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Influence of infiltration on suspended sediment under waves
Coastal Engineering 45 (2002) 111 – 123 www.elsevier.com/locate/coastaleng
Inf luence of infiltration on suspended sediment under waves C. Obhrai a,*, P. Nielsen b, C.E. Vincent a b
a School of Environmental Sciences, University of East Anglia, Norwich NR4 7TJ, UK Department of Civil Engineering, The University of Queensland, Brisbane, Queensland, Australia
Received 3 May 2001; received in revised form 11 December 2001; accepted 1 February 2002
Abstract The effect of percolation through a permeable bed on sediment suspension under regular waves was examined in a laboratory wave tank (28 m 1 m 1 m), using acoustic backscatter sensors to make rapid (3 Hz) suspended sand profile measurements (0.005 m vertical resolution). Waves of 1.7 s period and heights ranging from 0.14 to 0.185 m were used over sand with a D50 of 255 Am. Infiltration velocities of 0 – 5.0 10 4 m s 1 were used. With percolation through an initially flat bed, ripple development was suppressed, particularly at lower wave heights; ripples took longer to form and were more threedimensional. Suspension was also suppressed. The total suspended load was correlated with Shields number (at the 1% significance level) when the Shields number was modified to take account of both the infiltration [Nielsen, P., 1997. Coastal groundwater dynamics. Proceedings of Coastal Dynamics, American Society of Civil Engineers, pp. 546 – 555] and ripple steepness [Coastal Eng. (1986) 23]. The ripple steepness was found to be the most important factor relating to the reduction in the total suspended loads. The influence of infiltration on time-averaged concentration profiles over equilibrium ripples was investigated by switching the percolation on and off for 5-min periods. The total suspended loads were reduced by up to 50% with percolation on. These results suggest that fluctuation of the water table and drainage within a beach will affect sediment transport and ripple dynamics, and that for sand of 0.25 mm, percolation will tend to reduce suspension and transport. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Groundwater; Seepage; Sediment suspension; Sand; Nearshore
1. Introduction Vertical flow through the bed has several important implications for sediment transport. These include the altered effective weight of the surficial sediment due to vertical drag, and modified shear stresses exerted on the bed due to boundary layer ‘thinning’ or ‘stretching’ (Sleath, 1984). Nielsen (1997) was the first to quantify
*
Corresponding author. Fax: +44-1603-50-77-19. E-mail address: [email protected] (C. Obhrai).
these two opposing effects of infiltration by means of a modified Shields parameter. It had so far been unclear which of these processes dominates. Nielsen et al. (2001) found that infiltration had no clear effect on transport rates for sand but tended to reduce sediment mobility. Sediment suspension under steady flows and wave motion is governed by forces on the individual sediment grains. For non-cohesive sands, these forces include gravity, the surface drag force, forces due to pressure gradients in the fluid, the lift force due to flow over the sediment grain and the infiltration force
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due to flow across the fluid/sediment interface (Sleath, 1984; Putnam, 1949; Madsen, 1978). These forces may work to increase or reduce these forces on the sediment. It is likely that fluid flow into, or out of, the sand surface will have a significant effect on sediment transport and be important for modelling beach morphodynamics. Grant (1948) noted, by observations of the fluctuations in the width and slope of beaches in California, that the position of the groundwater table within the beach played an important role in sediment deposition and erosion of the foreshore and backshore. Oh and Dean (1994) tried to simulate the interaction between the groundwater table and the beach profile dynamics in a wave tank. They found that an increased water table resulted in a stronger landward transport, which was contradictory to previous studies. Beach dewatering (the artificial lowering of the water table within beaches by a system of drains and pumps) has been proposed as a practical alternative to more traditional methods of shoreline stabilisation. Within the last 15 years, several test sites have been installed and to date, there are seven commercial dewatering systems in operation. However, a review paper by Turner and Nielsen (1997) concluded that the effectiveness of the dewatering concept in maintaining beach stability and controlling coastal retreat is yet to be convincingly demonstrated.
2. Effects of infiltration Previous laboratory studies have tried to determine the influence of infiltration on the type and rate of sediment transport, but have provided conflicting results. Steady pipe flow experiments by Martin (1970) concluded that infiltration may either enhance or hinder incipient motion, depending on the relative magnitude of the boundary shear stress and the infiltration stress, both of which depend on the sediment properties. Comparisons were also made between nickel particles and quartz sand which had similar diameters (0.58 mm) but different specific gravities (8.75 and 2.65). For the heavier nickel particles, they found that incipient motion was enhanced while for the lighter quartz particles, incipient motion was reduced. For flow into the bed, they found that the size of the sand grain was important for
a given hydraulic gradient since incipient motion may be hindered for small grains and enhanced for larger grains. However, Oldenziel and Brink (1974) established that, for a range of sizes [130 – 570 Am], infiltration always decreased the rate of sand transport. Harrison (1968) on the other hand concluded that infiltration had an inverse relationship on sediment transport if dunes were present, since flow into the bed steepened the faces of the dunes, resulting in a channel with greater bed roughness and hence a greater transport rate. Baldock and Holmes (1998) concluded that exfiltration increased erosion under wave motion, while infiltration stabilised the bed, but they found that infiltration had no significant effect on incipient motion. They also found that infiltration considerably affected the formation of ripples and in some cases, they were suppressed completely. They found that infiltration with hydraulic gradients as low as 0.1 influenced ripple formation. Baldock and Holmes (1998) suggested that the changes in ripple regime due to infiltration/exfiltration will affect both the bed load and suspended load, hence changing the nearshore transport. The overall effect is complex as vertical flow through a porous bed is thought to modify the sediment mobility in two opposing ways: (1) infiltration forces change the effective weight of the surficial sediments, and (2) boundary layer ‘thinning’ results in an increase in the bed shear stress. By considering these two opposing forces, an infiltration Shields number hN has been derived in terms of the infiltration velocity (Nielsen, 1997). u2 0 1 aw=u*0 ð1Þ hN ¼ * gd50 ðs 1 bw=KÞ where u*0 is the friction velocity, w is the infiltration velocity (positive is upwards), a and b are two constants that have been determined experimentally, K is the hydraulic conductivity of the bed material, s is the relative density of the sediment, and w/K = dh*/dz, the hydraulic gradient (Darcy’s law). Eq. (1) shows the essence, in the linearized form, of the two opposing effects of the vertical infiltration velocity w (positive upward). The extra term in the numerator quantifies the shear stress increase due to the thinning of the boundary layer while the last term in the denominator represents the effects of w on the
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effective weight of the grains. The values of a and b used here are 16 and 0.4 respectively, derived from shear stress experiments of Conley (1993) and the slope stability experiments of Martin and Aral (1970), as discussed in detail by Nielsen et al. (2001). Nielsen et al. (2001) found that infiltration had no clear effect on the direction of net sand transport rates but infiltration tended to reduce sediment mobility over a flat bed. They also concluded that the two opposing effects of increased shear stress due to boundary layer thinning and the stabilising effect of the downward drag are successfully accounted for through the infiltration Shields number (Nielsen, 1997). The aim of this research is to extend the work of Nielsen et al. (2001) and investigate the effect of infiltration on suspended sediment over a flat and a rippled bed. In the first part of our experiments, we found that ripple steepness was an important factor. Nielsen (1986) suggested that for flow over ripples, the ordinary Shields number should be modified to take into account flow contraction over ripple crests in the following way. hR is referred to as the ripple Shields number hR ¼
h ð1 pg=kÞ
pgbk
ð2Þ
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time-averaged infiltration velocities ranging up to K/ 10, assuming that the water table heights were in equilibrium with the run-up distribution. For the dynamic scenario during a rising tide in the field where the water table rises rather rapidly, they found values in the range 0 < w < 0.6K. However, Turner and Nielsen (1997) suggested that these latter values were too large because they were based on the effective porosity being equal to the total drainable porosity. Instead of deriving the infiltration velocity from the water table measurements, one might use instead pressure-gradient measurements as done by Turner and Nielsen (1997) and Horn et al. (1994). Applying this method, Turner and Nielsen found peak infiltration velocities of the order 0.0003 m s 1 c 0.15K coinciding with changes in the water table height of the order 0.07 m s 1 during a falling tide. Horn et al. (1994) found similarly modest infiltration rates (w < 0.15K) generated by swash uprushes during a rising tide. Baldock et al. found swash zone infiltration gradients of up to 0.6 –0.8, and these could be reasonably described with a simple diffusion model. It should be noted, however, that the infiltration velocities used in these experiments are more typical of the infiltration rates observed in the swash zone.
where g is the ripple height and k is the ripple length. 4. Experimental method and instrumentation 3. Natural infiltration velocities The most abundant data relating to the infiltration of water in the swash zone are water table data. Static laboratory experiments by Kang et al. (1994) obtained
The experiments were conducted in a 28-m-long wave flume in the Civil Engineering Department at the University of Queensland Australia (Fig. 1). The wave absorber at the end of the flume reduced the reflection coefficient to less than 5%. The flume
Fig. 1. Flume setup.
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Table 1 Sediment properties Specific gravity, S D50 (mm) Hydraulic conductivity K (m/s) Porosity, N w/K (max) w/K (half)
of 0.25 mm. The sediment properties are given in Table 1. 2.65 0.25 5.2910 4 0.35 0.94 0.51
included a sand bed 3.5 m long and vertical infiltration was induced by means of an infiltration box, allowing infiltration flow across the full length of the test section. The downward infiltration rate was controlled by a tap and valve connected to a hose at the bottom of the sand bed. The flow rate of water out of the bed was measured and used to calculate the infiltration velocities. Throughout the experiments, we used a well-sorted sand with a mean grain size
5. The acoustic backscatter system (ABS) The ABS allows rapid, high-resolution measurement of suspended sediment concentration. A threefrequency system was used although the results presented here are from a 3.58-MHz transducer that has a narrow footprint (approximately 4 cm diameter at 3 dB points at the sand bed), and produced particularly consistent results. The ABS pings at 50 Hz and 12 pings were averaged before recording, giving a time resolution of f 4 Hz with a vertical resolution of 5 mm. With well-sorted sand, the accuracy of the concentration measurements (for a burst average concentration) is about F 50% although the precision is much better than this (a few percentages). The posi-
Fig. 2. Time series of suspended sediment concentration starting from a flat bed, H = 13.0 cm, depth = 50 cm, T = 1.7 s, ws = 0 m s 1.
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tion of the bed was identified through a break-in-slope in the ABS profile; the position of this break identifies the first lowest point in the suspension that is uncontaminated by an echo from the sea bed. The profile was then used to extrapolate back to obtain the reference concentration at the bed (C0).
6. Experimental conditions Using the ABS we were able to calculate sediment concentration profiles under different wave conditions, with and without infiltration. Monochromatic waves with heights of 12.0, 13.0, 14.5, 15.8 and 18.6 cm were used, each with a period of 1.7 s. All experiments worked with a mean water depth of 50 cm. Experiments were performed with no infiltration, half infiltration, and maximum infiltration (the values of w/K are given in Table 1). Infiltration velocities used in our experiments were relatively high when
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compared to natural infiltration velocities measured in the swash zone. At the beginning of each experimental run, the sand bed was raked and flattened. The first part of the experiment investigated the growth of ripples from an initially flat bed under different infiltration velocities. Continuous ABS measurements were made for the first 10 min, and then in 5-min bursts after 20, 35, 50 and 65 min. Visual observations suggested that the ripples had attained equilibrium after approximately 1 h. The aim of the second part of the experiment was to measure the effect of infiltration into the bed on suspended sediment over an equilibrium ripple bed. While the waves were running, infiltration was turned off and on at 5-min intervals. Observations of the ripple dimensions at the beginning and end of each 5-min interval were made, and no measurable changes in the ripple profile were detected. The ABS sampled continuously during this part of the experiment. For the later runs, a capacitance wave wire was installed
Fig. 3. Time series of suspended sediment concentration starting from a flat bed, H = 13.0 cm, depth = 50 cm, T = 1.7 s, ws = 3.6 10 4 m s 1.
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Fig. 4. Time series of suspended sediment concentration starting from a flat bed, H = 13.0 cm, depth = 50 cm, T = 1.7 s, ws = 5.0 10 4 m s 1.
next to the ABS sensors and a digital video camera recorded the bed morphodynamics under the instruments.
7. Experimental results Under wave motion, the sediment bed is subject to both vertical and horizontal pressure gradients. The additional forces due to infiltration will affect the suspension as the bed evolves from a flat bed to a rippled bed. The lower panels in Figs. 2 – 4 show the
wave-averaged time series of suspended sediment concentration from the bed upwards for the first 10 min of three runs with the same wave height of 13.0 cm but different infiltration velocities. Time t = 0 corresponds to when the first wave entered the test section and the concentration is on a logarithmic scale. The concentration data have been averaged over each wave. The upper panels in Figs. 2 –4 show the time series of total suspended load for the three different infiltration velocities. There is a clear difference in the magnitude of the total suspended loads, with the no infiltration condition having the highest
Table 2 Average and peak total suspended loads over the first 10 min of waves Wave height (cm)
13.0 12.0
Average total suspended load (kg/m2)
Peak total suspended load (kg/m2)
No infiltration
Half infiltration
Full infiltration
No infiltration
Half infiltration
Full infiltration
0.54 0.23
0.34 –
0.097 0.047
1.58 0.40
1.39 –
0.612 0.17
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Table 3 Ripple dimensions after 60 min Wave height (cm)
Ripple height (cm) No infiltration
Full infiltration
Ripple length (cm) No infiltration
Full infiltration
No infiltration
Full infiltration
18.3 15.8 14.5 13.0 12.0 Mean
2.06 1.95 2.06 1.6 1.5 1.83
1.55 1.75 1.63 1.45 1.2 1.52
9.5 9.75 9.5 8.0 7.0 8.75
9.56 10.0 10.75 8.0 7.6 9.18
0.22 0.20 0.21 0.20 0.21 0.21
0.16 0.17 0.15 0.18 0.16 0.16
suspended load and the highest infiltration velocity condition having the lowest. Infiltration clearly alters the evolution of the bed, which results in a reduction in suspension (Table 2). The suspension of sediment is directly related to the bed morphology and from the digital camera we were able to make detailed observations of the bed
Ripple steepness
morphodynamics. The scale underneath the lower panels describes the evolution of the bed. The bed morphology was split into five different regimes: 1.
Grain rolling occurred when the sediment grains were saltating along the bed but were not suspended.
Fig. 5. Time series of suspended sediment concentration starting from a flat bed, H = 12.0 cm, depth = 50 cm, T = 1.7 s, ws = 0 m s 1.
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2.
3. 4. 5.
Mini ripples corresponded to when the sediment was first suspended and ripples of no more than 0.5 cm. Small ripples were defined as ripples with a height of 0.5 – 1 cm. Finally there were irregular vortex ripples [3D ripple pattern with ripples > 1 cm]. Regular vortex ripples.
When regular vortex ripples were achieved, the bed was thought to be in equilibrium. When the bed was under the influence of infiltration, grain motion was initially patchy as the infiltration appeared be stronger over certain areas of the bed. As the bed was not perfectly flat, perturbations in the bed profile gradually spread until the whole bed was in motion. Therefore, the subjective judgment of incipient motion was determined from the digital camera footage and was defined as the time when a significant number of the
grains under the instruments first started to roll. Infiltration affected the time taken for incipient motion of the sand to occur. With no infiltration (Fig. 2), the sediment moves immediately and the first suspension occurs after only 30 s. However, under the influence of maximum infiltration (Fig. 4), sand only began to move after 43 s and the first suspension occurred after 81 s. There was also a clear effect on the ripple steepness (g/k) after 10 min; with no infiltration, half infiltration and maximum infiltration, the corresponding ripple steepness values were 0.21, 0.181, and 0.17, respectively. For this wave condition, we see that the infiltration seems to reduce the ripple steepness, which results in the reduction in the suspended sediment. Similar results in terms of the effects of infiltration on incipient motion, suspended load and ripple steepness (Table 3) were obtained for wave heights between 12 and 18 cm (but digital video data were
Fig. 6. Time series of suspended sediment concentration starting from a flat bed, H = 12.0 cm, depth = 50 cm, T = 1.7 s, ws = 5.0 10 4 m s 1.
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only available for the two lowest wave heights, 12 and 13 cm). Figs. 5 and 6 show the suspension for 12.0cm waves, where Fig. 5 is the no infiltration condition and Fig. 6 is the maximum infiltration condition. The upper panels show that there is a difference in magnitude of the total suspended load of the order factor 2. With no infiltration (Fig. 5), the sediment began to move almost immediately while with full infiltration (Fig. 6), the sediment did not move until 90 s. Under the influence of infiltration, vortex ripples formed after 5 min of wave motion (approx. 120 waves), whereas with no infiltration, vortex ripples formed after only 2 min, and the ripple steepness was 0.158 compared to 0.212 when there was no infiltration. When the bedforms reached equilibrium (i.e. when regular vortex ripples were achieved after approximately 60 min), the time-averaged concentration over 5 min was calculated. The average total suspended load was calculated for each wave condition and infiltration velocity. In Fig. 7, which shows the total suspended load against the ordinary Shields number, all the infiltration points lie below the no infiltration points confirming that infiltration is tending to inhibit sediment suspension. In Fig. 8, plotting the same data
against the infiltration Shields number (Nielsen, 1997) brings the infiltration data and the no infiltration data closer. However, the correlation between the infiltra-
Fig. 7. Total suspended load against the ordinary Shields number. . No infiltration, n half infiltration ws = 3.59 10 4 m s 1, E maximum infiltration ws = 5.0 10 4 m s 1.
Fig. 9. Total suspended load against the Nielsen Shields number with ripple correction. . No infiltration, n half infiltration ws = 3.59 10 4 m s 1, E maximum infiltration ws = 5.0 10 4 m s 1.
Fig. 8. Total suspended load against the Nielsen Shields number. . No infiltration, n half infiltration ws = 3.59 10 4 m s 1, E maximum infiltration ws = 5.0 10 4 m s 1.
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Fig. 10. Change in total suspended load over 5-min intervals, with ripple formed with no infiltration (ws = 5 10 4 m s 1, H = 18.3 cm).
tion Shields number and total suspended load is still not significant at the 5% level. From the previous tables, we saw that infiltration had an important effect on the ripple steepness, and if the ripple correction factor (Nielsen, 1986) for flow contraction over ripple crests is used (Fig. 9), then a statistically significant correlation is obtained (R2 of 0.74, significant at 1%). To further test the effects of infiltration on suspension and reduce the influence of bedform differences, infiltration was turned off and on for alternating 5-min intervals while waves were kept running. An average suspended load was then calculated for each of the 5min bursts. Initially, this was done as short exercise at the end of each experimental run but this was extended as preliminary results looked interesting. This accounts for the difference in the number of data points for each experimental run. Figs. 10 –12 show
the changes in the total suspended load as infiltration is turned off and on over an equilibrium ripple field initially generated with different infiltration conditions. The wave height used was H = 18.3 cm and Fig. 10 shows the variations in suspended load over ripples initially generated with no infiltration, as the infiltration was switched between no infiltration and a maximum infiltration velocity of 5 10 4 m s 1; Fig. 11 is the same experiment but conducted over ripples initially generated with maximum infiltration. In both cases, the total suspended load is reduced by a factor of approximately 30% when infiltration is occurring. In Fig. 12, an intermediate infiltration velocity of 3.01 10 4 m s 1 was used (over a bed initially generated using intermediate infiltration; the variation in total load is initially the same but reduces to zero after 30– 40 min).
Fig. 11. Change in total suspended load over 5-min intervals, with ripple formed with maximum infiltration (ws = 5 10 4 m s 1, H = 18.3 cm).
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Fig. 12. Change in total suspended load over 5-min intervals, with ripple formed with half infiltration (ws = 3.01 10 4 m s 1, H = 18.3 cm).
The average total suspended load for each wave condition and each infiltration velocity was taken and then plotted against the ordinary Shields number and the infiltration Shields number (Figs. 13 and 14). In Fig. 13, all of the no infiltration points lie above the infiltration points, which indicates that even over a rippled bed, infiltration is inhibiting suspended sediment. Plotting the data against the infiltration Shields number brings the no infiltration and infiltration points onto one line. This shows that over an existing ripple bed, the infiltration Shields number accounts well for the opposing effects of infiltration over a
rippled bed. As these measurements were made over an existing equilibrium ripple bed, we would not expect the bedforms to have changed significantly from run to run. There may have been some subtle changes in the ripple shape over the 5-min periods, which may have influenced the suspended sediment concentration but we were unable to measure any such changes. We therefore believe that these results indicate the effect of infiltration on the bed shear stress and the effective weight of the sediment grains.
8. Discussion and conclusions These experiments indicate that infiltration has a number of significant effects. 1.
2.
3.
4.
Fig. 13. . No infiltration, n half infiltration ws=3.5910 4 m s 1, E maximum infiltration ws = 5.0 10 4 m s 1, error bar shows standard deviation of results.
It increased the time taken for the bedforms to evolve from an initially flat bed; this effect was more pronounced for the lower wave heights. This agrees with the experimental results of Baldock and Holmes (1998). After equilibrium has been reached, the ripple steepness was lower when the bed was under the influence of infiltration. The equilibrium ripple field generated with infiltration had a lower average suspended load than that generated with no infiltration. For the two lowest wave heights (H = 13.0 cm, 12.0 cm), when detailed measurements of bedforms were made, infiltration increased the time taken for the entire bed to be in motion and had an important effect on the bed morphology.
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Vertically integrated suspended load was correlated with Shields number (at the 1% significance level) when the Shields number was modified to take account of both the infiltration (Nielsen, 1997) and ripple steepness (Nielsen, 1986). The ripple steepness was found to be the most important factor relating to the reduction in the suspended loads. When infiltration was switched off and on for 5min intervals over an equilibrium bed, the suspended load was significantly reduced when infiltration was occurring. However, the effect of infiltration on the total suspended load decreased significantly with time (Figs. 10 – 12). This may have been due to a systematic increase in the size of the sand; it was noted that towards the end of the experiment, the sand bed had changed colour due to the coarser component of the sand preferentially remaining, while the finer sand grains had been transported out of the sandbox and deposited on base of the flume on either side of the sandbox. Martin (1970) found that the size of the sand grains had an important effect on the incipient motion of the particles. In particular, he found that infiltration into the bed hindered the initial motion of smaller sand grains while enhancing that of larger sizes. We do not believe that ripple changes influenced this result as our measurements were made over an existing equilibrium ripple bed as the ripple dimensions did not change significantly over 5-min periods. This conclusion is supported by the strong correlation obtained between the total suspended load and the infiltration Shields number (Fig. 14) which, unlike the results shown in Figs. 7 – 9, does not require the inclusion of the ripple steepness. The general effect of infiltration in these tests was to provide an unambiguous stabilising effect on the sand bed for this grain size (D50 = 255 Am), indicating that the additional downward force of the infiltration flow on the grains dominates over the thinning of the boundary layer (and the consequential enhanced stress). However, there are indications from these experiments that this effect may decrease for sand with larger grain sizes. We also conclude that it is necessary to include both the effects of infiltration and ripple steepness if the suspended load is to be successfully predicted from the Shields number. However, it is important to note that in areas where ripples are present (i.e. the surf zone), infiltration rates are likely to be much smaller than those imposed during our
Fig. 14. . No infiltration, n half infiltration ws = 3.59 10 4 m s 1, E maximum infiltration ws = 5.0 10 4 m s 1, error bar shows standard deviation of results.
experiments. We would therefore expect the effect of infiltration on ripple development to be minor. References Baldock, T.E., Holmes, P., 1998. Infiltration effects on sediment transport by waves and currents. Proceedings of the 26th International Conference Coastal Engineering, Orlando. ASCE, USA, pp. 3601 – 3614. Conley, D.C., 1993. Ventilated oscillatory boundary layers. PhD Thesis, University of California, San Diego, 74 pp. Grant, U.S., 1948. Influence of the water table on beach aggradation and degradation. Journal of Marine Research, 660 – 665. Harrison, S.S., 1968. The effect of groundwater infiltration on a stream regimen — a laboratory study. PhD dissertation, University of North Dakota. Horn, D.P., Baldock, T.E., Bard, A.J., Mason, T.E., 1994. Field measurements of swash induced pressures within a sandy beach. Proceedings of the 26th International Conference Coastal Engineering, Copenhagen. ASCE, USA, pp. 2812 – 2825. Kang, H.Y., Nielsen, P., Hanslow, D.J., 1994. Watertable overheight due to wave runup on a sandy beach. Proceedings of the 24th International Conference Coastal Engineering, Kobe, ASCE, USA, pp. 2115 – 2124. Madsen, O.S., 1978. Wave induced pressures and effective stresses in a porous bed. Geotechnique, 377 – 393. Martin, C.S., 1970. Effect of a porous bed on incipient sediment motion. Water Resources Research, 1162 – 1174.
C. Obhrai et al. / Coastal Engineering 45 (2002) 111–123 Martin, C.S., Aral, M.M., 1970. Seepage force on interfacial bed particles. Journal of Hydraulic Division 7, 1081 – 1100. Nielsen, P., 1986. Suspended sediment concentration under waves. Coastal Engineering, 23 – 31. Nielsen, P., 1997. Coastal groundwater dynamics. Proceedings of Coastal Dynamics, American Society of Civil Engineers, USA, pp. 546 – 555. Nielsen, P., Robert, S., Moller-Christensen, B., Olivia, P., 2001. Infiltration effects and sediment mobility under waves. Coastal Engineering 42 (2), 105 – 114. Oh, T., Dean, R.G., 1994. Effects of controlled water table on beach profile dynamics. Proceedings of the 24th International Conference Coastal Engineering, Kobe, ASCE, USA, pp. 935 – 949.
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Oldenziel, D.M., Brink, W.E., 1974. Influence of suction and blowing on the entrainment of sand particles. Journal of Hydraulics Division. Proceeding of the American Society of Civil Engineers, USA, 935 – 949. Putnam, J.A., 1949. Loss of wave energy due to percolation in a permeable sea bottom. Transaction of the American Geophysical Union, 349 – 356. Sleath, J.F.A., 1984. Sea Bed Mechanics. Wiley, New York, 335 pp. Turner, I.L., Nielsen, P., 1997. Rapid water table fluctuations within the beach face: implications for swash zone sediment mobility. Coastal Engineering, 45 – 59.
Inf luence of infiltration on suspended sediment under waves C. Obhrai a,*, P. Nielsen b, C.E. Vincent a b
a School of Environmental Sciences, University of East Anglia, Norwich NR4 7TJ, UK Department of Civil Engineering, The University of Queensland, Brisbane, Queensland, Australia
Received 3 May 2001; received in revised form 11 December 2001; accepted 1 February 2002
Abstract The effect of percolation through a permeable bed on sediment suspension under regular waves was examined in a laboratory wave tank (28 m 1 m 1 m), using acoustic backscatter sensors to make rapid (3 Hz) suspended sand profile measurements (0.005 m vertical resolution). Waves of 1.7 s period and heights ranging from 0.14 to 0.185 m were used over sand with a D50 of 255 Am. Infiltration velocities of 0 – 5.0 10 4 m s 1 were used. With percolation through an initially flat bed, ripple development was suppressed, particularly at lower wave heights; ripples took longer to form and were more threedimensional. Suspension was also suppressed. The total suspended load was correlated with Shields number (at the 1% significance level) when the Shields number was modified to take account of both the infiltration [Nielsen, P., 1997. Coastal groundwater dynamics. Proceedings of Coastal Dynamics, American Society of Civil Engineers, pp. 546 – 555] and ripple steepness [Coastal Eng. (1986) 23]. The ripple steepness was found to be the most important factor relating to the reduction in the total suspended loads. The influence of infiltration on time-averaged concentration profiles over equilibrium ripples was investigated by switching the percolation on and off for 5-min periods. The total suspended loads were reduced by up to 50% with percolation on. These results suggest that fluctuation of the water table and drainage within a beach will affect sediment transport and ripple dynamics, and that for sand of 0.25 mm, percolation will tend to reduce suspension and transport. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Groundwater; Seepage; Sediment suspension; Sand; Nearshore
1. Introduction Vertical flow through the bed has several important implications for sediment transport. These include the altered effective weight of the surficial sediment due to vertical drag, and modified shear stresses exerted on the bed due to boundary layer ‘thinning’ or ‘stretching’ (Sleath, 1984). Nielsen (1997) was the first to quantify
*
Corresponding author. Fax: +44-1603-50-77-19. E-mail address: [email protected] (C. Obhrai).
these two opposing effects of infiltration by means of a modified Shields parameter. It had so far been unclear which of these processes dominates. Nielsen et al. (2001) found that infiltration had no clear effect on transport rates for sand but tended to reduce sediment mobility. Sediment suspension under steady flows and wave motion is governed by forces on the individual sediment grains. For non-cohesive sands, these forces include gravity, the surface drag force, forces due to pressure gradients in the fluid, the lift force due to flow over the sediment grain and the infiltration force
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due to flow across the fluid/sediment interface (Sleath, 1984; Putnam, 1949; Madsen, 1978). These forces may work to increase or reduce these forces on the sediment. It is likely that fluid flow into, or out of, the sand surface will have a significant effect on sediment transport and be important for modelling beach morphodynamics. Grant (1948) noted, by observations of the fluctuations in the width and slope of beaches in California, that the position of the groundwater table within the beach played an important role in sediment deposition and erosion of the foreshore and backshore. Oh and Dean (1994) tried to simulate the interaction between the groundwater table and the beach profile dynamics in a wave tank. They found that an increased water table resulted in a stronger landward transport, which was contradictory to previous studies. Beach dewatering (the artificial lowering of the water table within beaches by a system of drains and pumps) has been proposed as a practical alternative to more traditional methods of shoreline stabilisation. Within the last 15 years, several test sites have been installed and to date, there are seven commercial dewatering systems in operation. However, a review paper by Turner and Nielsen (1997) concluded that the effectiveness of the dewatering concept in maintaining beach stability and controlling coastal retreat is yet to be convincingly demonstrated.
2. Effects of infiltration Previous laboratory studies have tried to determine the influence of infiltration on the type and rate of sediment transport, but have provided conflicting results. Steady pipe flow experiments by Martin (1970) concluded that infiltration may either enhance or hinder incipient motion, depending on the relative magnitude of the boundary shear stress and the infiltration stress, both of which depend on the sediment properties. Comparisons were also made between nickel particles and quartz sand which had similar diameters (0.58 mm) but different specific gravities (8.75 and 2.65). For the heavier nickel particles, they found that incipient motion was enhanced while for the lighter quartz particles, incipient motion was reduced. For flow into the bed, they found that the size of the sand grain was important for
a given hydraulic gradient since incipient motion may be hindered for small grains and enhanced for larger grains. However, Oldenziel and Brink (1974) established that, for a range of sizes [130 – 570 Am], infiltration always decreased the rate of sand transport. Harrison (1968) on the other hand concluded that infiltration had an inverse relationship on sediment transport if dunes were present, since flow into the bed steepened the faces of the dunes, resulting in a channel with greater bed roughness and hence a greater transport rate. Baldock and Holmes (1998) concluded that exfiltration increased erosion under wave motion, while infiltration stabilised the bed, but they found that infiltration had no significant effect on incipient motion. They also found that infiltration considerably affected the formation of ripples and in some cases, they were suppressed completely. They found that infiltration with hydraulic gradients as low as 0.1 influenced ripple formation. Baldock and Holmes (1998) suggested that the changes in ripple regime due to infiltration/exfiltration will affect both the bed load and suspended load, hence changing the nearshore transport. The overall effect is complex as vertical flow through a porous bed is thought to modify the sediment mobility in two opposing ways: (1) infiltration forces change the effective weight of the surficial sediments, and (2) boundary layer ‘thinning’ results in an increase in the bed shear stress. By considering these two opposing forces, an infiltration Shields number hN has been derived in terms of the infiltration velocity (Nielsen, 1997). u2 0 1 aw=u*0 ð1Þ hN ¼ * gd50 ðs 1 bw=KÞ where u*0 is the friction velocity, w is the infiltration velocity (positive is upwards), a and b are two constants that have been determined experimentally, K is the hydraulic conductivity of the bed material, s is the relative density of the sediment, and w/K = dh*/dz, the hydraulic gradient (Darcy’s law). Eq. (1) shows the essence, in the linearized form, of the two opposing effects of the vertical infiltration velocity w (positive upward). The extra term in the numerator quantifies the shear stress increase due to the thinning of the boundary layer while the last term in the denominator represents the effects of w on the
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effective weight of the grains. The values of a and b used here are 16 and 0.4 respectively, derived from shear stress experiments of Conley (1993) and the slope stability experiments of Martin and Aral (1970), as discussed in detail by Nielsen et al. (2001). Nielsen et al. (2001) found that infiltration had no clear effect on the direction of net sand transport rates but infiltration tended to reduce sediment mobility over a flat bed. They also concluded that the two opposing effects of increased shear stress due to boundary layer thinning and the stabilising effect of the downward drag are successfully accounted for through the infiltration Shields number (Nielsen, 1997). The aim of this research is to extend the work of Nielsen et al. (2001) and investigate the effect of infiltration on suspended sediment over a flat and a rippled bed. In the first part of our experiments, we found that ripple steepness was an important factor. Nielsen (1986) suggested that for flow over ripples, the ordinary Shields number should be modified to take into account flow contraction over ripple crests in the following way. hR is referred to as the ripple Shields number hR ¼
h ð1 pg=kÞ
pgbk
ð2Þ
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time-averaged infiltration velocities ranging up to K/ 10, assuming that the water table heights were in equilibrium with the run-up distribution. For the dynamic scenario during a rising tide in the field where the water table rises rather rapidly, they found values in the range 0 < w < 0.6K. However, Turner and Nielsen (1997) suggested that these latter values were too large because they were based on the effective porosity being equal to the total drainable porosity. Instead of deriving the infiltration velocity from the water table measurements, one might use instead pressure-gradient measurements as done by Turner and Nielsen (1997) and Horn et al. (1994). Applying this method, Turner and Nielsen found peak infiltration velocities of the order 0.0003 m s 1 c 0.15K coinciding with changes in the water table height of the order 0.07 m s 1 during a falling tide. Horn et al. (1994) found similarly modest infiltration rates (w < 0.15K) generated by swash uprushes during a rising tide. Baldock et al. found swash zone infiltration gradients of up to 0.6 –0.8, and these could be reasonably described with a simple diffusion model. It should be noted, however, that the infiltration velocities used in these experiments are more typical of the infiltration rates observed in the swash zone.
where g is the ripple height and k is the ripple length. 4. Experimental method and instrumentation 3. Natural infiltration velocities The most abundant data relating to the infiltration of water in the swash zone are water table data. Static laboratory experiments by Kang et al. (1994) obtained
The experiments were conducted in a 28-m-long wave flume in the Civil Engineering Department at the University of Queensland Australia (Fig. 1). The wave absorber at the end of the flume reduced the reflection coefficient to less than 5%. The flume
Fig. 1. Flume setup.
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Table 1 Sediment properties Specific gravity, S D50 (mm) Hydraulic conductivity K (m/s) Porosity, N w/K (max) w/K (half)
of 0.25 mm. The sediment properties are given in Table 1. 2.65 0.25 5.2910 4 0.35 0.94 0.51
included a sand bed 3.5 m long and vertical infiltration was induced by means of an infiltration box, allowing infiltration flow across the full length of the test section. The downward infiltration rate was controlled by a tap and valve connected to a hose at the bottom of the sand bed. The flow rate of water out of the bed was measured and used to calculate the infiltration velocities. Throughout the experiments, we used a well-sorted sand with a mean grain size
5. The acoustic backscatter system (ABS) The ABS allows rapid, high-resolution measurement of suspended sediment concentration. A threefrequency system was used although the results presented here are from a 3.58-MHz transducer that has a narrow footprint (approximately 4 cm diameter at 3 dB points at the sand bed), and produced particularly consistent results. The ABS pings at 50 Hz and 12 pings were averaged before recording, giving a time resolution of f 4 Hz with a vertical resolution of 5 mm. With well-sorted sand, the accuracy of the concentration measurements (for a burst average concentration) is about F 50% although the precision is much better than this (a few percentages). The posi-
Fig. 2. Time series of suspended sediment concentration starting from a flat bed, H = 13.0 cm, depth = 50 cm, T = 1.7 s, ws = 0 m s 1.
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tion of the bed was identified through a break-in-slope in the ABS profile; the position of this break identifies the first lowest point in the suspension that is uncontaminated by an echo from the sea bed. The profile was then used to extrapolate back to obtain the reference concentration at the bed (C0).
6. Experimental conditions Using the ABS we were able to calculate sediment concentration profiles under different wave conditions, with and without infiltration. Monochromatic waves with heights of 12.0, 13.0, 14.5, 15.8 and 18.6 cm were used, each with a period of 1.7 s. All experiments worked with a mean water depth of 50 cm. Experiments were performed with no infiltration, half infiltration, and maximum infiltration (the values of w/K are given in Table 1). Infiltration velocities used in our experiments were relatively high when
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compared to natural infiltration velocities measured in the swash zone. At the beginning of each experimental run, the sand bed was raked and flattened. The first part of the experiment investigated the growth of ripples from an initially flat bed under different infiltration velocities. Continuous ABS measurements were made for the first 10 min, and then in 5-min bursts after 20, 35, 50 and 65 min. Visual observations suggested that the ripples had attained equilibrium after approximately 1 h. The aim of the second part of the experiment was to measure the effect of infiltration into the bed on suspended sediment over an equilibrium ripple bed. While the waves were running, infiltration was turned off and on at 5-min intervals. Observations of the ripple dimensions at the beginning and end of each 5-min interval were made, and no measurable changes in the ripple profile were detected. The ABS sampled continuously during this part of the experiment. For the later runs, a capacitance wave wire was installed
Fig. 3. Time series of suspended sediment concentration starting from a flat bed, H = 13.0 cm, depth = 50 cm, T = 1.7 s, ws = 3.6 10 4 m s 1.
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Fig. 4. Time series of suspended sediment concentration starting from a flat bed, H = 13.0 cm, depth = 50 cm, T = 1.7 s, ws = 5.0 10 4 m s 1.
next to the ABS sensors and a digital video camera recorded the bed morphodynamics under the instruments.
7. Experimental results Under wave motion, the sediment bed is subject to both vertical and horizontal pressure gradients. The additional forces due to infiltration will affect the suspension as the bed evolves from a flat bed to a rippled bed. The lower panels in Figs. 2 – 4 show the
wave-averaged time series of suspended sediment concentration from the bed upwards for the first 10 min of three runs with the same wave height of 13.0 cm but different infiltration velocities. Time t = 0 corresponds to when the first wave entered the test section and the concentration is on a logarithmic scale. The concentration data have been averaged over each wave. The upper panels in Figs. 2 –4 show the time series of total suspended load for the three different infiltration velocities. There is a clear difference in the magnitude of the total suspended loads, with the no infiltration condition having the highest
Table 2 Average and peak total suspended loads over the first 10 min of waves Wave height (cm)
13.0 12.0
Average total suspended load (kg/m2)
Peak total suspended load (kg/m2)
No infiltration
Half infiltration
Full infiltration
No infiltration
Half infiltration
Full infiltration
0.54 0.23
0.34 –
0.097 0.047
1.58 0.40
1.39 –
0.612 0.17
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Table 3 Ripple dimensions after 60 min Wave height (cm)
Ripple height (cm) No infiltration
Full infiltration
Ripple length (cm) No infiltration
Full infiltration
No infiltration
Full infiltration
18.3 15.8 14.5 13.0 12.0 Mean
2.06 1.95 2.06 1.6 1.5 1.83
1.55 1.75 1.63 1.45 1.2 1.52
9.5 9.75 9.5 8.0 7.0 8.75
9.56 10.0 10.75 8.0 7.6 9.18
0.22 0.20 0.21 0.20 0.21 0.21
0.16 0.17 0.15 0.18 0.16 0.16
suspended load and the highest infiltration velocity condition having the lowest. Infiltration clearly alters the evolution of the bed, which results in a reduction in suspension (Table 2). The suspension of sediment is directly related to the bed morphology and from the digital camera we were able to make detailed observations of the bed
Ripple steepness
morphodynamics. The scale underneath the lower panels describes the evolution of the bed. The bed morphology was split into five different regimes: 1.
Grain rolling occurred when the sediment grains were saltating along the bed but were not suspended.
Fig. 5. Time series of suspended sediment concentration starting from a flat bed, H = 12.0 cm, depth = 50 cm, T = 1.7 s, ws = 0 m s 1.
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2.
3. 4. 5.
Mini ripples corresponded to when the sediment was first suspended and ripples of no more than 0.5 cm. Small ripples were defined as ripples with a height of 0.5 – 1 cm. Finally there were irregular vortex ripples [3D ripple pattern with ripples > 1 cm]. Regular vortex ripples.
When regular vortex ripples were achieved, the bed was thought to be in equilibrium. When the bed was under the influence of infiltration, grain motion was initially patchy as the infiltration appeared be stronger over certain areas of the bed. As the bed was not perfectly flat, perturbations in the bed profile gradually spread until the whole bed was in motion. Therefore, the subjective judgment of incipient motion was determined from the digital camera footage and was defined as the time when a significant number of the
grains under the instruments first started to roll. Infiltration affected the time taken for incipient motion of the sand to occur. With no infiltration (Fig. 2), the sediment moves immediately and the first suspension occurs after only 30 s. However, under the influence of maximum infiltration (Fig. 4), sand only began to move after 43 s and the first suspension occurred after 81 s. There was also a clear effect on the ripple steepness (g/k) after 10 min; with no infiltration, half infiltration and maximum infiltration, the corresponding ripple steepness values were 0.21, 0.181, and 0.17, respectively. For this wave condition, we see that the infiltration seems to reduce the ripple steepness, which results in the reduction in the suspended sediment. Similar results in terms of the effects of infiltration on incipient motion, suspended load and ripple steepness (Table 3) were obtained for wave heights between 12 and 18 cm (but digital video data were
Fig. 6. Time series of suspended sediment concentration starting from a flat bed, H = 12.0 cm, depth = 50 cm, T = 1.7 s, ws = 5.0 10 4 m s 1.
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only available for the two lowest wave heights, 12 and 13 cm). Figs. 5 and 6 show the suspension for 12.0cm waves, where Fig. 5 is the no infiltration condition and Fig. 6 is the maximum infiltration condition. The upper panels show that there is a difference in magnitude of the total suspended load of the order factor 2. With no infiltration (Fig. 5), the sediment began to move almost immediately while with full infiltration (Fig. 6), the sediment did not move until 90 s. Under the influence of infiltration, vortex ripples formed after 5 min of wave motion (approx. 120 waves), whereas with no infiltration, vortex ripples formed after only 2 min, and the ripple steepness was 0.158 compared to 0.212 when there was no infiltration. When the bedforms reached equilibrium (i.e. when regular vortex ripples were achieved after approximately 60 min), the time-averaged concentration over 5 min was calculated. The average total suspended load was calculated for each wave condition and infiltration velocity. In Fig. 7, which shows the total suspended load against the ordinary Shields number, all the infiltration points lie below the no infiltration points confirming that infiltration is tending to inhibit sediment suspension. In Fig. 8, plotting the same data
against the infiltration Shields number (Nielsen, 1997) brings the infiltration data and the no infiltration data closer. However, the correlation between the infiltra-
Fig. 7. Total suspended load against the ordinary Shields number. . No infiltration, n half infiltration ws = 3.59 10 4 m s 1, E maximum infiltration ws = 5.0 10 4 m s 1.
Fig. 9. Total suspended load against the Nielsen Shields number with ripple correction. . No infiltration, n half infiltration ws = 3.59 10 4 m s 1, E maximum infiltration ws = 5.0 10 4 m s 1.
Fig. 8. Total suspended load against the Nielsen Shields number. . No infiltration, n half infiltration ws = 3.59 10 4 m s 1, E maximum infiltration ws = 5.0 10 4 m s 1.
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Fig. 10. Change in total suspended load over 5-min intervals, with ripple formed with no infiltration (ws = 5 10 4 m s 1, H = 18.3 cm).
tion Shields number and total suspended load is still not significant at the 5% level. From the previous tables, we saw that infiltration had an important effect on the ripple steepness, and if the ripple correction factor (Nielsen, 1986) for flow contraction over ripple crests is used (Fig. 9), then a statistically significant correlation is obtained (R2 of 0.74, significant at 1%). To further test the effects of infiltration on suspension and reduce the influence of bedform differences, infiltration was turned off and on for alternating 5-min intervals while waves were kept running. An average suspended load was then calculated for each of the 5min bursts. Initially, this was done as short exercise at the end of each experimental run but this was extended as preliminary results looked interesting. This accounts for the difference in the number of data points for each experimental run. Figs. 10 –12 show
the changes in the total suspended load as infiltration is turned off and on over an equilibrium ripple field initially generated with different infiltration conditions. The wave height used was H = 18.3 cm and Fig. 10 shows the variations in suspended load over ripples initially generated with no infiltration, as the infiltration was switched between no infiltration and a maximum infiltration velocity of 5 10 4 m s 1; Fig. 11 is the same experiment but conducted over ripples initially generated with maximum infiltration. In both cases, the total suspended load is reduced by a factor of approximately 30% when infiltration is occurring. In Fig. 12, an intermediate infiltration velocity of 3.01 10 4 m s 1 was used (over a bed initially generated using intermediate infiltration; the variation in total load is initially the same but reduces to zero after 30– 40 min).
Fig. 11. Change in total suspended load over 5-min intervals, with ripple formed with maximum infiltration (ws = 5 10 4 m s 1, H = 18.3 cm).
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Fig. 12. Change in total suspended load over 5-min intervals, with ripple formed with half infiltration (ws = 3.01 10 4 m s 1, H = 18.3 cm).
The average total suspended load for each wave condition and each infiltration velocity was taken and then plotted against the ordinary Shields number and the infiltration Shields number (Figs. 13 and 14). In Fig. 13, all of the no infiltration points lie above the infiltration points, which indicates that even over a rippled bed, infiltration is inhibiting suspended sediment. Plotting the data against the infiltration Shields number brings the no infiltration and infiltration points onto one line. This shows that over an existing ripple bed, the infiltration Shields number accounts well for the opposing effects of infiltration over a
rippled bed. As these measurements were made over an existing equilibrium ripple bed, we would not expect the bedforms to have changed significantly from run to run. There may have been some subtle changes in the ripple shape over the 5-min periods, which may have influenced the suspended sediment concentration but we were unable to measure any such changes. We therefore believe that these results indicate the effect of infiltration on the bed shear stress and the effective weight of the sediment grains.
8. Discussion and conclusions These experiments indicate that infiltration has a number of significant effects. 1.
2.
3.
4.
Fig. 13. . No infiltration, n half infiltration ws=3.5910 4 m s 1, E maximum infiltration ws = 5.0 10 4 m s 1, error bar shows standard deviation of results.
It increased the time taken for the bedforms to evolve from an initially flat bed; this effect was more pronounced for the lower wave heights. This agrees with the experimental results of Baldock and Holmes (1998). After equilibrium has been reached, the ripple steepness was lower when the bed was under the influence of infiltration. The equilibrium ripple field generated with infiltration had a lower average suspended load than that generated with no infiltration. For the two lowest wave heights (H = 13.0 cm, 12.0 cm), when detailed measurements of bedforms were made, infiltration increased the time taken for the entire bed to be in motion and had an important effect on the bed morphology.
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Vertically integrated suspended load was correlated with Shields number (at the 1% significance level) when the Shields number was modified to take account of both the infiltration (Nielsen, 1997) and ripple steepness (Nielsen, 1986). The ripple steepness was found to be the most important factor relating to the reduction in the suspended loads. When infiltration was switched off and on for 5min intervals over an equilibrium bed, the suspended load was significantly reduced when infiltration was occurring. However, the effect of infiltration on the total suspended load decreased significantly with time (Figs. 10 – 12). This may have been due to a systematic increase in the size of the sand; it was noted that towards the end of the experiment, the sand bed had changed colour due to the coarser component of the sand preferentially remaining, while the finer sand grains had been transported out of the sandbox and deposited on base of the flume on either side of the sandbox. Martin (1970) found that the size of the sand grains had an important effect on the incipient motion of the particles. In particular, he found that infiltration into the bed hindered the initial motion of smaller sand grains while enhancing that of larger sizes. We do not believe that ripple changes influenced this result as our measurements were made over an existing equilibrium ripple bed as the ripple dimensions did not change significantly over 5-min periods. This conclusion is supported by the strong correlation obtained between the total suspended load and the infiltration Shields number (Fig. 14) which, unlike the results shown in Figs. 7 – 9, does not require the inclusion of the ripple steepness. The general effect of infiltration in these tests was to provide an unambiguous stabilising effect on the sand bed for this grain size (D50 = 255 Am), indicating that the additional downward force of the infiltration flow on the grains dominates over the thinning of the boundary layer (and the consequential enhanced stress). However, there are indications from these experiments that this effect may decrease for sand with larger grain sizes. We also conclude that it is necessary to include both the effects of infiltration and ripple steepness if the suspended load is to be successfully predicted from the Shields number. However, it is important to note that in areas where ripples are present (i.e. the surf zone), infiltration rates are likely to be much smaller than those imposed during our
Fig. 14. . No infiltration, n half infiltration ws = 3.59 10 4 m s 1, E maximum infiltration ws = 5.0 10 4 m s 1, error bar shows standard deviation of results.
experiments. We would therefore expect the effect of infiltration on ripple development to be minor. References Baldock, T.E., Holmes, P., 1998. Infiltration effects on sediment transport by waves and currents. Proceedings of the 26th International Conference Coastal Engineering, Orlando. ASCE, USA, pp. 3601 – 3614. Conley, D.C., 1993. Ventilated oscillatory boundary layers. PhD Thesis, University of California, San Diego, 74 pp. Grant, U.S., 1948. Influence of the water table on beach aggradation and degradation. Journal of Marine Research, 660 – 665. Harrison, S.S., 1968. The effect of groundwater infiltration on a stream regimen — a laboratory study. PhD dissertation, University of North Dakota. Horn, D.P., Baldock, T.E., Bard, A.J., Mason, T.E., 1994. Field measurements of swash induced pressures within a sandy beach. Proceedings of the 26th International Conference Coastal Engineering, Copenhagen. ASCE, USA, pp. 2812 – 2825. Kang, H.Y., Nielsen, P., Hanslow, D.J., 1994. Watertable overheight due to wave runup on a sandy beach. Proceedings of the 24th International Conference Coastal Engineering, Kobe, ASCE, USA, pp. 2115 – 2124. Madsen, O.S., 1978. Wave induced pressures and effective stresses in a porous bed. Geotechnique, 377 – 393. Martin, C.S., 1970. Effect of a porous bed on incipient sediment motion. Water Resources Research, 1162 – 1174.
C. Obhrai et al. / Coastal Engineering 45 (2002) 111–123 Martin, C.S., Aral, M.M., 1970. Seepage force on interfacial bed particles. Journal of Hydraulic Division 7, 1081 – 1100. Nielsen, P., 1986. Suspended sediment concentration under waves. Coastal Engineering, 23 – 31. Nielsen, P., 1997. Coastal groundwater dynamics. Proceedings of Coastal Dynamics, American Society of Civil Engineers, USA, pp. 546 – 555. Nielsen, P., Robert, S., Moller-Christensen, B., Olivia, P., 2001. Infiltration effects and sediment mobility under waves. Coastal Engineering 42 (2), 105 – 114. Oh, T., Dean, R.G., 1994. Effects of controlled water table on beach profile dynamics. Proceedings of the 24th International Conference Coastal Engineering, Kobe, ASCE, USA, pp. 935 – 949.
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Oldenziel, D.M., Brink, W.E., 1974. Influence of suction and blowing on the entrainment of sand particles. Journal of Hydraulics Division. Proceeding of the American Society of Civil Engineers, USA, 935 – 949. Putnam, J.A., 1949. Loss of wave energy due to percolation in a permeable sea bottom. Transaction of the American Geophysical Union, 349 – 356. Sleath, J.F.A., 1984. Sea Bed Mechanics. Wiley, New York, 335 pp. Turner, I.L., Nielsen, P., 1997. Rapid water table fluctuations within the beach face: implications for swash zone sediment mobility. Coastal Engineering, 45 – 59.