Statistical Seismic Landslide Hazard Analysis: an Example from Taiwan Chyi-Tyi Lee Graduate Institute of Applied Geology, National Central University, Taiwan Seismology Forum 27: Natural Hazards and Surface Processes, Taipei, 7 March 27
INTRODUCTION There are two different approaches to perform seismic landslide hazard analysis: Deterministic approach by using Newmark displacement method (Jibson et al., 2). Statistical approach via landslide susceptibility analysis (Lee, 24). Both need an prior analysis for intensity parameters as input for landslide hazard analysis. The weakness of deterministic approach is the critical acceleration at each study point is vary and is difficult to achieve, because failure depth, material strength, and groundwater data are not feasible to investigate in a large region. 2
What is landslide hazard analysis? Landslide hazard analysis analyzes the probability of landslide occurrence in a given region and a given time period. Steps in Natural Hazard Assessment Inventory Construction Susceptibility Analysis Hazard Analysis Risk Analysis Construction of time series inventory of hazard Dividing a region into successive classes representing different grades of slope instability Calculation of the probability of a hazard level in a given region and a given time period Calculation of the lost of life or property in a given region and a given time period. 3
Deterministic approach by Newmark displacement method Sliding block Newmark Displacement a c ( FS ) g sin a c : critical acceleration, FS : factor of safety, α : slope angle. 4
Statistical approach via landslide susceptibility analysis The basis of statistical approach is an event-based landslide susceptibility analysis which divides a region into successive classes representing different grades of slope instability. Comparing the training data with the susceptibility model, we can build a probability of failure curve and use this curve to complete a probability of failure map for a region. Because the susceptibility model is event-based, scenario earthquake intensity can be input into the model to find a susceptibility index at a grid-point, and then, this index can be used to find a probability of failure at the grid-point..8 Probability of Failure.5.2.9.6.3 y.28x ( x).63.2.4.6.8 Landslide Suscepitility Index Probability of failure curve is used to transfer susceptibility index into landslide probability. Lee, C.T. (24) Statistical Seismic Landslide Hazard Analysis: an Example from Taiwan, Engineering Geology, 82, 2-22. 5
Landslide Probability (%) Model Training Event Chi-Chi Earthquake-induced Landslide Inventory 2.5% 2.%.5% Rock Deep Shallow.%.5%.% log cumulative counts 4.5 4 3.5 3 2.5 2.5.5 Total landslide area 2 3 4 5 6 7 log(area)(m^2) all ls rock fall shallow ls deep ls Chi-Chi EQ-induced landslides Number Area (km 2 ) Rock falls 326 4.493 Shallow slides 2,65 9.77 Deep slides 98 24.834 All 3,75 9.54 Chi-Chi EQ-induced landslides within/outside 25 gal isoseismal Number Area (km 2 ) Rock falls 3/ 6 4.29/.2 Shallow slides 2,98/453 86.78/ 3.4 Deep slides 95/ 3 24.57/.27 All 2,73/472 5.64/ 3.87 93.5% within 25 gal isoseismal 6
Basis for Analysis of Landslide Susceptibility Definition of flat area: flat area and gentle slopes where slope gradient is less than % and area is greater than hectare are regarded as stable area and is not taken in the analysis. Selection of training area: an training area must be selected to build a susceptibility model for further analysis. The training area is ideally a homogenous area in topography, geology, climate, and is not far from the 25 gal isoseismal of the training event. Only shallow landslides (including fall type) were used in the analysis; deep-seated landslides were not included. 7
Frequency 4% 3% 2% % Selection of Effective Landslide Causative Factors Non-landslide D=.79 % 4 8 2 6 2 Slope, % Landslide Exp. Cum. Prob. P-P Plot Obs. Cum. Prob. Prob. of Failure % 8% 6% 4% 2% Probability of Failure Curve % 4 8 2 6 2 Slpoe, % Portion of Landslide.8.6.4.2 Curve AUC=.767.2.4.6.8 Visual inspection of frequency distribution of the two groups, and calculation of discriminator D. Discriminator D j : non-landslide group, S Pj Test of normal distribution of the factor. Examination of probability of failure curve to see if landslide probability increases with the factor value., where, A j is average of landslide group, is pooled standard deviation of two groups, j indicates j th factor. B j Examination of success rate curve to check the ability of interpreting landslides of the factor. is average of 8
Selection of an Analytical Method Portion of landslides within the predicted hazard area Portion of landslides within the predicted hazard area.8.6.4.2 Kuohsing Quadrangle, Hilly terrain Hilly Terrain LOGISTIC : Logistic Regression DA : Discriminant Analysis NN : Neural Network DN : Newmark Displacement NN LOGISTIC DN DA.2.4.6.8 23Portion of areas predicted as hazard area Portion of areas predicted as hazard (Lee, 26) Logistic regression is an effective and robust method for building a susceptibility/hazard model. NN may built a success model but sometimes fail in prediction. DN commonly involves problems of lacking local soil depth, strength parameters, and groundwater data. 9
Frequency, % 8 6 4 2 Statistics of Slope Gradient D =.97 2 3 Slope, % from Landslide Inventory (/2) Probability of Failure, % 4 3 2 2 3 Slope, % Frequency distribution Landslide probability Success rate.8.6.4.2 AUC=.76.2.4.6.8 Differences between landslide group and non-landslide group, landslide probability, and success rate counted within 25 gal isoseismal of the Chi-Chi Earthquake for slope-gradient factor and all types of landslides. (Flat area are not counted in the computing of the above figures) Slope gradient is always an important factor controlling the occurrence of landslides. Slope Gradient
Deep Slide Shallow Slide Rock Fall Statistics of Slope Gradient from Landslide Inventory (2/2) Frequency, % Frequency, % Frequency, % 6 4 2 2 3 Slope, % 8 6 4 2 D =.982 2 3 6 Slope, % 4 2 D =.865 D =.859 2 3 Slope, % Probability of Failure, % Probability of Failure, % Probability of Failure, % 2 8 4 2 3 Slope, % 8 6 4 2 2 3 5 Slope, % 4 3 2 2 3 Slope, %.2.4.6.8 Frequency distribution Landslide probability Success rate.8.6.4.2.2.4.6.8.8.6.4.2.8.6.4.2 AUC=.96 AUC=.765 AUC=.727.2.4.6.8
Landslide Probability (%) Statistics of Slope Aspect from Landslide Inventory 2.5% 2.%.5% Rock Deep Shallow.%.5%.% Landslide probability for different slope aspects in three types of landslide, counted within 25 gal isoseismal. 2
Probability of Failure (%) 2.%.8%.6%.4%.2%.%.8%.6%.4%.2%.% Terrace Deposits Pleistocene Series Pliocene Series Upper Miocene Series Lower Miocene Series Slates Eocene Quartize Statistics for Formations from Landslide Inventory 3
Frequency, % 8 6 4 2 Statistics of Terrain Roughness D.=.856 4 8 2 6 2 Terrain Roughness, m from Landslide Inventory Probability of Failure, % 6 2 8 4 4 8 2 6 2 Terrain Roughness, m Frequency distribution Landslide probability Success rate.8.6.4.2 AUC=.739.2.4.6.8 Differences between landslide group and non-landslide group, landslide probability, and success rate counted within 25 gal isoseismal of the Chi-Chi Earthquake for slope-gradient factor and all types of landslides. (Flat area are not counted in the computing of the above figures) Terrain roughness is also an effective factor controlling the occurrence of landslides. Terrain Roughness 4
Frequency, % 2 8 4 Statistics of Slope Roughness D.=.725 2 4 6 8 Slope Roughness, % from Landslide Inventory Probability of Failure, % 8 6 4 2 2 4 6 8 Slope Roughness, % Frequency distribution Landslide probability Success rate.8.6.4.2 AUC=.77.2.4.6.8 Differences between landslide group and non-landslide group, landslide probability, and success rate counted within 25 gal isoseismal of the Chi-Chi Earthquake for slope-gradient factor and all types of landslides. (Flat area are not counted in the computing of the above figures) Slope roughness is also an effective factor controlling the occurrence of landslides. Slope Roughness 5
Statistics of Curvatures from Landslide Inventory.8.6.4.2.2.4.6.8 plane curvature.8.6.4.2 AUC=.55 AUC=.5.2.4.6.8.8.6.4.2 AUC=.528.2.4.6.8 profile curvature.8.6.4.2 AUC=.634.2.4.6.8 tangential curvature total curvature Success rate curves for curvature factors to interpret shallow landslides within 25 gal isoseismal. Only the total curvature shows a fairly good success rate (AUC=.634), others are very poor. Total Curvature 6
Statistics of Slope Heights from Landslide Inventory Relative Slope Height = Slope Height / Total Slope Height.8.6.4.2 AUC=.542.2.4.6.8.8.6.4.2 AUC=.577.2.4.6.8.2.4.6.8 local slope height total slope height relative slope height Only the Total-slope-height factor shows a poor success rate (AUC=.577), others are very poor. (within 25 gal isoseismal).8.6.4.2 AUC=.523 Total Slope Height 7
Statistics of Distances from Landslide Inventory Landslide Probability (%) 4. 3.5 3. 2.5 2..5..5..54 2.35 3.38.99.78.8..7.4.2..2 Distance to Epicenter (km) Epicenter - -2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9- - > Landslide Probability (%) 4. 3.5 3. 2.5 2..5..5..59.94 3.29 2.34.7.88..7.4.2..2 Distance to Hypocenter (km) Hypocenter - -2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9- - > Landslide Probability (%) 3. 2.5 2..5..5. 2.6 2.48.72.77 Surface Rupture.2.2... - -2 2-3 3-4 4-5 5-6 6-7 7-8 >8 Distance to Surface Rupture (km) Landslide Probability (%) 3. 2.5 2..5..5. 2.67.23.2 Fault Plane.6..2..2. - -2 2-3 3-4 4-5 5-6 6-7 7-8 >8 Distance to Fault Plane (km).8.6.4.2 AUC=.633.2.4.6.8.8.6.4.2 AUC=.632.2.4.6.8.2.4.6.8 Landslide probability for all types. Success rate and AUC computed within the 25-gal isoseismal. Distance-to-fault-rupture-plane and distance-to-fault-rupture-line are both the factors most affecting landslide occurrence, and distance-toepicenter and distance-to-hypocenter are also both effective factors..8.6 Epicenter Hypocenter Surface Rupture Fault Plane.4.2 AUC=.663.8.6.4.2 AUC=.66.2.4.6.8 8
Statistics for Arias Intensity Frequency, % 6 4 2 D =.757 4 8 2 6 2 Arias intensity, m/s Probability of Failure, % 4 3 2 4 8 2 6 2 Arias intensity, m/s.2.4.6.8 Frequency distribution Landslide probability Success rate Differences between landslide group and non-landslide group, landslide probability, and success rate counted within 25 gal isoseismal of the Chi-Chi Earthquake for Arias intensity factor and all types of landslides. (Flat area are not counted in the computing of the above figures) Arias intensity is always an important factor controlling the occurrence of landslides..8.6.4.2 AUC=.77 Arias Intensity 9
Frequency, % 4 3 2 D.=.556 4 8 2 Arias intensity, m/s Statistics for Topographic Corrected Arias Intensity Probability of Failure, % 6 4 2 4 8 2 Arias intensity, m/s.2.4.6.8 Frequency distribution Landslide probability Success rate The following the empirical formula proposed by Lin and Lee (23) is used in the topographic correction, I a = f I a, f h / 93.8.287.464 where I a is the Arias intensity; I a is the corrected one; f is the amplification factor; and h is the height relative to riverbed in meters..8.6.4.2 AUC=.859 Topographic Corrected Arias intensity is the most effective factor controlling the occurrence of landslides. Corrected Arias Intensity 2
Correlaiton Coefficient between two Factors Slope Terrain Roughness Slope Roughness Total Curvature Total Slope Height Arias Intensity (Topographic Amplification) Slope.823.785.479.698.37 Terrain Roughness.86.538.48.3 Slope Roughness.5.453.259 Total Curvature.443.39 Total Slope Height Arias Intensity (Topographic Amplification).29 2
Model Result The logistic regression model is, p ln p.66l +.228L 2 +.433L 3 +.58L 4 +.2L 5 -.22L 6 +.L 7 -.347A -.66A 2 +.48A 3 +.87A 4 +.282A 5 +.A 6 -.24A 7 -.6A 8 +.52F +.24F 2 +.F 3 +.845F 4 +.257F 5 +.246F 6-3.495. Where, L ~L 7 are lithological units, A ~A 8 are aspect factors, F ~F 5 are causative factors, and F 6 is triggering factor. F : Slope gradient. F 2 : Terrain roughness. F 3 : Slope roughness. F 4 : Total curvature. F 5 : Total slope height. F 6 : Arias intensity..8.6.4.2 Success Rate AUC=.98.2.4.6.8 Probability of Failure.8.5.2.9.6.3 y.28x ( x).63.2.4.6.8 Landslide Suscepitility Index Probability of failure curve is used to transfer susceptibility index into landslide probability which is used in mapping. 22
Validation by Rueili Data.8.6.4.2 Prediction Rate AUC=.756.2.4.6.8 The Rueili Earthquake of M L 6.2 occurred on July 7, 998, at central Taiwan, about 4 km south to the epicenter of Chi-Chi Earthauake. It triggered 847 shallow landslides totaling 478.7 hectares. Factors and these landslides were used to validate the Chi-Chi seismic landslide hazard model. The result is fair with AUC equal to.756. 23
Seismic Hazard Analysis Procedure 24
Regional Source(Depth 35km) Source Model Regional Source(Depth>35km) 25
Active faults in Taiwan Source Model Assessment of Fault Parameters 26
Site and Attenuation Model Vs3 (Lee et al., 22) Attenuation curves with different Vs3 2 2 ln I a 3.757.43( M 6) 8.77ln( M / 6) 2.25ln( R 9.56 ).42ln( V 3).24F.22F s3 N R σ =.994 (Lee and Tsai, 28) M : moment magnitude of earthquake, R : rupture distance in km, h : hypocentral depth in km, F N : mormal faulting mechanism, F R : reversel faulting mechanism. 27
475 year Arias Intensity Map Arias Intensity Hazard Map Corrected Arias Intensity We used our seismic hazard model (Cheng et al., 27) and a new Arial intensity attenuation relationship (Lee et al., 22) to perform a PSHA and got a 475-year Arial intensity map for Taiwan (left). Then the Arial intensity was topographically corrected by an empirical formula proposed by Lee et al. (28). The corrected Arial intensity (right) is then applied to the Chi-Chi seismic landslide hazard model, and then a 475-year seismic landslide hazard map for whole Taiwan is constructed. 28
2475 year Arias Intensity Map Arias Intensity Hazard Map Corrected Arias Intensity We used our seismic hazard model (Cheng et al., 27) and a new Arial intensity attenuation relationship (Lee et al., 22) to perform a PSHA and got a 2475-year Arial intensity map for Taiwan (left). Then the Arial intensity was topographically corrected by an empirical formula proposed by Lee et al. (28). The corrected Arial intensity (right) is then applied to the Chi-Chi seismic landslide hazard model, and then a 2475-year seismic landslide hazard map for whole Taiwan is constructed. 29
Seismic Landslide Harzard Map of Taiwan % probability of Exceedance In 5 years 2% probability of Exceedance In 5 years Landslide Probabilithy Map for 475-year EQ Landslide Probabilithy Map for 2475-year EQ 3
Model Applications Predion of seismic landslide probability under an earthquake event. Mapping of seismic landslide hazard probability under a certain return-period earthquake. Decision Making for regional planning, site selection, and hazard mitigation. Sediment Estimation for a drainage basin after an extreme event. 3
SUMMARY We used a multivariate statistical approach with logistic regression to analyze the Chi-Chi earthquake-induced landslides and their controlling factors, and a susceptibility model is built. The susceptibility model was then used to build a hazard model through using 475-year return period earthquake intensity and a probability of failure curve to transfer the susceptibility values to spatial probabilities. Results of the analysis are good, provided that careful validation at a neighboring region was made. We conclude that this statistical approach of seismic landslide hazard analysis is feasible, and that the hazard model can be used to predict landslides after a major earthquake and to be used to produce a seismic landslide hazard map of a wide region. 32
SUMMARY The Arias intensity is found to be the most effective factor to interpret landslide distribution among different intensity measures, like peak ground acceleration, peak ground velocity, closest distance to fault line, closest distance to fault plane etc. It is also the most effective factor among different causative factors, like slope gradient, terrain roughness, surface curvature, and slope height, and thus improves the quality of the model, and makes the model temporally significant. The statistical approach of seismic landslide hazard has an advantage over deterministic methods in that it does not require failure depth, material strength, or groundwater data, and may have a better prediction rate. However, a deterministic model can be used anywhere once the parameters required by the model are available. The statistical approach, by contrast, may be applicable only to the vicinity of the study region where the model was trained, and may be limited within or not too far from the earthquake intensity range they were trained. 33
SUMMARY This seismic landslide hazard map is for the evaluation of shallow landslides and rock falls only. Deep-seated landslides are most of structural controlled and need specific study site by site, these are not included in the present hazard map. They may be presented in a separated sheet of the hazard map or included in the same sheet with different symbol. A nationwide rain-induced landslide hazard map has also been completed in 23 (Lee and Fei, 25). Deep seated landslides, and debris hazard maps are also completed. These nationwide landslide hazard maps both for earthquake and rainfall are in to 5 thousand scale. Further study will also include the estimation of location, size, volume, and recurrence of landslides. 34
Thanks for your attention! 35
Sediment Estimation (/3) From probability of landslide occurrence map, we may estimate shallow landslide area A sl as follow, A ap sl ls i i where, P ls i is probability of failure at cell i, a is area of a cell; it is m2 in this study. From spatial landslide probability map of Chi-Chi earthquake event, we can estimate landslide area to be,898,848m2, Actual landslide from the inventory is 2,977 landslides with a total area of 9,572,4m2. The difference indicates that mapping of the landslide inventory may have missed some landslides in shadows of the SPOT images. Furthermore, missing of small-scale landslides and deleting of repeated landslides in the event-based landslide inventory may also reduce the total area of landslide as compared to the prediction ones. 36
Sediment Estimation (2/3) We further adopted a soil-thickness prediction model from Chung (28) as follow, where, h is soil thickness (m), S is slope ( ). Inserting slope data into above equation, we can get soil thickness at each grid-cell in the study area and further estimate landslide volume V sl as follow, h 4.9429.939ln S V (494.29P 9.39P ln S ) sl lsi lsi i i Using the above equation, we could estimate shallow landslide volume induced by Chi-Chi earthquake to be 6,256,4 m 3. Actual landslide volume using landslide area from inventory is 44,757,92 m3. Again, the difference is because of we have missed small-scale landslides, landslides in shadows and repeating landslides. 37
Sediment Estimation (3/3) To this step, we can successfully predict landslide location, area and volume in a drainage basin or catchment area using GIS. However, the amount of sediment yield in a catchment still requires estimation of soil erosion on the slope and sediment transportation in the stream. A distributed hydrological and sediment transport modeling should be further carried out so that sediment problem like that in the Shihmen Reservoir catchment area could be interpreted. GIS is a useful tool for managing and processing the model factors and also good for construction of a hazard map and application in regional planning, hazard mitigation, and sediments yield estimation. 38