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Rainfall Records

Rainfall Records. Professor Steve Kramer. 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 + s. Mean. Mean - s. Rainfall Records.

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Rainfall Records

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  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 + s Mean Mean - s

  3. Rainfall Records • Rainfall also varies substantially within each year Atlanta - wet years Cleveland - wet summers SF – dry summers LV – dry 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 7 For a given rain gauge, list precipitation data from significant storms in N years

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

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

  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)

  10. Rainfall Records Every 30 years, on average, we can expect to see more than 0.66 inches of rainfall in a 10-min period of time • Choose a particular duration (say 10 min) • List maxima for all storms in order of decreasing rainfall (most intense 10 min for each)

  11. Rainfall Records Every 15 years, on average, we can expect to see more than 0.60 inches of rainfall in a 10-min period of time • Choose a particular duration (say 10 min) • List maxima for all storms in order of decreasing rainfall (most intense 10 min for each)

  12. Rainfall Records 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 • Choose a particular duration (say 10 min) • List maxima for all storms in order of decreasing rainfall (most intense 10 min for each)

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

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

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

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

  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 Tr 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 Tr 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

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

  24. Rainfall Records 2-yr, 30-min rainfall Seattle 0.3 in San Francisco 0.8 in Houston 2.0 in Boston 0.9 in Chicago 1.1 in Can use to plot rainfall maps

  25. Rainfall Records 2-yr, 1-hr rainfall Seattle 0.4 in San Francisco 1.0 in Houston 2.4 in Boston 1.1 in Chicago 1.5 in Can use to plot rainfall maps

  26. Rainfall Records 100-yr, 30-min rainfall Seattle 0.8 in San Francisco 2.0 in Houston 3.6 in Boston 2.1 in Chicago 2.2 in Can use to plot rainfall maps

  27. Rainfall Records 100-yr, 1-hr rainfall Seattle 1.0 in San Francisco 2.5 in Houston 4.6 in Boston 2.8 in Chicago 2.7 in Can use to plot rainfall maps

  28. Slope Stability Analysis

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

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

  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. Perform analyses 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

  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. Resisting force FS = Driving force 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

  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 Resisting force Average available shear strength FS = = Driving force Average shear stress required for equilibrium

  45. t Displacement 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

  46. b b z g, f Sliding surface Slope Stability Analysis • Limit equilibrium analyses used • Consider infinite slope in frictional soil W T N

  47. For equilibrium, T b b W N b z g, f Slope Stability Analysis • Limit equilibrium analyses used • Consider infinite slope in frictional soil W W = gbz N = W cos b = gbz cos b T = W sin b = gbz sin b T N

  48. For equilibrium, T b b W N b z g, f Slope Stability Analysis • Limit equilibrium analyses used • Consider infinite slope in frictional soil W T • Driving force • FD = W sin b = gbz sin b • Resisting force • FR = N tan f = gbz cos b tan f N

  49. For equilibrium, T b b W N b z g, f gbz cos b tan f = gbz sin b FR tan f FS = = FD tan b Slope Stability Analysis • Limit equilibrium analyses used • Consider infinite slope in frictional soil W T N

  50. Slope Stability Analysis • Limit equilibrium analyses used • Consider infinite slope in general soil b zw c, f, gsat gm z Seepage forces

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