RAPID METHODS FOR ESTIMATING NAVIGATION CHANNEL SHOALING

Transcription

1 RAPID METHODS FOR ESTIMATING NAVIGATION CHANNEL SHOALING Julie Dean Rosati 1 an Nicholas C. Kraus 2 ABSTRACT The US Army Corps of Engineers navigation mission is to provie safe, reliable, an efficient waterborne transportation systems (channels, harbors, an waterways) for the movement of commerce, national security nees, an recreation. Feerally maintaine channels through as many as 600 coastal inlets an through bays, estuaries, an rivers are therefore rege. Many of these navigation channels have been eepene, wiene, an lengthene to accommoate larger vessels an greater transit spee, an to increase maneuverability. These channel expansions have le to increasing an, at many sites, unanticipate maintenance reging requirements, because in part the relationship between an increase in channel cross-sectional area an the subsequent shoaling rate is nonlinear. As waterborne commerce an the nee for national security continue to grow, vessels are expecte to become larger, wier, or both ue to economies of scale an increase cargo capacity. It is anticipate that coastal inlet entrance channels will continue to be enlarge in the future. This paper iscusses empirical an analytical relationships for preicting channel shoaling base upon historical maintenance reging ata for Corps channels that have been eepene, wiene, an lengthene. A new analytical relationship base on an equilibrium channel epth an with is presente to calculate channel infilling an bank encroachment, an teste with the available ata. Keywors: inlets, reging, infilling, migration, siltation, analytical techniques. INTRODUCTION Channel epth at many eep-raft ports is constraining the new an larger classes of container ships. In the Unite States, in year 2000 approximately 30%, or 30,000 vessels ha a maximum esign raft greater than the channel epth of the port at which they calle (Hackett 2003). If all channel an port moifications planne through 2020 are complete, constraine calls are expecte to remain relatively constant; without navigation improvements, constraine calls are forecast to increase to 54,000. Investment ecisions require analysis to etermine the benefit of eepening, wiening, an lengthening of a channel. Such analysis primarily concerns estimation of future long-term annual reging maintenance volume for the propose improvements. To support cost-benefit analyses for navigation channel eepening an wiening, preictive methos are typically neee at two stuy phases: a time-limite planning or ecision-support phase uring which a potential project is examine an further stuy justifie base on information reaily available, an a longer term feasibility phase in which the esign is evelope an optimize. The problem is to estimate the increase reging maintenance volume an reging cycle for a eepene an/or wiene channel. A channel may be eepene without wiening, an occasionally a portion of a channel may be wiene for improve navigation throughput or as part of avance reging maintenance. If a channel is eepene, reging maintenance volume is expecte to increase because navigation channels are typically rege to the epth contour equal to the project epth, an greater epth or with makes the channel a more efficient seiment trap. A eeper channel is longer relative to a shallow channel an woul be expecte to capture a greater volume of seiment. To illustrate this increase in reging maintenance with increase rege epth, Figure 1 shows historical maintenance reging rates for St. Marys Entrance, locate on the FL/GA borer. In 1881, St. Marys Entrance ha a natural channel inlet throat epth of 5.8 m mean low water (MLW). Beginning in 1924, the channel was eepene to 8.5 m, an continue to be eepene to 10.4 m in 1954 an to 12.2 m in From 1987 to 1988, the seawar en of the channel was eepene from 12.2 to 15.5 m MLW an wiene from 122 to 152 m. Cumulative rege volume plotte in Figure 1a inicates a 265% increase in average volume after eepening an wiening in At St. Marys Entrance, the recor shows that the reging rate epens more on channel epth than length. Figure 1b shows that the reging rate normalize by channel length is correlate with the channel epth, with square correlation coefficient R 2 = High correlation inicates that epth is a ominant factor in capturing 1 Research Hyraulic Engineer, U.S Army Engineer Research an Development Center, Coastal & Hyraulics Laboratory, 109 St. Joseph Street, Mobile, AL 36628, USA, ; Julie.D.Rosati@usace.army.mil. 2 Senior Scientist, U.S. Army Engineer Research an Development Center, Coastal & Hyraulics Laboratory, 3909 Halls Ferry Roa, Vicksburg, MS 39180, USA, ; Nicholas.C.Kraus@usace.army.mil. 176

2 seiment in the channel at St. Marys Entrance, regarless of channel length. This result is interprete as stating the ominant cross-channel shoaling takes place in the nearshore an aroun the ebb shoal, where breaking waves, wave-inuce transport, an transport uner floo tie are strong, as compare to shoaling seawar of the ebb shoal where the waves an currents are less energetic. Figure 2 shows how channel shoaling (as inferre from maintenance reging ata) varies along the length of the channel epening on the forcing processes an seiment grain size. Preictive technology is neee to estimate such increases. Cumulative Volume Drege, 10 6 cu m Pre-Deepening New Work Post-Deepening 169,000 cu m/year Depths m MLW 618,000 cu m/year Depths m MLW Year a. Cumulative reging volume prior to an after navigation channel eepening an wiening. 35 Annual Dreging Rate Normalize by Channel Length, cu m/m/year R 2 = Channel Depth, m MLW b. Correlation between normalize reging rate an channel epth. Figure 1. Shoaling rates for St. Marys Entrance Channel, FL/GA. 177

3 station Littoral seiment Littoral seiment Clay & silt Strong current Beform& shoal migration Limit of ebb shoal Episoic shoaling relate to storms Littoral seiment & shoal migration along channel slope Silt & clay, uniform shoaling from ebb flow eposition Minor Shoaling Moerate Shoaling Significant Shoaling N 340 St. Marys Entrance, FL 0 10,000 Feet 3 Km Figure 2. Channel shoaling along St. Marys Entrance, FL/GA (after Johnston et al. 2002) Numerically intensive or meso-physics base moels are available for use in a feasibility phase of channel maintenance evaluation (e.g., Kaib 1976, Bijker 1980, Van Rijn 1991, Walstra et al. 1999, Ree et al. 2005). As Trawle (1981) has note, however, reging ata sets that woul serve for moel valiation typically exhibit large variability. Such moels require substantial ata input an computational resources to etermine the wave an current forcing at the site, from which seiment transport rates an channel shoaling can be calculate (Manzenrieer 1994). It appears that evelopment of empirically base approaches for estimating channel maintenance reging requirements can benefit ecision-support planning, as well as provie guiance for establishing an interpreting computation-intensive engineering moels. Because an inlet an its navigation channel are part of a seiment-sharing system with the ajacent beaches, the rate of natural seiment bypassing must be consiere in aition to the channel infilling rate. Navigation channel performance can be limite by bank encroachment, typically as intrusion by a spit, shoal, or san wave into a channel; through eposition or infilling of seiment along the channel bottom; an by bank erosion (Figure 3). Bank encroachment together with bank erosion result in migration or meanering of the channel. If the channel fills above project epth, or if some minimum with is reache, maintenance reging is necessary. Project epth is the minimum allowable epth for supporting the esign vessel. For iscussions herein, the term shoaling inclues is the sum of infilling from the be (eposition) an bank encroachment. Dreging requirements must be estimate in esign an moification of channels base on hyrographic survey ata an estimate shoaling rates available from the existing channel. Deepening an wiening may be consiere as part of avance maintenance to reuce reging frequency an cost, an to promote favorable environmental consequences. Savings can be accrue by reucing the number of rege mobilizations an emobilizations, an channel-conition surveys, an by scheuling reges when equipment can be share among regional projects. Avance maintenance may also be scheule to accommoate favorable weather an enangere species winows to reuce the cost of reging, avoi isturbance to the environment, an to maintain the channel through storm seasons when reging is more expensive or risky. 178

4 Chart Datum Direction of Preominant Transport Bank Encroachment hp Bank Erosion Project Depth, hph Depth Immeiately after Dreging Deposition Avance Depth Allowable Overepth Design Cross Section Figure 3. Schematic of channel evolution by bank encroachment, eposition, an bank erosion. This paper reviews available analytical an empirical methos an introuces a morphology-base mathematical moel of channel shoaling by cross-channel seiment transport. The morphologic moel calculates channel shoaling either by infilling from the be or by bank encroachment, an inclues time-epenent bypassing as a function of the magnitue of shoaling. The moel takes avantage of information typically available in engineering projects: the epth an with of the channel in its natural state prior to reging, an an estimate of longshore (cross-channel) seiment transport that contributes to shoaling of the channel. Graients in transport along the channel are not represente irectly, but o enter inirectly through incorporation of the natural channel epth. The moel has a close-form solution for the simple case of constant input transport rate an yiels quantitative preictions of the ecrease in epth by shoaling, channel narrowing by bank encroachment, an san bypassing. Comparisons are mae to an existing analytical metho an channel survey ata to emonstrate the applicability of the moel an emonstrate content of ata sets typically available in practical situations. REVIEW OF ANALYTICAL AND EMPIRICAL METHODS This section reviews analytical an empirical methos for calculating channel infilling by cross-channel transport that o not epen on intensive hyroynamic an wave moeling to assess existing preictive capability. Common notation is aopte to ai comparison. Various authors have consiere ifferent sections of an inlet entrance channel, such as the offshore, outsie the area of breaking waves; on the ebb-tial shoal; an in the surf zone. Although most quantitative methos appear to focus on one such section of the channel such as illustrate in Figure 2, they appear to be applicable to any section if the inputs are specifie appropriately. The main requirement is that the channel fills by cross-channel transport of seiment, whatever the origin of the transport-forcing mechanism. Seiment intercepte by a navigation channel can reuce channel with by accumulating on the sies (bank encroachment) an reuce channel epth through eposition on the bottom (infilling) (Figure 3). Figure 4a shows an example of bank encroachment at Shinnecock Inlet, NY, an Figure 4b shows be eposition at St. Marys Entrance, FL/GA. The calculation methos reviewe in this section have not accounte for channel bank encroachment. Seiment can also pass over a channel by moving in suspension, an material eposite in the channel can be re-suspene an transporte out; both processes contribute to channel bypassing. At inlets, the net bypassing rate in the preominant irection of transport to the own-rift beach enters in seiment bugets, an the gross rate of longshore transport relates to channel reging requirements. 179

5 N 25, 29 Sep Apr 01 Elevation, m (MLW) West East Distance Along Transect (m) a. Channel shoaling by bank encroachment, Shinnecock Inlet, NY -6-7 Mar 2000 Nov Elevation, m (NAVD) South North Distance, m b. Channel shoaling by be eposition, St. Marys Entrance, FL/GA (Station shown in Figure 3) Figure 4. Channel cross-sections immeiately after reging (soli line) an with shoaling (otte line). 180

6 Gole an Tarapore (1971) presente an empirical metho for estimating channel infilling by cross-channel transport seawar of the wave-breaking zone, for fine-graine seiments. However, the metho appears equally applicable to san in the wave-breaking zone, if a ecrease in channel with by bank encroachment is not of concern. For the region seawar of the wave-breaking zone, tial or other regional currents carry the cross-channel transport into the channel. Bypassing was represente by calculating the amount of suspene loa of certain seiment fall spee that woul be transporte over the channel for a specifie with, unaltere cross-channel current upstream of the channel, an seiment fall spee. A epth-average current upstream of the channel was assume, giving the current in the channel by assumption of constant ischarge. These two assumptions are common to all methos escribe below an will not be repeate in this review. Assuming further that the seiment-carrying capacity is proportional to the square of the velocity, the rate of infilling was erive to be proportional to ( h ha ) / h, in which h = epth of initially rege channel, an h a = ambient epth upstream of the channel. The metho is calibrate by an empirical multiplicative coefficient that was etermine by comparison to reging ata. Data for four ports in Inia gave a coefficient value ranging from to 0.30, inicating relative robustness of the metho. This metho is not reaily aaptable for preictions of infilling if the channel imensions are to be change, because of the ata epenence an lack of accounting for channel with. Mayor-Mora et al. (1976) evelope an analytical metho for infilling in a rege channel by settling of suspene seiment. Mikkelsen et al. (1980) subsequently verifie the metho with ata from a test pit ug near the location of the channel uner consieration. The test pit was 200 m wie (channel with), 400 m long, an 2 m eeper than the ambient epth of 7 m. Current velocity, waves, suspene seiment concentration insie an up rift of the test pit, an seiment grain size were measure, an echo sounings were mae about every 3 weeks over a 5-month perio. The centerline of the pit fille at a rate of 1.7 cm/ay shortly after reging, ecreasing to 1.2 cm/ay near the en of the monitoring. The preictive expression of Mayor-Mora et al. (1976) is: Fha / h F qr = qin (1 e ) qh (1 e ) cos α (1) where q R = infilling rate per meter length of channel, q in = input transport rate of suspene seiments at equilibrium uprift of the channel at ambient epth h a, q h = transport rate of suspene seiment in the equilibrium conition in the channel at epth h, α = angle between the irection of the current an a normal to the channel, an the coefficient F given by: 2 w W0 F = ε V cos α s (2) where w = seiment fall spee, W 0 = initial with of channel (assume not to change), = seiment ey iffusion coefficient, an V = current velocity upstream of the channel, etermine by another moel or specifie irectly. Derivation of Equation (1) epens on an assume steay current an wave fiel (waves enter in etermination of the equilibrium suspene transport both up rift an in the channel, an in the iffusivity coefficient), equilibrium forms for the velocity profiles, an moification of the concentration profile with epth, among other factors. Elapse time oes not enter, which gives a constant infilling rate unless Equation (1) is re-evaluate with upate forcing conitions. For large grain sizes, the value of F is large, meaning that Equation (1) reuces to qr qin q. h Although not escribe in the original papers, the bypassing rate can be consiere to be equivalent to q h. Mikkelsen et al. (1980) calculate q a, q h, an ε from micro-scale physics relations, making this proceure ifficult for ecision-support or initial planning stuies that must be one quickly. s Vicente an Uva (1984) present a metho base on the assumption that a channel will infill exponentially towar equilibrium as governe by the equation: h K( h he ) t = (3) ε s 181

7 where h = epth in the channel (they use elevation in the channel, here converte to epth), K = empirical relaxation coefficient, an h e = equilibrium epth of the channel in the zone of interest, also etermine empirically. If the forcing is assume constant over the time interval of interest, Equation (3) has the solution: Kt h = h ( h h )(1 e ) (4) e Vincente an Uva (1984) etermine K an h e by fitting to channel survey ata, noting that only two surveys are necessary. The metho is rational in assuming exponential behavior an an equilibrium epth, but by etermining the equilibrium epth an relaxation time through ata fitting, it is highly empirical an hols few avantages over simply estimating channel infilling base on experience. Also, channel with an bypassing rate are not consiere explicitly, making the metho ifficult to apply to new channel esigns for which ata are not available. Manzenrieer (1994) gave a similar proceure in which the volume of material rege beyon a natural epth (calle the artificial volume) was assume to ecrease exponentially. Fitting to ata for a section of channel at Wilhelmshalfen, Germany, where the channel is oriente perpenicular to the tial current, gave the half-life of the artificial volume. Galvin (1982) refine an empirical metho presente in Galvin (1979) to calculate the rate of infilling of channels together with the bypassing rate at the crest of an ebb-tial shoal, assume to be the constraining epth for navigation. The metho appears applicable to any location along an inlet channel subjecte to seimentation by waves an tial current. The metho is expresse in terms of a bypassing transport ratio, here calle T, efine as the ratio of the bypassing rate after reging to the bypassing rate before reging. By taking a ratio, an unknown multiplicative empirical coefficient entering both transport rates cancels. Base on assumptions of shallow-water wave theory an on the seiment transport being proportional to the prouct of a bottom shear an current velocity, Galvin (1982) fins the transport ratio as: T m ha = h (5) in which the exponent m ranges between 3/2 < m < 5/2, the limits epening on whether one assumes the tial ischarge through the inlet section remains the same (m = 3/2) or increases (m = 5/2) after reging. Therefore, the Galvin (1982) metho can account for some along-channel transport processes. The eposition ratio is 1 T an, for an input longshore seiment transport rate per unit length of channel q, the infilling rate becomes: m m h q q h h a = (1 T ) = m t W W h (6) Galvin (1982) notes several physically reasonable properties of this channel infilling an bypassing metho: (1) the maximum rate of infilling occurs immeiately after reging, (2) the channel fills faster if the post-reging velocity is reuce by increasing channel imensions, an (3) infilling epth approaches the ambient epth h a more slowly if the epth of the rege cut, h h a, is smaller, for h hel constant. Forman an Vallianos (1984) applie the Galvin metho to a project stuy, calculating statistical estimates of aily infilling rates. Galvin (1982) also gives an estimate of the time t p to reach project epth h p after reging: W ha t p ( h hp ) (ln A ln B) q + m (7) where 182

8 m 1 h h 1+ h ha 2 ha A =, B = h h p m 1 h h p 1+ 2 h a a a (8) Equation (7) is an approximate solution of an integral that cannot be solve in close form. Van e Kreeke et al. (2002) presente an analytical solution of channel infilling an migration uner a tial current, with waves as a stirring mechanism. The moel is applicable to eeper water an computes wiening an infilling of a Gaussian-shape channel through seiment iffusion processes for both be loa an suspene loa, riven by tially average moments of the current. Van e Kreeke et al. applie the analytical solution to the access channel to the Port of Amsteram, for which the ambient epth h a = 17 m, channel with = 600 m, meian san size = 0.2 mm, an maximum channel epth = 20 m. For the analytical solution to be applicable, seven imensionless quantities must be of orer ε, where ε = (h h a )/ h a. The van e Kreeke et al. analytical solution is applicable for long time perios, with channel time scales measure in hunres of years. The require time perio relate to nearshore forcing makes irect aaptation of this solution infeasible, where the majority of channel infilling occurs by wave-inuce longshore currents, requiring maintenance reging on orer of a few years. Of the methos available for empirical estimation of channel infilling an bypassing, only the Galvin (1982) metho can be applie to (1) estimate changes in the channel infilling rate ue to channel moifications, (2) the nearshore, where wave-riven cross-channel currents are the ominant forcing mechanism for channel infilling, an (3) estimate channel bypassing. None of the methos reviewe allow calculation of bank encroachment, although the van e Kreeke et al. (2002) solution gives channel migration as a requirement at secon orer. MORPHOLOGIC CHANNEL SHOALING MODEL The paraigm for evelopment of this moel is that a channel that may infill from the be, ecreasing the navigable epth (terme channel infilling), an from the up-rift bank, ecreasing the navigable with (terme bank encroachment). Dreging is assume to occur at intervals such that channel meanering an migration are prevente before significant lateral eformation can occur. Bypassing is represente by suspene loa transporte over the channel an by re-suspension an transport of material that has been eposite in the channel. Such processes are epicte schematically in Figure 5. Moel assumptions an evelopment follow those of Kraus an Larson (2003). Assumptions for the present version of the moel are: 1. Shoaling (both channel infilling an bank encroachment) occurs by cross-channel transport, whatever the type (primarily ue to wave-generate current, but also potentially ue to tie, win, an regional currents). 2. The graient in along-channel transport is negligible for each segment of the channel analyze. 3. A natural channel epth, h n an with, W n exist an can be ientifie, which represent the long-term timeaverage or equilibrium epth an with, respectively, of the navigation channel if it were not maintaine. If a natural channel was not present prior to reging, then h n is the local ambient epth h a, an W n = The rate of seiment leaving the channel is the prouct of the rate of seiment entering the channel an a ratio relating the natural, rege, an actual conitions at that time. For channel infilling, the ratio relates natural, rege, an actual channel epths; for bank encroachment, it represents the natural, rege, an actual channel withs. The conceptual framework of the moel for the situation of transport irecte to the right, assume to be the ominant irection of transport, is shown in Figure 5. The own-rift bank of the channel is assume to be stable. The causes an circumstances of channel migration are not well unerstoo, an some channels remain in position, whereas others migrate, a topic beyon the scope of this paper. Immeiately after reging, the channel has with W an epth h. 183

9 A rege channel, if not maintaine, is assume to fill until the natural epth is re-establishe. In applications, this epth can be etermine by examination of the channel at a coastal inlet prior to reging, through survey ata uring times when reging may have been elaye, or as the epth at ajacent channel sections where reging is minimal or not require. q q b q s h q q y r q x h n h p h W n h q c W 0 Figure 5. Definition sketch for channel shoaling moel. The moel is erive by consiering the seiment pathways as shown in Figure 5: q = qb + q + q (9) s in which q = total rate of seiment approaching channel per unit channel length, q b = transport contributing to bank encroachment per unit channel length, q = eposition rate per unit channel length, an q s = suspene transport that bypasses the channel per unit channel length. The rate of channel infilling is given by, qc = qb + q q (10) r in which q c = rate of channel infilling per unit channel length an q r = rate of resuspension from the channel be per unit channel length. The rate of seiment bypassing per channel length, q y, is: qy = qr + q (11) s Assigning proportionality factors to simplify as a b = q b /q, a = q /q, an a s = q s /q, there results ab + a + as = 1. Thus, once two of the proportionality factors have been estimate, the thir may be calculate. 184

10 The rate of seiment q r that is resuspene an leaves the channel is assume to be proportional to the eviation of the existing epth from the natural epth (Moel Assumption 4, above): h h h h q = q = a q r h hn h hn (12) which follows an assumption introuce in the Inlet Reservoir Moel for coastal inlet morphology change an bypassing (Kraus 2000) an applie to channel infilling by Kraus an Larson (2003). Equation (12) expresses the physical picture that the seiment resuspension rate, etermine by q r, is smallest shortly after reging an then increases (linearly) as the channel approaches the natural epth. If there is no input rate of transport (no crosschannel current), then no seiment is expecte to leave the channel. For the situation of a portion of channel crossing the surf zone, the transport rate per unit channel length can be estimate as the total longshore transport rate Q multiplie by the ratio of effective length of channel being consiere, Lc, to the total with of the surf zone. San volume increases if the channel shoals, an the continuity equation becomes, for small time interval t an applying Equation (12) for q r : h h n ( W x) h = ( qr q ) t = aq t (13) h hn in which h = epth change, an x=istance of bank encroachment over t. The governing equation for channel infilling is then: h aq h h n = t W x h hn (14) For constant input rate an a b = 0 (no bank encroachment, so x = 0), the solution of Equation (14) is: in which: h = h + h h e τ (15) t / n ( n ) W ( h hn ) τ = (16) a q is a characteristic time escribing the uration of channel infilling for constant input rate of seiment approaching the channel. The form of Equation (15) is ientical to the solution of Vicente an Uva (1984), Equation (4), except their values of K in the exponential an the equilibrium epth h e, are to be etermine through fitting to reging ata, whereas the two quantities τ an h n in the present formulation can be estimate from site evaluation. From Equation (15), the shoaling rate is given as, for the situation of negligible bank encroachment: h t a t / τ = q e (17) W for which the negative sign means that channel epth ecreases as the channel fills. For short elapse time, to secon orer, the solution is: 2 2 h a q a q + t t W W 2 ( h h ) (18) n 185

11 At first orer, the initial infilling rate is inepenent of the rege epth an natural epth, epening irectly on the input rate an inversely with channel with. A larger seiment volume eficit, h h, ecreases the infilling n rate at secon orer. The time t p for the channel to fill to project epth h p is given from Equation (15): t p h h n = τ ln hp h n For calculating bank encroachment, the rate of seiment input to the bank is qb = abq, an the output rate is: x ( qb ) out = qb ( W W ) n (19) (20) where W n is the natural channel with prior to reging. From Figure 5, the rate of bank encroachment x/t is: x ab q x = 1 t h ha W Wn (21) If h = constant, meaning no infilling takes place, such as for an inlet where the ajacent beaches are primarily gravelly (a = a s =0), Equation (21) has the solution in which: t / ( ) b x = ( W W ) 1 e τ (22) n ( W W )( h h ) n a τ = (23) b q is a characteristic time escribing the uration of bank evelopment for constant input rate of seiment eposite on the sie of the channel. In the general case of both channel shoaling an bank encroachment, Equations (14) an (21) form a set of couple, first-orer, nonlinear ifferential equations. Kraus an Larson (2003) escribe an analytical solution for similar equations not involving the natural epth an with obtaine by linearization uner the assumption of small change in epth or bank growth. In the present stuy, Equations (14) an (21) are solve numerically by a trapezoial or mi-point solution metho. EXAMPLE APPLICATIONS This section escribes tests of the moel an a methoology for its application. First, sensitivity testing of the numerical metho was conucte by separately varying rege channel epth an with for a range of reging intervals. These tests inicate that moel performance is in accor with general physical expectations that (1) the rate of channel shoaling (infilling an bank encroachment) is greatest immeiately after reging an ecreases with time, an (2) the channel shoaling rate increases as imensions of the rege channel increase relative to the natural channel imensions. The following examples emonstrate comparison with the Galvin (1982) moel an example ata set, an with fiel ata at three sites. 186

12 Galvin s (1982) Example The shoaling moel was applie to a realistic example presente by Galvin (1982) to compare with his relationship an to test trens in performance. Galvin s example has two parts, in which a channel with the following characteristics must be eepene to a epth, h, such that it will remain at or below the project epth, h p, for 8 months: h n = 2.5 m, h p = 4 m, W 0 = 30 m, effective channel length L c = 150 m, Q = 10,000 cu m/year (uring the 8- month perio consiere), an require t p = 8 months = 0.67 year. The ambient epth, h a, is not given an is not require if bank encroachment is neglecte (a b = 0). The Galvin metho gave the solution as h = 5.35 m. With a = 1.0 an a b = 0, the present shoaling moel preicte the require rege epth to maintain at least a 4-m project epth as h = 6.0 m, or 12% greater than the Galvin metho value. The secon part of the example asks for the maximum reuction in the bypassing rate, which Galvin etermines from to the maximum channel trapping rate right after reging. Galvin set h = 5.1 m an obtaine the first month s channel trapping rate = 1,040 cu m/month. With the shoaling moel, h was set to 5.1 m, an this same quantity was calculate as 960 cu m/month, 92% of the Galvin metho value. Thus, for this hypothetical example, the shoaling moel agrees favorably with the Galvin (1982) moel. Fiel Applications Shinnecock Inlet is a meso-tial inlet locate on the south shore of Long Islan, NY, with a meian grain size of 0.35 mm. Net longshore san transport is from the east, with a nominal rate of 200,000 cu m/year (Research Planning Institute 1983; Kana 1995). At Shinnecock Inlet, four channel transects were evaluate, as shown in Figure 6 an Table 1. Here, the longshore transport was assume to have a triangular istribution across shore, with a peak at the transect with the greatest shoaling rate an ecreasing both seawar an shorewar of that transect. The increase in channel elevation, h, an the bank encroachment istance, x, were evaluate an moele for these four transects. The east jetty transect was the only one that exhibite bank encroachment (a jetty tip shoal shown in Figure 8a), an this process was moele with a b = Calibration of all transects resulte in a values ranging from 0.18 to 0.5, an a s values ranging from 0.35 to 0.82 (Table 1). These calibrations illustrate the capability of the couple ifferential equations to simulate variations in channel bank encroachment, infilling, an suspene transport bypassing the channel. Table 1. Channel Transects Evaluate with Morphologic Shoaling Moel Shinnecock Inlet: Sep 1998 to Apr 2001 Transect Measure (m) Moel Parameters Preicte (m) Average h x a a b a s h x East Jetty T T T Freeport Entrance Jetty Channel: 1983 to 1988 (pre-eepening an wiening) to x 0.15= Freeport Entrance Jetty Channel: 1992 to 2002 (eepene an wiene) to x 0.15= Keystone Harbor: Oct 1987 to May T Keystone Harbor: May 1990 to May T Calibration of moel. 2 Verification of moel, using calibrate parameters. 187

13 0 0 25, 29 Sep Apr 01-2 x = 7 m -1 West East -2-4 Elevation, m (MLW) h avg = 0.4 m Elevation, m (MLW) , 29 Sep Apr N h avg= 0.96 m -6-7 West East a. East jetty transect c. Transect , 29 Sep Apr 01 N , 29 Sep Apr 01 N Elevation, m (MLW) h avg = 0.78 m Elevation, m (MLW) h avg = 0.93 m -7 West East Distance Along Transect, m -7 West East Distance Along Transect, m b. Transect 1. Transect 3 Figure 6. Shinnecock Inlet, NY, channel cross-sections. To further test the moel, two time perios of channel shoaling ata for ifferent channel configurations at one location were esire. Data for Freeport Entrance, TX, locate in the Gulf of Mexico in a micro-tial environment were available to calibrate the moel base on reging from 1983 to 1988, when the channel was maintaine at 11- m epth an 61-m with. The moel was then teste by holing the parameter values constant for a post-eepening an wiening conition from 1992 to 2002, when the channel was maintaine at 13.7-m epth an 122-m with. Samples of rege seiment in the jetty entrance channel inicate approximately 15% san, 35% silt an 50% clay. Channel shoaling occurs entirely by infilling (no bank encroachment). It is likely that the silts an clays move from the river an bay into the jetty channel via along-channel transport, rather than by cross-channel processes. Thus, 15% of the observe infilling was attribute to longshore (cross-channel) transport an serve for comparison with moel simulations. Net longshore san transport was estimate to be 250,000 cu m/year to the south (U.S. Army Engineer District, Galveston 1992). Because of the observe uniform infilling on the channel transects an those at the tips of the jetties (Figure 7), longshore san transport was assume uniformly istribute. Starting with the pre-eepening an wiening channel configuration, the moel was calibrate to reprouce the observe infilling rate of 2.1 m x 0.15 = 0.32 m for a 915-m long by 61-m wie section of the jetty channel. The calibrate moel parameters were a = 0.08 an a b = 0. Keeping these parameters fixe, the eepene an wiene channel configuration was moele, resulting in a preicte infilling elevation of 0.17 m for the 915-m long by 122- m wie section, versus 1.4 m x 0.15 = 0.21 m of infilling that occurre. Thus, the moel preicte approximately 80% of the infilling that occurre in the channel, after a 150% increase in channel cross-sectional area. The Galvin (1982) moel was also applie to the Freeport ata set with a value of 15% for the percentage of crosschannel transport by san infilling. The Galvin moel over-preicte the infilling rate by 43% an 20% for the first an secon time perios, respectively, with the parameter m=3/2 (no change in tial flow). With m=5/2 (tial flow increase), the Galvin moel over-preicte the infilling rate by 84% an 42% for the same time perios. To obtain best results with the Galvin moel, the percentage san infilling by cross-channel transport was calibrate to 8% (for m=5/2) to 10% (for m=3/2) of the full value; however, there are no ata to support this calibration. The benefits of the present moel over the Galvin metho are: (1) the present moel gives linear equations to lowest 188

14 0-2 July 2000 Sep Sep Elevation, m (MTL) South Jetty North Jetty Distance Along Baseline, m Figure 7. Freeport Entrance Channel, TX, channel cross-section at jetty tips. orer; (2) reaily available morphological quantities of equilibrium epth an with are incorporate an etermine the solution structure; (3) for long time perios, Galvin s moel preicts channel infilling to the ambient epth, whereas the present moel returns the channel to the natural with an epth; an (4) bank encroachment can be escribe. For example, the Galvin metho coul not treat the Shinnecock Inlet east jetty transect example escribe above or the following application. As a final example with a ifferent (extreme) seiment size, channel shoaling at Keystone Harbor, WA, is consiere (Larson an Kraus 2003). The channel of this small harbor, locate on a gravelly coast facing Puget Soun, becomes limite ue to bank encroachment from the north (Figure 8). Gravel moves along the coast an enters the channel, graually restricting its with. The north bank grows southwar without ecrease in epth. There is negligible tial prism in this channel, with the main current supplie by ferries that enter an leave the harbor at relatively great spee. With a b = 0.7 to represent gravel, an the remainer of material assume to be silt that washes away (a = 0), calibration of the moel with ata from October 1997 to May 1990 perio gives channel bank encroachment equal to 8.5 m for q = 5,000 cu m/year, h = 7 m, an h n = 0 (no natural channel because there is no tial forcing in this artificially create harbor). Keeping the same values of a b an a for a secon time perio from May 1990 to May 1991 gives bank encroachment equal to 3.7 m, as compare to a measure value of 3.5 m. CONCLUSIONS A morphology change moel for channel shoaling was evelope base on partitioning of seiment-transport processes occurring at a rege channel as infilling, bank encroachment, an seiment bypassing the channel. The moel an methoology are applicable to channels on the open coast an in estuaries, bays, an lakes. Data require are those typically available: ambient epth ajacent to the channel, natural channel epth an with (prior to reging), rege channel epth, channel imensions, an estimate of the cross-channel seiment transport rate (the longshore transport rate in nearshore applications). Successful moel performance inicates that stuy shoul be mae of epth an with of natural channels to evelop empirical preictive relations base on the tial an other forcing. 189

15 3 1 Keystone Harbor, Transect 2 Oct 87 - May 91 Elevation, m (MLLW) /87 5/90 5/ Distance Across Entrance, m Figure 8. Keystone Harbor, WA, channel cross-sections. Parameters relating to the percentage of channel shoaling by bank encroachment an by infilling (or, alternatively, the percentage of seiment transport bypassing the channel) must be specifie by the user, or can serve as calibration coefficients. Sensitivity tests inicate rational performance of the moel. Preictions of the moel compare favorably with an inepenently publishe example, an the moel reprouce channel performance at three sites, Shinnecock Inlet, NY, Freeport Entrance, TX, an Keystone Harbor, WA. The moel was calibrate an valiate for the jetty channel at Freeport, TX, an reprouce 80% of the infilling that occurre after channel eepening an wiening. Keystone Harbor provie an example of bank encroachment, for which the simple morphologic moel preicte a ecrease in channel with only 6% greater than the measure value. REFERENCES Bijker, E. W. (1980). Seimentation in channels an trenches. Proc. 17 th Coastal Eng. Conf., ASCE, Reston, VA, 1,708-1,718. Forman, J. W., Jr., an Vallianos, L. (1984). Proceure for etermining reging requirements in coastal inlet channels. Proc. 19 th Coastal Eng. Conf., ASCE, Reston, VA, 1,668-1,684. Galvin, C. (1979). Shoaling rate at Moriches Inlet, Appenix D: Shoaling of a rege cut thru the bar seawar of an inlet. Report prepare for U.S. Army Engineer District, New York, 25 July 1979, Galvin, C. (1982). Shoaling with bypassing for channels at tial inlets. Proc. 18 th Coastal Eng. Conf., ASCE, Reston, VA, 1,486-1,513. Gole, C. V., an Tarapore, Z. S. (1971). Preiction of siltation in harbour basins an channels. Proc. 14 th Congress of IAHR, Société Hyrotechnique e France, Paris, France, D5-1-D-5-8. Hackett, B. (2003). National reging nees stuy of U.S. ports an harbors: upate U.S. Army Corps of Engineers, Institute of Water Resources Report 00-R-04, May, 116 p. Johnston, S., Kraus, N. C., Brown, M. E., an Grosskopf, W. G. (2002). DMS: Diagnostic Moeling System, Report 4: Shoaling analysis of St. Marys Entrance, Floria. ERDC/CHL TR-99-19, U.S. Army Engineer Research an Development Center, Coastal an Hyraulics Laboratory, Vicksburg, MS. Kaib, A. A. (1976). Seimentation problems at offshore rege channels. Proc. 15 th Coastal Eng. Conf., ASCE, Reston, VA, 1,756-1,774. Kana, T. W. (1995). A mesoscale seiment buget for Long Islan, New York. Marine Geology, 126,

16 Kraus, N. C. (2000). Reservoir moel of ebb-tial shoal evolution an san bypassing. J. Waterway, Port, Coastal, an Ocean Eng., 126(6), Kraus, N. C., an Larson, M. (2003). Analytical moel of navigation channel infilling by cross-channel transport. Proc. 28 th Coastal Eng. Conf., Worl Scientific Press, Hackensack, NJ, 3,698-3,710. Manzenrieer, H. (1994). Half-life perio of seimentation moel test on a scale 1:1. Proc. 24 th Coastal Eng. Conf., ASCE, Reston, VA, 3,139-3,153. Mayor-Mora, R., Mortensen, P., an Fresoe, J. (1976). Seimentation stuies on the Niger River elta. Proc. 15 th Coastal Eng. Conf., ASCE, Reston, VA, 2,151-2,169. Mikkelsen, L., Mortensen, P., an Sorensen, T. (1980). Seimentation in rege navigation channels. Proc. 17 th Coastal Eng. Conf., ASCE, Reston, VA, 1,719-1,734. Ree, C. W., Das, H., an Nieoroa, A. W. (2005). Application of a preictive channel shoaling an migration moel, M3D, to St Marys Entrance, Floria, Proc. 29 th Coastal Eng. Conc., Worl Scientific Press, Singapore, 2,232-2,242. Research Planning Institute. (1983). Seiment buget summary, final report for the reformulation stuy. Beach Erosion Control an Hurricane Protection Project, Fire Islan Inlet to Montauk Point prepare for U.S. Army Engineer District, New York. Trawle, M. J. (1981). Effects of epth on reging frequency: Report 2, Methos of estuarine shoaling analysis. Technical Report H-78-5, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS. U.S. Army Engineer District, Galveston. (1992). Inlets along the Texas Gulf coast. Planning Assistance to States Program, Section 22 Report, U.S. Army Engineer District, Galveston, TX. Van e Kreeke, J., Hoogewoning, S. E., an Verlaan, M. (2002). An analytical moel for the morphoynamics of a trench in the presence of tial currents. J. Continental Shelf Res., 22(11-13), Elsevier Science Lt., Orlano, FL, 1,811-1,820. Van Rijn, L. C. (1991). Seimentation of rege channels an trenches. J.B. Herbich, e., Hanbook of Coastal an Ocean Eng., Vol. 2, Gulf Pub. Co., Houston, TX, Vicente, C. M., an Uva, L. P. (1984). Seimentation in rege channels an basins, preiction of shoaling rates. Proc. 19 th Coastal Eng. Conf., ASCE, Reston, VA, 1,863-1,878. Walstra, D. J. R., Van Rijn, L. C., Hoogewoning, S. E., an Aarninkhof, S. G. J. (1999). Morphoynamic moelling of rege trenches an channels. Proc. Coastal Seiments 99, ASCE, Reston, VA, 2,355-2,