Prediction of Flood/Debris Flow Hydrograph Due to Landslide Dam Failure by Overtopping and Sliding

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Prediction of Flood/Debris Flow Hydrograph Due to Landslide Dam Failure by Overtopping and Sliding 京都大学防災研究所年報 第51号 B 平成 20 年 6 月 Annuals of Disas. Prev. Res. Inst., Kyoto Univ., No. 51 B, 2008 Prediction of Flood/Debris Flow Hydrograph Due to Landslide Dam Failure by Overtopping and Sliding Ripendra AWAL*, Hajime NAKAGAWA, Kenji KAWAIKE, Yasuyuki BABA and Hao ZHANG * Graduate School of Engineering, Kyoto University Synopsis An integrated model was developed by combining three separate models: (i) model of seepage flow, (ii) model of slope stability and (iii) model of dam surface erosion and flow to predict flood/debris flow hydrograph resulted from failure of landslide dam by overtopping and sudden sliding. The main advantage of an integrated model is that it can detect failure mode due to either overtopping or sliding based on initial and boundary conditions. The proposed model is tested for three different experimental cases of landslide dam failure due to overtopping and sliding, and reasonably reproduced the resulting flood/Debris flow hydrograph. Keywords: landslide dam, slope stability, seepage flow, overtopping flow, flood/debris flow hydrograph 1. Introduction dam near the Mimi-kawa river (Mizuyama, 2006). The catastrophic failure of landslide dam may Earthquakes or heavy rainfall and snow melt occur shortly after its formation. Prediction of may cause landslides and debris flow on the slopes potential peak discharge and resulting hydrograph in the vicinity of river channel. If the sediment mass is necessary for the management of dam-break generated by such landslides are big enough and flood hazards and to decide appropriate mitigation reaches the river may sometimes block a river flow measures including evacuation. The predicted and create a landslide dam naturally. Formation and outflow hydrograph will serve as an upstream failure of landslide dam are one of the significant boundary condition for subsequent flood routing to natural hazards in the mountainous area all over the predict inundation area and hazard in the world. Landslide dams are also common in Japan downstream. Sudden, rapid and uncontrolled because of widespread unstable slopes and narrow release of water impounded in landslide dam has valleys exist in conjunction with frequent been responsible for some major disasters in hydrologic, volcanic and seismic landslide mountainous region. Peak discharge produced by triggering events (Swanson, 1986). Historical such events may be many times greater than the documents and topography have revealed the mean annual maximum instantaneous flood formation of many landslide dams, some of which discharge. broke and caused major damage in Japan (Tabata et Basically, there are two methods to predict al., 2002). The 2004 Chuetsu earthquake resulted in probable peak discharge from potential failure of many landslide dams particularly in the Imo River landslide dam (Walder and O’Connor, 1997). One basin. In 2005, typhoon 14 caused a large landslide method relies on regression equations that relate - 603 - Fig. 1 General flow chart of an integrated model to predict flood/debris flow hydrograph due to landslide dam failure. observed peak discharge of landslide dam failure to based on sediment concentration. some measure of impounded water volume: depth, Most of the existing models are applicable to volume, or some combination thereof (Costa, 1985, overtopping failure of landslide dam. Some model Costa and Schuster 1988, Walder and O’Connor, has limitation to represent downstream batter slopes 1997) and regression equations that relate of greater than 1 in 5 (Davies, 2007). Infiltration experimental peak discharge to some measure of process is neglected in almost all available models. impounded water volume: depth, torrent bed In this context, an attempt has been made to gradient and inflow discharge (Tabat et al., 2001). incorporate integration of three separate models: (i) The other method employs computer model of seepage flow, (ii) model of slope stability implementation of a physically based mathematical and (iii) model of dam surface erosion and flow to model. Several researchers have developed predict the outflow hydrograph resulted from physically based model such as Fread (1991), failure of landslide dam by overtopping and sudden Takahashi and Kuang (1988), Takahashi and sliding. The main advantage of an integrated model Nakagawa (1994), Mizuyama (2006) and Satofuka is that it can predict time at which landslide dam et al. (2007). Although, landslide dam failure is may fail and also detect failure mode due to either frequently studied as an earthen dam failure, very overtopping or sliding based on initial and few models are developed for landslide dam failure boundary conditions. that can treat the flow as both sediment flow and debris flow. If the concentration of sediment is 2. Numerical model above 10%, non-newtonian viscous flow has to be taken into account. During surface erosion of The model of the landslide dam failure to predict landslide dam, sediment concentration increased flood/debris flow hydrograph consists of three more than 10%, so the model to predict the models. The seepage flow model calculates pore flood/debris flow hydrograph due to landslide dam water pressure and moisture content inside the dam failure should be capable to treat all types of flow body. The model of slope stability calculates the - 604 - factor of safety and the geometry of critical slip involves calculating the factor of safety and surface according to pore water pressure, moisture searching for the critical slip surface that has the movement in the dam body and water level in the lowest factor of safety. Many attempts have been upstream reservoir. The model of dam surface conducted to locate the position of critical slip erosion and flow calculates dam surface erosion due surface by using general noncircular slip surface to overflowing water. General outline of proposed theory coupled with different non-linear integrated model is shown in Fig. 1. A brief programming methods. The numerical procedure description of each model is given below. behind the identification of critical noncircular slip surface with the minimum factor of safety based on 2.1 Model of seepage flow dynamic programming and the Janbu’s simplified The seepage flow in the dam body is caused by method is mainly based on research by Yamagami the blocked water stage behind the dam. The and Ueta (1986). The algorithm combines the transient flow in the dam body after formation of Janbu’s simplified method with dynamic landslide dam can be analyzed by Richards’ programming on the basis of Baker’s successful equation. To evaluate the change in pore water procedure. pressure in variably saturated soil, pressure based Janbu’s simplified method can be used to Richards’ equation is used (Awal et al., 2007). calculate the factor of safety for slip surfaces of any shape. The sliding mass is divided into vertical slices and the static equilibrium conditions of each ∂h ∂ ⎛ ∂h ⎞ ∂ ⎛ ⎛ ∂h ⎞⎞ C = ⎜ K x ()h ⎟ + ⎜ K z ()h ⎜ +1⎟⎟ (1) slice are considered as sum of the vertical forces ∂t ∂x ⎝ ∂x ⎠ ∂z ⎝ ⎝ ∂z ⎠⎠ equal to zero and sum of the forces parallel to failure surface equal to zero. For the soil mass as a where h is the water pressure head, K x (h) and K (h) are the hydraulic conductivity in x and z z whole, sum of the vertical forces ∑ Fy = 0 and direction, C is the specific moisture capacity sum of the horizontal forces are (∂θ / ∂h) , θ is the soil volumetric water content, ∑ Fx = 0 t is the time, x is the horizontal spatial coordinate considered as equilibrium condition. and z is the vertical spatial coordinate taken as Based on the above considerations the factor of positive upwards. Eq.(1) represents flow in both safety, Fs for Janbu’s simplified method is defined the unsaturated domain as well as in the saturated as: domain. Line-successive over-relaxation (LSOR) 1 is often a very effective method of treating F = × s n cross-sectional problem grids. LSOR scheme is ∑Wi tanαi used in this study for the numerical solution of i=1 Richards’ equation. ⎧ ⎫ In order to solve Richards’ equation, the n ⎪ ⎪ ⎪cl cosα + ()W − u l cosα tanφ ⎪ ⎨ i i i i i i ⎬ (2) constitutive equations, which relate the pressure ∑ ⎛ 1 ⎞ i=1 ⎪ cos2 α ⎜1+ tanα tanφ ⎟ ⎪ head to the moisture content and the relative ⎪ i ⎜ i ⎟ ⎪ ⎩ ⎝ Fs ⎠ ⎭ hydraulic conductivity, are required. In this study, constitutive relationships proposed by van where W is the weight of each slice including Genuchten (1980) are used for establishing i surface water, l is the length of the base of each relationship of K − h and θ − h , with i slice, u is the average pore water pressure on the m = 1− (1/η). i base of the slice, α is the inclination of the base i to the horizontal, n is the total number of slices, and 2.2 Model of slope stability The evaluation of transient slope stability of c and φ are the Mohr-Coulomb strength landslide dam by the limit equilibrium method parameters. - 605 - The details of transient slope stability analysis dam body satisfy the critical condition for the of landslide dam by using dynamic programming occurrence of a debris flow. and Janbu’s simplified method can be found in The main governing equations are briefly Awal et al. (2007). discussed here. The depth-wise averaged two-dimensional momentum conservation equation 2.3 Model of dam surface erosion and flow for the x -wise (down valley) direction is There are only a few two-dimensional (2D) numerical models for dam-break erosion by ∂M ' ∂(uM ) ' ∂(vM ) + β + β = gh sinθbxo overtopping flow. Takahashi and Nakagawa (1994) ∂t ∂ x ∂ y used 2D model to predict flood/debris flow ∂(h + zb ) τ bx − gh cosθbxo − (3) hydrograph due to natural dam failure caused by ∂ x ρT overtopping. Broich (1998) used 2D model using different numerical schemes for shallow water and for the y -wise (lateral) direction, equations, Exners equation and sediment transport formulae.
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