward) and vertical (Downward and Upward) wave forces as a function relative depth of burial of the pipeline, e/d for different relative water depth, d/l and for Hi/d=0.55 is provided in Figure 15, 16, 17 and 18 respectively. In these figures, e is the depth of burial (distance between the seafloor and pipeline bottom) and D is pipe diameter (Hence e/d=0 means pipeline is sitting on the sea floor and e/d=1 means that the pipeline is just completely buried and so on). (F xp ) Ave.Max and (F xn ) Ave.Max are the average maximum shoreward and seaward wave force on the pipeline and (F zp ) Ave.Max and (F zn ) Ave.Max are the average maximum downward and uplift wave force on the submarine pipeline respectively. ρ is the mass density of water, g is acceleration due to gravity, H = H i and is the incident wave height acting on the pipeline and A is the pipeline International Journal of Ocean and Climate Systems

13 S. Neelamani & K. Al-Banaa 237 Figure 15. Effect of relative burial depth of submarine pipeline and relative water depths on Shoreward force coefficients (Hi/d=0.555). Figure 16. Effect of relative burial depth of submarine pipeline and relative water depths on Seaward force coefficients (Hi/d=0.555). exposed area (A=diameter x length of pipe). The negative value of y-axis in Figure 16 and Figure 18 indicates that the wave force is acting towards seaward and upward direction and the positive value of y-axis in Figure 15 and Figure 17 indicates that the wave force is acting towards shoreward and downward direction respectively. From Figure 15 and 16, it is found that for any d/l value, change in e/d from 0.0 to 2.0 consistently reduces the magnitude of horizontal force coefficient. The gradient of force coefficient reduction from e/d=0.0 to 1.0 is steep compared to the gradient from 1.0 to 2.0. d/l has some conspicuous influence on the horizontal wave force coefficient for e/d=0.0 but the effect disappears when pipeline is buried in the sand. It is also clear from Figure 15 and 16 that the submarine pipeline resting on the seafloor receives the maximum shoreward and seaward force. For e/d=1.0, the normalised force reduction is almost 75% (Change from 0.52 to 0.13). From Figure 17 and 18, it is found that the magnitude of the vertical force coefficient is minimum when e/d=0.5 (Half buried case) which is due to the absence of pressure lag between upper and lower part of the submarine pipe and small difference in the magnitude of dynamic pressure as shown in Figure 19. The vertical force coefficient is maximum when e/d=1.0 (just fully buried case). The reason

14 238 Minimum Safe Burial Depth of Submarine Pipelines in Well Graded and High Hydraulic Conductivity Sand Figure 17. Effect of relative burial depth of submarine pipeline and relative water depths on Downward force coefficients (Hi/d=0.555) Figure 18. Effect of relative burial depth of submarine pipeline and relative water depths on Upward force coefficients (Hi/d=0.555) Figure 19. Magnitude and phase lag between dynamic pressures from sensors, which contributes significantly for the vertical wave force on the submarine pipeline for e/d=0.5, H i =0.15 m and T=3.0 s in a soil with high hydraulic conductivity International Journal of Ocean and Climate Systems

15 S. Neelamani & K. Al-Banaa 239 for this is due to the presence of phase lag and noticeable difference in the magnitude of dynamic pressure between the top and bottom of the submarine pipeline (Refer Figure 12). Further increase in e/d resulted in the reduction of vertical wave force coefficient due to the reduction in the magnitude of dynamic pressure. It is also seen from Figure 17 and 18 that the value of vertical force coefficient is smaller for the larger d/l value (d/l=0.225) and higher for the smaller d/l value (d/l=0.074). This is due to the fact that when d/l is smaller, the condition is closer to shallow water condition and the water particle in the wave has significant power to penetrate into the soil for causing dynamic pore water pressures and hence forces when compared to the case when d/l is larger. Hence long period waves are more important while designing buried pipeline. 3.3 Effect of relative depth of burial, e/d and relative wave height, Hi/d on horizontal and vertical wave forces on the submarine pipeline The effect of e/d on the shoreward, seaward, downward and upward force coefficients for the high conductivity soil for d/l=0.074 and for six different H i /d values are presented in Figure 20, 21, 22 and 23 Figure 20. Effect of relative burial depth of submarine pipeline and relative wave height on Shoreward force coefficients (d/l=0.074). Figure 21. Effect of relative burial depth of submarine pipeline and relative wave height on Seaward force coefficients (d/l=0.074).

16 240 Minimum Safe Burial Depth of Submarine Pipelines in Well Graded and High Hydraulic Conductivity Sand Figure 22. Effect of relative burial depth of submarine pipeline and relative wave height on Downward force coefficients (d/l=0.074). Figure 23. Effect of relative burial depth of submarine pipeline and relative wave height on Upward force coefficients (d/l=0.074). respectively. It is comprehensible that the values of vertical force coefficient increases with increase in H i /d value but the effect on horizontal force coefficient is trivial. Overall, it is clear that variation of d/l and H i /d has noteworthy effect on varying the vertical force coefficients and trivial on varying the horizontal force coefficients. The highest vertical force coefficient occurs when d/l is smaller (coastal waters rather than offshore conditions) and for high H i /d values, which are normally the design conditions. 3.4 Variation of horizontal (shoreward and seaward) and vertical (downward and upward) force coefficients for different relative burial depth and for a wide range of wave conditions The variation of shoreward and seaward force coefficient (F xp ) Ave.Max /0.5ρgHA and (F xn ) Ave.Max /0.5ρgHA and the downward and upward force coefficient (F zp ) Ave.Max /0.5ρgHA (F zn ) Ave.Max /0.5ρgHA for all the 62 wave height and period combinations in the order given in table 1 is presented in Figure 24 to 27. In these plots on the x-axis, run 1 is for lowest H i /d and highest d/l combinations (H i /d, d/l) of (0.111, 0.302) and the last point is for the highest H i /d and lowest d/l International Journal of Ocean and Climate Systems

17 S. Neelamani & K. Al-Banaa 241 combinations (H i /d, d/l) of (0.666, 0.074). Though the change in the incident wave character (H i /d, d/l) has influence on the horizontal and vertical force coefficients, the sensitivity of the force coefficient for changing e/d from 0.0 to 2.0 is significant. Also it can be seen from Figure 24 and 25 that change in the incident wave character (H i /d, d/l) has prominent variation on the horizontal force coefficient for e/d=0.0. For e/d=0.5 or higher, there is no appreciable change in the horizontal force coefficient. But from Figure 26 and 27, it can be observed that varying (H i /d, d/l) has appreciable effect for buried pipeline in high conductivity soil for e/d=1.0 and 1.5 both for the upward and downward force coefficients. It is interesting to note that the minimum vertical force coefficient occurs for half buried pipeline (e/d=0.5), which is a notable information for submarine pipeline in high hydraulic conductivity soil. Figure 24. The shoreward horizontal force coefficient for different depth of burial. Figure 25. The seaward horizontal force coefficient for different depth of burial.

18 242 Minimum Safe Burial Depth of Submarine Pipelines in Well Graded and High Hydraulic Conductivity Sand Figure 26. The downward vertical force coefficient for different depth of burial. Figure 27. The upward vertical force coefficient for different depth of burial. The results presented here can be used for selecting minimum burial depth of submarine pipelines both from safety and economic point of view. A worked out example is given for selecting minimum safe burial depth of a typical crude oil pipe in this type of soil. 4. WORKOUT EXAMPLE Consider a marine project, where a submarine pipeline is required to be installed in a well graded and high hydraulic conductivity soil as reported in this paper for crude oil transport from land to ship, which is moored in deeper waters. Assume the pipeline is made out of steel of 1.0 m OD, wall thickness of 15 mm. Let the water depth for the purpose of calculation be 2.25 m, wave period is 6.7 s and let the design wave height be 1.6 m at this water depth. International Journal of Ocean and Climate Systems

19 S. Neelamani & K. Al-Banaa 243 It is required to find the minimum safe burial depth of the pipeline against pullout in the vertical direction due to the wave induced uplift force on the buried pipeline. It is also necessary to make sure that the pipeline is also stable in the horizontal direction due to horizontal hydrodynamic forces acting on it at any burial depth. At any depth of burial, the forces counteracting the uplift and buoyancy force on the submarine pipeline is the weight of the pipeline material, the fluid inside the pipe and the natural backfill material on the pipe. If the counteracting forces are not enough, then it is necessary to use additional surcharge weights (like rip-rap cover or other solutions like mats). In such situation, it is necessary to estimate the weight of additional surcharge needed for the pipe/m run at any selected burial depth, in order to get a factor of safety of 1.5 against uplift. It is also needed to make sure that the factor of safety against horizontal sliding is 1.1 (DNV Code, 1981) at any buried depth. However, factor of safety of 1.5 is used as a conservative measure. First the pipeline must be stable against vertical uplift. Then it is needed to make sure it is also stable against horizontal sliding. 4.1 Stability against Up-Lift Force The given problem is for a model scale of 1:5, since the model pipe dia is 0.2 m, water depth in the model is 0.45 m and the peak model wave period is 3.0 sec. The wave height for this model scale is 1.0 m. However, it is proposed to check the pipeline for a higher wave height of 1.6 m since such wave height represents the design wave height for a water depth of 2.25 m (H i /d = 0.71). It is also found from the study that change in wave height has insignificant effect on the horizontal force coefficient (Figure 20 and 21) and has some effect on the change of vertical wave force coefficient (Figure 22 and 23). The wave length for this wave period and water depth condition is m. Pipeline OD, D = 1.0 m and Pipeline ID = 0.97 m Density of steel = 7.6 t/m 3 Seawater density = 1.04 t/m 3 The weight of the pipe/m run, W pipe = π/4 ( ) x 7.6 = t/m Weight of fluid inside the pipe/m, W fluid = π/4 ( ) x Fluid density inside the pipe Buoyancy force on the pipe/m run, F B = π/4 x 1 2 x 1.04 = t/m Uplift force due to the design wave/m run, F v = (Coefficient of vertical force in the upward direction) x 0.5ρgH s A Let us assume that for any depth of burial of the pipeline, the native soil will be used as backfill on the top of the pipeline for vertical stability, called surcharge. For pipeline resting on the bed (e/d=0.0), the surcharge due to the native soil cover, W native soil fill = 0.0 t/m For pipeline half buried (e/d=0.5), the surcharge due to the native soil cover = 0.0 t/m For pipeline with e/d=1.0, the surcharge = (1.0 x π/8 x 1 2 ) x submerged density of the soil in t/m 3 The submerged density of soil user for the present study is t/m 3 respectively. For pipeline with e/d=1.5, the surcharge due to the native soil cover = (1.0 x π/8 x 1 2 ) x submerged density of the soil in t/m 3. For pipeline with e/d=2.0, the surcharge due to the native soil cover = (1.0 x π/8 x 1 2 ) x submerged density of the soil in t/m 3. The total downward force on the pipeline, W down = Weight of pipe/m (W pipe ) + Weight of fluid inside the pipe/m (W fluid ) + Surcharge load over the pipe due to the native soil fill up to the original sea bed (W native soil fill ) The total upward force on the pipeline, W up = Buoyancy force/m run (F B ) + Hydrodynamic uplift force/m run (F v )

20 244 Minimum Safe Burial Depth of Submarine Pipelines in Well Graded and High Hydraulic Conductivity Sand The factor of safety against uplift, FS Uplift = W down / W up It is advisable to have the value of factor of safety against uplift equal to 1.5. If the factor of safety against uplift is less than 1.0 for a particular depth of burial, then the pipeline will not be stable in the vertical direction and will pop up above the seabed and receive direct wave loading. In such situation, it is necessary to go for additional surcharge by either placing sufficient weight/m run of pipe using rip-raps or any other stabilization method. If the pipeline is buried, and still it is not safe against the uplift force, then the weight of additional surcharge required/m run, W as on the pipe for a factor of safety of 1.5 against uplift can be estimated as follows:- W as = (1.5 x W up ) Weight of pipe/m Weight of fluid inside the pipe/m Weight of native surcharge over the top surface of the submarine pipeline up to the original sea bed. It is necessary to check the stability of the pipeline against horizontal sliding. 4.2 Stability against Horizontal Sliding of the Submarine Pipeline The restraining force preventing the submarine pipeline against horizontal sliding due to the hydrodynamic force in the horizontal direction, F H is the frictional force, F friction and the passive earth resistance, F passive of the soil surrounding the pipeline. The frictional force, F friction between the pipe and the sea bed soil depends up on the coefficient of friction, µ between the pipe and sea bed soil. where µ = F friction = µ [Weight of pipe/m (W pipe ) + Weight of fluid inside the pipe/m (W fluid ) + Surcharge load over the pipe due to the native soil fill up to the original sea bed (W native soil fill ) Buoyancy force/m run (F B ) Hydrodynamic uplift force/m run (F v )] F passive = 0.5 γ sub e 2 K p for partially buried pipe. = 0.5 γ sub D 2 K p for just buried pipe. = 0.5 γ sub (2 e D D 2 ) K p for buried pipe with depth of burial e > D. Where, γ sub is the submerged weight of the soil, e is the vertical distance between the seabed and the pipeline bottom and K p is the passive earth pressure resistance of the surrounding soil. The factor of safety against horizontal sliding, FS Horizontal sliding = (F friction + F passive ) / F H If FS Horizontal sliding is greater than 1.0, then it is safe against sliding. However, it is recommended to take a value of 1.5 for the purpose of safety. If the pipeline is not safe against horizontal sliding with a factor of 1.5, then the additional surcharge load needed is estimated using the formula W as = [(1.5 x F H - F passive ) / µ] (W pipe + W fluid + W native soil fill - F B - F v ) The estimate of the minimum safe burial depth against uplift forces and horizontal force for the given pipe of 1.0 m OD is carried out considering crude oil as flow material. 4.3 Minimum Safe Burial Depth against Uplift and horizontal sliding of Submarine Pipeline Carrying Crude Oil. The density of the crude oil at 48 C is 0.79 t/m 3. Table 3 lists the e/d values studied, factor of safety against uplift, FS Uplift, minimum safe e/d value to prevent vertical pop-up, the factor of safety against horizontal sliding, FS Horizontal sliding, and the minimum safe e/d value to prevent horizontal sliding. The International Journal of Ocean and Climate Systems

21 S. Neelamani & K. Al-Banaa 245 Table 3. Minimum safe relative burial depth, e/d of a submarine pipeline against vertical pop-up and horizontal sliding for crude oil transport for the marine soil studied for a typical design input condition Minimum Minimum safe e/d Minimum value safe e/d safe e/d considering Minimum W as value to value to both W as for W as for for satisfying prevent prevent vertical and FS Uplift FS Horizontal both FS Uplift and vertical FS Horizontal horizontal horizontal of 1.5 sliding of FS Horizontal sliding e/d FS Uplift pop-up sliding sliding stability (t/m) 1.5 (t/m) of 1.5 (t/m) e/d between 1.5 and 2.0 e/d between 1.5 and e/d=

22 246 Minimum Safe Burial Depth of Submarine Pipelines in Well Graded and High Hydraulic Conductivity Sand minimum safe e/d value considering both vertical and horizontal stability is also listed in column 7. This value is the highest among the two values listed in column 4 and 6. It can be seen that the minimum safe burial depth is governed by the vertical force and not by the horizontal force for any e/d values. The weight of additional surcharge, W as required to obtain factor of safety against uplift, FS Uplift of 1.5 and factor of safety against horizontal sliding, FS Horizontal sliding of 1.5 is also listed in column 8 and 9. The minimum weight of additional surcharge, W as for satisfying both FS Uplift and FS Horizontal sliding of 1.5 is listed in column 10. This value must be the higher value among column 8 and 9. It can be seen that for e/d=0.0, the horizontal wave force dictates the additional surcharge weight for stability. For e/d from 0.5 onwards, the vertical force dictates the additional surcharge weight. 5. CONCLUSIONS Evaluation of minimum safe burial depth of submarine pipelines is an important question and a challenge for coastal engineers. Submarine pipelines are largely used for transporting crude oil from the land to the ship, which is moored in deeper waters. If the pipeline is buried much more than what is needed for its safety, then the cost of burial in the open marine environment will be prohibitive. On the other hand, if the burial is not sufficient, then during design environmental condition, the pipeline experience pullout from its burial and subsequently will experience failure due to repeated direct hydrodynamic loadings and large dynamic responses. Such type of failures can be prevented by proper selection of the burial depth or by providing surcharges of required load/m run on the pipe, once a particular burial is decided. Well planned physical model investigations were carried out on a scaled submarine pipeline model. The main aim of the investigation is to obtain the minimum safe burial depth of submarine pipeline. It depends on the hydrodynamic forces in the vertical and horizontal directions on the buried pipeline, which in turn depends on the design wave condition, water depth and the properties of the sea bed soil like its porosity, hydraulic conductivity, saturated and submerged density, angle of shearing resistance etc. An attempt is made to solve this problem for a typical well graded and high hydraulic conductivity soil. Such soils are widely used for backfilling of pipelines during laying. Physical modeling is used as the tool. The investigations were carried out for a wide range of wave conditions and for different burial depths of the submarine pipeline. The important conclusions obtained from this study are: 5.1 General The horizontal force reduces non-linearly with increase in depth of burial. The horizontal force reduction due to varying the relative burial depth from e/d=0.0 to 1.0 is is almost 75% in the soil with hydraulic conductivity of 1.84 mm/s. In this type of soil, the vertical force reduces to a minimum when the e/d is changed from e/d=0.0 to 0.5 and increases up to e/d=1.0, mainly due to the significant change in the magnitude as well as the phase difference between the pore water pressures in the vertical direction. Further increase in e/d results in the reduction of vertical force due to the reduction of the magnitude of dynamic pore water pressure around the pipe. For any burial depth and for a constant wave height, increase in wave period has noticeable increase in the vertical wave force than the horizontal wave force on the submarine pipeline. For any burial depth and for a constant wave period, increase in wave height has reasonable increase in the vertical force coefficient than the horizontal wave force coefficient. In other words, the variation of vertical force is non-linear when wave height is increased, compared to the variation of horizontal force on the submarine pipeline. In general, the horizontal wave force dictates the stability of the submarine pipeline, when the pipeline is placed on the sea floor. For buried pipeline, the upward wave force dictates the stability of the pipeline. 5.2 Specific conclusion from the case study for a crude oil pipe to be buried in high hydraulic conductivity soil The specific conclusions for typical marine conditions (Steel pipeline of 1.0 m OD, wall thickness of 15 mm, water depth of 2.25 m, peak wave period of 6.7 s and design significant wave height of 1.6 m) is as follows: International Journal of Ocean and Climate Systems

23 S. Neelamani & K. Al-Banaa 247 For crude oil transportation, it is safe to bury the pipeline with relative burial depth e/d between 1.5 and 2.0 with the native soil filling over the buried pipeline. For the pipeline to be buried at a particular e/d level, the additional weight of surcharge needed/m run (Over and above the native soil fill, up to the original sea floor level) for obtaining a factor of safety of 1.5 is estimated and tabulated for ready reference. For instance, if the pipeline is decided to be placed on the seafloor (e/d=0.0), or partially buried (e/d=0.5) or fully buried (e/d=1.0, 1.5 and 2.0) in the soil of the type described, then additional surcharge of 1.10 t/m, 0.46 t/m, 0.58 t/m, 0.08 t/m and 0.0 t/m is required respectively for the input conditions of the worked out example, to prevent it from horizontal sliding and uplift. 6. ACKNOWLEDGEMENTS The authors would like to acknowledge with thanks the financial support of Kuwait Pipe Industries and Oil Services Co. (KSC) and Kuwait Foundation for the Advancement of Sciences (KFAS), Kuwait for carrying out this interesting project. Thanks to the upper management of Kuwait Institute for Scientific Research, Kuwait for all the R&D facility for the completion of the work. 7. REFERENCES DNV Code Rules for Submarine pipeline systems. Rules for the design, construction and inspection of submarine pipelines and pipeline risers. Det Norske Veritas, Norway. Lennon, G.P Wave-induced forces on buried pipelines. Jl. of Waterway, Port, Coastal and Ocean Engg., ASCE, 111 (3): Mac Pherson, H Wave forces on pipelines buried in permeable seabed. Jl. of Waterways, Port, Coastal and Ocean Engg., ASCE, 104 : Madhu Shudan. Ch., V. Sundar and S. Narasimha Rao Wave induced forces around buried pipeline. Ocean Engg., 29 (5): Magda, W Wave - induced cyclic pore-pressure perturbation effects in hydrodynamic uplift force acting on submarine pipeline buried in seabed sediments. Coastal Engg., 39: McDougal, W.G., S. H. Davidson, P. L. Monkmeyer and C. K. Sollitt Wave-Induced forces on buried pipelines. Jl. of Waterway, Port, Coastal and Ocean Engg., ASCE, 114 (2): Murthy, V.N.S Geotechnical Engineering. Principles and practices of soil mechanics and foundation engineering. Marcel Dekker, Inc, New York, USA. Neelamani, S., K. Al-Banaa, W.Al-Nassar, A. Al-Ragum, and J. Ljubic Optimum Burial Depth of Submarine Pipelines for Kuwaiti Marine Environmental Conditions. Final Report, July 2010, Kuwait Institute for Scientific Research, Kuwait, 420 pages. Spierenburg, S.E.J Wave-induced pore pressures around submarine pipeline. Coastal Engg., 10: Vijaya kumar, A., S. Neelamani and S. Narasimha Rao Environmental loads on submarine pipeline in clayey soil. ICOE-2001, Dec. 2001, IIT Madras, India, pp Vijayakumar, A., S. Neelamani and S. Narasimha Rao Scour around submarine pipeline in clayey soil. First International Conference on Scour of Foundations, ICSF-1, Texas A&M University, USA. Vijayakumar, A., S. Neelamani and S. Narasimha Rao Wave pressures and uplift forces on and scour around submarine pipelines in clayey soil. Ocean Engg., 30: Vijaya kumar, A. and S. Neelamani. 2005a. Experimental studies on Wave induced Scour around, pressures and forces on buried and unburied pipeline. Oceanic Engg. International, Canada, 9 (2): Vijayakumar, A., S. Neelamani and S. Narasimha Rao. 2005b. Wave interaction with a submarine pipeline in clayey soil due to random waves. Ocean Engg., 32 (13): Xu, J., G. Li, P. Dong and J. Shi Bedform evolution around a submarine pipeline and its effects on wave-induced forces under regular waves. Ocean Engineering, 37 (2-3):