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(Extraído de Hidrotécnica Potuguesa. 1991) r:!HO

LNEC - Proc. 604/1/11668 89

NINISTÉRIO DO EQUIPAMENTO SOCIAL

LABORATÓRIO NACIONAL DE ENGENHARIA CIVILC.D.U.: 556.545.6

SEDIMENTATION IN DREDGED CHANNELSAND BASINS

Prediction of Shoaling Rates

C. MARTINS VICENTECivil Engineer, Research Officer,

Hydraulics Department

LUÍS P. UVACivil Engineer, Research Assistant,

Hydraulics Department

LISBOA 1985

SEDIMENTATION IN DREDGED CHANNELS AND BASINS

Prediction of Shoaling Rates

SYNOPSIS

A method is presented for predicting shoaJing in dredged channels and basins where deposition of fine rsediment fractions carried in suspension by tidal currents occurs.

The method is based on the analysis of hydrographic surveys of difTerent dates, which show thehydrographic evolution of dredged areas located in the site or in its vicinity. It can also be applied toexperimental dredged pits.

Results obtained from the analysis of surveys are worked out by using mathematical expressionsdeduced frorn a simplified hipothesis, empirically based. Pararneters are determined which can be used topredict shoaJing either when new dredgings are made or when previously dredged sites are deepened.

SEDIMENTAÇÃO EM CANAIS E BACIAS DRAGADOS

Previsão de Taxas de Assoreamento

RESUMO

É apresentado um método de previsao de assoreamento em canais e bacias dragados, sujeitos adeposição de sedimentos finos transportados em suspensão por correntes de maré.

O método é baseado na análise de levantamentos hidrográficos de diferentes datas, que documentem aevolução hidrográfica de áreas dragadas situadas no próprio local ou na sua vizinhança. O método podetambém ser aplicado a dragagens experimentais, expressamente realizadas com o fim de caracterizar ascondições locais de sedimentação.

Os resultados obtidos da análise dos levantamentos são elaborados utilizando expressões matemáticasdeduzidas de uma hipótese simplificada, de base empírica. São determinados parâmetros que podem serutilizados para prever as taxas de assoreamento respeitantes a novas dragagens ou ao aprofundamento dedragagens já existentes.

SEDIMENTATION IN DREDGED CHANNELS AND BASINS

Prediction of Shoaling Rates

1 - DESCRIPTION OF METHOD"

The basic assumption, of empirical nature, considers that the shoaling rate ísproportional to the relative bottom elevation. This proportionality is expressed by

(1)

where:

C is a variable that represents the difTerent bottom elevations at instant t; C, is aconstant that represents the bottom natural equilibrium elevation in the zonestudied, and K is a constant sedimentation coefTicient that expresses theproportionality already mentioned.

To establish this assumption three aspects were considered which experience in thefield of the maintenance of dredged zones in estuaries has shown to be very general:

- Sedimentation occurs whenever dredging is carried out to make deeper a zonepreviously in natural equilibrium;

- The sedimentation rate increases as a function of the thickness of the dredgedlayer;

- The bottom tends to shoal back to its natural equilibrium elevationcorresponding to the situation prior to the first dredging operation whenevermaintenance dredging is discontinued for a sufficient number of years.

When applying the method it is assumed that the natural equilibrium elevation C,and the sedimentation coefficient K are constant throughout the zone under analysisand do not significantly vary in the course of time. So that this may be true, thefollowing conditions seem to be required:

- The zone analysed must not be too large so that there can be approximateuniformity of the characteristics of sediments in suspension and ofhydrodynamic conditions, concentrations and salinities

- The time interval between two surveys must not be less than one year so thatthe semidiumal and fortnightly tidal variations as well as the seasonalvariations which hydrodynamic conditions, concentrations and salinitiesordinarily present can be eliminated or markedly filtered.

By integrating equation (1), one obtains:

C= Co +(Ce -Co)' (l-e-Kt) (2)

1

This expression is graphically represented by a family of curves, each one givingthe time variation of a point of the bottom with the initial gerieric elevation C,(Fig. 1).

The existence of a curve for each initial elevation C, enables expression (2) todescribe the evolution of a zone with different bottom elevations. The shoaling ratedecreases as elevation C increases, the evolution of erosion prone zones locatedabove natural equilibrium elevation (C> Ce) being also reproduced.

The family curves have the elevation C, as asymptote. C, represents the elevationto which all points at different depths will tend if they are let to evolve naturallyduring a sufficiently long period.

From expression (2) it may be deduced that, if the evolution of each point in a setfollows a family curve, then the mean elevation of that set will also be represented byone of the curves.

a~m

p(l

It is of interest to compare expressions (1) and (2) with other expressions andempirical methods described in the technicalliterature on this subject.

A) Lyakhnitsky and Smirnov [2] presented a shoaling coefficient similar to K.It was defined by

Se= 11 h

where S is the mean thickness of the silt layer settled to the bottom of the channelduring one year, and I1h is the thickness of the dredged layer.

B) The Balanin formula presented by Djunkovski and Smirnov [1] describes thetime variation of shoaling in a dredged channel. It can be expressed through

where:

h, is the thickness of the sediment deposit after t years; H is the channel depth; H; isthe initial natural depth; p is a coeficient characteristic of sedimentation at the placein questiono

If t= 1 year, we obtain

h p=--

H-Ho 1-p

·s that with Balanin's formula the shoaling rate (h) is proportional to the)f dredging, that is, to its depth with reference to the bottom natural

m elevation (H - H o), as established in (1).

restrelo [3] in his studies of shoaling of dredged basins in the Tagus estuary.ally fitted exponential curves expressed as in (2), to the points that showed the

~ .volution of the bottom elevation.

2

This expression is graphically represented by a family of curves, each one givingthe time variation of a point of the bottom with the initial gerieric elevation C,(Fig. 1).

The existence of a curve for each initial elevation C, enables expression (2) todescribe the evolution of a zone with different bottom elevations. The shoaling ratedecreases as elevation C increases, the evolution of erosion prone zones locatedabove natural equilibrium elevation (C> Ce) being also reproduced.

The family curves have the elevation C, as asymptote. C, represents the elevationto which all points at different depths will tend if they are let to evolve naturallyduring a sufficiently long period.

From expression (2) it may be deduced that, if the evolution of each point in a setfollows a family curve, then the mean elevation of that set will also be represented byone of the curves.

It is of interest to compare expressions (1) and (2) with other expressions andempirical methods described in the technicalliterature on this subject.

A) Lyakhnitsky and Smirnov [2J presented a shoaling coefficient similar to K.It was defined by

S10= 11 h

where S is the mean thickness of the silt layer settled to the bottom of the channelduring one year, and I1h is the thickness of the dredged layer.

B) The Balanin formula presented by Djunkovski and Smirnov [IJ describes thetime variation of shoaling in a dredged channel. It can be expressed through

where:

h, is the thickness of the sediment deposit after t years; H is the channel depth; H; isthe initial natural depth; p is a coeficient characteristic of sedimentation at the placein questiono

If t = 1 year, we obtain

h PH-Ho l-p

which shows that with Balanin's formula the shoaling rate (h) is proportional to thethickness of dredging, that is, to its depth with reference to the bottom naturalequilibrium elevation (H - H o), as established in (1).

C) Perestrelo [3J in his studies of shoaling of dredged basins in the Tagus estuaryempirically fitted exponential curves expressed as in (2), to the points that showed thetime evolution of the bottom elevation.

2

tr to K.

This author used this expression only to characterize dredged zones ofapproximately constant depth. He also considered that, contrary to the presentmethod, the shoaling coefficient depends on the dredged depth.

D) One of the empirical procedures used in USA and cited by Trawle [4Jconsiders the shoaling rate to be proportional to the area of the dredged channelsection, measured below the bottom natural equilibrium elevation. This procedureagrees with expression (1) if the section can be considered nearly rectangular, i. e.,when the channel bottom width is much larger than the width of its side slopes.

ie givingation C,

m (2) toling ratelocated

.levationiaturally

. in a setented by

From the analysis of expression (2) it can be concluded that there are twoprocedures to obtainthe values of K and C, which characterize the family of curves(Fig. 1):

ons anda) From the evolution of mean elevation of a deep zone;b) From the variation between times t1 and t2, of the elevation of a set of points of

a zone with varied depths.

c

í,

channel

ibes the1

I _

CE'----:-. C2~~~-·_·_·-

h; H; iste place

t2

Fig. 1 - Family of curves C = C, + (C. - Co) (1 - e- K~

I to thenatural

Using procedure a) one immediately extracts parameters K and C, from theexponential equation which best fits the evolution of bottom .mean elevation.

Using procedure b) parameters are obtained as follows: let t1 and t2 «. <t2) be thedates of the two surveys, and C 1 and C2 elevations at times tI and t 2 respectively.Then from (2) we have:

estuaryved the

C2 =C1 +(Ce-C1)·(1-rK(t,-t.l)

(C2-C1)=A C1 +B

1. e.

3

In case the basic assumption holds, the straight line indicated should fit shoalingat different depths. The straight line coefficients are:

andB=(l-e-K(C,-C,}). C,

From coefficients A and B one obtains parameters K and C, .

2 - APPLlCATIONS

Both procedures were applied. Procedure a) was applied to the evolution of themean elevations of two zones. Data concemed Macao outer harbour in the southcoast of China (Fig. 2) and a dredged basin in the Tagus estuary in the west coast ofPortugal.

Both sets of data correspond to periods during which no maintenance dredgingwas carried out. To these data could be fitted exponential regression curves such asthose already mentioned, and high correlation coefficients were obtained (Figs. 3 and4). Data used in Fig. 4 were taken frorn Perestrelo's works [3] referred to above.

Procedure b) was applied in three sites: three applications in a channel of Aveirolagoon (Mira channel) located in the west coast of Portugal (Fig. 5); one in a dredgedchannel in the Tagus estuary (Fig. 6); one in Macao, in the Ka-Ho experimentaldredged pit (Fig. 2). J

Fig. 2 - Location map of Macao; Macao outer harbourand Ka-Ho experimental dredged pit

4

.ling c--s. 99. c-e. Hh5. 99)( 1- e 1-0. 0S7t:)

CORR . COEFF .• e .9987e. 5·. '0. '5.

t (iEARSl20.

00 ----------------- Ce

K..••e. a87 "'(F:AR - 1Cel:-8. la •••

Fig. 3 - Application of procedurea). Macao outer harbour

-2.50

J -5.00

f theouthist of

C--9. ee. (-:3.29.9.89)( l-e -0. 947l )

lgingch asIandte.veirodgedental

.aa

CORA. CQEFF. =0. 97910. 10. 20. 3a .

(MONTHSl.a.

-S.0e

------------------~Fig. 4 - Application of procedure a) to adredged basin in the Tagus estuary

1(-0. e"17 NONHr'

Ce-J.20 m

u

Fig. 5 - Location map of Mirachannel, Aveiro lagoon

5

o 450 .••

Fig. 6 - Location map of a dredged channel in the Tagus estuary

The calculation was as follows: a mesh was established with about one thousandpoints, equally located in the two hydrographic surveys of dates t 1 and t2 to becompared; the points were grouped according to the elevation ranges of the earliersurvey; in each range the mean values of elevations C 1 and of the correspondingshoaling (C2 - C 1) were determined; the regression line best fitting the set of points sodefined was determined; parameters K and C, were determined from the coefficientsof the lines following the expressions indicated.

In Figs. 7 to 11 the results of instances of application corresponding to suchgrouping are presented. The amplitude of each range is 0.20 m.

The number of points in each range varied; that is why weighted values wereconsidered in the linear regression. This aspect is clearly shown in the example ofTable 1. Notice that the largest deviations from the fitted line were found in ranges towhich corresponded a small number of bottom points.

The hydrographic surveys were made at time intervals varying between 1 and 6years. During those intervals no maintenance dredging was made.

Linear regression was also established between variables C 1 and (C2 - C 1) byconsidering the points not grouped (Examples in Figs. 12 and 13).

Application of the procedure b) brought to light the following aspects:

- It was always possible to establish a good linear correlation between the meanvalues of depth C1 and shoaling (C2 -C1). From the line obtained one coulddeduce with dose approximation the mean shoaling for sets of pointscontained in each depth range.

6

C2-C,.-0. 454C, t 0. 770

CORR. COEFF. -0. 9929

c2-e,--0. J7ZC, -a. 517

CORR. COEFF. -0. 9774

-i.ee~Ú

J< 3.00

2 .•••

++++

1. •••

.00

-1.00

-2.00-4.0 -2.0

K-0.1ee YEAR-1

(e-1 .3' ...+.

e , • .I .I .+

IIII . .III

(el, .3' ..e 2 .e 4 .•

C, I.'

ú~ 3.00

2.00+.... .•

.+ K::00.1e2 rEAR-1

Ce-l.69",

, .ee

. 00 ---------------IIIIIIIII

cel, .69 m

-2.00+---~--~--_+~--~-4.0

-1.09

-Z.0 .0 2.0 4.0(, (m)

Fig. 7 - Application of procedure b). Mirachannel (Aveiro lagoon). Surveys: Sep.-Oct. 1975

and Sep. 1981. Range 0.20 m

Fig. 8 - Application of procedure b). Mirachannel (Aveiro lagoon). Surveys: Sep.-Oct. 1975

and Jan. 1980. Range 0.20m

usandto beearliermdingints soicients

CZ-C,--0.1B2C,t0.J6J

CORR. COEFF. _0. 9078

C2-C,--0. 069C,-0. 316

C~. COEFF. =0. 8388

+.ee

Ú

LJN 3.0a

) such2.00 2.00

~Ú

uN ,....s wereiple ofiges to

K-0.121 lEAR-1

Ce-2.00 '"1.00

.e eand 6 I

IIIIIIII

celz.ee '"·2 .•• +---~--~----=+---~

-4.0 -'.e,.,

-1.00 -1.00

-2. e .a Z.0 4.0(, (1'1'I)

-7.0 -5.a -u.eC,

e mean~ couldpoints

Fig. 9 - Application of procedure b). Mirachannel (Aveiro lagoon). Surveys: Jan. 1980 and

Sep. 1981. Range 0.20 m

Fig. 10 - Application of procedure b) to adredged channel in the Tagus estuary. Surveys:

Oct. 1978 and Nov. 1979. Range 0.20m

7

TABLE I

(2-(,--0.283C,.1.321

CORR. COEFF. -0. 8991

Application of procedure b). Mira channel (Aveirolagoon) Surveys: Sep.-Oct. 1975 and Sep. 1981.

Range O.20m

ELEVATlON RANGE! HEAN HEANELEVATION !

FI RST SURVEY !FI RST SURVEY I SHOALI NG(1"1) (H) (1"1)

2. ao!

Ú

S' 1.00

++.

-3.40-3.20-3.00

! -2.80-2.60-2.40-2.20-2.00-1.80-1.60-1.40-1.20-1.00-0.80-0.60-0.40-o .20-0.00

0.20Q.400.600.801.001. :'01.401.601.802.002.202.402.602.803.003. ~o3.403.603.80

00 ----------- .f.1'++ I

IIIIIIII

ce!·,,\.66 rn

-2.00+----,----;+.--,-9.0

-,. ao

-7 .e -6. e -3. e(, (".)

Fig. 11 - Application of procdure b). Ka-Ho(Macao). Surveys: Apr. 1974 and Apr. 1975.

Range O.20m

(2- C,--0. 464C, ~e. 71,9

CORR. COEFF. -0. 906-'1

"'\.ee!

ÚN 3. aeu .

2.08 +++

1.1313

00

-1.08 :

.69 m

-2.00+----r----.--~_.--__,-1.0 -2 .e .0 2. e .q e

c, (...)

-3.20-3.00-2.80-2.60-2.40-2.20-2.00-1.80 I

-1.60-1.40-1. ?O-1.00-0.80-0.60-0.40 I-0.20 I

-0.000.200.400.600.80 !1.001.20l.401.601.802.002.202.402.602.803.003.203.403.603.804.00

-3.35-3.09-2.90-2.71-2.59-2.27-2.08-1.91-1.69-1.'50-1.30-1.09-0.92-0.71-0.54-0.31-0.120.100.280.490.710.901.111.301.481. 711.892.082.272.442.602.873.053.33

3.80

3.311.831. 791.722.11l.581.621. 711.531. 441.401. 271. 221.111.090.940.86Q.750.650.590.460.330.180.140.040.06

-0.06-0.21-0.27-0.31-0.13-0.58-0.30-0.83

-1.00

NUHBEROF

POINTS

TOTAL NUHBER OF POINTS 1025

C2-C,--I2I. 282C,-I. J12

C~. COEFF.• 0. 5259

2.00,

U

N I eeU

••

-1.00

. -2.00 +----,-----;'-t---,-9.9 -7.0 -5 0 -3.0

(1 (",)

Fig. 12 - Application of procedure b). Mirachannel (Aveiro lagoon). Surveys: Sep-Oct. 1975

and Sep. 1981. Points not grouped

Firg. 13 - Application of procedure b). Ka-Ho(Macao). Surveys: Apr. 1974 and Apr. 1975.

Points not grouped

8

'0

1.

- Higher correlations were obtained when surveys were made at larger timeintervals.

- In the case of Aveiro lagoon for which three surveys of the same zone wereavailable, K and C, were found to take very dose values in the two successivetime intervals defined by these three surveys. In the periods 1975-80 and1980-81, K values were found to amount 0.108 and 0.121 year-1, whereas C,values were 1.39 and 2.00 m.

- A study of the distributions of deviations between shoaling values observed andthose calculated by the regression line, considering points not grouped, showedthat distributions were similar in all cases analysed regardless of the place andof the time interval between two surveys (Examples in Figs. 14 and 15).

Ninety per cent of the deviations fell in a range of ± 50 cm. It is assumedthat ± 25 em is the range of deviations corresponding to inaccuracies insurveys and in their comparison. The remainder is believed to be due to theapproximations inherent in the basic assumption which disregards theinfluence of other variables besides depth influencing the shoaling rate.

The occurrence of identical deviation distributions in all the cases analysedexplains why the correlation coefficient improved as the time interval betweentwo surveys increased. With large time intervals shoaling takes higher values,and the relative value of deviations decreases. This aspect is shown in Figs. 12and 13.

(x) 10

30

Ho75. Fig. 14 - Deviation histogram. Mira channel

(Aveiro lagoon). Surveys: Sep.-Oct. 1975 and Sep.1981. Points not grouped

2.

,.

-1.2 -0.8 -0.4 e.e 0.4 0.8

DEVIATION (m)

(11/) 40'

30

20

t e

1.2 -1.2 -8.8 -0.4 e.a 9.4 0.8 1.2

DEVIATION (m)

Fig. 15 - Deviation histogram. Ka-Ho (Macao).Surveys: Apr. 1974 and Apr. 1975. Points not

grouped

9

- The fact that high correlations are usually not found except when referred tomean values of the two variables will not permite as a rule to predict shoalingaccurately enough at a given point but only in a zone or at a numerous set ofpoints of the bottom. This limitation does not seem to be very inconvenientsince the practical purpose of the method is to predict the evolution either ofreaches only or of the whole of dredged channels and basins.

3 - CONCLUSIONS

High correlations could be established between mean values of depth and ofshoaling in different dredged zones where deposition of finer sediment fractionscarried in suspension by tidal currents occurs. ln every case data were fitted byempirically based expressions that were worked out to represent the variation ofbottom elevations with space and time.

The results of the comparison of surveys can be used to predict volumes ofmaintenance dredging of channels and basins to be established or deepened in thezone under study. It is assumed that this zone will not be subjected to long termvariations of sedimentation characteristics.

The procedure to be used for this prediction consists in the definition of thesedimentation coefficient K and equilibrium elevation Ce, based on the analysis oftwo or more surveys. Once these parameters are known, annual maintenance ratesfor ditTerent alternative dredging elevations C, can be estimated by using theexpression derived from (2), with t = 1 year.

It is worth mentioning that procedure b) requires only two surveys provided theyare carried out within and interval of at least one year during which no dredgings aremade. Such a feature makes it largely adequate to practical use due to ordinary,limitations as regards field data to characterize shoaling conditions.

REFERENCES

[1] DJUNKOVSKI, N. N. and SMIRNOV, G. S., 1957 - XIX International NavigationCongresso London. 1957. Section 11. Communication 3.

[2] LYAKHNITSKY,V. E. and SMIRNOV,G.S., 1961 - XX International Navigation CongressoBaltimore. 1961. Section 11. Subject 2.

[3] PERESTRELO,J. F., 1971 - Comportamento de canais e bacias dragados em fundos lodososde estuários. Instituto Superior Técnico. Lisboa.

[4] TRAWLE, M. L, 1981 - Effects of depth on dredging frequency. Report 2. Methods ofestuarine shoaling analysis. U. S. Army Waterways Experiment Station. Technical reportH-78-5.

10

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