Risk Assessment of Dams (Springer Tracts in Civil Engineering) 3030471381, 9783030471385

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Springer Tracts in Civil Engineering

Aytaç Güven Alper Aydemir

Risk Assessment of Dams

Springer Tracts in Civil Engineering Series Editors Giovanni Solari, Wind Engineering and Structural Dynamics Research Group, University of Genoa, Genova, Italy Sheng-Hong Chen, School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan, China Marco di Prisco, Politecnico di Milano, Milano, Italy Ioannis Vayas, Institute of Steel Structures, National Technical University of Athens, Athens, Greece

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Aytaç Güven Alper Aydemir •

Risk Assessment of Dams

123

Aytaç Güven Department of Civil Engineering University of Gaziantep Şehitkamil, Gaziantep, Turkey

Alper Aydemir Department of Civil Engineering Nuh Naci Yazgan Üniversitesi Kayseri, Turkey

ISSN 2366-259X ISSN 2366-2603 (electronic) Springer Tracts in Civil Engineering ISBN 978-3-030-47138-5 ISBN 978-3-030-47139-2 (eBook) https://doi.org/10.1007/978-3-030-47139-2 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

This book covers the risk assessment of dams which is one of essential processes for design and operation period of dams. This edition is updated for use of civil engineering dam safety lectures as well as dam design stages. Importance of renewable energy resources is increasing nowadays. Effective use of water resources can play important role on economics. One of the most efficient way to manage water resources is by using dams to collect water so that construction of dams is being an important subject for collecting, storage and distribution of water in the future. Main purpose of this edition is defining dam safety procedures and obtaining a general process which could be used for inspection of dams. Risk assessment could be a complex process because it has many different parameters that include uncertainties. Expertise of authors in water resources engineering guided editing procedure of the book. While risk analysis is a wide area and it could be time-consuming during design stages of a dam. But this book creates a rapid process for investigating important parameters including failure time, peak breach discharge and discharge width. Gaziantep, Turkey Kayseri, Turkey

Aytaç Güven Alper Aydemir

v

Contents

1 Dams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Risk Assessment of Dams . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Definition of Dams . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 History of Dams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 History of Dams by Type . . . . . . . . . . . . . . . . . 1.3.2 History of Dams in Turkey . . . . . . . . . . . . . . . . 1.3.3 Benefits of Dams . . . . . . . . . . . . . . . . . . . . . . . 1.3.4 Flood Control . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.5 Hydropower . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.6 Irrigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Classification of Dams . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.1 Classification of Dams on Size . . . . . . . . . . . . . 1.4.2 Classification of Dams by Height . . . . . . . . . . . 1.4.3 Classification of Dams by Construction Purpose 1.4.4 According to Hydraulic Design . . . . . . . . . . . . . 1.4.5 Classification of Dams by Design of Dam Body 1.4.6 Classification of Dams by Body Material . . . . . 1.4.7 Dams in the World . . . . . . . . . . . . . . . . . . . . . 1.4.8 Dams in Turkey . . . . . . . . . . . . . . . . . . . . . . . . 1.4.9 Definition of Small Dams . . . . . . . . . . . . . . . . . 1.4.10 Environmental Negative Impacts of Dams . . . . .

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2 Dam Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Risk, Hazard and Vulnerability . . . . . . . . . . . . 2.1.1 Definition of Risk . . . . . . . . . . . . . . . 2.2 Hazard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Hazard Potential . . . . . . . . . . . . . . . . . 2.2.2 Hazard Potential Classification System 2.3 Risk Assessment . . . . . . . . . . . . . . . . . . . . . . .

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Contents

2.4 Dam Safety Studies . . . . . 2.5 Failure Modes of Dams . . 2.5.1 Flood . . . . . . . . . 2.5.2 Earthquake . . . . . 2.5.3 Overtopping . . . . . 2.5.4 Piping . . . . . . . . . 2.5.5 Normal Stability . . 2.6 Problems and Solutions for Situations . . . . . . . . . . . . .

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3 Risk Assessment of Dams . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Risk Prioritization of Dams . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Process Outline . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Definitions of Mostly Used Terms in Dam Safety 3.1.4 Failure Mode Evaluation . . . . . . . . . . . . . . . . . . 3.1.5 Failure Mode Descriptions and Evaluation . . . . . . 3.1.6 Consequence Assessment . . . . . . . . . . . . . . . . . . 3.1.7 Life Loss Potential . . . . . . . . . . . . . . . . . . . . . . . 4 Dam Failure Modelling Parameters . . . . . . . . . . . . . . . . 4.1 Prediction of Dam Failure Parameters . . . . . . . . . . . . 4.1.1 Some Important Variables . . . . . . . . . . . . . . 4.1.2 Calculation and Implementation of the Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.3 Peak Breach Discharge . . . . . . . . . . . . . . . . . 4.1.4 Breach Width . . . . . . . . . . . . . . . . . . . . . . . 4.1.5 Failure Time . . . . . . . . . . . . . . . . . . . . . . . . 4.1.6 Breach Side Slope Factor . . . . . . . . . . . . . . .

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5 Dam Breach Parameter Estimation: Case Studies . . . . . . . . 5.1 Applications of Breach Parameter Prediction Methods . . . 5.1.1 Case Study 1: Kayacık Dam . . . . . . . . . . . . . . . . 5.1.2 Case Study 2: Karaova Dam . . . . . . . . . . . . . . . . 5.1.3 Case Study 3: Çoğun Dam . . . . . . . . . . . . . . . . . 5.1.4 Comparison of Dam Breach Prediction Methods . 5.2 Comparison of Dam Breach Prediction Methods Results . . 5.2.1 Suggestions About Dam Risk Assessment Studies

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References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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About the Authors

Aytaç Güven is working as professor in Civil Engineering Department in the University of Gaziantep. His main research areas are hydrology, dam safety, water resources management, hydropower, artificial intelligence techniques and computational fluid dynamics. He received B.Sc., M.Sc. and Ph.D. degrees in the University of Gaziantep. He was awarded with the Excellent Scientist Award by the University of Gaziantep (2016). He teaches Engineering Hydrology, Water Resources Management, Hydropower Engineering and Advanced Hydrology courses. Prof. Dr. Aytaç Güven published more than 50 international strong journal papers in his subject areas. Alper Aydemir is working as assistant professor in Civil Engineering Department of Nuh Naci Yazgan University. His main research areas include hydraulics, water resources, dam safety and risk assessment of dams. He is serving fluid mechanics, hydraulics, hydrology, water resources, water supply, graduation project and civil engineering design lectures. He received B.S. degree of Civil Engineering from Yıldız Technical University and during that period he also received Business Administration Degree (Open Teaching) from Anatolian University. Both M.Sc. and Ph.D. degrees were completed in Hydraulics Division—Civil Engineering Department of Gaziantep University. His M.Sc. Thesis was awarded as the most successful Master of Science Thesis (2012) and his Ph.D. Thesis was awarded as third most successful Doctorate thesis (2017) by Dam Safety Association (Turkey). He has attended many national and international congresses and published papers about dam safety as well as hydropower potential of dams.

ix

Chapter 1

Dams

Abstract Water play vital role in all known forms of life, so the effective use of water resources is an important subject for human life. In this chapter the main properties of existing dams are given with historical data. Definition for small dams is not common around the World. Almost all countries have published definitions for small dams but they all vary from each other. Therefore, a definition of small dams is given. While using dams there could be negative impacts on environment. Some of them are negligible but if not controlled some of them could be very harmful. Detailed information about environmental negative impacts of dams are described in this chapter.

1.1 Risk Assessment of Dams 1.1.1 Introduction Water is one of biggest surface covers for earth. It covers almost 70% of surface but despite that only 1% of existing volume is suitable for drinking water source. More than 50% and in some species 90% of the weight of living forms made by water so it’s vital for every known forms of living organisms including human. Renewable energy is energy which comes from natural sources. For example, sunlight, wind, rain, tides and geothermal heat are most common sources of renewable energy. Main streams for renewable energy sources are wind, hydropower, solar, biomass, biofuel, geothermal. High density of water when compared to air, make water to yield considerable amounts of energy while even in a slow flow. Global warming is the rise of average temperature of atmosphere and oceans. Increase of average temperature in global temperature will cause rise of sea levels, and the amount and pattern of precipitation will change accordingly. Nowadays the importance of renewable energy sources is increased because of global warming.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020 A. Güven and A. Aydemir, Risk Assessment of Dams, Springer Tracts in Civil Engineering, https://doi.org/10.1007/978-3-030-47139-2_1

1

2

1 Dams

Water play vital role in all known forms of life, so the effective use of water resources is an important subject for human life. Agriculture, drinking water, washing, transportation, chemical uses, fire extinction, recreation, industrial applications are the most common use of water. A dam is defined as a kind of barrier used to regulate water flow and store it behind that barrier. Collecting water by using dams is one the most efficient way to manage water resources which is used for ages. Hence, dams are being an important subject for storage and future distribution. Dams store water for many purposes such as irrigation, flood control, hydropower. But besides these benefits, if the dam fails this would likely cause, significant social and economic losses as well as loss of many lives. To prevent this kind of catastrophic accidents dams should be constructed within engineering standards of design and construction. Operation, maintenance and surveillance steps must be under continual control. For this purpose many countries have different regulations and standards for dams [1].

1.2 Definition of Dams A dam is a manmade structure or naturally occurring barrier across a river which controls the flowing water. Wide scale for dam size could be used. For example this scale start with small sized embankment dams used only for irrigation and end with very high concrete structures used for many purposes same time [2]. The relocation of almost all infrastructure facilities including; villages, individual houses, farms, highways, railroads and utilities, is a results for a dam construction project [2]. Figure 1.1 shows effect of dam construction in Halfeti. Halfeti can be a good example for showing the effect of dam construction over human life. Turkish Government constructed several dams in the area and near places in Southeastern Anatolia Project (GAP) field which is an initiative for economic and mostly agricultural. Halfeti is a small town remaining within the dam construction area and the rising water level of the surrounding dams created changes in river flows and all of these changes in nature caused the evacuation of the city. Basic livelihoods for people lived in Old Halfeti were fishing, farming on the riverbank of the Euphrates for especially growing peanuts and the area’s famous black roses. But area was flooded in 1999 and when the waters came and ‘new’ Halfeti was built. New buildings for people of the region, including the jail, were rebuild in the new town.

1.3 History of Dams

3

Fig. 1.1 Town of Old Halfeti after dam construction [3]

1.3 History of Dams The history of dam building dates back to antiquity, and is bound up with the earlier civilizations of the Middle East and the Far East. Generally accepted oldest dam is the one build around 2600 B.C. at Sadd-el-Kafara in Egypt. It has 14 m dam height and was constructed with an earth fill central zone flanked by rock shoulders and with rubble masonry face protection. After a relatively short period of service, it was breached probably as a consequence of overtopping flood event [4]. Du Jiang Yan is the oldest surviving irrigation system in China that included a dam that directed water flow. It was finished in 251 B.C. A large earthen dam, made by the Prime Minister of Chu (state), Sunshu Ao, flooded a valley in modernday northern Anhui province that created an enormous irrigation reservoir 100 km (62 miles) in circumferences, a reservoir that is still present today [5]. The Grand Anicut, also known as the Kallanai is an ancient dam built on the Kaveri River in the state of Tamil Nadu in Southern India. It was built by the Chola king Karikalan around the 2nd Century AD and is considered one of the oldest water-diversion or water-regulator structures in the world, which is still in use [6]. Small earth dams and networks of canals constructed as far back as 2000 BC found in recent archaeological findings indicate that people used these structures as a reliable source of water they need to live. As an old dam project example; the building of the Marib Dam in Yemen started around 750 BC and ended 100 years later. It includes a 4-m-high earth embankment and stone sluices to regulate discharges for

4

1 Dams

irrigation in domestic use. This dam was raised to a height of 38 m which creates a reservoir that have 98 million cubic meters of water volume [2].

1.3.1 History of Dams by Type Historical dams can be classified according to following types [7]: Gravity dams: Gravity dam is designed with equilibrium of forces caused by water and weight force of dam body. Gravity dams build without cement were constructed thousands of years before Christ. According to information obtained from wrecks, first constructed gravity dams, foundation width was four times bigger than height of dam. Earth fill dams: It is known that one of first earth fill dam was 17,6 km length and with height of 21 m which was constructed by year of B.C. 504 in Sri Lanka island near south of India. Rock fill dams: Rock fill dams are used since 1800 s. From end of 19th Century to 1930 s many rock fill dams are constructed. This type of dam construction was decreased after 1930. Because search and settlement of rock type material was expensive. After 1960 s construction projects of rock fill dams increased. Arch dams: Principle of arch design has been used since year B.C. 2000, according to engineering history first arch dam was Pantalto dam in Austria which is built in 1611. But first arch dam with height of 78 m was built in Denver (USA) in 20th Century. Number of arch dams build between these years is not more than 100. Buttress dams: Fist concrete buttress dam was Ambursen (USA) build in 1903. So that these kinds of dams are called Ambursen dams. Roller compacted concrete dams: Construction of roller compacted concrete dams are started during Second World War. Besides that, Shimajigana Dam in Japan was first roller compacted concrete dam completed in 1980. After Shimajigana Dam, in 1982, Willow Creek Dam in USA was another example for this type of dam.

1.3.2 History of Dams in Turkey Anatolia’s oldest dam is Hitit Dam which is at age of 3250 and it was constructed with a spring temple near Konya, in Turkey. According to texts with cuneiform writing, Alaca Höyük is reported to be a city rich in water resources. In historical site it is possible to see clean and waste water canals at age of 3250. Especially dimensions of the main waste water canals are magnificent even when they are compared with dimensions of today’s canals [8]. Figure 1.2 shows Hitit Dam, which is the first dam constructed in Anatolia. First hydropower dam in Turkey was built in Tarsus. This dam was completed in 15 September 1902. Transmission gained from a water mill was converted to 2 Kw electricity and this energy was used in lights of Tarsus streets.

1.3 History of Dams

5

Fig. 1.2 Hitit Dam-First dam in Anatolia [9]

1.3.3 Benefits of Dams Water has a vital part for all living organisms on world. Increasing World population also increases the demand of water every year. One of most efficient way to manage water resources is using dams to collect water so that construction of dams is being an important subject for storage and future distribution. Water supply is the fundamental benefit of dams and reservoirs in all over the World. Other key benefits and purposes of dams are [10]: • • • • •

Irrigation water supply for agriculture, Control of floods, Generate energy (hydropower), Navigation in inlands, Recreation. Federal Emergency Management Agency classifies benefits of dams as [11]:

• • • • • • • • • •

Irrigation, Electrical Generation, Flood Control, Renewable, Clean energy, Water storage, “Black Start” capabilities, Sediment/hazardous material control, Navigation, Fisheries,

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1 Dams

• Recreation, • Mining. Most common benefits of dams are flood control, irrigation and hydropower.

1.3.4 Flood Control Dams have a critical role to reduce the negative effects of floods occurred along river courses [12]. Basin general development plans are used to define dam construction stages and these are established by comprehensive planning for economic development and with public involvement. Climate changes river flows that result bigger floods. So flood control is one of the significant purpose for some of existing and currently under construction major dams all over the world [10].

1.3.5 Hydropower Hydropower is the world’s largest source of renewable energy and has an important role to play responding to challenges facing the world because of climate change. As a clean and renewable energy source, hydropower can help to reduce climate change by cutting our dependence on carbon-based fuels [13]. Turkey has an economic capacity of 128 billion kWh per year hydroelectric energy potential. However, Turkey is using 36% of this capacity, currently generating 46 billion kWh per year electricity from hydroelectric power plants. Another 11 billion kWh per year capacity is under construction by the private and the public sector. Turkey’s geography, a rectangular plateau peninsula surrounded on three sides by seas, is highly conducive to hydroelectric power generation; around 1% of World hydroelectric potential is available in Turkey. Turkey has five separate watersheds which include many rivers [14].

1.3.6 Irrigation Agricultural irrigation is of main biggest use of water on a worldwide scale. It is estimated that 80% of additional food production by the year 2025 will come from irrigated land. Arid zones, which represents a major portion of the developing countries, need most water for irrigation [10].

1.4 Classification of Dams

7

1.4 Classification of Dams Dams can be classified in various ways [7]: • • • • • • •

Classification of dams on size, Classification of dams by height, Classification of dams by construction purpose, Classification of dams by functions of dam, Classification of dams by design of dam body, Classification of dams by hydraulic properties, Classification of dams by body material.

1.4.1 Classification of Dams on Size Dams are classified mostly based on size. Figure 1.3 illustrates dam size parameters [15]. V = Reservoir Volume Hf = Height of Dam • Large Dam: Hf > 15 m (or) 10 m ≤ Hf ≤ 15 m, V > 106 m3 , L > 500 m • High Dam: Hf > 50 m • Small Dam: Hf < 10 m International Commission of Large Dams (ICOLD) classifies dams in 2 ways: • Large Dams: A dam above 15 m in height measured or a dam between from the lowest portion of the general foundation area to the crest, or a dam between 10 m and 15 m in height provided it complies with at least one of the following conditions: – The length of the crest of the dam to be not less than 500 m – The capacity of the reservoir formed by the dam to be not less than one million m3 – The maximum flood discharge dealt with by the dam to be less than 2000 m3 /s – The dam has especially difficult foundation problems or the dam is of unusual design

Fig. 1.3 Dam size parameters

8

1 Dams

• Small Dams: A dam below 15 m in height measured is called as definition of small dam which given by ICOLD.

1.4.2 Classification of Dams by Height Dams could also be classified according to dam height as follows [7]: • If height of dam is above than 100 m these kinds of dams called as high dams, • If height of dam is between 50 and 100 m than these dams are classified as average height dams, • If height of dam is less than 50 m these are called as low dams.

1.4.3 Classification of Dams by Construction Purpose Single purpose • • • •

Dams only used for storage, Dams only used for diversion, Dams only used for detention, Dams only used for hydropower. Multiple purpose: Serves for all or most of the above purposes [7].

1.4.4 According to Hydraulic Design • Overflow Dams: diversion dams • Non-overflow Dams: earth fill, rock fill dams [7].

1.4.4.1

According to Functions of Dams

• Water storage • Flood detention • Raise water level [7].

1.4 Classification of Dams

9

1.4.5 Classification of Dams by Design of Dam Body • • • • • • • • • • • • • • •

Gravity dams Concrete gravity Pre-stressed concrete Roller compacted concrete Hard fill Arch dams Constant-angle arch Constant-center arch Variable-angle, variable center arch Buttress Dam Flat-slab buttress Multiple-arch buttress Embankment (fill) dams Earth fill Rock fill [15].

1.4.6 Classification of Dams by Body Material • • • •

Embankment dams Masonry and rubble dams Concrete dams Steel and timber dams [7].

1.4.7 Dams in the World There are about 50 000 large dams under operation in World and predominant type is embankment which followed by gravity and arch dams. The number of World’s large dams based on construction year are given in Fig. 1.4: Dam age is an important parameter because while dams getting older unexpected deficiencies could start to occur. Number of dams by age are given in Fig. 1.5. Distribution of large dams vary between continents. Most of large dams are located in Asia. Figure 1.6 shows distribution of large dams by geographical area. Number of large dams according to countries and years are given in Table 1.1. If the countries of the world classified according to number of large dams than China could get first place.

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1 Dams 7511

Numbers of dams

8000 7000

5942

5574

6000 5000 4000

3213

3354

3000 2000 1000

863 546 838

10151119 1114

1990-1999

1980-1989

1970-1979

1960-1969

1950-1959

1940-1949

1930-1939

1920-1929

1910-1919

1900-1909

30 m; Q = 16.6(Hw )1.85 If Hw < 30 m; Q = 4.2 × 10−4 × [S × Hw /(B × H )]1.35

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4.1.3.2

4 Dam Failure Modelling Parameters

Macdonald & Langridge-Monopolis Method

Macdonald & Langridge-Monopolis offered below formula for maximum discharge [41]: Q = 1.175 × (S × Hw )0.41

4.1.3.3

Costa Method

Costa offered Q = 0.763 × (S × Hw )0.42 formulation for calculating peak breach discharge [42].

4.1.3.4

Froelich Method

Froelich offered Q = 0.607 × (S)0.295 × (Hw )1.24 formulation for dam breach studies [43].

4.1.4 Breach Width The top, lower or average width occurred after breach is referred as breach width which is effective especially for dam body investigations in dam safety studies. Results of these studies showed that breach width is more effective for large dams than small ones. Because it produced larger changes (35–87%) in peak outflow and smaller changes (6–50%) for small reservoirs [44].

4.1.4.1

Johnson and Illes (1976)

They were the first to predict failure shapes for earth, gravity, and arch concrete dams. For earth dams, their proposition was that the breach shape begins as a triangle and ends as a trapezoid [44]. They also realized that failure width (general) B is given by Johnson and Illes [45]. 0.5 h < B < 3 h for earthfall dams.

4.1 Prediction of Dam Failure Parameters

4.1.4.2

61

Singh and Snorrason (1984)

Their study was conducted on 20 case studies and they came up with the following [46]. The breach width is constrained by: 2H < B < 5H

4.1.4.3

Federal Energy Regulatory Commission (1987)

Federal Energy Regulatory Commission [47] offered: 2H < B < 4H formula for embankment dam breach width.

4.1.4.4

US Bureau of Reclamation Formula (1988)

US Bureau of Reclamation offered that breach width can be calculated with [48]: B = 3 × Hw

4.1.5 Failure Time Researchers found that if failure time were reduced by half its initial value, the peak outflow for a PMF hydrograph would increase by 13–83%. But for large reservoirs, the change in peak outflow was much smaller showing a variation of only 1–5% [49]:

4.1.5.1

Singh and Snorrason (1984)

Singh and Snorrason offered that failure time Tf changes between 0, 25 h and 1 h [46]. 0.25 < T f < 1

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4.1.5.2

4 Dam Failure Modelling Parameters

Ferc (1987)

Federal Energy Regulatory Commission [47] offered that failure time Tf changes between 0.1 and 0.5 h. 0.1 < T f < 0.5

4.1.5.3

Froelich (1995)

Froelich [43] offered below formula for time of failure: t f = 3.84 × Vw0.53 × H −0.90

4.1.5.4

US Bureau of Reclamation Formula

US Bureau of Reclamation [48] offered that time of failure changes with breach width and they offered below formula: t f = 0.011 × B where, tf is the failure time, B is the breach width.

4.1.5.5

Von Thun and Gillette (1990)

Von Thun and Gillette offered 2 formulas for failure time. These methods are dependent on the amount of erosion that occurs [50]: t f = 0.020 × Hw + 0.25 (er osionr esistant) t f = 0.015 × Hw (easilyer odible) where tf should be in hours and Hw in meters.

4.1 Prediction of Dam Failure Parameters

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4.1.6 Breach Side Slope Factor 4.1.6.1

Federal Energy Regulatory Commission Formula

Breach side slope for failure of embankment dam change between 1 and 2 according to Federal Energy Regulatory Commission [47]. 1