1. Rainfall Records Professor Steve Kramer

2. Rainfall Records Measured at single point by rain gauge Over extended period of time, can establish: –Mean annual rainfall –Standard deviation of annual rainfall Mean Mean -  Mean + 

3. Rainfall Records Rainfall also varies substantially within each year SF – dry summers LV – dry years Cleveland - wet summers Atlanta - wet years

4. Rainfall Records Rainfall also varies within a rainy season –Few areas (other than Seattle) have continuous rainfall –In many areas, most precipitation occurs in large storms with: Intense rainfall Limited duration Limited frequency –Useful to quantify intensity-duration-frequency relationship Basic concept of hydrology Useful for flooding, water resource evaluation Also useful for rainfall-induced landslide prediction

5. Rainfall Records For a given rain gauge, list precipitation data from significant storms in N years

6. Rainfall Records For a given rain gauge, list precipitation data from significant storms in N years 7

7. Rainfall Records For a given rain gauge, list precipitation data from significant storms in N years 7

8. Rainfall Records For a given rain gauge, list precipitation data from significant storms in N years 10-min duration events 7

9. Rainfall Records Choose a particular duration (say 10 min) –List maxima for all storms in order of decreasing rainfall (most intense 10 min for each) Event, m10-min rainfall (in) 10.66 20.60 30.55 40.50 …… 280.12 290.11 300.09

10. Rainfall Records Choose a particular duration (say 10 min) –List maxima for all storms in order of decreasing rainfall (most intense 10 min for each) Event, m10-min rainfall (in) T r (yrs) (= N/m) 10.6630.0 20.6015.0 30.5510.0 40.507.5 ……… 280.121.071 290.111.034 300.091.000 Every 30 years, on average, we can expect to see more than 0.66 inches of rainfall in a 10-min period of time

11. Rainfall Records Choose a particular duration (say 10 min) –List maxima for all storms in order of decreasing rainfall (most intense 10 min for each) Event, m10-min rainfall (in) T r (yrs) (= N/m) 10.6630.0 20.6015.0 30.5510.0 40.507.5 ……… 280.121.071 290.111.034 300.091.000 Every 15 years, on average, we can expect to see more than 0.60 inches of rainfall in a 10-min period of time

12. Rainfall Records Choose a particular duration (say 10 min) –List maxima for all storms in order of decreasing rainfall (most intense 10 min for each) Event, m10-min rainfall (in) T r (yrs) (= N/m) 10.6630.0 20.6015.0 30.5510.0 40.507.5 ……… 280.121.071 290.111.034 300.091.000 Every 1.07 years, on average, we can expect to see more than 0.12 inches of rainfall in a 10-min period of time

13. Rainfall Records Repeat for other durations –As duration increases, rainfall amount (in) goes up 10-min duration events

14. Rainfall Records Repeat for other durations –As duration increases, rainfall amount (in) goes up 15-min duration events

15. Rainfall Records Repeat for other durations –As duration increases, rainfall amount (in) goes up 20-min duration events

16. Rainfall Records Repeat for other durations –As duration increases, rainfall amount (in) goes up 40-min duration events

17. Rainfall Records Repeat for other durations –As duration increases, rainfall amount (in) goes up –As duration increases, rainfall intensity (in/hr) goes down –Eventually, will generate intensity-duration-return period “triples” –Common to plot contours of constant T r on intensity-duration plot

18. Rainfall Records Repeat for other durations –As duration increases, rainfall amount (in) goes up –As duration increases, rainfall intensity (in/hr) goes down –Eventually, will generate intensity-duration-return period “triples” –Common to plot contours of constant T r on intensity-duration plot

19. 1 hr Every 2 yrs, can expect more than 1.2 inches of rainfall in one hour

20. 1 hr Every 3 yrs, can expect more than 1.6 inches of rainfall in one hour

21. 1 hr Every 10 yrs, can expect more than 2.0 inches of rainfall in one hour

22. 1 hr Every 100 yrs, can expect more than 3.0 inches of rainfall in one hour Note similarity to seismic hazard curve, which showed return periods for exceeding different levels of ground shaking Low levels of rainfall intensity (or ground motion) are exceeded relatively frequently (short return period) High levels of rainfall intensity (or ground motion) are exceeded only rarely Note similarity to seismic hazard curve, which showed return periods for exceeding different levels of ground shaking Low levels of rainfall intensity (or ground motion) are exceeded relatively frequently (short return period) High levels of rainfall intensity (or ground motion) are exceeded only rarely

23. Rainfall Records Can use to plot rainfall maps 2-yr, 30-min rainfall 2-yr, 1-hr rainfall 100-yr, 30-min rainfall 100-yr, 1-hr rainfall

24. Rainfall Records Can use to plot rainfall maps 2-yr, 30-min rainfall Seattle0.3 in San Francisco0.8 in Houston2.0 in Boston0.9 in Chicago1.1 in

25. Rainfall Records Can use to plot rainfall maps 2-yr, 1-hr rainfall Seattle0.4 in San Francisco1.0 in Houston2.4 in Boston1.1 in Chicago1.5 in

26. Rainfall Records Can use to plot rainfall maps 100-yr, 30-min rainfall Seattle0.8 in San Francisco2.0 in Houston3.6 in Boston2.1 in Chicago2.2 in

27. Rainfall Records Can use to plot rainfall maps 100-yr, 1-hr rainfall Seattle1.0 in San Francisco2.5 in Houston4.6 in Boston2.8 in Chicago2.7 in

28. Slope Stability Analysis

29. Slope Stability Evaluation Involved, multi-disciplinary process (to do it right) Identification of problem  Maps – topographic and geologic Contours of planar surface

30. Slope Stability Evaluation Involved, multi-disciplinary process (to do it right) Identification of problem  Maps – topographic and geologic Ground moving down Ground moving up

31. Slope Stability Evaluation Involved, multi-disciplinary process (to do it right) Identification of problem  Maps – topographic and geologic

32. Slope Stability Evaluation Involved, multi-disciplinary process (to do it right) Identification of problem  Maps – topographic and geologic  Airphotos – stereo-paired photograph interpretation

33. Slope Stability Evaluation Involved, multi-disciplinary process (to do it right) Identification of problem  Maps – topographic and geologic  Airphotos – stereo-paired photograph interpretation Installation and observation of instrumentation  Survey monuments – benchmarks checked at regular intervals  Tiltmeters – placed on ground surface, structures to detect rotation  Inclinometers – measure lateral displacements in vertical hole

34. Slope Stability Evaluation Involved, multi-disciplinary process (to do it right) Field reconnaissance  Cracks in ground  Differences in vegetation  Seepage

35. Slope Stability Evaluation Involved, multi-disciplinary process (to do it right) Field reconnaissance  Cracks in ground  Differences in vegetation  Seepage  Hummocky terrain

36. Slope Stability Evaluation Involved, multi-disciplinary process (to do it right) Field reconnaissance  Cracks in ground  Differences in vegetation  Seepage  Hummocky terrain  Leaning trees  Displaced pipes, fences, etc.

37. Slope Stability Evaluation Involved, multi-disciplinary process (to do it right) Subsurface exploration  Geophysical methods (e.g., seismic refraction)

38. Slope Stability Evaluation Involved, multi-disciplinary process (to do it right) Subsurface exploration  Geophysical methods (e.g., seismic refraction)  Drilling and sampling

39. Slope Stability Evaluation Involved, multi-disciplinary process (to do it right) Subsurface exploration  Geophysical methods (e.g., seismic refraction)  Drilling and sampling Evaluation of soil properties  Field testing – insitu strength measurement

40. Slope Stability Evaluation Involved, multi-disciplinary process (to do it right) Subsurface exploration  Geophysical methods (e.g., seismic refraction)  Drilling and sampling Evaluation of soil properties  Field testing – insitu strength measurement  Laboratory testing – direct shear, triaxial, etc.

41. Slope Stability Evaluation Involved, multi-disciplinary process (to do it right) Subsurface exploration  Geophysical methods (e.g., seismic refraction)  Drilling and sampling Evaluation of soil properties  Field testing – insitu strength measurement  Laboratory testing – direct shear, triaxial, etc Stability analysis  Identify (idealize) problem geometry  Identify (idealize) strength properties  Identify (idealize) loading conditions Perform analyses

42. Slope Stability Evaluation Involved, multi-disciplinary process (to do it right) Evaluation/interpretation of results  Recommendations - Allowable slope angles, heights, rates of construction - Required soil improvement  Decisions - Consequences of failure - Methods of remediation - Cost of remediation

43. Slope Stability Analysis Requires comparison of capacity and demand Capacity – measure of resistance to significant downslope deformation Demand – measure of loading causing downslope deformation All methods are based on equilibrium analysis Potentially unstable zone treated as free body Evaluate driving (destabilizing) forces or stresses Evaluate resisting (stabilizing) forces or stresses Express “state” of stability, most commonly in terms of FS = Resisting force Driving force

44. Slope Stability Analysis Requires comparison of capacity and demand Capacity – measure of resistance to significant downslope deformation Demand – measure of loading causing downslope deformation All methods are based on equilibrium analysis Potentially unstable zone treated as free body Evaluate driving (destabilizing) forces or stresses Evaluate resisting (stabilizing) forces or stresses Express “state” of stability, most commonly in terms of FS = Resisting force Average available shear strength Driving force Average shear stress required for equilibrium =

45. Slope Stability Analysis Limit equilibrium analyses used Assumes material above failure surface is rigid Assumes elastic-perfectly plastic behavior No deformation required to mobilize strength No loss of strength with increasing deformation  Displacement

46. Slope Stability Analysis Limit equilibrium analyses used Consider infinite slope in frictional soil b z    W N T Sliding surface

47. Slope Stability Analysis Limit equilibrium analyses used Consider infinite slope in frictional soil b z    W N T For equilibrium, W N T W =  bz N = W cos  =  bz cos  T = W sin  =  bz sin  

48. Slope Stability Analysis Limit equilibrium analyses used Consider infinite slope in frictional soil b z    W N T For equilibrium, W N T  Driving force F D = W sin  =  bz sin  Resisting force F R = N tan  =  bz cos  tan 

49. Slope Stability Analysis Limit equilibrium analyses used Consider infinite slope in frictional soil b z    W N T For equilibrium, W N T  FS = FRFR FDFD =  bz sin   bz cos  tan  tan  tan  =

50. Slope Stability Analysis Limit equilibrium analyses used Consider infinite slope in general soil z  zwzw c,  sat mm Seepage forces

51. Slope Stability Analysis Limit equilibrium analyses used For more general conditions

52. Slope Stability Analysis Limit equilibrium analyses used For more general conditions

53. Slope Stability Analysis Limit equilibrium analyses used For more general conditions

54. Slope Stability Analysis Limit equilibrium analyses used For more general conditions WjWj NjNj TjTj EjEj VjVj V j+1 E j+1 Repeat for N slices Write equations for equilibrium of each slice (force and moment) Write equations for overall equilibrium (force and moment) Solve system of equations, and compute FS j th slice

55. Slope Stability Analysis Limit equilibrium analyses used For more general conditions Compute FS values for multiple potential failure surfaces

56. Slope Stability Analysis Limit equilibrium analyses used For more general conditions Compute FS values for multiple potential failure surfaces Identify critical failure surface – one with lowest FS

57. Slope Stability Analysis How well do we know the parameters that go into a slope stability analysis? Cohesion, c Water table depth, z w Unit weights,  m,  sat,  b Friction angle,  Slope angle,  Depth of failure surface, z COV ~ 0.3 Varies case-by-case COV ~ 0.05 COV ~ 0.1 Varies case-by-case

58. Slope Stability Analysis How does the uncertainty in these inputs affect the factor of safety? FS = f (c, z w, z,  m,  b,  sat, ,  ) Y = f (X) = f (x 1, x 2, x 3, …, x N )

59. Slope Stability Analysis How does the uncertainty in these inputs affect the factor of safety? Expand Y as Taylor series blah, blah, blah … where all partial derivatives are taken at means

60. Slope Stability Analysis How does the uncertainty in these inputs affect the factor of safety? In vicinity of mean, (X i -  Xi ) will be small, so squares, cubes, higher powers will be very small. If we ignore them, i.e., keep only the first- order terms, then From this, we can show that

61. Slope Stability Analysis How does the uncertainty in these inputs affect the factor of safety? Separating out the variances (diagonal of covariance matrix),

62. Slope Stability Analysis How does the uncertainty in these inputs affect the factor of safety? What do we need? Mean value of each variable Standard deviation of each variable Correlation coefficients Gradients f XiXi ff XiXi

63. Slope Stability Analysis Shear strength of partially saturated soils Principle of effective stress  =  ’ + u Total stress Effective stress Porewater pressure

64. Slope Stability Analysis Shear strength of partially saturated soils Principle of effective stress Saturated soil

65. Slope Stability Analysis Shear strength of partially saturated soils Principle of effective stress Saturated soil

66. Slope Stability Analysis Shear strength of partially saturated soils Principle of effective stress Partially saturated soil Air Menisci

67. Slope Stability Analysis Shear strength of partially saturated soils Principle of effective stress Partially saturated soil

68. Slope Stability Analysis Shear strength of partially saturated soils Principle of effective stress Partially saturated soil Porewater suction Intergranular forces Zero total stress

69. Slope Stability Analysis Shear strength of partially saturated soils Principle of effective stress  =  ’ + u  = +  ’ + (-u) Total stress Effective stress Porewater pressure Negative porewater pressure (suction) associated with partial saturation can produce high effective stresses Since soil shear strength depends on effective stresses, soil can have high shear strength when partially saturated, even at shallow depths (where gravity-induced effective stresses are low) Saturation of partially saturated soil will reduce (or eliminate) porewater suction, causing effective stresses and strength to be reduced Negative porewater pressure (suction) associated with partial saturation can produce high effective stresses Since soil shear strength depends on effective stresses, soil can have high shear strength when partially saturated, even at shallow depths (where gravity-induced effective stresses are low) Saturation of partially saturated soil will reduce (or eliminate) porewater suction, causing effective stresses and strength to be reduced

70. Bedrock Root zone Unsaturated zone Saturated zone Bedrock Infinite Slope H

71. Bedrock Root zone Unsaturated zone Saturated zone Bedrock Precipitation Infinite Slope

72. Bedrock Root zone Unsaturated zone Saturated zone Bedrock Evapotranspiration Infinite Slope

73. Bedrock Root zone Unsaturated zone Saturated zone Bedrock Evapotranspiration Unsaturated flow Saturated flow Infinite Slope D

74. Shallow Sliding Critical saturated depth for triggering shallow (infinite slope) slide Actual saturated thickness, H(t), varies with time. Depends on … Intensity of rainfall Slope angle Permeability of soil and bedrock Root zone storage Evapotranspiration Temperature Hours of daylight (latitude, season) Vapor pressure (humidity)

75. Shallow Sliding Simple model for saturated zone thickness Instantaneous unit hydrograph time flow

76. Shallow Sliding Simple model for saturated zone thickness Instantaneous unit hydrograph time flow Rainfall intensity duration intensity Return period

77. Shallow Sliding Simple model for saturated zone thickness Permeability Slope angle

78. Shallow Sliding Thickness of soil changes with time – depends on … Age Topography (ridges, hollows) Bedrock weathering rate (rock type, groundwater conditions) Soil creep Simple model Initial thickness Thickening rate due to creep Weathering rate when D = 0 Weathering decay coefficient

79. Shallow Sliding Simple model Soil age (yrs) Soil thickness (m) no creep -0.05 cm/yr creep +0.05 cm/yr creep Rainfall is time-dependent, thickness of saturated zone is time- dependent, soil thickness is time-dependent, and uncertainty exists in all parameters and relationships

80. Shallow Sliding Preceding equations can be used with Monte Carlo approach to simulate many years of rainfall, infiltration, evapotranspiration, soil accumulation, etc. Steps: 1.Divide area of interest into grid of cells of known elevation East of Hamada city in Shimane Prefecture Triangles indicate grid cells with known historical instability

81. Shallow Sliding Preceding equations can be used with Monte Carlo approach to simulate many years of rainfall, infiltration, evapotranspiration, soil accumulation, etc. Steps: 1.Divide area of interest into grid of cells of known elevation 2.Set initial soil depth to nominal value 3.Compute change in soil thickness for Year 1 4.Compute rainfall for Year 1 (consistent with I-D-F model) 5.Compute maximum saturated depth, H max, for each cell 6.If H max > H cr, landslide occurs and soil depth reset to zero; otherwise, soil depth continues to increase 7.Repeat for each cell for Years 2, 3, 4, …, N

82. Shallow Sliding Results

83. Shallow Sliding Results Grayscale shading represents return period of landsliding in each cell. Dark shading indicates short return period – unstable areas Light shading indicates long return periods – relatively stable areas Can use analyses like these for siting purposes – avoid most unstable areas with structures, pipelines, transmission towers, etc.