1. 降雨誘發廣域山崩模型之力學 參數逆分析實際案例 報告者：陳麒任 指導教授：董家鈞

2. Introduction Classification of landslide assessment: Qualitative analysis Empirical method Quantitative analysis Statistic method Discriminant analysis Logistic regression Conditional Probability Approach Artificial intelligence Fuzzy Theory neural network Deterministic analysis Infinite –slope stability analysis 2

3. Deterministic analysis of rain fall-induced landslides Observed landslide inventory Deterministic analysis Parameters Back calculate Lab test DEM Slope Soil depth Rainfall intensity hydraulic conductivity In situ test or Empirical methods Remote sensing unit weight of soil Lab test Deterministic analysis Predicted landslide inventory DEM Slope Soil depth Rainfall intensity Godt et al. (2008) Cohesion Friction angle hydraulic conductivity In situ test or Empirical methods Remote sensing unit weight of soil Back analysis of strength has advantages over lab testing in that the scale is much larger. (Gilbert,1998) 3

4. Confusion matrix Observed Unstable Stable Predicted Unstable Stable True Positives (TP) False Positives (FP) False Negatives (FN) True Negatives (TN) Efficiency: ( + )/( + + + )Sensitivity: /( + )Specificity: /( + ) trial and error Cohesion =1 to 50 kPa Friction angle=1 ° to 50 ° Cohesion =1 to 50 kPa Friction angle=1 ° to 50 ° Deterministic analysis Predicted landslide inventory Observed landslide inventory Observed Predicted 4

5. 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) 。 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) 。 Criterion ROC 林衍承 (2009) FS=1FS=1.5 Sensitivity 4)Maximum Develop Sensitivity 5)Maximum the average of Efficiency, Sensitivity and Specificity 4)Maximum Develop Sensitivity 5)Maximum the average of Efficiency, Sensitivity and Specificity Sensitivity: /( + ) Specificity FS=0.5 5

6. 6 Observed Predicted Observed Predicted 100%

7. 7 6)Minimum distance between the corner(1,1,1) and the plane.

8. Objective 1.Compare results of each criterion 2.Back calculate the parameters (friction angle and cohesion) 8

9. Rainfall-induced landslide model – This research use TRIGRS, a Fortran program developed by USGS. The Transient Rainfall Infiltration and Grid-Based Regional Slope- Stability. – Parameters : precipitation intensity, slope, soil depth, initial water- table depth, saturated vertical hydraulic conductivity, hydraulic diffusivity, cohesion for effective stress, angle of internal friction for effective stress, total unit weight of soil. 9

10. 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, γ w is unit weight of groundwater, and γ s is soil unit weight, β is slope angle, ψ is pressure head. 10

11. Richards equation coordinate system One-dimensional form (linear diffusion equation) (initial condition) (boundary condition) Transient vertical groundwater 11

12. Combined Iverson(2000) and Savage et al.(2003). 12

13. Flow Chart TRIGRS Cohesion=1,50 Friction angle=1,50 Parameter Predicted landslide inventory Observed landslide inventory Sensitivity Efficiency Specificity Criterion Cohesion Friction angle 13 Discussion

14. Study Area 14

15. Input Data Slope Soil depth 15

16. parameterCohesion (kPa) Friction angle(°) Unit weight of soil(kN/m 3 ) saturated vertical hydraulic conductivity(m/ s) Initial infiltration rate (m/s) hydraulic diffusivity (m 2 /s) initial water-table depth (m) Value19.62919.61E-41E-62E-2Assume equal to soil depth Input parameters Iverson (2000) 、吳佳郡 (2006) 、中興工程 顧問公司 (2004) 、 Paolo (2001) 和 Lancaster (2002) 2001/7/29 ~ 2001/7/30 Storm event 16

17. Result of maximum AUC criterion Five largest AUC parameters Parameter number of maximum value within 1% is 1467. It’s hard to distinguish the most suitable parameter. Cohesion( kPa) Friction angle AUCSensitivityEfficiencySpecificityDevelop sensitivity 43330.839 0.1270.8820.9790.109 44270.839 0.1580.8800.9720.130 44360.839 0.1120.8870.9860.101 45350.839 0.1110.8870.9860.100 46330.839 0.1200.8870.9840.106 True value Cohesion( kPa) Friction angle AUCSensitivityEfficiencySpecificityDevelop sensitivity 19.6290.8340.7240.7970.8060.287 17

18. Landslide inventory Five largest Efficiency parameters Parameter number of maximum value within 1% is 489. Cohesion( kPa) Friction angle AUCSensitivityEfficiencySpecificityDevelop sensitivity 42440.8370.0760.8900.9940.072 43 0.8380.0790.8900.9930.075 44430.8380.0720.8900.9940.069 46400.8380.0870.8900.9920.082 47390.8380.0880.8900.9920.083 Cohesion=47 kPa Friction angle=39 degree 18

19. Sensitivity First Cohesion(kPa)Friction angle SensitivityEfficiencySpecificity 17400.6020.8380.868 19370.6030.8390.869 21340.6030.8400.870 22320.6090.8370.866 24290.6000.8390.870 Efficiency greater than 80%, Sensitivity greater than 60% and Specificity greater than 90% Specificity First Cohesion(kPa)Friction angle SensitivityEfficiencySpecificity 18420.5240.8590.902 20390.5330.8600.902 21380.5260.8630.906 22360.5300.8610.903 24330.5250.8600.902 Parameter number of maximum value within 1% is 18 19

20. Develop Sensitivity criterion Five largest Develop Sensitivity parameters Cohesion(k Pa) Friction angle Develop sensitivity SensitivityEfficiencySpecificity 2332 0.3030.5850.8480.881 2136 0.3030.5680.8520.889 2038 0.3040.5580.8560.894 2137 0.3060.5480.8590.899 2333 0.3030.5610.8540.891 Parameter number of maximum value within 1% is 7 20

21. Cohesion=23kPa Friction angle=32degree 21

22. The average of Efficiency, Sensitivity and Specificity criterion Cohesion( kPa) Friction angle AverageSensitivityEfficiencySpecificityDevelop sensitivity 2226 0.7790.7170.8040.8160.293 2423 0.7780.7030.8090.8220.293 2521 0.7770.7030.8080.8210.293 2029 0.7760.7240.7980.8070.288 2128 0.7760.7070.8050.8170.290 Five largest value parameters Parameter number of maximum value within 1% is 77. 22

23. Cohesion=20kPa Friction angle=29degree 23

24. 24 Minimum distance between the (1,1,1) and the plane Cohesion( kPa) Friction angle DistanceSensitivityEfficiencySpecificityDevelop sensitivity 2226 0.3900.7170.8040.8160.293 2029 0.3930.7240.7980.8070.288 2224 0.3930.7380.7900.7970.284 2127 0.3930.7230.7970.8070.288 2225 0.3940.7260.7960.8050.287 Five largest value parameters Parameter number of maximum value within 1% is 6.

25. Criterion Parameter number of maximum value within 1% AUC1467 Efficiency489 Efficiency greater than 80%, Sensitivity greater than 60% and Specificity greater than 90% 18 Develop Sensitivity7 Average of Efficiency, Sensitivity and Specificity77 Minimum distance between the (1,1,1) and the plane 6 C: Efficiency greater than 80%, Sensitivity greater than 60% and Specificity greater than 90% D: Develop Sensitivity E: Average of Efficiency, Sensitivity and Specificity F: Minimum distance between the corner and the plane 25

26. 26 Criterion Average distance Efficiency greater than 80%, Sensitivity greater than 60% and Specificity greater than 90% 7.7 Develop Sensitivity8.7 Average of Efficiency, Sensitivity and Specificity 7.0 Minimum distance between the (1,1,1) and the plane 4.1 C: Efficiency greater than 80%, Sensitivity greater than 60% and Specificity greater than 90% D: Develop Sensitivity E: Average of Efficiency, Sensitivity and Specificity F: Minimum distance between the corner and the plane

27. 27 Criterion Average value C(kPa) φ Efficiency greater than 80%, Sensitivity greater than 60% and Specificity greater than 90% 2231 Develop Sensitivity2137 Average of Efficiency, Sensitivity and Specificity 2325 Minimum distance between the (1,1,1) and the plane 2226 C: Efficiency greater than 80%, Sensitivity greater than 60% and Specificity greater than 90% D: Develop Sensitivity E: Average of Efficiency, Sensitivity and Specificity F: Minimum distance between the corner and the plane

28. Future work Using Bayesian inference to calculate the probability of parameters. 28

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