On-bottom stability design of subsea pipelines transporting hydrocarbons is important to ensure safety and reliability but is challenging to achieve in the onerous metocean (meteorological and oceanographic) conditions typical of large storms (such as tropical cyclones, hurricanes or typhoons). This challenge is increased by the fact that industry design guidelines presently give no guidance on how to incorporate the potential benefits of seabed mobility, which can lead to lowering and self-burial of the pipeline on a sandy seabed. In this paper, we demonstrate recent advances in experimental modelling of pipeline scour and present results investigating how pipeline stability can change in a large storm. An emphasis is placed on the initial development of the storm, where scour is inevitable on an erodible bed as the storm velocities build up to peak conditions. During this initial development, we compare the rate at which peak near-bed velocities increase in a large storm (typically less than 10−3 m s−2) to the rate at which a pipeline scours and subsequently lowers (which is dependent not only on the storm velocities, but also on the mechanism of lowering and the pipeline properties). We show that the relative magnitude of these rates influences pipeline embedment during a storm and the stability of the pipeline.
The lateral stability of subsea pipelines and cables in large storms is an important design requirement for oil and gas developments and is also of importance for data communication infrastructure and marine renewable electricity networks. To ensure lateral stability two approaches are commonly employed in practice. Firstly, the pipeline or cable self-weight may be increased (known as primary stabilization) with the addition of, for example, a concrete coating in the case of pipelines. Secondly, additional means of stabilization may be adopted (known as secondary stabilization), which may include trenching, anchoring, placement of mattresses or overweight clamps and/or rock dumping. Presently, each of these approaches are known to provide reliable design solutions, but they come at a cost, with accounts suggesting that stabilization comprises 30% of the cost of recent pipeline projects . This is a substantial amount given that the total capital cost of pipelines typically exceeds US $4 million per kilometre of pipe .
Primary and secondary stabilization solutions are designed on the basis of conventional design approaches, incorporating industry guidelines such as DNV-RP-F109  and industry best practices (e.g. ). However, it is widely accepted that these design approaches are simplified and may be overly conservative on a sandy seabed, because they do not account for any variation in pipeline embedment due to scour following the initial placement of the pipeline. This is despite the fact that the same wave and current velocities that are evaluated to assess pipeline stability will almost always have the potential to mobilize sediment on a sandy seabed well before they can mobilize the pipeline . A more correct stability analysis must therefore account for scour of sediment from beneath the pipeline and the potential for pipeline lowering, which will alter pipeline embedment and have a direct impact on hydrodynamic loading and lateral soil resistance. It is noted that previous work has incorporated changes to pipeline embedment into stability analysis (e.g. [6,7]), but this work has focused on changes in embedment due to cyclic loading of the pipeline as opposed to changes in embedment due to scour.
The detailed processes of pipeline scour and lowering have been described at length by Fredsøe et al.  and Sumer & Fredsøe [9,10]. They are known to commence due to pre-existing gaps under the pipeline or when a scour hole initiates beneath a pipeline due to ‘piping’ (e.g. [11,12]) or, for example, due to variations in sediment supply . The scour hole then tends to expand vertically beneath the pipe in a process known as tunnel erosion, which occurs at a rate that is dependent on the near-seabed velocity, the pipeline geometry and the pipeline initial embedment [10,14]. The scour hole will also begin to extend along the pipeline at a rate that is dependent on these same parameters in addition to the three-dimensional geometry of the scour hole and the span shoulders [15–18].
At some point, the scour hole(s) become sufficiently long that lowering of the pipeline occurs. In principle, two mechanisms can cause this lowering (figure 1). Firstly, if scour holes initiate at locations that are widely spaced along the pipeline (relative to a length lC∼(100D×EI/w′)1/4, where D is the pipeline diameter, EI is the bending stiffness of the pipeline and w′ is the submerged weight per unit length), the pipeline can ‘sag’ into the hole . Alternatively, if the scour holes are closely spaced (i.e. lIP<lC, where lIP is the spacing between initiation points of scour along the pipeline), then the pipeline can ‘sink’ into the supporting soil between spans when these span shoulders become short . Detailed analysis of pipeline field observations has identified both of these lowering mechanisms on the North West Shelf of Australia .
Incorporating scour and pipeline lowering into stability design requires that the cumulative effects of scour can be estimated for all velocities contributing to sediment mobility prior to the time at which stability is to be analysed. In a large storm, this therefore requires that scour associated with the storm velocities leading up to peak conditions is included in the analysis. This type of analysis leads to some general questions. Firstly, does the stability of a pipeline increase during the initial stages of a storm due to scour? And secondly, if the stability of a pipeline increases (continuously or eventually) with scour, can sufficient scour happen during the initial development of a storm to ensure stability at the peak? Or, put more simply, how does the rate of scour and pipeline lowering compare with the rate at which near-bed current and wave velocities increase in a typical storm, so as to influence the stability of a pipeline?
The principal aims of this paper are to investigate aspects of these questions by building on previous literature that has focused mainly on scour in stationary velocities (i.e. steady, periodically steady or statistically stationary conditions). Since scour and pipeline lowering during a storm is a problem of fluid–structure–seabed interaction that is difficult to model numerically, physical experiments have been performed in a large recirculating (O-Tube) flume using an actively controlled pipeline (see [20,21] for more details). This facility is unique in that it can reproduce steady and oscillatory velocities that approach those measured and expected at the seabed during large storms, while simulating a section of pipeline free to translate (but not roll). The O-Tube facility has been used within the STABLEpipe JIP, which has aimed to improve stability design of pipelines by accounting for the effects of sediment transport and scour.
The remainder of this paper is structured as follows. In §2, the rates at which near-bed velocities increase in storms offshore of North West Australia are reviewed based on available measurements. These rates are then used to provide the context for a series of experiments performed in the O-Tube and described in §3 to measure variations in pipeline stability due to scour in the development stage of a storm. Detailed results and analysis of these experiments are presented for both the mechanisms of sagging and sinking in §§4 and 5, respectively. Discussion of the results is given in §6.
2. Storm development
In many offshore locations around the world, extreme environmental loading conditions are dominated by rapidly rotating low-pressure weather systems called cyclones (also called hurricanes in the North Atlantic and North East Pacific Oceans or typhoons in the North West Pacific Ocean). This is particularly true in North West Australia, where approximately four or five cyclones occur during November to April each year . These cyclones tend to generate in the warmer waters of the Arafura and Timor Seas, before travelling a few thousand kilometres in a west to southwest direction over their lifetime . The intensity of a cyclone (which can be defined in terms of the maximum wind speed at the centre of the storm ) and the direction (or track) can change continuously during its lifetime.
In intense cyclones (i.e. category 4/5 or 5/5) offshore of North West Australia, significant wave heights can exceed 10–15 m, with the actual height being dependent on the central pressure in the cyclone, the geometry of the cyclone (often defined in terms of the radius to maximum winds) and the forward velocity of the cyclone . In addition to increased waves, currents driven by the pressure and wind forcing associated with a cyclone can reach values in excess of 2 m s−1 near the water surface . This magnitude is a function of the intensity of the cyclone (through the pressure and wind forcing) and the storm track relative to the coastline and the underlying bathymetry [23,27].
To provide some insight into the development of cyclonic storms, figure 2 reproduces surface wave measurements and current measurements obtained in approximately 125 m water depth on the North West Shelf of Australia at the North Rankin A (NRA) gas production platform operated by Woodside. These measurements have been collated from a limited range of publications (cited in the figure captions). Cyclone storm tracks for each of these storm time series (obtained from ) are shown in figure 3 and summary statistics are given in table 1.
Figure 2 indicates that the significant wave heights at NRA tend to increase to a peak storm value over a period of approximately 12–36 h. During this period, the significant wave height increases continuously with a rate reaching approximately 0.3–1 m h−1 in the 3–6 h before peak conditions (table 1). Adopting linear wave theory, this indicates a rate of increase in the amplitude of equivalent near-bed wave velocity of between 10−6 m s−2 and 10−5 m s−2 at NRA (where equivalent near-bed wave velocity has been calculated using the approach outlined in ; table 1).
The only current measurements in figure 2 are for Cyclone Orson. It can be seen that these near-surface currents oscillate prior to the arrival of peak wave conditions due to the semi-diurnal tide, but then accelerate at a maximum rate of around 0.25 m s−1 h−1 (or 6.9×10−5 m s−2) close to peak storm conditions. In the case of Cyclone Orson accelerations of currents closer to the bed are less severe than those near the surface in figure 2. However, across a range of cyclones, the acceleration of near-bed currents is likely to be dependent on the amplification of both barotropic and baroclinic currents, and this makes them difficult to predict.
The ratio of steady current to wave velocity is important in assessing pipeline stability, because it has a strong influence on pipeline hydrodynamics and scour (for example, the equilibrium scour depth ). Although little comparative data are available, a general increase in the ratio of current to wave velocities is expected with increasing water depth.
In combination, the measurements in figure 2 and table 1 lead to several observations. Firstly, peak conditions occur after a finite ramp-up time, and so there is always likely to be some time prior to peak storm conditions when the effects of scour can accumulate. Secondly, the acceleration associated with near-bed velocities for a particular location appears to be dependent on a number of factors, including not only the cyclone intensity but also the storm track. For instance, the present measurements show that fast ramp-up rates are experienced at NRA both in large storms (Orson) and in smaller storms (Tiffany) that track differently towards NRA but at a similar forward speed. Thirdly, using NRA as a reference, the acceleration associated with the amplitude of near-bed wave velocity appears to be less than 10−5 m s−2 and the acceleration associated with surface current velocity is of the order of 10−4 m s−2 (note that in the remainder of the paper the term ‘acceleration’ will be used to refer specifically to the rate of increase of the amplitude in wave velocity or maximum combined wave and current velocity, not the instantaneous velocity). In an attempt to generalize this third observation, it is clear that accelerations below these values are expected for lower-intensity cyclones, or for cyclones tracking further from the design location. Conversely, for sites that are in much shallower water depth than NRA, the increase in significant wave heights shown in figure 2 could lead to larger accelerations in wave velocity. However, it is unlikely they these accelerations will exceed 10−3 m s−2 at the seabed unless the water depth is extremely shallow (i.e. less than 10 m) and the rate of increase in wave height is significantly higher than that in figure 2 (i.e. around five times higher than observed for Olivia). In the remainder of this paper, we will therefore adopt 10−3 m s−2 as an upper estimate of the likely acceleration associated with significant wave velocity in a large storm. We will also adopt a similar acceleration (with less certainty) for near-bed current velocity and maximum combined near-bed wave and current velocity.
3. Experiments performed in O-tube facility
A series of 12 experiments is reported in this paper. The first nine of these experiments investigate scour leading to the mechanism of sinking and the last three investigate scour leading to the mechanism of sagging. The key difference between the sinking and sagging experiments is that in the former the pipeline is actively load-controlled (using the approach outlined in ) to simulate the self-weight of the pipe while allowing for horizontal and vertical translations. Consequently, it is possible to model the pipeline sinking into the seabed due to scour and to capture stability directly, by allowing the pipeline to translate due to any hydrodynamic forcing that exceeds the available soil resistance. By contrast, for the sagging experiments, the displacement of the pipeline is controlled so as to mimic vertical movement at the middle of a long span section of pipeline as it moves down into the centre of a scour hole (i.e. point A in figure 1). This approach to model sagging is similar to that used previously by Fredsøe et al. .
The model pipeline used in the experiments is 196 mm in diameter and extends across the complete width of the O-Tube (figure 4). This diameter is close to 1:1 scale for smaller-diameter pipelines and umbilicals used on the North West Shelf of Australia and elsewhere. Extrapolation above or below this diameter (so as to consider gas export pipelines, for example) could be undertaken using scaling arguments but is not considered in this paper. Consequently, the metocean (meteorological and oceanographic) conditions and the accelerations observed in §2 are compared directly to the experimental results to estimate scour and lowering of a 196 mm pipeline in field conditions. The ability to model at close to 1:1 scale is a significant advantage of the O-Tube compared to other hydrodynamic flumes. Current velocities in the present experiments, for example, exceed 2 m s−1 in current-only conditions and reach a peak velocity of 1.5 m s−1 (with a 12 s period) in combined wave and current conditions.
The experimental set-up used in all experiments is shown in figure 4. The O-Tube working section is 1 m wide, 1 m high (above the un-scoured sand bed, which is 0.4 m deep) and 17 m long, with transparent front and rear walls. An acoustic Doppler velocimeter (ADV) was used to measure the velocity upstream of the pipeline, while a video camera was used to capture the scour profile. Measurements of pressure were made at 16 points around the circumference of the pipeline at the mid-point between the walls , and these were integrated to determine the hydrodynamic drag and lift forces on the pipeline. Load cells mounted between the pipeline and the actuator arms were also used . Artificial silica sand with average grain diameter (d50) of 0.24 mm was used throughout. The grain size distribution of this sand is close to uniform and the specific gravity relative to water is s=2.65. It should be noted that the onset of scour is a critical factor for determining the potential benefits of scour on stability. The onset of scour due to piping, for example, is dependent on the soil properties (in particular, the porosity and therefore the grain size distribution). Care must therefore be taken in extrapolating the results in this paper (which are for uniform sand) to other well-graded sediments.
Table 2 lists the 12 experiments performed. In the sinking experiments, a focus is placed on understanding the effect on pipeline stability of the rate at which the storm velocities increase. Therefore, the acceleration as associated with current and maximum regular wave velocity has been varied for two storm conditions. These storms have M equal to 0.5 and , respectively, where M=Uc/Uw with Uc the current velocity at 0.4 m above seabed (ASB) and Uw the maximum rectilinear wave velocity at 0.4 m ASB. This value of M is kept constant during the ramp-up stage of the storms. The condition corresponding to is a good base case and may be representative of relatively deep-water conditions where amplification of wave velocities is minimal at depth but barotropic and baroclinic currents are amplified due to passage of a cyclone. The case of M=0.5 includes both regular waves and currents and is modelled with a period of 12 s (similar to that observed for Cyclone Olivia, for example). The pipeline weight is set to SG=1.5 throughout and the initial pipeline embedment relative to the far-field seabed ef has been varied across three values (see figure 1 for definition of ef). Pipeline bending stiffness is not relevant in the sinking experiments, because it is assumed that scour holes are sufficiently close (as required for sinking) that curvature of the pipeline is minimal.
In the sagging experiments, the only variable that is altered is the simulated pipeline bending stiffness to submerged weight ratio EI/w′. As will be explained later, this ratio determines the speed at which the pipeline lowers into the centre of the scour hole. The focus of these experiments is therefore to investigate the effect on pipeline stability of the rate at which the pipeline lowers. The value of EI/w′=104 m3 is typical of 200 mm diameter pipelines on the North West Shelf of Australia. The values of 101 m3 and 106 m3 are representative of a relatively ‘flexible’ and a ‘stiff’ pipeline, respectively.
In addition to the experiments outlined in table 2, one supplementary experiment was performed to better explore sagging. This experiment is explained further in §5.
4. Pipeline sinking
In experiments PRS-01 to PRS-09, the pipeline was placed on the seabed (at a particular embedment depth) and scour was observed at the edges of the pipeline as the current and wave velocities increased. Following this, one of two outcomes was observed: (i) the storm velocities increased rapidly and were sufficient to move the pipeline laterally (i.e. the pipeline was unstable) before the pipeline lowered significantly due to scour; or (ii) scour continued to develop and propagated inwards towards the middle of the pipeline, which then began to sink vertically into the seabed due to its own weight and remained laterally stable until it was completely buried.
Figure 5 presents two snapshots of experiment PRS-04 consistent with the first of these two outcomes. This pipeline became unstable after only 50 s of a current increasing from zero at an acceleration of 2×10−2 m s−2. Figure 6 presents snapshots for experiment PRS-01, which modelled the same pipeline but in a current accelerating at 2×10−3 m s−2, equivalent to the upper end of expected accelerations during a cyclone (as discussed in §2). In this experiment, the outcome was of the second type noted above, with the pipeline sinking by more than one diameter. The scour process observed in PRS-01 was similar to that drawn in figure 7, with scour developing first at the sides of the pipeline in the O-Tube and then propagating at some velocity vh towards the middle of the pipeline. This pattern of scour was consistent across all experiments where scour development and pipeline lowering had time to occur. Preferential scour initiation at the ends of the pipeline occurred in each of these experiments primarily because of the local geometry of the seal between the end of the model pipeline and the wall of the flume, which resulted in a very small reduction in effective pipeline diameter at the walls of the flume.
In combination, the results in figures 5 and 6 demonstrate clearly how the rate at which the near-bed velocities increase can have a significant effect on the stability of the pipeline. A summary of the first six experiments in current-only conditions is presented in terms of the initial and final digitized seabed profiles in figure 8. For an initial far-field embedment of zero, a ‘critical’ acceleration exists between 2×10−3 and 2×10−2.75 m s−2. When the rate is lower than this critical value, the pipeline experiences sufficient scour in the initial stages (less than 1 h) of the storm to bury completely. By contrast, when the rate is higher than this critical value, the pipeline becomes laterally unstable during the development of the storm.
For experiments PRS-05 and PRS-06, the initial embedment of the pipeline was increased artificially at the start of each experiment by translating the pipeline laterally across the seabed several times with amplitude of movement equal to one pipe diameter. This procedure could, for example, represent the embedment increase due to pipe oscillations during the laying process, or when subjected to other cyclic loading (as noted in the Introduction). In both of these experiments, subsequent lowering of the pipeline due to scour was delayed compared with experiment PRS-01, which was conducted at the same acceleration but with no initial embedment. This delay is shown clearly in figure 9, which presents the vertical displacement of the pipeline in time and the centroid of the pipeline as the pipeline lowers due to scour. The delay indicates that a higher velocity was required to initiate scour at the ends of the pipeline when the pipeline was more highly embedded. This is consistent with the findings of Sumer et al. , who show that the critical velocity to cause onset of scour due to piping increases with increased embedment.
In the present experiments, the pipeline was found to be stable in both PRS-05 and PRS-06; however, the delay in the onset of scour due to increased embedment suggests that the critical acceleration might reduce with pipeline embedment when the embedment is small. This result is in agreement with the experimental results reported in Cheng et al. , which show that a pipeline with 10% initial embedment does become unstable earlier in a storm than the same pipeline with almost no initial embedment. However, at a deeper initial embedment level this initial trend of decreasing critical acceleration with increasing embedment depth must reverse; the extreme case being when the pipe has initial embedment larger than it could achieve through scour and lowering, in which case the stability is greater than that with zero nominal embedment regardless of acceleration. Based on these arguments, a possible trend in the critical acceleration with embedment is indicated by the thick dashed line in figure 8. This trend is indicative, since the actual trend is difficult to draw without quantitative experimental results covering a larger parameter space.
Extrapolating the results from figure 8 to predict the critical storm build-up rate for pipelines with different diameter, weight or embedment requires that the mechanism of sinking (and in particular the effect of these parameters on the rate of sinking) is clearly understood. Sumer & Fredsøe  suggested that pipeline sinking at a span shoulder can be explained as a continuous bearing failure of an equivalent rectangular footing. However, although figure 9 indicates that the vertical lowering of the pipeline is similar to that shown by Sumer & Fredsøe , the present experiments show two notable differences. Firstly, the vertical displacement of the pipeline in the present experiments is not smooth and continuous throughout, but instead includes small ‘jumps’ in vertical displacement. This is indicative of episodic ‘collapse’ of the span shoulder, rather than a continuous bearing failure. With each collapse, the pipeline most probably experiences an increase in contact area with the shoulder following a period of rapid lowering ; 36. Unfortunately, direct evidence of this collapse, or the bearing mechanism, could not be captured in the present O-Tube experiments. The only information available regarding the shoulder length was that it did not appear to exceed 200 mm once the pipeline started to sink (based on pore pressure transducer measurements spaced at 100 mm centres along the pipeline). This corresponds to a span to shoulder length ratio of 4:1. The second notable difference in figure 9 is that lowering of the pipeline is associated with a movement upstream of the pipeline. This suggests that the bearing failure mechanism at the shoulder is not symmetric about the axis of the pipe.
Given the apparent complexity of the mechanism of pipeline sinking at the span shoulder, we do not attempt to systematically investigate it in this paper. Instead, the results in figure 8 are presented on the qualification that they are an experimental 1:1 scale representation of a 196 mm pipe with scour initiation points spaced regularly at 1 m spacing (equal to the width of the O-Tube owing to the scour pattern shown in figure 7). If this is representative of field conditions, then it is apparent that the pipeline would be stable under ramping currents up to and including 2×10−3 m s−2 (which is the upper end of what is observed in field conditions) at least when the initial embedment is less than 0.2D. In situations where the pipeline has scour initiation points more widely spaced than 1 m, but still sufficiently close for sinking to be the main mechanism of lowering, the rate of lowering will be less than that observed in the O-Tube experiments. Correcting the results in figure 8 to account for this increased spacing (while maintaining all other pipeline and soil properties) needs to incorporate the additional time required for scour to propagate along the pipe (at a velocity vh) until the shoulder length is sufficiently short for sinking to occur, and to account for the changes in loading at the shoulder due to the larger pipeline span length.
Figure 10 presents a summary for the final three sinking experiments PRS-07 to PRS-09. In combined wave and current conditions, it can be seen that, once again, there is a critical rate at which the pipeline is just stable. This is in the range of 2×10−4 to 2×10−3.5 m s−2 and is notably lower than that for current-only conditions owing to the higher forces associated with waves. Based on the results in figure 10, it is apparent that a 196 mm pipeline with SG=1.5, no initial embedment and scour initiation points spaced at 1 m centres would not be stable in a large storm having a rate higher than 2×10−4 m s−2 and a period of 12 s. In contrast, it would appear to be stable for the rates representative of the storms listed in table 1.
5. Pipeline sagging
For widely spaced scour holes, the pipeline can sag into the centre of the scour hole. At any time, the amount of sagging is related to the length of the scour hole, the flexural rigidity of the pipeline and the submerged weight of the pipeline. Assuming that at both ends of the scour hole the constraint on the pipeline is somewhere between fixed and pinned, Fredsøe et al.  suggested that the vertical deflection of the pipeline can be given by 5.1 where ls is the length of the scour hole. (Deflection of the pipeline under different end constraints can also be determined easily; see, for example, Recommended Practice DNV-RP-F105.) Generally, the length of the scour hole will vary in time according to 5.2 where, as noted in §4, vh is the rate of scour along the pipeline (taken to be the average rate propagating in either direction). Cheng et al. [16,17] have recently given empirical expressions to predict this rate in currents and collinear waves and currents, which is dependent on the free field seabed shear stress, the soil grain size, pipeline diameter and the wave and/or current direction. Combining (1) and (2) gives the rate of vertical lowering of the pipeline 5.3 Experiments PRS-10 to PRS-12 have been undertaken to explore scour and the hydrodynamic forces on the pipeline as it lowers at a rate according to equation (3). In the experiments, all parameters, including the flow acceleration, are kept constant except the ratio of pipeline bending stiffness to submerged weight. This is equivalent to varying the rate of vertical displacement or lowering of the pipeline while holding all other parameters constant. A similar approach to this was used by Fredsøe et al.  to explore sagging under constant currents, although they modelled a pipeline that dropped at a fixed rate. Using the model pipe in the O-Tube, it is relatively easy to adopt the more appropriate rate due to equation (3), which varies in time due to scour along the pipeline and the nonlinear relationship between vertical deflection and span length.
Figure 11 presents the experimental results for PRS-10 to PRS-12, giving the calculated vertical displacement of the pipeline (worked out using vh from  and equation (3)) and the scour hole depth as a function of time. The experimental velocity time series is also shown. The point in time when the vertical displacement of the pipeline matches the scour hole depth signifies when the pipeline has ‘touched down’ into the scour hole. At this point (identified as a spike in the vertical force reading via the load cells), no further vertical movement of the pipeline was simulated in the experiment. In all three experiments, backfilling of the scour hole through sediment deposition then commenced.
With respect to figure 11, it is clear that the final burial depth differs significantly across the experiments. The most flexible pipeline drops fastest into the scour hole, but only reaches a depth of 0.58D. In contrast the stiff pipeline drops later and over a longer period of time, leading to a final depth of 1.28D. Consequently, for the experiments considered herein, the potential changes to stability as a result of sagging are experienced faster for the flexible pipeline, but the extent of lowering and the potential for greater long-term stability are larger for the stiffer pipeline provided it does not become unstable during the lowering process.
The reason for the difference in final lowered depth across the three experiments is due to the fact that the vertical position of the pipeline has an effect on scour locally beneath the pipeline. This interaction is clear in figure 12 which presents the scour profile around the pipeline as it moves vertically into the scour hole; as the pipeline drops (but has not yet touched the bottom of the hole), the scour hole increases in depth and the side slopes become steeper and more symmetric. This increase in scour hole depth does, however, take a finite time to occur. Consequently, the stiffer pipeline, which drops more slowly into the hole and allows sufficient time for the additional scour to develop, can lower to a greater depth.
In the sinking experiments (discussed in §4), load control of the pipeline allowed stability of the pipeline to be observed directly, since translations of the pipeline were permitted during testing. By contrast, for the sagging experiments, changes to stability can be partially interpreted through the influence of sagging on the hydrodynamic forces experienced by the pipeline. To explore this influence, figure 13 presents the lift and drag coefficients for experiments PRS-10 and PRS-11 based on integration of the pressure transducers around the pipeline. Initially, prior to any scour, the lift and drag coefficients are both large and positive. However, following the start of scour (indicated by increasing S/D in figure 11), but prior to vertical movement of the pipeline, there is a gradual reduction in drag coefficient and the lift coefficient becomes negative. These trends in the drag and lift coefficients are similar to those reported by Jensen et al.  using fixed seabed measurements and by Zhao & Cheng  using computational fluid dynamics. It is noted, however, that the magnitudes of the present results are lower than these early studies. Finally, as the pipe begins to sag into the scour hole, the drag force continues to reduce, while the lift coefficient becomes positive owing to the loss of flow beneath the pipeline. For completeness, figure 14 presents the scour profile observed in the present experiments with that modelled by Jensen et al.  and simulated by Zhao & Cheng  at four scour hole depths prior to vertical movement of the pipeline.
Comparing the two experiments in figure 13, it is clear the stiffer pipe (RPS-11) eventually achieves a lower drag force because it can sag to a greater depth. The rate at which the pipeline sags into the scour hole, and how this affects the scour process and the final lowered depth of the pipeline, is therefore of clear importance to assess stability for a sagging pipeline.
To better quantify how the rate at which the pipeline sags alters the scour process, a supplementary experiment was performed in which the pipeline was held fixed above the seabed with a far-field embedment of zero. Scour was then allowed to develop until apparent equilibrium conditions were reached at a steady current velocity. Following this, the pipeline was then lowered in discrete steps to vertical positions of zp/D=0.2, 0.33, 0.46, 0.58, 0.71 and 0.84. For each position, scour was allowed to develop until the scour depth appeared to reach a constant value over a period between 1 and 5 min (it should be noted that only this short time period was considered since waiting for longer, as could be appropriate for a pipeline much stiffer than any considered herein, could result eventually in backfill and a reduction in scour depth for larger zp). Live bed scour was observed at all times. Figure 15 summarizes the results from this supplementary experiment in terms of the scour hole depth. Each vertical dashed line indicates when the pipeline was lowered.
Two quantities are of interest in figure 15: (i) the evolution in apparent equilibrium scour depth Seq and (ii) the rate of scour with vertical movement of the pipeline. The first of these quantities clearly increases as the pipe moves downwards. This increase in depth, relative to the depth for zp=0, is shown to agree very well in figure 16 with the trend suggested by Sumer & Fredsøe  based on results from Hansen et al. . To investigate the second quantity, the following expression has been fitted to each interval of the data in figure 15: 5.4 where T defines a time scale of scour and t0 can be interpreted as an ‘offset’ in time required to ensure that (4) agrees with the measured scour depth at the start of an interval after the pipeline has been lowered. The form of (4) when t0=0 is the same as that introduced by Fredsøe et al.  to describe the scour hole development in steady currents for a pipeline with zp=0. Adequate fitting of (4) using the equilibrium scour depths in figure 16 was achieved (figure 15) when using a single value of T=350 s. For the first interval of zp/D=0, this result is slightly lower than a value of 540 s calculated according to the empirical formula suggested by Fredsøe et al.  for the sediment used in the experiment, the pipe diameter and the flow velocity.
The reasonable fit between (4) and the measurements in the supplementary experiment suggests that the scour development observed in figure 11 might be well predicted for any pipeline vertical position using equation (4). Pursuing this approach, the rate of change in scour hole depth for a sagging pipeline may be predicted according to 5.5 where S′=S/D and z′p=zp/D.
Using the vertical pipeline position z′p, equation (5) has been used to back-calculate the changes in scour depth with time in figure 11 according to 5.6 where the equilibrium scour depth has been estimated according to the expression indicated by the dashed line shown in figure 16: 5.7 It should be noted that this expression is likely to have some upper limit of validity for large values of z′p, although we are not able to state this limit based on the experiments presented herein. The time scale has been assumed to be independent of pipe position, based on the results in the supplementary experiments, and is calculated according to Fredsøe et al.  as 5.8 where g is acceleration due to gravity and θ is the non-dimensional shear stress. The constant 0.86 in (7) equals the equilibrium scour depth measured in the supplementary experiment for zp=0 and the constant 0.65 in (8) is the ratio of time scale (350 s) in the supplementary experiment to that obtained using the formula given by Fredsøe et al.  (540 s). The non-dimensional shear stress has been computed using the measured velocity at 0.4 m ASB assuming a logarithmic velocity profile and a bed roughness of z0=d50/12.
Within the limits of the data presented in this paper, it is apparent in figure 11 that equation (6) gives reasonable predictions of the scour depth observed in the experiments both prior to any pipeline vertical displacement (i.e. when z′p∼0) and during vertical displacement of the pipeline. Furthermore, the final lowered depth of the pipeline agrees to within 10–20%.
In this paper, we have presented experimental results at approximately 1:1 scale using a unique recirculating O-Tube flume to assess the stability of a 196 mm pipeline during the development stage of a storm. Stability has been assessed directly for the case of a sinking pipeline, while hydrodynamic forces have been measured to interpret stability for a sagging pipeline. The experiments have focused on the rate at which the storm velocities increase (shown herein only for sinking pipelines) and the rate at which the pipeline lowers (shown herein only for sagging pipelines), and the effect that these rates have on stability of a pipeline on a mobile seabed.
Experiments concerning a sinking pipeline have shown that there is a critical flow acceleration that defines if the pipeline is laterally stable in a storm. For a 196 mm pipe with scour initiation points spaced at 1 m centres along the pipeline and SG=1.5, the critical acceleration is between 2×10−3 and 2×10−2.75 m s−2 in currents, and between 2×10−4 and 2×10−3.5 m s−2 in combined waves and currents (with M=0.5 and regular wave period of 12 s). These accelerations may be similar to those observed offshore of North West Australia, although at NRA the accelerations are likely to have been lower in previous large cyclones. Extrapolation of the critical acceleration to pipeline diameters, seabed velocities and soil conditions not studied in this paper requires more detailed understanding of the sinking mechanism. However, it is expected that the critical acceleration will increase if pipeline SG increases (so that sinking can occur more quickly). Changes in the critical acceleration are also expected when the distance between scour initiation points and the initial pipeline embedment are different.
In the case of sagging pipelines, the rate of sagging has been shown to have a direct effect on the final lowered depth, in broad agreement with Fredsøe et al. . For a 196 mm pipeline having a bending stiffness to weight ratio of 1×104 m3, the final lowered depth can exceed one diameter, which is much greater than the equilibrium scour depth without vertical movement of the pipe. Furthermore, across the range of pipe properties investigated, as the pipe stiffness to weight ratio increases, the lowered depth can increase further. Traditional design approaches that ignore scour, and consequently design to increase the weight of the pipeline (through the addition of armour wires, for example) may therefore actually limit long-term stability of the pipeline contrary to the design intention. For sagging pipelines in steady currents, we have also shown that a simple model of scour, which is applicable as the pipeline lowers, gives good agreement with experiments in current-only conditions. This provides a valuable tool for estimating the scoured embedment and ultimately the stability in sagging. Future work is required to investigate this model over a wider range of soil conditions, flow velocities and pipeline properties.
Collectively, the results in this paper have demonstrated that scour can happen quickly in the development stage of a storm, leading to significant changes in pipeline embedment in less than 1–2 h for the 196 mm pipeline modelled. This time frame is within that observed for the ramp-up period of large storms and suggests that it is essential to account for scour of a sandy seabed in large storms so as to correctly assess pipeline stability. This means that metocean design criteria are needed not only for the return period design conditions at the peak of the storm, but also for the storm time series leading up to the peak conditions so as to achieve a safe, reliable and not too conservative stability assessment.
The first author kindly acknowledges the support of the Lloyd’s Register Foundation. Lloyd’s Register Foundation helps to protect life and property by supporting engineering-related education, public engagement and the application of research. The fourth author acknowledges the support of Shell Australia. This research is also generously supported through ARC Discovery Grants Program: DP130104535.
The authors thank the reviewers for their comments, which have significantly improved the manuscript. The authors also thank Qin Zhang for figure 4.
One contribution of 12 to a Theme Issue ‘Advances in fluid mechanics for offshore engineering: a modelling perspective’.
- © 2014 The Author(s) Published by the Royal Society. All rights reserved.