**5.2 An approach of simulating debris flow**

Many studies on debris flow focused on estimation of an alluvial fan for predicting debris ow inundation areas (Glade,2005;Berti and Simoni,2007). They can be divided into three categories: dynamic models, volume-based models and topographic based models. For the 2008 Wenchuan earthquake, an empirical formula of estimating alluvial fan has been presented by Tang et al. (2010) based on statistical analysis.

In this study, we propose an approach for numerical simulation of debris flow to analyze or predict the peak discharge and the volume of a debris ow and its inundation area. The approach consists of the following 5 procedures.

1. Identify the earthquake induced landslides

The earthquake induced landslides can be identified by RS technique using aerial photos and satellite imagines. The locations and the shapes of all the debris deposits in a drainage area should be obtained from this procedure.

2. Make field investigations.

408 Earthquake Research and Analysis – Statistical Studies, Observations and Planning

The critical precipitation for triggering debris flow got decreased obviously after the earthquake. For example, the critical precipitation of 37mm became lower after the earthquake in Zhouqu County areas. A 22mm rainfall could trigger a debris flow during the past 3 years. According to preliminary analysis by Tang et al. (2009), the critical cumulative precipitation has been reduced about 14.8%-22.1%, the critical rainfall intensity per hour

Fig. 23. (a): The destroyed check dam in Qingping debris flow; (b): Ming river blocked at

The disasters chain induced by the earthquake is very significant. The earthquake induced landslides caused debris flows which blocked rivers, and flooding disasters occurred. For example, Jianjiang River was blocked at 3 locations and half blocked at 8 locations by debris flows during the rainstorm on Sept. 24, 2008. Mianyuan River was blocked at 2 locations and half blocked at 11 locations by debris flows occurred on Aug. 13, 2010. Ming River was blocked at 1 location and half blocked at 5 locations by debris flows occurred on Aug. 14,

Many studies on debris flow focused on estimation of an alluvial fan for predicting debris ow inundation areas (Glade,2005;Berti and Simoni,2007). They can be divided into three categories: dynamic models, volume-based models and topographic based models. For the 2008 Wenchuan earthquake, an empirical formula of estimating alluvial fan has been

In this study, we propose an approach for numerical simulation of debris flow to analyze or predict the peak discharge and the volume of a debris ow and its inundation area. The

The earthquake induced landslides can be identified by RS technique using aerial photos and satellite imagines. The locations and the shapes of all the debris deposits in a drainage

Yingxiu town by Hongchungou debris flow ( photographs from Tang chuan)

3. The low critical precipitation for triggering debris flow

about 25.4 %~31.6% in Beichuan County area.

4. River blocking

2010 (see Fig. 23 (b)).

**5.2 An approach of simulating debris flow** 

approach consists of the following 5 procedures. 1. Identify the earthquake induced landslides

area should be obtained from this procedure.

presented by Tang et al. (2010) based on statistical analysis.

The thicknesses of all the debris deposits and the geological and geotechnical behaviors should be investigated in this procedure.

3. Generate the grids using GIS.

Grids are required for solving equations with finite different method. A DEM map can be converted to a raster image using GIS for the drainage area. The grids can be obtained by saving the raster data.

4. Solve the equations.

The debris and water mixture is assumed to be a uniform continuous, incompressible, unsteady Newtonian fluid. The following Navier-Stokes equations are used for debris flow governing equations:

$$\begin{aligned} \nabla \mu &= 0\\ \rho \frac{\partial \mu}{\partial t} + \rho \boldsymbol{\mu} \cdot \nabla \boldsymbol{\mu} &= \rho \boldsymbol{g} - \nabla p + \mu \nabla^2 \boldsymbol{\mu} \end{aligned} \tag{11}$$

where *u uvw* (,, ) is velocity; is the mass density; *p* is the pressure; is dynamic viscosity; *g g* (0,0, ) , *g* is the gravitational constant and *t* is time.

Fig. 24. Definition of coordinate system for 2D governing equations

The so-called depth-averaged model as shown in Fig. 24 is used. And then the following equations are used instead of Eq. (11). They are solved by finite difference method (FDM).

$$\frac{\partial \mathbf{l}}{\partial t} + \frac{\partial \mathbf{M}}{\partial \mathbf{x}} + \frac{\partial \mathbf{N}}{\partial y} = \mathbf{0} \tag{12}$$

$$\frac{\partial M}{\partial t} + a \frac{\partial (M\mathcal{U})}{\partial \mathbf{x}} + a \frac{\partial (M\mathcal{V})}{\partial \mathbf{y}} = -\frac{\partial H}{\partial \mathbf{x}}gh + \nu \beta (\frac{\partial^2 M}{\partial \mathbf{x}^2} + \frac{\partial^2 M}{\partial y^2}) - gh \cos \theta\_\mathbf{x} \tan \xi \tag{13}$$

Earthquake Induced a Chain Disasters 411

Fig. 25. The blocked Ming River and new Yingxiu town in flood by Hongchungou debris

Fig. 26. (a): Aerial photography of Hongchun valley; (b): identified landslides in Hongchun

The obtained landslides are shown in Fig. 26(b). It can be seen that all the landslides were

Combining with field investigation, we finally selected four landslides: H1, H2, H3, H4 as the main loose source material of the debris flow (Fig. 27). The area of each landslide is 7,688

Since only a 20m DEM map is available for generating grids, the 4,000mX3,400m area is divided into 200X170 grids by using GIS. The rheological parameters are assumed constant

*<sup>d</sup>* =2050kg/m3,

The results from FDM are converted to GIS layers for visualizing. The movements of the debris flow are illustrated in Fig. 28(a)-(d) for different time. It can be seen that the river is blocked in Fig. 28(d). The distribution of the maximum depth of the whole flow is shown in Fig. 28(e). According to the simulation results, the debris flow takes 150*s* to travel about

=1.25, =1.0,

=0.11, *g* = 9.8m/s2,

accurately recognized. There is not so-called 'salt and pepper' appearance.

3,300 m along the valley with an average flow velocity of about 22m/s.

m2 for H1, 5,137 m2 for H2, 2,002 m2 for H3, 4 4,567 m2 for H4.

(Tang et al., 2011a), and they are:

flow.

valley

tan=0.6.

$$a\frac{\partial N}{\partial t} + a\frac{\partial (N\mathcal{U})}{\partial \mathbf{x}} + a\frac{\partial (N\mathcal{V})}{\partial y} = -\frac{\partial H}{\partial y}gh + \nu \beta (\frac{\partial^2 N}{\partial \mathbf{x}^2} + \frac{\partial^2 M}{\partial y^2}) - gh\cos\theta\_y \tan\xi \tag{14}$$

Where *M Uh* and *N Vh* are the *x* and *y* components of the flow flux;*U* and*V* are the *x* and *y* components of the depth-average velocity; *H* is the height of the free surface; *h* is the flow depth; *<sup>x</sup>* and *<sup>y</sup>* are the angle of inclination at the bed along the *x* and *y* directions, respectively; and are the momentum correction factors; / *<sup>d</sup> v* is kinematic viscosity, *<sup>d</sup>* is the equivalent density of the debris mixture, and *d ss ww v v* , *<sup>s</sup>* and *<sup>w</sup>* are the densities of solid grains and water, *<sup>s</sup> v* and *wv* are the volumetric concentrations of solids particles and water in the mixture; and tan is the dynamic friction coefficient.

#### 5. Visualize the results

The results from FDM are converted to GIS layers. The maps of maximum surge peak discharge, velocity distribution and in inundation area can be made by GIS. Also the animation of debris flow can be easily made.

#### **5.3 Numerical simulation of the Hongchungou debris flow**

The proposed approach has been used to simulate the Hongchungou debris flow occurred in Hongchungou drainage area on August 14, 2010. The materials carried by the debris flow blocked Ming River just at a little upper side about 200m from Yingxiu town, the epicenter of the 2008 Wenchuan Earthquake (Fig. 25), . The road along the river became the new temporary river channel and water flowed into Yingxiu town. As the result, serious flood occurred in the newly reconstructed town. The disaster claimed 13 lives and 59 missing persons.

The distribution of the earthquake induced landslides has been identified by using RS with the aerial photographs taken by The Ministry of Land and Resources of China. The aerial photograph 0.3m resolution of Hongchungou area is shown in Fig. 26(a).

In this study, the object-based analysis (OBA) is adapted for imagine analysis unlike traditional spectral information based image analysis method since there exists the so-called 'salt and pepper' appearance in the output of the latter (Tapas R. Martha et al., 2010). The analysis includes the following steps.


() () ( ) cos tan 

Where *M Uh* and *N Vh* are the *x* and *y* components of the flow flux;*U* and*V* are the *x* and *y* components of the depth-average velocity; *H* is the height of the free

The results from FDM are converted to GIS layers. The maps of maximum surge peak discharge, velocity distribution and in inundation area can be made by GIS. Also the

The proposed approach has been used to simulate the Hongchungou debris flow occurred in Hongchungou drainage area on August 14, 2010. The materials carried by the debris flow blocked Ming River just at a little upper side about 200m from Yingxiu town, the epicenter of the 2008 Wenchuan Earthquake (Fig. 25), . The road along the river became the new temporary river channel and water flowed into Yingxiu town. As the result, serious flood occurred in the newly reconstructed town. The disaster claimed 13 lives and 59 missing

The distribution of the earthquake induced landslides has been identified by using RS with the aerial photographs taken by The Ministry of Land and Resources of China. The aerial

In this study, the object-based analysis (OBA) is adapted for imagine analysis unlike traditional spectral information based image analysis method since there exists the so-called 'salt and pepper' appearance in the output of the latter (Tapas R. Martha et al., 2010). The

1. The aerial photos are ortho-rectified based on the 20m DEM obtained from the China Geology Survey Bureau, in order to remove the distorting effects of tilt and terrain

2. The image is divided into objects based on homogeneity of pixel values through edgebased segmentation algorithm (Kerle et al., 2009), since it is very fast and only one parameter is needed for scale level. Scale level 30 and merge level 93 are used for image

3. NDVI index is used to separate vegetation from other objects. Spatial, spectral and texture attributes are separately computed for each object. Then, various land covers are classifies based on user-defined training data, selected by combing with 3 dimensional

4. The non-landslide objects are eliminated by the assumption that landslide will not

photograph 0.3m resolution of Hongchungou area is shown in Fig. 26(a).

image in order to improve the interpretation refinement;

occur for the slope gradient less than 5°.

*N NU NV H N M gh gh t x yy x y*

volumetric concentrations of solids particles and water in the mixture; and tan

*<sup>s</sup>* and 

surface; *h* is the flow depth;

dynamic friction coefficient. 5. Visualize the results

kinematic viscosity,

 *v v* ,

*d ss ww* 

persons.

relief.

segmentation.

and *y* directions, respectively;

> *<sup>x</sup>* and

animation of debris flow can be easily made.

analysis includes the following steps.

 and 

**5.3 Numerical simulation of the Hongchungou debris flow** 

2 2 2 2

*<sup>y</sup>* are the angle of inclination at the bed along the *x*

are the momentum correction factors;

*<sup>d</sup>* is the equivalent density of the debris mixture, and

*<sup>w</sup>* are the densities of solid grains and water, *<sup>s</sup> v* and *wv* are the

 *y*

(14)

 / *<sup>d</sup> v* is

> is the

Fig. 25. The blocked Ming River and new Yingxiu town in flood by Hongchungou debris flow.

Fig. 26. (a): Aerial photography of Hongchun valley; (b): identified landslides in Hongchun valley

The obtained landslides are shown in Fig. 26(b). It can be seen that all the landslides were accurately recognized. There is not so-called 'salt and pepper' appearance.

Combining with field investigation, we finally selected four landslides: H1, H2, H3, H4 as the main loose source material of the debris flow (Fig. 27). The area of each landslide is 7,688 m2 for H1, 5,137 m2 for H2, 2,002 m2 for H3, 4 4,567 m2 for H4.

Since only a 20m DEM map is available for generating grids, the 4,000mX3,400m area is divided into 200X170 grids by using GIS. The rheological parameters are assumed constant (Tang et al., 2011a), and they are: *<sup>d</sup>* =2050kg/m3, =1.25, =1.0, =0.11, *g* = 9.8m/s2, tan=0.6.

The results from FDM are converted to GIS layers for visualizing. The movements of the debris flow are illustrated in Fig. 28(a)-(d) for different time. It can be seen that the river is blocked in Fig. 28(d). The distribution of the maximum depth of the whole flow is shown in Fig. 28(e). According to the simulation results, the debris flow takes 150*s* to travel about 3,300 m along the valley with an average flow velocity of about 22m/s.

Earthquake Induced a Chain Disasters 413

3. The landslides in the hanging wall are more than the footing wall and about 70%

5. There is a clear relationship between the sliding direction of landslides and the fault

6. Large quantities of long run-out landslides occurred and are listed in this chapter. Regression formulas of run-out distance have been obtained based on the areas and

The susceptibility analysis of the earthquake induced landslides has been carried out by both statistical analysis and ANN analysis based on slope units rather than the traditional grids. The relationship of landslide distribution with individual causative factor has been investigated. It has been found that slope gradient, elevation, slope range, the distances to the fault, the distances to a stream have contributed to landslides while specific catchment area, slope aspect and lithology have no clear relationship. A susceptibility map has been

A Multiplex Acceleration Model has been proposed for analysis of the long run-out mechanism based on trampoline effect. Table model tests and DDA simulation were carried out. It has been shown that the proposed Multiplex Acceleration Model is reasonable and

The earthquake induced landslides can easily form debris flows after the earthquake. The characteristics of the debris flows arising from the 2008 Wenchuan earthquake have been

1. There is a clear relation to the earthquake according to the distribution of the debris

4. Many rivers were blocked by the debris flows and serious damages have been caused

An approach of simulating debris flow has been proposed. The earthquake induced landslides are identified by RS with object-based analysis method, which can overcome the problem of the so-called 'salt and pepper' appearance existed in the traditional spectral information based image analysis method. A practical simulation has been carried out and the proposed approach has been shown effective and useful for estimating the movement

The presented research work and the preparation of this paper have received financial support from the Global Environment Research Found of Japan (S-8), Grants-in-Aid for Scientific Research (Scientific Research (B), 22310113, G. Chen) from JSPS (Japan Society for

Berti, M., Simoni,A. (2007). Prediction of debrisow inundation areas using empirical mobility relationships.*Geomorphology,* Vol. 90,(Octorber 2007), pp. 144-161

the Promotion of Science). These financial supports are gratefully acknowledged.

landslides are located in the region of 3km from the fault.

7. A large number of landslide dams (34) were formed.

strike.

applicable.

summarized as follows.

by the debris dams.

**7. Acknowledgment** 

**8. References** 

flows along the earthquake fault.

volumes of landslides.

4. Large-scale landslide can occur at the locking segment of the rupture fault.

made for analysis of the earthquake induced landslides in Qingchuan County.

2. Most of debris flows have large surge peak discharges and huge volumes.

3. The critical precipitation for triggering debris flow became lower.

behaviours of a potential debris flow arising from a strong earthquake.

Comparing the simulated results with the actual event, we found that they are in good agreement with each other. Therefore, the proposed approach has been shown applicable and useful for predicting the movement of potential debris flow arising from earthquake.

Fig. 27. Identified landslides as loose material of the debris flow

Fig. 28. The movement of the debris flow (a) for t=10s, (b) t=76s, (c) t=120s, (d) t=150s and (e) for the distribution of the maximum depth of Hongchungou debris flow.
