GeoScience Enginee ing Vol. 69 (2023), No. 2
geoscience.cz pp. 160–178, ISSN 1802-5420
DOI 10.35180/gse-2023-0097
SEDIMENT TRANSPORT MODELING AT THE OUED FODDA
WATERSHED LEVEL USING HEC-RAS 1D SOFTWARE
Souhila BENKACI , Boualem REMINI
Blida 1 Uni e si y, Facul y o Technology, Depa men o Wa e Science and En i onmen , 9000 Blida, Alge ia
E-mail: ssbenkaci7[email p o ec ed], eminib@yahoo.
ABSTRACT
The objec i e o he cu en wo k is o de e mine he amoun o sedimen s anspo ed ups eam and a he le el
o Oued Fodda dam. The la e is conside ed one o he i s la ge dams buil in Alge ia. I ’s exposed o a se ious
sil a ion p oblem ha educes i s capaci y e e y yea . The simula ion was execu ed using he HEC-RAS so wa e,
o he pe iod a ied om Janua y 01, 2016 o Ap il 30, 2016. The modeled sec ion consis ed o abou 9999 m
leng h, subdi ided in o 141 i e s a ions dis an om each o he by 70 m. The obse a ion o he s udied i e
sec ion bed- p o ile was selec ed as a c i e ion o compa ing he esul s o he model wi h he eal alues obse ed.
A oughness coe icien o 0.031 was used. A quan i a i e es ima e wi h a de e mina ion coe icien , R2, o 0.92
was used o suppo he alidi y. The mass and concen a ion o sedimen s inc eased signi ican ly in he c oss-
sec ions loca ed a he dam ups eam. A o al cumula i e mass was es ima ed a app oxima ely 712699 ons, jus
ups eam o he dyke, and a maximum concen a ion o 22.35 g/l was obse ed, pa icula ly o h ee main sec ions
selec ed ups eam o he Fodda wadi. Howe e , a he ese oi le el, he concen a ion a iabili y is obse ed
du ing lood pe iods, i.e., only o he mos impo an lows.
Keywo ds: GIS; HEC-RAS; Oued Fodda dam; Sedimen anspo ; Sil a ion.
1 INTRODUCTION
Due o i s impo ance, he anspo o solid ma e ials is a majo p oblem in he Magh eb coun ies [1]. In Alge ian
i e s, his p oblem has always a isen in an acu e way. Due o he lack o da a, i s assessmen emains complex.
The eno mous quan i ies o sedimen s anspo ed a e a he o igin o he p og essi e educ ion o he ese oi s
s o age capaci y. In ac , a ound 65 million cubic me e s o sil is deposi ed annually in Alge ian dams [2]. The
a ious ba hyme ic su eys e ec ed du ing he pe iod (1986–2008) by he Na ional Agency o Dams and
T ans e s (ANBT) on all 59 dams in exploi a ion e ealed ha he olume los h ough sil ing was 898 mm³, i.e.
13.4% o he o al ese oi s olume [3–4].
Nume ous me hods o es ima ing solid anspo exis in he li e a u e, including models ha explo e physical
laws such he S . Venan equa ion o he liquid phase, and he anspo equa ions o he solid phase [5]. Al hough
hey ai h ully ep esen anspo phenomena, hese models equi e he in oduc ion o a la ge numbe o
pa ame e s. Ma hema ical models ha e been de eloped using h ee app oaches: empi ical models, which ela e
he low o sedimen o he ou all, he a ious clima ic and biophysical explana o y a iables [5]. I s majo
disad an age is he di icul y o i s calib a ion o la ge basins [6]. Reg essi e models ( low-TSS) deduced om
he a io, be ween he obse ed low, he alues o he suspended solids concen a ion (Le ki , 2009), and he
concep ual models, which conside e osion dynamics. These models ha e he ad an age o es ima ing lows o
di e en ime s eps, bu hey equi e a ela i ely long calib a ion pe iod, and peaks in TSS concen a ion which
a e gene ally unde es ima ed [7].
Resea ches has in ensi ied and expanded o es ablish new me hods: 1D models, nume ous 2D models and inally
3D models, which ha e been de eloped o simula e sedimen anspo p ocesses [8]. In iew o his, ou wo k is
161
GeoScience Enginee ing Vol. 69 (2023), No. 2
geoscience.cz pp. 160–178, ISSN 1802-5420
DOI 10.35180/gse-2023-0097
a pa o a one-dimensional solid ma e ial anspo modeling using he HEC-RAS so wa e. This code was c ea ed
by he U.S. A my Co ps o Enginee s and has been employed by se e al enginee ing i ms and go e nmen al
o ganiza ions [9]. I calcula es he sedimen anspo capaci y associa ed wi h each c oss-sec ion as a con ol
olume o all g ain sizes [10]. The Wadi Fodda sub-wa e shed was selec ed o his s udy. This basin is exposed
o a majo p oblem o soil deg ada ion, which accele a es he sil ing phenomenon a he le el o he Wadi Fodda
dam. The la e is conside ed one o he i s la ge dams buil in Alge ia. I ’s in ended o he i iga ion o he
Middle Cheli pe ime e [11]. I s s o age capaci y has dec eased conside ably o e he las 18 yea s. The sil a ion
a e has been es ima ed a abou 54.29% and he ba hyme ic condi ion o he ese oi has become e y wo ying
[12].
2 STUDY AREA
The Uppe and Middle Cheli wa e shed is loca ed in he wes o he Fodda Wadi basin, which is co e ing a
su ace a ea o 1153.5 km2. The la ge Cheli wa e shed, which is in he no hwes e n Alge ia, is mos ly occupied
by he la e and loca ed in i s no heas e n po ion (Fig. 1).
Figu e 1. Oued Fodda wa e shed
The Oued Fodda sub-basin has a conside able elie , an elonga ed shape (Fig. 2), and a highes poin can each
1950,7 m [13]. Wi h 282 empo a y wadis and 81 pe manen wadis o aling oughly 1053.45 km and 897.16 km,
espec i ely, i ea u es a complex hyd og aphic ne wo k. I is mos ly d ained o e a 92.14 km leng h by he Oued
Rouina [11]. Ou s udy a ea is exposed o a se ious p oblem o soil deg ada ion. Gully e osion has been iden i ied
owa ds he ups eam o he basin [14] (Fig. 3). This is a he o igin o an impo an p oduc ion o sedimen , which
accele a es he sil ing p ocess a he le el o he Wadi Fodda dam ese oi (Figs. 4 and 5). I collec s an annual
olume o sil o 3.2 million m3 [15]. An annual loss o i s s o age capaci y has been es ima ed o be abou
4,248 km3, i.e. a sil ing a e o 45.43% in 2015 [13].
162
GeoScience Enginee ing Vol. 69 (2023), No. 2
geoscience.cz pp. 160–178, ISSN 1802-5420
DOI 10.35180/gse-2023-0097
Figu e 2. Hypsome ic Oued Fodda wa e shed map
Figu e 5. Vase deposi ups eam o he Oued Fodda dam (Pho o: Benkaci, Augus 2017)
Figu e 3. Gully o ma ion a he Oued
Fodda wa e shed
Figu e 4. Oued Fodda dam ese oi iew wi h an
ini ial capaci y o 228 Mm3 (Pho o: Remini, 2008)
163
GeoScience Enginee ing Vol. 69 (2023), No. 2
geoscience.cz pp. 160–178, ISSN 1802-5420
DOI 10.35180/gse-2023-0097
The physiog aphic cha ac e is ics o he Oued Fodda sub-wa e shed we e calcula ed based on A cGisTM so wa e
[16] and summa ized in Table 1 below:
Table 1. Physiog aphic cha ac e is ics o he Oued Fodda sub-basin
Cha ac e is ics
Value
Obse a ion
A ea (km2)
1153.5
-
Compac ness index Kc
1.74
he basin is elonga ed a o ing slow low o uno
Max. Al i ude (m)
1950.7
Highes poin o he basin
A e age Al i ude (m)
709.40
-
Median Al i ude (m)
750
Rep esen s 50% o he o al su ace a ea o he basin
Minimal Al i ude (m)
142
Wa e shed ou all
Equi alen ec angle leng h (km)
93.144
-
Equi alen ec angle wid h (km)
12.384
-
Mean slope index Imoy (%)
1.72
-
Global slope Index Ig
0.1
S ong elie
D ainage densi y Ds (m)
328.16
-
3 MATERIALS AND METHODS
A he Wadi Fodda dam ese oi , he HEC-RAS p og am was p ima ily used o model he anspo o sedimen .
I enables o all g ain sizes and a con ol olume calcula ion o he anspo capaci y associa ed wi h each c oss-
sec ion (Fig.6). The Exne equa ion, also known as he mass conse a ion and he sedimen con inui y equa ion,
p o ides he ounda ion o i s basic idea [10]:
(1−𝜆𝑝)𝐵 𝜕𝜂
𝜕𝑡 =−𝜕𝑄𝑠
𝜕𝑥 (1)
whe e:
𝜆𝑝 po osi y o ac i e laye ,
B channel wid h [m],
𝜂 channel ele a ion [m],
𝑄𝑠 sedimen load anspo ed [m3/s],
X dis ance [m],
T ime [s].
Figu e 6. Con ol olume used in HEC-RAS sedimen calcula ions [17]
164
GeoScience Enginee ing Vol. 69 (2023), No. 2
geoscience.cz pp. 160–178, ISSN 1802-5420
DOI 10.35180/gse-2023-0097
3.1 Model inpu pa ame e s
The calcula ion o sedimen anspo ups eam and a he Fodda Wadi Dam equi es h ee inpu da a iles, as
shown in Fig. 7.
Figu e 7. Me hodological diag am o he inpu pa ame e s in he HEC-RAS model
The Manning’s coe icien is he mos impo an pa ame e o be adjus ed in he calib a ion o he HEC-RAS
model. The use o a single Manning’s coe icien may no be su icien and adequa e o ep esen he ue oughness
o a i e unde di e en low condi ions [18]. Due o assump ions in he da a o he model limi a ions, no model
will gi e indings ha a e exac ly in line wi h he eal esul s. Bu i is necessa y o achie e a easonable co ela ion
be ween obse ed alues and model ou comes [10].
Fo ou model, he adjus men o he Manning coe icien is pe o med ollowing he hyd aulic simula ion o he
uns able low o e a pe iod om Janua y 01, 2016 un il Ap il 30, 2016. The wa e su ace ele a ions (WSEl)
associa ed wi h he measu ed low a es and he ou pu low a es es ima ed by he HEC RAS so wa e a e
compa ed as pa o he calib a ion p ocedu e. The alues o he obse ed (measu ed) liquid lows a e based on
he daily liquid lows ob ained a he le el o he Oued Fodda dam di ec ion du ing he conside ed pe iod. Se e al
oughness alues we e es ed: 0.030, 0.031, 0.032, 0.033, 0.034 and 0.035. The Manning alue e ained ( o which
he e o is minimal) is equal o 0.031 [13].
3.1.1 Geome ic Da a
The geome y o he s udied sec ion was ini ially c ea ed in A cGisTM using a o m o digi al geog aphic ec o
da a “TIN” (Fig. 8) ex ac ed om he SRTM Wo ldwide Ele a ion Da a (3 a c second Resolu ion 90 m) o he
Oued Fodda wa e shed (Fig. 9). These da a a e hen expo ed using he HEC-GeoRas so wa e and isualized
h ough he “Geome ic Da a” window (Fig. 10) wi h he HEC-RAS so wa e [13]. The modeled sec ion was
app oxima ely 9999 m in leng h ، subdi ided in o 141 i e s a ions o app oxima ely 70 m pe pa . Sec ion 69 is
loca ed downs eam (immedia ely ups eam o he Wadi Fodda dam) a a dis ance o abou 50 m (Fig. 11). On he
o he hand, sec ion 9945 is loca ed ups eam. I is he e o e, conside ed as he i s sec ion o he ups eam Oued
Fodda.
Model inpu pa ame e s
Geome ic Da a
-
Image Shu le Rada Topog aphy
Mission (SRTM)
T iangula ed i egula ne wo k (TIN)
Flow Da a Daily liquid low a es
Mean slope
Sedimen Da a
Ini ial condi ions and anspo pa ame e s
Bed g ada ion
Sedimen bounda y condi ions

165
GeoScience Enginee ing Vol. 69 (2023), No. 2
geoscience.cz pp. 160–178, ISSN 1802-5420
DOI 10.35180/gse-2023-0097
Figu e 8. T iangula ed i egula ne wo k (Tin) o he Oued Fodda wa e shed
Figu e 9. Shu le Rada Topog aphy Mission image, SRTM Wo ldwide Ele a ion Da a (3 a c second
Resolu ion) o he Oued Fodda wa e shed
166
GeoScience Enginee ing Vol. 69 (2023), No. 2
geoscience.cz pp. 160–178, ISSN 1802-5420
DOI 10.35180/gse-2023-0097
Figu e 10. Geome ical da a window isualized h ough a Google Ea h image
Figu e 11. Cha ac e is ics o he ups eam c oss-sec ion (69) o he Oued Fodda Dam dike
167
GeoScience Enginee ing Vol. 69 (2023), No. 2
geoscience.cz pp. 160–178, ISSN 1802-5420
DOI 10.35180/gse-2023-0097
3.1.2 Flow da a and bounda y condi ion
The simula ion o sedimen anspo begins wi h he c ea ion o a quasi-uns able low ile. Two bounda y
condi ions a e conside ed (Fig. 12).
• The i s is selec ed a he i s c oss sec ion o he Fodda wadi (sec ion 9945). Fo his condi ion, he da a
o he daily liquid lows obse ed a he dam ups eam ha e been in oduced wi h a ime s ep o 12 days
conside ing he du a ion o he simula ion, which uns om Janua y 1, 2016 o Ap il 30, 2016.
• The second bounda y condi ion is loca ed a he downs eam (wadi Fodda dam dike). I simply
co esponds o he alue o he a e age slope (0.0242) a he le el o he c oss-sec ion conside ed (sec ion
69).
Figu e 12. HEC-RAS window o he quasi-uns able low bounda y condi ions
The ob ained low hyd og aph (Fig. 13) illus a es he occu ence o wo majo loods in Ma ch 2016. The i s is
obse ed on Ma ch 12, co esponding o a low a e o abou 27 m3/s, and he second is obse ed on Ma ch 20
wi h an es ima ed low a e o 20.66 m3/s.
Figu e 13. Flow hyd og aph
168
GeoScience Enginee ing Vol. 69 (2023), No. 2
geoscience.cz pp. 160–178, ISSN 1802-5420
DOI 10.35180/gse-2023-0097
3.1.3 Sedimen s da a
The sedimen da a ile is based on h ee main inpu quan i ies. These a e illus a ed in Fig. 14.
Figu e 14. Me hodological diag am o he sedimen da a ile
3.1.3.1 Bed g ada ion
The "bed g ada ion" da a ile is based on he esul s o he G anulome ic analysis (Table 2). Samples we e
collec ed om se e al segmen s along Wadi Fodda, jus a he dam ups eam. The g anulome ic analysis sample
was e ec ed a he Na ional Labo a o y o Habi a and Cons uc ion (LNHC) o Oued Sama (Algie s). The cu e
is ep esen ed in Fig. 15.
Figu e 15. G ading cu e o he sample aken along he ups eam sec ion
o he Oued Fodda dam
Sedimen Da a
Ini ial condi ions and
T anspo pa ame e s
T anspo
Func ions
Bed e olu ion
Func ions
Sedimen a y
Sedimen a ion a e
Bed
G ada ion
G anulome ic
Analysis
Sedimen bounda y
condi ions
Ra ing cu e
Solid Flow
175
GeoScience Enginee ing Vol. 69 (2023), No. 2
geoscience.cz pp. 160–178, ISSN 1802-5420
DOI 10.35180/gse-2023-0097
Figu e 24. Tempo al concen a ion a iabili y a he ups eam sec ions o he Fodda Wadi Dam
Figu e 25. Tempo al concen a ion a iabili y a he Wadi Fodda Dam

176
GeoScience Enginee ing Vol. 69 (2023), No. 2
geoscience.cz pp. 160–178, ISSN 1802-5420
DOI 10.35180/gse-2023-0097
The spa ial a ia ion p o ile o he sedimen concen a ion can be displayed o du a ion o simula ion. A e y
signi ican a ia ion is obse ed a he ups eam c oss-sec ions o he Fodda wadi and also a he sec ions om he
downs eam. An example is illus a ed (Fig. 26) conside ing he wo loods: 23 Janua y and 2 Feb ua y 2016. The
maximum alue o he sedimen concen a ion was es ima ed a ound 6736.267 mg/l o he Janua y 23 d lood and
12278.532 mg/l o he Feb ua y 2nd lood.
Figu e 26. Spa ial sedimen concen a ion a iabili y (Example o : 23 Janua y and 02 Feb ua y 2016 loods)
5 CONCLUSION
HEC RAS so wa e was used o model solid anspo a he Fodda Wadi dam ese oi . Once all o he pa ame e s
we e se o wi hin hei use ul anges, he model wo ked as expec ed. The obse a ion o he bed p o ile was chosen
as a s anda d o con as ing he ou pu o he model wi h he ac ual alues ha we e obse ed. Also he R2, which
is equal o 0,92, is he coe icien o de e mina ion ha suppo ed he alida ion. This demons a es s ong
conco dance be ween model p edic ions and ac ual da a. We can he e o e accep ou model as sui able o
simula ing sedimen a y anspo in one dimension. The ba hyme ic le ees a Alge ian ese oi s a e a ely
pe o med. The employed me hod is especially use ul o wa e sheds missing ba hyme ic da a o wi hou
hyd ome ic s a ions ups eam o dams.
ACKNOWLEDGEMENT
I would like o add ess a g ea hanks o he Algie s di ec ion o dams and ans e s (ANBT), o he chie o
exploi a ion and all he s a o he Oued Fodda dam, who acili a ed my access o he Oued Fodda dam and who
pu a my disposal all he necessa y echnical and ope a ing da a, and who accompanied me pa icula ly, o he
eco e y o he samples o sil a he le el o he dam and a he le el o he wadis loca ed ups eam.
REFERENCES
[1] MEDDI, M. Con ibu ion à l’é ude du anspo solide en Algé ie du No d [Con ibu ion o he s udy o solid
anspo in no he n Alge ia]. La hyss Jou nal. 2015, no. 24, pp. 315–336. ISSN 1112-3680. A ailable a :
h ps://la hyss.ne /ojs/index.php/la hyss/a icle/ iew/346
[2] REMINI, B. and D. BENSAFIA. (2016). En asemen des ba ages dans les égions a ides [Sil a ion o dams
in a id egions: Alge ian examples]. La hyss Jou nal. 2016. no. 27, pp. 63–90. ISSN 1112-3680. A ailable
a : h ps://la hyss.ne /ojs/index.php/la hyss/a icle/ iew/450
177
GeoScience Enginee ing Vol. 69 (2023), No. 2
geoscience.cz pp. 160–178, ISSN 1802-5420
DOI 10.35180/gse-2023-0097
[3] TOUAHIR, S., A. ASRI, B. REMINI & S. HAMOUDI. P édic ion de l’é osion hyd ique dans le bassin
e san de l’oued Zeddine e de l’en asemen du ba age Ouled Mellouk (No d-Oues algé ien) [P edic ion
o wa e e osion in wadi Zeddine wa e shed and he sil ing o he Ouled Mellouk Dam (No h-Wes o
Alge ia)]. Géomo phologie: Relie , P ocessus, En i onnemen . 2018, ol. 24(2), pp. 167–182. ISSN 1957-
777X. DOI: 10.4000/geomo phologie.12083
[4] MINISTRY OF WATER RESOURCES REALIZATION. Sil a ion o dams. MEDA p og am o he
Eu opean Union – Di ec o a e o hyd aulic s udies and de elopmen . 2010, ol. 3.
[5] LEFKIR, A. Modélisa ion du anspo solide pa les modèles neu o lous [Modeling o solid anspo by
neu o lous models]. Alge , 2009. Doc o al hesis. Ecole Na ionale Poly echnique, Dépa emen
d'Hyd aulique.
[6] RASSI, W. Le anspo solide: es ima ion e mesu e [Solid T anspo : Es ima ion and Measu emen ].
Limoges: O ice in e na ional de l’eau, 2004.
[7] PICOUET, C., B. HINGRAY & J.C. OLIVRY. Empi ical and concep ual modelling o he suspended
sedimen dynamics in a la ge opical A ican i e : he Uppe Nige Ri e basin. Jou nal o Hyd ology.
2001, ol. 250(1–4), pp. 19–39. ISSN 0022-1694. DOI: 10.1016/S0022-1694(01)00407-3
[8] GHARBI, M. É ude des inonda ions e du anspo de sédimen s associé – applica ion au bassin e san de
la Medje da [S udy o loods and associa ed sedimen anspo – applica ion o he Medje da wa e shed].
Toulouse, 2016. Doc o al hesis. Uni e si é de Toulouse, Ins i u Na ional Poly echnique de Toulouse.
A ailable a : h ps://oa ao.uni - oulouse. /17382/
[9] ÉCOLE DE TECHNOLOGIE SUPÉRIEURE. HEC-RAS Ri e Analysis Sys em Guide de labo a oi e:
Exemple pou la i iè e du Loup [Example labo a o y guide o he Ri iè e du Loup]. Ve sion 3.1.3, CTN-
762 Ressou ces hyd iques. Quebec: Uni e si y o Quebec, École de echnologie supé ieu e, Dépa emen de
Génie de la cons uc ion.
[10] BEEBO, Q.N. & R.A. BILAL. Simula ing ba hyme ic changes in ese oi s due o sedimen a ion.
Applica ion o Sakuma dam, Japan. Lund, Sweden: Lund Uni e si y, Depa men o Building and
En i onmen al Technology, Di ision o Wa e Resou ces Enginee ing, 2012. A ailable a :
h ps://lup.lub.lu.se/luu /download? unc=downloadFile& eco dOId=3051998& ileOId=3052010
[11] AGENCE DU BASSIN HYDROGRAPHIQUE CHELIFF-ZAHREZ. Cadas e hyd aulique du bassin
hyd og aphie du Cheli – A al du ba age de Boughzoul [Hyd aulic cadas e o he Cheli hyd og aphic
basin – Downs eam o he Boughzoul dam. Chle : ABH CZ, 2004.
[12] Rappo echnique du ba age oued Fodda, Wilaya De Chle . 2004.
[13] BENKACI, S. Impac du anspo solide su l’é olu ion des dépô s boueux dans les ba ages [Impac o
solid anspo on he e olu ion o muddy deposi s in dams]. Blida, 2020. Doc o al hesis. Uni e si é Saad
Dahlab de Blida, Facul é de Technologie, Dépa emen de Science de l’Eau e En i onnemen .
[14] BENKACI, S., D. ABIR, A. OUMELLAL & B. REMINI. Modélisa ion de l’é osion du bassin hau e moyen
Cheli pa l’applica ion Model builde su A cGis [Modeling o he e osion o he uppe and middle Cheli
basin by he Model builde applica ion on A cGis]. Jou nal o Ma e ials and Enginee ing S uc u es. 2018,
ol.5(1), pp. 81–93. ISSN 2170-127X. A ailable a :
h ps:// e ue.umm o.dz/index.php/JMES/a icle/ iew/1676
[15] REMINI, B. & W. HALLOUCHE. E olu ion de l’en asemen du ba age d’Oued El Fodda (Algé ie)
[E olu ion o he sil ing up o he Oued El Fodda dam (Alge ia)]. Wasse Ene gie Lu / Eau éne gie ai /
Acqua ene gia a ia. 2007, ol. 99(1), pp. 75–78. ISSN 0377-905X. A ailable a : h ps://www.e-
pe iodica.ch/cn mng?pid=wel-004%3A2007%3A99%3A%3A414
[16] ESRI. A cGis 10.2.1 o desk op [so wa e]. Janua y 29, 2019. A ailable a : h ps://suppo .es i.com/en-
us/pa ches-upda es/2019/a cgis-10-2-1- o -desk op-engine-se e -u ili ies-and- -7680
[17] BRUNNER, G.W. HEC-RAS Ri e Analysis Sys em Use ’s Manual. Ve sion 4.1, CPD-68. Da is, CA: US
A my Co ps o Enginee s, Hyd ological Enginee ing Cen e (HEC), 2010. A ailable a :
h ps://www.hec.usace.a my.mil/so wa e/hec- as/documen a ion/HEC-RAS_4.1_Use s_Manual.pd
[18] ENVIRONMENTAL CONSULTING & TECHNOLOGY. Appendix I: HEC-RAS Modeling o Rainbow
Ri e . MFL Technical Suppo – F eshwa e S eam. Final Repo . Tampa, FL: En i onmen al Consul ing
& Technology, Inc., 2017. A ailable a : h ps://www.sw wmd.s a e. l.us/si es/de aul / iles/documen s-and-
epo s/appendix/Appendix_I.pd
[19] BRUNNER, G.W. HEC-RAS, Ri e Analysis Sys em Hyd aulic Re e ence Manual. Ve sion 4.1, CPD-69.
Da is, CA: US A my Co ps o Enginee s, Hyd ologic Enginee ing Cen e (HEC), 2010. A ailable a :
h ps://www.hec.usace.a my.mil/so wa e/hec- as/documen a ion/HEC-RAS_4.1_Re e ence_Manual.pd
[20] BRUNNER, G.W. HEC-RAS, Ri e Analysis Sys em Hyd aulic Re e ence Manual. Ve sion 5.0, CPD-69.
Da is, CA: US A my Co ps o Enginee s, Hyd ologic Enginee ing Cen e (HEC), 2016. A ailable a :
178
GeoScience Enginee ing Vol. 69 (2023), No. 2
geoscience.cz pp. 160–178, ISSN 1802-5420
DOI 10.35180/gse-2023-0097
h ps://www.hec.usace.a my.mil/so wa e/hec- as/documen a ion/HEC-
RAS%205.0%20Re e ence%20Manual.pd
[21] JIMENEZ, J.A. & O.S. MADSEN. A Simple Fo mula o Es ima e Se ling Veloci y o Na u al Sedimen s.
Jou nal o Wa e way, Po , Coas al, and Ocean Enginee ing. 2003, ol. 129(2), pp. 70–78. ISSN 0733-950X.
DOI: 10.1061/(ASCE)0733-950X(2003)129:2(70)