The influence of swash infiltration exfiltration on beach face sediment transport: onshore or offshore?

Transcription

1 Ž. Coastal Engineering elseier.comrlocatercoastaleng The influence of sash infiltration exfiltration on beach face sediment transport: onshore or offshore? Tony Butt a,), Paul Russell a, Ian Turner b a Institute of Marine Studies, Plymouth EnÕironmental Research Centre, UniÕersity of Plymouth, Drake Circus, Plymouth PL4 8AA, UK b Water Research Laboratory, School of CiÕil and EnÕironmental Engineering, UniÕersity of Ne South Wales, King Street, Manly Vale, Sydney, NSW, 2093, Australia Receied 30 June 1999; receied in reised form 28 April 2000; accepted 3 May 2000 Abstract Measurements ere obtained from the sash-zone of a high-energy macrotidal dissipatie beach of pore-pressure at four leels belo the bed, and cross-shore elocity at a single height aboe the bed. Time-series from relatiely high ŽHsf2.0 m. energy conditions ere chosen for analysis from the mid-sash-zone at high tide. Calculation of upards-directed pore-pressure gradients shos that, in this case, fluidisation of the upper layer of sediment, leading to enhanced backash transport, is unlikely. An apparent conflict exists in the literature regarding the net effect of infiltration exfiltration on the sediment transport, through the combined effects of stabilisation destabilisation and boundary layer modification. This is examined for the data collected using a modified Shields parameter. Inferred instantaneous transport rates integrated oer a single sash cycle sho a decrease in uprush transport of 10.5% and an increase in backash transport of 4.5%. Sensitiity tests suggest that there is a critical grain size at hich the influence of infiltration exfiltration changes from offshore to onshore. The exact alue of this grain size is highly sensitie to the method used to estimate the friction factor. q 2001 Elseier Science B.V. All rights resered. Keyords: Backash; Infiltration; Pore-pressure; Sediment; Sash; Uprush 1. Introduction One of the factors hich may need to be taken into consideration for sediment transport in the sash-zone is the ertical flo of ater into and out of the bed, and its effect on sediment mobility. In the past, the effect of infiltration on sediment transport in the sash-zone has been assumed to be ) Corresponding author. address: tbutt@plymouth.ac.uk Ž T. Butt.. mainly connected ith the percolation of ater into the beach face, and hence the reduction of olume on the backash Že.g. Grant, 1946, 1948; Emery and Gale, 1951; Duncan, 1964; Waddell, Hoeer, on fine to medium sand beaches, this mechanism is likely to be relatiely unimportant compared ith coarse sand or shingle. It has more recently been hypothesised that fluidisation of the upper layer of sediment may occur due to rapid outflo of ater from the beach face caused by sub-surface pressure forces acting ertically up r01r$ - see front matter q 2001 Elseier Science B.V. All rights resered. Ž. PII: S

2 36 ( ) T. Butt et al.rcoastal Engineering ards on the backash ŽQuick, 1991; Baird et al., 1996; Horn et al., On the uprush, the ater pressure ill propagate rapidly into the upper layers of the sediment; then on flo reersal to backash and subsequent reduction in sash depth, there ill be a rapid decrease of pore-pressure, producing forces acting ertically upards just belo the surface. This may lead to rapid groundater outflo and hence fluidisation. If the upper layers of sediment become fluidised, then this might considerably increase the sediment transport since the fluidised layer ould quickly become entrained by the seaard flo in the backash. This hypothesis as tested using a model by Baird et al. Ž 1996., ho concluded that fluidisation may occur, especially in the latter stages of the backash. Een if the upards-directed pressure gradients are too small to produce fluidisation, they may still increase sediment transport on the backash by re- ducing the effectie eight of the sediment Ži.e. destabilise the bed.. Conersely, donards-directed pressure gradients on the uprush ill increase the effectie eight of sediment Ži.e. bed stabilisation., thereby decreasing the potential for sediment transport Ž Hughes et al., 1998; Nielsen, Therefore, the net effect of the stabilisation destabilisation process ould be to bias the transport in the offshore direction. Another mechanism hich may hae the opposite effect is the altering of the thickness of the boundary layer due to ertical flo into and out of the beach face. This as inestigated in the laboratory by Conley and Inman Ž 1994., albeit outside the breakpoint. They confirmed that the thickness of the boundary layer is reduced by infiltration and increased by exfiltration, therefore making the near-bed elocity relatiely greater during infiltration. The turbulent ortices during infiltration are maintained Ž. Ž. Fig. 1. Schematic representation of sediment stabilisation top panel and boundary layer thinning bottom panel due to infiltration on the uprush.

3 ( ) T. Butt et al.rcoastal Engineering closer to the bed, thereby increasing the potential for sediment transport. During exfiltration, the turbulent ortices are eleated further from the bed, effectiely thickening the boundary layer and decreasing the potential for sediment transport. In the sash-zone, this process ould tend to enhance uprush transport and decrease backash transport, i.e. bias the net transport onshore. Schematic illustrations of the to processes aboe are shon in Figs. 1 and 2. The balance beteen the to processes of bed stabilisation destabilisation and boundary layer modification has been quantified by Nielsen Ž and Turner and Masselink Ž Žhereafter referred to as TM98., by defining a modified Shields parameter. On the uprush, the numerator increases ith decreasing Ž upards through-bed flo elocity., to account for the increased shear stress due to boundary layer thinning, and the denominator also increases ith decreasing, to account for the stabilisation brought about by infiltration. On the backash, both the numerator and denominator decrease ith increasing to account for boundary layer thickening and destabilisation from exfiltration. Nielsen Ž hypothesised that quartz sands ith a median grain size Ž d. 50 of about 0.58 mm are likely to be stabilised by infiltration Ži.e. decreased transport on the uprush., hereas ith larger grain sizes, the boundary layer effects may start to become dominant, effectiely increasing uprush transport. The numerator of TM98, unlike Nielsen s, did not assume a linear relation beteen shear stress and infiltration elocity. They tested the modified Shields parameter using pore-pressure data from a beach ith d50 s 0.5 mm. Cross-shore elocities ere obtained using a model. It as found that the effect of boundary layer modification appeared to dominate, ith increased uprush transport and reduced backash transport. The purpose of this paper is to examine subsurface pore-pressures and cross-shore elocities col- Ž. Ž. Fig. 2. Schematic representation of sediment destabilisation top panel and boundary layer thickening bottom panel due to exfiltration on the backash.

4 38 ( ) T. Butt et al.rcoastal Engineering lected from the sash-zone of a natural beach, as a step toards improing the understanding of ho infiltration exfiltration influences the sediment transport in the sash-zone. The question of hether fluidisation is likely to be an important factor is still unclear. Therefore, a useful step is to inestigate, using pore-pressure gradients, hether fluidisation as likely during the present study. The apparently conflicting results of TM98 and Nielsen Ž suggest that more study is required of the relatie effects of the to processes hich combine to cause a net onshore or offshore transport influence. The modified Shields parameter, together ith the measured elocities, is used to assess hich process as dominant during the present study. A representatie sash eent, obtained from ensembles of seen sash eents from the data, is examined in detail. Finally, some sensitiity tests are performed hich attempt to identify the most important factors in determining hich process ill dominate under arious different conditions. The equations deried contain some parameters Ž e.g. friction factor. hich are difficult to estimate, and tests are done to assess the relatie sensitiity of the results to changes in these parameters. 2. Field experiment The data used in the present study ere obtained from a field experiment performed at Perranporth Beach, UK during March 1998 ŽButt and Russell, The field site is shon in Fig. 3. Perranporth is a macrotidal dissipatie beach ith a mean tidal range of 5.25 m. Significant ae height and period Ž H and T. s s during the experiment ere 2.0 m and 8 s, respectiely. The conditions ere infragraitydominated, ith a broad-banded incident ae-field hich contained a mixture of sell and ind-aes. The aerage beach slope Ž b. 20 m either side of the instrument rig position as Ži.e. tan b s The beach as linear and there as an absence of along-shore ariations in topography. Sediment samples taken from the study site indicated the median grain size Ž d. 50 to be 0.24 mm. The measurements presented here are of crossshore elocity ithin the sash zone and sub-surface pore-pressure. Velocity as measured using a miniature electromagnetic current meter ith a 2-cm diameter discus head, manufactured by Valeport, UK. The instrument as mounted nominally at 5 cm aboe the bed. The minimum sensing olume of the discus-type head is recommended by the manufacturers as being a cylinder of the same diameter as the sensor, projecting from its face by half its diameter. In other ords, the sensing face of the 2 cm head must be placed at least 1 cm from any solid object Ž in this case, the sea bed.. Preious trials reealed that the approximate accuracy of these current meters is about "8% Ž Butt, Pore-pressure as measured at distances of 2, 5, 9 and 13 cm belo the bed. The miniature pressure transducers ere Druck PDCR830. These instruments had also been used for preious measurements of pore-pressure in the sash-zone ŽBaird et al., Published accuracy of the pressure transducers Žcombined non-linearity, hysteresis and repeatability. is "0.1%. The transducers ere coered in a Terram geotextile shroud to preent the impingement of sand grains that could alter the output. Great care had to be taken to ensure the transducers ere ertically aligned to aoid any horizontal pressure gradients from being mistaken for ertical gradients. The data analysed are from a 17-min time series, recorded on 26 March Because of the considerable tidal range at this site, to obtain maximum stationarity in the data, and to minimise any direct effects of cross-shore tidal elocities, the time-series ere recorded oer high-tide slack ater. The instruments ere located in the mid sashzone Žapproximately half ay beteen the run-up limit and the run-don limit., and so ere periodically submerged. The data ere sampled at 18 Hz, then block aeraged at 2 Hz. Note that the pressure measurements presented are in hpa, here 1 hpa is hydrostatically equialent to 1 cm head of ater. 3. Pore-pressure gradients and potential fluidisation The hypothesis that fluidisation of the upper layers of the bed might be a significant contributing factor for sediment transport on the backash Že.g.

5 ( ) T. Butt et al.rcoastal Engineering Fig. 3. Location of Perranporth. Baird et al., may be inestigated using the data collected in the present study. Folloing TM98 Ž their Eqs. 12 to 17., it may be shon that the condition for fluidisation is gien by: Ž sy1. G Ž 1. K a here is the ertical fluid elocity in the bed Ž positie upards., K is the hydraulic conductiity y1 m s x, s s rsrr is the specific graity of the sediment, here r and rs are the fluid and sediment densities, respectiely, and a is the ratio beteen the seepage force acting in the surficial layers of sedi- ment and that acting ithin the bed Ž Martin, Using a series of slope instability tests, Martin and Aral Ž experimentally determined that the seepage force in the top layer of sediment particles is approximately half that ithin the bed. Hence, a f 0.5. Therefore, the condition for fluidisation is gien by: G2Ž sy1.. Ž 2. K If the ater density is taken as 1025 kg m y3 and the y3 sediment density as 2650 kg m Ž for quartz., then fluidisation ill occur if rk exceeds about 3.2.

6 40 ( ) T. Butt et al.rcoastal Engineering To obtain alues for rk in the present study, the assumption is made that the flo is Darcian, therefore: Eh sy Ž 3. K Ez here h is the hydraulic head in cm Ž 1 cm'1 hpa., and z is the ertical distance beteen sensors. Fig. 4 shos time-series of Ž. a cross-shore elocity, Ž. b pore-pressure difference beteen the top and bottom sensors minus the hydrostatic pressure, Ž. c rk calculated from Eq. Ž. 3 aboe, and Ž. d porepressure at 2, 5, 9 and 13 cm belo the bed. Note that, for all subsequent analysis in the paper, the pore-pressure gradient beteen the top and bottom sensors is used. Sensors used in Turner and Fig. 4. Representatie time-series of cross-shore elocity, pressure difference beteen top and bottom sensors, rk, and sub-surface pore-pressures. The loest pore-pressure trace corresponds to the transducer nearest the bed. Pressures are gauge, i.e. zero corresponds to atmospheric. 1 hpa'1 cm head of ater.

7 ( ) T. Butt et al.rcoastal Engineering Ž. Nielsen 1997 and TM98 ere placed approximately 1 and 16 cm belo the surface. Therefore, the top and bottom sensors ere selected for the present study to allo comparison ith the results of the preious to studies. In Fig. 4, large, short duration, donards-directed pore pressure gradients can be seen on the uprush, and longer duration upards pressure gradients on the backash. These pore-pressure gradients ithin the bed coincide ith the ariation in sash depth, hich is the driing force for through-bed ertical flo. The alues of rk only reach about 0.2, so fluidisation is unlikely in this case. 4. Reised Shields parameters The Shields parameter, u Ž Shields, 1936., expresses the ratio beteen the disturbing and stabilising forces on sediment at the bed: t us Ž 4. r gdž sy1. here t is the bed shear stress, r is the fluid density, d is the median grain size, and ssrsrr is the specific graity of the sediment, here rs is the sediment density. For the purposes of the present study, the denominator may be simplified to W, the immersed sediment eight per unit area. Hence, using the suffix 0 for the specific case of no through-bed flo: t 0 u s. Ž 5. 0 W 0 To quantify the effects of infiltration exfiltration, modifications to the numerator and denominator of this equation hae recently been made by Nielsen Ž and TM98, i.e.: t u s Ž 6. W here the suffix means that this parameter contains extra terms to account for through-bed flo. The to opposing effects of infiltration exfiltration may be quantified using Eq. Ž. 6. For example, on the uprush, hen there is infiltration, the numerator ill increase due to the thinning of the boundary layer but the denominator ill also increase due to the extra stabilisation imparted on the sediment grains. On the backash, hen there is exfiltration, the numerator decreases due to the thickening of the boundary layer but denominator ill also decrease due to destabilisation. Therefore, the Shields parameter ill hae a net increase or decrease according to the balance beteen the to opposing processes. A simple and ell-proen model for sediment transport Ž e.g. Meyer-Peter and Muller, is one in hich the dimensionless sediment transport rate is proportional to u 3r2, i.e. QAu 3r2, here Q is the dimensionless transport. This reduces to a elocitycubed dependence analogous to the energetics approach Ž Bailard, 1981., and as applied in the surfzone by Russell and Huntley Ž Hence: 3r2 t W / Q s Ž 7. ž and 3r2 t 0 W 0 / Q s Ž 8. 0 ž The difference beteen Eqs. Ž. 7 and Ž. 8 ill isolate that part of the dimensionless sediment transport due to infiltration exfiltration, and therefore gie a simple indication of hether infiltration exfiltration effects are biasing the sediment transport one ay or another: QInfiltsQ yq0 Ž 9. i.e.: 3r2 3r2 0 / ž / 0 u t t QInfilts ž y. Ž 10. < u< W W The right-hand-side of Eq. Ž 10. is multiplied by ur< u< to presere the net direction of potential sediment transport. For example, if the total transport Ž including that due to infiltration exfiltration. is greater than the transport ithout infiltration exfiltration, the effect of Qinfilt ill be to increase the sediment transport in the direction of the flo. If this happens during the uprush, then the dominant process ill be boundary layer thinning, but if it hap-

8 42 ( ) T. Butt et al.rcoastal Engineering Table 1 Various solutions of Eq. Ž 10. ur< u< Flo direction Balance of terms Qinfilt Dominant process inside bracket q1 onshore term1) term2 qe Ž onshore. boundary layer thinning q1 onshore term1- term2 ye Ž offshore. stabilisation y1 offshore term1) term2 ye Ž offshore. destabilisation y1 offshore term1- term2 qe Ž onshore. boundary layer thickening pens during the backash, then the dominant process ill be destabilisation. The four basic scenarios are illustrated in Table Deriations of the modified Shields parameter The immersed sediment eight per unit olume of the bed Ž W. may be adjusted for infiltration exfiltration by simply adding the eight loss or gain caused by seepage to the denominator of Eq. Ž. 4 Žnote that the ertical elocity Ž. is positie upards.: W sr gdž sy1. y0.5rgd K i.e.: W sr gd sy1y0.5. Ž 11. K ž / To modify the numerator, Nielsen Ž hypothesised a linear relation beteen shear stress Ž t. and the relatie ertical elocity Ž ru.. Based on this assumption, the folloing may be defined: y1r2 0ž / t st 1ya f Ž 12. u here f is a friction factor and a is an empirical constant. TM98 hae deried an alternatie form for the modified numerator, hich as based on the ork by Mickley et al. Ž 1954., and Conley and Inman Ž The numerator, unlike Nielsen s, does not assume a linear relation beteen shear stress and infiltration elocity. The modified shear stress may be defined as follos: ž / F tst 0 Ž 13 F. e y1 here: c Fs Ž 14. f < u< here c is an empirical constant, hich is about 2.0 for quasi-steady flo Ž Mickley et al., 1954., and f is the friction factor. Using the quadratic stress la, i.e.: ts0.125r fu 2 Ž 15. and Eqs. Ž 10. Ž 14., an expression for the relatie sediment transport due to the effects of infiltration exfiltration Ž Q. is gien by: Q su 3 Infilt or: Q su 3 Infilt ž infilt f ž 1ya f y1r2 / 0 u 8 gdž sy1y0.5rk. ž / 3r2 3r2 f 3 yu Ž gdž sy1. ffrž e F y1. 3r2 8 gdž sy1y0.5rk./ ž / 3r2 f 3 yu. Ž gdž sy1.

9 ( ) T. Butt et al.rcoastal Engineering Note that it is unnecessary to multiply the right hand side by ur< u< to presere the direction of transport. This is clarified by taking u 3 outside the brackets. 6. Quantification of transport modification from infiltration exfiltration Before Eq. Ž 16. or Ž 17. can be applied, the alues of arious parameters must be determined. For quartz sand in ater, s f 2.6. With a knoledge of the hydraulic conductiity Ž K., a alue for may be obtained from Eq. Ž. 3. To obtain a alue for K, the empirical formulation of Bear Ž is used, i.e.: ž / ž / r g n 3 d 2 Ks Ž m Ž ny y3 y2 here r is ater density, mf10 N s m ŽWil- liams and Elder, is the dynamic iscosity, nf0.45 is the porosity Ž Dyer, and dsd 50 the median grain size. For the grain size of 0.24 mm in the present study, K is estimated to be of the order of m s y1. The friction factor Ž f. is estimated using a formula for steady flo, since it is preferred to treat the flo in the sash-zone as quasi-steady, and the use of a formula for orbital flo Že.g. Sart, 1974; Wilson, 1989., is considered inappropriate Žc.f. TM98; see also belo.. The friction factor is often estimated by combining arious basic equations relating to the boundary layer Ž e.g. Hughes, The on Karmen Prantl equation Ž la of the all. gies the elocity profile in the boundary layer: u k ž z / ) 0 už z. 1 z s ln Ž 19. here uz Ž. is the elocity at height z aboe the bed; u) is the friction elocity here u 2 ) strr; kf0.4 is the on Karman constant, and z0 is the roughness length of the bed. If the depth-aeraged elocity is assumed to occur here zshref0.37h, and the roughness length is approximately kr30 here h is the ater depth and k is the Nikuradse effectie bed Ž. Ž. roughness an Rijn, 1993, then Eq. 19 may be ritten as: u u ) ž / h s2.5ln 11. Ž 20. k Ž. Ž. Combining Eq. 15 ith Eq. 20 : ž ž // y2 h fs1.28 ln 11. Ž 21. k To obtain a alue for k, it ill be assumed that the bed is approximately flat, and any bedforms are negligible. Van Rijn Ž reasoned that the grain roughness Ž k. presented to the flo is related to the grain size, and proposed: kf6d 50. Ž 22. Therefore, for a particular grain size, the friction factor becomes a function of the ater depth, i.e. it is time-dependent. Eq. Ž 16. contains the empirical constant a for hich a suitable alue is presently unknon ŽP. Nielsen, pers. comm, The sensitiity of the equation to this parameter is quite lo Žthe alue of a as arbitrarily aried oer three orders of magnitude and the aerage and maximum alues of Q infilt ere only found to ary by 1.14% and 3.1%, respectiely.. Hoeer, it is still preferred to use Eq. Ž 17., hose numerator is also able to take into account the possible non-linear relation beteen shear stress and elocity Ž Conley and Inman, Fig. 5 shos a representatie section of the timeseries of Q calculated from Eq. Ž 17. infilt. Also shon for comparison are the cross-shore elocity Ž u.,up- ards elocity Ž., and the no through-bed flo equialent transport Ž Q. 0. Both on the uprush and backash, the effects of infiltration exfiltration appear to be biasing the potential sediment transport toards the offshore. This means that, on the uprush, the stabilising effect is dominating oer boundary layer thinning, and on the backash, destabilising is dominating oer boundary layer thickening. This finding appears to contradict the results of TM98, hich shoed the opposite trend that modified boundary layer effects ere dominant for the simulated sash cycle.

10 44 ( ) T. Butt et al.rcoastal Engineering Fig. 5. Representatie time series of cross-shore elocity, ertical elocity Ž positie upards., dimensionless sediment transport ithout infiltration exfiltration Ž Q. and dimensionless transport solely due to infiltration exfiltration effects Ž Q. calculated from Eq. Ž infilt A time-series of cross-shore elocity and subsurface pore-pressure for a single infragraity sash cycle Ž Tf40 s. ere obtained by taking an ensemble of seen sash eents from the entire timeseries. Since each eent as not of the same duration, the time scale had to be normalised to the eent duration. To illustrate the effects of infiltration exfiltration oer a single sash cycle, Eq. Ž 17. as then computed using the ensembled sash eents. A comparison of Q0 and Q computed from the separate terms in Eq. Ž 17., together ith Q are shon infilt oer the ensembled sash cycle Ž see Fig. 6.. Here, decrease in transport on the uprush and the Ž smaller. increase in transport on the backash can clearly be seen. A useful exercise is to obtain the total amount of sediment transported oer the uprush and backash by integrating under the cures in Fig. 6, and then calculating the difference due to infiltration exfiltration. This proides useful insight to the net effect of infiltration exfiltration integrated oer the entire sash cycle.

11 ( ) T. Butt et al.rcoastal Engineering Fig. 6. Comparison of transport ith Ž Q. and ithout Ž Q. 0 infiltration exfiltration oer a single sash cycle, taken from the ensembles of indiidual sash cycles in the time-series. Top panel Ž Q. is the transport solely due to the effects of infiltration exfiltration. infilt The total sediment transported ithout taking infiltration exfiltration into account Ž S. 0 is gien by: For the uprush: H ts0.5 S Ž uprush. s Ž Q. d t Ž ts0 and for the backash: H ts1 S Ž backash. s Ž Q. d t. Ž ts0.5 Taking infiltration exfiltration into account, the total sediment transported Ž S. is gien by: For the uprush: H ts0.5 S Ž uprush. s Ž Q. d t Ž 25. ts0 and for the backash: H ts1 S Ž backash. s Ž Q. d t. Ž 26. ts0.5 Since both the instantaneous transport and time are dimensionless, then S and S hae no physical 0 units, and are used for comparison only. The most useful parameter here is the ratio beteen S and S0 for the uprush, and the same ratio for the backash. This gies an indication of the bulk effect of infiltration exfiltration oer the uprush and oer the backash. From the ensembled sash cycles Ž see Fig. 6., simple finite difference integration gies S rs Ž 0 up- rush. s and S rs Ž backash. 0 s This means that, from the data collected in the present study, infiltration exfiltration is likely to decrease the total amount of sediment moed upslope on the uprush by about 10.5%, and increase the total amount of sediment moed donslope on the backash by about 4.5%. 7. Sensitiity tests The study of TM98 concluded that there as a dominance of boundary layer modification oer sta-

12 46 ( ) T. Butt et al.rcoastal Engineering bilisation destabilisation. As a result, they asserted that the role of infiltration exfiltration in the sashzone is generally to enhance uprush transport. This appears to conflict ith the results of the present study. Potentially important differences in theoretical approach and experimental conditions beteen the to studies are the folloing. In the present study, the cross-shore elocity as measured at the field site. TM98 only measured sub-surface pore pressures: the cross-shore elocity as predicted using a model. The median grain size Ž d. 50 at Perranporth as 0.24 mm, hereas at Duck, USA Ž TM98., it as 0.5 mm. TM98 used a friction factor calculation after Wilson Ž 1989., hich as originally designed for oscillatory flo. Hoeer, they acknoledge that the flos in the sash-zone are quasi-unidirectional since the constant Ž c. in the non-linear relation beteen t and ru is assumed to be 2.0 rather than 0.9 for oscillatory flo. In the present study, the friction factor as calculated from a formula for steady flo, and aried ith ater depth. The friction factor in TM98 as assumed to remain constant at It ould therefore seem appropriate to examine the sensitiity of the calculations made in the present study, to arious parameters. In other ords, if certain parameters ere alloed to ary, could the balance of transport due to infiltration exfiltration be made to change from offshore to onshore? An interesting exercise is to examine the dependency of grain size on the balance beteen the to processes. Nielsen Ž suggested that boundary layer effects are only likely to dominate at grain sizes aboe about d50 s0.58 mm. To assess the effect of grain size, the aerage alue of Q oer the hole time-series, ² Q : infilt infilt, as calculated from Eq. Ž 17., hich as then repeated hile arying the grain size from 0.1 to 1.0 mm. Results are shon in Fig. 7. Where the cure crosses zero is the point here the balance goes from offshore to onshore. Fig. 7 shos that the direction of ² Q : infilt be- comes more onshore ith increasing grain size. This is in general accordance ith nature, here coarser sediments are associated ith beaches exhibiting steeper beachface gradients. The grain size at hich the balance changes Žthe crossoer point, denoted here as d. Q0 is at about 0.55 mm, ith a dominance of stabilisation destabilisation belo this alue and a dominance of boundary layer effects aboe it. It can also be seen that around this area dq0 is highly sensitie to errors or ariations in the method of calculating Q infilt. The other noteorthy point from Fig. 7 is that, belo about ds0.25 mm, the offshore influence of infiltration exfiltration increases much more sharply ith decreasing grain size, indi- Fig. 7. Grain size dependency of the transport due to infiltration Ž Q., computed from Eq. Ž 17. infilt and aeraged oer the time-series. dq0 is the point here ² Q : goes from offshore to onshore. infilt

13 ( ) T. Butt et al.rcoastal Engineering cating that the dominance of stabilisation destabilisation is much more pronounced at smaller grain sizes. The other to parameters, hich may be important, and hich are not so straightforard to assess, are the friction factor Ž f. and the constant c in Eq. Ž 14.. The estimation of a friction factor is alays a difficult task, especially for flos in the sash-zone hich could be considered either quasi-steady or oscillatory, and in hich the depth aries considerably. Some methods demand iteratie techniques, and estimates can ary oer an order of magnitude. In TM98, f as kept constant at 0.01, after using a formula for oscillatory flo folloing Masselink and Hughes Ž In the present study, it is considered more appropriate to use a formula for unidirectional flo, and the friction factor is not fixed but aries ith ater depth. The constant c relates to the non-linear relation beteen shear stress and infiltration ŽConley and Inman Its alue seems to be dependent on hether or not the flo is considered oscillatory. In the present study, the uprush and backash are considered as to separate quasi-steady flos, and in considering the alue of c, TM98 hae also assumed the flo to be quasi-steady. Hoeer, along ith Masselink and Hughes Ž 1998., they hae assumed the flo to be oscillatory hen choosing a formula for f. It is therefore interesting to see ho the balance beteen onshore and offshore transport might change if either f or c are aried. This as accomplished by calculating a family of cures of ² Q : infilt s. d50 Ž similar to the one in Fig. 7. for a range of friction factors, and then calculating a further number of families of cures hile alloing c to ary. The result is a four-dimensional array hich is difficult to isualise. Therefore, it as decided to extract the alue of d from each ² Q : Q0 infilt s. d50 cure, and plot this as a contour-plot in f c space. This then gies an idea of ho ariation of f and c affects the grain size at hich the balance changes from offshore to onshore. Results are shon in Fig. 8. Each contour line has a unique ² Q : infilt s. d50 cure associated ith it, ith its on dq0 alue. Note that for the purpose of this sensitiity test, the friction factor is forced to arious different alues, although in the present study f is dependent upon the depth, hich changes ith time. It is instructie to focus on the region of Fig. 8 in the area around dq0 s 0.24 mm, i.e. d50 for the Ž. Fig. 8. Contours of the critical changeoer alue of grain size d for different alues of friction factor and the constant c. Q0

14 48 ( ) T. Butt et al.rcoastal Engineering present study. If different methods ere used in estimating f andror c, resulting in a point in f c space to the left-hand-side of the 0.24-mm contour Ž i.e. d -d. Q0 50, then the balance ould change to onshore, indicating a dominance of boundary layer effects oer stabilisation destabilisation. It can also be seen that, around this region, the calculations are much more sensitie to f than c. For the same alues of f, using c s 0.9 Žoscillatory flo. or c s 2.0 Ž steady flo. appears to make little difference. On the other hand, small changes in f may tip the balance one ay or the other. If f had been assumed fixed in the present study, and the method of estimation had resulted in a alue belo about 0.006, then the balance probably ould hae been onshore. Therefore, careful consideration of the method of calculating the friction factor is important if correct assessment of the direction of influence of infiltration exfiltration on the sediment transport is to be achieed. Perhaps the most important aspect to consider is the changing relatie magnitudes of the to processes of effectie sediment eight and boundary layer modification as a function of beachface grain size. To examine this, to dimensionless parameters may be defined Ž c.f. TM98.: t R is the shear stress ith infiltration exfiltration relatie to ithout infiltration exfiltration; W is the effectie eight ith R infiltration exfiltration relatie to ithout infiltra- Ž. tion exfiltration. From Eq. 13 : t F t R s s Ž 27 F. t e y1 0 Ž. Ž. and from Eqs. 4 and 11 : W WR s W i.e.: 0 sy1y0.5rk s sy1 W WR s s1y0.5. Ž 28. W KŽ sy1. 0 By calculating t R and WR for a range of different grain sizes, hile keeping all the other parameters constant, an idea may be obtained of hether, hen the grain size is changed, either the shear stress changes more than the effectie eight or ice-ersa. To ealuate Eqs. Ž 27. and Ž 28. oer a range of grain sizes, alues of < u< and of 0.1 and m y1 s Ž Turner and Nielsen, hae been used. Note that, in this case, since has been chosen as positie upards Ž exfiltration., then through-bed flo ill result in a simultaneous reduction of both shear stress and effectie eight. Fig. 9 shos a plot of WR and t R against d 50. It can be seen that, at small Fig. 9. Sensitiity to grain size of relatie shear stress Ž t. and relatie effectie eight Ž W.. R R

15 ( ) T. Butt et al.rcoastal Engineering Table 2 Comparison of relatie eight Ž W. and relatie shear stress Ž t. R R dependence on grain size, at different ranges of grain sizes d Ž mm. W slope t slope Ratio R 0.1- d d grain sizes, WR decreases rapidly ith decreasing grain size, hereas the slope of t R remains fairly constant ith grain size. This suggests that stabilisation destabilisation has the greater influence on the characteristics of the ² Q : s. d plot Ž Fig. 7. infilt 50. To summarise the difference in sensitiity of the to processes to changes in grain size, the cures in Fig. 9 ere split into to sections Ž0.1 mm-d mm and 0.3 mm- d mm. 50 and each section as linearly regressed. The ratio of the slopes of the regression lines ere then found for each section of the cures Ž see Table 2.. Aboe d50 s0.3 mm, effectie eight has about 50% more sensitiity than shear stress to changes in grain size, and belo d50 s 0.3 mm, effectie eight is 15 times more sensitie than shear stress to changes in grain size. That is to say, if the grain size changes, then this ill affect the stabilisation destabilisation of the sediment more than it ill affect the boundary layer modification. In summary, if to different beaches are considered, then the difference in grain size ill change the ay infiltration exfiltration biases the sediment transport, primarily through the effectie eight of the sediment. The grain size does not need to be ery different for infiltration exfiltration to bias the sediment transport onshore on one beach, but offshore on another. Inspection of Fig. 8 reeals that if a fixed friction factor of 0.01 as used as in TM98, then the critical changeoer point Ž d. Q0 ould be 0.45 mm. The grain size in TM98 as larger than this, confirming their findings of onshore transport dominance. The grain size in the present study as smaller than d, suggesting offshore dominance. Q0 8. Discussion The principle finding from the present study is that there appears to be some critical grain size R belo hich effectie eight effects dominate, causing infiltration exfiltration to bias the transport offshore, and aboe hich modified boundary layer effects dominate, causing infiltration exfiltration to bias the transport onshore. The apparent conflict beteen the present study and that of TM98 is therefore explained by the fact that TM98 as undertaken on a significantly coarser beach. Obtaining a alue for the critical changeoer point Ž d. Q0 is not straightforard, and it is sensitie to the method used hen estimating arious empirical constants, especially the friction factor. The alue of dq0 appears to lie somehere beteen 0.45 mm Ž using the methods of TM98. and 0.58 mm Žsug- gested by Nielsen, Other differences in approach may also be important, such as modelled Ž TM98. s. measured Ž present study. elocities, and linear Ž Nielsen, s. non-linear Žpresent study and TM98. elocity stress relationships. It is clear that if further studies are to be conducted to obtain a alue for the critical changeoer point, then methods must be standardised. Different experimental approaches and methods of estimating the arious constants can make the results appear contradictory. The friction factor seems to be particularly important, and also one of the most difficult parameters to estimate. A comprehensie analysis of friction factors for the uprush as performed by Hughes Ž 1995., and it as suggested that the flo should be considered sheet flo Ž Wilson, The most appropriate formulation ould therefore be: ž / y2 h fs20 ln 0.5. Ž 29. u d Since the Shields parameter Ž u. appears in this formula, hich is in turn dependent on the friction factor, then iteratie techniques ould hae to be used to sole it. Also, the ork of Hughes Ž as based upon a model of uprush folloing bore collapse on a steep beach, hich is quite different from the conditions encountered in the present study. As mentioned aboe, TM98 assume oscillatory flo hen calculating f, but steady-flo hen choosing a alue for c. In the present study, quasisteady flo is assumed for both. Oscillatory friction factor formulae Ž albeit different ones. ere also used

16 50 ( ) T. Butt et al.rcoastal Engineering by Hughes et al. Ž and Masselink and Hughes Ž 1998., ho acknoledge that Eq. Ž 29.Ž aboe. might be more appropriate. Een if an oscillatory formula as used, it ould be far from obious hich one to choose for the sash-zone Ž see Nielsen, Obiously, more ork, perhaps in the laboratory, is required to find out the nature of the boundary layer in the sash-zone, and the most appropriate ay to estimate the friction factor. For the present study, the relatie effect of infiltration exfiltration oer a single sash cycle as estimated to be a reduction of about 10% of the total sediment moed on the uprush and an increase of about 4.5% of the total sediment moed on the backash. Although the direction is different from that in TM98 Ž due to grain size., infiltration exfiltration has more influence on the uprush than on the backash in both studies. Inspection of the yehrez time-series shos that the uprush is characterised by higher, more abrupt donard forces brought about by the sudden arrial of the sash-front at the measurement position, hereas the backash is characterised by longer duration but loer magnitude upard forces. The difference in the nature of uprush and backash flos is therefore further highlighted. The magnitudes of infiltration exfiltration influence on the uprush and on the backash ere estimated by TM98 by comparing simulated peak transport rates. If this is done for the single sash cycle analysed here, an approximate 16% decrease in peak uprush transport and a 6% increase in backash transport is found. TM98 obtained uprush increases of beteen 10% and backash decreases of 5% to 10%, for a position in the mid-sash-zone. They also suggested that the influence of infiltration exfiltration decreases ith increasing distance up the beach-face. Baird et al. Ž performed model simulations using the field data of Hughes Ž to inestigate the hypothesis that fluidisation of the bed might occur ithin the sash zone during the backash. They concluded that, for one case out of fie, fluidisation might be likely on the ery last stages of the backash. This as achieed by adjusting the assumed alue of K to m s y1, about fie times smaller than that obtained in the present study. The estimation of K is, again, not straightforard and arious empirical formulations are normally used, based on the grain size, porosity and sorting characteristics. In the present study, the formula of Bear Ž as used, hich is the most up to date Fig. 10. Schematic illustration of the ertical position of the pressure transducers belo the bed, and the indiidual pressure gradients, aeraged oer the time-series, beteen each pair of sensors.

17 ( ) T. Butt et al.rcoastal Engineering formula suggested by Domenico and Schartz Ž Baird et al. Ž found that, by using the older method of Krumbein and Monk Ž 1942., alues ere an order of magnitude smaller than those carefully measured ith permeameters. For the grain characteristics at Canford Cliffs, UK Žthe field site used by Baird et al., 1998., estimation of K using the formula of Bear Ž results in a alue much nearer to that measured. Therefore, it appears that fluidisation is of lesser importance, and no field eidence is aailable Žin- cluding from the present study. to suggest that fluidisation occurs in the sash-zone. The fact is also highlighted that care must be taken in any estimation of K, hich is, along ith the friction factor, another parameter notoriously difficult to estimate. Since the pressure as originally measured at four depths ithin the bed, it as considered instructie to note ho the pressure gradient might change ith depth. Fig. 10 shos a schematic representation of the position of each sensor and the time-aeraged pressure gradient beteen each pair of sensors ² yeprez :. The diagram shos that the gradients decrease ith distance belo the surface, suggesting that pressure propagation attenuates ith depth. In the present study, to allo comparison ith the results from preious ork, the pressure gradient beteen the top and bottom sensors ere used as these ere positioned at depths closely corresponding ith those of Turner and Nielsen Ž and TM98. It is important to stress that using pressure gradients at different depths from those preiously published ould only hae added to the uncertainty, ith the already highlighted difficulty estimating parameters such as K and f. ŽK, for example, can ary oer an order of magnitude depending on the method used to estimate it.. The implications of the attenuation of pressure ith depth for sediment transport should be the topic of future inestigation. A reie of the theory has been presented concerning the to competing processes hich may be important in altering the uprush and backash transport through infiltration exfiltration, namely Ž. a stabilisation or destabilisation of the surface layers, and Ž. b boundary layer thickening or thinning. A modified Shields parameter has been deried ith extra terms to take account of these processes, folloing the ork of Nielsen Ž and Turner and Masselink Ž It as found that the net direction of Qinfilt as offshore for the data in the present study, i.e. uprush transport as inhibited and backash transport enhanced by infiltration exfiltration. By alloing the grain size to ary in the computations, it as found that, aboe a particular critical grain size, the effects of infiltration exfiltration change from biasing the transport offshore to onshore, indicating a shift from a dominance of stabilisation destabilisation to a dominance of boundary layer effects. The exact alue of the critical grain size changeoer point Ž d. Q0 is not straightforard to estimate, and it has been suggested that experimental methods and the method of estimating arious constants be standardised before a reliable alue of d Q0 can be found. Sensitiity tests on the friction factor Ž f. and the constant Ž c. in the shear-stress elocity relationship hae found that, although c is less sensitie, relatiely small changes in the estimation of f might change the direction of the apparent influence of infiltration exfiltration. A suitable formula for f in the sash-zone has not yet been found. The net influence of infiltration exfiltration oer a single sash cycle as to decrease the total sediment transported by about 10.5% on the uprush, and to increase the total sediment transported by about 4.5% on the backash. 9. Conclusions Examination of time-series of sub-surface pore pressures has shon that upards-directed pressure gradients on the backash are not sufficient to cause fluidisation of the top layer of sediment leading to enhanced offshore transport. Acknoledgements The authors ish to thank Nick Berringer, and the Perranporth Surf Life Saing Club for their generosity in alloing us to use their clubhouse during the data collection. The assistance of Peter Ganderton

18 52 ( ) T. Butt et al.rcoastal Engineering and Jon Miles in conducting the field experiment is gratefully acknoledged. We ould also like to thank Andy Baird Ž Sheffield Uniersity. for kindly lending us the pressure transducers. References Bailard, J.A., An energetics total load sediment transport model for a plane sloping beach. J. Geophys. Res. 86, Baird, A.J., Horn, D., Mason, T., Mechanisms of beach ground-ater and sash interaction. 25th International Conference Coastal Engineering ASCE, pp Baird, A.J., Mason, T., Horn, D., Validation of a Boussinesq model of beach ground ater behaiour. Mar. Geol. 148, Bear, J., Dynamics of Fluids in Porous Media. Elseier, 764 pp. Butt, T., Sediment Transport in the Sash-Zone of Natural Beaches. PhD thesis, Uniersity of Plymouth, UK, 262 pp. Butt, T., Russell, P., Sediment transport mechanisms in high energy sash. Mar. Geol. 161, Conley, D.C., Inman, D., Ventilated oscillatory boundary layers. J. Fluid Mech. 273, Domenico, P.A., Schartz, W., Physical and Chemical Hydrology. 2nd edn. Wiley, 506 pp. Duncan, J.R., The effects of ater table and tide cycle on sash backash sediment distribution and beach profile deelopment. Mar. Geol. 2, Dyer, K.R., Coastal and Estuarine Sediment Dynamics. Wiley, 324 pp. Emery, K.O., Gale, J.F., Sash and sash marks. Trans. Am. Geophys. Union 32, Grant, U.S., Effects of ground ater table on beach erosion. Bull. Geol. Soc. Am. 57, Grant, U.S., Influence of the ater table on beach aggradation and degradation. J. Mar. Res. 7, Horn, D.P., Baldock, T., Baird, A., Field measurements of sash induced pressure gradients ithin a sandy beach. Proc. 26th International Conference Coastal Engineering ASCE, pp Hughes, M.G., Application of a non-linear shallo ater theory to sash folloing bore collapse on a sandy beach. J. Coastal Res. 8, Hughes, M.G., Friction factors for ae uprush. J. Coastal Res. 11, Hughes, M.G., Masselink, G., Hanslo, D., Mitchell, D., Toards a better understanding of sash-zone sediment transport. Proc. Coastal Dynamics 97, ASCE, Krumbein, W.C., Monk, G., Permeability as a function of the size parameters of unconsolidated sand. Trans. Am. Inst. Min. Metall. Eng. 151, Martin, C.S., Effect of a porous bed on incipient sediment motion. Water Resour. Res. 6, Martin, C.S., Aral, M., Seepage force on interfacial bed particles. J. Hydraul. Di. 7, Masselink, G., Hughes, M., Field inestigation of sediment transport in the sash-zone. Cont. Shelf Res. 18, Meyer-Peter, E., Muller, R., Formulas for bed-load transport. Proceedings of the 2nd Congress of the International Association for Hydraulics Structures Research, Stockholm, pp Mickley, H.S., Ross, R., Squyers, A., Steart, W., Heat, mass and momentum transfer oer a flat plate ith bloing. Tech. Note Nat. Ad. Comm. Aeronaut., Washington, 149 pp. Nielsen, P., Coastal bottom boundary layers and sediment transport. Adanced Series on Ocean Engineering, ol. 4, World Scientific, Singapore, 324 pp. Nielsen, P., Coastal groundater dynamics. Proc. Coastal Dynamics 97, ASCE, Quick, M.C., Onshore offshore sediment transport on beaches. Coastal Eng. 15, Russell, P.E., Huntley, D., A cross-shore sediment transport shape function for high energy beaches. J. Coastal Res. 15, Shields, A., Anendung der Aehnlichkeitsmechanik und Turbulenzforschung auf die Geschiebebeegung. Mitt Preuss Versuchsanstalt fur Wasserbau und Schiffbau Ž No. 26., Berlin. Sart, D.H., A schematization of onshore offshore transport. Delft Hydraulics Lab. Publ Turner, I.L., Nielsen, P., Rapid ater table fluctuations ithin the beach face: implications for sash-zone sediment mobility? Coastal Eng. 32, Turner, I.L., Masselink, G., Sash infiltration exfiltration and sediment transport. J. Geophys. Res. 103, an Rijn, L.C., Equialent roughness of alluial bed. J. Hydraul. Di. ASCE, No. HY10. an Rijn, L.C., Principles of Sediment Transport in Riers, Estuaries and Coastal Seas. Aqua Publications, The Netherlands, 584 pp. Waddell, E., Sash groundater beach profile interactions. In: Dais, R.A., Etherington, L. Ž Eds.., Beach and Nearshore Sedimentation, ol. 24, pp , SEPM Special Publication. Williams, J.M., Elder, S., Fluid Physics for Oceanographers and Physicists. 2nd edn. Butterorth-Heinemann, Oxford, 395 pp. Wilson, K.C., Frictional behaiour of sheet-flo. Progress Report 67, Institute of Hydrodynamic and Hydraulic Engineering. Tech. Uni. Denmark, pp Wilson, K.C., Friction of ae induced sheet-flo. J. Hydraul. Eng. 113,