Scour around submarine pipes due to high-amplitude transient waves

Hassan Vosoughi, Hooman Hajikandi*

Department of Civil Engineering, Central Tehran Branch, Islamic Azad University, Tehran 1469669191, Iran

Abstract Estimation of scour dimensions below submarine pipelines is a vital step in designing offshore infrastructure. Extreme events like tsunami waves produce strong erosive forces below the underwater pipes,apt to create scour holes,jeopardizing the safety of the structure.Despite the importance of this issue, previous studies have mainly focused on steady flow cases, and the scour pattern below submarine pipes induced by high-amplitude transient waves has rarely been investigated. This paper reports the results of 40 experimental runs on transient wave-induced scour below a model pipe in a laboratory flume under a variety of initial conditions.The variables included the bed particle size and gradation,initial water depth,wave height,and slope of the bed layer.Waves were generated by a sudden release of water from a sluice gate,installed in the middle of the flume. A pressure transducer data acquisition system was used to record the wave heights at different time steps. The results indicate that, with a shallower initial depth of flow, the scour depth is relatively large. It was also found that there exists a direct correlation between the induced wave height and the size of the scour hole. It was observed that, in clear water conditions, the size of the scour hole in coarse sediments is smaller, while in live-bed conditions, larger scour holes are created in coarser sediments. It was also observed that at high wave amplitudes, the live-bed conditions are dominant, and consequently the bed elevation is altered.

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Keywords: Submarine pipe; Scour hole; Transient wave; Flume experiment; Live-bed condition; Sediment

1. Introduction

Use of submarine pipelines to convey oil, gas, or other hydrocarbons from the sea bed or river crossing is quite common in water communities. Pipe-bed and pipe-current interactions are significant problems, which should be considered for design purposes. Current-induced forces,together with wave-induced vibrations, are potentially apt to create a hole around the pipe and leave the pipe unsupported for considerable lengths, causing stability problems and possible leakage of the liquids due to pipe failures.Therefore,prediction of scour geometry around the pipe is a primary part of the design (Breusers and Raudkivi, 1991).

Studies carried out in this field can be categorized in four groups. The earliest set of studies focused on understanding the mechanism of scour beneath pipelines as well as the prediction of maximum scour depth. Chao and Hennessy (1972)carried out the pioneer research on this topic. They estimated the maximum scour depth below submarine pipes under steady flow conditions through an analytical approach.Following the same line of research, many scientists developed experimental models and proposed empirical relations of the scour depth in terms of non-dimensional parameters, such as the densimetric Froude number and diameter of the pipe,sediment properties,and flow hydrodynamics(Kjeldsen et al.,1973; Ibrahim and Nalluri, 1986; Mao, 1987, 1988; Chiew,1990, 1991; Zhang et al., 2016). Sumer and Fredsoe (2002)studied the onset of scour under the sand bed and confirmed that the scour initiation is driven by the pressure difference between the upstream and downstream sides of the pipe.They introduced three phases of scour evolution: piping, tunneling,and lee-wake vortices. Subhasish and Navneet (2008) studied the effective parameters of scour around submarine pipelines in uniform and non-uniform sediment layers. Mao (1988)described the role of vortices in scour development and reported the observation of three different types of vortices around the pipe. He also described the role of the pressure gradient measured by Bearman and Zdravkovich (1978) in initiating the seepage and piping effects.

The second category of studies was devoted to numerical efforts to model both the flow dynamics and the scour pattern in the vicinity of submarine pipes (Maza, 1987;Moncada and Aguirre, 1999; Lee et al., 2017). Hansen et al. (1985) used a numerical approach, based on potential flow theory, to implement a modified Muller method and integrate the sediment continuity equation.

The third generation of studies consists of a group of recent studies interested in wave-pipe interactions. Most have dealt with the effect of regular waves on scour below pipelines(Brennodden et al., 1989; Foda et al., 1990; Gao et al., 2002;Wagner et al., 1989). Çevik and Yu¨ksel (1999) performed experiments to study scour below submarine pipelines as a result of mutual interactions between currents, regular waves,and sediments. They conducted experiments on both horizontal and sloping beds in a shoaling region, and concluded that the wave height,wave period,and pipe diameter were the dominant parameters in the development of scour. Kızıl¨oz et al. (2013, 2015) studied scour around rigid pipelines under the effect of irregular waves on a horizontal beach and a sloping beach with a gradient of 0.1.

Finally, more recent studies have simulated the structural behavior of submarine pipes under the mutual effects of waves and currents (Zhang et al., 2016; Zeinoddini et al., 2013;Alvisi and Franchini, 2010; Chen et al., 2014; Ferrante et al.,2016). Liu et al.(2015)used a computational finite difference(CFD) approach to simulate the impact of submarine landslide-induced forces on undersea pipelines. They derived an empirical formula for estimating normal and axial forces induced by debris flow on a pipeline.

All of the studies mentioned above were carried out under steady flow conditions.To the authors'knowledge,no research has yet been carried out on scour due to high-amplitude transient waves. Tsunamis, natural hazards that occur as a result of rapid transmission of large amounts of seismic energy,are the most common forms of such transients.Tsunami scour is distinguished from other types of wave-induced scour by its long-period waves(Synolakis et al., 1997).On average,the tsunami wave period is longer than 10 min and the flood wave period is a few days, while both phenomena are categorized as high-amplitude transient waves. Francis (2006)studied scour damage of roads, bridges, and foundations caused by tsunami waves. The 2011 Bangkok flood is an example of flood-induced scour in which about 300 thousand houses were completely destroyed. According to the World Bank, the flood led to an economic loss of 2.7 billion USD(Poaponsakorn and Meethom, 2012). Hence, it is evident that the study of scour around infrastructure due to transient waves in extreme events is quite necessary.

In this study, experiments on scour around submarine pipelines under a single non-periodic transient wave were carried out. The considered variables included the sediment particle size, channel slope, normal water depth, and wave height. The results of this research may be applied in the evaluation of pipe-soil interaction under flash flood waves or similar transient waves,such as tsunami waves and dam break waves,or waves generated by a sudden opening of gates due to disoperation of the control valves or gates.

2. Dimensional analysis

The relevant parameters governing the flow are shown in Eq. (1):

whereLis the characteristic length of the scour hole;gis the gravitational acceleration;s0is the bed slope;d50is the median grain size of the sediment particles; σ is geometrical standard deviation of the sediment particles;vwandhware the wave velocity and wave height, respectively;y0is the water depth above the sediment recess;μ is the dynamic viscosity of water; ρwand ρsare the densities of water and sediment,respectively; anddpis the pipe diameter. With the Backinghum π theorem, the following dimensionless equation is obtained:

The last two terms on the right side of Eq. (2) are, respectively, the Reynolds number and the inverse of the densimetric Froude number. Within the limits of present work, the variations of the Reynolds number and Froude number were only dependent on the wave velocity because the diameter of the pipe and fluid properties were kept constant. Since the flow under consideration was dominated by the force of gravity, for simplicity, the Reynolds number was omitted from the list of non-dimensional parameters. Furthermore,combining the third and fourth terms on the right side of Eq. (2) results in the following:

whereFrdis the densimetric Froude number.

3. Experimental setup

Fig. 1. Experimental setup (units: m).

The experiments were carried out in a 10-m long, 0.6-m wide, and 0.6-m deep glass-sided flume. Fig. 1 shows the experimental setup. A centrifugal pump, with a maximum discharge capacity of 80 L/s,provided discharge into the flume through a 30-cm-diameter galvanized pipe. The flow rate was controlled by a propeller valve installed on the inlet pipe.Meanwhile, a calibrated ultrasonic flowmeter, with a measurement accuracy of 1 L/s for the range of discharge in the current work, was installed in the inflow pipe to measure the discharge. A sluice gate was installed in the middle of the flume,as shown in Fig.1(a).The first half of the flume length was used to store water upstream of the sluice gate and provided water heads to create transient waves. Prior to each run of experiments, the gate was closed and water was stored upstream of the gate to obtain the desired elevation.In order to ensure a constant opening velocity of the gate at different experimental runs,a rotary motor installed on a roof beam was used to open the gate. The motor turned a gear and pulled up the gate through a steel cable.The opening velocity of the gate was fixed at 1 m/s, causing the gate to be completely opened within 0.6 s. This velocity was sufficient to generate transient waves with an amplitude high enough. The model pipe was made of PVC with a nominal diameter of 4 cm.It was initially laid on a 3-m long and 15-cm thick sediment recess (see Fig. 1). The pipe ends were fixed in two lateral grooves opposite each other on the inside walls of the flume, in the middle of the recess. The grooves were carefully designed to keep the pipe fixed and stable against great forces on the pipe induced by the transient wave and to prevent the pipe's displacement. Prior to each run, the sediment recess was leveled and the pipe was smoothly laid on the initial bed layer(without any gap between the pipe invert and the bed layer)and fixed between the grooves. Also, to protect the sediment recess, riprap layers on the two sides of the sediment layer were designed. At the end of the flume, a tailgate with adjustable height was used to provide the desired depth of flow in the flume. The depth of flow over the sediment recess was measured by a point gage with a measurement accuracy of 0.05 cm. The point gage was also used to measure the scour geometry beneath the pipe. The device was mounted on a carriage located above flume walls. The carriage was able to move on two rail bars in both longitudinal and transverse directions. Meanwhile, the carriage was equipped with displacement sensors with a resolution of 0.5 cm.The sensors detected both longitudinal and transverse displacements.

4. Results and discussion

4.1. Test conditions

The variables of the experiments included two different bed slopes (a horizontal bed and a sloping bed with a gradient of 0.006), five heads of water, two types of sediment particles,and two different initial depths of flow over the sediment recess.Hence,in total,40 experimental runs were carried out.Table 1 shows the summary of the experimental conditions,wherehis the head of water upstream of the sluice gate,prior to the opening of the gate. Two types of sediment particles,fine and coarse,with respective mean particle diameters of 3.1 and 5.8 mm, were used in the tests. The properties of the sediment particles are summarized in Table 2. The geometric standard deviation of both types of the sediment particles were less than 1.3, which is within the uniformity criteria of the particles (Wagner et al., 1989).

4.2. Measurement procedure

At the beginning of each test, the depth of water above the sediment recess was adjusted with the tailgate.When the water surface reached the desired level, the sluice gate was closed.Then, the head of water upstream of the sluice gate started to increase. When the water head reached the desired level, the motor was turned on, and the sluice gate was opened in lessthan a second. Then a transient wave propagated over the whole flume length and overtopped from the tailgate. When the wave passed the pipe,a high-intensity transient current dug a large hole below the pipe. The digital head transducer measured the static pressure at three different locations: upstream of the sluice gate (P3), above the pipe (P2), and near the tailgate(P1)(see Fig.1).P2 was connected to the pipe wall and others were stuck to the inner wall of the flume. P1 was installed at the crest level upstream of the tailgate,and P3 was installed 20 cm upstream of the sluice gate at a height of 20 cm from the flume bed. The device consisted of pressure sensors connected to the data logger by long cables. It included a six-channel data logger, measuring static pressure heads with an accuracy of 0.01 Pa and a sampling frequency of 50 Hz. The data were saved in a Microsoft word file. Fig. 2 shows typical diagrams of the data logger output for Run 22 and Run 17.

Table 1 Initial conditions of tests.

Table 2 Sediment properties in tests.

As shown in Fig. 2(a), water was stored upstream of the sluice gate until the pressure at the transducer probe P3 reached 2 200 Pa (see the curve identified by Channel 3 in Figs.1 and 2),which was equivalent to a water head of 22 cm above the probe or 42 cm above the bed. At timet= 5.2 s(measured from the beginning of data recording), the gate opened. Then, the probe at P3 measured a sudden pressure drop. Up tot= 5.6 s, there was no sign of pressure increase as measured by the second probe P2, which was attached to the top face of the pipe (Channel 2). Fromt= 5.8 s tot= 6.05 s, the pressure head at the pipe increased from 735 Pa(a water head of 7.5 cm)to 1 325 Pa(a water head of 13.5 cm), which implies that the wave front reached the pipe in 0.6 s. Given the distance between the sluice gate and the pipe (1.5 m), the wave velocity was measured as 2.5 m/s. As seen,beforet=7.3 s,the water surface at P1 was flat,but att= 7.3 s, the head of water above the tailgate increased suddenly. The wave velocity calculated for the propagation distance from P2 to P1 was 2.94 m/s. The lower wave velocity measured at P2 was probably due to the closeness of the pipe to the sluice gate and durative opening of the gate.The complete opening of the sluice gate took about 0.6 s,which influenced the wave velocity at P2. In general, the wave velocities ranged from 2.6 m/s to 3.3 m/s for the distance between the pipe and tailgate.

Fig. 2. Typical data logger outputs.

Through comparison of the curves in Fig. 2(a), it was found that aftert= 12.2 s, the water surface in the flume showed a negative slope and water turned back from the end of the flume to the upstream. This inverse flow was not observed in the sloping bed tests withs0= 0.006. Investigation of the scour images showed that this backward flow was not able to influence the scour and deposition in the vicinity of the pipe because the reflected wave was not strong enough to influence the scour size. Comparison of the scour holes at different time intervals revealed that the scour geometry after the wave passage was not altered. Furthermore,investigation of water surface profiles in Fig. 2 proved that,after the wave passage, the water depths measured at P2 and P3 were almost equal. Hence, the reflected wave energy was dissipated.

The initial depth of water above the bed in Run 17 was 15.5 cm,which resulted in a lower wave height in the flume.In this run, the initial head of water upstream of the sluice gate was 42 cm(similar to Run 22).Att=3.2 s,the sluice gate was opened,and att=3.7 s,the wave reached the pipe.The wave velocity in the region from the sluice gate to the pipe was measured as 3 m/s. When the wave front passed the pipe, the pressure head above the pipe increased from 1 500 Pa to 1 740 Pa, which indicated an increase in depth of flow by 2.5 cm. Finally, att= 4.92 s, the wave reached the tailgate.The wave velocity measurement throughout the whole flume length was 3.2 m/s. Higher wave velocities in this run,compared to Fig.2(a),were due to the sloping bed.At the end of each experiment, the water inside the flume was drained.Then the scour geometry around the pipe was measured with the point gage. The surveying mesh depends on the scouring and deposition slopes. The finest mesh in this study was 0.5 cm×0.5 cm and the largest mesh size was 2 cm×2 cm.

Fig. 3 illustrates the evolution of the scour hole for a typical test run. The scour development was monitored by a digital video camera with an image resolution of 1 024×576 pixels at a video rate of 50 fps.Considering Fig.2 again,it is evident that the wave height was reduced as the wave propagated along the channel. This feature was designed for dam break waves, tsunami waves, and tidal waves. A dam break wave is an important example of rapidly varied flow.When a dam breaks, the released water propagates quickly in the downstream valley. A dam break wave is governed by the shallow water equations.Failure characteristics of earth dams are different from those of concrete dams.The initial stage of an embankment dam break starts with the formation of a breach with an average width ofHd＜bave＜ 3Hd, wherebaveis the average width of a breach, andHdis the dam height(Fread, 1984). Concrete dams tend to fail through partial breaching, but in laboratory tests it is quite common to simulate the dam break wave by suddenly releasing water restored upstream of a sluice gate. The laboratory methods for the generation of tsunami waves are quite similar to those for the generation of dam break waves,although the scientific basis of tsunami waves in nature is different from that of dam failures. The hydrostatic pressure difference between upstream and downstream faces of the water body is the initial force that produces motion. As the wave starts to propagate along a channel, the bed friction resists the flow and dissipates the wave energy. Hence, the wave under consideration was categorized as a bore-like wave.

Fig. 3. Evolution of scour hole in Run 22.

An observation of the images in the experiments reveals that scour due to transient waves is generated and developed in three phases. Fig. 3(a) shows the occurrence of a scour hole(flow from right to left)in Run 22(Fig.2)as the wave passed through the pipe att=5.8 s,when the wave front was exactly passing over the pipe.As seen,in this phase a small gap below the pipe was formed due to the differential hydraulic head between the upstream and downstream of the pipe. Sediment particles were transferred downstream and, then, piping was followed by tunneling, which deepened the scour depth and extended the scour length. In phase two att= 6 s, the wave crest was transferred toward downstream of the pipe(Fig. 3(b)) and lee-wake vortices were formed. In this phase sediment deposition created a hill downstream of the pipe. In the final stage att=6.2 s,the wave front passed over the pipe and moved downstream (Fig. 3(c)). In this phase, both the scour and deposition rates increased, and the hill height grew.The sediments were transferred due to the drag force induced by the wave evolution downstream. Fig. 3(d) shows a typical plan view of the pipe and scour hole.

4.3. Quantitative analysis

Fig.4 shows the variation of dimensionless scour depth(the ratio of scour depth at different longitudinal positions along the flume centerline(ds)to the pipe diameter)around the pipe in horizontal bed tests.In this case,the depth of flow over the pipe was 15.5 cm and fine sediments were used as the bed layer. The horizontal axis in Fig. 4 denotes the distance from the pipe centerline to the point of considerationX,normalized by the pipe diameter. The pipe was initially laid on the sediment recess at pointX/dp= 0. By increasing the head of water upstream of the sluice gate, both the induced wave velocity and wave height above the pipe increase,and as a result,a deeper scour hole is formed below the pipe. Also, comparison of the two-dimensional scour profiles in Fig. 4 confirms that higher heads produce scour with larger lengths. For a water headh= 49 cm upstream of the sluice gate, live-bed conditions dominate flow conditions and sediment particles move from upstream locations,filling the scour hole.Hence,a more gradual profile with a shallower scour depth is formed(see the curve fory0/h= 0.32). Also, the scour depth increases with the wave height(hw)and decreases with the depth of water above the pipe(y0).Meanwhile,it is observed that as the densimetric Froude number and the ratio of water head upstream of the sluice gate to the depth of water above the pipe(h/y0)increase,the point of the maximum scour depth is transferred to downstream locations.

Fig.4.Variation of normalized scour depth with longitudinal distance in fine sediment condition (s0= 0).

Variations of the maximum scour depth with the densimetric Froude number are presented in Fig.5.Fig.5(a)shows that, in horizontal bed tests, the maximum scour depth increases with the Froude number,following a semi-linear trend up to a limiting Froude number of about 3.75.Meanwhile,for higher densimetric Froude numbers, the flow regime is changed from clear water conditions to live-bed conditions,and, consequently, the scour depth decreases. It is also clear that,as the initial depth of water above the pipe decreases,the scour depth increases.

Similarly, Fig. 5(b) shows the variation of the maximum scour depth with the densimetric Froude number for the sloping bed (s0= 0.006) with fine sediments. As shown, atFrd= 3.75, the flow changes from clear water conditions to live-bed conditions. Comparison of Fig. 5(a) and (b) shows that, for similar initial conditions, the scour depths on the sloping bed are larger.

Fig.6 compares a scour profile on a horizontal bed to that on a sloping bed.Both series of data points were in the case of coarse sedimentswithy0/h=0.39.Itisevident that theshearstressatthe bed increases with the bed slope, and the live-bed condition dominates the flow,which is apt to create a larger scour hole.

The variation of normalized scour depth with the densimetric Froude number for fine and coarse sediments on the sloping bed withs0=0.006 is presented in Fig. 7. As expected,coarse sediment particles produce a smaller scour size.By implementation of multi-variable regression, an empirical formula for the relationship was derived as follows:

5. Conclusions

This paper presents the results of an experimental study on scour around submarine pipes under transient waves generated by the sudden release of flow from an upstream sluice gate.The effects of relevant parameters,including the head of water upstream of the sluice gate, channel slope, densimetric Froude number, and sediment gradation, were investigated.Based on the experimental findings, the following conclusions are made:

Fig. 5. Variations of maximum scour depth with densimetric Froude number in fine sediment condition.

Fig. 6. Comparison of scour profiles in horizontal and sloping bed tests in coarse sediment condition (y0/h = 0.39).

Fig. 7. Comparison of scour profiles on sloping bed.

(1) In clear water conditions, the scour hole dimensions,including the maximum scour depth,the length of the scour hole,and the height of the deposition hill downstream of the pipe,increase with the upstream water head.The size of the scour hole is relatively smaller in the coarse sediment condition.With a shallower initial depth of water in the flume,the size of the scour hole is relatively larger.

(2)For the initial conditions in which the live-bed condition is dominant, due to the interaction between the bed and highintensity waves, the accumulated sediments from upstream zones partly fill the hole,resulting in a reduced scour hole size.

(3) The results of the current research are useful for designing pipelines against transient currents. The time variation of the scour hole and its correlation with wave parameters will be further studied in future research.

Declaration of competing interest

The authors declare no conflicts of interest.