J. Mt. Sci. (2011) 8: 544–550 DOI: 10.1007/s11629-011-2128-1

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Abstract: The geometry of a landslide dam is an important component of evaluating dam stability. However, the geometry of a natural dam commonly cannot be obtained immediately with field investigations due to their remote locations. A rapid evaluation model is presented to estimate the geometries of natural dams based on the slope of the stream, volume of landslides, and the properties of the deposit. The proposed model uses high resolution satellite images to determine the geometry of the landside dam. These satellite images are the basic information to a preliminary stability analysis of a natural dam. This study applies the proposed method to two case studies in Taiwan. One is the earthquake-induced Lung-Chung landslide dam in Taitung, and the second is the rainfall-induced Shih-Wun landslide dam in Pingtung. Keywords: Landslide dam; Geometries; Stability

Introduction

Landslides are a frequent natural hazard in Taiwan, where they result from an earthquake or a rainfall event. The landslide dam serves to block river flow, storing water behind the dam, and forming a landslide lake. The lifespan of a landslide dam ranges from less than a day to several years. The stability of the dam is the main factor that determines the lifespan of the dam. This study

proposes a rapidly-applied algorithm to analyze the geometry of a landslide dam and the stability of the dam using satellite images. The proposed algorithm provides useful information for preparing emergency evacuation plans at the early stages of dam formation.

When a landslide dam fails due to dam breaching and erosion by an overflow stream, the material in the dam and the released water surge can lead to catastrophic downstream flooding. The flooding endangers downstream properties, residential homes and the local population. Therefore, rapid evaluation of dam stability is very important.

Knowledge of the geometry of the landslide dam is essential for determining its stability. The geometry is affected by geological conditions, particle size, landslide type, and terrain. The locations of landslides are usually in mountainous areas, which are not easy to reach during and shortly after the landslide event. Rapid analysis of all information regarding the landslide and its stability are crucial to the safety of downstream areas.

1 Existing Methods for Analyzing the Geometry of the Landslide Dam

Landslide dam stability is highly correlated with its geometry, typically found by field observation. Due to the location of landslide dams

Analysis of Landslide Dam Geometries

KUO Yu-Shu*, TSANG Yun-Chung, CHEN Kun-Ting, SHIEH Chjeng-Lun

Department of Hydraulic and Ocean Engineering, National Cheng-Kung University, Chinese Taipei, 70101

* Corresponding author, e-mail: kuoyushu@mail.ncku.edu.tw

© Science Press and Institute of Mountain Hazards and Environment, CAS and Springer-Verlag Berlin Heidelberg 2011

Received: 30 January 2011 Accepted: 20 May 2011

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in mountainous areas, a lack of field observations results in insufficient data for understanding landslide dam geometry. The geometry of landslide dams is usually evaluated through laboratory experiments or numerical models.

Takahashi and Kuang (1988) proposed a 2D landslide dam-geometry evaluation model. This model assumes that a landslide mass with width, W, and volume, V, of a uniform deposit at a cross section of the river channel. For the vertical section along the river channel, the shape of the landslide mass body changes from rectangular to parallelogram, then becomes trapezoidal or triangular. Based on the assumption of constant volume, the geometry of a landslide dam is influenced by the quantity of the sediment mass. According to lab experiments, Takahashi and Kuang (1988) claimed that the shape of the landslide dam is a triangle if the sediment volume is greater than a critical volume Vsc and is a trapezoid if the volume is smaller than the critical volume. The critical volume Vsc is defined as:

Kθ

WBVsc

2)cos(2= (1)

where B is the width of the river channel, K is a parameter related to the angle of repose φr and the slope of stream θ:

)sin()90sin(sin

)tan(cos

θφφθ

θφθ

−+++

+=

r

r

r

Ko

(2)

When the shape of the landslide dam is trapezoid, both angles at the bottom sides of the dam are the angle of repose φr. The top length of the dam, LT, and the bottom length of the dam, LB, are:

KBWθV

θWL

2cos

cosB += (3)

KBWθV

θWL

2cos

cosT −= (4)

The maximum height of the dam, Dmax, is:

)(2

maxTB LLB

VD+

= (5)

When the shape of the landslide dam is triangular, the bottom length of the dam is:

⎟⎠⎞

⎜⎝⎛ +⎟⎟

⎠

⎞⎜⎜⎝

⎛= K

BWVW

VVL sc

scB 2

sincos

21

θθ

(6)

The Takahashi and Kuang (1988) model obtained good results in laboratory experiments. However, this model assumes that the landslide mass is entirely deposited in the river channel. This assumption is not applicable to most landslides in Taiwan. In addition to this assumption, the angle of repose is related to geographic conditions, particle size distribution, and water content in the sediment. The method proposed by Takahashi and Kuang (1988) is also limited to evaluating a dam shape for 2D cases. For 3D cases, numerical models were adopted to analyze the geometry of the dams formed by landslides and debris flow (Hunger 1995; Hunger 2006). These numerical models can handle dams formed by composite materials. The composite material model considers Bingham flow (Sousa and Voight 1985), shear flow (Savage and Hutter 1989), and shear flow considering pore pressure (Hunger 1995) to evaluate the geometry of the landslide dam. However, the proportions of the above-mentioned materials is determined by field investigation and laboratory experiment. Therefore, the geometry of natural dams is very difficult to evaluate when the dam is newly formed.

2 The Relationship Between the Geometry and the Causes of Landslide Dams

The major sediment sources that form landslide dams are landslides from both sides of a river channel. The major causes of the landslides include earthquakes, precipitation, snow melt, and volcano eruption. Costa and Suhuster (1988) analyzed 128 landslide dams around the world. According to them, fifty percent of the landslides are induced by precipitation and snow melt and forty percent by earthquakes. In Taiwan, Chen (1999) indicated that five landslide dams have occurred at Tsao-Ling, including three that were earthquake-induced and two that were rainfall-induced. A major earthquake on September 21st, 1999 resulted in the formation of ten landslide dams.

For rainfall-induced landslide dams, the strength of the sediment material is reduced due to the increased water content. These dams are composed of non-cohesive material and tend to fail

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soon after formation. Most dams fail because the water behind overflows and erodes the spillway that drains the lake (Casagli et al. 2003; Ermini and Casagli 2003; Tabata and Mizuyama 2002; Hyndman and Hyndman 2008). Table 1 shows that the failure percentage of the dams formed by rainfall-induced landslides is much higher than for the dams formed by earthquake-induced landslides. Chen and Hsu (2009) and Chen et al. (2010) studied landslide cases in Taiwan and indicated that the height of rainfall-induced landslide dams is lower than the height of earthquake-induced landslide dams (Figure 1).

Based on the analyses of landslide dams in Taiwan, a linear relationship between the slope of the stream, θ, and the angle of the dam in a downstream direction φd is shown in Figure 2. However, this relationship is not observed upstream (Figure 3). The angle of the dam in the upstream direction can be estimated using the regression curve obtained between the slope of the stream and the deposition angle of the dam in the downstream direction (Figure 4).

Figure 1 The relationship between the height and the volume of the dam for earthquake-induced and rainfall-induced dams

Table 1 The failure of earthquake-induced and rainfall induced landslide dams

Landslide Dam Type

Rainfall-induced

Earthquake-induced

Not Failure (%) 18 43

Failure (%) 82 57

Source: Casagli et al. (2003); Tabata and Mizuyama (2002)

Figure 3 The relationship between the slope of the stream and the angle of dam in the upstream direction for earthquake-induced and rainfall-induced dams

Figure 4 The relationship between the slope of the stream and the ratio of the angle of the dam in upstream direction to downstream direction

Figure 2 The relationship between the slope of the stream and the angle of the dam in downstream direction for earthquake-induced and rainfall-induced dams

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3 Rapid Evaluation of Landslide Dam Geometry

Based on field investigations of landslide dams in Taiwan, a landslide dam can be triangular or trapezoidal. This study first focuses on triangular dams, and Figure 5 illustrates a triangular dam and the parameters used in this study.

When a landslide dam is formed field measurements are unavailable. Satellite images can provide information for determining the characteristic length of dam, l , in the downstream direction. A problem with satellite images is that a landslide dam may breach or deform before a current image is taken or made available for study. In addition, the length of the dam in the upstream direction, Lu, is difficult to determine from a satellite image because point C (Figure 5) is beneath the water stored in the upstream lake. To obtain the geometry of the dam, the characteristic height, H´, can be obtained by comparing the position of the collapsed mass deposited along the river sides from satellite images and from a topographic map. The slope of the stream, θ, can be obtained using satellite images and a historical topographic map.

From triangle geometry, the angle of dam in downstream direction, φd, is:

⎟⎠⎞

⎜⎝⎛ ′

= −

l

Hd

1tanφ (7)

When satellite images are not available, dφ can

be approximated using the regression shown in Figure 2. The relationship is:

7.12.1 += θφd (8)

The height of the dam Hd and the length of the downstream part at the bottom of the dam, Ld, can be expressed as:

θθ sincos l−′= HHd (9)

θθ

tancos dd HL += l

(10)

If the landslide dam forms a reservoir and stores water, the location of point C is not available from satellite images. Therefore, Ld cannot be calculated from satellite images. As can be seen in Figure 4, φu can be calculated using the relationship between φu and φd.

θ

φφ 17.078.2 −= ed

u (11)

where φd is obtained from equation (7). With equation (11), Lu can be calculated using the slope of the stream, θ, and the height of the dam, Hd.

)tan( u

du

HLφθ +

= (12)

The proposed algorithm is for rapid analysis of the geometry of the landslide dams. The geometry can provide important information for the stability of the dams. The following case studies show examples of how the proposed algorithm yields the dam parameters.

4 Case Study

4.1 Earthquake-induced landslide dam

Lung-Chung landslide dam, formed at Taitung, Taiwan on July 16th, 2006, was induced by an earthquake of magnitude 4.2 on the Richter scale. The landslides occurred on the right side of the river (Figure 6). The volume of the dam was about 600,000 cubic meters. The collapsed mass remained partially on the right hand side of the river channel. The lake volume at full water level was estimated as 800,000 cubic meters. On July 25th, the landslide dam overflowed from the south-east side because of precipitation with Typhoon

Figure 5 Illustration of a triangle landslide dam

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Kaemi. To lower the water level, construction was performed at the site of the spillway in November, 2007. The height of the spillway was lowered by 5 meters. A second construction was performed in April, 2008 and the height was lowered by an additional 10 meters. After that, on-site measurement shown on Figure 7 was performed in September, 2008. The height of the Lung-Chung landslide dam is approximately 35 meters, and the length is about 500 meters.

With geometric evaluation of landslide dams using satellite images and topographic maps, the following parameters are obtained: H´=53.7m, l = 358 m, and θ = 3.5o. Equations (7), (9), (10), (11), and (12) are used to obtain φd = 8.5o, Hd = 31.7 m, Ld = 360.6 m, φu = 13o, and Lu = 103.7 m, respectively. Figure 7 shows the comparison of the dam geometry obtained from the field measurement and the proposed algorithm. The

result shows that the proposed algorithm provides a good estimation of dam geometry.

4.2 Rainfall-induced landslide dam

The Shih-Wun landslide dam, Pingtung, Taiwan, was induced by heavy rainfall from Typhoon Morakot. The landslide moved in a direction parallel to the bedding of the dip slope and blocked the river. The material of the landslide dam is metamorphic sandstone, shale, and slate. Due to the overflow with the typhoon rainfall, the existing dam has a height of 20 m, and the width of the spillway is 15 m. The catchment area is 3,315.7 ha and the water depth is about 15 m. The distance to the closest residential community is 27 kilometers.

Figure 8 shows the Shih-Wun landslide dam. The locations of A and B were identified using satellite images from Formosa-2. Based on these satellite images, the following parameters are obtained: l = 500m, H´ = 58 m, and θ = 1.4°. Then equations (7), (9), (10), (11), and (12) are used to obtain φd = 6.62°, Hd = 45.8 m, Ld = 501.3 m, φu = 14.5°, and Lu = 157.97 m, respectively. Figure 9 shows the comparison of the dam geometry obtained between the field measurement and the proposed algorithm. The result shows that the proposed algorithm provides a good estimation of dam geometry.

4.3 Stability analysis of the landslide dams

Ermini and Casagli (2003) proposed a dimensionless blockage index (DBI) using

Figure 6 Lung-Chung landslide lake

Figure 8 Shih-Wun landslide lake

Figure 7 Comparison between field measurement and calculated elevation profile of Lung-Chung Dam

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geomorphic variables dam height (Hd), watershed area (Ab), and dam volume (Vd) to evaluate the stability of a landslide dam.

⎟⎟⎠

⎞⎜⎜⎝

⎛ ×=

d

db

VHA

DBI log (13)

If DBI is larger than 3.08, the dam is classified as unstable. If DBI is smaller than 2.75, the dam is classified as stable. If DBI has a value between 3.08 and 2.75, the stability of the dam is uncertain. According to the definition of DBI, the areas of catchment of Lung-Chung and Shih-Wun dam (Ab) are 12,000,000 m2 and 33,157,000 m2, respectively. The volume of the dam (Vd) is calculated using the area of the calculated triangle times the width of the river. The width of the river at Lung-Chung dam and Shih-Wun dam are 64 m and 170 m, respectively. The volume of the dam is 470,986 m3 for the Lung-Chung dam and 2,566,538 m3 for the Shih-Wun dam. The DBI’s of the Lung-Chung landslide dam and Shih-Wun landslide dam are 2.91 and 2.77, respectively. The values of DBI for both cases are located in the uncertain range (Figure 10).

5 Conclusion

Landslide lakes produce a common natural hazard in Taiwan. Due to the location of the dams, geometry data is usually unavailable when the dams are newly formed. This data insufficiency results in difficulty for evaluating the stability of the landslide dam. This study analyzed landslide dam data in Taiwan and obtained the regression relationship between the slope of the stream and the angle of the dam in the upstream and downstream directions. The characteristic heights and lengths of the dams in the downstream direction were obtained from the satellite images and a topographic map. The proposed algorithm can provide a rapid analysis of the geometry of the landslide dam. The proposed algorithm, applied to an earthquake-induced landslide dam and a rainfall-induced landslide dam, show its accuracy and the applicability.

Acknowledgements

This study was supported by National Science Council, Taiwan, China. The project name is Numerical Approach to Estimate the Stability and Deformation Response of Landslide Dams (NSC 99-2625-M-006-004) and Modeling of The Compound Disaster in Hsiaolin Village (NSC 99-2218-E-006-238).

Figure 9 The comparison between field measurement and calculated elevation profiles of the Shih-Wun Landslide Dam

Figure 10 Stability analyses of the landslide dams

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