Analysis of the Influence Relationship for the Earth Dam-Break

Outflow Estimation Parameters

Liu Jie

, Xu Jiajun, He Hujun and Li Xuewei

School of Civil and Building Architecture Engineering College of Pan Zhihua University,

No.10 Airport Road, PanZhihua, China

Keywords: Dam-Break, Breach Outflow, Breach Width, Breach Water Surface Velocity, Breach Water Depth.

Abstract: In order to exploration the relationship between breach hydrograph and other breach parameters, a series earth

dam-break experimental with spatial breach overtopping tests were conducted in an 4m wide, 50m long and

2m high with glass side-walls flume at the State Key Laboratory of Hydraulics and Mountain River

Engineering of Sichuan University. An industry camera and two digital video recorders were used to record

the dam breach process, and the Large-Scale Particle Image Velocimetry (LSPIV) technique was introduced

to measure water surface velocity of dam breach. The results showed that the dam breach process can be

divided into two stages, the main feature of first stage was “headcut” while the second stage was“surface”

erosion. The length rate of CSC and CS was approximately 0.85 at peaking discharge moment in the present

study. The breach hydrograph may be the function of breach water width and breach water velocity. The

breach water depth can be estimated by using

() () ()tan

cw c d

ht z t X t z

=+ −

, and the breach depth at 100s

was approximately equal to 13cm based on this formula. The time of breach peak discharge was nearly the

same as the breach width reach the maximum. However, there was about 30s time lag for breach peak

discharge relative to time of peak breach water surface velocity

1 INTRODUCTION

The earth dams have served mankind as hydropower

generating industry, water supply, irrigation systems

and flood control. If the inflow exceeds the storage

capacity of the reservoir and/or the spillway design in

the time of cloudburst, the dam-break may happen

and the rushing flood would cause damage and

disruption to people and economies. (Wang and Chen,

2010).

Over the past several decades, the model of

estimating the earth dam failures discharge due to

overtopping has been developed, mainly using

mathematical techniques. Besides, many researchers

attempted to find a general formula to describe the

time history of breach hydrograph, since the

hydrograph can be used to predict the downstream

flood levels and discharges routing (Singh 1996;

Hanson et al., 2005). Such formulas for dam

breaching according to the basis of data from dozens

https://orcid.org/0000-0003-0947-5590.

Liu Jie(1986-), man, Doctor, Associate professor, Mainly

engaged in dam-break and disaster research

of historic dam failures were called parameter

method. The common parameters include reservoir

volume, reservoir water depth, breach width, breach

shape, breach water velocity and so on (Wu, 2011).

The advantages of parameter method are quick and

easy and can be used to estimate real-time discharge.

For example, Coleman et al.(2002) proposed the

concept of “curved section”, which was the highest

points of the inlet of breach channel (Coleman et al.,

2002). In this cross-section, the hydrograph was

related to the water height above the breach channel

during dam failure process. However, the reservoir

water level for all of Coleman’s experiments were

considered keeping constant during whole dam-break

process. In other words, Coleman ignored the effects

of the reservoir volume. Following Coleman’s

research, Al-Riffai (2014) conduct a series

experiments to estimate the width of “curved

section”. Since the shape of “curved section” was not

a straight line, Al-Riffai (2014) assumed the shape to

be a circular, and then the distance ratio of curved line

150

Jie, L., Jiajun, X., Hujun, H. and Xuewei, L.

Analysis of the Inﬂuence Relationship for the Earth Dam-Break Outﬂow Estimation Parameters.

DOI: 10.5220/0011950300003536

In Proceedings of the 3rd International Symposium on Water, Ecology and Environment (ISWEE 2022), pages 150-155

ISBN: 978-989-758-639-2; ISSN: 2975-9439

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

and straight line and how the “curved section”

influence the breach discharge was discussed (Al-

Riffai, 2014). Walder et al. (2015) employed the

photogrammetric method to measure the “curved

section” shape, believing the vertical cross section

was a parabolic, and obtained a discharge estimating

formula that based on area of “curved

section”(Walder et al., 2015). Liu et al. (2021) used

LSPIV technology to measure the surface velocity of

“curved section”, analysing the effects of different

vertical velocity profile approximation and

suspended sediment concentration (Liu et al., 2021).

However, very few work have carried to investigation

the relationship between breach hydrograph and other

breach parameters, especially whether the peak time

for those parameters are synchronized. In order to

better understanding this relationship, a series earth

dam-break experimental with spatial breach

overtopping tests were conducted, and the focus of

this paper was to analyse the experiments data and

provides the research basis for the following

manuscript.

2 EXPERIMENTAL SETUP

The experiments flume was built in Jiang’an campus

of Sichuan University, and the scale was 4m in width,

2 m in height and 40 m in length with a concrete bed.

The flume side walls were built using bricks and

concrete with glass view windows at the middle

centre. The model dam was an isosceles trapezoid

homogenous sand dam, with the 0.05 m depth initial

breach through the middle of dam crest. The dam

height is 50 cm, top width is 50 cm and the bottom

width is 250cm. Two pressure transducers labeled

Y0043, Y0044 were deployed to measure the time

history of water depth along the flume. In addition,

two industrial cameras labeled CCD1 and CCD2, and

one high speed digital cameras labeled DV1 were

used to record the dam break process. The schematic

views of the whole flume and the photo image of

experiment field were shown as Figure 1. The inflow

to the reservoir was supplied by two symmetry

channel and measured with a Sharp-crested weir at

upstream of reservoir after all the equipment were

ready. The inflow discharge stabilized quickly until

the water level rail up to 40cm and then maintained at

a relatively constant flow of about 0.00167m3/s for

all tests. Once the upstream water level reaches and

overtops the dam crest, the dam breach process

commences. In order to obtain the water surface

velocity based on LS-PIV technology, the scraps of

paper with 1cm by 1cm in size and white in colour

were throw into reservoir as tracers to visualize the

flow pattern when the test begins.

(a)Schematic view of whole experiment field

(b) The photo image of whole experiment field

Figure 1: The schematic views of the whole flume and the

photo image of experiment field

3 OBSERVATION AND

DISCUSSION

3.1 Dam Breaching Process

Snapshots of the breach development in the idealized

dam are captured and presented in Figure 2. The

starting time of dam-break was defined as the water

flows through the initial breach channel and reached

the dam toe (Figure 2(0s)). In the early stage of dam

failure, since the discharge was too small, the most of

water was permeated into dam and the sand can’t be

moved far away, the initial breach flow resulted in

sheet and rill erosion in downstream slope, a large

amount of sand accumulate at the toe of dam and

formed a deposition fan. This phenomenon would last

until the time of 50s. During this stage, the depth

erosion was faster than width erosion at downstream

but at crest the depth erosion and width erosion was

nearly the same (Figure 2(30s)). Observations from

other researcher’s laboratory experiments and case

studies suggest that the earth dam breaching

mechanism for the typical overtopping erosion model

relay on dam material and compaction, which is head-

cut erosion for cohesive earth dam while progressive

surface erosion for non-cohesive dam, but there are

no strict definition for the transition point between

surface erosion and head-cut (Hanson et al., 2005).

CCD1 CCD2

DV1

Reservoir

0.5m

1.5m

22.25m 0.5m

Side view

YL0044

YL0043

Reservoir

Plan view

2.5m

Analysis of the Inﬂuence Relationship for the Earth Dam-Break Outﬂow Estimation Parameters

151

Referring this definition, the head-cut was the main

feature for the stage of 0s~50s of our experiments.

Erosion further advanced form downstream slope to

upstream, resulting the dam crest width decreasing.

The breach side wall mass failure often interdicted

breach flow. When the head-cut sheet advanced to the

water line on the upstream slope of the dam, the

breach outflow increased significantly. From this

moment, the breach inlet enlarge rapidly, a large

amount of water swarmed into breach, the carrying

sand ability enhances, the breach erosion model was

changed from “head-cut” into “surface” erosion

(Figure 2(80s~480s)). Therefore, the breach erosion

model is not only related to the material and

compaction, but also be related to breach outflow.

(a) The first stage of breach deformation process

(b) The second stage of breach deformation process

Figure 2: The breach deformation process of two stages

3.2 The Parameters of Breach Outflow

Estimation

Many researchers attempted to investigation the

common parameters to quantify the breach outflow.

According to Coleman, the best cross-section for

calculate real-time discharge is at the “curve section”

(Coleman et al., 2002). Generally, the breach

discharge can be defined as

out

QAV=

(

was average

cross-section area,

was average water velocity).

While the average cross-section can be express as

ABh=

(

was average length of breach width,

was average breach water depth), and the average

water surface was often the function of water surface

velocity. Therefore, the breach discharge can be

estimated as

()

out surf

QBhfu=⋅

(

urf

was the water

surface velocity)(Mahmoud et al., 2022).

3.2.1 The Length of “Curve Section”

The length of “curve section” was difficult to measure

directly since its irregular shape (Figure 3). One of the

common methods was using other distance to replace

it. For example, the dash line in Figure was the “curve

section”(CS), which can be replaced by the dot dash

line or solid line. The dot dash line was the chord of

“curve section”(CSC), the solid line was breach water

width at initial breach inlet position(IB). The location

of dash line and dot dash line moving upstream but

the solid line stood still during whole dam-break

process.

Figure 3: Sketch of different breach length location

Coleman’s study showed the length of “curve

section” was the function of time while not the

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152

sediment, the function was

30.616

1.29 10 ( )Lt

−

=×

(

was dimensionless length,

was dimensionless

time). For the present experiment, we measured the

time history length of these three lines, and compared

the experiments data with Coleman’s function dada,

which was shown Figure 4. It found that the

calculated data fitting to the CSC data better than CS

data and IB data before 120s. However, the calculated

data separated a lot to all experiments data after 120s.

This was because Coleman’s formula was based on

the condition of constant reservoir, which was not

appropriate for present experiments. Comparison

other three experiments data, the length of “curve

section” was longest, the CSC was second long and

the IB was shortest. At the beginning time and ending

time of dam-break, the CS and CSC was the same

length, while at other period the CS length was larger

than CSC length. There were many investigators to

estimate the length rate of CSC and CS. For example,

Das’s (1997, p. 89) study showed the rates were 0.46

and 0.67 for two dam-break experiments (Das et al.,

1997). Walder et al.(2015, p. 6710) presented several

dam failure test showing the rate may increase from

0.1to 0.5 as dam height decreasing (Walder et al.,

2015). It was found that the rate was approximately

0.85 at peaking discharge moment in the present

study. The profile of final breach was showed in

Figure 5, In addition to these three sections, the length

of other section form upstream to downstream was

also different. Therefore, which section was most

suitable for measuring the dam-break outflow? This

is a long-term task that needs more work to confirm.

Figure 4: Comparison of breach length of different section

and empirical formula

Figure 5: The profile for final breach

3.2.2 The Water Depth Estimation at

“Control Section”

The location of the “control section” as a function of

time, moved upstream during outflow rush out from

dam breach, was recorded by using the video above

the dam crest. The distance between every location

and initial location can be measured by using

photogrammetric method. As Figure 6 showed, the

curvature of “control section” was decreasing when it

moving upstream but the length was increasing.

Figure 6: The location of “control section” moving

upstream process

Following Walder’s (2015) method, the flow depth at

the “control section” was defined as follows:

() () ()

cwc

ht z t zt=−

)

As Figure 7 showed,

was the water depth at the

“control section”,

was the water free surface

elevation over the “control section”, and

was the

bottom elevation of the “control section”,

was the

distance form initial location to present location,

was the upstream slope of the dam,

was the initial

dam height. Among these parameters,

and

can be measured directly. For artificial earth dam,

was usually a given factor, while it should be assumed

for nature dam. Therefore, the equation 1 can be

0 50 100 150 200 250 300 350 400 450

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Time/s

Breach Length /m

Length of CS

Length of CSC

Length of IB

Coleman.et al.(2002)

0.8 1.2 1.6 2.0 2.4 2.8 3.2

0.0

0.1

0.2

0.3

100s

140s

180s

220s

260s

Locotion (m)

Length (m)

Analysis of the Inﬂuence Relationship for the Earth Dam-Break Outﬂow Estimation Parameters

153

expressed as equation 2. Based on equation 2, the

breach water depth was about 13cm at 100s.

However, the equation 2 worked well in the early

period of the second stage of dam break but not all: it

failed when the breach water depth become too large.

() () ()tan

cw c d

ht z t X t z

=+ −

)

Figure 7: Sketch of the breach water depth estimation

3.2.3 Comparison Breach Hydrograph and

Other Parameters

The breach discharge was the most important

parameters for dam-break problem since it

determines the downstream inundated area, which

was often estimated using water volume balance of

reservoir.

in out

=−

(2)

where

was the inflow;

out

was the breach

discharge;

was the water volume of the upstream

reservoir.

(a) Comparison breach hydrograph and water depth of

reservoir

(b) Comparison breach hydrograph and breach length of

“control section”

velocity

Figure 8: Comparison breach hydrograph and other

parameters

In order to better understand the time correlation of

breach discharge and other parameter such as

reservoir water depth, breach width and breach water

surface velocity, the breach hydrograph and these

parameters were put together and showed in Figure

8a~c. According to equation 3, the discharge curve

was derived from water depth of reservoir, and the

peak discharge time would come out at maximum

slope of reservoir water level curve, as shown in

Figure 8a. Comparison of time history of dam breach

discharge and the breach length of “control section”,

it can be found that when the length of “control

section” reach the maximum, the discharge was also

the maximum (Figure 8b). The water surface velocity

at “control section” was measured by using LS-PIV

technology, and there exist about 30s interval for peak

water surface velocity to peak discharge (Figure 8c).

Therefore, according to

out

QAV=

(

was average

cross-section area,

V was average water velocity), the

contribution of cross-section area was larger than

water velocity for dam breach outflow estimation.

4 SUMMARY AND

CONCLUSIONS

This study presents the experimental investigation of

the breach parameter relationship for earth dam

failure due to overtopping. The experiment was

conducted in a flume of 50m*4m*2m with an

idealized earthen dam placed in the middle.

According to experiments data, it showed that the

dam breach process can be divided into two stages,

the main feature of first stage was “head-cut” while

the second stage was “surface” erosion. It was found

that the length rate of CSC and CS was approximately

0.85 at peaking discharge moment in the present

study. The breach water depth can be estimated by

𝜑

𝑧



𝑧



ℎ



𝑋



Flow direction

𝑧



𝜑

0 50 100 150 200 250 300 350 400 450

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

Breach Outflow

Time/s

Outflow/(m

/s)

100

200

300

400

500

600

Water Depth of Reservoir

Water Depth/mm

0 50 100 150 200 250 300 350 400 450

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

Breach Outflow

Time/s

Outflow/(m

/s)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Length of CS

Length of CS/m

0 50 100 150 200 250 300 350 400 450

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

Breach Outflow

Outflow/(m

/s)

Time/s

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Surface Velocity

Surface velocity/(m/s)

ISWEE 2022 - International Symposium on Water, Ecology and Environment

154

using

() () ()tan

cw c d

ht z t X t z

=+ −

, and the based on

this formula, the breach depth at 100s was

approximately equal to 13cm. The peak time of

discharge was nearly the same as maximum breach

width time and maximum reservoir water depth

decreasing slope time but delayed to peak water

surface velocity time about 30s.

ACKNOWLEDGMENT

This research was jointly supported by the youth

program of Sichuan Science foundation:

Experimental study and numerical simulation of

landslide surge superimposed in different stages of

earth-rock dam break process (Grant No.

2022NSFSC1068), and the open project of key

laboratory of scientific research projects of colleges

and universities of Sichuan province (Grant No. SC_

FQWLY-2021-Y-03), the 2022 open project of

failure mechanics engineering disaster prevention of

key Lab of Sichuan Province: The investigation of the

impact force of surge wave on dam and its damage

mechanism research (Grant No. FMEDP202210), the

2022 open project of failure mechanics engineering

disaster prevention of key Lab of Sichuan Province:

Study on the rule and mechanism of dynamic crack

propagation under blasting (Grant No.

FMEDP202208).

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Analysis of the Inﬂuence Relationship for the Earth Dam-Break Outﬂow Estimation Parameters

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