**4. Analysis of Long run-out mechanism based on trampoline effect**

The estimation of the movement behaviour of a potential landslide is very important in order to mitigate the landslide disaster. Especially, the run-out distance is one of the major parameters in landslide risk assessment and preventive measure design. Long run-out is one of the major characteristics of earthquake induced landslides. However its mechanism has not been understood very well.

Many researchers have made great effort to understand how and why large falling masses of rock can move unusually long run-out distance. Researchers have repeatedly revisited the problem using a wide variety of approaches. These efforts have yielded no less than 20 mechanical models for explaining long run-out in high-volume rapid landslides. Shaller and Shaller (1996) made a detail summary of the existed models and divided these models into four categories (1) bulk fluidization and flow of landslide debris; (2) special forms of lubrication along the base of the slides; (3) mass-loss mechanisms coupled with normal frictional sliding; and (4) individual-case mechanisms.

Actually, most of the existed models are helpful in the estimation of the run-out distance. However, very less of them considered the earthquake dynamical behaviour. For this reason, in this study, we take into account the so-called trampoline effect of earthquake on landslides and propose a multiplex acceleration model (MAM) to explain the long run-out mechanism. Since the MAM model can be easily incorporated into numerical methods, it can be applied to simulate the long run-out landslide very well.

#### **4.1 Multiplex acceleration model**

For an earthquake induced landslide, the following effects on the movements of the falling stones from the landslide can be considered: (1) a falling stone can obtain kinetic energy

The landslide susceptibility map is made from the ANN results (Fig. 10). The high susceptible zone occupies 7.42%, the low susceptible zone 86.53% of the whole area. In

Landslide susceptible analysis has been carried out in Qingchuan County. 55,899 slope units have been extracted and used for the analysis. The relationship between landslide distribution and the individual causative factor has been investigated by statistical analysis. The clear relationship can be identified for slope gradient, elevation, slope rang, the distances to the fault and the distances to a stream. The ANN analysis also showed the same results, that is, slope gradient, elevation, slope range, distance to the fault and distance to a stream have relatively larger weight. By removing the other three factors with smaller weights, the ANN analysis accuracy got improved. By comparing landslide occurrence locations with susceptibility zones, it has been shown that 99% of landslides can be predicated by the obtained ANN model, but 78.8% of predictions would be false. On the other hand, 99.4% of stable predications are correct and less than 0.2% landslides would not be alarmed. In addition, the gray zone occupies 6% of the whole area. Therefore, the landslide susceptibility classification presented in this study

**4. Analysis of Long run-out mechanism based on trampoline effect** 

The estimation of the movement behaviour of a potential landslide is very important in order to mitigate the landslide disaster. Especially, the run-out distance is one of the major parameters in landslide risk assessment and preventive measure design. Long run-out is one of the major characteristics of earthquake induced landslides. However its mechanism

Many researchers have made great effort to understand how and why large falling masses of rock can move unusually long run-out distance. Researchers have repeatedly revisited the problem using a wide variety of approaches. These efforts have yielded no less than 20 mechanical models for explaining long run-out in high-volume rapid landslides. Shaller and Shaller (1996) made a detail summary of the existed models and divided these models into four categories (1) bulk fluidization and flow of landslide debris; (2) special forms of lubrication along the base of the slides; (3) mass-loss mechanisms coupled with normal

Actually, most of the existed models are helpful in the estimation of the run-out distance. However, very less of them considered the earthquake dynamical behaviour. For this reason, in this study, we take into account the so-called trampoline effect of earthquake on landslides and propose a multiplex acceleration model (MAM) to explain the long run-out mechanism. Since the MAM model can be easily incorporated into numerical methods, it

For an earthquake induced landslide, the following effects on the movements of the falling stones from the landslide can be considered: (1) a falling stone can obtain kinetic energy

addition, 6.05% of the area is gray zone.

**3.5 Conclusions** 

is acceptable.

has not been understood very well.

**4.1 Multiplex acceleration model** 

frictional sliding; and (4) individual-case mechanisms.

can be applied to simulate the long run-out landslide very well.

from the colliding with the vibrating slope during earthquake; (2) the force of friction between a falling stone and the slope can decrease since the normal force varies with the contact condition during earthquake; (3) The flying and rotation movement of a falling stone may occur much easily in earthquake induced landslides.

In order to consider these effects, we divide a period of wave is divided into two phases: *P*phase and *N*-phase as shown in Fig. 11. The *P*-phase is defined as the period when the slope is moving in the outer normal direction of the slope surface. The slope is pushing the falling stones on its surface and lets them obtain kinetic energy in the *P*-phase. The *N*-phase is defined as the period when the slope is moving in the inner normal direction of the slope surface. Since the normal force will decrease when the slope surface moves apart from the falling stones, the force of friction will get decreased in the *P*-phase.

Fig. 11. *P*-phase and *N*-phase definition in MAM

By the repeated exchange of two phases during an earthquake, the falling stone get multiplex accelerated. The MAM model can be seen more clearly by apparent friction angle analysis.

Supposing that a stone with mass *m* moves from position A to position B during a landslide without earthquake (see Case 1 in Fig. 12), the potential energy decreases by *mgh*. Based on the energy conservation law, it is easy to obtain the following equation for a falling stone movement in the case without earthquake.

$$
tanh - \sum\_{i=1}^{n} l\_i mgk\_i \tan \varphi\_{si} \cos \theta\_i = 0 \tag{1}
$$

The first term here is for potential energy and the second term is for the work of friction force between the slope and the falling stone, where the sliding movement is considered and the whole curve path is divided into finite linear segments. And *m* = mass, *g* = gravity acceleration, *h* = the falling height, *l* = the segment length, *θ* is the segment slope angle, *φ* is the friction angle, *k* is the coefficient of conveying from static to dynamic friction and *i* is the index of segment.

Earthquake Induced a Chain Disasters 401

In *P*-phase, a falling stone can obtain kinetic energy from the colliding with the vibrating slope. According to elastic collision theory, when two objects with different masses collide with each other, the object with smaller mass could obtain larger velocity. Since the mass of a slope is much larger than the mass of a falling stone, the velocity of the falling stone can be much larger than the vibrating velocity of the slope. That is to say the *VTR* in Eq. (4) can be

The *VTR* can be examined by the simple model shown in Fig. 13(a) and (b). The masses of the two blocks are *m*1 and *m*2 respectively. Before the colliding, the block 1 has initial velocity *V*10 toward block 2 which is standstill, i.e. *V*20=0. The friction between blocks and the base is negligible. After the colliding, the velocity of block 1 becomes *V*11 while block 2

(c)

collision, (c) *VTR* obtained by DDA comparing with analytical solution.

Fig. 13. The colliding model and *VTR* with mass ratio. (a) before the collision, (b) after the

By solving Eqs. (6) and (7), we can obtain the *VTR* for the case of *V*20=0 as follows

velocity from block one. The *VTR* is calculated from the ratio of *V*21 to *V*10.

2

It can be seen from the analytical solution Eq. (8) that if *m*1 is much larger than *m*2, *VTR* is to approach to 2.0. Therefore, since the mass of a slope is far larger than the falling stone, the velocity of the falling stone obtained from the slope vibration will be two times of that of the

The results of *VTR* given in Eq. (8) have been verified by DDA simulation. The model shown in Fig. 13 is used in DDA simulations. The block one with mass of *m*1 has the initial velocity of 10 *m/s* and the block two with mass of *m*2 is at a standstill. After the block one impacted the block two, the velocities of both blocks changed. The block two obtained the

*<sup>m</sup> VTR*

According to the principles of the conservation of both energy and momentum, we have the

1 1 2

*m m*

<sup>2222</sup> *mV mV mV mV* 1 10 2 20 1 11 2 21 (6)

*mV mV mV mV* 1 10 2 20 1 11 2 21 (7)

(8)

**4.2 Colliding effect** 

larger than 1.0.

(a)

(b)

obtains a velocity *V*21.

following equations.

slope vibration velocity during earthquake.

Fig. 12. Apparent friction angle

The apparent friction angle, usually used for the discussion of run-out distance, can be obtained from Eq. (1) as follows

$$\tan \overline{\varphi\_1} = \frac{h\_1}{D\_1} = \sum\_{i=1}^n w\_i k\_i \tan \varphi\_{si} \tag{2}$$

When we consider the effects of slope vibration due to earthquake, the kinetic energy of falling stone obtained from the collision with the vibrating slope and the movement patterns (sliding, rolling and flying) should be considered. Thus, Eq. (1) becomes

$$\log \text{h} + \sum\_{j=1}^{m} \frac{1}{2} m \upsilon\_{\epsilon j}^{2} - \sum\_{i=1}^{n} l\_{i} \log k\_{\, i}^{\*} \tan \varphi\_{\text{si}} \cos \theta\_{i} = 0 \tag{3}$$

The second term here is for the kinetic energy of a falling stone obtained from the collision with the vibrating slope and *v*ej is the velocity obtained in *j*th *P*-phase and can be expressed as follows

$$\upsilon v\_{ej} = VTR \int\_{t\_j}^{t\_j + \Delta t} f(t)dt \tag{4}$$

*f*(*t*) is the acceleration of slope vibration due to earthquake, *VTR* is called the velocity transmission ratio due to collision.

The apparent friction angle for the case 2 in Fig. 12 can be obtained from Eq. (3) as follows

$$\tan\overline{\varphi\_2} = \frac{h\_2}{D\_2} = \sum\_{i=1}^n w\_i k\_i^{\ast} \tan\varphi\_{si} - \sum\_{j=1}^m \frac{\upsilon\_{ej}}{2\,\text{g}D\_2} \tag{5}$$

Comparing Eq.(5) with Eq.(2), it can be seen clearly that the mechanism of long run-out distance is as follows.


#### **4.2 Colliding effect**

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

The apparent friction angle, usually used for the discussion of run-out distance, can be

*n*

1 1 tan tan 

*i <sup>h</sup> w k*

When we consider the effects of slope vibration due to earthquake, the kinetic energy of falling stone obtained from the collision with the vibrating slope and the movement patterns

2 \*

The second term here is for the kinetic energy of a falling stone obtained from the collision with the vibrating slope and *v*ej is the velocity obtained in *j*th *P*-phase and can be expressed

> *j j t t*

*f*(*t*) is the acceleration of slope vibration due to earthquake, *VTR* is called the velocity

Comparing Eq.(5) with Eq.(2), it can be seen clearly that the mechanism of long run-out

1. The kinetic energy of a falling stone obtained from the collision with the vibrating slope

2. The coefficient of conveying from static to dynamic friction *k*\* in Eq. (5) can be smaller than *k* in Eq. (3) because of the *N*-phase effect, air cushion effect, movement pattern.

The apparent friction angle for the case 2 in Fig. 12 can be obtained from Eq. (3) as follows

2 \*

tan tan

may result in long run-out distance from the second term of Eq. (5).

2

<sup>1</sup> tan cos 0

*i*

( )

2 2 1 1

*D gD*

*n m ej i i si i j h v w k*

 

*ej i si i*

*D* (2)

*i i si*

 

*ej <sup>t</sup> v VTR f t dt* (4)

2

(5)

2

*mgh mv l mgk* (3)

1

1

(sliding, rolling and flying) should be considered. Thus, Eq. (1) becomes

1 1

2

*j i*

*m n*

Fig. 12. Apparent friction angle

obtained from Eq. (1) as follows

transmission ratio due to collision.

distance is as follows.

as follows

In *P*-phase, a falling stone can obtain kinetic energy from the colliding with the vibrating slope. According to elastic collision theory, when two objects with different masses collide with each other, the object with smaller mass could obtain larger velocity. Since the mass of a slope is much larger than the mass of a falling stone, the velocity of the falling stone can be much larger than the vibrating velocity of the slope. That is to say the *VTR* in Eq. (4) can be larger than 1.0.

The *VTR* can be examined by the simple model shown in Fig. 13(a) and (b). The masses of the two blocks are *m*1 and *m*2 respectively. Before the colliding, the block 1 has initial velocity *V*10 toward block 2 which is standstill, i.e. *V*20=0. The friction between blocks and the base is negligible. After the colliding, the velocity of block 1 becomes *V*11 while block 2 obtains a velocity *V*21.

Fig. 13. The colliding model and *VTR* with mass ratio. (a) before the collision, (b) after the collision, (c) *VTR* obtained by DDA comparing with analytical solution.

According to the principles of the conservation of both energy and momentum, we have the following equations.

$$m\_1V\_{10}^2 + m\_2V\_{20}^2 = m\_1V\_{11}^2 + m\_2V\_{21}^2\tag{6}$$

$$m\_1V\_{10} + m\_2V\_{20} = m\_1V\_{11} + m\_2V\_{21} \tag{7}$$

By solving Eqs. (6) and (7), we can obtain the *VTR* for the case of *V*20=0 as follows

$$VTR = 2 \cdot \frac{m\_1}{m\_1 + m\_2} \tag{8}$$

It can be seen from the analytical solution Eq. (8) that if *m*1 is much larger than *m*2, *VTR* is to approach to 2.0. Therefore, since the mass of a slope is far larger than the falling stone, the velocity of the falling stone obtained from the slope vibration will be two times of that of the slope vibration velocity during earthquake.

The results of *VTR* given in Eq. (8) have been verified by DDA simulation. The model shown in Fig. 13 is used in DDA simulations. The block one with mass of *m*1 has the initial velocity of 10 *m/s* and the block two with mass of *m*2 is at a standstill. After the block one impacted the block two, the velocities of both blocks changed. The block two obtained the velocity from block one. The *VTR* is calculated from the ratio of *V*21 to *V*10.

Earthquake Induced a Chain Disasters 403

The movements of 4 kinds of stones with different shapes have been investigated under the earthquake conditions of 0, 200gal and 400gal sine wave of 3Hz. More than 10 times of repeated experiments have been carried out for each case. The following results have been

1. The movement distance for the case of a 400gal earthquake is 3.4 times longer than the case of no earthquake for the No.4 stone. Therefore, the effect of earthquake on the

2. The movement distance for the case of a 400gal earthquake is longer than the case of a 200gal earthquake. So it seems that the movement distance is proportional to the

3. The shape of the falling stone has effect on the movement distance. The movement distance of the No. 5 stone is much smaller than that of No. 4. This is because that the earthquake can change the movement pattern and cause the rotation motion. It can be seen that the No. 5 stone has very sharp edges and vertices, which may stop its rotation

It should be noticed that it is difficult to distinguish the velocity obtained from *P*-phase because the model slope is too small and there are very few *P*-phase during the movements.

Simulation of landslide by using numerical methods is an effective way in order to overcome the dimension limit of the model test by using shaking table. In this study, Discontinue Deformation Analysis (DDA), developed by Shi and Goodman (Shi et al., 1984), is used since it is applicable to simulating the rigid body movements and large deformations of a rock block system under general loading and boundary conditions. Several extensions of the original DDA have been made in this study so that earthquake wave can be taken into

Before simulating a real landslide, the applicability of the extended DDA has been verified by various simple models with theoretic solutions. For example, a simple model shown in

The theoretical solution of movement distance can be calculated by the following formula:

Fig. 17 is calculated by both the theoretical solution and DDA simulation.

obtained.

movement distance is very large.

Fig. 16. Difference from shape of falling stone

the simulation for different ways.

**4.4 Numerical simulation of landslide by using DDA** 

earthquake magnitude.

movement (Fig. 16).

The results obtained from DDA simulations by changing *m*1 are shown in Fig. 13(c), together with the theoretical analytical values. The line is calculated from the analytical solution Eq.(8) and the dots are obtained from DDA simulations.

It can be seen that the *VTR* obtained from DDA is in quite good agreement with the analytical solution. However, by close examination, it can be found that the *VTR* values from DDA are little smaller than the analytical values when the mass ratio of *m*1 to *m*2 is larger than 4.0. This is because elastic strains of the two blocks are led to energy transformed into potential energy of deformation by the collision in DDA simulation while no strain is considered in analytical solution.

Furthermore, when the block 2 has an initial velocity toward block 1, the *VTR* could become the larger and larger. Fig. 14 shows the results from DDA simulation. This may happen when a stone fall down to the slope in a *P*-phase, it will get larger rebounding velocity. That means, a trampoline effect can be produced by strong earthquake.

Fig. 14. The VTR variation with the initial velocity of block 2

#### **4.3 Model tests by shaking table**

Model tests using shaking table were carried out in order to investigate the effects of earthquake on the movement of debris. The model slope has the height of 180cm and the slope angle can be adjusted from 30° to 35° as shown in Fig. 15.

Fig. 15. Model tests by shaking table

The results obtained from DDA simulations by changing *m*1 are shown in Fig. 13(c), together with the theoretical analytical values. The line is calculated from the analytical solution

It can be seen that the *VTR* obtained from DDA is in quite good agreement with the analytical solution. However, by close examination, it can be found that the *VTR* values from DDA are little smaller than the analytical values when the mass ratio of *m*1 to *m*2 is larger than 4.0. This is because elastic strains of the two blocks are led to energy transformed into potential energy of deformation by the collision in DDA simulation while no strain is

Furthermore, when the block 2 has an initial velocity toward block 1, the *VTR* could become the larger and larger. Fig. 14 shows the results from DDA simulation. This may happen when a stone fall down to the slope in a *P*-phase, it will get larger rebounding velocity. That

Model tests using shaking table were carried out in order to investigate the effects of earthquake on the movement of debris. The model slope has the height of 180cm and the

Eq.(8) and the dots are obtained from DDA simulations.

means, a trampoline effect can be produced by strong earthquake.

Fig. 14. The VTR variation with the initial velocity of block 2

slope angle can be adjusted from 30° to 35° as shown in Fig. 15.

considered in analytical solution.

**4.3 Model tests by shaking table** 

Fig. 15. Model tests by shaking table

The movements of 4 kinds of stones with different shapes have been investigated under the earthquake conditions of 0, 200gal and 400gal sine wave of 3Hz. More than 10 times of repeated experiments have been carried out for each case. The following results have been obtained.


It should be noticed that it is difficult to distinguish the velocity obtained from *P*-phase because the model slope is too small and there are very few *P*-phase during the movements.

Fig. 16. Difference from shape of falling stone

#### **4.4 Numerical simulation of landslide by using DDA**

Simulation of landslide by using numerical methods is an effective way in order to overcome the dimension limit of the model test by using shaking table. In this study, Discontinue Deformation Analysis (DDA), developed by Shi and Goodman (Shi et al., 1984), is used since it is applicable to simulating the rigid body movements and large deformations of a rock block system under general loading and boundary conditions. Several extensions of the original DDA have been made in this study so that earthquake wave can be taken into the simulation for different ways.

Before simulating a real landslide, the applicability of the extended DDA has been verified by various simple models with theoretic solutions. For example, a simple model shown in Fig. 17 is calculated by both the theoretical solution and DDA simulation.

The theoretical solution of movement distance can be calculated by the following formula:

$$S\_0 = \frac{1}{2}at^2\tag{9}$$

Earthquake Induced a Chain Disasters 405

We applied the extended DDA to simulate the Dongheko landslide in Qingchuan prefecture. The vertical section shown in Fig. 19 is taken along the red line in Fig. 19. The DDA software and the model are shown in Fig. 20. The parameters for both the material and

Since the real earthquake curves are not available, a sine wave is used. The movements of

It has been shown that an 800gal sine wave can cause long distance movements of debris like real one. The rotation and flying movements are the major reasons for long-distance

Fig. 20. DDA software developed by Chen and the model of Dongheke landslide

debris at different times obtained from DDA simulation are shown in Fig. 21.

DDA program are also shown in Fig. 20.

Fig. 19. Vertical section of the Donghekou landslide

movement, which can be easily observed in DDA simulations.

where

$$\alpha = \lg[\sin\theta - (k\tan\phi\_0)\cos\theta] \tag{10}$$

The results of the movement distance are in good agreement with each other as shown in Fig. 18.

Fig. 17. The DDA model

Fig. 18. The results

 *g k* [sin ( tan )cos ] 

The results of the movement distance are in good agreement with each other as shown in

0 1 2

where

Fig. 18.

Fig. 17. The DDA model

Fig. 18. The results

2

0

 

*S at* (9)

(10)

We applied the extended DDA to simulate the Dongheko landslide in Qingchuan prefecture. The vertical section shown in Fig. 19 is taken along the red line in Fig. 19. The DDA software and the model are shown in Fig. 20. The parameters for both the material and DDA program are also shown in Fig. 20.

Since the real earthquake curves are not available, a sine wave is used. The movements of debris at different times obtained from DDA simulation are shown in Fig. 21.

Fig. 19. Vertical section of the Donghekou landslide

It has been shown that an 800gal sine wave can cause long distance movements of debris like real one. The rotation and flying movements are the major reasons for long-distance movement, which can be easily observed in DDA simulations.

Fig. 20. DDA software developed by Chen and the model of Dongheke landslide

Earthquake Induced a Chain Disasters 407

Since the material sources of debris flow got much richer after earthquake, it is easy to form large scale debris flow. For example, the surge peak discharge reached 260 *m*3/*s* in the debris flow occurred in Beichuan town on Sept. 24, 2008. The volume was too large to a basin with the area of 1.54*km*2. The cover of debris is so thick that it buried the fourth floor of some buildings. Another example is Sanyanyu debris flow. The volume of the debris reached 144.20 million *m*3. The debris flow carried many huge stones and destroyed houses

Fig. 22. 46 debris flows in the Beichuan area(Picture from Tangchuan et cl., 2010)

Many preventive structures designed based on the standard of conventional debris flow were also destroyed by the large scale debris flows after the earthquakes. For example, 19 check dams were destroyed by the Wenjia debris flow occurred in Mianzhu Qingping town area on Aug. 13, 2010. The Fig. 23(a) shows one of the check dam destroyed by the debris flow. The extreme large scale and destructive impact of the debris flow seems beyond

2. Large surge peak discharge and huge volume

and bridges (Tang et al., 2009).

imagination.

Fig. 21. The numeric simulation of debris movements by the extended DDA
