Landslide Potential Evaluation Using Fragility Curve Model

*Yi-Min Huang,Tsu-Chiang Lei, Bing-Jean Lee and Meng-Hsun Hsieh*

## **Abstract**

The geological environment of Taiwan mainly contains steep topography and geologically fragile ground surface. Therefore, the vulnerable environmental conditions are prone to landslides during torrential rainfalls and typhoons. The rainfallinduced shallow landslide has become more common in Taiwan due to the extreme weathers in recent years. To evaluate the potential of landslide and its impacts, an evaluation method using the historical rainfall data (the hazard factor) and the temporal characteristics of landslide fragility curve (LFC, the vulnerability factor) was developed and described in this chapter. The LFC model was based on the geomorphological and vegetation factors using landslides at the Chen-Yu-Lan watershed in Taiwan, during events of Typhoon Sinlaku (September 2009) and Typhoon Morakot (August 2009). The critical hazard potential (*Hc*) and critical fragility potential (*Fc*) were introduced to express the probability of exceeding a damage state of landslides under certain conditions of rainfall intensity and accumulated rainfall. Case studies at Shenmu village in Taiwan were applied to illustrate the proposed method of landslide potential assessment and the landslide warning in practice. Finally, the proposed risk assessment for landslides can be implemented in the disaster response system and be extended to take debris flows into consideration altogether.

**Keywords:** landslide, fragility, landslide potential, probabilistic model

## **1. Introduction**

Taiwan is on the path of western Pacific typhoon path and on the circum-Pacific earthquake belt, indicating that Taiwan suffered from two or more natural disasters, which was the highest in the world [1]. Besides, most of the land in Taiwan, about 70% of total area, is hillside. Given the conditions of increasing impacts of climate change and extreme weathers, the rainfall-induced landslide has become a serious issue in Taiwan.

Most landslide researches used the landslide susceptibility analysis (LSA) to develop landslide evaluation model [2]. The LSA models basically use factors and observed data to construct the description of landslides. The factors include rainfall intensity, accumulated rainfall, slope degree, vegetation, etc. The common models developed for landslide hazard or landslide evaluation are usually deterministic analysis, including the traditional slope stability analysis [2]. Recently, a novel concept of applying probability to landslide evaluation had been proposed. The fragility curves, which are commonly used in the earthquake-induced structure analysis, had been adopted to represent the probability of landslide [3–5]. The process of applying fragility curve to landslide evaluation is to consider and estimate the recurrence and the probability of exceedance of a damage level for a landslide [3, 4].

In this chapter, the preparation of landslide fragility curves was introduced. The procedure of developing the landslide fragility curve (LFC) model was the researches of rainfall-induced shallow landslide in the past years [2–5]. The proposed LFC model considered the impacts of rainfall and the vulnerability of environment. Instead of using one-variable triggering factor (rainfall intensity or accumulation) in the previous research [2], the newly improved LFC model used bivariate approach in the model [3, 4]. The improved LFC model introduced the landslide fragility surface (LFS) by considering the influence of both rainfall intensity and accumulation at the same time [4, 5].

The spatial statistics and geographic information system (GIS) were used for data processing. The data of each factor used in the model was further divided into groups. Classification of factors represented the environmental characteristics of a specific area. The analysis basis was conducted spatially on the slope units, which are topographically defined as the parts of a watershed [5]. With the LFS model, the risk assessment of landslide then was analyzed in association with the rainfall hazard potential [4, 5]. The Shenmu area of Chen-Yu-Lan watershed was selected as the study area, and historical cases were used to illustrate the application of LFS model.

Water Conservation Bureau manual [9]. There are seven slope levels of 5% or less, 5–15%, 15–30%, 30–40%, 40–55%, 55–100%, and slope exceeding 100%. The slopes <15% are recognized as flat ground or very gentle slopes and not included in this study. Slopes of levels 3–7 were studied in the landslide model.

4. Slope aspect (A): the slope aspect represents the vulnerable directions of occurring landslide when given a known topography. This factor may

5.Landslide area (LA): observing the landslide distribution through image classification results can obtain the information about the land cover change. The change from events of Typhoon Sinlaku (in 2008) and Typhoon Morakot

6. Incremental landslide area (IA): to understand the landslide increment, the images before and after a landslide were considered. The landslides are classified into five categories (shown in **Figure 2**): (1) the original landslide area (number 1 + 2), (2) the original landslide area extension (number 2), (3) new landslide area on single period (number 3), (4) new landslide area on pre-/post periods (number of 2 + 3), and (5) vegetation restoration area (number of 1). In this study, the new landslide area on pre-/post periods

7.Ratio of incremental landslide area (RIL): to obtain the ratio of incremental landslide area, this study used the incremental landslide area from image of

8.Vegetation index (N): to determine the density of vegetation on a patch of land, researchers must observe the distinct colors (wavelengths) of visible and near-infrared sunlight reflected by the plants [10]. Nearly almost satellite vegetation indices employ the difference formula, ð Þ *NIR* � *R =*ð Þ *NIR* þ *R* [11], to quantify the density of plant growth on the earth—the subtraction of nearinfrared radiation (NIR) and red radiation (R) divided by the addition of near-infrared radiation and red radiation. The result of this formula is called the normalized difference vegetation index (NDVI). The values for NDVI in this study were obtained from SPOT image. The range of NDVI is �1 to 1.

represent the "weak" aspect of a slope in terms of landslide.

(in 2009) was identified using GIS software.

*The definition of rainfall indices: Imax and Rte (modified after [2–4]).*

*Landslide Potential Evaluation Using Fragility Curve Model*

*DOI: http://dx.doi.org/10.5772/intechopen.89183*

(number of 2 + 3) was considered.

**Figure 1.**

**181**

two periods to determine this factor.

## **2. The factors and environmental database**

When considering the factors to be used in the landslide problem, these factors are generally classified as triggering and environmental factors [6–8]. Among these factors, the rainfall is usually the major concern, and for environmental vulnerability, many factors can be chosen from. Not every chosen environmental factor can be used in developing a landslide model because of (1) few data in the database, (2) lack of data, and (3) low influence in the model. In this chapter, the cumulative rainfall and maximum hourly rainfall (rainfall intensity) were used for triggering factors, whereas slopes, slope aspects, landslide area, incremental landslide area, ratio of incremental landslide area, normalized difference vegetation index, distance to the nearest river, and geology were used for environmental factors of hillside slope in the study. A GIS database to describe landslide areas was created and was later applied in developing the proposed fragility curve model. These indexes, factors, and symbol definitions are explained in the following:


*Landslide Potential Evaluation Using Fragility Curve Model DOI: http://dx.doi.org/10.5772/intechopen.89183*

**Figure 1.**

The fragility curves, which are commonly used in the earthquake-induced structure analysis, had been adopted to represent the probability of landslide [3–5]. The process of applying fragility curve to landslide evaluation is to consider and estimate the recurrence and the probability of exceedance of a damage level for a

In this chapter, the preparation of landslide fragility curves was introduced. The procedure of developing the landslide fragility curve (LFC) model was the researches of rainfall-induced shallow landslide in the past years [2–5]. The proposed LFC model considered the impacts of rainfall and the vulnerability of environment. Instead of using one-variable triggering factor (rainfall intensity or accumulation) in the previous research [2], the newly improved LFC model used bivariate approach in the model [3, 4]. The improved LFC model introduced the landslide fragility surface (LFS) by considering the influence of both rainfall

The spatial statistics and geographic information system (GIS) were used for data processing. The data of each factor used in the model was further divided into groups. Classification of factors represented the environmental characteristics of a specific area. The analysis basis was conducted spatially on the slope units, which are topographically defined as the parts of a watershed [5]. With the LFS model, the risk assessment of landslide then was analyzed in association with the rainfall hazard potential [4, 5]. The Shenmu area of Chen-Yu-Lan watershed was selected as the study area, and historical cases were used to illustrate the application

When considering the factors to be used in the landslide problem, these factors are generally classified as triggering and environmental factors [6–8]. Among these factors, the rainfall is usually the major concern, and for environmental vulnerability, many factors can be chosen from. Not every chosen environmental factor can be used in developing a landslide model because of (1) few data in the database, (2) lack of data, and (3) low influence in the model. In this chapter, the cumulative rainfall and maximum hourly rainfall (rainfall intensity) were used for triggering factors, whereas slopes, slope aspects, landslide area, incremental landslide area, ratio of incremental landslide area, normalized difference vegetation index, distance to the nearest river, and geology were used for environmental factors of hillside slope in the study. A GIS database to describe landslide areas was created and was later applied in developing the proposed fragility curve model. These indexes, factors, and symbol definitions are explained in the following:

1.Maximum rainfall intensity (*Imax*): the maximum rainfall intensity is the rainfall in the form of rainfall per unit time. In this study, *Imax* refers to the maximum hourly rainfall (**Figure 1**) and was used as a triggering factor for

2.Effective accumulated rainfall (*Rte*): the *Rte* is defined as the accumulated rainfall before the maximum rainfall intensity in a continuous raining event (**Figure 1**), by considering the influence of antecedent 7-day rainfall.

3.Hillside slope (S): the dynamic behavior of the landslide has close relationship with the slope. Hence, the degree of slope may be a prominent factor of triggering landslides. In this study, the slope was classified based on the Soil and

intensity and accumulation at the same time [4, 5].

**2. The factors and environmental database**

landslide [3, 4].

*Landslides - Investigation and Monitoring*

of LFS model.

LFC model.

**180**

*The definition of rainfall indices: Imax and Rte (modified after [2–4]).*

Water Conservation Bureau manual [9]. There are seven slope levels of 5% or less, 5–15%, 15–30%, 30–40%, 40–55%, 55–100%, and slope exceeding 100%. The slopes <15% are recognized as flat ground or very gentle slopes and not included in this study. Slopes of levels 3–7 were studied in the landslide model.


north peak of Yu Mountain and is one of the upper rivers of the Zhuoshui River system, which is the largest river system in Taiwan. Chen-Yu-Lan River has a length of 42.4 km with an average declination slope of 5%, and its watershed area is

The Shenmu area is a location where debris flows frequently occurred [5]. The local village is adjacent to the confluence of three streams: Aiyuzi Stream (DF226), Huosa Stream (DF227), and Chushuei Stream (DF199). In Shenmu, the debris flows usually occurred at the Aiyuzi Stream due to its shorter length and large landslide area (**Table 1**) in its upstream [5]. **Figure 4** shows the terrain of three streams. In addition to the basic terrain data of Shenmu area, the hydrologic and geographic factors are needed in modeling. To obtain these factors, an environment database of Chen-Yu-Lan watershed was prepared. Among the data collection, the landslide increment (i.e., new landslides) after a rainfall event was also obtained by

To develop the LFC model, the local environmental data was collected for the study area, and GIS was used to process the data. The environment database of Chen-Yu-Lan watershed includes data of geology, geological layers, rock property,

**) Landslide area (km2**

**)**

. This area was fragile after the Chi-Chi Earthquake (occurred on

about 450 km<sup>2</sup>

**Figure 3.**

**Table 1.**

**183**

September 21, 1999).

*Chen-Yu-Lan watershed [2].*

*Landslide Potential Evaluation Using Fragility Curve Model*

*DOI: http://dx.doi.org/10.5772/intechopen.89183*

image processing method in this study.

*The landslide area in Shenmu after 2009 [5].*

slope and slope aspects, and DEM, as shown in **Figures 5**–**8**.

**Debris flow no. Stream Length (km) Catchment area (km2**

DF199 Chushuei stream 7.16 8.62 0.33 DF227 Huosa stream 17.66 26.20 1.49 DF226 Aiyuzi stream 3.30 4.00 1.00

**Figure 2.** *Concept of mapping landslide area change: differences between two periods of SPOT image [2].*


## **3. Study area and material**

To explain the landslide fragility model, the Shenmu area in Taiwan was used as a case to demonstrate the development of LFC of a given site. The Shenmu area locates in the watershed of Chen-Yu-Lan River. Chen-Yu-Lan watershed is at the central part of Taiwan (**Figure 3**). The Chen-Yu-Lan River originates from the

*Landslide Potential Evaluation Using Fragility Curve Model DOI: http://dx.doi.org/10.5772/intechopen.89183*

**Figure 3.** *Chen-Yu-Lan watershed [2].*

north peak of Yu Mountain and is one of the upper rivers of the Zhuoshui River system, which is the largest river system in Taiwan. Chen-Yu-Lan River has a length of 42.4 km with an average declination slope of 5%, and its watershed area is about 450 km<sup>2</sup> . This area was fragile after the Chi-Chi Earthquake (occurred on September 21, 1999).

The Shenmu area is a location where debris flows frequently occurred [5]. The local village is adjacent to the confluence of three streams: Aiyuzi Stream (DF226), Huosa Stream (DF227), and Chushuei Stream (DF199). In Shenmu, the debris flows usually occurred at the Aiyuzi Stream due to its shorter length and large landslide area (**Table 1**) in its upstream [5]. **Figure 4** shows the terrain of three streams.

In addition to the basic terrain data of Shenmu area, the hydrologic and geographic factors are needed in modeling. To obtain these factors, an environment database of Chen-Yu-Lan watershed was prepared. Among the data collection, the landslide increment (i.e., new landslides) after a rainfall event was also obtained by image processing method in this study.

To develop the LFC model, the local environmental data was collected for the study area, and GIS was used to process the data. The environment database of Chen-Yu-Lan watershed includes data of geology, geological layers, rock property, slope and slope aspects, and DEM, as shown in **Figures 5**–**8**.


**Table 1.**

*The landslide area in Shenmu after 2009 [5].*

9.Distance to the nearest river (R): the landslide may be triggered due to the erosion by the river at the toe section. The distance to the river reflects the

10.Geology (G): the geological time scale of the area and the rock types of the site were combined into consideration as the geology factor. In the past studies, the geology-related information (like the rock types and rock strength) was not usually available. Therefore, to simplify the classification, the geological

To explain the landslide fragility model, the Shenmu area in Taiwan was used as a case to demonstrate the development of LFC of a given site. The Shenmu area locates in the watershed of Chen-Yu-Lan River. Chen-Yu-Lan watershed is at the central part of Taiwan (**Figure 3**). The Chen-Yu-Lan River originates from the

time scale was chosen to represent the possible influence of geology.

potential of landslide contributed from the river system.

*Concept of mapping landslide area change: differences between two periods of SPOT image [2].*

**3. Study area and material**

*Landslides - Investigation and Monitoring*

**Figure 2.**

**182**

The new landslide areas (**Figures 9** and **10**) were identified by using pre- and post-event satellite images of Typhoon Sinlaku in 2008 and Typhoon Morakot in 2009 (**Table 2**). These landslide areas were used for later LFC model analysis. Another important factor in the LFC model is the vegetation conditions. The information of vegetation status was also obtained by image processing the same as the determination of new landslides.

In addition to the hydrologic and geographic data, the landslide triggering factors were also considered in data preparation. **Table 3** defines the rainfall indices. It should be noted that the effective accumulated rainfall was calculated by including the antecedent 7-day accumulated rainfall. The antecedent 7-day accumulated rainfall is the total weighted rainfall counted from the 7-day duration before the starting of current rainfall event. Take Typhoon Sinlaku (September 11–16, 2008) for example. The starting date of Typhoon Sinlaku was September 11, 2008, and the antecedent 7-day accumulation rainfall was the total weighted rainfall during September 3 to September 10, as described as *Ra* in **Table 3**.

**Figures 11** and **12** show the rainfall interpolation of the events of Typhoon Sinlaku (September 11–16, 2008) and Typhoon Morakot (August 5–10, 2009). The red spots in the figure are the locations of rainfall stations. It was noted that the rainfall intensity and the cumulative rainfall of event of Typhoon Morakot were much higher than those of Typhoon Sinlaku. Both events had caused serious landslides in the central Taiwan.

**Figure 5.**

**185**

*Chen-Yu-Lan watershed: (a) geological time scale and (b) rock types.*

*Landslide Potential Evaluation Using Fragility Curve Model*

*DOI: http://dx.doi.org/10.5772/intechopen.89183*

*Landslide Potential Evaluation Using Fragility Curve Model DOI: http://dx.doi.org/10.5772/intechopen.89183*

The new landslide areas (**Figures 9** and **10**) were identified by using pre- and post-event satellite images of Typhoon Sinlaku in 2008 and Typhoon Morakot in 2009 (**Table 2**). These landslide areas were used for later LFC model analysis. Another important factor in the LFC model is the vegetation conditions. The information of vegetation status was also obtained by image processing the same as the

In addition to the hydrologic and geographic data, the landslide triggering factors were also considered in data preparation. **Table 3** defines the rainfall indices. It should be noted that the effective accumulated rainfall was calculated by including the antecedent 7-day accumulated rainfall. The antecedent 7-day accumulated rainfall is the total weighted rainfall counted from the 7-day duration before the starting of current rainfall event. Take Typhoon Sinlaku (September 11–16, 2008) for example. The starting date of Typhoon Sinlaku was September 11, 2008, and the antecedent 7-day accumulation rainfall was the total weighted rainfall during

**Figures 11** and **12** show the rainfall interpolation of the events of Typhoon Sinlaku (September 11–16, 2008) and Typhoon Morakot (August 5–10, 2009). The red spots in the figure are the locations of rainfall stations. It was noted that the rainfall intensity and the cumulative rainfall of event of Typhoon Morakot were much higher than those of Typhoon Sinlaku. Both events had caused serious land-

September 3 to September 10, as described as *Ra* in **Table 3**.

determination of new landslides.

*The terrain and landslide areas of Shenmu area.*

*Landslides - Investigation and Monitoring*

**Figure 4.**

slides in the central Taiwan.

**184**

**Figure 6.** *Five-meter DEM of Chen-Yu-Lan watershed (after [2]).*

Finally, the database was used to analyze the study area on the basis of slope units. The slope unit was defined as in **Figure 13**. A slope unit is defined as one slope part or the left/right part of a watershed. Slope units can be topologically divided by the watershed divide and drainage line, with the help of GIS tool [12]. The application of slope unit in the development of LFC was based on the physical interpretation of slopes in the mountain area. The environmental database was applied in accordance with the slope units at the site of interest. **Figure 14** shows the slope unit

To develop the empirical landslide fragility model, a probability distribution was chosen to describe the potential of landslide fragility. When the probability distribution was determined, the parameters of probability, the median and standard deviation, were obtained by fitting the data from the environmental database and the landslide areas. The use of slope unit was adopted here, and the classification of environmental factors was applied to represent the conditions of landslide given rainfall intensity and accumulated rainfall. The procedure of developing the empirical landslide fragility curve was described in the following.

The fragility analysis is usually used to describe the potential of hazard in terms of potential levels or probability of exceedance of a level. To describe the probability

distribution (total 5872 units) of Chen-Yu-Lan watershed.

*Landslide Potential Evaluation Using Fragility Curve Model*

*DOI: http://dx.doi.org/10.5772/intechopen.89183*

**4.1 Probability distribution of LFC**

**Figure 8.**

**187**

*The slope aspects of Chen-Yu-Lan watershed.*

**4. Development of empirical landslide fragility model**

**Figure 7.** *The slope of Chen-Yu-Lan watershed.*

*Landslide Potential Evaluation Using Fragility Curve Model DOI: http://dx.doi.org/10.5772/intechopen.89183*

**Figure 8.** *The slope aspects of Chen-Yu-Lan watershed.*

**Figure 6.**

**Figure 7.**

**186**

*The slope of Chen-Yu-Lan watershed.*

*Five-meter DEM of Chen-Yu-Lan watershed (after [2]).*

*Landslides - Investigation and Monitoring*

Finally, the database was used to analyze the study area on the basis of slope units. The slope unit was defined as in **Figure 13**. A slope unit is defined as one slope part or the left/right part of a watershed. Slope units can be topologically divided by the watershed divide and drainage line, with the help of GIS tool [12]. The application of slope unit in the development of LFC was based on the physical interpretation of slopes in the mountain area. The environmental database was applied in accordance with the slope units at the site of interest. **Figure 14** shows the slope unit distribution (total 5872 units) of Chen-Yu-Lan watershed.

## **4. Development of empirical landslide fragility model**

To develop the empirical landslide fragility model, a probability distribution was chosen to describe the potential of landslide fragility. When the probability distribution was determined, the parameters of probability, the median and standard deviation, were obtained by fitting the data from the environmental database and the landslide areas. The use of slope unit was adopted here, and the classification of environmental factors was applied to represent the conditions of landslide given rainfall intensity and accumulated rainfall. The procedure of developing the empirical landslide fragility curve was described in the following.

#### **4.1 Probability distribution of LFC**

The fragility analysis is usually used to describe the potential of hazard in terms of potential levels or probability of exceedance of a level. To describe the probability

#### **Figure 9.**

*Satellite images of pre- (a) and post-event (b) Typhoon Sinlaku and the new landslide areas (c) in Chen-Yu-Lan watershed.*

about a hazard fragility, a feasible probability distribution can be assumed and applied in the model. The fragility curve of landslide, therefore, was assumed to be a lognormal distribution [12, 13]. The lognormal distribution can be constructed simply by the values of median and lognormal standard deviation and are called bivariate parameters (Eq. (1)):

$$f\_j(\mathbf{x}; c\_j, \zeta\_j) = \frac{\mathbf{1}}{\sqrt{2\pi}\zeta\_j \mathbf{x}} e^{-\frac{1}{2}\left(\frac{\ln\left(\mathbf{x}/c\_j\right)}{\zeta\_j}\right)^2} \tag{1}$$

where *fj* is the probability density function of lognormal distribution, *cj* is the median, *ζ<sup>j</sup>* is the log-standard deviation, and *x* is the variable. The cumulative distribution of Eq. (1) is used as the fragility curve. The cumulative density function

*Satellite images of pre- (a) and post-event (b) Typhoon Morakot and the new landslide areas (c) in Chen-Yu-*

2 þ 1 <sup>2</sup> *erf* *ln <sup>x</sup>=cj* � �

3

5 (2)

2 4

*ζj* ffiffi 2 p

of lognormal distribution is expressed as Eq. (2):

*Landslide Potential Evaluation Using Fragility Curve Model*

*DOI: http://dx.doi.org/10.5772/intechopen.89183*

**Figure 10.**

**189**

*Lan watershed.*

*Fj x;cj, ζ<sup>j</sup>* � � <sup>¼</sup> <sup>1</sup> *Landslide Potential Evaluation Using Fragility Curve Model DOI: http://dx.doi.org/10.5772/intechopen.89183*

#### **Figure 10.**

about a hazard fragility, a feasible probability distribution can be assumed and applied in the model. The fragility curve of landslide, therefore, was assumed to be a lognormal distribution [12, 13]. The lognormal distribution can be constructed simply by the values of median and lognormal standard deviation and are called

*Satellite images of pre- (a) and post-event (b) Typhoon Sinlaku and the new landslide areas (c) in Chen-*

<sup>¼</sup> <sup>1</sup> ffiffiffiffiffi <sup>2</sup>*<sup>π</sup>* <sup>p</sup> *<sup>ζ</sup>jx e* �1 2

*ln x=<sup>c</sup>* ð Þ*<sup>j</sup> ζj* � �<sup>2</sup>

(1)

*fj x*; *cj, ζ<sup>j</sup>* � �

bivariate parameters (Eq. (1)):

*Landslides - Investigation and Monitoring*

**Figure 9.**

**188**

*Yu-Lan watershed.*

*Satellite images of pre- (a) and post-event (b) Typhoon Morakot and the new landslide areas (c) in Chen-Yu-Lan watershed.*

where *fj* is the probability density function of lognormal distribution, *cj* is the median, *ζ<sup>j</sup>* is the log-standard deviation, and *x* is the variable. The cumulative distribution of Eq. (1) is used as the fragility curve. The cumulative density function of lognormal distribution is expressed as Eq. (2):

$$F\_j(\mathbf{x}; c\_j, \zeta\_j) = \frac{1}{2} + \frac{1}{2} \operatorname{erf} \left[ \frac{\ln \left( \begin{smallmatrix} \mathbf{x} \\ \zeta\_j \end{smallmatrix} \right)}{\zeta\_j \sqrt{2}} \right] \tag{2}$$


#### **Table 2.**

*Satellite images of events at Chen-Yu-Lan watershed.*


*\*Antecedent 7-day accumulated rainfall (Ra) can be calculated by Ra* <sup>¼</sup> <sup>P</sup><sup>7</sup> *<sup>i</sup>*¼<sup>1</sup> <sup>0</sup>*:*7*<sup>i</sup> Ri, where Ri is the daily rainfall of the* i*th day before.*

**Table 3.**

*The rainfall indices.*

Since both the rainfall intensity and rainfall accumulation contribute to the probability of triggering a landslide, the bivariate lognormal distribution was

> 2 6 4

*ln <sup>x</sup>=cxj* � �<sup>2</sup> *ζ*2 *xj*

where �∞ <*x, y, ζxj, ζyj* < ∞, *cxj* >0, *cyj* > 0, and �1<*ρ<sup>j</sup>* <1. In Eq. (3), *x* and *y* are maximum hourly rainfall and effective accumulated rainfall, respectively; *cxj* and *cyj* are the median; *ζxj* and *ζyj* are log-standard deviation; *ρ<sup>j</sup>* is the correlation coefficient of *x* and *y*. Because the maximum hourly rainfall and the effective accumulated rainfall are treated independently, the *ρ<sup>j</sup>* is zero. Thus, the cumulative density

� 2*ρ<sup>j</sup>*

*ln <sup>x</sup>=cxj* � � *ln <sup>y</sup>*

*ζxjζyj*

*=cyj* � �

þ

*ln <sup>y</sup> =cyj* � �<sup>2</sup> *ζ*2 *yj*

3 7 5

(3)

9 >= >;

applied in the developing LFC model [4, 14], as in Eq. (3):

8 >< >:

*Slope unit delineation, the left and right slope units of a watershed [3, 4].*

2 1 � *<sup>ρ</sup>*<sup>2</sup> *j* � �

1

ffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> � *<sup>ρ</sup>*<sup>2</sup> *j* <sup>q</sup> *exp* � <sup>1</sup>

*Rainfall indices of Typhoon Morakot: (a) Imax and (b) Rte.*

*Landslide Potential Evaluation Using Fragility Curve Model*

*DOI: http://dx.doi.org/10.5772/intechopen.89183*

function of Eq. (3) becomes as follows:

2*πyζxjζyj*

*fj* ð Þ¼ *x, y*

**191**

**Figure 12.**

**Figure 13.**

**Figure 11.** *Rainfall indices of Typhoon Sinlaku: (a) Imax and (b) Rte.*

Eq. (2) represents the *j*th fragility, and *erf()* is the Gaussian error function. When the median and log-standard deviation are determined, the fragility curve of *j*th level can be obtained. The maximum likelihood estimation (MLE) can be applied to determine the median and log-standard deviation [13]. The aforementioned equations are suitable for one-variable estimation model.

*Landslide Potential Evaluation Using Fragility Curve Model DOI: http://dx.doi.org/10.5772/intechopen.89183*

**Figure 12.** *Rainfall indices of Typhoon Morakot: (a) Imax and (b) Rte.*

**Figure 13.** *Slope unit delineation, the left and right slope units of a watershed [3, 4].*

Since both the rainfall intensity and rainfall accumulation contribute to the probability of triggering a landslide, the bivariate lognormal distribution was applied in the developing LFC model [4, 14], as in Eq. (3):

$$f\_{j}(\mathbf{x},y) = \frac{1}{2\pi y \zeta\_{xj}\zeta\_{yj}\sqrt{1-\rho\_{j}^{2}}} \exp\left\{ -\frac{1}{2\left(1-\rho\_{j}^{2}\right)} \left[ \frac{\ln\left(\frac{\mathbf{x}\_{j}}{\mathcal{L}\_{yj}}\right)^{2}}{\zeta\_{xj}^{2}} - 2\rho\_{j}\frac{\ln\left(\frac{\mathbf{x}\_{j}}{\mathcal{L}\_{yj}}\right)\ln\left(\frac{\mathbf{y}\_{j}}{\mathcal{L}\_{yj}}\right)}{\zeta\_{xj}\zeta\_{yj}} + \frac{\ln\left(\frac{\mathbf{y}\_{j}}{\mathcal{L}\_{yj}}\right)^{2}}{\zeta\_{yj}^{2}} \right] \right\},\tag{3}$$

where �∞ <*x, y, ζxj, ζyj* < ∞, *cxj* >0, *cyj* > 0, and �1<*ρ<sup>j</sup>* <1. In Eq. (3), *x* and *y* are maximum hourly rainfall and effective accumulated rainfall, respectively; *cxj* and *cyj* are the median; *ζxj* and *ζyj* are log-standard deviation; *ρ<sup>j</sup>* is the correlation coefficient of *x* and *y*. Because the maximum hourly rainfall and the effective accumulated rainfall are treated independently, the *ρ<sup>j</sup>* is zero. Thus, the cumulative density function of Eq. (3) becomes as follows:

Eq. (2) represents the *j*th fragility, and *erf()* is the Gaussian error function. When the median and log-standard deviation are determined, the fragility curve of *j*th level can be obtained. The maximum likelihood estimation (MLE) can be applied to determine the median and log-standard deviation [13]. The aforementioned

**Watershed Event Image time Satellite Incremental area (km2**

Post-Morakot October 14, 2009 SPOT5

*Imax* The maximum hourly rainfall in a rainfall event

Pre-Morakot November 28, 2008 SPOT5 10.21 (2.28%)

*R*te The antecedent 7-day accumulated rainfall (with reduction factor of

before the max. hourly rainfall in current event

0.7\*) before the starting of current event and the accumulated rainfall

*<sup>i</sup>*¼<sup>1</sup> <sup>0</sup>*:*7*<sup>i</sup>*

*Ri, where Ri is the daily rainfall of*

Chen-Yu-Lan 448.14 km2 Pre-Sinlaku February 21, 2008 SPOT5 9.52 (2.12%) Post-Sinlaku November 28, 2008 SPOT5

**Table 2.**

Max. hourly rainfall

Effective accumulated rainfall

*the* i*th day before.*

*The rainfall indices.*

**Table 3.**

**Figure 11.**

**190**

*Satellite images of events at Chen-Yu-Lan watershed.*

*\*Antecedent 7-day accumulated rainfall (Ra) can be calculated by Ra* <sup>¼</sup> <sup>P</sup><sup>7</sup>

**Index Symbol Definition**

*Landslides - Investigation and Monitoring*

**)**

equations are suitable for one-variable estimation model.

*Rainfall indices of Typhoon Sinlaku: (a) Imax and (b) Rte.*

$${}^{1}F\_{j}\left(\mathbf{x},\mathbf{y};\mathbf{c}\_{\mathbf{x}\dot{\mathbf{y}}},\mathbf{c}\_{\mathbf{y}\dot{\mathbf{y}}},\boldsymbol{\zeta}\_{\mathbf{x}\dot{\mathbf{y}}},\boldsymbol{\zeta}\_{\mathbf{y}\dot{\mathbf{y}}}\right)=\frac{1}{4}\left[\mathbf{1}+\,{}^{\text{eff}}\left(\frac{\ln\left({}^{\text{x}}\boldsymbol{\zeta}\_{\mathbf{x}}}{\zeta\_{\mathbf{x}\dot{\mathbf{y}}}\sqrt{2}}\right)\right)\left[\mathbf{1}+\,{}^{\text{eff}}\left(\frac{\ln\left({}^{\text{y}}\boldsymbol{\zeta}\_{\mathbf{y}}}{\zeta\_{\mathbf{y}\dot{\mathbf{y}}}\sqrt{2}}\right)\right)\right] \tag{4}$$

based on the available data and appropriate judgment to simplify the process. There

The geology is an important factor when considering the potential of landslide. However, the geological conditions, like soil layer depth, rock type, and strength at the site, are not usually available to researchers. Therefore, a simplified step can be used at the geology time scale to generally represent the older and younger stratum of the study area. For Chen-Yu-Lan watershed, the rock type of the area was first used to highlight the geological time scale. The same geology era contained different rock formations, and the factor of geology was classified into two groups, as shown in **Table 4** and **Figure 15**. It was noted that there are 1798 slope units of G1 and 2463

Based on the Soil and Water Conservation Bureau manual, the hillside slope is

The distance to the nearest river channel was classified into two groups, with the threshold value of 300 m. **Table 6** and **Figure 17** show the classification results, in

Oligocene Thick or massive white medium to very coarse quartzite and

G1 Eocene Dark gray slate and phyllite slate, interbedded with quartz sandstone Eocene Slate and phyllite quartzite sandstone Oligocene Hard shale sandwiched to thick sandstone

hard shale

Pliocene Shale, sandy shale, mudstone Pliocene Sandstone, mudstone, shale interbed

Gravel

Pleistocene Gravel, sand, and clay

Mid-Miocene Sandstone and shale interbed, coal seam Late Miocene Sandstone and shale interbed, coal seam Miocene to Pliocene Sandstone and shale interbed, coal seam

G2 Miocene Hard shale, slate, phyllite sandstone

classified as seven levels. In the fragility model, level 3 to level 7 slopes were considered and simply further classified as three groups, as shown in **Table 5**. **Figure 16** shows the classification results in the Chen-Yu-Lan watershed, and 137

which there are 2482 and 1779 slope units of R1 and R2, respectively.

slope units were classified as S1, 827 as S2, and 3297 as S3.

*4.2.3 Distance to nearest river channel*

**Classification Geology time scale Rock type**

Pliocene to Pleistocene

**Table 4.**

**193**

*The geology classification.*

were total of 48 combinations of classification, as described below.

*Landslide Potential Evaluation Using Fragility Curve Model*

*DOI: http://dx.doi.org/10.5772/intechopen.89183*

*4.2.1 Geology*

slope units of G2.

*4.2.2 Hillside slope*

Eq. (4) represents the j-th fragility curve of landslide, including four fragility parameters. The cumulative density function of Eq. (4) is a fragility surface of probability.

The parameters in Eq. (4) can be obtained by using the least square estimate. When the landslide locations and areas are available, meaning the classification of landslide based on the factors (see next section), the fragility curve of landslide (a surface) of a specific classification can be determined.

## **4.2 Classification of factors**

The environmental factors, geology, slope, distance to river, slope aspect, and vegetation index, were classified into levels in order to group similar slope units. The triggering factors of rainfall intensity and effective accumulated rainfall were also redistributed onto slope unit scale. These factors were classified into groups, i.e., two groups of G, three of S, two of R, two of A, and two of N (**Tables 4**–**8**),

**Figure 14.** *The slope units of Chen-Yu-Lan watershed.*

based on the available data and appropriate judgment to simplify the process. There were total of 48 combinations of classification, as described below.

## *4.2.1 Geology*

*Fj x, y;cxj, cyj, ζxj, ζyj* � �

*Landslides - Investigation and Monitoring*

**4.2 Classification of factors**

probability.

**Figure 14.**

**192**

*The slope units of Chen-Yu-Lan watershed.*

¼ 1 4

surface) of a specific classification can be determined.

2 4

1 þ *erf*

*ln <sup>x</sup>=cxj* � �

1 A

3

2 4

5 1 þ *erf*

*ln <sup>y</sup> =cyj* � �

1 A

3 5 (4)

0 @

*ζyj* ffiffi 2 p

0 @

*ζxj* ffiffi 2 p

Eq. (4) represents the j-th fragility curve of landslide, including four fragility parameters. The cumulative density function of Eq. (4) is a fragility surface of

The parameters in Eq. (4) can be obtained by using the least square estimate. When the landslide locations and areas are available, meaning the classification of landslide based on the factors (see next section), the fragility curve of landslide (a

The environmental factors, geology, slope, distance to river, slope aspect, and vegetation index, were classified into levels in order to group similar slope units. The triggering factors of rainfall intensity and effective accumulated rainfall were also redistributed onto slope unit scale. These factors were classified into groups, i.e., two groups of G, three of S, two of R, two of A, and two of N (**Tables 4**–**8**),

The geology is an important factor when considering the potential of landslide. However, the geological conditions, like soil layer depth, rock type, and strength at the site, are not usually available to researchers. Therefore, a simplified step can be used at the geology time scale to generally represent the older and younger stratum of the study area. For Chen-Yu-Lan watershed, the rock type of the area was first used to highlight the geological time scale. The same geology era contained different rock formations, and the factor of geology was classified into two groups, as shown in **Table 4** and **Figure 15**. It was noted that there are 1798 slope units of G1 and 2463 slope units of G2.

## *4.2.2 Hillside slope*

Based on the Soil and Water Conservation Bureau manual, the hillside slope is classified as seven levels. In the fragility model, level 3 to level 7 slopes were considered and simply further classified as three groups, as shown in **Table 5**. **Figure 16** shows the classification results in the Chen-Yu-Lan watershed, and 137 slope units were classified as S1, 827 as S2, and 3297 as S3.

## *4.2.3 Distance to nearest river channel*

The distance to the nearest river channel was classified into two groups, with the threshold value of 300 m. **Table 6** and **Figure 17** show the classification results, in which there are 2482 and 1779 slope units of R1 and R2, respectively.


**Table 4.** *The geology classification.*


#### **Table 5.**

*The slope classification.*


#### **Table 6.**

*The classification of distance to river.*


#### **Table 7.**

*The classification of slope aspects.*


land cover status of a given site. Satellite images of SPOT (February 21, 2008, November 28, 2008, and October 14, 2009) were used to calculate the NDVI of the ground surface, and an empirical NDVI threshold was applied to classify barren land and non-barren land. **Table 8** summarized the classification, and **Figure 20** shows the results, in which there are 2765 and 1496 slope units of N1 and N2,

The rainfall data from Typhoon Sinlaku in 2008 and Typhoon Morakot in 2009 was applied to obtain the rainfall intensity and effective accumulated rainfall in the Chen-Yu-Lan watershed. The hourly rainfall data measured at the surrounding weather stations was used to get the rainfall of each slope unit by interpolation. **Figures 21** and **22** show the rainfall distribution during the two typhoon events.

Based on the site investigation in the past after typhoon events, the expected

of *<sup>V</sup>* <sup>¼</sup> <sup>0</sup>*:*<sup>2</sup> � *<sup>A</sup>*<sup>1</sup>*:*<sup>3</sup> [15], the landslide area on the slope can be obtained. Therefore, in

. By applying the relationship

*4.2.6 Maximum rainfall intensity and effective accumulated rainfall*

average landslide volume (V) was set as V = 6000 m<sup>3</sup>

respectively.

**Figure 15.**

*The geology classification of Chen-Yu-Lan watershed.*

*Landslide Potential Evaluation Using Fragility Curve Model*

*DOI: http://dx.doi.org/10.5772/intechopen.89183*

*4.2.7 Landslide area*

**195**

*\*NDVIc is the threshold value to classify low and mid-to-high vegetation index. In this study, the NDVIc was 0.35.*

#### **Table 8.**

*The vegetation classification.*

## *4.2.4 Slope aspects*

The slope aspect was considered in the beginning to distinguish the range of frequent landslide on a given mountain slope. There are eight slope aspects (**Figure 18**) used in the study that were grouped into two classes as shown in **Table 7** and **Figure 19**, in which there are 2051 and 2210 slope units of A1 and A2, respectively.

#### *4.2.5 Vegetation index*

The land cover status was also an important factor when estimating the landslide potential. The normalized difference vegetation index was used to represent the

*Landslide Potential Evaluation Using Fragility Curve Model DOI: http://dx.doi.org/10.5772/intechopen.89183*

**Figure 15.** *The geology classification of Chen-Yu-Lan watershed.*

land cover status of a given site. Satellite images of SPOT (February 21, 2008, November 28, 2008, and October 14, 2009) were used to calculate the NDVI of the ground surface, and an empirical NDVI threshold was applied to classify barren land and non-barren land. **Table 8** summarized the classification, and **Figure 20** shows the results, in which there are 2765 and 1496 slope units of N1 and N2, respectively.

## *4.2.6 Maximum rainfall intensity and effective accumulated rainfall*

The rainfall data from Typhoon Sinlaku in 2008 and Typhoon Morakot in 2009 was applied to obtain the rainfall intensity and effective accumulated rainfall in the Chen-Yu-Lan watershed. The hourly rainfall data measured at the surrounding weather stations was used to get the rainfall of each slope unit by interpolation. **Figures 21** and **22** show the rainfall distribution during the two typhoon events.

## *4.2.7 Landslide area*

Based on the site investigation in the past after typhoon events, the expected average landslide volume (V) was set as V = 6000 m<sup>3</sup> . By applying the relationship of *<sup>V</sup>* <sup>¼</sup> <sup>0</sup>*:*<sup>2</sup> � *<sup>A</sup>*<sup>1</sup>*:*<sup>3</sup> [15], the landslide area on the slope can be obtained. Therefore, in

*4.2.4 Slope aspects*

*The vegetation classification.*

**Table 5.**

**Table 6.**

**Table 7.**

**Table 8.**

*The slope classification.*

*The classification of distance to river.*

*Landslides - Investigation and Monitoring*

**Classification Definition**

*The classification of slope aspects.*

NE

respectively.

**194**

*4.2.5 Vegetation index*

The slope aspect was considered in the beginning to distinguish the range of

*\*NDVIc is the threshold value to classify low and mid-to-high vegetation index. In this study, the NDVIc was 0.35.*

Non-barren land N1 N2

**Classification SWCB slope level Technical regulations for soil and water conservation**

S1 3 15% < S ≦ 30% 8.53 < S ≦ 16.70

S2 5 40% < S ≦ 55% 21.80 < S ≦ 28.81 S3 6 55% < S ≦ 100% 28.81 < S ≦ 45.00

**Classification Definition Distance (m)** R1 Close ≤300 m R2 Not close >300 m

A1 Weak aspect: the four slope aspects of higher ratio of incremental landslide area. In

A2 Strong aspect: the four slope aspects of lower RIL. In this study, A2 are W, NW, N, and

this study, A1 are E, SE, S, and SW

**Image process Classification**

Pre-event image Barren land N1 N1

**Slope range degree (°)**

**Low vegetation Mid-to-high vegetation <sup>1</sup> <sup>&</sup>lt; NDVI <sup>≦</sup> NDVIc\* NDVIc\* <sup>&</sup>lt; NDVI <sup>≦</sup> <sup>1</sup>**

4 30% < S ≦ 40% 16.70 < S ≦ 21.80

7 S > 100% S > 45.00

The land cover status was also an important factor when estimating the landslide potential. The normalized difference vegetation index was used to represent the

frequent landslide on a given mountain slope. There are eight slope aspects (**Figure 18**) used in the study that were grouped into two classes as shown in **Table 7** and **Figure 19**, in which there are 2051 and 2210 slope units of A1 and A2,

**Figure 16.** *The slope classification of Chen-Yu-Lan watershed.*

association with the slope classification, the determination of landslide of a given slope unit was decided based on the following criteria:

1.Slope S1: the slope unit is counted as a landslide when its landslide area ratio (LAR) is equal to or higher than 5% or the projected landslide area on the slope is greater than 2800 m<sup>2</sup> (0.28 ha). Otherwise, the slope unit is not counted as a landslide area.

**Figure 17.**

**Figure 18.** *The slope aspects.*

**197**

*The classification of distance to the river of Chen-Yu-Lan watershed.*

*Landslide Potential Evaluation Using Fragility Curve Model*

*DOI: http://dx.doi.org/10.5772/intechopen.89183*


The landslide area classification of Chen-Yu-Lan watershed is shown in **Figure 23**. There were 1810 slope units of landslide after Typhon Sinlaku and 1544 ones after Typhoon Morakot, as shown in colored slope units in **Figure 23**.

*Landslide Potential Evaluation Using Fragility Curve Model DOI: http://dx.doi.org/10.5772/intechopen.89183*

**Figure 17.** *The classification of distance to the river of Chen-Yu-Lan watershed.*

**Figure 18.** *The slope aspects.*

association with the slope classification, the determination of landslide of a given

1.Slope S1: the slope unit is counted as a landslide when its landslide area ratio (LAR) is equal to or higher than 5% or the projected landslide area on the slope is greater than 2800 m<sup>2</sup> (0.28 ha). Otherwise, the slope unit is not counted as a

2. Slope S2: the slope unit is counted as a landslide when its landslide area ratio is equal to or higher than 5% or the projected landslide area on the slope is greater than 2400 m<sup>2</sup> (0.24 ha). Otherwise, the slope unit is not counted as a

3. Slope S3: the slope unit is counted as a landslide when its landslide area ratio is equal to or higher than 5% or the projected landslide area on the slope is greater than 2200 m<sup>2</sup> (0.22 ha). Otherwise, the slope unit is not counted as a

The landslide area classification of Chen-Yu-Lan watershed is shown in **Figure 23**. There were 1810 slope units of landslide after Typhon Sinlaku and 1544

ones after Typhoon Morakot, as shown in colored slope units in **Figure 23**.

slope unit was decided based on the following criteria:

*The slope classification of Chen-Yu-Lan watershed.*

*Landslides - Investigation and Monitoring*

landslide area.

**Figure 16.**

landslide area.

landslide area.

**196**

**Figure 19.** *The slope aspect classification of Chen-Yu-Lan watershed.*

## **4.3 The LFC of Chen-Yu-Lan watershed**

The environmental database and rainfall data of typhoon events were applied to classify the slope units and the landslide areas. With the classification described in previous sections, there were a total of 48 classes with combinations of factors G, S, A, R, and N. Each classification was in association with two rainfall indices, the rainfall intensity and effective accumulated rainfall. The fragility of landslide, or the probability of exceeding a level of hazard, was constructed and used for landslide potential assessment. **Tables 9** and **10** summarized the fragility parameters obtained from the two events, and some examples of fragility curves were shown in **Figure 24**. It should be noted that during the classification, insufficient samples of certain classification had led to difficulty of finding parameters needed. Therefore, these samples were combined with other classifications in order to get reasonable probability values of median and standard deviation.

**4.4 The LFC of Shenmu area**

**Figure 20.**

**199**

were determined using the following equations:

*The vegetation index classification of Chen-Yu-Lan watershed.*

*Landslide Potential Evaluation Using Fragility Curve Model*

*DOI: http://dx.doi.org/10.5772/intechopen.89183*

q

*ζx,m* ¼

*cx, <sup>m</sup>* <sup>¼</sup> <sup>X</sup>*<sup>m</sup>*

X*<sup>m</sup> i*¼1 *i*¼1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

*wi* � *<sup>ζ</sup>xi* ð Þ<sup>2</sup>

The fragility curves of 48 classification slope units represented the local environmental characteristics of a given area. Instead of directly using 48 set fragility curves, it should be practical to obtain one set of representative fragility curve for a given site or location. To achieve this goal, the weighted fragility curves were introduced and applied to the Shenmu village. The weighted fragility parameters

*wi* � *cxi, cy, <sup>m</sup>* <sup>¼</sup> <sup>X</sup>*<sup>m</sup>*

*, ζy,m* ¼

*i*¼1

r

X*<sup>m</sup> i*¼1

*wi* � *cyi* (5)

(6)

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

*wi* � *<sup>ζ</sup>yi* � �<sup>2</sup>

*Landslide Potential Evaluation Using Fragility Curve Model DOI: http://dx.doi.org/10.5772/intechopen.89183*

**Figure 20.** *The vegetation index classification of Chen-Yu-Lan watershed.*

## **4.4 The LFC of Shenmu area**

The fragility curves of 48 classification slope units represented the local environmental characteristics of a given area. Instead of directly using 48 set fragility curves, it should be practical to obtain one set of representative fragility curve for a given site or location. To achieve this goal, the weighted fragility curves were introduced and applied to the Shenmu village. The weighted fragility parameters were determined using the following equations:

$$c\_{\mathbf{x},m} = \sum\_{i=1}^{m} w\_i \times c\_{\mathbf{x}i}, c\_{\mathbf{y},m} = \sum\_{i=1}^{m} w\_i \times c\_{\mathbf{y}i} \tag{5}$$

$$\zeta\_{\mathbf{x},m} = \sqrt{\sum\_{i=1}^{m} \left(w\_i \times \zeta\_{\mathbf{x}i}\right)^2}, \zeta\_{\mathbf{y},m} = \sqrt{\sum\_{i=1}^{m} \left(w\_i \times \zeta\_{\mathbf{y}i}\right)^2} \tag{6}$$

**4.3 The LFC of Chen-Yu-Lan watershed**

*The slope aspect classification of Chen-Yu-Lan watershed.*

*Landslides - Investigation and Monitoring*

**Figure 19.**

**198**

probability values of median and standard deviation.

The environmental database and rainfall data of typhoon events were applied to classify the slope units and the landslide areas. With the classification described in previous sections, there were a total of 48 classes with combinations of factors G, S, A, R, and N. Each classification was in association with two rainfall indices, the rainfall intensity and effective accumulated rainfall. The fragility of landslide, or the probability of exceeding a level of hazard, was constructed and used for landslide potential assessment. **Tables 9** and **10** summarized the fragility parameters

obtained from the two events, and some examples of fragility curves were shown in **Figure 24**. It should be noted that during the classification, insufficient samples of certain classification had led to difficulty of finding parameters needed. Therefore, these samples were combined with other classifications in order to get reasonable

**Figure 21.**

*The rainfall of Chen-Yu-Lan watershed during Typhoon Sinlaku: (a) max. hourly rainfall (Imax) and (b) effective accumulated rainfall (Rte).*

**Figure 23.**

**201**

*The landslide area of Chen-Yu-Lan watershed during (a) Typhoon Sinlaku and (b) Typhoon Morakot.*

*Landslide Potential Evaluation Using Fragility Curve Model*

*DOI: http://dx.doi.org/10.5772/intechopen.89183*

**Classification** *Imax* **(mm)** *Rte* **(mm) Combined with\* Median Std. deviation Median Std. deviation** G1S1A1R1N1 64.40 0.21 485.00 0.28 With 21111 G1S1A1R1N2 27.53 1.24 383.77 0.29 With 21112 G1S1A1R2N1 33.70 0.31 1112.62 0.10 With 21121 G1S1A1R2N2 37.94 0.16 239.39 0.27 With 21122 G1S1A2R1N1 44.40 1.10 290.86 0.24 With 21211 G1S1A2R1N2 43.91 0.16 1007.19 0.71 With 21212 G1S1A2R2N1 32.48 0.77 320.60 0.39 With 21221 G1S1A2R2N2 40.58 0.45 332.07 0.22 With 21222 G1S2A1R1N1 40.44 0.58 235.49 0.79 With 22111 G1S2A1R1N2 72.70 0.32 384.00 0.67 With 22112 G1S2A1R2N1 22.60 0.34 407.35 0.26 With 22121 G1S2A1R2N2 74.16 1.17 527.59 1.20 With 22122 G1S2A2R1N1 22.41 0.70 399.60 1.23 With 22211 G1S2A2R1N2 42.39 0.28 252.25 0.62 With 22212 G1S2A2R2N1 14.08 0.11 706.36 0.80 With 22221 G1S2A2R2N2 115.74 0.61 207.21 0.77 With 22222

G1S3A1R1N1 18.81 0.21 135.69 1.06

**Figure 22.**

*The rainfall of Chen-Yu-Lan watershed during Typhoon Morakot: (a) max. hourly rainfall (Imax) and (b) effective accumulated rainfall (Rte).*

*Landslide Potential Evaluation Using Fragility Curve Model DOI: http://dx.doi.org/10.5772/intechopen.89183*

**Figure 23.** *The landslide area of Chen-Yu-Lan watershed during (a) Typhoon Sinlaku and (b) Typhoon Morakot.*


**Figure 21.**

**Figure 22.**

**200**

*(b) effective accumulated rainfall (Rte).*

*(b) effective accumulated rainfall (Rte).*

*Landslides - Investigation and Monitoring*

*The rainfall of Chen-Yu-Lan watershed during Typhoon Sinlaku: (a) max. hourly rainfall (Imax) and*

*The rainfall of Chen-Yu-Lan watershed during Typhoon Morakot: (a) max. hourly rainfall (Imax) and*


#### **Table 9.**

*Fragility parameters of G1 classification.*


*wi* <sup>¼</sup> *ni Ni*

*Examples of fragility curves of Chen-Yu-Lan watershed: (a) G1S3A1R1N1, (b) G2S2A1R1N1,*

After the weighted calculation, the fragility parameters of Shenmu area are median *Imax* ¼ 33 mm and median *Rte* ¼ 413 mm. **Figure 25** shows the weighted

classification, and *Ni* is the total number of slope units.

*The fragility surface and fragility curves of Shenmu area.*

fragility curves of Shenmu area.

**Figure 24.**

**Figure 25.**

**203**

*(c) G1S3A1R2N1, and (d) G2S3A1R2N1.*

*Landslide Potential Evaluation Using Fragility Curve Model*

*DOI: http://dx.doi.org/10.5772/intechopen.89183*

where *x* and *y* are rainfall indices, *cx, <sup>m</sup>* and *cy, <sup>m</sup>* are the weighted median values, *ζx, <sup>m</sup>* and *ζy, <sup>m</sup>* are weighted standard deviation, *m* is the number of classifications, *wi* is the weighting factor of a classification, *ni* is the number of slope units of a given

(7)

#### **Table 10.**

*Fragility parameters of G2 classification.*

*Landslide Potential Evaluation Using Fragility Curve Model DOI: http://dx.doi.org/10.5772/intechopen.89183*

**Figure 24.**

**Classification** *Imax* **(mm)** *Rte* **(mm) Combined with\* Median Std. deviation Median Std. deviation**

*Due to the insufficient data, some classifications were combined together in order to obtain reasonable parameters.*

**Median Std. deviation Median Std. deviation**

**Classification** *Imax* **(mm)** *Rte* **(mm)**

G2S1A1R1N1 64.40 0.21 485.00 0.28 G2S1A1R1N2 27.53 1.24 383.77 0.29 G2S1A1R2N1 33.70 0.31 1112.62 0.10 G2S1A1R2N2 37.94 0.16 239.39 0.27 G2S1A2R1N1 44.40 1.10 290.86 0.24 G2S1A2R1N2 43.91 0.16 1007.19 0.71 G2S1A2R2N1 32.48 0.77 320.60 0.39 G2S1A2R2N2 40.58 0.45 332.07 0.22 G2S2A1R1N1 40.44 0.58 235.49 0.79 G2S2A1R1N2 72.70 0.32 384.00 0.67 G2S2A1R2N1 22.60 0.34 407.35 0.26 G2S2A1R2N2 74.16 1.17 527.59 1.20 G2S2A2R1N1 22.41 0.70 399.60 1.23 G2S2A2R1N2 42.39 0.28 252.25 0.62 G2S2A2R2N1 14.08 0.11 706.36 0.80 G2S2A2R2N2 115.74 0.61 207.21 0.77 G2S3A1R1N1 16.70 0.13 604.42 0.53 G2S3A1R1N2 72.54 0.58 305.93 0.41 G2S3A1R2N1 21.81 1.31 387.14 0.84 G2S3A1R2N2 56.01 1.07 527.88 0.69 G2S3A2R1N1 23.20 0.78 378.00 0.66 G2S3A2R1N2 14.50 0.11 151.30 0.10 G2S3A2R2N1 23.76 0.66 270.92 0.28 G2S3A2R2N2 29.86 1.02 249.28 0.80

G1S3A1R1N2 14.51 0.12 295.58 0.29 G1S3A1R2N1 75.05 0.29 225.74 0.88 G1S3A1R2N2 28.07 0.38 269.76 0.55 G1S3A2R1N1 35.79 0.57 967.74 0.35 G1S3A2R1N2 44.53 1.54 554.12 1.26 G1S3A2R2N1 29.66 0.72 298.05 0.30 G1S3A2R2N2 34.00 0.89 269.00 0.69

*\**

**Table 9.**

**Table 10.**

**202**

*Fragility parameters of G2 classification.*

*Fragility parameters of G1 classification.*

*Landslides - Investigation and Monitoring*

*Examples of fragility curves of Chen-Yu-Lan watershed: (a) G1S3A1R1N1, (b) G2S2A1R1N1, (c) G1S3A1R2N1, and (d) G2S3A1R2N1.*

**Figure 25.** *The fragility surface and fragility curves of Shenmu area.*

$$w\_i = \frac{n\_i}{N\_i} \tag{7}$$

where *x* and *y* are rainfall indices, *cx, <sup>m</sup>* and *cy, <sup>m</sup>* are the weighted median values, *ζx, <sup>m</sup>* and *ζy, <sup>m</sup>* are weighted standard deviation, *m* is the number of classifications, *wi* is the weighting factor of a classification, *ni* is the number of slope units of a given classification, and *Ni* is the total number of slope units.

After the weighted calculation, the fragility parameters of Shenmu area are median *Imax* ¼ 33 mm and median *Rte* ¼ 413 mm. **Figure 25** shows the weighted fragility curves of Shenmu area.

## **5. Case studies and results**

The risk of landslide was demonstrated by using the critical values of rainfall hazard and landslide fragility. The concept of landslide warning was adopted in this study, and by combining both *Hc* and *Fc*, the warning status includes safe stage and unsafe stages, as illustrated in **Figure 26**. It should be noted that there are two stages of unsafe status, Red I and Red II. Red I stage indicates that the situation has pass *Hc* and a rainfall hazard could occur. Red II stage implies the most serious condition that in addition to the rainfall hazard, a landslide could occur as well. Both stages are determined with a probability when given a rainfall condition. The procedure of determining safe stage was designed to match the needs of disaster preparation and prediction of government.

Cases of landslides and debris flows in Shenmu were collected from the disaster notices issued by Soil and Water Conservation Bureau of Taiwan. As shown in **Table 11** and **Figure 27**, a total of seven cases were used to determine the critical values of *Hc* (=0.91) and *Fc* (=0.23) of Shenmu. These cases were used in the assumption that whenever there was a debris flow, there should be landslides at the upper stream areas before or during the debris flow.

The rainfall history of Typhoon Morakot in 2009 and 0601 Heavy Rainfall in 2016 were used to evaluate the landslide risk assessment in Shenmu. **Figure 28**

#### **Figure 26.** *The warning conditions based on landslide fragility (Fc) and rainfall hazard (Hc).*


shows the results of event, and the dots in the figure represent the rainfall condition (hourly rainfall and cumulative rainfall) and the probability of hazard. It was noted that the dots behaved like a "snake" line going from Safe stage to Red I and Red II stages. Also, the snake line stayed shortly at Red I stage for both events and passed to Red II in a jump. This condition implied that when the situation was beyond the *Hc* line, the landslide hazard was very likely to occur. The results conformed to the

*The change of probability in Shenmu area during (a) Typhoon Morakot (2009) event and (b) 0601 heavy*

*The probability thresholds of rainfall hazard and landslide fragility in Shenmu area: (a) rainfall warning*

**Figure 27.**

**Figure 28.**

**205**

*rainfall in 2016 (after [4, 5]).*

*threshold and (b) landslide warning threshold.*

*Landslide Potential Evaluation Using Fragility Curve Model*

*DOI: http://dx.doi.org/10.5772/intechopen.89183*

#### **Table 11.**

*The disaster notices around Shenmu area.*

*Landslide Potential Evaluation Using Fragility Curve Model DOI: http://dx.doi.org/10.5772/intechopen.89183*

**5. Case studies and results**

*Landslides - Investigation and Monitoring*

prediction of government.

**Figure 26.**

**Table 11.**

**204**

*The disaster notices around Shenmu area.*

The risk of landslide was demonstrated by using the critical values of rainfall hazard and landslide fragility. The concept of landslide warning was adopted in this study, and by combining both *Hc* and *Fc*, the warning status includes safe stage and unsafe stages, as illustrated in **Figure 26**. It should be noted that there are two stages of unsafe status, Red I and Red II. Red I stage indicates that the situation has pass *Hc* and a rainfall hazard could occur. Red II stage implies the most serious condition that in addition to the rainfall hazard, a landslide could occur as well. Both stages are determined with a probability when given a rainfall condition. The procedure of determining safe stage was designed to match the needs of disaster preparation and

Cases of landslides and debris flows in Shenmu were collected from the disaster

The rainfall history of Typhoon Morakot in 2009 and 0601 Heavy Rainfall in 2016 were used to evaluate the landslide risk assessment in Shenmu. **Figure 28**

notices issued by Soil and Water Conservation Bureau of Taiwan. As shown in **Table 11** and **Figure 27**, a total of seven cases were used to determine the critical values of *Hc* (=0.91) and *Fc* (=0.23) of Shenmu. These cases were used in the assumption that whenever there was a debris flow, there should be landslides at the

upper stream areas before or during the debris flow.

*The warning conditions based on landslide fragility (Fc) and rainfall hazard (Hc).*

**Year Event Disaster Village** *Imax* **(mm)** *Rte* **(mm)** 2009 Typhoon Morakot Debris flow, flood Tongfu 85.5 1130 2009 Typhoon Morakot Debris flow Wangmei 85.5 1130 2009 Typhoon Morakot Landslide Shenmu 47.5 829.5 2009 Typhoon Morakot Debris flow Shenmu 42.5 750 2009 Typhoon Morakot Debris flow Shenmu 33.5 641 2009 Typhoon Morakot Landslide Shenmu 20 476.5 2009 Typhoon Morakot Debris flow Shenmu 38.5 877 2012 0610 Heavy rainfall Debris flow, flood Shenmu 18.5 450.6

**Figure 27.** *The probability thresholds of rainfall hazard and landslide fragility in Shenmu area: (a) rainfall warning threshold and (b) landslide warning threshold.*

#### **Figure 28.**

*The change of probability in Shenmu area during (a) Typhoon Morakot (2009) event and (b) 0601 heavy rainfall in 2016 (after [4, 5]).*

shows the results of event, and the dots in the figure represent the rainfall condition (hourly rainfall and cumulative rainfall) and the probability of hazard. It was noted that the dots behaved like a "snake" line going from Safe stage to Red I and Red II stages. Also, the snake line stayed shortly at Red I stage for both events and passed to Red II in a jump. This condition implied that when the situation was beyond the *Hc* line, the landslide hazard was very likely to occur. The results conformed to the

records of Typhoon Morakot. Severe landslides occurred at the upper stream areas in Shenmu during the typhoon. Therefore, the proposed risk assessment and warning stages of landslide were reasonably useful in this case.

## **6. Summary and conclusions**

This study had developed the landslide fragility curve model by using the spatial data and statistical methods. The fragility curves of the study area were derived for all combinations of environmental and triggering factors. The data sets included the geomorphological and vegetation condition factors, based on the landslides at the Chen-Yu-Lan watershed in Taiwan, during Typhoon Sinlaku (September 2008) and Typhoon Morakot (August 2009). This study also proposed landslide risk assessment using rainfall hazard potential and landslide fragility curves and concluded findings as follows:


**Author details**

Yi-Min Huang<sup>1</sup>

Taichung, Taiwan

**207**

\*, Tsu-Chiang Lei2

*Landslide Potential Evaluation Using Fragility Curve Model*

*DOI: http://dx.doi.org/10.5772/intechopen.89183*

\*Address all correspondence to: ninerh@mail.fcu.edu.tw

provided the original work is properly cited.

1 Department of Civil Engineering, Feng Chia University, Taichung, Taiwan

2 Department of Urban Planning and Spatial Information, Feng Chia University,

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

, Bing-Jean Lee<sup>1</sup> and Meng-Hsun Hsieh<sup>1</sup>

## **Acknowledgements**

The authors would like to express their gratitude to research assistant Xingping Wang, for helping in collecting all the data relevant to the landslides in the Chen-Yu-Lan watershed. The authors also would like to thank the Soil and Water Conservation Bureau in Taiwan for supporting this research.

*Landslide Potential Evaluation Using Fragility Curve Model DOI: http://dx.doi.org/10.5772/intechopen.89183*

records of Typhoon Morakot. Severe landslides occurred at the upper stream areas in Shenmu during the typhoon. Therefore, the proposed risk assessment and warn-

This study had developed the landslide fragility curve model by using the spatial data and statistical methods. The fragility curves of the study area were derived for all combinations of environmental and triggering factors. The data sets included the geomorphological and vegetation condition factors, based on the landslides at the Chen-Yu-Lan watershed in Taiwan, during Typhoon Sinlaku (September 2008) and Typhoon Morakot (August 2009). This study also proposed landslide risk assessment using rainfall hazard potential and landslide fragility curves and concluded

1.Overall, the proposed model provides considerably accurate and reliable

3.The classifications of slope unit can be applied to different areas, and the

4.The procedure of risk assessment was useful for practical landslide disaster

5.The LFC model was developed using two typhoon events. More events and landslide cases are needed to improve the LFC model in the future.

Furthermore, the classification of upstream areas based on their environment

6.The applicability of factors should be considered before developing the model. The concerns about the model factors and the limits of satellite images can be resolved by using different methods to obtain necessary data. For example, the information of LIDAR may be used with the satellite images to provide better description on landslide identification. Therefore, the LFC model could be

The authors would like to express their gratitude to research assistant Xingping Wang, for helping in collecting all the data relevant to the landslides in the Chen-Yu-Lan watershed. The authors also would like to thank the Soil and Water Con-

2.Adoption of slope unit was physically proper in modeling landslide locations.

results on landslide estimations in terms of spatial distribution.

fragility curve of each classification can be used directly.

improved when more factors are available and applicable.

servation Bureau in Taiwan for supporting this research.

ing stages of landslide were reasonably useful in this case.

**6. Summary and conclusions**

*Landslides - Investigation and Monitoring*

preparation and prediction.

**Acknowledgements**

**206**

is suggested for better possible estimation.

findings as follows:

## **Author details**

Yi-Min Huang<sup>1</sup> \*, Tsu-Chiang Lei2 , Bing-Jean Lee<sup>1</sup> and Meng-Hsun Hsieh<sup>1</sup>

1 Department of Civil Engineering, Feng Chia University, Taichung, Taiwan

2 Department of Urban Planning and Spatial Information, Feng Chia University, Taichung, Taiwan

\*Address all correspondence to: ninerh@mail.fcu.edu.tw

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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[2] Lei TC, Huang YM, Lee BJ, Hsieh MH, Lin KT. Development of an empirical model for rainfall-induced hillside vulnerability assessment: A case study on Chen-Yu-Lan Watershed, Nantou, Taiwan. Natural Hazards. 2014; **74**:341-373

[3] Lee BJ, Lei TC, Huang YM, Hsieh MH. 2015 Application of Landslide Fragility Curves in Landslide Risk and Warning Criteria, Project Report. Soil and Water Conservation Bureau, Taiwan (in Chinese). 2016. p. 341

[4] Lee BJ, Lei TC, Huang YM, Hsieh MH. 2016 Application of Landslide Fragility Curves in Landslide Risk and Warning Criteria, Project Report. Soil and Water Conservation Bureau, Taiwan (in Chinese). 2017. p. 224

[5] Lee CY et al. Risk assessment of landslide by using fragility curves: A case study in Shenmu, Taiwan. In: Proceedings of the 5th International Conference on Geotechnical Engineering for Disaster Mitigation and Rehabilitation (5th GEDMAR); 14–17 December 2005; Taipei, Taiwan: Airiti Press Inc. 2017. pp. 137-148

[6] Pradhan B, Lee S. Delineation of landslide hazard areas on Penang Island, Malaysia, by using frequency ratio, logistic regression, and artificial neural network models. Environmental Erath Science. 2009;**60**(5):1037-1054

[7] Lei TC, Wan S, Chou TY, Pai HC. The knowledge expression on debris

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[8] Wan S, Lei TC, Chou TY. A landslide expert system: Image classification through integration of data mining approaches for multi-category analysis. International Journal of Geographical Information Science. 2012;**26**:747-770

[9] Soil and Water Conservation Bureau. Soil and Water Conservation Handbook. Taiwan: Soil and Water Conservation Bureau; 2016. Available from: https:// drive.google.com/file/d/1FzwMzkd\_ 12qzGhOGjcQX7F-x2ihHvr6e/view

[10] Lillesand TM, Kiefer RW. Remote Sensing and Image Interpretation. New York: John Wiley and Sons; 1999. 736 p

[11] Bannari A, Morin D, Bonn F, Huete AR. A review of vegetation indices. Remote Sensing Reviews. 1995; **13**:95-120

[12] Xie M, Esaki T, Zhou G. GIS-based probabilistic mapping of landslide hazard using a three-dimensional deterministic model. Natural Hazards. 2004;**33**:265-282. DOI: 10.1023/B: NHAZ.0000037036.01850.0d

[13] Shinozuka M, Feng MQ, Lee J, Naganuma T. Statistical analysis of fragility curves. ASCE Journal of Engineering Mechanics. 2000;**126**(12): 1224-1231

[14] Hsieh MH, Lee BJ, Lei TC, Lin JY. Development of medium- and low-rise reinforced concrete building fragility curves based on Chi-Chi Earthquake data. Natural Hazards.2013;**69**(1):695- 728. DOI: 10.1007/s11069-013-0733-8

[15] AECOM. A study of sediment management policies on climate change for river basins in southern *Landslide Potential Evaluation Using Fragility Curve Model DOI: http://dx.doi.org/10.5772/intechopen.89183*

Taiwan- Gaoping river case study. Project Report. Water Resources Planning Institute, Water Resources Agency, Ministry of Economic Affairs, Taiwan. 2011. 342 p. Available from: https://www.wrap.gov.tw/library\_1. aspx?id=22547 Accessed: 19 July 2019]

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risk-analysis; 2005

**74**:341-373

[2] Lei TC, Huang YM, Lee BJ,

Hsieh MH, Lin KT. Development of an empirical model for rainfall-induced hillside vulnerability assessment: A case study on Chen-Yu-Lan Watershed, Nantou, Taiwan. Natural Hazards. 2014;

[3] Lee BJ, Lei TC, Huang YM, Hsieh MH. 2015 Application of Landslide Fragility Curves in Landslide Risk and Warning Criteria, Project Report. Soil and Water Conservation Bureau, Taiwan (in Chinese). 2016. p. 341

[4] Lee BJ, Lei TC, Huang YM, Hsieh MH. 2016 Application of Landslide Fragility Curves in Landslide Risk and Warning Criteria, Project Report. Soil and Water Conservation Bureau, Taiwan (in Chinese). 2017. p. 224

[5] Lee CY et al. Risk assessment of landslide by using fragility curves: A case study in Shenmu, Taiwan. In: Proceedings of the 5th International

Engineering for Disaster Mitigation and Rehabilitation (5th GEDMAR); 14–17 December 2005; Taipei, Taiwan: Airiti

[6] Pradhan B, Lee S. Delineation of landslide hazard areas on Penang Island, Malaysia, by using frequency ratio, logistic regression, and artificial neural network models. Environmental Erath Science. 2009;**60**(5):1037-1054

[7] Lei TC, Wan S, Chou TY, Pai HC. The knowledge expression on debris

**208**

Conference on Geotechnical

Press Inc. 2017. pp. 137-148

[1] Dilley M, Chen RS, Deichmann U, Lerner-Lam AL, Arnold M, Agwe J, et al. Natural Disaster Hotspots: A Global Risk Analysis (English). Washington, DC: World Bank. Available from: http://documents.worldbank.org/ curated/en/621711468175150317/ Natural-disaster-hotspots-A-global-

*Landslides - Investigation and Monitoring*

flow potential analysis through PCA +LDA and rough sets theory: A case study of Chen-Yu-Lan Watershed, Nantou, Taiwan. Environmental Earth

[8] Wan S, Lei TC, Chou TY. A landslide expert system: Image classification through integration of data mining approaches for multi-category analysis. International Journal of Geographical Information Science. 2012;**26**:747-770

[9] Soil and Water Conservation Bureau. Soil and Water Conservation Handbook. Taiwan: Soil and Water Conservation Bureau; 2016. Available from: https:// drive.google.com/file/d/1FzwMzkd\_ 12qzGhOGjcQX7F-x2ihHvr6e/view

[10] Lillesand TM, Kiefer RW. Remote Sensing and Image Interpretation. New York: John Wiley and Sons; 1999. 736 p

[12] Xie M, Esaki T, Zhou G. GIS-based probabilistic mapping of landslide hazard using a three-dimensional deterministic model. Natural Hazards. 2004;**33**:265-282. DOI: 10.1023/B: NHAZ.0000037036.01850.0d

[13] Shinozuka M, Feng MQ, Lee J, Naganuma T. Statistical analysis of fragility curves. ASCE Journal of Engineering Mechanics. 2000;**126**(12):

[14] Hsieh MH, Lee BJ, Lei TC, Lin JY. Development of medium- and low-rise reinforced concrete building fragility curves based on Chi-Chi Earthquake data. Natural Hazards.2013;**69**(1):695- 728. DOI: 10.1007/s11069-013-0733-8

[15] AECOM. A study of sediment management policies on climate change for river basins in southern

[11] Bannari A, Morin D, Bonn F, Huete AR. A review of vegetation indices. Remote Sensing Reviews. 1995;

**13**:95-120

1224-1231

Sciences. 2011;**63**(5):981-997

*Edited by Ram Ray and Maurizio Lazzari*

*Landslides - Investigation and Monitoring* offers a comprehensive overview of recent developments in the field of mass movements and landslide hazards. Chapter authors use in situ measurements, modeling, and remotely sensed data and methods to study landslides. This book provides a thorough overview of the latest efforts by international researchers on landslides and opens new possible research directions for further novel developments.

Published in London, UK © 2020 IntechOpen © Cesare Ferrari / iStock

Landslides - Investigation and Monitoring

Landslides

Investigation and Monitoring

*Edited by Ram Ray and Maurizio Lazzari*