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SCIENCE CHINA Technological Sciences, Volume 62 , Issue 10 : 1773-1782(2019) https://doi.org/10.1007/s11431-018-9367-4

An approach to quick and easy evaluation of the dam breach flood

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  • ReceivedJul 21, 2018
  • AcceptedSep 28, 2018
  • PublishedMar 21, 2019

Abstract

In the context of an impending dam failure, quick evaluation of dam breach flood is necessary. Previous studies provided an approach to calculate the dam breach hydrograph using an Excel spreadsheet based on the improved soil erosion model and numerical algorithm. However, calculation of the breach lateral enlargement requires the modeling of the successive collapse of the breach banks. It is time-consuming with special training, which is difficult to provide during an emergency. This study proposes that the lateral enlargement process can be modeled using a hyperbolic relationship with sufficient accuracy. Consequently, field engineers can perform the dam breach analysis along with the sensitive study for a target case within 1 h in an Excel spreadsheet which is self-tutorial. This paper presents this easy and quick approach based on only fifteen input parameters that can be determined based on the experience. This approach can also be used for the preliminary study when a dam safety planning work is undertaken.


Funded by

the National Natural Science Foundation of China(Grant,No.,41731289)

the Foundation of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin(Grant,No.,2016ZY08)

the Consultation and evaluation project of the Chinese Academy of Sciences(Grant,No.,2018-Z02-A-008)


Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant No. 41731289), the Foundation of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin (Grant No. 2016ZY08) and the Consultation and Evaluation Project of the Chinese Academy of Sciences (Grant No. 2018-Z02-A-008).


References

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  • Figure 1

    Flow over a broad-crested weir.

  • Figure 2

    Relationship between soil erosion rate and shear stress in the hyperbolic model.

  • Figure 3

    Modeling the lateral enlargement. (a) Circular slip surfaces; (b) straight line simplifications.

  • Figure 4

    Ctive earth pressure applied on a vertical wall.

  • Figure 5

    Hyperbolic relationship between Δβ and Δz by Eq. (12).

  • Figure 6

    Hyperbolic relationship between Δβ and Δz by eq. (13).

  • Figure 7

    Empirical linear relationship between φ and m2, γ =16 kN/m3.

  • Figure 8

    Empirical chart for contours of equal m1 (deg−1) based on tanφ and c, γ =16 kN/m3.

  • Figure 9

    Empirical linear relationship between φ and m2, γ =22 kN/m3.

  • Figure 10

    Empirical chart for contours of equal m1 based on tanφ and c, γ=22 kN/m3.

  • Figure 11

    Flowchart for the improved numerical method (refer to [7] for undefined symbols and equations in this chart).

  • Figure 12

    Measured profile of the breach.

  • Figure 13

    (Color online) Excel spreadsheet calculating the Banqiao dam hydrograph.

  • Figure 14

    Discharge versus time (a) and breach width versus time (b) for the Banqiao dam breach.

  • Table 1   Suggested values for and for preliminary studies

    Erodibility

    Soil materials

    a

    b

    Very high

    Fine sand, Non-plastic silt

    1.0–1.1

    0.0001–0.0003

    High

    Medium sand, Low plasticity silt

    1.0–1.1

    0.0003–0.0005

    Medium

    Jointed rock (spacing <30 mm), Fine gravel, Coarse sand, High plasticity silt, Low plasticity clay, All fissured clays

    1.1–1.2

    0.0005–0.0007

    Low

    Jointed rock (30–150 mm spacing), cobbles, Coarse gravel, High plasticity clay

    1.1–1.2

    0.0007–0.001

    Very low

    Jointed rock (150–1500 mm spacing), Riprap

    1.2–1.5

    0.001–0.01

    Non-erosive

    Intake rock, Jointed rock (spacing >1500 mm)

    1.2–1.5

    0.01–0.1

  • Table 2   and Δ associated with the toe cutting depth Δ

    Step

    Δz (m)

    β (°)

    Δβ (°)

    1

    1.500

    123.43

    6.93

    2

    3.052

    125.80

    9.30

    3

    4.573

    128.93

    12.43

    4

    6.236

    130.78

    14.28

    5

    8.232

    130.54

    14.04

    6

    10.141

    131.58

    15.08

    7

    11.921

    133.96

    17.46

    8

    13.954

    134.94

    18.44

    9

    15.686

    138.31

    21.81

    10

    18.559

    136.46

    19.96

    11

    20.991

    138.22

    21.72

    12

    23.764

    138.86

    22.36

    13

    26.899

    138.92

    22.42

    14

    30.448

    138.34

    21.84

    15

    33.014

    141.49

    24.99

  • Table 3   and associated with different shear strength parameters

    φ (°)

    c (kPa)

    z0 (m)

    β0 (°)

    m1 (deg−1)

    m2 (m/°)

    37

    15

    50.142

    116.5

    0.230

    0.035

    25

    37.607

    116.5

    0.545

    0.032

    50

    25.071

    116.5

    0.896

    0.033

    75

    12.536

    116.5

    1.307

    0.03

    100

    7.521

    116.5

    1.504

    0.033

    27

    15

    40.796

    121.5

    0.128

    0.028

    25

    30.597

    121.5

    0.317

    0.024

    50

    20.398

    121.5

    0.417

    0.029

    75

    10.199

    121.5

    0.645

    0.027

    100

    6.119

    121.5

    0.781

    0.028

    17

    15

    33.786

    126.5

    0.107

    0.016

    25

    25.339

    126.5

    0.162

    0.017

    50

    16.893

    126.5

    0.312

    0.018

    75

    8.446

    126.5

    0.432

    0.019

    100

    5.068

    126.5

    0.607

    0.018

  • Table 4   Input parameters for DB-IWHR

    Area

    Item

    Symbol

    Equation No.

    Default

    Remarks

    Geography

    Reservoir storage

    p1, p2, p3, H0

    (2)

    Can be obtained either from historical records or quick survey

    Natural inflow

    q

    (1)

     

    Hydraulics

    Broad-crested weir coefficient

    C

    (1)

    1.42

    Can be followed by sensitivity analysis

    Water drop coefficient

    m

    (3)

    0.8

    Can be followed by sensitivity analysis

    Incipient velocity

    Vc

    (4)

    Many empirical suggestions are available, e.g., Briaud [17]

    Soil erosion

    a, b

    (4)

    Table1

    (Refer to Table1)

    Geotechnique

    Initial breach width and elevation

    B0, z0

    Based on inflow q or other approaches (Section 2.2)

    Material property

    γ, c, φ

    Can be obtained based on experience or some quick and simple tests

  • Table 5   Inputs for Banqiao dam reach analysis

    Categories

    Item

    Parameter

    Input

    Remarks

    Geography

    Reservoir storage

    Initial reservoir water level

    p1, p2, p3, H0

    H0

    1.99, −30.68, 187.17

    117.94 m

    Adapted from [20]

    Natural inflow

    q

    5000 m3/s

     

    Hydraulics

    Broad-crested weir coefficient

    C

    1.42

    Default value

    Water drop coefficient

    m

    0.8

    Default value

    Incipient velocity

    Vc,

    2.4 m/s

    Adapted from [20]

    Soil erosion

    a, b

    1.0, 0.0003

    From Table1

    Geotechnique

    Material property

    γ, c, φ

    16 kN/m3, 30 kPa, 25°

    Adapted from [20]

    Lateral enlargement coefficient

    m1, m2

    0.27, 0.02

    Determined byFigures 7 and 8

    Initial channel bed elevation

    z0

    115.79 m

    Adapted from [20]

  • Table 6   Comparison between calculated and the measured results

    Parameter

    Symbol (unit)

    Calculated results

    Measured data

    Peak flow

    Qp (m3/s)

    78622

    78100

    Time at peak

    tp (h)

    4.70

    3.5

    Average breach width

    Bavg (m)

    311

    291

  • Table 7   Input of the three cases for validation

    Categories

    Parameters

    Yigong [9]

    Xiaogangjian [10]

    Yibadao [10]

    Geography

    p1, p2, p3, H0

    0.31, 16.28, −121.78, 2262.82

    0.01, −0.53, 9.54, 844.57

    0.0029, 0.098, −0.58, 762.57

    q

    H0

    859 m3/s

    2262.82 m

    15 m3/s

    844.57 m

    Upstream dam breach flood

    Hydraulics

    C

    1.42

    1.42

    1.42

    m

    0.8

    0.8

    0.8

    Vc

    2 m/s

    2.7 m/s

    2.7 m/s

    a, b

    0.3, 0.00038

    0.2, 0.0002

    0.2, 0.0002

    Lateral enlargement for the hyperbolic model

    γ, c, φ

    18.5 kN/m3, 13 kPa, 37°

    18.5 kN/m3, 41.6 kPa, 19°

    18.5 kN/m3, 41.6 kPa, 19°

    m1, m2

    0.2, 0.03

    0.25, 0.02

    0.25, 0.02

    Lateral enlargement for the stepped failure

    Β0

    5 m

    30 m

    15 m

    β0, βend

    119°, 145°

    129°, 170°

    134°, 157°

    z0, zend

    2261 m,2210 m

    842 m,813 m

    760 m,752 m

  • Table 8   Comparisons between both approaches

    Parameter

    Symbol (unit)

    Mode

    Yigong

    Xiaogangjian

    Yibadao

    Calculated

    Measured

    Calculated

    Measured

    Calculated

    Measured

    Peak flow

    Qp (m3/s)

    Stepped failure

    106062

    94013

    2251.47

    3330

    3950

    Hyperbolic

    102437

    2272.86

    3329

    Time at peak

    tp (h)

    Stepped failure

    6.77

    6.17

    0.93

    0.45

    1.02

    0.45

    Hyperbolic

    6.56

    0.91

    1.00

    Breach width

    Bend (m)

    Stepped failure

    424.0

    430

    106.6

    122

    64.6

    57

    Hyperbolic

    420.0

    100.4

    60.7

    The calculation for the Yibadao dam has incorporated the dam breach flow of the upper stream Xiaogangjian dam [10].

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