Slide 1

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 2

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 3

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 4

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 5

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 6

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 7

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 8

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 9

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 10

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 11

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 12

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 13

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 14

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 15

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 16

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 17

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 18

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 19

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 20

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 21

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 22

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 23

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 24

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 25

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 26

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 27

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 28

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion


Slide 29

降雨誘發淺層山崩模型土壤強
度參數逆分析之比較與驗證
Adviser:董家鈞、劉家男
Student:陳麒任

• Introduction
– Objective
– Literature Review

• Methodology
– Data base
– Back analysis

• Result and Discussion
• Conclusions and Recommendation

Qualitative analysis
Empirical method

Quantitative analysis
Statistic method
Discriminant analysis
Logistic regression
Conditional Probability Approach

Artificial intelligence
Fuzzy Theory
neural network

Deterministic analysis
Rainfall trigger landslide
Earthquake trigger landslide

Cohesion

Friction
angle

Lab test

Lab test
hydraulic

hydraulic
conductivity

conductivity
unit weight
of soil

In situ test or
In situ test or
depth
Empirical methods EmpiricalSoil
methods

Remote sensing
Observed landslide
inventory

DEM

Remote sensing

Slope

unit weight
of soil
Deterministic
analysis

Deterministic
analysis

Parameters

Soil depth

DEM
Slope

Rainfall intensity Rainfall intensity

Predicted landslide
inventory

Godt et al. (2008)

4

Observed
Predicted

1) Extensive work to get reliable data. [林衍丞，2009]
2) Strength parameter and hydraulic parameter are difficult to
obtain. [李錫堤，2009]
3) There are scale issues involved in the translation of laboratory
values to the field problem. [Guimaraes, 2003]
4) Back analysis of strength has advantages over lab testing in
that the scale is much larger. [Gilbert ,1998]
5) Back analysis is reliable only when the model and all
assumptions are reasonable and accurate representations of
the real system[Deschamps, 2006]

• Exist many back analysis criterion.
Efficiency: (

+

)/(

Sensitivity:
Specificity:

Observed
Predicted

+
/(
/(

+
+
+

+
)
)

Observed

Unstable

Stable

Unstable

True Positives
(TP)

False Positives
(FP)

Stable

False Negatives
(FN)

True Negatives
(TN)

Predicted

7

)

However, the output of back analysis is usually uncertain because
of the random factors existing in the problem. [Zheng, 2008]
Methodologies used for back analysis can be classified into two
groups, i.e., deterministic method and probabilistic
method.[Zhang, 2010]

1) Compare the existing back analysis criterion.
2) Compare the result of deterministic method and
probabilistic method.

Rainfall-induced landslide model
This research use TRIGRS, a Fortran program developed by USGS.
The Transient Rainfall Infiltration and Grid-Based Regional SlopeStability.

Theoretical Basis
• Infinite-slope stability
– Landslide with planar failure surfaces.
– Slide depth is much smaller than length and width.

where c’ is soil cohesion for effective stress, Φ’ is the soil friction angle for effective
stress, γw is unit weight of groundwater, and γs is soil unit weight, β is slope angle, ψ is
pressure head.

11

Back analysis parameters

林衍丞，2009

Collect the back analysis criterion
1) Maximum Efficiency(林衍丞，2009) 。
2) Maximum AUC (林衍丞，2009) 。
3) Efficiency greater than 80%, Sensitivity
greater than 60% and Specificity greater
than 90%(中興工程顧問社 ，2004)。

FS=1.5
FS=1

ROC

FS=0.5
Sensitivity

4) Maximum Develop Sensitivity

Specificity

林衍承(2009)

Study Area

14

Input Data
Soil depth

15

Input Data
Slope

Storm event

2001/7/29 ~ 2001/7/30

Input parameters

Unit weight
parameter
of soil
(kN/m3)

Value

20

saturated
vertical
hydraulic
conductivity
(m/s)

5E-5

Initial
infiltration
rate (m/s)

1E-6

initial
hydraulic
water-table
diffusivity (m2/s)
depth (m)

5E-5

Equal to soil
depth

Consider Salciarini(2008) , Godt(2008)

Result and Discussion

(A) Develop sensitivity
(B) Efficiency
(C) Efficiency greater than 80%,
Sensitivity greater than 60%
and Specificity greater than
90%
(D) AUC

Criterion B :Efficiency

1.
2.
3.
4.

Low failure ratio
Overestimate parameters
Underestimate landslide
Select parameters hardly

Sensitivity Efficiency Specificity
0.076

0.890

0.994

Develop
sensitivity
0.072

Criterion A,C

1.
2.
3.
4.

Good constrain
Low friction angle
High cohesion
Assumption problem
(depth, variable)

Sensitivity Efficiency Specificity

0.717

0.804

0.816

Develop
sensitivity
0.293

Author

Date

Sensitivity Specificity Efficiency

Godt

2008

0.42

0.84

0.80

Tiwari (2000,2005) assumed factor of safety is equal to 0.98 for
back analysis cohesion and friction angle.
Sensitivity= 0.4~0.44
Specificity=0.80~0.88
Efficiency=0.75~0.85

Sensitivity
0.4050

Efficiency Specificity
0.8258

0.8794

Develop
sensitivity
0.2080

Bayesian theorem:
Updates a probability given new information

雙
變
量
常
態
分
布
(mean)

凝聚力

山崩

摩擦角
不山崩
(coefficient of
variance)

cohesion

8 kPa

0.2

Friction angle

30°

0.1

Chen et al.(2005)

Zhang et al.(2010):Back analysis of slope failure with Markov chain Monte Carlo simulation
Gilbert et al.(1998):Uncertainty in back analysis of slopes: Kettlemen Hills case history

P

P

1

Fs

0.42
0.84
0.8

多
變
Sensitivity 量
常
Specificity 態
Efficiency 分
布

Mean of
Mean of cohesion

COV of

COV of
friction

(kPa)

cohesion

friction angle

angle(°)
After update
Before update

1600

8.87

0.13

8

0.2

(a)

0.03

30

0.1

800

(b)
600

Number of sample

1200

Number of sample

35.58

800

400

400

200

0

0
30

31

32

33

34

35

36

37

Friction angle

38

39

40

41

3

4

5

6

7

8

9

10 11 12 13 14 15

Effective soil cohesion