Assessment of the Breaching Event, Breach Parameters and Failure Mechanisms of the Spillway Collapse in the Swa Dam, Myanmar

The spillway of the Swa earthen dam, constructed in Yedashe Township, Bago Region, Myanmar, collapsed suddenly on 29 August 2018 and resulted in a huge flood to downstream areas causing fatalities and the displacement of thousands of localities. This study aimed to assess the spillway breaching process in terms of the breaching parameters such as the average breach width, failure time and peak outflow, and failure mechanisms. We analyzed the event from the changes in the study site before and after the event and used water discharge conditions from satellite data and water level records during the event. We compared the breaching parameters using empirical equations from past failed events with tested scenarios for failure mechanisms, such as overtopping and piping. According to satellite data, 97% of the storage from the reservoir was discharged, and the peak breach outflow rate was 7643 m3/s calculated from the water level records. The selected empirical formulas were applied, and the estimated average breach widths, failure times and peak discharge from the formulas were larger in overtopping and nearer in piping than that of the observed data for the Swa Dam. Thus, a concrete spillway might impact the erodibility rate of breaching compared with concrete-faced and earthen dam types.


Introduction
Although dams provide various benefits for livelihood, their failures also cause adverse effects on localities downstream. A dam break can be highly fatal due to the huge and rapid-moving waves made by the release of the reservoir water and can wash away every obstacle downstream. By analyzing data from historical dam failures, it is established that the majority of dam failure incidents belong to earth-fill dams [1,2]. For earth-fill dams, the failure is characterized by a gradual erosion of the dam material, due either to overflow or seepage, with a peak discharge more delayed with respect to the beginning of the erosion [3][4][5][6]. For a concrete dam, the failure is quite instantaneous, and the potential energy linked to the reservoir level is turned into kinetic energy. Therefore, the peak discharge occurs in a very short time [7][8][9]. For instance, the Malpasset Dam, a concrete dam in France with a height of 66.5 m and a reservoir volume of 55 million m 3 , broke in 1959 and caused flooding which killed 421 people [10]. Examples of the failure of earth dams are the Banqiao and Shimantan dams in Henan Province, China, which collapsed in 1975 due to Typhoon Nina causing reservoirs to swell with rainwater and resulted in a death toll of 85,000 and the loss of millions of homes and businesses [11]. Different case studies have shown that dam hazards occur because of several failure mechanisms, such as overtopping due to flooding, piping through the embankment or foundation, sliding downstream or upstream, technical problems in different dam elements such as spillways, foundation and slopes, poor management and natural disasters such as landslides and earthquakes [12][13][14].

Meteorological and Hydrological Conditions of the Study Site
The site is affected by tropical monsoons, and there are no rainfall stations within the catchment area of Swa Dam. Thus, rainfall data for the study site were collected from the rainfall station of Yedashe Township, located 16 km east of Swa Dam, which included the yearly rainfall records of the Hydrology branch of the Irrigation and Water Utilization Management Department (IWUMD) of Myanmar. According to the records, the average annual precipitation in the Swa Dam catchment is about 1700 mm, ranging from 939 to 2817 mm. The average annual inflow from the catchment of the study site is about 696 million m 3 , ranging from 426 to 1119 million m 3 . The condition of the average annual rainfall and inflow data are shown in Figure A1 (Appendix B).

Swa Dam
The Swa Dam is an earthen embankment dam, and the reservoir function is to store water for irrigation. For the dam dimensions, the dam crest is 7.3 m wide, the dam height is 29.56 m and the dam length is 2012 m. The upstream slope is 1:3, whereas the downstream slope is 1:2.5 until the first berm and 1:2.75 for the rest. The storage capacity of the reservoir is 267 million cubic meters at the full storage water level (R.L-102.7 m), and the water surface area is 2792 ha at that level. The dam is filled with clay material at the center and clay or sandy clay at the upstream and downstream sides. The average maximum dry density (MDD) of CL is 105 pounds per cubic foot (pcf) and the optimum moisture content (OMC) is 17.8%. The average MDD of SC is 112.6 pcf and OMC is 15.8%. The average plasticity index of CL is 18.2% and that of SC is 13.8%. The grain size

Meteorological and Hydrological Conditions of the Study Site
The site is affected by tropical monsoons, and there are no rainfall stations within the catchment area of Swa Dam. Thus, rainfall data for the study site were collected from the rainfall station of Yedashe Township, located 16 km east of Swa Dam, which included the yearly rainfall records of the Hydrology branch of the Irrigation and Water Utilization Management Department (IWUMD) of Myanmar. According to the records, the average annual precipitation in the Swa Dam catchment is about 1700 mm, ranging from 939 to 2817 mm. The average annual inflow from the catchment of the study site is about 696 million m 3 , ranging from 426 to 1119 million m 3 . The condition of the average annual rainfall and inflow data are shown in Figure A1 (Appendix B).

Swa Dam
The Swa Dam is an earthen embankment dam, and the reservoir function is to store water for irrigation. For the dam dimensions, the dam crest is 7.3 m wide, the dam height is 29.56 m and the dam length is 2012 m. The upstream slope is 1:3, whereas the downstream slope is 1:2.5 until the first berm and 1:2.75 for the rest. The storage capacity of the reservoir is 267 million cubic meters at the full storage water level (R.L-102.7 m), and the water surface area is 2792 ha at that level. The dam is filled with clay material at the center and clay or sandy clay at the upstream and downstream sides. The average maximum dry density (MDD) of CL is 105 pounds per cubic foot (pcf) and the optimum moisture content (OMC) is 17.8%. The average MDD of SC is 112.6 pcf and OMC is 15.8%. The average plasticity index of CL is 18.2% and that of SC is 13.8%. The grain size distribution of CL is clay 25.4%, silt 41.3% and sand 33.3%, and those of SC are clay 15.3%, silt 26.8%, sand 57.2% and gravel 0.7%. The soil parameters of the filling material of the main dam and saddle dam are as follows: dry density (r d ) (108.88 pcf), saturated density (r sat ) (130.5 pcf), water content (17.75%), soil specific gravity (2.68), cohesion (C) (0.67 kg/cm 2 ), internal friction angle (21 • ). The average permeability rate of the filling material is 4.3 × 10 −7 cm/sec and was found to be within the approved range for dam safety. To prevent seepage injection from the upstream side, a 0.6 m-thick diaphragm cut off wall was constructed using plastic concrete with a total length of 750 m and an average depth of 11.5 m. At the downstream end of the main dam, the seepage in the dam toe is 12 gal/min; therefore, an inverted sand filter and rock toe was constructed to protect from seepage landslide. The dam has a 1.6 m-thick sand and gravel layered horizontal filter. The dam was designed and constructed by the IWUMD under the Ministry of Agriculture, Livestock and Irrigation of Myanmar. The typical cross-section of the Swa Dam is shown in Figure A2 (Appendix B).

Spillway Description
The spillway is a reinforced concrete bath tube (duckbill) type ogee spillway, which has a 122 m total overflow length, and is 171 m long; the width of spillway is 36.6 m at the bottom and about 64 m maximum at the crest of the main dam. The height of the spillway at the dam crest is 13.7 m. The longitudinal gradient of the spillway is 1:0.7 in the mouth of the duckbill, 1:25 in the floor of the duckbill, 1:500 in the transition and 1:10 in the chute portion, as shown in Figure 2. The floor of the spillway is covered by 15 cm-thick lean concrete over 0.3 m-thick reinforced cement concrete at the duckbill part and 1.2 m-thick mass concrete at the transition and chute portions. The foundation test for the spillway was performed by 7 test holes at the transition portion (left and right), Duckbill and chute portion and the bulk density is from 1.52 to 1.67 t/m 3 , the moisture content is from 18.49 to 24.53% and the bearing capacity is from 3.26 to 4.2 kg/cm 2 (2.98 T.S.F to 3.84 T.S.F), and the largest values are found to be under the left side of the transition portion. Based on the rainfall data from the Yedashe Township station, projected floods in the Swa catchment for different return periods (20 years to 1000 years) were prepared by the IWUMD, as shown in Table A1 (Appendix A). The peak flood (Q p ) ranged from 1758 to 3491 m 3 /s with respect to the return periods. The spillway was designed to tolerate a flood that happened once in a 200-year period (2693 m 3 /s), and the overflow length of 120 m was designed for that flood. distribution of CL is clay 25.4%, silt 41.3% and sand 33.3%, and those of SC are clay 15.3%, silt 26.8%, sand 57.2% and gravel 0.7%. The soil parameters of the filling material of the main dam and saddle dam are as follows: dry density (rd) (108.88 pcf), saturated density (rsat) (130.5 pcf), water content (17.75%), soil specific gravity (2.68), cohesion (C) (0.67 kg/cm 2 ), internal friction angle (21 °). The average permeability rate of the filling material is 4.3 × 10 −7 cm/sec and was found to be within the approved range for dam safety. To prevent seepage injection from the upstream side, a 0.6 m-thick diaphragm cut off wall was constructed using plastic concrete with a total length of 750 m and an average depth of 11.5 m. At the downstream end of the main dam, the seepage in the dam toe is 12 gal/min; therefore, an inverted sand filter and rock toe was constructed to protect from seepage landslide. The dam has a 1.6 m-thick sand and gravel layered horizontal filter. The dam was designed and constructed by the IWUMD under the Ministry of Agriculture, Livestock and Irrigation of Myanmar. The typical cross-section of the Swa Dam is shown in Figure A2 (Appendix B).

Spillway Description
The spillway is a reinforced concrete bath tube (duckbill) type ogee spillway, which has a 122 m total overflow length, and is 171 m long; the width of spillway is 36.6 m at the bottom and about 64 m maximum at the crest of the main dam. The height of the spillway at the dam crest is 13.7 m. The longitudinal gradient of the spillway is 1:0.7 in the mouth of the duckbill, 1:25 in the floor of the duckbill, 1:500 in the transition and 1:10 in the chute portion, as shown in Figure 2. The floor of the spillway is covered by 15 cm-thick lean concrete over 0.3 m-thick reinforced cement concrete at the duckbill part and 1.2 m-thick mass concrete at the transition and chute portions. The foundation test for the spillway was performed by 7 test holes at the transition portion (left and right), Duckbill and chute portion and the bulk density is from 1.52 to 1.67 t/m 3 , the moisture content is from 18.49 to 24.53% and the bearing capacity is from 3.26 to 4.2 kg/cm 2 (2.98 T.S.F to 3.84 T.S.F), and the largest values are found to be under the left side of the transition portion. Based on the rainfall data from the Yedashe Township station, projected floods in the Swa catchment for different return periods (20 years to 1000 years) were prepared by the IWUMD, as shown in Table A1 (Appendix A). The peak flood (Qp) ranged from 1758 to 3491 m 3 /s with respect to the return periods. The spillway was designed to tolerate a flood that happened once in a 200-year period (2693 m 3 /s), and the overflow length of 120 m was designed for that flood.

Hydrological Conditions before the Breach Event
Before the breach event, 20 rainy days were observed in August; on 20 August, a maximum rainfall of about 60 mm was observed, according to the records of the Hydrology branch of the IWUMD. According to the records, starting from 25 August 2018, rainfall had continued for four days, and the spillway began to overflow on 26 August, as

Hydrological Conditions before the Breach Event
Before the breach event, 20 rainy days were observed in August; on 20 August, a maximum rainfall of about 60 mm was observed, according to the records of the Hydrology branch of the IWUMD. According to the records, starting from 25 August 2018, rainfall had continued for four days, and the spillway began to overflow on 26 August, as shown in Figure 3. The estimated outflow from the spillway was about 213 m 3 /s on 26 August. From 25 to 28 August 2018, the total rainfall was about 88 mm, and the water level in the reservoir was raised to R.L 103.2 m, 0.5 m above the full reservoir level (R.L 102.68 m). When the water level in the reservoir rose to R.L 103.1 m, the estimated outflow from the spillway changed to about 1911 m 3 /s on 28 August. In addition, the water level of the reservoir rose from 99 m (1 August) to 103.2 m (28 August), according to the records of the Hydrology branch of the IWUMD.
August. From 25 to 28 August 2018, the total rainfall was about 88 mm, and the water level in the reservoir was raised to R.L 103.2 m, 0.5 m above the full reservoir level (R.L 102.68 m). When the water level in the reservoir rose to R.L 103.1 m, the estimated outflow from the spillway changed to about 1911 m 3 /s on 28 August. In addition, the water level of the reservoir rose from 99 m (1 August) to 103.2 m (28 August), according to the records of the Hydrology branch of the IWUMD.

Failure Event and Consequences Downstream
Before the event, the spillway overflowed at about 0.5 m water depth above the spillway weir crest, and the water level was about 103.2 m which was about 4.1 m from the crest of the dam embankment. The water level in the reservoir remained at that level until the early morning of 29 August. According to the witnesses of the breach event, Swa's spillway seemed to have collapsed before 5 a.m LT on the morning of 29 August 2018; however, the water levels could be recorded at 5:00 a.m. The gauge watcher of the Swa Dam noticed that the water level at the gauge of the Swa Dam suddenly went down at about 4:00 a.m. LT and the villagers in the nearest village to the dam also reported that they found water under their residences. When the watcher reached the event site at 6:00 A.M, the spillway had already broken and the breach opening at the spillway had already extended to the right-side embankment of the Swa Dam. The left side of the duckbill part remained undestroyed during the event. The water from the reservoir flowed out from the opening continuously from 29 August to the next day, 30 August. The conditions of the study site before and after the spillway broke can be visualized using Google Earth images from December 2017 and 2019 as shown in Figure 4. The breach opening expanded to the right embankment was clearly identified by comparing the images in Figure 4.

Failure Event and Consequences Downstream
Before the event, the spillway overflowed at about 0.5 m water depth above the spillway weir crest, and the water level was about 103.2 m which was about 4.1 m from the crest of the dam embankment. The water level in the reservoir remained at that level until the early morning of 29 August. According to the witnesses of the breach event, Swa's spillway seemed to have collapsed before 5 a.m. LT on the morning of 29 August 2018; however, the water levels could be recorded at 5:00 a.m. The gauge watcher of the Swa Dam noticed that the water level at the gauge of the Swa Dam suddenly went down at about 4:00 a.m. LT and the villagers in the nearest village to the dam also reported that they found water under their residences. When the watcher reached the event site at 6:00 A.M, the spillway had already broken and the breach opening at the spillway had already extended to the right-side embankment of the Swa Dam. The left side of the duckbill part remained undestroyed during the event. The water from the reservoir flowed out from the opening continuously from 29 August to the next day, 30 August. The conditions of the study site before and after the spillway broke can be visualized using Google Earth images from December 2017 and 2019 as shown in Figure 4. The breach opening expanded to the right embankment was clearly identified by comparing the images in Figure 4.  As the water spilled out from the reservoir into surrounding farmland, the spillway failure instigated immense flooding in 85 villages of 17 village tracts in Yedashe Township and affecting over 63,000 people [37]. Then, the flood water from the spillway breach flowed across the downstream and toured down into the Sittaung River. The collapse of As the water spilled out from the reservoir into surrounding farmland, the spillway failure instigated immense flooding in 85 villages of 17 village tracts in Yedashe Township and affecting over 63,000 people [37]. Then, the flood water from the spillway breach flowed across the downstream and toured down into the Sittaung River. The collapse of the spillway submerged the road section between mileposts 161 and 166 on the Yangon-Mandalay Highway (5.2 km from the dam), and the road sections between mileposts 169 and 204 on the Yangon-Mandalay old express road (10 km from the dam) were submerged 0.3 m (1 ft) to 1 m (4 ft) under water for some time, according to the media records during the event [37]. According to the Ministry of Social Welfare, Relief and Resettlement, Myanmar, four people died and three were missing because of the downstream flood. The cause of the breach had not yet been identified, and the spillway collapsed because of progressive failure, according to the records [37].

Field Observation and Causes of Failure
The investigation team from the IWUMD visited the spillway collapse site in November 2018 to find the causes of the spillway collapse. With limited information because of the condition of the study site, the team figured that the failure causes might be related to the foundation and climate-change-related issues. The spillway foundation was found to be composed of sand, rocks and mudstones, and weathering was observed in the foundation as shown in Figure 5. Duckbill-type ogee structures might suffer uplift of the water head during high water periods; although reinforcement bars were provided in the concrete structure of the ogee spillway to resist the uplift of the water head and other tension stresses. On the other hand, foundation rocks become weak against tension stress caused by uplift of the water head and the slaking would have probably occurred to those stones according to the technical report of the investigation team. The weathering including slaking of the foundation and uplift of the water head may have acted against ogee spillway, and many specialists in Myanmar fault the main reason of failure on the foundation of the spillway.

Changes in the Study Site before and after the Dam Breach
As topographic data before the breach were not available for the study site, ALOS World 3D 30 m DEM by the Japan Aerospace Exploration Agency (JAXA) [38] was used to assess the topographic condition of the study site before the event. Meanwhile, topographic data after the breach were gathered from elevation contours prepared by the IWUMD from a field survey of the collapse site, which was conducted after the breach event. AW30D DEM (survey date between 2006 and 2011) [38] was compared with the topographic data of the field survey. The final breach opening was confirmed to have laterally expanded to the right bank, whereas the left bank of the spillway was almost not damaged at all, as shown in Figure 5.  Actually, after the impoundment of the Swa Dam in 2005, water has overflowed from the spillway every year according to the records of the IWUMD. On the other hand, the water level of the reservoir comes down lower than the bottom of ogee elevation starting in the dry season of 2009 according to the records of the IWUMD. Thus, the repetition of wet and dry conditions would lead the foundation toward slaking which would be one of the causes of weathering in the foundation. Therefore, the changing of the climate pattern of the study site might also be one of the factors of the failure. The team also recognized that seepage happened at the construction joint of the spillway, and each block of the spillway weir had a smooth surface, as shown in Figure 5. The team described that the seepage that happened at the construction joint might be one of the factors that affected the stability of the structure.

Changes in the Study Site before and after the Dam Breach
As topographic data before the breach were not available for the study site, ALOS World 3D 30 m DEM by the Japan Aerospace Exploration Agency (JAXA) [38] was used to assess the topographic condition of the study site before the event. Meanwhile, topographic data after the breach were gathered from elevation contours prepared by the IWUMD from a field survey of the collapse site, which was conducted after the breach event. AW30D DEM (survey date between 2006 and 2011) [38] was compared with the topographic data of the field survey. The final breach opening was confirmed to have laterally expanded to the right bank, whereas the left bank of the spillway was almost not damaged at all, as shown in Figure 5.  ). By applying a threshold value, the water pixels can be separated from the non-water pixels by the SNAP software version 8. In the SNAP software version 8, the color manipulation tab showed backscatter values, with low values corresponding to water and high values to non-water. For the Swa Dam case, a threshold value (e.g., 0.0515) was used to get the best representation of water, and this threshold value was applied to calculate the water area for both images. After analyzing the images, the results were visualized using the ArcGIS software version 10.3, and the water spread area calculation was analyzed using the reclassify tool of ArcGIS version 10.3.

Calculated Outflow Using Water Level Records during the Event
The water level of Swa Dam was measured daily (5:00 a.m. LT) for the non-flood season and hourly for the flood season (from July to October) at the gauge post located in the conduit tower of the Swa Dam. For the breach event, the water level was measured at 1 h intervals, starting from 5:00 a.m. on 29 August 2018 to 9:00 a.m. on 30 August 2018, using the water volume change with respect to time and water balancing in the Swa reservoir, as shown in Equation (1).
where V is the reservoir water volume with respect to the recorded water height (m 3 ), t is time (s), Q b is the breach discharge rate (m 3 /s), Q in is the inflow rate of the reservoir (m 3 /s), and Q f is the outflow through the conduit (m 3 /s). Q in for the Swa Dam was recorded daily by the IWUMD, whereas Q f was zero for the breach event as the conduit was closed at that time, according to the information from the IWUMD.

Dam Breaching Parameters
In this study, breach parameters were applied to assess the characteristics of breach events, such as the dimension of the breach channel, breach outflow and failure time. According to previous studies, several breach parameters describe the characteristics of the breach channel, such as the depth of the breached channel (H b ), and average width (B avg ) and characteristics of the breach event, such as the height of the water surface from the bottom of the breached channel (H w ), the total breach outflow volume (V w ), the failure time of the breach (T f ) and the peak outflow of the breach (Q p ) [42]. Moreover, the relationships between parameters were examined by collecting actual dam breach cases [43,44]. As a result, several empirical relationships were found (see Tables 1 and 2). In addition, previous studies reported that some breaching parameters are related to reservoir properties [45], such as the dam height (H d ), the dam width (W avg ), and the reservoir storage (V), as shown in Figure 6. Thus, we compared the relationships found in this study with previous empirical relationships to clarify the similarities and differences of the spillway breaching event in the Swa Dam and other dam breach events. Table 1. Selected empirical equations for dam types, failure modes and erodibilities.  Table 2. Empirical equations of Froehlich and Xu and Zhang.

Equation Developer
Average Breach Width Failure Time Peak Outflow

Xu and Zhang (2009) [26]
Note(s): The symbols are the same as those in Table 1. 1.
Breach parameters for the breach channel: The depth of the breached channel (H b ) is mentioned as a breach height in many works in the literature. It is the vertical extent of the breach measured from the crest of the dam down to the bottom of the breach [17][18][19][20][21][22][23][24][25][26]. Previous studies advise that if there is no information for the breach height (H b ), the height of the dam (H) could be taken as the breach height. average breach width was 110.33 m taken from the topographic survey data of the IWUMD (Figure 7). This average width measured from the survey data was applied as the observed average breach width in the comparison of the resulting average breach widths (B avg ) by empirical equations.   (Figure 7). This average width measured from the survey data was applied as the observed average breach width in the comparison of the resulting average breach widths (Bavg) by empirical equations.

Breach parameters for water discharge:
The height of the water surface from the breach inverted (Hw) is the vertical extent of the water measured from the top of the water surface before dam failure to the bottom of the breach, whereas Vw is the volume of water with respect to Hw [17][18][19][20][21][22][23][24][25][26]. In previous studies, if there was no information for the breach water height (Hw) and its corresponding water volume (Vw), the dam height (H) could be assumed as Hw in some cases such as overtopping cases, and the full storage water level and full storage reservoir, V, could be taken as parameters in other cases such as piping cases. For the Swa Dam case, Hw was measured from the overflow water surface (R.L 103.2 m) before the breach day to the final The dam breach procedure should be divided into two stages (i.e., breach initiation and beach formation), so that the failure time could be separated into two parts (i.e., initiation time and formation time) corresponding to that in [43]. The initiation time initiates with the first flow of water over or through the dam and ends when erosion reaches the upstream face of the dam and produces a rapid acceleration of breach outflow and an unstoppable failure of the dam. Meanwhile, the formation time begins when the initiation time ends and continues until the breach has reached its maximum size [43]. However, previous studies stated that the formation time is not until the absolute draining end of the reservoir [43]. Several previous studies also stated that the failure time of a breach (Tf) is generally described as the time between the initiation of the breach and the development of its peak discharge (Qp). For example, Froehlich (2008) [24] stated that the failure time is from the initiation of a breach until it reaches its maximum size.
Two-time parameters were examined in the Swa Dam case for the failure time of a breach (Tf) according to previous studies. In the Swa Dam, the water discharge rate increased from zero at 5:00 a.m. LT to the maximum breach discharge rate, which was about 7643 m 3 /s at 7:00 a.m. LT on 29 August 2018 Therefore, the time taken to peak discharge was 2 h, which was from 5:00 a.m. to 7:00 a.m. LT. After that, the water discharge rate dramatically decreased to 3000 m 3 /s at 9:00 a.m. After the drastic decrease, the water discharge decreased gradually with the decrease in the water level. Therefore, the breach development time or failure time for the Swa Dam breach was taken as 4 h. The detailed water discharge conditions are described in Table A3.   Breach parameters for water discharge: The height of the water surface from the breach inverted (H w ) is the vertical extent of the water measured from the top of the water surface before dam failure to the bottom of the breach, whereas V w is the volume of water with respect to H w [17][18][19][20][21][22][23][24][25][26]. In previous studies, if there was no information for the breach water height (H w ) and its corresponding water volume (V w ), the dam height (H) could be assumed as H w in some cases such as overtopping cases, and the full storage water level and full storage reservoir, V, could be taken as parameters in other cases such as piping cases. For the Swa Dam case, H w was measured from the overflow water surface (R.L 103.2 m) before the breach day to the final breach bottom elevation (R.L 81 m), which was 22.2 m. This height was applied as H w in the empirical calculation.
The dam breach procedure should be divided into two stages (i.e., breach initiation and beach formation), so that the failure time could be separated into two parts (i.e., initiation time and formation time) corresponding to that in [43]. The initiation time initiates with the first flow of water over or through the dam and ends when erosion reaches the upstream face of the dam and produces a rapid acceleration of breach outflow and an unstoppable failure of the dam. Meanwhile, the formation time begins when the initiation time ends and continues until the breach has reached its maximum size [43]. However, previous studies stated that the formation time is not until the absolute draining end of the reservoir [43]. Several previous studies also stated that the failure time of a breach (T f ) is generally described as the time between the initiation of the breach and the development of its peak discharge (Q p ). For example, Froehlich (2008) [24] stated that the failure time is from the initiation of a breach until it reaches its maximum size.
Two-time parameters were examined in the Swa Dam case for the failure time of a breach (T f ) according to previous studies. In the Swa Dam, the water discharge rate increased from zero at 5:00 a.m. LT to the maximum breach discharge rate, which was about 7643 m 3 /s at 7:00 a.m. LT on 29 August 2018 Therefore, the time taken to peak discharge was 2 h, which was from 5:00 a.m. to 7:00 a.m. LT. After that, the water discharge rate dramatically decreased to 3000 m 3 /s at 9:00 a.m. After the drastic decrease, the water discharge decreased gradually with the decrease in the water level. Therefore, the breach development time or failure time for the Swa Dam breach was taken as 4 h. The detailed water discharge conditions are described in Table A3.

Empirical Equations from Previous Studies
Empirical equations from previous studies were used to clarify the characteristics of the breach event that happened in the Swa Dam. The empirical equations were simplified equations derived from regression analyses of past dam failure cases [42]. Several world dam failure datasets were compiled in previous studies and various empirical equations have been proposed on the basis of these datasets to qualify relationships between breach parameters such as peak outflow (Q p ), average width (B avg ) and failure time of a breach (T f ). From the empirical equations established between the 1980s and 2022, eight of them were selected to assess the Swa Dam breach. These empirical equations could be divided into two categories according to their distinguishing variables. Six equations were categorized as equations for any failure modes, levels of erodibility and dam types. They include those of the Bureau of Reclamation (USBR) (1982) [ [20] used 166 case studies and Sharharm (2013) [21] collected data from 142 damaged dams. Each equation comprised three equations for three breach parameters: the average breach width (B avg ), failure time (T f ) and peak outflow (Q p ). Pierce (2010) [19] only had an equation for peak outflow, whereas Soliman (2015) [20] did not have a peak outflow equation and Sharharm (2013) [21] had no equation for failure time, as described in Table 1.
Most of the equations depended on the water height from the breach bottom (H w ) and the water volume at failure time (V w ) ( Table 1). Some equations were governed by the height of a breach (H b ) and the average dam width (W avg ) ( Table 1). Soliman's (2015) [20] equation was based on dam characteristics such as the storage volume (V), dam height (H) and average dam width (W avg ), as shown in Table 1. Here, Tegos's (2022) equation for peak breach outflow was also presented as it is the most updated empirical formula which was constructed on dam characteristics such as the storage volume (V) and dam height (H) using the database of 161 historical dam failures [22].
The second category included Froehlich's equations and Xu and Zhang's (2009) [26] equations, as shown in Table 2 Table 2 [45]. Meanwhile, Xu and Zhang (2009) [26] distinguished the effects of the types of dams, failure modes and erodibility by inserting the coefficients b 3 , b 4 and b 5 , respectively, for each breach parameter, as described in Table A2 (Appendix A). The reference height H r = 15 m was used in Xu and Zhang's equations to separate large dams from small dams according to the International Commission of Large Dams (1998) [12], and the reference time T r = 1 h was applied in Xu and Zhang's (2009) equation of failure time [26]. Thus, the comparison between the calculated characteristics using previous empirical equations and the observed characteristics in the Swa Dam data is considered effective for clarifying the characteristics of the breach phenomenon in the Swa Dam compared with previous events. Further, as cases of spillway failure are very rare, this comparison may provide insight into the role of spillways on earthen embankment dams in reducing flood damage due to dam breaches.

Tested Scenarios for Failure Mechanisms
Most previous studies on dam failure have focused on two main mechanisms: overtopping erosion and piping failure of the dam body. Meanwhile, an ogee-type spillway failure happened in the Swa Dam case, indicating that the dam failure mechanism was not the same as those of previous events. However, two probable processes, overtopping erosion and piping erosion, were also considered in the spillway failure in the Swa Dam. Because the water level data indicated that the overflow occurred at the start of the breach, we cannot eliminate the possibility of overtopping erosion. Thus, we set two scenarios, Scenario 1 (overtopping erosion) and Scenario 2 (piping erosion) as described in Figure 8, to apply the selected empirical equations from previous studies.
We set the same water height from the breach bottom (H w ) and height of the breach (H b ) for both scenarios based on the collected survey data for the Swa Dam's collapse site (mentioned in Section 2.8.1). The water surface level was about R.L 103.2 m at the beginning of the breach and the bottom level of the breach was R.L 81 m which was the final level of the breach opening (detailed description in Section 2.8.1). The detailed setting for the two scenarios is described in Table A4. In addition, the dam height (29.6 m), dam width (170.7 m) and storage volume (266,863,398 m 3 ) of the Swa Dam were applied as parameters related to reservoir properties such as the dam height (H), dam width (W avg ) and reservoir storage (V). The specific values for the coefficients of the empirical equations of Xu and Zhang (2009) [26] were set up for the Swa Dam breach according to Table A2. The values for b 4 (failure mode) in Xu and Zhang (2009) [26] were different for each scenario. Xu and Zhang (2009) [26] showed three values for b 5 (erodibility), and we performed trial calculations using such three values as there was no direct evidence of such in the Swa Dam. Three values were also described for b 3 in Xu and Zhang's equations, which were related to the types of dams, and two values were selected for the two dam types (concrete-faced dam and homogeneous earth-filled dam) for the Swa Dam according to the material of the dam and the failure that happened in the concrete spillway.
(Hb) for both scenarios based on the collected survey data for the Swa Dam's collapse site (mentioned in Section 2.8.1). The water surface level was about R.L 103.2 m at the beginning of the breach and the bottom level of the breach was R.L 81 m which was the final level of the breach opening (detailed description in Section 2.8.1). The detailed setting for the two scenarios is described in Table A4. In addition, the dam height (29.6 m), dam width (170.7 m) and storage volume (266,863,398 m 3 ) of the Swa Dam were applied as parameters related to reservoir properties such as the dam height (H), dam width (Wavg) and reservoir storage (V). The specific values for the coefficients of the empirical equations of Xu and Zhang (2009) [26] were set up for the Swa Dam breach according to Table A2. The values for b4 (failure mode) in Xu and Zhang (2009) [26] were different for each scenario. Xu and Zhang (2009) [26] showed three values for b5 (erodibility), and we performed trial calculations using such three values as there was no direct evidence of such in the Swa Dam. Three values were also described for b3 in Xu and Zhang's equations, which were related to the types of dams, and two values were selected for the two dam types (concrete-faced dam and homogeneous earth-filled dam) for the Swa Dam according to the material of the dam and the failure that happened in the concrete spillway.

Water Discharge Characteristics
Using SAR data from Sentinel 1, water area changes in the study site before and after the dam breach were analyzed, as shown in Figure 9. Before the breach happened, the reservoir water area of the Swa Dam and along the Swa creek was about 27 km 2 , according to a satellite image on 19 August 2018 (Figure 9a). The water area at the Swa Dam was reduced to 3.74 km 2 after the breach with respect to a 31 August satellite image (Figure 9b). The water area indicated that the water level after the breach was around 84.5 m. According to the height-volume relationship of the Swa Dam, the total volume of discharged water was estimated at around 259 million cubic meters, indicating that 97% of the full storage was discharged. The calculated water volume above the elevation of the spillway floor (R.L 89 m) was 39 million cubic meters.

Water Discharge Characteristics
Using SAR data from Sentinel 1, water area changes in the study site before and after the dam breach were analyzed, as shown in Figure 9. Before the breach happened, the reservoir water area of the Swa Dam and along the Swa creek was about 27 km 2 , according to a satellite image on 19 August 2018 (Figure 9a). The water area at the Swa Dam was reduced to 3.74 km 2 after the breach with respect to a 31 August satellite image ( Figure  9b). The water area indicated that the water level after the breach was around 84.5 m. According to the height-volume relationship of the Swa Dam, the total volume of discharged water was estimated at around 259 million cubic meters, indicating that 97% of the full storage was discharged. The calculated water volume above the elevation of the spillway floor (R.L 89 m) was 39 million cubic meters. On the day of the collapse (29 August 2018), no rainfall was recorded, the overflow depth of the spillway was about 0.5 m (water level 103.2 m) and the water discharge rate drastically increased from 0 to 7217.9 m 3 /s within 1 h (Figure 10). The maximum breach discharge was about 7642.8 m 3 /s at a 101.1 m water level and happened at 7:00 a.m. LT on On the day of the collapse (29 August 2018), no rainfall was recorded, the overflow depth of the spillway was about 0.5 m (water level 103.2 m) and the water discharge rate drastically increased from 0 to 7217.9 m 3 /s within 1 h (Figure 10). The maximum breach discharge was about 7642.8 m 3 /s at a 101.1 m water level and happened at 7:00 a.m. LT on 29 August 2018, as shown in Figure 10. This peak discharge is around five times larger than the discharge rate for the spillway design discharge (1486 m 3 /s). Moreover, the estimated peak discharge was around two times larger than the designed peak flow (3491 m 3 /s) because of rainfall that occurs once in 1000 years. The peak discharge continued for 1 h until 7:00 a.m. LT, although the water level in the reservoir dropped from 102.2 to 101.1 m. After that, the water discharge rate dramatically decreased to 3000 m 3 /s in 1 h with a decrease in the water level from 100.1 to 99.5 m. After the drastic decrease, the water discharge decreased gradually with the decrease in the water level, but the discharge rate was still larger than 1500 m 3 /s until 14:00 LT, suggesting that the water discharge exceeded the spillway design discharge rate for around 9 h. The discharge rate became 500 m 3 /s 24 h after the peak discharge. The recorded hourly water level and corresponding water volume in the reservoir are described in Table A3 (Appendix B). The total discharged volume until 24 h from the beginning of the breach (29 August 2018, 5:00 a.m. to 30 August 2018, 5:00 a.m.) was around 215.5 million cubic meters, as shown in Table A3.

Calculated Results Using Empirical Equations
The observed breach parameters, such as the peak outflow (Qp), average breach width (Bavg) and the failure time of the breach (Tf) of the Swa Dam, were compared with the calculated parameters from empirical formulas of previous research. Table 3 explains the assessment between the calculated results from empirical equations and the observed data for the Swa Dam for overtopping and piping scenarios.

Calculated Results Using Empirical Equations
The observed breach parameters, such as the peak outflow (Q p ), average breach width (B avg ) and the failure time of the breach (T f ) of the Swa Dam, were compared with the calculated parameters from empirical formulas of previous research. Table 3 explains the assessment between the calculated results from empirical equations and the observed data for the Swa Dam for overtopping and piping scenarios.

Average Breach Width (B avg )
The average breach width (B avg ) was calculated for 22 cases (Table 3). Nine cases were calculated based on Scenario 1 using equations or coefficients for overflow events and nine cases were calculated for Scenario 2 using coefficients for piping events. For the other four cases, we used empirical formulas based on both overtopping erosion and piping failure.  Here, we calculated the absolute relative errors for all empirical equations applied to the 22 cases to evaluate the performance of these equations as shown in Figure 11. The least error value (0.03) was found in Shahram's equation, and Xu and Zhang's equation for concrete-faced dams with medium erodibility (piping scenario) has a minimum error value (0.08) for the calculated average breach width. The error values ranged from 0.03 to 1.43 as shown in Figure 11. The average breach width (Bavg) was calculated for 22 cases (Table 3). Nine cases were calculated based on Scenario 1 using equations or coefficients for overflow events and nine cases were calculated for Scenario 2 using coefficients for piping events. For the other four cases, we used empirical formulas based on both overtopping erosion and piping failure. Here, we calculated the absolute relative errors for all empirical equations applied to the 22 cases to evaluate the performance of these equations as shown in Figure 11. The least error value (0.03) was found in Shahram's equation, and Xu and Zhang's equation for concrete-faced dams with medium erodibility (piping scenario) has a minimum error value (0.08) for the calculated average breach width. The error values ranged from 0.03 to 1.43 as shown in Figure 11.

Failure Time (T f )
The breach failure time (T f ) was calculated for 18 cases. Six cases were calculated for Scenario 1 using equations or coefficients for overflow events and six cases were calculated for Scenario 2 using coefficients for piping events. For the other six cases, we used empirical formulas based on both overtopping erosion and piping failure. The average calculated duration was 7.8 h for all cases and ranged from 0.73 h (by USBR, 1982) to 25.6 h (lowerodibility overtopping erosion case of an earthen dam by Xu and Zhang, 2009) [26]. The durations of low-erodibility cases of both earthen and concrete-faced dams by Xu and Zhang (2009) [26] were dramatically longer than other estimations. Except for the lowerodibility cases of Xu and Zhang (2009) [26], the longest calculated T f was 8.2 h (median erodibility overtopping erosion case of an earthen dam by Xu and Zhang, 2009) [26] and the average T f became 4.3 h. By comparing these with the observed values in the Swa Dam (4 h), the average calculated durations for all cases were two times larger than the duration for the Swa Dam. When we did not consider the low-erodibility cases, the average of the calculated durations was about 1.2 times larger than that of the Swa Dam for both scenarios. The average duration for Scenario 1 was 5 h, if we did not include low-erodibility cases. Similarly, the average duration for Scenario 2 was 4.9 h, if we did not consider low-erodibility cases. Furthermore, the calculated formation time for a medium-erodibility concrete dam using Xu and Zhang's (2009) [26] equation was 4.86 h in Scenario 2 (piping) and was 1.2 times the observed time for the Swa Dam.
We calculated the absolute relative errors for all empirical equations applied to 18 cases to evaluate the performance of these equations as shown in Figure 12 [26]. The durations of low-erodibility cases of both earthen and concrete-faced dams by Xu and Zhang (2009) [26] were dramatically longer than other estimations. Except for the low-erodibility cases of Xu and Zhang (2009) [26], the longest calculated Tf was 8.2 h (median erodibility overtopping erosion case of an earthen dam by Xu and Zhang, 2009) [26] and the average Tf became 4.3 h. By comparing these with the observed values in the Swa Dam (4 h), the average calculated durations for all cases were two times larger than the duration for the Swa Dam. When we did not consider the low-erodibility cases, the average of the calculated durations was about 1.2 times larger than that of the Swa Dam for both scenarios. The average duration for Scenario 1 was 5 h, if we did not include lowerodibility cases. Similarly, the average duration for Scenario 2 was 4.9 h, if we did not consider low-erodibility cases. Furthermore, the calculated formation time for a mediumerodibility concrete dam using Xu and Zhang's (2009) [26] equation was 4.86 h in Scenario 2 (piping) and was 1.2 times the observed time for the Swa Dam. We calculated the absolute relative errors for all empirical equations applied to 18 cases to evaluate the performance of these equations as shown in Figure 12

Peak Discharge (Qp)
The peak discharge (Qp) was calculated for 20 cases. Seven cases were calculated for Scenario 1 using equations or coefficients for overflow events and, seven cases were calculated for Scenario 2 using coefficients for piping events. For the other six cases, we used empirical formulas based on both overtopping erosion and piping failure. The calculated discharge ranged from 3057 m 3 /s calculated by Froehlich (2016) [25] with a piping coefficient to 24,912 m 3 /s calculated by Xu and Zhang (2009) [26], assuming a

Peak Discharge (Q p )
The peak discharge (Q p ) was calculated for 20 cases. Seven cases were calculated for Scenario 1 using equations or coefficients for overflow events and, seven cases were calculated for Scenario 2 using coefficients for piping events. For the other six cases, we used empirical formulas based on both overtopping erosion and piping failure. The calculated discharge ranged from 3057 m 3 /s calculated by Froehlich (2016) [25] with a piping coefficient to 24,912 m 3 /s calculated by Xu and Zhang (2009) [26], assuming a concrete-faced high-erodibility dam with an overtopping erosion coefficient. By comparing these with the observed values in the Swa Dam (7643 m 3 /s), the average calculated peak discharge for all cases was 10,203 m 3 /s and 1.3 times larger than that of the Swa Dam. The average peak discharge for Scenario 1 was 14,630 m 3 /s and 1.9 times larger than that of the Swa Dam. For Scenario 2, the average peak discharge was 7416 m 3 /s, almost the same (0.97 times) as the observed peak flow. The observed peak discharge of the Swa Dam was within the range of both Scenarios 1 and 2.
We considered the absolute relative errors for all empirical equations applied to 20 cases to evaluate the performance of these equations as shown in Figure 13. The least error value (0.05) was found in Froehlich's 2016 [25] equation for a piping scenario, and Xu and Zhang's equation for a concrete-faced dam with medium erodibility (piping scenario) also had a minimum error value (0.14) for the calculated peak outflow. Xu and Zhang's equations for concrete-faced and earth dams with medium and high erodibility for the overtopping scenario are found to have high relative errors. The error values ranged from 0.05 to 2.26 as shown in Figure 13.

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almost the same (0.97 times) as the observed peak flow. The observed peak discharge of the Swa Dam was within the range of both Scenarios 1 and 2.
We considered the absolute relative errors for all empirical equations applied to 20 cases to evaluate the performance of these equations as shown in Figure 13. The least error value (0.05) was found in Froehlich's 2016 [25] equation for a piping scenario, and Xu and Zhang's equation for a concrete-faced dam with medium erodibility (piping scenario) also had a minimum error value (0.14) for the calculated peak outflow. Xu and Zhang's equations for concrete-faced and earth dams with medium and high erodibility for the overtopping scenario are found to have high relative errors. The error values ranged from 0.05 to 2.26 as shown in Figure 13.

Occurrence of Spillway Breach
By compiling 13 years of water level records from the IWUMD, the spillway overflowed 38 times; 8 times in 2017 and 6 times in 2011. Generally, the maximum overflow occurred in August and October of each year, according to the records. We compared the overflow depth of the spillway in August 2018 with the highest overflow depth in each year, and the overflow depth of the breach day was about 0.5 m, which was not high enough compared with those in previous events, as shown in Figure 14. The largest overflow depth happened in 2013, which was 1.53 m and around three times larger than the highest overflow depth on the breach day. This suggests that the overflow depth cannot fully explain the occurrence of the spillway breach. The surface or interior of the spillway might have weakened over time because of other reasons.

Occurrence of Spillway Breach
By compiling 13 years of water level records from the IWUMD, the spillway overflowed 38 times; 8 times in 2017 and 6 times in 2011. Generally, the maximum overflow occurred in August and October of each year, according to the records. We compared the overflow depth of the spillway in August 2018 with the highest overflow depth in each year, and the overflow depth of the breach day was about 0.5 m, which was not high enough compared with those in previous events, as shown in Figure 14. The largest overflow depth happened in 2013, which was 1.53 m and around three times larger than the highest overflow depth on the breach day. This suggests that the overflow depth cannot fully explain the occurrence of the spillway breach. The surface or interior of the spillway might have weakened over time because of other reasons. On the other hand, the overflow rate at the last 6 h before the breach (212 m 3 /s) was smaller than the designed flow rate of the spillway (1486 m 3 /s). The drastic increase in the outflow rate immediately after the start of the breach suggests that the cross-section of the water flow suddenly increased after the start of the breach. One probable explanation for this is that the intake of the spillway was suddenly broken and the outflow rate dramatically increased. A similar sudden collapse also happened in the spillway of the Montedoglio earth-fill dam in Italy during its stability test. The reservoir water level was raised to the crest level of the spillway during the stability test, and three concrete blocks 10 m high fractured out. In addition, no rainfall was recorded on the breach day, similar to the Swa Dam case [21].

Erosion of the Spillway
According to the observed water level and corresponding calculated outflow rate, the water level decreased with time; however, the discharge rate remained nearly constant in the peak 2 h (from 5 a.m. to 7 a.m.), as in Figure 10. This suggests that the cross-sectional area of outflow gradually enlarged with time for the first 2 h. Two possibilities for this process are (1) the gradual erosion of the spillway intake, and (2) the gradual erosion of the right bank and bed of the spillway. At peak flow periods, the flow rate was very large, suggesting that the shear stress of flow to the bed and side bank of the spillway was much larger than designed, and the drastic erosion and collapse might have occurred because of the large shear stress. Moreover, the water flow might have been subjected to the right bank side because only the right side of the spillway was eroded in the event. This agreed well with the foundation test of the spillway, which found that the bearing capacity of the left side was larger than that of the right side of the spillway (Section 2.4).

The Effectiveness of the Presence of the Spillway
The effects of the concrete spillway in the event were analyzed on the basics of the erodibility and dam type, referring to the calculated results from Xu   On the other hand, the overflow rate at the last 6 h before the breach (212 m 3 /s) was smaller than the designed flow rate of the spillway (1486 m 3 /s). The drastic increase in the outflow rate immediately after the start of the breach suggests that the cross-section of the water flow suddenly increased after the start of the breach. One probable explanation for this is that the intake of the spillway was suddenly broken and the outflow rate dramatically increased. A similar sudden collapse also happened in the spillway of the Montedoglio earth-fill dam in Italy during its stability test. The reservoir water level was raised to the crest level of the spillway during the stability test, and three concrete blocks 10 m high fractured out. In addition, no rainfall was recorded on the breach day, similar to the Swa Dam case [21].

Erosion of the Spillway
According to the observed water level and corresponding calculated outflow rate, the water level decreased with time; however, the discharge rate remained nearly constant in the peak 2 h (from 5 a.m. to 7 a.m.), as in Figure 10. This suggests that the cross-sectional area of outflow gradually enlarged with time for the first 2 h. Two possibilities for this process are (1) the gradual erosion of the spillway intake, and (2) the gradual erosion of the right bank and bed of the spillway. At peak flow periods, the flow rate was very large, suggesting that the shear stress of flow to the bed and side bank of the spillway was much larger than designed, and the drastic erosion and collapse might have occurred because of the large shear stress. Moreover, the water flow might have been subjected to the right bank side because only the right side of the spillway was eroded in the event. This agreed well with the foundation test of the spillway, which found that the bearing capacity of the left side was larger than that of the right side of the spillway (Section 2.4).

The Effectiveness of the Presence of the Spillway
The effects of the concrete spillway in the event were analyzed on the basics of the erodibility and dam type, referring to the calculated results from Xu and Zhang's (2009) equations. Once we assumed the erodibility level to be the medium erodibility and homogeneous earthen dam, the calculated peak flow, Q p, was about 1.1 to 2.1 times larger than the observed peak discharge. Meanwhile, in the case of the low-erodibility and concrete-faced dam, the calculated peak flow was 0.4 to 0.8 times lower than the observed peak discharge, as shown in Figure 15. This indicates that the case of the Swa Dam was intermediate between low and medium erodibility and was relatively close to low erodibility, rather than medium erodibility. This suggests that the spillway in the Swa Dam might have had a reduced erodibility compared with that of a homogeneous earthen dam. This agrees well with the condition of the Swa Dam, where the floor of the spillway was covered by 15 cm-thick lean concrete over 0.3 m-thick reinforced cement concrete at the duckbill part. Moreover, the side bank of the spillway might be considered as contributing to reducing the breach width because the left bank of the spillway was not eroded. The collapse event that happened in the spillway of the Montedoglio earth-fill dam in Italy also concluded that the presence of the spillway channel walls reduced the breach outflow [27]. Dam might have had a reduced erodibility compared with that of a homogeneous earthen dam. This agrees well with the condition of the Swa Dam, where the floor of the spillway was covered by 15 cm-thick lean concrete over 0.3 m-thick reinforced cement concrete at the duckbill part. Moreover, the side bank of the spillway might be considered as contributing to reducing the breach width because the left bank of the spillway was not eroded. The collapse event that happened in the spillway of the Montedoglio earth-fill dam in Italy also concluded that the presence of the spillway channel walls reduced the breach outflow [27].

Lessons from the Disaster
Further analyses are necessary to accurately determine the reason for the Swa Dam's sudden collapse. However, the spillway may have simply depreciated over time because of the several reasons including the changing climate pattern. However, the Swa Dam case suggested that even in the ordinal magnitude of rainfall, dam collapse may occur. In the Swa Dam 1 year before the breach the overflow rate in the spillway was immediately larger than other years after 2013 (described in Section 4.1). Therefore, regular onsite inspection is important to check the changes in the body of the dam and its appurtenance structures and must be done at least once a year.
Once the collapse begins, the breach flow rate increases sharply and the evacuation time in the downstream area becomes extremely limited, according to the previous failures. For example, in the case of the Niedow Dam failure in Poland, the earthen dam was completely swept away within 80 min, which means that the abandon time was less than 80 min [46]. Thus, to mitigate damage, we must prepare hazard maps and alter systems in advance. If we find signature characteristics of the collapse during regular inspections, we must develop hazard maps and alter systems as was done in the previous studies which prepared the hazard systems for emergency preparedness for the breach [47,48].
Another suggestion is that the previous empirical equations established from the past dam failure cases seemed to be applicable when they were applied to the spillway failure case. However, to apply these equations for hazard mapping before the breach, we must set the breach height (Hb) or the water height during the breach (Hw) as all the equations were dominated by the heights and storage volume of the reservoir relating to those heights. In this regard, we must determine Hb or Hw and related parameters before using these empirical equations.

Lessons from the Disaster
Further analyses are necessary to accurately determine the reason for the Swa Dam's sudden collapse. However, the spillway may have simply depreciated over time because of the several reasons including the changing climate pattern. However, the Swa Dam case suggested that even in the ordinal magnitude of rainfall, dam collapse may occur. In the Swa Dam 1 year before the breach the overflow rate in the spillway was immediately larger than other years after 2013 (described in Section 4.1). Therefore, regular onsite inspection is important to check the changes in the body of the dam and its appurtenance structures and must be done at least once a year.
Once the collapse begins, the breach flow rate increases sharply and the evacuation time in the downstream area becomes extremely limited, according to the previous failures. For example, in the case of the Niedow Dam failure in Poland, the earthen dam was completely swept away within 80 min, which means that the abandon time was less than 80 min [46]. Thus, to mitigate damage, we must prepare hazard maps and alter systems in advance. If we find signature characteristics of the collapse during regular inspections, we must develop hazard maps and alter systems as was done in the previous studies which prepared the hazard systems for emergency preparedness for the breach [47,48].
Another suggestion is that the previous empirical equations established from the past dam failure cases seemed to be applicable when they were applied to the spillway failure case. However, to apply these equations for hazard mapping before the breach, we must set the breach height (H b ) or the water height during the breach (H w ) as all the equations were dominated by the heights and storage volume of the reservoir relating to those heights. In this regard, we must determine H b or H w and related parameters before using these empirical equations.

Conclusions
The spillway breach that suddenly happened in the Swa Dam for unknown reasons was assessed in terms of changes in topography and water discharge circumstances and breach parameters of the event. We applied selected empirical formulas from previous studies to calculate the breach parameters and tried to find the causes of the failure. From the field investigation, we found that the observed average breach width was about 110 m, and the breach opening was expanded to the right side of the dam embankment and became wider from the original spillway width. The water discharge hydrograph for the breach event was implemented from the water level records and elevation-storage data of the Swa reservoir and the peak outflow was about 7643 m 3 /s, calculated from the water level records of the event. The observed failure time is difficult to determine because of the lack of evidence; however, we assumed it to be 4 h in this study according to the water level records.
As the spillway breach was assessed in terms of breach parameters, the empirical equations were applied to evaluate three breaching parameters: the average breach width, failure time and peak discharge, and the calculated results were compared to the observed values. Additionally, we evaluated the performance of the empirical equations by the absolute relative errors of them. From the empirical equations applied in this study, Froehlich's equations and Xu and Zhang's 2009 equations exhibit the highest among the empirical formulas; however, considering the high uncertainty of the breach phenomenon and the lack of real-world sample to calibrate the models, all models with low absolute errors (i.e., lower than 0.5) set out above are recommended for further application. In this study, the effect of the spillway in the dam breaching process could be clarified in Xu and Zhang's empirical equations with dam types and erodibility factors.
The failure modes are uncertain because of the inconsistency of the results. From the calculated peak outflow results, the failure reason is overtopping as the relative error is very low in Froehlich's 2016 equation for overtopping scenario. However, the results from Xu and Zhang's concrete-faced dam with medium erodibility equation suggested that the failure mode is piping in the average breach width and failure time calculation. In this regard, no definitive suggestions may be raised because of the lack of evidence. Therefore, the lessons we learned from this event are that the dam breach parameters and peak outflow could be predicted only if the appropriate empirical formulas are selected with enough information. The uncertainty of these empirical equations was also high as described in the study by Tony Whal (2004) [49].
Furthermore, dam breach analysis also could be performed using other methods such as machine learning algorithms or numerical models such as two or three dimensional CFD models. For example, the seepage rate prediction was taken at a rockfill dam in Japan to compare the predicted and observed dam leakages using three machine learning algorithms such as random forest (RF), extremely randomized trees (ERT) and support vector regression (SVR) and found that they were in good agreement with each other [50]. Furthermore, the performance of the Flow-3D model was satisfied in the Mahabad Dam (Iran) and Tignes Dam (France) cases compared to a laboratory experiment and other models [51]. Therefore, further studies based on the hypothesis of this study should be performed, while taking into consideration these overestimations and uncertainties, and studies on selecting suitable empirical formulas or the use of the numerical modelling for other dams in Myanmar should be conducted.

Data Availability Statement:
The data presented in this study are available upon request from the corresponding author.