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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308

(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, March - April (2013), © IAEME

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MATHEMATICAL MODEL OF RCC DAM BREAK BASTORA RCC

DAM AS A CASE STUDY

NajmObaidSalim Alghazali1

and Dilshad A.H. Alhadrawi2

(1)Corresponding author, Asst. Prof. Doctor, Civil Engineering Department, Babylon

University, Iraq. (2)

M.Sc. Student, Civil Engineering Department, Babylon University, Iraq.

ABSTRACT

This is the first study on the failure of roller compacted concrete (RCC) dams. A

mathematical model for over-stressing type of RCC dam failure is presented and a scenario

for breach formation is presented. The hypothetical failure of Bastora dam, a RCC dam

located north east of Iraq, due to overstress is selected as a case study. The reservoir outflow

hydrograph is computed using the proposed mathematical model and then the outflow is

routed downstream Bastora dam. The maximum water levels, maximum discharges and

rescue level at the available (11) sections of Bastora River downstream Bastora dam are

determined.

Keywords: HEC- RAS, level pool routing method, mathematical model for RCC dam break,

over-stressing failure, roller compacted concrete (RCC) dams

1. INTRODUCTION

ACI 207.5R [1] defines Roller-Compacted Concrete (RCC) as "a concrete of no-

slump consistency in its unhardened state that is transported, placed, and compacted using

earth and rock-fill construction equipment."ICODS [2] defines RCC damas" a concrete

gravity dam constructed by the use of a dry mix concrete transported by conventional

construction equipment and compacted by rolling, usually with vibratory rollers."

RCC is an economical method and accepted material for constructing dams and

rehabilitating and modifying existing concrete and embankment dams [1], [3], [4].The

worldwide acceptance of RCC dams is due to their low cost, reduction period of construction,

and successful performance [5].RCC dams were constructed in all types of climates and in all

types of countries from the most developed to the still developing [6].There are more than

250 RCC dams constructed throughout the world [7].

INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND

TECHNOLOGY (IJCIET)

ISSN 0976 – 6308 (Print)

ISSN 0976 – 6316(Online)

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2

RCC gravity dams are designed to the same criteria as conventional concrete (CVC)

gravity dams with respect to stability and allowable stresses in the concrete [5], [8], [9].

However, there are differences in the uplift within the body of the dam and the minimum

sliding factors of safety [9].

One significant difference between a RCC dam and a CVC dam is the continuous

placing of a horizontal lift of concrete from one abutment to the other, rather than

constructing the dam in a series of separate monoliths [3].Lift thicknesses depend on the

placement size, production capacity of the concrete batch plant, mixture proportions, and

compaction equipment [9], [10].There is no limited lift thickness used in all RCC dams. The

lift thicknesses used in RCC dams are 0.30 m (1 layer) [11], 0.60 m (composed of four 0.15

m layers) [9], 2 m (composed of eight layers of 0.25 m) [5], and 0.75 to 1 m (0.3 m layers)

[7], [12]. By the use of sloped layer method (SLM), the lift thickness is 3 to 4 m [13].

A dam is a sword of two limits [14]. It is mainly used to supply the necessary quantity

of water downstream it, generates power, and protect from flood. On the other hand flood

resulting from dam failure is considered as a national disaster and classified as first degree

accidents for the damage it causes to human life, properties and economic systems.In many

countries the determination of the wave parameters that would follow the collapse of every

large dam is demanded by law to organize the defense of inhabitants and structures in the

valley downstream [15].

For the knowledge of the researchers there is no study in literature on the failure of

RCC dams. This is the first study on the failure of RCC dams and it opens the door for further

researches.A mathematical model for over-stressing type of RCC dam failure is presented

and a scenario for breach formation is presented.

Bastora dam, located north east of Iraq, is designed as a RCC gravity dam.Fig. (1)

shows the typical section of Bastora dam. The failure of Bastora RCC dam due to over-

stressing is selected as a case study. The wave parameters that would follow the hypothetical

collapse of Bastora dam are determined.

Drainag gallery

No. of steps = 97

All steps with

s:l = 0.9m:0.63m

except the first step with

s:l = 1.1:0.77

73.62m

13mDam crest

EL. 897.5m asl

EL. 810m asl0.7

1

Detail B

0.9

0

0.9

00.9

0

1.1

0

0.630.630.77Detail B

Figure (1): Schematic view of the typical Bastora dam section (All dimensions are in meters)

[16]



3

2. OBJECTIVES OF THE PRESENT STUDY

I. Presenting a mathematical model for RCC dam break due to overstress.

II. Determining the wave parameters that would follow the hypothetical collapse of

Bastora damdue to overstress.

3. MATHEMATICAL MODEL OF CVC DAM BREAK

A study of the different conventional concrete (CVC) gravity dam failures indicates

that concrete gravity dams breach by sudden collapse, overturning, sliding away of the dam

due to inadequate design, earthquakes, enemy attack and over-stressing [17]. Failure of

concrete gravity dams are often more catastrophic, because they have less obvious symptoms

prior to failure, collapse may be very rapid, with little or no advance warning [18].

For the lack of data on the change of breach geometry with time or in order to

simplify the analysis, CVC dams’ break studies were based on the assumption of complete

(or partial) instantaneous removal of the dam [19], [20], [21]. Complete instantaneous failure

of a dam is conservative in the sense of simulating the worst possible downstream flooding

conditions but, in most cases, is unrealistic.

4. MATHEMATICAL MODEL OF RCC DAM BREAK

RCC gravity dams like CVC gravity dams, they may fail due to sudden collapse,

overturning, sliding away of the dam due to inadequate design, earthquakes, enemy attack

and over-stressing. In this study, the failure of RCC gravity dams due to over-stressing is

investigated.

According to the characteristics of RCC gravity dams, mentioned in the introduction,

it cannot be assumed that their failure due to overstressing is instantaneous but it can be

assumed gradual with a short time. The hydraulics of instantaneous and gradual collapse of a

dam is in fact quite different. Instantaneous failure of a dam causes a positive wave in the

downstream direction and a negative wave in the upstream direction. In gradual failure, the

breach dimensions grow with time and the reservoir level drops uniformly. Complete gradual

failure of a RCC dam due to overstressing can be assumed in the sense of simulating the

worst case.

To build a mathematical model for the failure of RCC gravity dams due to

overstressing, the data on the change of breach geometry with time and the breach outflow

equation are required.

In 2010, two studies for the failure of CVC gravity dams were presented. In the first

study, presented by Asrate [22], the breach width should be taken 0.2-0.5 times the crest

length of the dam and the breach development time should be about 0.2 hour. This means that

the failure of CVC gravity dams is gradual with a short time. This can be used for the gradual

failure of RCC gravity dams since for overstress failure type the breach shape and

development for these two types of dams are equal. For other types of failure such as sliding

failure type the breach shape and development for these two types of dams are not equal

because there are differences in the uplift within the body of the dam and the minimum

sliding factors of safety [9]. In the second study, presented by Welch [23], the breach

outflowof CVC gravity dams is computed by using Eq. (1):



4

�� 0.9 � � � �.� 1�

Where Qd = the discharge at the dam site (m3/s), hd = breach head (m) - defined as a depth of

water, and b = breach width (m).

This study is also for the gradual failure of CVC gravity dams. Based on the assumption that

failure of RCC gravity dams due to over stress is gradual, Eq. (1) can be used to compute the

breach outflowof RCC gravity dams.

In summary, the failure of RCC gravity dams due to overstress is gradual with a short

time. The breach outflow can be computed by using Eq. (1) and the breach width should be

taken 0.2-0.5 times the crest length of the dam and the breach development time should be

about 0.2 hour.

5. THE HYPOTHETICAL FAILURE OF BASTORA DAM DUE TO OVERSTRESS

5.1 Methodology

I. Computing the reservoir outflow hydrograph using the proposed mathematical model

with actual field data.

II. Routing the reservoir outflow hydrograph downstream Bastora dam using the

computer program HEC-RAS 3.1.3 (2005) (The Hydrologic Engineering Center -

River Analysis System) to determine the maximum discharges, maximum stages and

rescue level at selected sections of Bastora River downstream Bastora dam.

5.2 Assumptions

The following assumptions are adopted in this study:

I. The hypothetical failure of Bastora dam is due to overstressing.

II. The breach dimensions grow linearly with time.

III. The beauty of one-dimensional analysis using cross-sectional averaged flow quantities

is that the details of two-or-three-dimensional variations of these variables in the

channel can be avoided in the computation while a reasonable solution of the flow can

be obtained [24]. Therefore, the flow in Bastora River is assumed to be one

dimensional.

IV. The cross sections of Bastora River remain constant during the flood routing.

V. The Manning’s roughness coefficient (n = 0.0255) is assumed to remain constant with

time and distance along the study reach.

6. RESERVOIR OUTFLOW HYDROGRAPH

Determination of the reservoir outflow hydrograph is divided into two tasks:

I. Simulating the dam breach.

II. Routing the reservoir outflow hydrograph through the breached and outlet structures.



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6.1 Simulating the dam breach

The breach width is taken 0.2-0.5 times the crest length of Bastora dam and the

breach development time is 0.2 hour. The breach side slopes is taken equal to zero.The

breach shape develops in time from initiation to its ultimate configuration.

6.2 Routing the Reservoir Outflow Hydrograph

The reservoir outflow hydrograph is computed using the level pool routing method

[25]. The reservoir flood routing process requires determination of the following:

6.2.1 Bastora reservoir elevation-storage relationship

Eq. (2) represents the Bastora Reservoir Storage-Elevation Relationship [16]:

�� 9.669 � 10��.�801.5��.� � 2�

where: El. = reservoir water surface elevation (m asl)

Volume = volume of the reservoir (MCM) at elevation (El.)

6.2.2 The inflow and outflow from the reservoir for the initial condition

The maximum mean monthly outflow from Bastora reservoir was (21.6 m3/s) which occurred

on December 1976 [26]. This flow is assumed to be the initial inflow and outflow from

Bastora reservoir.

6.2.3 The initial elevation of the reservoir water surface before the failure

Bastora reservoir is assumed to be full to its maximum live storage capacity. This

corresponds to spillway sill level of (892.5 m asl).

6.2.4 The inflow to Bastora reservoir at failure time

The flood hydrograph of 1000 years return period computed by [16], shown in Table (1),is

selected as the inflow to Bastora reservoir at failure time.This flood hydrograph represents

the maximum instantaneous inflow hydrograph.

Table (1): Flood hydrograph for 1000 years Return Period at Bastora Dam [16]

Time

(hr)

Inflow

(CMS)

Time

(hr)

Inflow

(CMS)

0 0.0 7 97.4

1 120.9 8 43.8

2 510.0 9 18.5

3 680.6 10 7.4

4 567.0 11 2.9

5 364.9 12 0.0

6 199.4



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6.2.5 Modeling outlet works, spillway and breach flows models

It is assumed that at the onset of failure the outlets are locked for any reason. Therefore, their

flows are not modeled.The reservoir water surface elevation was assumed to be at elevation

(892.5m asl) at the onset of failure which is at the spillway sill level. Therefore, the spillway

flows are not modeled.The breach is defined by its sill elevation and width, both given as a

function of time. Eq. (1) is used to calculate breach outflow.

6.3 Bastora Dam Break Simulation

Five different cases of breach width are investigatedfor the analysis of Bastora dam

break simulations (0.2, 0.3, 0.35, 0.4, and 0.5 times Bastora dam crest length) to determine

the peak outflow. In all these five cases, the initial breach elevation is taken corresponding to

the top of Bastora dam (EL. 897.5 m asl). The final bottom elevation of the breach is taken as

(EL. 810.0 m asl) corresponding to the average foundation level of Bastora dam at the

location of the breach.

The growth of the breach is proceeded vertically down at a rate of 7.3 m/ minute until

the breach reaches its final elevation and horizontally towards the dam sides at the same rate

until the dam destroyed completely except the dam parts that lie above the reservoir water

surface elevation.

The breach parameters for the five cases of failure and discharges through the breach

are shown in Table (2). The outflow hydrographs for various breach widths are shown in Fig.

(2). Based on the results shown in Table (2), the breach parameters corresponding to case 5

are selected because the outflow is maximum which represents the worst case. For case 5,

shown in Fig. (2), after about 16 minutes from the dam failure, the peak breach outflow is

(138023.92 m3/s) and after about 99 minutes from the dam failure, the whole volume of the

reservoir is going out to the river reach, and this indicates that the reservoir was depleted at

the end of the simulation time. The breach formation is assumed to consist of two phases. The

sketch of case (5) is presented in Fig. (3).

Table (2): The Breach Parameters and Discharges

Caseno. Breach width(w)

(m)

Breach elevation(m) Max. dischargethrough the

breach (m3/s)

Initial Final

1 115.46 897.50 810.00 116218.90

2 173.19 897.50 810.00 120890.47

3 202.06 897.50 810.00 124243.07

4 230.92 897.50 810.00 128171.92

5 288.65 897.50 810.00 138023.92



7



8

7. ROUTING THE RESERVOIR OUTFLOW HYDROGRAPH DOWNSTREAM

BASTORA DAM

The (HEC-RAS) computer program is used to route the reservoir outflow hydrograph

downstream Bastora dam. This software is based on the four-point implicit finite difference

solution of the one dimensional unsteady flow equations of Saint-Venant. The derivation of

Saint-Venant equations, the continuity equation (conservation of mass) and momentum

equation (conservation of momentum) are available in most text books of open channel

hydraulics, e.g., [27], [28], [29].

The one dimensional Saint-Venant equations,after neglecting the eddy losses, wind

shear effect and lateral flow, are written as:

"�"# $ "%

"& � 0 3�

"�"& $

" �� %⁄ �"# $ )% *"+"# $ ,-. � 0 4�

where Q = discharge (L3T

-1), A = cross - sectional area of flow (L

2), z = water surface

elevation (L), x = distance along the channel (L), t = time (T), g = gravity - acceleration

constant (LT-2

), Sf = friction slope, defined as

,- � 0��

%�1 �⁄ 5�

in whichn = Manning’s roughness coefficient and R = hydraulic radius (L)

The basic data requirements for performing the one dimensional flow calculations

using HEC-RAS are classified as geometric data and hydraulic data [30].

7.1 Geometric Data

According to the available data, a reach distance along Bastora River of (14 Km)

downstream Bastora dam is considered. The site of (11) cross sections in this reach is shown

in Fig. (4).



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7.2 Hydraulic Data

7.2.1 Manning’s Coefficient

Manning’s roughness coefficient (n = 0.0255) determined by [26] is used in this study

and it is assumed to remain constant with time and distance.

7.2.2 Unsteady Flow Data

7.2.2.1 Initial Condition

As mentioned in paragraph 6.2.2, the inflow to and outflow from Bastora reservoir for

the initial condition is assumed (21.6m3/s) which is the maximum mean monthly. Therefore,

this outflow from Bastora reservoir is the initial flow for the (14 Km) reach along Bastora

River.Table (3) shows the initial water surface elevation along the study reach for the steady

flow of (21.6 m3/s).

.

Table (3): Bed Channel and Water Surface Elevation

Section

No.

Distance Downstream

Bastora Dam (km)

Channel Bed Elevation

(m asl)

Water Surface

Elevation (m asl)

1 0.00 586.20 586.72

2 1.00 575.70 576.33

3 2.50 565.40 565.64

4 4.25 554.90 555.66

5 6.00 544.70 545.27

6 7.00 534.30 534.45

7 8.50 523.90 524.71

8 10.25 513.50 514.20

9 11.50 503.10 503.83

10 12.75 492.80 493.48

11 14.00 482.40 483.47

7.2.2.2 Boundary Conditions

7.2.2.2.1 Upstream Boundary Condition

The reservoir outflow hydrograph for case (5), shown in Fig.(2), is used as the

upstream boundary condition.

7.2.2.2.2 Downstream Boundary Condition

The downstream boundary condition is a rating curve at the last section of the routed reach.

The best fit equation for the discharge - stage data at the last sectionis:

+ � 483.81 $ 0.07471 �3.� � 1.407 exp �� 6� wherez = water surface elevation (m asl) and Q = discharge (m

3/s). The coefficient of

determination (R2) for Eq. (6) is 0.997.



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8. RESULTS OF FLOOD ROUTING

The computed discharge hydrographs at the (11) sections in Bastora River are shown

in Fig. (5).The computed peak discharges, maximum water levels and their time of

occurrence at the (11) sections in Bastora River are listed in Table (4). The computed peak

discharges and the computed peak elevations at the (11) sections in Bastora River are shown

in Fig. (6) and Fig. (7)respectively.

Table (4): Peak Discharges, Water Levels and their Time of Occurrence

Section

No.

Peak Discharge

(m3/s)

Time of

Occurrence (min)

Peak Elevation

(m asl)

Time of

Occurrence (min)

1 138023.9 16 593.92 18

2 135916.1 18 591.86 22

3 126939.6 22 576.62 26

4 123507.0 26 576.01 26

5 122401.5 26 561.48 28

6 121650.9 28 548.70 28

7 120092.7 28 538.71 30

8 117398.7 30 528.54 34

9 113848.9 32 516.92 36

10 110360.9 32 508.99 38

11 103945.0 36 508.96 38



11



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Rescue level is an elevation, which is considered safe from flooding. It is usually

taken 1 to 4 meters above the maximum calculated water levels, rounded to the next full

meter [31]. The rescue level is taken 2 meters above the maximum calculated water levels,

rounded to the next full meter. Fig. (8)shows the computed rescue levels along Bastora River

for the selected sections.

9. CONCLUSIONS

I. For the hypothetical failure of Bastora Dam due to overstress, case (5) represents the

worst case because it gives maximum outflow.

II. The values of computed peak discharges and maximum water levels at the (11) sections

in Bastora River may be considered high values. The 14 Km reach downstream Bastora

Dam is flooded in a short time. These are because:

A. The inflow and outflow from the reservoir for the initial condition is taken equal to (21.6

m3/s) which is the maximum mean monthly outflow from Bastora reservoir.

B. Bastora reservoir is assumed to be full to its maximum live storage capacity before the

failure of Bastora Dam.

C. The inflow to Bastora reservoir at failure time is taken as the flood hydrograph of 1000

years return period which is the maximum instantaneous inflow hydrograph.

D. The breach development time is taken equal to 0.2 hour.

According to this, the computed peak discharges and maximum water levels at the (11)

sections in Bastora River correspond to the worst case.



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10. RECOMMENDATIONS

I. A physical model based on Bastora dam data is required to show the validity of the

proposed mathematical model.

II. In addition to the overstress failure of RCC gravity dams, they, like CVC gravity

dams, may fail due to overturning, sliding, earthquakes, or enemy attack.

Constructing physical models to investigate these types of failures will led to novel

researches into RCC dams’ failures and new insights into RCC dam breach

mechanisms.

III. The last section (section 11) floods after (36 min); therefore, peoples must evacuate

from this area before this time when the dam breaks.

IV. The rescue level ranged from (596 m asl) at section (1) to (511 m asl) at section

(11). This can be used as a rescue boundary to evacuate peoples from the areas

which are threatened by the flood wave.

V. The rescue level determined in this study should be taken into consideration when it

is planned to construct any building downstream Bastora dam.

VI. When the cross sections within Bastora reservoir are available, the hypothetical

failure of Bastora dam can be studied by using the dynamic model and the results

can be compared with the hydrologic model used in this study.

VII. Cross sections data downstream section (11) are required in order to determine the

peak discharges and maximum water levels at these sections.

VIII. Downstreamwater levels can cause backwater effects into the breach, thus reducing

the outflow considerably. Hence it is required to take into consideration the

backwater effects.

IX. It is assumed that the streambed is fixed without erosion or sedimentation. Erosion

and sedimentation simulation are needed to be investigated.

REFERENCES

[1] ACI 207.5R, “Roller-Compacted Mass Concrete",1999.

[2] ICODS, “Federal Guidelines for Dam Safety: Glossary of Terms", FEMA Publication,

1-28, 2004.

[3] ACI 309.5R, "Compaction of Roller-Compacted Concrete", 2000.

[4] Hansen, K.D., and Reinhardt, W.G., “Roller- Compacted Concrete Dams”, McGraw-

Hill, USA, 1991.

[5] ICOLD, “Roller- Compacted Concrete Dams”, Bulletin 126, ICOLD, 2003.

[6] Dunstan, M.R.H., "The State-of-the-Art of RCC Dams in 2002", Proc. of RCC Dams

Workshop in Iran: 11-22, 2003.

[7] Kimitaka, U., "Roller Compacted Concrete Dam and Utilization of Fly Ash in Japan",

k.uji @ ecomp.metro-u-ac.jp, 2005.

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2-12, 1995.

[9] USACE, “Roller- Compacted Concrete”, EM 1110- 2- 2006, 2000.

[10] USACE, "Structural Design Using the Roller-Compacted Concrete (RCC) Construction

Process", ETL 1110-2-343, 1993.



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Experience Using the Horizontally Advancing Sloped layer Construction of RCC at

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Since, UK, 1995.

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Engineering College, California State University, 2010.

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Documentation”, V. 2. 30, 2010.

[24] Xia, R. and Yen, B.C., "Significance of averaging coefficients in open channel flow

equations", J. Hydr. Div., ASCE, 120(2), 169-189, 1994.

[25] Chow, V.T., Maidment, D.R. and Mays, L.W., “Applied Hydrology”, McGraw-Hill,

New York, 1988.

[26] El Concorde Consultant Engineers, “Bastora Dam and Irrigation Project”, Planning

Report, Volume-1, Dam Planning Report, Republic of Iraq, Ministry of Water

Resources, General Directorate for Engineering Designs, 2006.

[27] Henderson, F.M., “Open Channel Flow”, Macmillan, New York, 1966.

[28] Attari, J. and Yazdandoost, F., “Hydraulics of Dams & River Structures”, A. A.

Balkema, London, 2004.

[29] Chaudhry, M.H., “Open Channel Flow”, 2nd

ed., Columbia, 2008.

[30] HEC-RAS, “User's Manual”, Version 3.1.3, USACE, Hydrologic Engineering Center,

Davis, California, 2005.

[31] Swiss Consultants, “Mosul Flood Wave”, 1984.

[32] Karim M Pathan, “Finite Element Analysis Of 99.60 M High Roller Compacted

Concrete (RCC) Gravity Dam - Special Emphasis on Dynamic Analysis” International

Journal of Civil Engineering & Technology (IJCIET), Volume 3, Issue 2, 2012,

pp. 387 - 391, ISSN Print: 0976 – 6308, ISSN Online: 0976 – 6316, Published by

IAEME.

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