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Alliance for Disaster Risk Reduction (ALTER) Project
WP4: Transfer of Methods
Geghi Reservoir and Geghanoush Tailing Dam Break Analysis:
Methodology, Software and Data Requirements
Prepared by: Alexander Arakelyan, Ph.D GIS and Hydrology Expert
Yerevan, Armenia December, 2018
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Contents LIST OF TABLES ............................................................................................................................................................ 3 LIST OF FIGURES ........................................................................................................................................................... 4 LIST OF ABBREVIATIONS .............................................................................................................................................. 5 1. INTRODUCTION AND SCOPE OF WORK ................................................................................................................ 6 2. OBJECTS OF THE STUDY ....................................................................................................................................... 7
2.1 WATER RESERVOIR: GEGHI .............................................................................................................................................. 7 2.2 TAILING DAM: GEGHANOUSH ........................................................................................................................................... 7
3. METHODOLOGY ....................................................................................................................................................... 9 3.1 DAM BREACH ANALYSIS ............................................................................................................................................. 9
3.1.1 Dam Failure Types.............................................................................................................................................. 9 3.1.2 Breach Characteristics Analysis ....................................................................................................................... 10
3.1.2.1 Federal Agency Guidelines ........................................................................................................................................... 10 3.1.2.2 Regression Equations ................................................................................................................................................... 11 3.1.2.3 Physically-Based Breach Computer Models ................................................................................................................. 15
3.2 PEAK FLOW EQUATIONS AND ENVELOPE CURVES ............................................................................................................... 17 3.4 TAILING DAM BREACH OUTFLOW CALCULATION ................................................................................................................ 18 3.5 FLOOD MODELING: ONE-DIMENSIONAL AND TWO-DIMENSIONAL HYDRAULIC MODELS ............................................................ 22 3.5 FLUID DYNAMICS: STEADY AND UNSTEADY FLOW ............................................................................................................... 23 3.6 MANNING EQUATION AND N VALUES .............................................................................................................................. 25 3.7 POPULAR MODELS FOR DAM BREAK ANALYSIS AND FLOOD MAPPING .................................................................................... 29
4. REQUIRED DATA FOR DAM BREAK(CH) ANALYSIS AND MAPPING .......................................................................... 33 4.1 HYDRO-METEOROLOGICAL OBSERVATION DATA ................................................................................................................. 33
4.1.1 Meteorological Data ........................................................................................................................................ 33 4.1.2 Hydrological Data ............................................................................................................................................ 34
4.2 ELEVATION DATA AND ITS DERIVATIVES ............................................................................................................................ 35 4.3 LAND COVER ............................................................................................................................................................... 37 4.4 OTHER SPATIAL DATA ................................................................................................................................................... 37
5. DAM BREAK ANALYSIS AND FLOOD MAPPING IMPLEMENTATION......................................................................... 39 5.1 FLOOD HAZARD INDEX CALCULATION ............................................................................................................................... 39 5.2 RIVER MAXIMUM FLOW ANALYSIS .................................................................................................................................. 44 5.3 DAM BREACH MAXIMUM OUTFLOW AND BREACH HYDROGRAPH CALCULATION ...................................................................... 45
6. CONCLUSIONS AND NEXT STEPS ............................................................................................................................ 48 7. REFERENCES ........................................................................................................................................................... 49 ANNEX 1. CALCULATION OF MAXIMUM FLOW OF DEIFFERENT PROBABILITIES FOR GEGHI-GEGHI HYDROPOST ....... 54 ANNEX 2. CALCULATION OF MAXIMUM FLOW OF DEIFFERENT PROBABILITIES FOR GEGHI-KAVCHUT HYDROPOST .. 56 ANNEX 3. CALCULATION OF MAXIMUM FLOW OF DEIFFERENT PROBABILITIES FOR VOGHJI-KAJARAN HYDROPOST 58 ANNEX 4. CALCULATION OF MAXIMUM FLOW OF DEIFFERENT PROBABILITIES FOR VOGHJI-KAPAN HYDROPOST .... 61 ANNEX 5. CALCULATION OF MAXIMUM FLOW OF DEIFFERENT PROBABILITIES FOR GEGHANOUSH-GEGHANOUSH HYDROPOST ............................................................................................................................................................... 64
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List of Tables Table 1. Possible Failure Modes for Various Dam Types ........................................................................ 10 Table 2. Ranges of Possible Values for Breach Characteristics ............................................................. 10 Table 3. Values of Cb from Reservoir Size ................................................................................................. 14 Table 4. Physically-Based Embankment Dam Breach Computer Models ............................................ 16 Table 5. Summary of the New Erosion Process Models .......................................................................... 16 Table 6. Differences between one- and two-dimensional models .......................................................... 22 Table 7. Manning's n for Channels (Chow, 1959) ..................................................................................... 26 Table 8. Comparison of dam break software ............................................................................................. 30 Table 9. Operational Monitoring Stations within Voghji River Basin ...................................................... 33 Table 10. Annual and monthly average air temperatures in the Voghji River Basin, օC ..................... 34 Table 11. Intra-annual distribution of atmospheric precipitation in the Voghji River Basin, mm ........ 34 Table 12. Cumulative Evaporation in the Voghji River Basin, According to Altitude Zones ............... 34 Table 13. Hydrological Monitoring Posts within Voghji River Basin ....................................................... 35 Table 14. Flow Characteristics in the Hydrological Monitoring Posts within Geghi River Basin ........ 35 Table 15. Classes, Rating and According Weights of FHI Assessment Parameters .......................... 40 Table 16. Classes, Rating and According Weights of FHI Assessment Parameters .......................... 40 Table 17. Maximum Flows of Different Probabilities Calculated for Hydroposts of Voghji River Basin* ............................................................................................................................................................... 44 Table 18. Necessary Input Data for TR-60 and TR-66 Models .............................................................. 45 Table 19. Calculated Values of Geghi Dam Breach Outflow and Timesteps using TR-60 and TR-66 models .............................................................................................................................................................. 46
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List of Figures Figure 1. Geghi Reservoir ............................................................................................................................... 7 Figure 2. Geghanush Tailing Dam ................................................................................................................. 8 Figure 3. Description of the Breach Parameters ....................................................................................... 11 Figure 4. Data on TSF Failures Compiled by Data in Rico et al. (2008) and Chambers and Bowker (CB) (2017) (Entries in bold are not suitable for analysis) ....................................................................... 20 Figure 5. Left: Relationship between VF and VT in x106 m3. Center: Dmax in km in relation to the dam factor (H x VF). Right: Dmax in km in relation to Hf (H x (VF/VT) xVF). All plots are in the log-log scale. CB points are added from Chambers and Bowker (2017) and R points are added from Rico (2008). ........................................................................................................................................................................... 21 Figure 6. 1D and 2D Model Domains .......................................................................................................... 23 Figure 7. Steady Flow .................................................................................................................................... 24 Figure 8. Unsteady Flow ............................................................................................................................... 24 Figure 9. Unsteady Dynamic Flow ............................................................................................................... 25 Figure 10. Hydro-Meteorological Monitoring Posts within Voghji River Basin ...................................... 33 Figure 11. Annual Distribution of River Flow In 4 Hydrological Posts of Voghji River Basin .............. 35 Figure 12. 5m DEM of Studied Area ............................................................................................................ 36 Figure 13. Slope Map of Studied Area ........................................................................................................ 36 Figure 14. Catchments and Drainage Network Delineated Using ArcHydro ........................................ 37 Figure 15. Land Cover Map of Studied Area .............................................................................................. 37 Figure 16. Survey Data on Dams ................................................................................................................. 38 Figure 17. Flowchart for FHI Assessment Method (Kazakis et al., 2015) ............................................. 39 Figure 18. Flow Accumulation (FAC) .......................................................................................................... 41 Figure 19. Distance from Drainage Network (DIST) ................................................................................. 41 Figure 20. Elevation Zones (ELEV) ............................................................................................................. 42 Figure 21. Land Cover (LC) .......................................................................................................................... 42 Figure 22. Rainfall (MFI) ................................................................................................................................ 42 Figure 23. Slope (SLOPE) ............................................................................................................................ 43 Figure 24. Geology (GEOLOGY) ................................................................................................................. 43 Figure 25. Flood Hazard Index (FHI) Map of Studied Area ..................................................................... 43 Figure 26. Flood Event Caused by an Accident in Geghi Reservoir (May 15, 2010) .......................... 44 Figure 27. Geghi Dam Breach Hydrographs .............................................................................................. 46
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List of Abbreviations
AHP Analytical Hierarchy Process
ALOS Advanced Land Observing Satellite
ALTER Alliance for Disaster Risk Reduction project
ASTER Advanced Spaceborne Thermal Emission and Reflection Radiometer
CJSC Close Joint-Stock Company
DEM Digital Elevation Model
FERC Federal Energy Regulatory Commission
FHI Flood Hazard Index
GIS Geographic Information System
HEC-RAS Hydrologic Engineering Center's River Analysis System
LTD Limited Liability Company
NWS National Weather Service
SCS Soil Conservation Service
SRTM Shuttle Radar Topography Mission
TR Technical Release
TSF Tailing Storage Facility
US United States
USACE United States Army Corps of Engineers
USBR U.S. Bureau of Reclamation
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1. Introduction and Scope of Work The Alliance for Disaster Risk Reduction project, or ALTER for short, focuses on establishing public-private partnerships to understand and address flood risks that may stem from water and mining dam failures. Know-how, technologies and experience from the European Union will be transferred to Armenia. Activities will stress the importance of full cooperation between local communities, non-governmental organizations, government ministries, and private-sector companies. Project’s duration is 24 months and is co-financed by the European Union’s Humanitarian Aid & Civil Protection Directorate. The project will focus on three pilot areas where dams and other activities present risks to local communities. The areas are the Akhtala and Teghut areas of Lori Marz along the Shamlugh River, the Vorotan Cascade and its associated dams in the Syunik Region, and the Kapan and Voghji River Basin of Syunik region.
One of the activities of the project is to identify the most suitable best practices on risks related to dams in earthquake zones. This study should be implemented for Project Area 3: Kapan and Voghji River Basin. This area is located about 300 km southeast of Yerevan and has a population of about 45,000. It contains some of Armenia’s most intensive mining activities and two of Armenia’s largest tailing dams – Artsvanik and Geghanush. Additionally, the Geghi Reservoir upstream of Kapan is also included. The villages Kavchut, Andiokavan, Hamletavan, Shgharjik, Syunik and the Kapan Town lie in the immediate floodplain of the Geghi and Voghji Rivers (below the confluence of the rivers). The village of Verin Giratagh and Nerkin Giratagh are not in the floodplain, however the only road access to these villages is through the floodplain below the Geghi dam. The two tailing dams also pose risk to Kapan’s airport which would be needed in an emergency and the main highway connecting Armenia and Iran.
Tailing and water dams in pilot area are hazardous hydro-technical structures because of their location in earthquake zone. In addition, dam break could occur due to the technical condition of the dams and improper exploitation. Catastrophic flooding caused by dam failure present high risks to property and life. Therefore, the assessment of dam break consequences has a crucial meaning for emergency management and development for measures and action plans for stakeholders and respective authorities.
In the scope of current assignment dam break analysis methodology both for water and tailing dams should be presented, software packages for dam break analysis and flood mapping should be reviewed, required input data should be analyzed and dam break flood mapping performed for Geghi Reservoir and Geghanoush Tailing Dams.
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2. Objects of the Study 2.1 Water Reservoir: Geghi About 80 reservoirs with the total volume of 988 mln. m3 were built in Armenia for the regulation of the flow of mountainous rivers, accumulation of rainfall and snowmelt waters for irrigation water supply, hydropower generation and mitigation of dry microclimate conditions.
The Geghi water reservoir is situated in the Syunik province of the Republic of Armenia at the elevation of 1402 m above sea level. The surface area of reservoir is 50 ha. The coordinates of the dam location are ϕ=39°13.6, λ=46°13.36. Dam height over the lower reach corresponds to 70 m, the length along the crest is 270 m, and the total volume of the water-filled reservoir should have comprised 15 million m3, the effective volume is about 12 million m3.
Figure 1. Geghi Reservoir
2.2 Tailing Dam: Geghanoush Tailing is the structure where toxic, hazardous chemical waste and mineral water formed in a result of chemical recycling are separated and stored. These structures are mainly constructed in areas nearby mines. From the first sight, operating tailings look like lakes, but unlike them, tailings are "rich" with life-threatening, toxic substances. Tailings work until exhaustion of the volume intended by their design or until the end of mine exploitation. After that tailing dams are closed by covering with soil layer on which vegetation grows. This is an attempt to prevent the infiltration of hazardous substances into the natural environment.
Tailing problem is particularly acute in small, densely populated countries where the mining, especially metal extraction is well developed. After the mineral processing, a large number of hazardous, residual chemical compounds remain. Therefore, the issue of isolation and storage of residues arise. Tailings are built to safely store the hazardous residuals.
New tailings are built with the increase of mining production, therefore new territories are occupied by them. After that these territories become unfit for further use. For Armenia, as for mountainous country with small area the above mentioned issues are very actual.
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Currently there are 23 tailings in Armenia from those 8 are closed, 15 are operating. The vast majority of tailings are located in Syunik and Lori Provinces. According to the experts in this field, design and management of most of the tailings in Armenia are not corresponding to international standards. It is very dangerous for the countries of like Armenia with high probability of earthquakes. Also risk is high because the tailings are located in areas near communities. In 2017, the Government of RA accepted the Resolution on technical requirements and parameters of tailing construction1 which establishes that the tailings should be constructed far from settlements, reservoirs and other critical infrastructure, but there is no exact information on the distance. According to the same Resolution, tailings should have a mechanical protective zone to ensure safety of people, animals and buildings. They should also have to be separated by sanitary zone. This is a necessary condition for reducing the risk of tailing dumps. Thus, assessment of the tailing dam break risk and consequences is very important for development of prevention measures and drawing up an action plan for decision makers in this field. The biggest tailing in Armenia is Artsvanik in Syunik Province, which is also one of the biggest tailings in the world. In Artsvanik tailing dam the Zangezur copper-molybdenum combine concentrate is accumulates2. Geghanoush TSF is located in the gorge of the Geghanoush River, in the southern part of Kapan. The difference of relative heights between the tailing dam, on one hand, and city buildings and transport infrastructure, on the other hand, is 75 meters. In case the reservoir dam is broken due to an earthquake, the sliding mass could cover industrial and residential buildings, and as a result of barrage, the polluted water could flood central quarters of the city. The existing Geghanoush Tailings Repository was designed in early 1960’s and had been operated between 1962 and 1983, when the Kajaran Tailings Repository at Artsvanik was commissioned. The Geghanoush tailings repository was re-commissioned in 2006 after the completion of the diversion works and continues to be used today along with an upstream extension currently under construction. The volume of the tailing is 5.4 mln. m3 and the dam height is 21.5 m (Georisk, 2017).
Figure 2. Geghanush Tailing Dam
1 https://www.e-draft.am/projects/128/about 2 https://ampop.am/tailing-risks-in-armenia/
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3. Methodology Despite their many beneficial uses and value, dams also present risks to property and life due to their potential to fail and cause catastrophic flooding. To mitigate these risks, we need to analyze dam properties and possible extent of flooding occurred in a result of dam failure.
The main questions in dam failure and flood modeling are:
• What will be the characteristics of the breach? • How the maximum flow and hydrograph will look like? • How long will it take for the reservoir to be emptied? • What will be the extent, area and depth of the flood associated to the dam failure? • When the flood wave will reach the certain location?
The two primary tasks in the analysis of a potential dam failure are the prediction of the reservoir outflow hydrograph and the routing of that hydrograph through the downstream valley to determine dam failure consequences. When populations at risk are located close to a dam, it is important to accurately predict the breach outflow hydrograph and its timing relative to events in the failure process that could trigger the start of evacuation efforts (Wahl, 2010). The comprehensive overview on dam breach characteristics analysis and peak outflow calculation equations presented in the document entitled “Using HEC-RAS for Dam Break Studies” compiled by Hydrologic Engineering Center of US Army Corps in 2014. As for the tailing dams, these equations and models can’t be directly applied. There are several scientific papers on the methods for the calculation of TSF failure outflow characteristics and maximum distance travelled by tailings. One of these methods applied for Geghanoush TSF in this Report.
Flood modeling basics are also presented in this chapter of the Report, including differences between 1D and 2D models, steady and unsteady flows, also the necessity of Manning N values usage.
3.1 Dam Breach Analysis In this Chapter the questions of dam failure types and breach development analysis, peak outflow calculation and dam break computer models are discussed for water reservoirs. Tailing dam failure analaysis methods are presented in Chapter 3.5.
3.1.1 Dam Failure Types There are many event types and phenomena that can lead to dam failure:
• Flood event • Landslide • Earthquake • Foundation failure • Structural failure • Piping/seepage (internal and underneath the dam) • Rapid drawdown of pool • Planned removal • Terrorism act
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Given the different mechanisms that cause dam failures, there can be several possible ways dam may fail for a given driving force/mechanism. Costa (1985) and Atallah (2002) analysed a list of dam types versus possible modes of failure.
Costa (1985) reports that of all dam failures as of 1985, 34 percent were caused by overtopping, 30 percent due to foundation defects, 28 percent from piping and seepage, and 8 percent from other modes of failure. Costa (1985) also reports that for earth/embankment dams only, 35 percent have failed due to overtopping, 38 percent from piping and seepage, 21 percent from foundation defects, and 6 percent from other failure modes (Table 1).
Table 1. Possible Failure Modes for Various Dam Types
Failure Mode Earthen/ Embankment
Concrete Gravity
Concrete Arch
Concrete Buttress
Concrete Multi-Arch
Overtopping X X X X X Piping/Seepage X X X X X
Foundation Defects X X X X X Sliding X X X
Overturning X X Cracking X X X X X
Equipment failure X X X X X
3.1.2 Breach Characteristics Analysis One of the most comprehensive summaries of the literature on historic dam failures is a U.S. Bureau of Reclamation (USBR) report written by Mr. Tony Wahl titled "Prediction of Embankment Dam Breach Parameters - A Literature Review and Needs Assessment" (Wahl, 1998). This report discusses all types of dams, however the report focuses on earthen/embankment dams for the discussion of estimating breach parameters. Much of what is presented in this section of the guidelines was extracted from that report. Guidelines for breach parameters for concrete (arch, gravity, buttress, etc.), steel, timber, and other types of structures, is very sparse, and is limited to simple ranges.
3.1.2.1 Federal Agency Guidelines Many federal agencies have published guidelines in the form of possible ranges of values for breach width, side slopes, and development time. Table 3 summarizes some of these guidelines. The guidelines shown in Table 2 should be used as minimum and maximum bounds for estimating breach parameters.
Table 2. Ranges of Possible Values for Breach Characteristics
Dam Type
Average Breach Width (Bave)
Horizontal Component of
Breach Side Slope (H) (H:V)
Failure Time, tf (hours)
Agency
Earthen/Rockfill (0.5 to 3.0) x HD (1.0 to 5.0) x HD (2.0 to 5.0) x HD (0.5 to 5.0) x HD*
0 to 1.0 0 to 1.0
0 to 1.0 (slightly larger) 0 to 1.0
0.5 to 4.0 0.1 to 1.0 0.1 to 1.0 0.1 to 4.0*
USACE 1980 FERC NWS USACE 2007
Concrete Gravity Multiple Monoliths Usually
Vertical Vertical
0.1 to 0.5 0.1 to 0.3
USACE 1980 FERC
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≤ 0.5 L Usually ≤ 0.5 L Multiple
Monoliths
Vertical Vertical
0.1 to 0.2 0.1 to 0.5
NWS USACE 2007
Concrete Arch Entire Dam Entire Dam (0.8 x L) to L (0.8 x L) to L
Valley wall slope 0 to valley walls 0 to valley walls 0 to valley walls
≤ 0.1 ≤ 0.1 ≤ 0.1 ≤ 0.1
USACE 1980 FERC NWS USACE 2007
Slag/Refuse (0.8 x L) to L (0.8 x L) to L
1.0 to 2.0 0.1 to 0.3 ≤ 0.1
FERC NWS
*Note: Dams that have very large volumes of water, and have long dam crest lengths, will continue to erode for long durations (i.e., as long as a significant amount of water is flowing through the breach), and may therefore have longer breach widths and times than what is shown in Table 4. HD = height of the dam; L = length of the dam crest; FERC - Federal Energy Regulatory Commission; NWS - National Weather Service
Figure 3. Description of the Breach Parameters
3.1.2.2 Regression Equations Several researchers have developed regression equations for the dimensions of the breach (width, side slopes, volume eroded, etc.), as well as the failure time. These equations were derived from data for earthen dams, earthen dams with impervious cores (i.e., clay, concrete, etc.), and rockfill dams. Therefore, these equations do not directly apply to concrete dams or earthen dams with concrete cores. The report by Wahl (1998) describes several equations that can be used for estimating breach parameters. Summarized in Figure 8 are the regression equations developed to predict breach dimensions and failure time from the USBR report (Wahl, 1998). Since the report by Wahl (1998), additional regression equations have been developed to estimate breach width and breach development time. In general, several of the regression equations should be used to make estimates of the breach dimensions and failure time. These estimates should then be used to perform a sensitivity analysis. The user should try to pick regression equations that were developed with data that is representative of the study dam. In many cases this may not be possible, due to the fact that most of the historic dam failures for earthen dams have occurred on smaller structures. In fact, out of the 108 historic dam breaches listed in the USBR report (Wahl, 1998), only thirteen of the dams are
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over 30.5 meters high and only five of the dams had a storage volume greater than 123.4x106 cubic meters at the time of failure. Additionally, most of the regression equations were developed from a smaller subset of this data (20 to 50 dams), and the dams included in the analysis are a mixture of homogenous earthen dams and zoned earthen dams (dams with clay cores, or varying materials). Therefore, the use of any of the regression equations should be done with caution, especially when applying them to larger dams that are outside the range of data for which the equations were developed. The use of regression equations for situations outside of the range of the data they for which were developed for may lead to unrealistic breach dimensions and development times. The following regression equations have been used for several dam safety studies found in the literature (except the Xu and Zhang equations, which are presented because of their wide range of historical data values), and are presented in greater detail in the document (Using HEC-RAS for Dam Break Studies, 2014):
Froehlich (1995a)
Froehlich (2008)
MacDonald and Langridge-Monopolis (1984)
Von Thun and Gillette (1990)
Xu and Zhang (2009) Froehlich (1995a): Froehlich utilized 63 earthen, zoned earthen, earthen with a core wall (i.e., clay), and rockfill data sets to develop as set of equations to predict average breach width, side slopes, and failure time. The data that Froehlich used for his regression analysis had the following ranges: Height of the dams: 3.66 – 92.96 meters (with 90% < 30 meters, and 76% < 15 meters); Volume of water at breach time: 0.0130 – 660.0 m3 x 106 (with 87% < 25.0 m3 x 106, and 76% < 15.0 m3 x 106). Froehlich's regression equations for average breach width and failure time are:
𝐵𝐵𝑎𝑎𝑎𝑎𝑎𝑎 = 0.1803𝐾𝐾0𝑉𝑉𝑤𝑤0.32ℎ𝑏𝑏0.19
𝑡𝑡𝑓𝑓 = 0.00254𝑉𝑉𝑤𝑤0.53ℎ𝑏𝑏−0.90 where:
Bave = average breach width (meters) Ko = constant (1.4 for overtopping failures, 1.0 for piping) Vw = reservoir volume at time of failure (cubic meters) hb = height of the final breach (meters) tf = breach formation time (hours)
Froehlich (2008): In 2008, Dr. Froehlich updated his breach equations based on the addition of new data. Dr. Froehlich utilized 74 earthen, zoned earthen, earthen with a core wall (i.e., clay), and rockfill data sets to develop as set of equations to predict average breach width, side slopes, and failure time. The data that Froehlich used for his regression analysis had the following ranges: Height of the dams: 3.05 – 92.96 meters (with 93% < 30 meters, and 81% < 15 meters); Volume of water at breach time: 0.0139 – 660.0 m3 x 106 (with 86% < 25.0 m3 x 106, and 82% < 15.0 m3 x 106). Froehlich's regression equations for average breach width and failure time are:
𝐵𝐵𝑎𝑎𝑎𝑎𝑎𝑎 = 0.27𝐾𝐾0𝑉𝑉𝑤𝑤0.32ℎ𝑏𝑏0.04
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𝑡𝑡𝑓𝑓 = 63.2√𝑉𝑉𝑤𝑤𝑔𝑔ℎ𝑏𝑏2
where:
Bave = average breach width (meters) Ko = constant (1.3 for overtopping failures, 1.0 for piping) Vw = reservoir volume at time of failure (cubic meters) hb = height of the final breach (meters) g = gravitational acceleration (9.80665 meters per second squared) tf = breach formation time (seconds)
MacDonald and Langridge–Monopolis (1984): MacDonald and Langridge-Monopolis utilized 42 data sets (predominantly earthfill dams, earthfill dams with a clay core, rockfill dams) to develop a relationship for what they call the "Breach Formation Factor". The Breach Formation Factor is a product of the volume of water coming out of the dam and the height of water above the dam. MacDonald and Langridge-Monopolis then related the breach formation factor to the volume of material eroded from the dam's embankment. The data that MacDonald and Langridge-Monopolis used for their regression analysis had the following ranges: Height of the dams: 4.27 – 92.96 meters (with 76% < 30 meters, and 57% < 15 meters) Breach Outflow Volume: 0.0037 – 660.0 m3 x 106 (with 79% < 25.0 m3 x 106, and 69% < 15.0 m3 x 106) The following is the MacDonald and Langridge-Monopolis equation for volume of material eroded and breach formation time, as reported by Wahl (1998): For earthfill dams:
𝑉𝑉𝑎𝑎𝑒𝑒𝑒𝑒𝑒𝑒𝑎𝑎𝑒𝑒 = 0.0261(𝑉𝑉𝑒𝑒𝑜𝑜𝑜𝑜 × ℎ𝑤𝑤)0.769
𝑡𝑡𝑓𝑓 = 0.0179(𝑉𝑉𝑎𝑎𝑒𝑒𝑒𝑒𝑒𝑒𝑎𝑎𝑒𝑒)0.364 For earthfill with clay core or rockfill dams:
𝑉𝑉𝑎𝑎𝑒𝑒𝑒𝑒𝑒𝑒𝑎𝑎𝑒𝑒 = 0.00348(𝑉𝑉𝑒𝑒𝑜𝑜𝑜𝑜 × ℎ𝑤𝑤)0.852 where:
Veroded = volume of material eroded from the dam embankment (cubic meters) Vout = volume of water that passes through the breach (cubic meters); for example, storage volume at time of breach plus volume of inflow after breach begins, minus any spillway and gate flow after breach begins. hw = depth of water above the bottom of the breach (meters). tf = breach formation time (hours).
The value of the Vout parameter is not exactly known before performing the breach analysis, as it is the volume of water that passes through the breach (not including flow from gates, spillways, and overtopping of the dam away from the breach area). A good first estimate is the volume of water in the reservoir at the time the breach initiates. Once a set of parameters are estimated, and a breach analysis is performed, the user should go back and try to make a better estimate of the actual volume of water that passes through the breach. Then recalculate the parameters with that volume. The recalculation of the volume makes the method iterative. The actual breach dimensions are a function of the volume eroded.
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Von Thun and Gillette (1990): Von Thun and Gillette used 57 dams from both the Froehlich (1987) paper and the MacDonald and Langridge-Monopolis (1984) paper to develop their methodology. The data that Von Thun and Gillette used for their regression analysis had the following ranges: Height of the dams: 3.66 – 92.96 meters (with 89% < 30 meters, and 75% < 15 meters) Volume of water at breach time: 0.027 – 660.0 m3 x 106 (with 89% < 25.0 m3 x 106, and 84% < 15.0 m3 x 106). The Von Thun and Gillette equation for average breach width is:
𝐵𝐵𝑎𝑎𝑎𝑎𝑎𝑎 = 2.5ℎ𝑤𝑤 + 𝐶𝐶𝑏𝑏
where: Bave = average breach width (meters) hw = depth of water above the bottom of the breach (meters)
Cb = coefficient, which is a function of reservoir size (Table 3).
Table 3. Values of Cb from Reservoir Size
Reservoir Size (m3) Cb (meters) <1.23*106 6.1
1.23∗106−6.17∗106 18.3 6.17∗106−1.23∗107 42.7
>1.23∗107 54.9
Von Thun and Gillette developed two different sets of equations for the breach development time. The first set of equations shows breach development time as a function of water depth above the breach bottom:
𝑡𝑡𝑓𝑓 = 0.02ℎ𝑤𝑤 + 0.25 (erosion resistant)
𝑡𝑡𝑓𝑓 = 0.015ℎ𝑤𝑤 (easily erodible)
where:
tf = breach formation time (hours) hw = depth of water above the bottom of the breach (meters)
The second set of equations shows breach development time as a function of water depth above the bottom of the breach and average breach width:
𝑡𝑡𝑓𝑓 = 𝐵𝐵𝑎𝑎𝑎𝑎𝑎𝑎4ℎ𝑤𝑤
(erosion resistant)
𝑡𝑡𝑓𝑓 = 𝐵𝐵𝑎𝑎𝑎𝑎𝑎𝑎4ℎ𝑤𝑤+61.0
(easily erodible)
where:
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Bave = average breach width (meters).
Xu and Zhang (2009): In 2009 a paper was published by Dr.'s Y. Xu and L.M. Zhang in the Journal of Geotechnical and Geo-Environmental Engineering. The database gathered by Dr.'s Xu and Zang contained 182 earth and rockfill dams from the United States and China, with nearly 50 percent of the dams greater than 15 meters in height. However, their final equations are based on a much smaller subset of these dams due to missing data. Their paper shows details for 75 dams that were comprised of homogeneous earth fill, zoned-filled, dams with corewalls, and concrete faced dams. Their final equation for the average breach width is based on 45 dam failures, and their equation for the time of failure is based on only 28 dam failures. The data that Xu and Zhang used for their regression analysis had the following ranges: Height of the dams: 3.2 – 92.96 meters (with 78% < 30 meters, and 58% < 15 meters) Volume of water at breach time: 0.105 – 660.0 m3 x 106 (with 80% < 25.0 m3 x 106, and 67% < 15.0 m3 x 106) Xu and Zhang’s regression equation for average breach width is:
𝐵𝐵𝑎𝑎𝑎𝑎𝑎𝑎ℎ𝑏𝑏
= 0.787 �ℎ𝑒𝑒ℎ𝑒𝑒�0.133
�𝑉𝑉𝑤𝑤1/3
ℎ𝑤𝑤�0.652
𝑒𝑒𝐵𝐵3
where:
Bave = average breach width (meters) Vw = reservoir volume at time of failure (cubic meters) hb = height of the final breach (meters) hd = height of the Dam (meters) hr = fifteen meters, is considered to be a reference height for distinguishing large dams from small dams hw = height of the water above the breach bottom elevation at time of breach (meters) B3 = b3+b4+b5 coefficient that is a function of dam properties b3 = -0.041, 0.026, and -0.226 for dams with corewalls, concrete faced dams, and homogeneous/zoned-fill dams, respectively b4 = 0.149 and -0.389 for overtopping and seepage/piping, respectively b5 = 0.291, -0.14, and -0.391 for high, medium, and low dam erodibility, respectively.
3.1.2.3 Physically-Based Breach Computer Models Several computer models have been developed that attempt to model the breach process using sediment transport theories, soil slope stability, and hydraulics. Mr. Wahl summarized some of these models in his report (Wahl, 1998). A table from Wahl's (1998) report, which summarizes the physically based computer models he reviewed, is shown in Table 4. In general, all of the models listed in Table 4 rely on the use of bed-load sediment transport equations, which were developed for riverine sediment transport processes. The use of these models should be viewed as an additional way of "estimating" the breach dimensions and breach development time. Of all the models listed in Table 4, the BREACH model developed by Dr. Danny Fread (1988) has been used the most for estimating dam breach parameters. Dr. Fread's model can be used for constructed earthen dams as well as landslide formed dams. The model can handle forming breaches from either overtopping or piping/seepage failure modes. The software uses weir and orifice equations for the hydraulic computation of flow rates. The Meyer-Peter and Muller sediment transport equation is used to compute transport capacity of the breach flow.
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Table 4. Physically-Based Embankment Dam Breach Computer Models
Model and Year Sediment Transport
Breach Morphology
Parameters Other Features
Cristofano (1965) Empirical formula Constant breach width
Angle of repose, others
Harris and Wagner (1967) BRDAM (Brown and Rogers, 1977)
Schoklitsch formula
Parabolic breach shape
Breach dimensions, sediments
Lou (1981); Ponce and Tsivoglou (1981)
Meyer-Peter and Müller formula
Regime type relation
Critical shear stress, sediment
Tailwater effects
BREACH (Fread, 1988)
Meyer-Peter and Müller modified by Smart
Rectangular, triangular, or trapezoidal
Critical shear, sediment
Tailwater effects, dry slope stability
BEED (Singh and Scarlatos, 1985)
Einstein Brown formula
Rectangular or trapezoidal
Sediments, others
Tailwater effects, saturated slope stability
FLOW SIM 1 and FLOW SIM 2 (Bodine, undated)
Linear predetermined erosion; Schoklitsch formula option
Rectangular, triangular, or trapezoidal
Breach dimensions, sediments
Breach enlargement is governed by the rate of erosion, as well as the collapse of material from slope failures. Dr. Fread's model can handle up to three material layers (inner core, outer portion of the dam, and a thin layer along the downstream face). The material properties that must be described are: internal friction angle; cohesive strength, grain size of the material (D50), unit weight, porosity, ratio of D90 to D30, and Manning's n. This software has been tested on a limited number of data sets, but has produced reasonable results. Additional research on the erosion process of earthen embankments that are overtopped is being conducted in the United States as well as Europe. The Agricultural Research Service (ARS) has been testing earthen embankment failures at sizes ranging from small scale laboratory models to near prototype scale dams (up to seven feet high) for several years (Hanson, et al., 2003; Hassan, et al., 2004). Similar tests have been performed in Norway for earthen dams, five to six meters high, constructed of rock, clay, and glacial moraine (Vaskinn, et al., 2004). The hope is that this research work will lead to the development of improved computer models of the breach process. A dam safety interest group made up of U.S. Government agencies (USBR, ARS, USACE), private industry, and Canadian and European research partners is currently evaluating new technologies for simulating the breach process. The goal of this effort is to develop computer simulation software that can model the dam breach process by progressive erosion for earthen dams initiated by either overtopping flow or seepage. Computer models that are currently being evaluated are: WinDAM (Temple, et al., 2006); HR-BREACH (Mohammed, 2002); and FIREBIRD (Wang and Kahawita, 2006). Table 5 provides a summary of these models capabilities (Wahl, 2009):
Table 5. Summary of the New Erosion Process Models
Model and Year Embankment Types Failure Modes Erosion Processes
WinDAM
Homogeneous with varying levels of
Overtopping
Headcut formation on downstream face,
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cohesiveness deepening, and upstream advancement; lateral widening
HR-BREACH
Homogeneous cohesive, or simple composite embankments with noncohesive zones, surface protection (grass or rock), and cohesive cores
Overtopping Piping
Variety of sediment transport/erosion equations and multiple methods of application. Discrete breach growth using bending, shear, sliding and overturning failure of soil masses.
FIREBIRD Homogeneous cohesive or noncohesive Overtopping
Coupled equations for hydraulics and sediment transport.
3.2 Peak Flow Equations and Envelope Curves Several researchers have developed peak flow regression equations from historic dam failure data. The peak flow equations were derived from data for earthen, zoned earthen, earthen with impervious core (i.e., clay, concrete, etc.) and rockfill dams only, and do not apply to concrete dams. Many of the equations were developed from limited data sets, and most were for smaller dams. Shown below is a summary of some of the peak flow equations that have been developed from historic dam failures:
USBR (1982): 𝑄𝑄 = 19.1(ℎ𝑤𝑤)1.85 (envelope equation)
MacDonald and Langridge-Monopolis (1984):
𝑄𝑄 = 1.154(𝑉𝑉𝑤𝑤ℎ𝑤𝑤)0.412
𝑄𝑄 = 3.85(𝑉𝑉𝑤𝑤ℎ𝑤𝑤)0.411 (envelope equation)
Froehlich (1995b): 𝑄𝑄 = 0.607𝑉𝑉𝑤𝑤0.295ℎ𝑤𝑤1.24
Xu and Zhang (2009): 𝑄𝑄
�𝑔𝑔𝑉𝑉𝑤𝑤5/3= 0.175 �ℎ𝑑𝑑
ℎ𝑟𝑟�0.199
�𝑉𝑉𝑤𝑤1/3
ℎ𝑤𝑤�−1.274
𝑒𝑒𝐵𝐵4
Kirkpatrick (1977): 𝑄𝑄 = 1.268(ℎ𝑤𝑤 + 0.3)1.24
Soil Conservation Service (SCS,1981): 𝑄𝑄 = 16.6(ℎ𝑤𝑤)1.85
Hagen (1982): 𝑄𝑄 = 0.54(ℎ𝑒𝑒)0.5
Singh & Snorrason (1984): 𝑄𝑄 = 13.4(ℎ𝑒𝑒)1.89
𝑄𝑄 = 1.776(𝑆𝑆)0.47
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Costa (1985): 𝑄𝑄 = 1.122(𝑆𝑆)0.57
𝑄𝑄 = 0.981(𝑆𝑆 ℎ𝑒𝑒)0.42 𝑄𝑄 = 2.634(𝑆𝑆 ℎ𝑒𝑒)0.44 (envelope equation)
Evans (1986): 𝑄𝑄 = 0.72(𝑉𝑉𝑤𝑤)0.53
where: Q = peak breach outflow (cubic meters per second) hw = depth of water above the breach invert at time of breach (meters) Vw = volume of water above breach invert at time of failure (cubic meters) S = reservoir storage for water surface elevation at breach time (cubic meters) hd = height of dam (meters) hr = fifteen meters, which is considered to be a reference height for distinguishing
large dams from small dams B4 = b3+b4+b5 coefficients that are a function of dam properties b3 = -0.503, -0.591, and -0.649 for dams with corewalls, concrete faced
dams, and homogeneous/zoned-fill dams, respectively b4 = -0.705 and -1.039 for overtopping and seepage/piping, respectively b5 = -0.007, -0.375, and -1.362 for high, medium, and low dam erodibility, respectively.
3.4 Tailing Dam Breach Outflow Calculation The failure of tailings storage facilities (TSF) can have disastrous consequences for nearby communities, the environment, and for the mining companies, who may consequently face high financial and reputational costs. In 2015, the breach of the Fundão TSF at Samarco mine in Minas Gerais (jointly owned by BHP Billiton Brasil and Vale S.A.) resulted in 19 fatalities, and was declared the worst environmental disaster in Brazil’s history. The company entered an agreement with the Federal Government of Brazil and other public authorities to remediate and compensate for the impacts over a 15 years period. Improvements in the design, monitoring, management, and risk analysis of TSFs are needed to prevent future failures and to estimate the consequences of a breach. The design of tailings dams has changed significantly from the 1930s to the present Design of Tailings Dams and Impoundments, 2017; Caldwell et al., 2011; Morgenstern et. al, 2010). Construction of the early TSFs was done by trial and error. During the 1960’s and 1970’s geomechanical engineering started to be used to assess the behavior of the tailings and the stability of the impoundments (Strachan et al., 2010). Currently, various studies are required to approve a TSF design and increasingly the plans for remediation and closure of the impoundments have to be included in the feasibility phase. Breach assessments are now part of the requirements in the permitting process of a new TSF or an expansion in many countries, including Armenia. Different parameters need to be estimated while conducting these assessments (Martin et al., 2017. These include the volume of tailings (VF) that could potentially be released, and the distance to which the material may travel in a downstream channel, called the run-out distance (Dmax). Empirical regression equations for this purpose were developed by Rico et al. (2008) using historical TSF failure data, and are commonly used to characterize such failures (similar empirical relationships have been developed for dams holding water (Pierce et. al, 2008; Pierce et. al, 2010),
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but the lack of tailings and differences in design and construction make them inapplicable to tailings dams). However, at site conditions in the mines can vary substantially and there is considerable residual uncertainty associated with the conditional mean value estimated by these equations. P. Larrauri and U. Lall (2018) updated these regression equations using an updated data set, and characterize the uncertainty associated with the prediction. Using the uncertainty distribution for the conditional estimation of VF and Dmax. applying TSF parameters provides a better way to interpret the TSF failure data and to characterize the risk associated with a potential failure. The calculation of VF
is of particular importance for inundation analyses. Typically, TSFs are not totally emptied in case of failure (as opposed to water dams), and only a portion of the tailings are released (Rico et al., 2008). In TSFs containing a large amount of water (supernatant pond), the breach would usually result in an initial flood wave followed by mobilized/liquefied tailings (Martin et. al, 2017). Therefore, the methods developed to estimate the released volume of water or the inundation extent from a regular dam does not apply to tailings dams. Empirical equations based on past failures, dam height, and the impounded volume of tailings, are commonly used to get a first estimate of the volume of tailings that could be released and the run-out distance. In Rico et al. (2008) VF is calculated using the total impounded volume (VT) in million m3 as in Equation (1):
𝑉𝑉𝐹𝐹 = 0.354 × 𝑉𝑉𝑇𝑇1.01 R2 = 0.86 (1)
and the outflow run-out distance travelled by the tailings in km (Dmax) is obtained using VF and the dam’s height in meters at the time of failure (H) as in Equation (2):
𝐷𝐷𝑚𝑚𝑎𝑎𝑚𝑚 = 1.61 × 𝐻𝐻𝑉𝑉𝐹𝐹0.66 R2 = 0.57 (2)
Many investigators directly use such regression equations in a deterministic way to specify exposure. However, at site conditions vary significantly, and there is considerable uncertainty that needs to be quantified. This uncertainty increases as we consider TSF volumes that are near or beyond the range of the data included in the regression equation. Equation (1) predicts that approximately a third of the tailings in the impoundment (including water) will be the outflow volume. This approach may result in unrealistic estimates when liquefaction is a known risk as it does not take into account the tailings mass rheology (viscosity and yield stress) (Martin et. al, 2017). As Rico et al. (2008) point out, some parameters contributing to the uncertainty in the predictions include sediment load, fluid behavior (depending on the type of failure), topography, the presence of obstacles stopping the flow, and the proportion of water stored in the tailings dam (linked to meteorological events or not). Therefore, it is important to account for the uncertainty in these estimates to derive a probabilistic measure of risk that also accounts for how well the regression fits in a certain range of values of the predictors. P. Larrauri and U. Lall (2018) combined the lists of TSF failures compiled by Rico et al. (2008) and Chambers and Bowker (TSF Failures 1915–2017 as of 16 August 2017, 2017) and compared the results of the original linear regressions done by Rico et al. (2008) with the results using the updated dataset. A new model for the calculation of Dmax was proposed introducing the predictor (Hf), which is defined as:
𝐻𝐻𝐹𝐹 = 𝐻𝐻 × �𝑉𝑉𝐹𝐹𝑉𝑉𝑇𝑇� × 𝑉𝑉𝐹𝐹 (3)
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This variable was introduced to consider that the potential energy associated with the release volume, may be better related to the fractional volume released as opposed to the total volume of the TSF. P. Larrauri ID and U. Lall (2018) compared the predicted intervals and observed values of VF and Dmax of three TSF failures across the models that were evaluated to see how well the prediction intervals fit the observed data. The indicated probability of exceeding of the observation as per each model was also assessed. Figure 4. Data on TSF Failures Compiled by Data in Rico et al. (2008) and Chambers and Bowker
(CB) (2017) (Entries in bold are not suitable for analysis)
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Figure 5 shows the relationships between VF and VT, and Dmax with H x VF (called dam factor in Rico (2008)) using the updated dataset (plots in log scale), and Dmax with Hf, (Equation (3)). VF and VT show a linear relationship in the log form, while for Dmax, there is greater dispersion with the dam factor and Hf.
Figure 5. Left: Relationship between VF and VT in x106 m3. Center: Dmax in km in relation to the dam factor (H x VF). Right: Dmax in km in relation to Hf (H x (VF/VT) xVF). All plots are in the log-log scale. CB points are added from Chambers and Bowker (2017) and R points are added from Rico (2008).
Using the updated TSF failure dataset and proposed Hf predictor, P. Larrauri and U. Lall (2018) developed a new regression equations for Vf and Dmax calculation:
log(𝑉𝑉𝐹𝐹) = −0.477 + 0.954 log(𝑉𝑉𝑇𝑇) or 𝑉𝑉𝐹𝐹 = 0.332 × 𝑉𝑉𝑇𝑇0.95 R2 = 0.887; standard error: 0.315 (4)
log(𝐷𝐷𝑚𝑚𝑎𝑎𝑚𝑚) = 0.484 + 0.545 log�𝐻𝐻𝑓𝑓� or 𝐷𝐷𝑚𝑚𝑎𝑎𝑚𝑚 = 3.04 ×𝐻𝐻𝑓𝑓0.545 Residual standard error= 0.658 (5)
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Equations (4) and (5) will be considered in the calculation of volume of tailings that potentially could be released in case of Geghanoush TSF dam break and travel distance of the tailings (see chapter 5.3).
3.5 Flood Modeling: One-Dimensional and Two-Dimensional Hydraulic Models The «Floods Directive» 2007/60/CE by the European Parliament requires the characterization of flood hazard by multi-scenario hydraulic analyses, based on the estimation of flow velocity and water depth or free-surface level over flooded areas. In principle, this evaluation demands a complete analysis of the watershed hydraulics, based on two- or even three-dimensional modelling. Since the latter, however, may hardly be applied at the watershed scale, 1D and 2D analyses represent the usual approaches to hydraulic risk mapping.
One-dimensional modeling requires that variables (velocity, depth, etc.) change predominantly in one defined direction along the channel. Because channels are rarely straight, the computational direction is along the channel centerline. Two-dimensional models compute the horizontal velocity components (Vx and Vy) or, alternatively, velocity vector magnitude and direction throughout the model domain3.
Main differences between one-dimensional and two-dimensional models are presented in the table below (Shahiri Parsa et al., 2016).
Table 6. Differences between one- and two-dimensional models
One-dimensional Two-dimensional Flow velocity perpendicular to the cross section considers
Speed in different directions are considered
Ability to model the flow is permanent and non-permanent
Ability to model the flow is turbulent
Only the channel cross sections are defined Model in computational mesh is divided into small pieces
Average speed in cross-section considers Flow rate can vary
The main assumption of 1D models is that the flow characteristics are calculated only for the cross-sections, while in 2D models allow to divide potential flooded area to computational mesh throughout entire territory.
3 http://ayresriverblog.com/2012/07/24/one-dimensional-versus-two-dimensional-modeling/
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Figure 6. 1D and 2D Model Domains
3.5 Fluid Dynamics: Steady and Unsteady Flow Velocity, pressure and other properties of fluid flow can be functions of time (apart from being functions of space). If a flow is such that the properties at every point in the flow do not depend upon time, it is called a steady flow. Steady flow means the velocity at any point in the flow field does not change with respect to time.
𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕
= 0
where P is a parameter like pressure, velocity or density. Thus,
𝜕𝜕 = 𝜕𝜕(𝑥𝑥, 𝑦𝑦, 𝑧𝑧)
For unsteady flow, the fluid properties are function of time (i.e., T = T(x, y, z, t), p = p(x, y, z, t) and ρ = ρ(x, y, z, t)). Unsteady flows can be further divided into periodic flow, non-periodic flow and random flow. For periodic flow, the property change is repeated in a predictable manner whereas the fluid motion and properties are difficult to predict in random flow as in turbulent flow. Some flows, though unsteady, become steady under certain frames of reference. These are called pseudosteady flows. Unsteady flows are undoubtedly difficult to calculate while with steady flows, we have one degree less complexity. The models like HEC-RAS can perform three types of calculations: (1) steady flow, (2) unsteady flow, and (3) movable boundary flow. The steady flow component uses the standard step method for the solution of steady gradually varied flow. The unsteady flow component uses a numerical solution of the complete equations of gradually varied unsteady flow, commonly referred to as the dynamic wave. The movable boundary component uses the sediment continuity and one of several sediment transport equations to calculate river bed aggradation and/or degradation. Under steady flow, the user specifies: (1) discharge at the upstream boundary, and (2) stage at the downstream boundary. The steady flow model proceeds to calculate stages throughout the interior points, while keeping the discharge constant.
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Figure 7. Steady Flow
Under unsteady flow, the user specifies: (1) a discharge hydrograph at the upstream boundary, and (2) a discharge-stage rating at the downstream boundary. The model proceeds to calculate discharges and stages throughout the interior points.
Figure 8. Unsteady Flow
Under steady flow, the discharge-stage ratings are unique, that is, they are the same as in unsteady kinematic flow. However, under unsteady dynamic flow, the model calculates looped discharge-stage ratings according to the variability of the flow. Therefore, the specification of a unique, that is, kinematic discharge-stage rating at the downstream boundary contradicts the solution at that boundary (Abbott, 1976). Simply stated, the wave cannot be kinematic at the downstream boundary and dynamic everywhere else.
A way out of this difficulty is: (1) to artificially move the downstream boundary further downstream, (2) to specify the unique discharge-stage rating at the new, artificial downstream boundary, and (3) to let the model calculate the looped ratings at all interior points, real and artificial, including the point where the actual physical downstream boundary is located (Ponce, 2001).
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Figure 9. Unsteady Dynamic Flow
Despite its apparent artificiality, this procedure works well and circumvents the need to know the discharge-stage rating at the downstream boundary before it is calculated (Ponce, 2011).
3.6 Manning Equation and N Values Roughness coefficients represent the resistance to flow in channels and floodplains. Roughness is usually presented in the form of a Manning's n value in dam break software. There is extensive research and literature on methods to determine n values; however most of this work is representative of only main channels and not floodplains. Additionally, the literature on Manning's n values is for historically experienced floods, which are much lower than the flood resulting from a dam break. The actual selection of n values to be used for each dam assessment will require judgment by the engineer responsible for hydraulic model development. A proper perspective is required before establishing a range of n values to be used in USACE risk assessment studies. The following general guidelines of factors that affect n values should be considered in developing representative values.
Base Surface roughness: Often represented by the size and shape of surface or channel and floodplain material that produces a friction effect on flow.
Stage and Discharge: The n value in most streams decreases with increase in stage and discharge. However, this is not always the case. If the channel bed is of lesser roughness than the channel banks, then the composite channel n values will increase with channel stage. Once the stage gets higher than the main channel banks, the roughness coefficient could begin to decrease. The main point here is that the variation of Manning's n with stage is site specific.
Obstructions: Objects constructed in the channel or in overbanks such as bridge piers or buildings can potentially cause increases in n value. It is especially difficult to estimate Manning's roughness coefficients to represent buildings in the floodplain, as there are many factors to consider: the area obstructed and the density of the buildings, direction of the flow in relation to the layout of the structures, roughness of all of the other boundaries, slope of the terrain, velocities of the flow, etc.
Irregularities: Variations in cross-section size and shape along the floodplain. Irregularities are often caused by natural constrictions and expansions, sand deposition and scour holes, ridges, projecting points and depressions, and holes and humps on the channel bed. Gradual and uniform changes will generally not appreciably affect n value. Whereas, areas that have lots of sharp channel irregularities will tend to have higher Manning's roughness coefficients.
Channel alignment: Smooth curvature with large radius will generally not increase roughness values, whereas sharp curvature with severe meandering will increase the roughness.
Vegetation: Dependent on height, density, distribution, and type of vegetation. Heavily treed areas can have a significant affect for dam failures. In general a lower average depth results in a higher n value. High velocities can potentially flatten the vegetation and lowering n values.
Silting, Scouring, and Debris: Silting may change a very irregular channel into a comparatively uniform one and decrease n and scouring may do the reverse. During a dam break flood wave, there will be a tremendous amount of scouring occurring, as well as lots of debris in the flow. The increase sediment load and debris will cause the flow to bulk
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up (increase in stage). One way to account for this increased sediment load and debris is to increase the Manning's n values.
The resulting maximum water surface profile associated with the failure of a dam will often be much higher than any historically observed flood profile. In such cases, there is no historical based model data to calibrate to floods of this magnitude. It is therefore incumbent upon the engineer to determine reasonable roughness coefficients for flows and stages that will be higher than ever experienced. To gain a perspective on how each modeling parameter affects results, a bounding type sensitivity analysis can be performed regardless of the methods used to establish n values. Manning's n Values Immediately below Dam. Significant turbulence, sediment load and debris should be expected for the immediate reach downstream of a failed dam. increased sediment and turbulence will cause higher water surfaces to occur. The only way to mimic this is by increasing the roughness coefficients. Proper modification and variation of n values is one of the many uncertainties in dam failure modeling. An accurate assessment can be confidently attained only after previous knowledge of a particular dam failure event. A reasonable modeling approach may be to assume double the normal n value directly downstream of the dam and transition to normal roughness coefficients where failure induced turbulence, sediment load, and debris transport are expected to recede. Roughness Coefficients for Steep Streams. Many of our dams are located in mountainous regions, where the slopes of the stream are significantly steep. It is very common to underestimate Manning's n values for steep terrain. Underestimation of the roughness coefficients can cause water surface elevations to be too low, increased velocities, and possibly even supercritical flow. In addition to this, abrupt changes in n values or underestimation of n values can cause the model to go unstable. Dr. Robert Jarrett (Jarrett, 1984) collected some extensive field data on steep streams (slopes greater than 0.002 feet/feet) in the Rocky Mountains. Dr. Jarrett measured cross sectional shape, flow rates, and water surface elevations at 21 locations for a total of 75 events. From this data Dr. Jarrett performed a regression analysis and developed an equation to estimate the Manning's roughness coefficient of the main channel.
𝑛𝑛 = 0.39𝑆𝑆0.38𝑅𝑅0.16
where: n = Manning's roughness coefficient of the main channel S = energy slope (slope of the energy grade line, feet/feet) R = hydraulic radius of the main channel (feet).
While Dr. Jarrett's equation is not necessarily applicable to all locations, it is often a useful check for reasonableness of the Manning's n values in steep terrain (Using HEC-RAS for Dam Break Studies, 2014).
Table 7. Manning's n for Channels (Chow, 1959)
Type of Channel and Description Minimum Normal Maximum
Natural streams - minor streams (top width at floodstage < 100 ft)
1. Main Channels
a. clean, straight, full stage, no rifts or deep pools 0.025 0.030 0.033
b. same as above, but more stones and weeds 0.030 0.035 0.040
c. clean, winding, some pools and shoals 0.033 0.040 0.045
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d. same as above, but some weeds and stones 0.035 0.045 0.050
e. same as above, lower stages, more ineffective slopes and sections 0.040 0.048 0.055
f. same as "d" with more stones 0.045 0.050 0.060
g. sluggish reaches, weedy, deep pools 0.050 0.070 0.080
h. very weedy reaches, deep pools, or floodways with heavy stand of timber and underbrush 0.075 0.100 0.150
2. Mountain streams, no vegetation in channel, banks usually steep, trees and brush along banks submerged at high stages
a. bottom: gravels, cobbles, and few boulders 0.030 0.040 0.050
b. bottom: cobbles with large boulders 0.040 0.050 0.070
3. Floodplains
a. Pasture, no brush
1.short grass 0.025 0.030 0.035
2. high grass 0.030 0.035 0.050
b. Cultivated areas
1. no crop 0.020 0.030 0.040
2. mature row crops 0.025 0.035 0.045
3. mature field crops 0.030 0.040 0.050
c. Brush
1. scattered brush, heavy weeds 0.035 0.050 0.070
2. light brush and trees, in winter 0.035 0.050 0.060
3. light brush and trees, in summer 0.040 0.060 0.080
4. medium to dense brush, in winter 0.045 0.070 0.110
5. medium to dense brush, in summer 0.070 0.100 0.160
d. Trees
1. dense willows, summer, straight 0.110 0.150 0.200
2. cleared land with tree stumps, no sprouts 0.030 0.040 0.050
3. same as above, but with heavy growth of sprouts 0.050 0.060 0.080
4. heavy stand of timber, a few down trees, little undergrowth, flood stage below branches 0.080 0.100 0.120
5. same as 4. with flood stage reaching branches 0.100 0.120 0.160
4. Excavated or Dredged Channels
a. Earth, straight, and uniform
1. clean, recently completed 0.016 0.018 0.020
2. clean, after weathering 0.018 0.022 0.025
3. gravel, uniform section, clean 0.022 0.025 0.030
4. with short grass, few weeds 0.022 0.027 0.033
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b. Earth winding and sluggish
1. no vegetation 0.023 0.025 0.030
2. grass, some weeds 0.025 0.030 0.033
3. dense weeds or aquatic plants in deep channels 0.030 0.035 0.040
4. earth bottom and rubble sides 0.028 0.030 0.035
5. stony bottom and weedy banks 0.025 0.035 0.040
6. cobble bottom and clean sides 0.030 0.040 0.050
c. Dragline-excavated or dredged
1. no vegetation 0.025 0.028 0.033
2. light brush on banks 0.035 0.050 0.060
d. Rock cuts
1. smooth and uniform 0.025 0.035 0.040
2. jagged and irregular 0.035 0.040 0.050
e. Channels not maintained, weeds and brush uncut
1. dense weeds, high as flow depth 0.050 0.080 0.120
2. clean bottom, brush on sides 0.040 0.050 0.080
3. same as above, highest stage of flow 0.045 0.070 0.110
4. dense brush, high stage 0.080 0.100 0.140
5. Lined or Constructed Channels
a. Cement
1. neat surface 0.010 0.011 0.013
2. mortar 0.011 0.013 0.015
b. Wood
1. planed, untreated 0.010 0.012 0.014
2. planed, creosoted 0.011 0.012 0.015
3. unplanned 0.011 0.013 0.015
4. plank with battens 0.012 0.015 0.018
5. lined with roofing paper 0.010 0.014 0.017
c. Concrete
1. trowel finish 0.011 0.013 0.015
2. float finish 0.013 0.015 0.016
3. finished, with gravel on bottom 0.015 0.017 0.020
4. unfinished 0.014 0.017 0.020
5. gunite, good section 0.016 0.019 0.023
6. gunite, wavy section 0.018 0.022 0.025
7. on good excavated rock 0.017 0.020
8. on irregular excavated rock 0.022 0.027
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d. Concrete bottom float finish with sides of:
1. dressed stone in mortar 0.015 0.017 0.020
2. random stone in mortar 0.017 0.020 0.024
3. cement rubble masonry, plastered 0.016 0.020 0.024
4. cement rubble masonry 0.020 0.025 0.030
5. dry rubble or riprap 0.020 0.030 0.035
e. Gravel bottom with sides of:
1. formed concrete 0.017 0.020 0.025
2. random stone mortar 0.020 0.023 0.026
3. dry rubble or riprap 0.023 0.033 0.036
f. Brick
1. glazed 0.011 0.013 0.015
2. in cement mortar 0.012 0.015 0.018
g. Masonry
1. cemented rubble 0.017 0.025 0.030
2. dry rubble 0.023 0.032 0.035
h. Dressed ashlar/stone paving 0.013 0.015 0.017
i. Asphalt
1. smooth 0.013 0.013
2. rough 0.016 0.016
j. Vegetal lining 0.030 0.500
3.7 Popular Models for Dam Break Analysis and Flood Mapping A lot of dam break analysis models both free and proprietary are currently available in the market. They have differences in user interface, input data requirements, accuracy and other characteristics. But all main dam break models use the same or similar algorithms for maximum outflow calculation and flood inundation mapping.
Comprehensive analysis of available models is presented in the paper «Selecting Dam Breach Innudation Software: Observations from Kentucky» by Shane Cook et al (2015).
Below some of the most popular dam breach programs compared.
Table 8. Comparison of dam break software
Software Developer Dimension Fluid Dynamics Model Input Model Output Price, USD
BOSS-DAMBRK
(FLDWAV)
BOSS International (now part of Autodesk)
1D Unsteady State
Typical breach parameters or hydrograph;
Cross-section data; Bridge/culvert geometry or rating
curves
High water profiles; Flood arrival times;
Hydrographs at selected locations 1495
DSS-WISE
Funded by DHS, developed by the NCCHE at
Ole Miss
2D computation
al engine (CCHE2DFL
OOD)
Steady/unsteady state
Typical breach parameters (for partial breach
scenario); Automatically utilizes NED, NBI,
NID, & NLCD
Inundation area; Arrival time shapefile; Max Depth
shapefile; Summary report
Freeware
HEC-RAS 1D US
Army Corps of Engineers
1D Steady/unsteady state
Cross section geometry, reach lengths,
Mannings n Discharge: peak flow (steady-state),
hydrograph (unsteady-state) Breach parameters or breach
hydrograph
Water surface elevation average velocity, and
other variables for each cross section
Depth grids, velocity grids using RASMAPPER
Freeware
HEC-RAS 1D US
Army Corps of Engineers
1D/2D Steady/unsteady state
Typical HEC-RAS setup, plus elevation
data to define 2D area
Typical HEC-RAS output (1D); Gridded Depths; WSELs; Velocities
at max and at time-steps
Freeware
FLO-2D FLO-2D Software, Inc. 1D/2D Steady/Unsteady
state
Typical breach parameters, physical breach
parameters (NWS-BREACH) or imported
hydrograph; Elevation dataset;
Roughness parameters
Grid and/or shaded contour plots of depth,
velocity, impact force; Animation of data;
Numerous plots, tables that can be constructed for individual cells;
Volume monitoring
Basic – Freeware;
Pro -995$/year
MIKE 11/21/FLOOD DHI 1D/2D Steady/unsteady
state
Breach parameters; Cross-section and/or elevation data; Roughness
parameters, etc.
Gridded Depths, velocities at maxand at time-steps; Animation of
data; Timesteps
7877
Volna «Titan-Optima» Ltd. 1D Steady/unsteady
state Dam and breach parameters;
Downstream elevation data; Cross-Maximum discharges and velocities
in cross-sections; 285 USD
(older
31
section data. Timesteps. version is freeware)
For our studies, HEC-RAS 2D model (5.0.x) will be applied and tested. GIS data and spatial analysis tools should assist to more efficient and precise mapping of flood inundation zones and determining of water depths. The detailed procedure and results of flood inundation mapping for Geghi and Geghanoush dam cases will be presented in next Report.
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4. Required Data for Dam Break(ch) Analysis and Mapping 4.1 Hydro-meteorological Observation Data Flood formation and its behavior is highly depends from hydro-meteorological conditions of the territory. Rainfall intensity and duration, snowmelt, air temperature and other meteorological factors are key drivers in flood development process.
Hydro-meteorological monitoring within the territory of Armenia is conducted by Hydromet Service of the Ministry of Emergency Situations of Armenia.
Figure 10. Hydro-Meteorological Monitoring Posts within Voghji River Basin
4.1.1 Meteorological Data There are 2 operational meteorological stations within Voghji River Basin: Kajaran and Kapan.
Table 9. Operational Monitoring Stations within Voghji River Basin
№ Name of Station Latitude Longitude H, m Observation
Period 1 Kajaran 39° 09’ 10” 46° 09’ 33” 1843 1975 – present 2 Kapan 39° 12’ 15” 46° 27’ 44” 705 1936 – present
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Thermal conditions normally decrease in the Voghji Basin as altitude increases. Multiyear annual average air temperature is in Kajaran is 6.8°C and in Kapan is 12.3°C (Table 10).
Table 10. Annual and monthly average air temperatures in the Voghji River Basin, օC
Meteorological Station
Absolute Altitude
(m)
Month
Year
I II III IV V VI VII VIII IX X XI XII
Kajaran 1980 -3.4 -3.0 0.5 5.7 10.2 14.2 17.1 16.6 13.3 8.2 3.2 -1.0
6.8
Kapan 704 0.8 2.4 6.3 12.3 16.1 20.4 23.7 23.1 19.0 13.0 7.5 2.9 12.3
Rainfall generally increases by altitude in the basin.
Table 11. Intra-annual distribution of atmospheric precipitation in the Voghji River Basin, mm
Meteorological station
Absolute Altitude
(m)
Month
Year
I II III IV V VI VII VIII IX X XI XII
Kajaran 1980 44 51 74 84 85 49 23 21 31 52 49 41 605 Kapan 704 25 31 59 75 94 66 31 28 41 49 40 25 565
The average annual relative humidity is 50-60%, and less than 30% at low altitudes (up to 1000 m). Frost-free days vary by altitude – annually from 260 (at the altitude of 700 m) to 50 days (higher than 3000 m). The annual average relative humidity is 60-80% (over 2600 m), and at lower altitudes - up to 30% (up to 1000 m).
Permanent snow cover starts at altitudes of 1200 m and it lasts for 35-165 days. The snow depth is 15-180 cm. It lasts 1-1.5 months at altitudes of up to 1500 m, and 6.5-7 months at altitudes of 3000 m and higher. The depth of snow cover is 15-20 cm at altitudes of 1300-1500 m and 120-180 cm at altitudes of 3000 m and higher (from place to place a 300 cm thick snow cover is formed, due to winds occurring in concavities).
Evaporation drops to 482-220 mm as altitude increases in the Voghji River Basin (Table 12). The highest value of evaporation, 500-480 mm. is observed at altitudes up to 800 m.
Table 12. Cumulative Evaporation in the Voghji River Basin, According to Altitude Zones
Altitude zones, m Cumulative evaporation, mm Up to 1000 482 1000-1500 438 1500-2000 382 2000-2500 328 2500-3000 270
3000 and higher 220
4.1.2 Hydrological Data There are 3 operational hydrological monitoring posts within Voghji River Basin: Voghji-Kajaran, Voghji-Kapan and Geghi-Kavchut. Data of closed monitoring posts of Geghi-Geghi and
35
Geghanoush-Geghanoush were analyzed as well due to their importance for the Geghi reservoir and Geghanoush tailings dam break modeling.
Table 13. Hydrological Monitoring Posts within Voghji River Basin
№ Water Object Name Name of station
Coordinates Latitude Longitude
1 Voghji River Kajaran 39° 08’ 59” 46 09’ 16” 2 Voghji River Kapan 39° 12’ 18” 46 24’ 43” 3 Geghi River Kavchut 39° 12’ 23” 46 14’ 50” 4 Geghi River Geghi 39° 13’ 21” 46 9’ 36”
5 Geghanoush River Geghanoush 39° 10’ 35” 46 25’ 24”
Table 14. Flow Characteristics in the Hydrological Monitoring Posts within Geghi River Basin
River-Post Discharge, m3/s
I II III IV V VI VII VIII IX X XI XII Annual Average Maximum
Geghi-Geghi 1.5 1.5 1.9 5.5 12.7 12.9 6.9 3.3 2.3 2.0 1.8 1.6 4.5 37.7
Geghi-Kavchut 1.4 1.5 2.3 5.9 12.5 12.0 6.3 3.0 2.1 1.9 1.7 1.5 4.4 87.5
Geghanoush-Geghanoush 0.2 0.2 0.7 1.9 1.8 0.9 0.4 0.3 0.3 0.3 0.3 0.2 0.6 21.3
Voghji-Kajaran 0.5 0.5 0.8 3.0 7.7 11.5 7.2 2.5 1.0 0.7 0.6 0.5 3.0 43.9
Voghji-Kapan 2.4 2.6 4.6 14.5 28.7 28.5 15.6 6.4 3.9 3.6 3.2 2.7 9.7 270.0
Figure 11. Annual Distribution of River Flow In 4 Hydrological Posts of Voghji River Basin
Maximum flow calculations for above-mentioned hydroposts are presented in Chapter 5.2
4.2 Elevation Data and its Derivatives Elevation data has a crucial meaning in each flood modeling process. There are various free digital elevation models (DEMs) available online (SRTM, ASTER, ALOS), the spatial resolution of which is ~30 m. This resolution is not enough for detailed flood mapping in mountainous areas.
0.05.0
10.015.020.025.030.035.0
1 2 3 4 5 6 7 8 9 10 11 12
m3/s
Months
Geghi-Geghi
Geghi-Kavchut
Geghanoush-Geghanoush
Voghji-Kajaran
36
Georisk CJSC provided linear shapefile of elevation isolines of 1:10,000 scale. From this shapefile, 5 m resolution DEM of studied area was calculated using Topo to Raster interpolation tool of ArcGIS Spatial Analyst toolbox (Figure 12):
Figure 12. 5m DEM of Studied Area
Geomorphometric parameters (slope, aspect and shaded relief) were derived from DEM (Figure 13):
Figure 13. Slope Map of Studied Area
Using ArcHydro Tools, following raster layers were calculated from DEM:
• Filled DEM (hydrologically-corrected); • Flow Direction; • Flow Accumulation; • Streams (defined and segmented); • Catchments GRID.
37
From these layers, catchment polygon and drainage line vector layers were obtained (Figure 14):
Figure 14. Catchments and Drainage Network Delineated Using ArcHydro
4.3 Land Cover Land cover information is very important in modeling of floods in order to understand the extent of the flood and vulnerability from it. Land cover dataset (5m spatial resolution, supervised classification) for Southern Basin Management Area of Armenia (Vorotan, Veoghji, Meghriget River Basins) developed by USAID Clean Energy and Water Program is accepted for defining the land cover classes in studied area.
Figure 15. Land Cover Map of Studied Area
4.4 Other Spatial Data GIS layers available in AUA and IGS geodatabases (infrastructure, buildings, administrative units, water objects, monitoring sites location, etc.), as well as CAD drawings of Geghi and Geghanoush Dam areas provided by National University of Architecture and Construction and Georisk CJSC are used in dam breach analysis, flood hazard assessment and mapping.
38
Figure 16. Survey Data on Dams
39
5. Dam Break Analysis and Flood Mapping Implementation 5.1 Flood Hazard Index Calculation Flood hazard index (FHI) represents the probability of flood events in studied area. FHI was calculated using multi-criteria approach. The method of Analytical Hierarchy Process (AHP) developed by Saaty (1990) was applied for defining the weight of each parameter.
Following parameters are accepted for flood hazard index calculation by above-mentioned method:
• Flow accumulation; • Distance from drainage network; • Elevation; • Land cover; • Rainfall intensity described by Modified Fourier Index (MFI); • Slope; • Geology.
Figure 17. Flowchart for FHI Assessment Method (Kazakis et al., 2015)
The proposed methodology suggests a pairwise comparison, using a 7×7 matrix, where diagonal elements are equal to 1. In Table 15 the criteria of the FHI method are sorted in a hierarchical manner, for the studied basin. The values of each row characterize the importance between two parameters. The first row of the table illustrates the importance of Flow accumulation in regard to the other parameters which are placed in the columns. For example, flow accumulation is significantly more important from geology and therefore assigned the value 7. Row describes the importance of geology. Therefore the row has the inverse values of the pairwise comparison (e.g. 1/7 for flow accumulation) (Kazakis et al., 2015). More details of how Analytical Hierarchy Process is applied can be found in Saaty (1990).
40
Table 15. Classes, Rating and According Weights of FHI Assessment Parameters
Parameters Flow Acc.
Drainage Distance Elevation Land
Cover Rainfall Slope Geology
Flow Acc. 1 2 2 3 3 5 7 Drainage Distance 1/2 1 1 3 3 4 6
Elevation 1/2 1 1 3 3 4 6 Land Cover 1/3 1/3 1/3 1 2 4 5
Rainfall Intensity 1/3 1/3 1/3 1/2 1 4 5
Slope 1/5 1/4 1/4 1/4 1/4 1 3 Geology 1/7 1/6 1/6 1/5 1/5 1/3 1
Classes of parameters their rating and weights are presented in the table below (Table 16):
Table 16. Classes, Rating and According Weights of FHI Assessment Parameters
Parameter Class Rating Weight
Flow Accumulation (cells)
0-5000 10
3 5000-20000 8
20000-100000 6 100000-1000000 4
1000000-11000000 2
Distance from Drainage Network, m
0-25 10
2.1 25-50 8 50-75 6 75-100 4 >100 2
Elevation, m
<1000 10
2.1 1000-1500 8 1500-2000 6 2000-2500 4
>2500 2
Land Cover
Urban; industrial; water objects 10
1.2
Arable land 8 Pastures and grassland;
permanent crops 6
Open Spaces with little or no vegetation 4
Forests and shrubs 2
Rainfall Intensity (MFI)
75-83 10
1 68-75 8 63-68 6 59-63 4 <59 2
Slope (degree)
0-5 10
0.5
5-15 8 15-30 6 30-45 4
>45 2
41
Geology
Alluvial deposits 10
0.3
Slope deposits 8 Volcanogenic and
volcanogenic-sedimentary rocks
6
Moraines 4 Eluvial, eluvial-deluvial deposits in watershed
zones 2
Raster layers for each of parameters were developed and classified using values presented in the Table 16 (Figures 18-24):
Figure 18. Flow Accumulation (FAC)
Figure 19. Distance from Drainage Network (DIST)
42
Figure 20. Elevation Zones (ELEV)
Figure 21. Land Cover (LC)
Figure 22. Rainfall (MFI)
43
Figure 23. Slope (SLOPE)
Figure 24. Geology (GEOLOGY)
Flood Hazard Index for Studied Area was calculated through the following equation in Raster Calculator using the above-presented layers on flood hazard parameters:
FHI = 3.0 x FAC + 2.1 x DIST + 2.1 X ELEV + 1.2 X LC + 1.0 X MFI + 0.5 X SLOPE + 0.3 X GEOLOGY
Figure 25. Flood Hazard Index (FHI) Map of Studied Area
44
5.2 River Maximum Flow Analysis Maximum flow probabilities were calculated using annual absolute maximum time-series for hydroposts of Voghji River Basin, mathematical-statistical methods applied in hydrology (Luchsheva, 1983)., StokStat 1.2 hydrologic software and Rybkin-Alekseev equations
Table below presents calculated values of maximum flow of different probabilities for 5 hydrologic monitoring posts in Voghji River Basin: Geghi-Geghi, Geghi-Kavchut, Voghji-Kajaran, Voghji-Kapan and Geghanoush-Geghanoush.
Table 17. Maximum Flows of Different Probabilities Calculated for Hydroposts of Voghji River Basin*
River-Post Q0 Cv Cs Probability 0.01 0.1 1 2 5 10 25 50 95 99
Geghi-Geghi 23.85 0.336 0.159 56.31 50.38 43.40 40.92 37.31 34.27 29.14 23.69 11.03 6.06 Geghi-
Kavchut 23.2 0.341 0.296 57.82 51.02 43.27 40.66 36.79 33.55 28.25 22.79 10.93 6.58
Voghji-Kajaran 17.5 0.373 1.38 62.31 50.70 38.82 35.17 30.21 26.23 20.69 16.06 9.86 8.88
Voghji-Kapan 52.8 0.469 1.05 203.12 166.72 128.58 116.20 99.36 85.99 66.17 48.59 20.61 14.17 Geghanoush-Geghanoush 8.5 0.62 1.359 44.02 34.96 25.58 22.68 18.73 15.56 11.14 7.34 2.28 1.39
*Q0 is time-series average value; Cv is variation coefficient; Cs is asymmetry or skewness coefficient.
Annual maximum flow time-series and probability calculation (including probability curve) are presented in Annexes 1-5.
On May 15, 2010 in a result of the accident in Geghi Reservoir, water level in Geghi and Voghji Rivers increased rapidly and water flooded a large area downstream, including arable land and buildings in Kapan Town. Maximum discharge in Geghi-Kavchut hydropost was 87.5 m3/s (which is greater than 0.01% probability flow by 1.5 times) and 133 m3/s in Voghji-Kapan hydropost (which is greater than 1% probability flow).
Figure 26. Flood Event Caused by an Accident in Geghi Reservoir (May 15, 2010)
In August 29,1956 mudflow with 270m3/s discharge was recorded. This discharge is 1.3 times greater than 0.01% probability maximum flow.
45
5.3 Dam Breach Maximum Outflow and Breach Hydrograph Calculation Dam breach maximum flow and hydrograph for Geghi Dam calculated using TR-60 and TR-66 simplified dam breach outflow and routing models developed by the Engineering division of Soil Conservation Service of US Department of Agriculture (SCS, 1981).
The necessary input data for maximum outflow Qmax and hydrograph calculations are:
Table 18. Necessary Input Data for TR-60 and TR-66 Models
Elevations Top of Dam 4,609.6 Ft* msl Water Surface@Breach 4,599.8 Ft msl Average Valley Floor 4,379.9 Ft msl Wave Berm 4,489.9 Ft msl Stability Berm 4,489.9 Ft msl
Length of Dam@Breach Elev 886 Ft Storage Volume@Breach Elev 12,161 Ac Ft Top Width 32.8 Ft Upstream Slope Above Berm 2.5 :1 Upstream Slope Below Berm 2 :1 Downstream Slope Above Berm 2.5 :1 Downstream Slope Below Berm 2 :1
US Wave Berm Width 50 Ft DS Stability Berm Width 50 Ft
Theoretical breach width is calculated using following equation:
𝜕𝜕 =65(𝐻𝐻𝑤𝑤0.35)
0.416
Maximum outflow is calculated using following equation:
𝑄𝑄𝑚𝑚𝑎𝑎𝑚𝑚 = 65�𝐻𝐻𝑤𝑤1.85�
where Hw is height of the breach (ft).
Calculations for Geghi were made in US (Imperial) units and then converted to SI (Metric) units. Three scenarios of dam break are considered for Geghi Dam. The results are presented in the Table below.
46
Table 19. Calculated Values of Geghi Dam Breach Outflow and Timesteps using TR-60 and TR-66 models
Timesteps Breach Outflow, m3/s
Worst Case
Average Case
Best Case
0 min 56.31* 56.31* 56.31* 6 min 39700.6 13895 3970 12 min 5968.7 12936.2 7576.6 18 min 2339.6 10081.2 8771.1 24 min 938.1 6099.2 8084.2 30 min 396.8 2977.4 6721.1 36 min 187.8 1478.1 5368.7 42 min 107.1 881.3 3680.2 48 min 75.9 592.0 2219.8 54 min 63.9 270.3 1493.1 60 min 59.2 239.9 773.8 66 min 57.4 186.5 593.4 72 min 56.7 160.0 378.3 78 min 56.5 133.9 235.1 84 min 56.4 108.0 163.6 90 min 56.3 82.1 92.1
*Maximum flow of 0.01% probability in Geghi-Geghi monitoring post (calculated in previous Chapter)
The hydrographs for three dam-break scenarios are presented in FIgure 27:
Figure 27. Geghi Dam Breach Hydrographs
05000
1000015000200002500030000350004000045000
0min
6min
12min
18min
24min
30min
36min
42min
48min
54min
60min
66min
72min
78min
84min
90min
Qmax, m3/s
Worst Case
Average Case
Best Case
47
Geghanoush TSF dam failure maximum outflow and tailing travel distance were calculated using methodology presented in Chapter 3.5:
𝑉𝑉𝐹𝐹 = 0.332 × 𝑉𝑉𝑇𝑇0.95 𝐷𝐷𝑚𝑚𝑎𝑎𝑚𝑚 = 0.332 × 𝐻𝐻𝐹𝐹0.545 𝐻𝐻𝑓𝑓 = 𝐻𝐻 × (𝑉𝑉𝐹𝐹 𝑉𝑉𝑇𝑇⁄ ) × 𝑉𝑉𝐹𝐹
where: VT is total impounded volume (Million m3), VF is the volume of tailings that could potentially be released (Million m3), Dmax is the distance to which the material may travel in a downstream channel (run-out distance, km), Hf is predictor. Total impounded volume in Geghanoush TSF is 4.6 Million m3. Thus, according to the equations above, volume of tailings that could potentially be released (VF) is 1.4 Million m3 and run-out distance is 15.4 km.
48
6. Conclusions and Next Steps As can be concluded from the chapter on Methodology, a large number of scientific works have been conducted in past and during last years on the analysis of dam break characteristics and maximum outflow formed in a result of dam failure. Various methods and algorithms have been developed for estimating the above-mentioned parameters, but basically all of them are based on a statistical analysis of past dam failure cases.
In this Report, the possible dam break characteristics for Geghi Reservoir Dam were calculated using TR-60 and TR-66 simplified dam breach outflow and routing models developed by the Engineering division of Soil Conservation Service of US Department of Agriculture (SCS, 1981).
TSF dam break analysis is more complicated task due to the specifics of its content. Statistical method was also applied in development of regression equations for TSF dam break parameters calculation (Concha Larrauri et al., 2018). In this Report, we calculated the volume of tailings that could potentially be released and the distance to which the material may travel in a downstream channel (run-out distance) for Geghanoush TSF.
Spatial data on downstream area of dam is very important for definition of dam-break flood extent and characteristics. In this Report, hydro-meteorological, elevation, land cover and other spatial data for studied area is presented. Using these data, raster layer of flood hazard index for studied area was developed and river maximum flows of different probability were calculated, which will assist in development of flood inundation maps for different scenarios.
Dam-break flood inundation maps will be developed through HEC-RAS 2D (RAS-Mapper) or analogue models and GIS software (QGIS, ArcGIS) using the data collected, analyzed and processed and approaches presented in this Report. Description of applied methodology and results will be presented in next Report.
49
7. References 1. Abbott, M. 1976. Computational hydraulics: A short pathology. Journal of Hydraulic
Research, Vol. 14, No. 4.
2. Ackerman, Cameron T., 2014. Adapted from lecture material provided during HEC-RAS training courses.
3. Álvarez, M.; Puertas, J.; Peña, E.; Bermúdez, M. Two-dimensional dam-break flood analysis in data-scarce regions: The case study of Chipembe dam, Mozambique. Water 2017, 9, 432.
4. Atallah, Tony A., 2002. A Review on Dams and Breach Parameters Estimation. Master of Science in Hydrosystems Engineering, Virginia Polytechnic Institute & State University, Blacksburg, VA, January 2002.
5. BHP Billiton Results for The Year Ended 20 June 2016. Available online: http://www.bhp.com/-/media/bhp/documents/investors/news/2016/160816_bhpbillitonresultsyearended30june2016.pdf?la=en.
6. Blight, G.E.; Robinson, M.G.; Diering, J.A.C. The flow of slurry from a breached tailings dam. J. South. Afr. Inst. Min. Metall. 1981, 1, 1–10.
7. Brown, R. J. and Rogers, D. C., 1977. A simulation of the hydraulic events during and following the Teton Dam failure. Proceedings of Dam-Break Flood Routing Model Workshop, Bethesda, MD, pages 131 - 163; 18 – 20 October.
8. Caldwell, J.A.; Van Zyl, D. Thirty years of tailings history from tailings & mine waste. In Proceedings of the 15th International Conference on Tailings and Mine Waste, Vancouver, BC, Canada, November 2011.
9. Cannata, M.; Marzocchi, R. Two-dimensional dam break flooding simulation: A GIS-embedded approach. Nat. Hazards 2012, 61, 1143–1159.
10. Chow, V. T. Open-Channel Hydraulics. McGraw-Hill, New York, 1959.
11. Chronologies of Major Tailings Dams Failures. Available online: http://www.patagoniaalliance.org/swpcontent/uploads/2014/09/Chronology-of-major-tailings-dam-failures.pdf.
12. Concha Larrauri, P.; Lall, U. Tailings Dams Failures: Updated Statistical Model for Discharge Volume and Runout. Environments 2018, 5, 28.
13. Cook, S., Timberlake, T., Murphy, D., Stahl, J. Selecting Dam Breach Innudation Software: Observations from Kentucky. The Journal of Dam Safety, Volume 13, Issue 1, 2015, p. 41-52.
14. Costa, John E., 1985. Floods from Dam Failures. United States Department of the Interior, Geological Survey, Open-File Report 85-560, Denver, CO.
15. Cristofano, Eugene A., 1965. Method of Computing Erosion rate for Failure of Earthfill Dams.
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16. Design of Tailings Dams and Impoundments. Available online: http://www.infomine.com/library/publications/docs/Davies2002b.pdf.
17. Dewey, R. and Gillette, D., 1993. Prediction of Embankment Dam Breaching for Hazard Assessment. ASCE Specialty Conference on Geotechnical Practice in Dam Rehabilitation, Raleigh, North Carolina, 25-28 April 1993.
18. Evans, Stephen. G., 1986. The maximum discharge of outburst floods caused by the breaching of man-made and natural dams. Canadian Geotechnical Journal, 1986, 23(3), pages 385 - 387.
19. Failures 1915–2017 as of 16 August 2017. Available online: http://www.csp2.org/tsf-failures-1915-2017.
20. Fernandes, G.W.; Goulart, F.F.; Ranieri, B.D.; Coelho, M.S.; Dalesf, K.; Boesche, N.; Bustamante, M.; Carvalho, F.A.; Carvalho, D.C.; Dirzo, R.; et al. Deep into the mud: Ecological and socio-economic impacts of the dam breach in Mariana, Brazil. Nat. Conserv. 2016, 14, 35–45.
21. Fonseca do Carmo, F.; Kamino, L.H.Y.; Tobias, R.; de Campos, I.C.; Fonseca do Carmo, F.; Silvino, G.; de Castro, K.J.S.X.; Mateus Leite, M.; Rodrigues, N.U.A.; et al. Fundão tailings dam failures: The environment tragedy of the largest technological disaster of Brazilian mining in global context. Perspect. Ecol. Conserv.2017, 15, 145–151.
22. Form 20-F, Annual Report Pursuant to Section 12 or 15(d) of the Securities Exchange Act of 1934. Available online: http://www.vale.com/EN/investors/information-market/annual-reports/20f/20FDocs/Vale_20-F_FY2016_-_i.pdf.
23. Fread, Dr. Danny L., 1988 (revised 1991). BREACH: An Erosion Model for Earth Dam Failures. Hydrologic Research Laboratory, National Weather Service, National Oceanic and Atmospheric Administration (NOAA), Silver Springs, MD, July 1988 (revised August 1991).
24. Fread, Dr. Danny L., 1993. NWS FLDWAV model: The replacement of DAMBRK for dam-break flood prediction. 10th Annual Conference of the Association of State Dam Safety Officials, Kansas City, MO, 26 - 29 September 1993, pages 177–184.
25. Froehlich, David C., 1987. Embankment-Dam Breach Parameters. Hydraulic Engineering, Proceedings of the 1987 National Conference, ASCE, Williams burg, VA, pages 570 - 575.
26. Froehlich, David C., 1995. "Peak Outflow from Breached Embankment Dam". ASCE Journal of Water Resources Planning and Management, Volume 121, Issue 1, January 1995, pages 90 - 97.
27. Froehlich, David C., 1995. Embankment Dam Breach Parameters Revisited. First International Conference, Water Resources Engineering, Environmental and Water Resources Institute (EWRI), 14 - 18 August 1995. ASCE, Water Resources Engineering Proceeding, pages 887 - 891.
28. Froehlich, David C., 2008. Embankment Dam Breach Parameters and Their Uncertainties. ASCE, Journal of Hydraulic Engineering, Vol. 134, No. 12, December 2008, pages 1708-1721.
51
29. Georisk CJSC, Assessment of the Multi-Component Risk Determined by the Maximum Seismic Impact on the Kapan City (Multi-Hazard City Scenario). Project # ARM 10-0000005849, Final Report, Yerevan, 2017
30. Hagen, V. K., 1982. Re-evaluation of design floods and dam safety. Proceedings of 14th ICOLD Congress, Rio De Janeiro, Brazil. Vol. 1, pages 475 - 491, 1982.
31. Hanson, Gregory J., Cook, K.R., and Britton, S.L., 2003. Observed Erosion Processes During Embankment Overtopping Tests. American Society of Agricultural Engineers (ASAE), Annual Meeting, Proceedings, Paper No. 03-2066, July 2003.
32. Harris ,G.W. and Wagner, D.A., 1967. Outflow from Breached Earth Dams. University of Utah, Salt Lake City, UT.
33. Hassan, M., Morris, M., Hanson, G.J., and Lakhal, K., 2004. Breach formation: Laboratory and numerical modeling of breach formation. Proceedings of the Annual Conference of the Association of State Dam Safety Officials (ASDSO), Phoenix, AZ, 2004, pages 1321-1337.
34. Hydrologic Engineering Center, 1980. Flood Emergency Plans - Guidelines for Corps Dams, RD-13, June 1980. U.S. Army Corps of Engineers, Hydrologic Engineering Center, 609 Second Street, Davis, CA.
35. Jarrett, Dr. Robert D, 1984. Hydraulics of High-Gradient Streams. ASCE, Journal of Hydraulics, Volume 110, No. HY 11, pages 1519 - 1539; November 1984.
36. Johnson, F.A. and Illes, P., 1976. A Classification of Dam Failures. Water Power and Dam Construction, pages 43 - 45; December 1976
37. Kazakis, N, Kougias, I, Patsialis, T. Assessment of flood hazard areas at a regional scale using an index-based approach and Analytical Hierarchy Process: Application in Rhodope–Evros region, Greece. Science of the Total Environment 538 (2015) 555–563.
38. Kirkpatrick, Gerald. W., 1977. Evaluation guidelines for spillway adequacy, The Evaluation of Dam Safety. Engineering Foundation Conference, ASCE, New York, pages 395 - 414, 1977.
39. Los Frailes Tailings Incident, Mining & Environment Research Network. Available online: http://www.pebblescience.org/pdfs/LosFrailes.pdf.
40. Luchsheva A.A. Practical Hdrometry (in Russian). Leningrad, 1983, 423 p.
41. MacDonald, T.; Langridge-Monopolis, J. Breaching characteristics of dam failures. J. Hydraul. Eng. 1984, 110, 567–586.
42. MacDonald, Thomas C., and Langridge-Monopolis, J, 1984. Breaching characteristics of dam failures. ASCE Journal of Hydraulic Engineering, Vol. 110, No. 5, May 1984, pages 567 - 586.
43. Martin, V.; Akkerman, A. Challenges with conducting tailings dam breach studies. In Proceedings of the 85th Annual Meeting of International Commission on Large Dams, Prague, Czech Republic, July 2017.
44. Mohamed, M.A.A., 2002. Embankment Breach Formation and Modeling Methods. The Open University, England, UK.
52
45. Morgenstern, N.R. Improving the safety of mine waste impoundments. In Tailings and Mine Waste 2010; CRC Press: Vail, CO, USA, 2010; pp. 3–10.
46. Pierce, M.W.; Thornton, C.I.; Abt, S.R. Predicting peak outflow from breached embankment dams. J. Hydraul. Eng. 2010, 15, 338–349.
47. Ponce, V. M., and A. Lugo. 2001. Modeling looped ratings in Muskingum-Cunge routing. ASCE Journal of Hydrologic Engineering,Vol. 6, No. 2, March/April, 119-124.
48. Ponce, V.M., 2011. Unsteady flow with HEC-RAS.
49. Ponce, Victor M., and Tsivolgou , Andrew J., 1981. Modeling Gradual Dam Breaches. ASCE Journal of the Hydraulics, Proceedings, Volume107, No. 7, pages 829 - 838.
50. Renova Foundation Update. Available online: http://www.bhp.com/-/media/documents/media/reportsand-presentations/2017/170607_renovafoundationupdate.pdf.
51. Rico, M.; Benito, G.; Diez-Herrero, A. Floods from tailings dam failures. J. Hazard. Mater. 2008, 154, 79–87.
52. Saaty, Thomas L., 1990a. How to make a decision: the analytic hierarchy process (ISSN 03772217).
53. Samuels, P.G., 1989. Backwater lengths in rivers. Proceedings of the Institution of Civil Engineers, Part 2, Volume 87, pages 571 - 582.
54. SCS, 1981. Simplified Dam-Breach Routing Procedure. United States Department of Agriculture, Soil Conservation Service (SCS), Technical Release No. 66 (Rev. 1), 39.
55. Shahiri, P. Floodplain Zoning Simulation by Using HEC-RAS and CCHE2D Models in the Sungai Maka River. Air, Soil and Water Research, 2016 (9), p. 55–62 doi:10.4137/ASWR.S36089
56. Singh, Krishan P. and Snorrason A., 1982. Sensitivity of Outflow Peaks and Flood Stages to the Selection of Dam Breach Parameters and Simulation Models. University of Illinois, State Water Survey Division, Surface Water Section, Champaign, IL, 179 pages; June1982.
57. Singh, Krishan P., and Snorrason, A., 1984. Sensitivity of outflow peaks and flood stages to the selection of dam breach parameters and simulation models. Journal of Hydrology, Vol 68, Issues 1-4, February 1984, pages 295 - 310. Global Water: Science and Engineering The Ven Te Chow Memorial Volume.
58. Singh, V. P. and Scarlatos, P. D., 1985b. Breach erosion of earth-fill dams and flood routing: BEED Model. Military Hydrology Report, page 131; U.S. Army Engineer Waterways Experiment Station, Environmental Laboratory, Vicksburg, MS.
59. Singh, V.P., Scarlatos, P.D., Collins, J.G. and Jourdan, M.R., 1988. Breach Erosion of Earthfill Dams (BEED) Model. Natural Hazards, Volume 1, pages 161 - 180.
60. Strachan, C.; Caldwell, J. New directions in tailings management. In Tailings and Mine Waste 2010; CRC Press: Vail, CO, USA, 2010; pp. 41–48.
53
61. Tailings Dams Risk of Dangerous Occurrences. Lessons Learnt from Practical Experiences. Available online: http://www.unep.fr/shared/publications/pdf/2891-TailingsDams.pdf.
62. Temple, Darrel M., G.J. Hanson, and Neilsen, M.L., 2006. WINDAM – Analysis of Overtopping Earth Embankment Dams. ASABE Annual International Meeting Proceedings, Paper No. 06- 2105; 9 - 12 July 2006, Portland, OR.
63. U.S. Bureau of Reclamation, Engineering and Research Center, Denver CO; 1965.
64. United States Federal Energy Regulatory Commission (FERC) - Notice of Revised Emergency Action Plan Guidelines, 22 February 1988.
65. USBR, 1982. Guidelines for defining inundated areas downstream from Bureau of Reclamation dams. Reclamation Planning Instruction, No. 82-11; 15 June 1982, U.S. Bureau of Reclamation.
66. Van Niekerk, H.J.; Viljoen, M.J. Causes and consequences of the Merriespruit and other tailings-dam failures. L. Degrad. Dev. 2005, 16, 201–212.
67. Vaskinn, Kjetil A., Lovoll, M.A., Hoeg, K., Morris, M., Hanson, G., and Hassan, M., 2004. Physical Modeling of Breach Formation; Large Scale Field Tests. State Dam Safety Officials Association Proceedings. Phoenix, AZ, September 2004.
68. Von Thun, J. Lawrence, and Gillette, D. R., 1990. Guidance on breach parameters. Unpublished internal document, U.S. Bureau of Reclamation, Denver, CO. March 1990, 17 pages.
69. Wahl, Tony L., 1998. Prediction of Embankment Dam Breach Parameters - A Literature Review and Needs Assessment. Dam Safety Research Report, DSO-98-004. Water Resources Research Laboratory, U.S. Dept. of the Interior, Bureau of Reclamation, Dam Safety Office (DSO), July 1998.
70. Wahl, Tony L., 2009. "Evaluation of New Models for Simulating Embankment Dam Breach. Association of State Dam Safety Officials (ASDO) Conference, Hollywood, Florida, 27 September - 1 October 2009.
71. Wahl,T. Dam Breach Modeling – an Overview of Analysis Methods. Joint Federal Interagency Conference on Sedimentation and Hydrologic Modeling. June 27 - July 1, 2010, Las Vegas, NV
72. Walder, Joseph S. and O'Connor, J. E., 1997. Methods for predicting peak discharge of floods caused by failure of natural and constructed earth dams. Water Resources Research, Vol. 33 Issue 10, pages 2337 - 2348. October 1997.
73. Wang, P., Kahawita, R., Mokhtari, A., Phat, T.M. and Quach, T.T., 2006. Modelling breach formation in embankments due to overtopping. ICOLD Conference, Barcelona, Spain, June 2006.
74. Xu, Y. and Zhang , L. M., 2009. Breaching Parameters for Earth and Rockfill Dams. ASCE Journal of Geotechnical and Geoenvironmental Engineering, Volume 135, No. 12, pages 1957 - 1970, December 2009.
54
Annex 1. Calculation of Maximum Flow of Deifferent Probabilities for Geghi-Geghi Hydropost
N Year Max. m3/s
Observation Date
Max. m3/s, descending
Probability, (m/(n+1))x100
1 1959 21.5 27/05 37.7 2.9 2 1960 33.4 29 - 31.05 37.3 5.7 3 1961 9.00 06,07.05 35.7 8.6 4 1962 13.5 22/05 35.1 11.4 5 1963 30.7 02.06 33.4 14.3 6 1964 21.7 09,10.05 31.6 17.1 7 1965 20.4 29.05,07.06,12.07 30.9 20.0 8 1966 21.6 25.05 30.9 22.9 9 1967 29.5 14.05 30.8 25.7
10 1968 37.7 17.06 30.7 28.6 11 1969 29.7 14.05 30.3 31.4 12 1970 16.0 18.04 29.9 34.3 13 1971 12.8 09,10.05 29.7 37.1 14 1972 27.2 31.07 29.5 40.0 15 1973 22.3 16.06 27.2 42.9 16 1974 16.6 21.05 22.3 45.7
17 1975 18.1 02,05,30.05 -
01.06 21.7 48.6 18 1976 35.1 20.05 21.7 51.4 19 1977 30.3 20.06 21.6 54.3 20 1978 30.8 17.06 21.5 57.1 21 1979 21.7 02,07.06 20.4 60.0 22 1980 19.9 20.05 19.9 62.9 23 1981 17.8 03.06 , 06.07 (2) 18.4 65.7 24 1982 18.4 19.05 18.1 68.6 25 1983 30.9 06.06 17.8 71.4 26 1984 31.6 10.06 16.6 74.3 27 1985 29.9 02.06 16.0 77.1 28 1986 30.9 24.06 15.0 80.0 29 1987 37.3 11,12.05 (2) 14.7 82.9 30 1988 35.7 19.05 14.6 85.7 31 2004 15.0 12/05 14.6 88.6 32 2006 14.6 24 - 27.05(3) 13.5 91.4 33 2007 14.7 23 - 27.05(5) 12.8 94.3 34 2008 14.6 23 - 27.05 9.00 97.1
55
Q0 (time-series average value) = 23.85; Cv (variation coefficient) = 0.336; Cs (asymmetry or skewness coefficient) = 0.159; Cs/Cv = 0.47
P 0.01 0.1 1 2 5 10 25 50 95 99
Φ 4.05 3.31 2.44 2.13 1.68 1.3 0.66 -0.02 -1.6 -2.2
Φ*Cv 1.36 1.11 0.82 0.72 0.56 0.44 0.22 -0.01 -0.54 -0.75
Kh=1+Φ*Cv 2.36 2.11 1.82 1.72 1.56 1.44 1.22 0.99 0.46 0.25
Qh=Kh*Q0 56.31 50.38 43.40 40.92 37.31 34.27 29.14 23.69 11.03 6.06
56
Annex 2. Calculation of Maximum Flow of Deifferent Probabilities for Geghi-Kavchut Hydropost
N Year Max. m3/s
Observation Date
Max. m3/s, descending
Probability, (m/(n+1))x100
1 1959 21.5 27.05 37.7 2.3 2 1960 33.4 29 - 31.05 37.3 4.7 3 1961 9.00 06,07.05 35.7 7.0 4 1962 13.5 22.05 35.1 9.3 5 1963 30.7 02.06 33.4 11.6 6 1964 21.7 09,10.05 32.3 14.0 7 1965 20.4 29.05,07.06,12.07 31.6 16.3 8 1966 21.6 25.05 31.2 18.6 9 1967 29.5 14.05 30.9 20.9 10 1968 37.7 17.06 30.9 23.3 11 1969 29.7 14.05 30.8 25.6 12 1970 16.0 18.04 30.7 27.9 13 1971 12.8 09,10.05 30.3 30.2 14 1972 27.2 31.07 29.9 32.6 15 1973 22.3 16.06 29.7 34.9 16 1974 16.6 21.05 29.5 37.2
17 1975 18.1 02,05,30.05 -
01.06 27.2 39.5 18 1976 35.1 20.05 22.3 41.9 19 1977 30.3 20.06 21.7 44.2 20 1978 30.8 17.06 21.7 46.5 21 1979 21.7 02,07.06 21.6 48.8 22 1980 19.9 20.05 21.5 51.2 23 1981 17.8 03.06 , 06.07 (2) 20.4 53.5 24 1982 18.4 19.05 19.9 55.8 25 1983 30.9 06.06 18.7 58.1 26 1984 31.6 10.06 18.5 60.5 27 1985 29.9 02.06 18.4 62.8 28 1986 30.9 24.06 18.1 65.1 29 1987 37.3 11,12.05 (2) 17.8 67.4 30 1988 35.7 19.05 17.4 69.8 31 2004 15.0 12.05 16.6 72.1 32 2006 14.6 24 - 27.05(3) 16.0 74.4 33 2007 14.7 23 - 27.05(5) 15.7 76.7 34 2008 14.6 23 - 27.05(3) 15.4 79.1 35 2009 32.3 24.04 15.0 81.4
57
36 2011 13.8 31.05 14.7 83.7 37 2012 31.2 23.05 14.6 86.0 38 2013 17.4 29,30.05(2) 14.6 88.4 39 2014 15.4 22,23.04(2) 13.8 90.7 40 2015 18.5 14.05 13.5 93.0 41 2016 18.7 06,18.05(2) 12.8 95.3 42 2017 15.7 12.06 9.00 97.7
Q0 (time-series average value) = 23.2; Cv (variation coefficient) = 0.341; Cs (asymmetry or skewness coefficient) = 0.296; Cs/Cv = 0.87
P 0.01 0.1 1 2 5 10 25 50 95 99 Φ 4.38 3.52 2.54 2.21 1.72 1.31 0.64 -0.05 -1.55 -2.1
Φ*Cv 1.49 1.20 0.87 0.75 0.59 0.45 0.22 -0.02 -0.53 -0.72 Kh=1+Φ*Cv 2.49 2.20 1.87 1.75 1.59 1.45 1.22 0.98 0.47 0.28 Qh=Kh*Q0 57.82 51.02 43.27 40.66 36.79 33.55 28.25 22.79 10.93 6.58
58
Annex 3. Calculation of Maximum Flow of Deifferent Probabilities for Voghji-Kajaran Hydropost
N Year Max. m3/s
Observation Date
Max. m3/s, descending
Probability, (m/(n+1))x100
1 1959 21.3 15.06 43.9 1.7 2 1960 43.9 04,05,21,24.07 32.4 3.3 3 1961 8.70 10.05(6) 31.2 5.0 4 1962 10.6 07.06 26.3 6.7 5 1963 22.9 02.07 25.8 8.3 6 1964 24.8 27,29.05 25.5 10.0 7 1965 17.6 09.06 25.3 11.7 8 1966 26.3 08.06 25.0 13.3 9 1967 17.1 14,15.06 24.8 15.0
10 1968 25.5 15.06 22.9 16.7 11 1969 19.0 06.06 22.9 18.3 12 1970 15.3 20.06 21.9 20.0 13 1971 12.0 08,09.06 21.3 21.7 14 1972 19.2 19.06 20.9 23.3 15 1973 25.3 26.06 20.8 25.0 16 1974 16.7 21.05 20.2 26.7 17 1975 20.8 11.06 20.1 28.3 18 1976 21.9 20.05 20.1 30.0 19 1977 19.9 21.06 19.9 31.7 20 1978 18.8 18.06 19.2 33.3 21 1979 11.2 30.06,01.07 19.0 35.0 22 1980 12.7 22.05 18.8 36.7 23 1981 18.1 24,25.06 (2) 18.4 38.3 24 1982 13.0 23-,4.06 (2) 18.3 40.0 25 1983 17.6 06.06 18.1 41.7 26 1984 18.3 10.06 - 12.07 (3) 17.8 43.3 27 1985 16.3 17-19.06 (3) 17.6 45.0 28 1986 16.9 27- 29.06 (3) 17.6 46.7 29 1987 13.7 05.06 17.1 48.3 30 1988 18.4 13.06 16.9 50.0 31 1989 14.8 27.05 16.7 51.7 32 1990 16.4 23.05, 03.06 (2) 16.4 53.3 33 1991 14.2 28.06 16.3 55.0 34 1992 22.9 07,11.07 (2) 15.8 56.7 35 1993 20.1 03.07 15.3 58.3 36 1994 14.7 15.06 14.8 60.0
59
37 1995 11.4 03-,4.06 (2) 14.7 61.7 38 1996 11.9 28,29.05 (2) 14.7 63.3 39 1997 12.9 31.05 14.7 65.0 40 1998 14.0 07.06 14.2 66.7 41 1999 13.3 31.05 14.0 68.3 42 2000 15.8 05.06 13.7 70.0 43 2001 9.00 08.06 13.3 71.7 44 2002 20.2 28.06 13.0 73.3 45 2003 25.0 18.06 12.9 75.0 46 2004 32.4 06,07.06(2) 12.7 76.7 47 2005 17.8 17,18.06(2) 12.0 78.3 48 2006 25.8 18 - 21.06(4) 11.9 80.0 49 2007 20.9 30,31.05(2) 11.6 81.7 50 2008 14.7 24.06 11.4 83.3 51 2009 14.7 28.05 11.4 85.0 52 2010 31.2 09.06 11.2 86.7 53 2011 20.1 31.05 10.6 88.3 54 2012 5.78 30.05 - 01.08(3) 9.19 90.0 55 2013 11.4 01,02.07(2) 9.00 91.7 56 2014 11.6 07,08.06(2) 8.70 93.3 57 2015 9.19 14/05 8.50 95.0 58 2016 8.50 06.05 - 20.06(6) 7.44 96.7 59 2017 7.44 17.06 - 02.07(14) 5.78 98.3
Q0 (time-series average value) = 17.5; Cv (variation coefficient) = 0.373; Cs (asymmetry or skewness coefficient) = 1.38; Cs/Cv = 3.70
P 0.01 0.1 1 2 5 10 25 50 95 99 Φ 6.87 5.09 3.27 2.71 1.95 1.34 0.49 -0.22 -1.17 -1.32
Φ*Cv 2.56 1.90 1.22 1.01 0.73 0.50 0.18 -0.08 -0.44 -0.49 Kh=1+Φ*Cv 3.56 2.90 2.22 2.01 1.73 1.50 1.18 0.92 0.56 0.51 Qh=Kh*Q0 62.31 50.70 38.82 35.17 30.21 26.23 20.69 16.06 9.86 8.88
60
61
Annex 4. Calculation of Maximum Flow of Deifferent Probabilities for Voghji-Kapan Hydropost
N Year Max. m3/s Observation Date
Max. m3/s, descending
Probability, (m/(n+1))x100
1 1935 27.3 20.05 133 1.5 2 1936 34.3 26,27.06 118 3.0 3 1946 51.7 18.05 109 4.5 4 1947 38.8 13.06 96.2 6.0 5 1948 58.7 20.06 90.3 7.5 6 1949 38.0 13.05 88.2 9.0 7 1950 33.6 01.06 84.4 10.4 8 1951 24.6 01.06 83.6 11.9 9 1952 49.4 27.05 83.5 13.4 10 1953 45.0 21.06 80.5 14.9 11 1954 46.1 08,28.05,01,08.06 78.5 16.4 12 1955 29.3 25.05 75.1 17.9 13 1956 44 06,10.06 73.6 19.4 14 1957 39.5 20.05 72.8 20.9 15 1958 44.6 26.05 71.7 22.4 16 1959 70.0 13.05 70.5 23.9 17 1960 56.4 12.05 70.0 25.4 18 1961 22.9 07.05 68.6 26.9 19 1962 45.0 30.05 65.5 28.4 20 1963 65.5 11.05 65.0 29.9 21 1964 80.5 24.05 64.5 31.3 22 1965 78.5 12.07 59.1 32.8 23 1966 64.5 25.05 58.7 34.3 24 1967 109 14.05 57.3 35.8 25 1968 83.6 19.04 56.7 37.3 26 1969 68.6 16.06 56.4 38.8 27 1970 32.8 05,06.06 52.6 40.3 28 1971 31.6 29 - 31.05 52.0 41.8 29 1972 52.0 29.05 51.7 43.3 30 1973 90.3 05.06 50.5 44.8 31 1974 65.0 13.05 49.4 46.3 32 1975 70.5 21.05 49.3 47.8 33 1976 118 20.05 48.6 49.3 34 1977 72.8 11.06 46.1 50.7 35 1978 83.5 10.06 45.5 52.2 36 1979 73.6 18.05 45.0 53.7 37 1980 71.7 22.05 45.0 55.2
62
38 1981 48.6 25.06, 02.07(2) 44.6 56.7 39 1982 33.4 17,19.05(2) 44.5 58.2 40 1983 41.8 07.06 44 59.7 41 1984 56.7 10.06 41.8 61.2 42 1985 59.1 02.06 39.5 62.7 43 1986 75.1 22,23.06 (2) 38.8 64.2 44 1987 96.2 23.05 38.0 65.7 45 1988 84.4 24.05 35.3 67.2 46 1989 26.3 04.05 34.3 68.7 47 1990 50.5 25.05 33.6 70.1 48 1991 32.0 17.05 33.4 71.6 49 2000 26.4 03,4.06 (2) 32.8 73.1 50 2001 11.4 26,27.05(2) 32.5 74.6 51 2002 52.6 31.05 32.0 76.1 52 2003 88.2 06.04 31.6 77.6 53 2004 57.3 09.06 31.6 79.1 54 2005 45.5 01.06 30.2 80.6 55 2006 31.6 08.05 30.1 82.1 56 2007 44.5 06.05 29.9 83.6 57 2008 23.9 08.07 29.3 85.1 58 2009 35.3 24.04 - 16.06(3) 27.3 86.6 59 2010 133 15,16.05(2) 26.4 88.1 60 2011 32.5 31.05 26.3 89.6 61 2012 49.3 23.05 26.2 91.0 62 2013 29.9 27.05 24.6 92.5 63 2014 21.7 25.05 23.9 94.0 64 2015 30.1 14.05 22.9 95.5 65 2016 30.2 05.05 21.7 97.0 66 2017 26.2 24.04 11.4 98.5
Q0 (time-series average value) = 52.8; Cv (variation coefficient) = 0.469; Cs (asymmetry or skewness coefficient) = 1.05; Cs/Cv = 2.23
P 0.01 0.1 1 2 5 10 25 95 99 Φ 6.07 4.6 3.06 2.56 1.88 1.34 0.54 -1.3 -1.56
Φ*Cv 2.85 2.16 1.44 1.20 0.88 0.63 0.25 -0.61 -0.73 Kh=1+Φ*Cv 3.85 3.16 2.44 2.20 1.88 1.63 1.25 0.39 0.27 Qh=Kh*Q0 203.12 166.72 128.58 116.20 99.36 85.99 66.17 20.61 14.17
63
64
Annex 5. Calculation of Maximum Flow of Deifferent Probabilities for Geghanoush-Geghanoush Hydropost
N Year Max. m3/s
Observation Date
Max. m3/s, descending
Probability, (m/(n+1))x100
1 1961 4.22 25/04 21.3 3.6 2 1962 3.08 05/04 19.8 7.1 3 1963 19.8 11.05 17.2 10.7 4 1964 7.00 27,30.04 15.6 14.3 5 1965 1.60 20.04(4),26.06 14.8 17.9 6 1966 12.7 22.04 12.7 21.4 7 1967 4.94 18.05 11.8 25.0 8 1968 6.72 21.06 9.75 28.6 9 1969 17.2 16.06 8.50 32.1
10 1970 4.44 20.04 7.9 35.7 11 1971 4.18 29.05 7.38 39.3 12 1972 7.3 13,29.05 7.33 42.9 13 1973 7.33 05.06 7.3 46.4 14 1974 14.8 07.07 7.00 50.0 15 1975 6.40 06.05 6.72 53.6 16 1976 15.6 17.05 6.45 57.1 17 1977 5.27 19.05 6.40 60.7 18 1978 6.45 02.06 5.90 64.3 19 1979 8.50 08.05 5.27 67.9 20 1980 3.36 29.03 4.94 71.4 21 1981 9,75 19/01 4.60 75.0 22 1982 11.8 29/01 4.44 78.6 23 1983 5.90 28.04 4.22 82.1 24 1984 21.3 11.05 4.18 85.7 25 1985 4.60 21.05 3.36 89.3 26 1986 7.38 21.06 3.08 92.9 27 1987 7.90 28/01 1.60 96.4
Q0 (time-series average value) = 8.5; Cv (variation coefficient) = 0.62; Cs (asymmetry or skewness coefficient) = 1.359; Cs/Cv = 2.19
P 0.01 0.1 1 2 5 10 25 50 95 99 Φ 6.74 5.02 3.24 2.69 1.94 1.34 0.5 -0.22 -1.18 -1.35
Φ*Cv 4.18 3.11 2.01 1.67 1.20 0.83 0.31 -0.14 -0.73 -0.84 Kh=1+Φ*Cv 5.18 4.11 3.01 2.67 2.20 1.83 1.31 0.86 0.27 0.16 Qh=Kh*Q0 44.02 34.96 25.58 22.68 18.73 15.56 11.14 7.34 2.28 1.39
65
