Simulation and Hazard Map of Flooding Caused by the Break of a Concrete Gravitational Dam

Abstract

The simulation of Concrete Gravitational Dam burst floods is an important research content in the field of disaster prevention and mitigation in water conservancy projects. Due to the extreme rainfall, earthquake, structure failure and etc., the concrete gravitational dam usually breaks in a short time period. The dam break flood will give an extreme risk to the downstream communities. Taking the flood simulation of the Kaliwa Dam in the Philippines as an example, based on the downstream channel of the dam body and the measured terrain on both sides, a numerical simulation model of one-dimensional and two-dimensional coupled flood evolution is constructed, and the numerical simulation of the flood evolution process of the dam collapse is carried out, counts the inundation range, water depth, flow velocity, flood arrival time and other disaster causing factors in the downstream inundation area, and draws the flood hazard map of both banks downstream. The simulation results show that the KALIWA burst accident occurred, the total inundation area downstream is over 38 km² in the downstream of the Kaliwa Dam. The dam break flood peak takes 1.5 h to reach the downstream estuary, which is the shortest time. The General Nakar City and Infanta City are inundated completely with the depth of 1.0 m to 2.0 m. The terrain near the upper reaches of the lower estuary is open and flat, the downstream area will be affected seriously by the flood. It is proposed to build a flood warning system to give the people downstream of Kaliwa Dam. The results of the research will provide a scientific basis for dam-break flood risk analysis, disaster assessment.

1 Introduction

With the rapid economic development, all countries in the world have attached great importance to the safety of dams. While studying the possible dangers of dam-breaking floods to the downstream, they are also taking proactive preventive measures [1]. For example: the National Dam Safety Plan launched by the United States, the European Community organized more than 10 member countries to carry out cooperative research on dam failure issues, and the International Committee on Dams integrated and coordinated on this basis, and released ICOLD No. 111 Breakthrough The dam flood analysis guidelines have a clear normative and guiding role for the analysis and calculation of dam break floods [2].

KALIWA Dam in the Philippines is located in Metro Manila, Philippines. From left to right, there are gravity dam, spillway dam with gate, free spillway dam and gravity dam. The length of the dam is 247.19 m. The height of the dam is 73.30 m. The elevation of the dam is 173.30 m and the dam foundation elevation is 100 m. The dam breach will happen due to the structural failure. The breach can be assumed into Instantaneous breach in second with a final breach opening. It is different from the breach process in the earthen dam with a breaching period. At the plane of EI 124.5 m, the upstream vertical dam body becomes a slope of 1:0.25. And there is gallery of 3 m × 3.5 m at EI 124.5. In the spillway dam, the elevation of the spillway is at around 124.5 m. The flow will give a lot of pressure on the spillway when the flow goes through it. So the force distributions are very complex at the plane of EI 124.5 m, and outside forces can destroy the plane and trigger a dam break here. The layout of the KALIWA dam is shown in Fig. 1.

Due to the occurrence of extreme events such as super-standard floods, earthquakes, and structural damage, concrete gravity dams have the risk of dam failure in a short period of time, and the dam-breaking floods will bring extreme disaster losses to the downstream. Therefore, it is necessary to carry out research work on the flood risk of dam break. According to the terrain characteristics of the KALIWA dam in the Philippines, this paper establishes a two-dimensional coupled hydrodynamic model, conducts numerical simulation for the proposed dam break condition, and counts the disaster-causing factors such as the submerged range, water depth, flow velocity, and flood arrival time in the downstream submerged area, draws a flood risk map on both sides of the downstream under normal water level dam failure, and provides technical support for the later concrete dam failure flood risk analysis and disaster loss assessment [3].

Fig. 1.

Layout of Kaliwa dam.

2 Model Building

Dam-break flood propagation is an unsteady flow. According to ICOLD Bulletin 111, “Dam Break Flood Analysis,” Mike FLOOD software is recommended for use in the Kaliwa Dam dam break flood simulation. Mike FLOOD dynamically links two separate software packages: Mike 11 (1D) and Mike 21 (2D) [4].

2.1 Model Range

In order to fully reflect the inundation caused by the collapse of the dam flood to the downstream area, the upper boundary of the simulation range is the dam site, and the lower boundary is the river estuary.

This time, two topographic maps were collected, namely the topographic map of the power station area and the topographic map of the Kaliwa Dam site. The topographic map of the power station area adopts the contour line format, and the elevation interval is 3.0 m. Its coverage area is large, and its lower boundary is about 39 km away from the dam site, which is determined as the dam failure simulation area. The topographic map of the dam site only covers the dam site area and has a small range. It is represented by a mixed format of contour lines and elevation points. The two topographic maps are corrected and merged and superimposed with the image map based on the GIS platform, as shown in Fig. 2.

Fig. 2.

Schematic diagram of the simulation range.

2.2 Model Establishment

Based on the measured cross-section and the topographic map of both sides of the strait, based on the MIKE FLOOD simulation platform, the one-dimensional and two-dimensional numerical simulation models of flood evolution downstream of the dam are constructed. Among them, the two banks of the river are steep mountains, using a one-dimensional hydrodynamic model, and the downstream terrain is relatively flat, which is a two-dimensional hydrodynamic model.

The establishment of the numerical simulation model of Kaliwa dam failure follows the principle from simple to complex, from point to line, and the model is formed by connecting the former set of specific single network objects.

• (1) Terrain model

  Terrain data is the underlying data for the model. The creation and modification of cross-sections and submerged area meshes along the line are based on terrain data. Based on the GIS platform, a terrain model of the flood area on both sides of the river is generated. The 2D model simulates a range of about 492 km², with an average mesh size of 30 m, for a total of 615036 triangular grids.

• (2) Cross-section

  Cross-sections are the most basic elements in model calculations. Therefore, the accuracy of the cross-sectional data directly affects the accuracy of the calculation. The last section is about 39 km from the dam, which is consistent with the topographic map. The one-dimensional model reflects the terrain features in the cross-section of the river channel, and the number of cross-sections entered in the model is 32 (Fig. 3).

  Fig. 3.

  

  Dam break flood model of Kaliwa dam.

2.3 Model Solving

The basic theoretical method for the numerical simulation of flood in complex basin is the hydrodynamic equation, namely the saint venant equations, describing the hydraulic characteristics of water bodies.

• (1) The basic principle of the one-dimensional flow mathematical model of the river reach [5]:

• ① Basic equation

  Continuity equation:

  $$ B\frac{\partial Z}{{\partial t}} + \frac{\partial Q}{{\partial x}} = q $$

  (1)

  Momentum equation:

  $$ \frac{\partial Q}{{\partial t}} + \frac{\partial }{\partial x}(\alpha \frac{Q^2 }{A}) + gA\frac{\partial Z}{{\partial x}} + gA\frac{Q|Q|}{{K^2 }} - (V_x - \frac{Q}{A})q = 0 $$

  (2)

  where $K = AC\sqrt R$ is modulus of discharge; $\alpha = \frac{{\int_A {v^2 dA} }}{{\overline{v}^2 A}}$ is momentum correction coefficients: where Q - is flow (m³/s); A - is area (m); V - is velocity (m/s); R - is hydraulic radius (m); C - is Chezy coefficient (m^1/2/s); B - is width of river channel (m); q - is lateral inflow (m²/s); Vx - is the velocity component of the lateral inflow in the direction of flow (m/s); $\overline{v}$ – is mean velocity of cross section (m/s).

• ② Definite condition

  The control condition for the boundary of upstream and downstream are generally controlled in the forms of water level process, flow process and flow-water level relationship, which can be written in the following unified form:

  $$ \alpha (t)Z(x_b ,t) + b(t)Q(x_b ,t) + c(t) = 0 $$

  (3)

  When t = 0, the water level and flow of each cross section is known, that is,

  $$ \begin{gathered} Z(x,0) = Z_0 (x) \hfill \\ Q(x,0) = Q_0 (x) \hfill \\ \end{gathered} $$

  (4)

  The definite solution of one-dimensional flood motion is composed by the basic Eq. (1), Eq. (2), boundary condition (3) and initial condition (4).

• (2) Two-dimensional numerical simulation model of protection zone along the channel.

• ① Basic equation

  The conservation form of differential equation has the characteristics of maintaining the conservation nature of physical quantity, and has advantage of being easier in dealing with the nonlinear convection terms in the process of numerical discretization. Therefore, the conservation form of shallow water wave equation is adopted in this study as the control equation of two-dimensional flood motion.

  $$ \frac{\partial h}{{\partial t}} + \frac{\partial U}{{\partial x}} + \frac{\partial V}{{\partial y}} = s_0 $$

  (5)
  $$ \frac{\partial U}{{\partial t}} + \frac{\partial }{\partial x}(\frac{U^2 }{h}) + \frac{\partial }{\partial y}(\frac{UV}{h}) + gh\frac{\partial H}{{\partial x}} + gh(J_{fx} - J_{0x} ) = 0 $$

  (6)
  $$ \frac{\partial V}{{\partial t}} + \frac{\partial }{\partial x}(\frac{UV}{h}) + \frac{\partial }{\partial y}(\frac{V^2 }{h}) + gh\frac{\partial H}{{\partial y}} + gh(J_{fy} - J_{0y} ) = 0 $$

  (7)

  where h is the water depth; U and V are the single-width discharges in the $U = uh$ x and y directions, respectively: $V = vh$, $u$ and the flow velocity in the $v$ and direction, $y$ respectively $x$; $s_0$ the source term; $J_{ox}$ and $J_{oy}$ the $x$ bottom slope in the $J_{0x} = - \frac{\partial Z}{{\partial x}}$ and direction: $y$, $J_{0y} = - \frac{\partial Z}{{\partial y}}$, $Z$ the river bottom elevation; $J_{fx}$ and $J_{fy}$ are respectively the $x$ friction gradient in $J_{fx} = \frac{{n^2 u\sqrt {u^2 + v^2 } }}{{h^{4/3} }}$ and direction: $y$, $J_{fy} = \frac{{n^2 v\sqrt {u^2 + v^2 } }}{{h^{4/3} }}$, n is the Manning roughness coefficient.

• ② Definite condition

  Inflow and outflow boundary conditions:

  $$ aU(x_b ,y_b ,t) + bV(x_b ,y_b ,t) + cH(x_b ,y_b ,t) + d = 0 $$

  (8)

  The solid boundary is the condition of slip boundary:

  $$ \vec{U}_n (x_b ,y_b ,t) = 0 $$

  (9)

  The initial conditions are:

  $$ \left. \begin{gathered} U(x,y,0) = U_0 (x,y) \hfill \\ V(x,y,0) = V_0 (x,y) \hfill \\ h(x,y,0) = h_0 (x,y) \hfill \\ \end{gathered} \right\} $$

  (10)

3 Simulation Analysis of Dam Break Flood

3.1 Data Input

The study area in 2D model coupled 1D model is calculated from the upstream of Kaliwa Dam to the downstream with a length of 39 km. The computation mesh consists of the main river bed and river banks. The computation mesh in 2D model is set in an unstructured grid with the shape of triangles. Bathymetry of model domain in 2D model is collected from the measurement of the topographical map. The parameters of 2D model are set up as follows: Calculation time step is 5 s; Viscosity coefficient is 0.28 m²/s; Manning (M) coefficient arranges from 15–18 m^1/3/s. Because there are lack of flood data on the river channel and land, the Manning Coefficient in the land was used empirically. In the extreme flood simulations, the empirical Manning Coefficient performs very well. Testing the calculation results shows that Courant coefficient (Cr) is smaller than 1. It means that 2D model runs smoothly, and the detailed simulation the moving direction of flow.

Based on MIKE FLOOD, from upstream to downstream, lateral connection is adopted among adjacent sections of left and right bank and the coupling connection between the one-dimensional model of river channel and the two-dimensional model for both banks. Overflow weir is used to simulate the flood overflow on both banks. And the elevation of the dyke on left and right bank is reagred as the weir control elevation.

3.2 Dam Collapse Flood Simulation

According to ICOLD Bulletin 111 “Dam Break Flood Analysis”, the breach of the Kaliwa dam can be assumed into full breach [6]. In the ICOLD bulletin, all dam-breaking flow formulas are intended to calculate the dam-breaking flow for earth dykes, not concrete gravity dam-breaking flows. Based on the rectangular gap weir formula, the maximum flow can be calculated using the weir formula [7].

$$ Q_{max} = \frac{8}{27}\sqrt g \left( {\frac{B}{b_m }} \right)^\frac{1}{4} b_m H_0^\frac{3}{2} $$

(11)

which $Q_{max} { }$ is the maximum dam break discharge, g is the gravitational acceleration, B is the length of the dam, $b_m$ is the breach width, $H_0$ is the water depth in front of the dam.

According to formula (11), the maximum flow of Kaliwa dam failure under normal water level can be calculated to be 66953.09 m³/s. The parameters of the simulation scheme are set as shown in Table 1.

Table 1. Simulation scheme parameter settings.

The capacity of Kaliwa reservoir needs to be designed to ensure that it will not reduce water supply of 600 MLD during a 1:10 year drought condition. The Kaliwa Dam reservoir volume – area – water level relationship are shown in Fig. 4.

The KALIWA Dam burst flooding process is shown in Fig. 5 below. This flow process serves as an upper boundary input condition calculated by the downstream flood evolution model. Lower boundary conditions take the sea level water level of the estuary, 0 m.

Fig. 4.

Kaliwa dam reservoir volume – area – water level relationship.

Fig. 5.

Dam break discharge hydrograph in case of normal water level.

3.3 Simulation of Dam Collapse Flood Evolution

A numerical simulation model of one-dimensional and two-dimensional coupled flood evolution downstream of the dam body is used to simulate and calculate the above-mentioned dam collapse flood process.

3.3.1 Flood Inundation Results of the One - Dimensional Model

In the case with the full breach scenario in the condition of normal water level, the maximum dam break discharge is 66953 m³/s. The cross-section downstream of the dam break reaches the highest water level 123 m after the dam break occurs 7 min. It takes 30 min for the flood to reach the last cross-section. The peak water level reduces to 20 m at the last cross-section when the dam break occurs 45 min, where the peak discharge is 23000 m³/s. The flood last around 80 min. The water levels and discharges at different cross-sections are shown in Figs. 6 and Figs. 7.

Fig. 6.

Water level of different cross-sections.

Fig. 7.

Flood discharges in different cross-sections.

3.3.2 2D Dam Break Flood Inundation Simulation

In the condition of the Normal Water Level, the maximum breach discharge is 66953 m³/s when the full breach happens. The maximum inundation depth and the time to reach the maximum inundation depth, maximum inundation velocity and the time to reach the maximum velocity are shown in Figs. 8, Figs. 9, Figs. 10, Figs. 11, respectively.

Fig. 8.

Map of the maximum inundation depth of dam break flood at downstream.

Fig. 9.

Map of time table for the maximum inundation depth of dam break flood at downstream.

Fig. 10.

Map of the maximum inundation velocity of dam break flood at downstream.

Fig. 11.

Map of time table for the maximum inundation velocity of dam break flood at downstream.

The total inundation area downstream is about 38.77 km², with an average depth of 1.98 m and a maximum inundation depth of approximately 12.46 m in the downstream of the Kaliwa Dam. The dam break flood peak takes 1.5 h to reach the downstream estuary. In the upstream of the estuary, 7 km upstream of the estuary, the geometry becomes mild with low elevation. The dam break flood depth reduces to 1.0 m–5.0 m. The General Nakar City and Infanta City are inundated completely with the depth of 1.0 m to 2.0 m. The flood peak reaches General Nakar City and Infanta City around 50.0 min. The averaged velocities range from 1 m/s to 3 m/s in the flat estuary area.

4 Impact Analysis

The dam-break floods could affect the cities of Nakar, with a population of more than 30,000, and Infanta, with a population of more than 70,000. Both cities will be inundated by floodwaters with a depth of 1.0 m to 2.0 m. The estuary area will be flooded by dam-break floods. Farmland, roads, factories, houses will be destroyed by dam-breaking floods.

Since it takes around 50 min for the dam break flood peak to arrive at General Nakar City and Infanta City, it is proposed to build a flood warning system to give the people downstream of Kaliwa Dam. The waring time can be 80 min. People can be evacuated within 80 min if the Dam break happens.

Flood warning system is an important means to mitigate dam-break floods, and flood insurance may be another measure to mitigate dam-break floods. Flood insurance is recommended for people and property downstream of the Kaliwa Dam.

5 Conclusions

Kaliwa Dam is a concrete gravity dam, including gravity dam, spillway dam with gate, free spillway dam, and gravity dam. Concrete gravity dams usually burst within a short period of time due to extreme earthquakes, structural damage, etc. Dam-breaking floods will pose significant risks to downstream communities and infrastructure. In this paper, based on the one- dimensional and two-dimensional coupling technology, the numerical simulation analysis of the dam-break hydrological flow process and the flood inundation downstream of the dam-break is carried out. The main conclusions are as follows:

• (1) According to the ICOLD Bulletin 111 “DAM-BREAK FLOOD ANALYSIS”, the breach of the Kaliwa dam is assumed into the full breach, the breach width is 247.19 m. The elevation of the breach is assumed as 124.5 m. The Mike flood model was used to simulate dam break flooding downstream of the Kaliwa Dam. The maximum flow can be calculated by the weir formula, and the hydrograph of the dam-breaking flood can be calculated by the water balance formula. The propagation of dam-break floods is simulated under normal water level hydraulic boundary conditions.

• (2) According to the simulation of dam-break flood cases, the total submerged area downstream of the Kaliwa Dam exceeds 38 km². It takes 1.5 h for the flood peak to reach the downstream estuary. Due to the limitations of the river bank geometry, floodwaters can pass through the channel with a width of 200 m-350 m. The main water depth in the channel can reach 12.46 m. In the upper reaches of the estuary, that is, 7 km upstream of the estuary, the terrain is flat and the elevation is low. The dam-break flood depth is reduced to 1.0 m–5.0 m. The cities of Nakar and Infanta were completely submerged at a depth of 1.0 m to 2.0 m. The flood peak reaches General Nakar City and Infanta City around 50 min. The average flow velocity in the flat estuary area drops to 1.0 m/s–3.0 m/s.

• (3) The downstream areas will be severely affected by flooding due to the failure of the Kaliwa Dam. The cities of Nakar and Infanta will be inundated with water depths exceeding 1.0 m. The estuary area will be inundated with a flood depth of more than 1.0 m, especially the area 7.0 km upstream of the estuary to the sea. It will take about 50 min for the dam break to reach the city of General Santos, and a flood warning system is recommended to provide information to people downstream of the Kaliwa Dam. The minimum alert time is 80 min. If the dam breaks, people can evacuate within 80 min.