Rainfall Records

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Rainfall Records

• Professor Steve Kramer

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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
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Rainfall Records

• Rainfall also varies substantially within each
  year

Atlanta - wet years
Cleveland - wet summers
SF dry summers
LV dry years
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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

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Rainfall Records

• For a given rain gauge, list precipitation data
  from significant storms in N years

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Rainfall Records

• For a given rain gauge, list precipitation data
  from significant storms in N years

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Rainfall Records

• For a given rain gauge, list precipitation data
  from significant storms in N years

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Rainfall Records

• For a given rain gauge, list precipitation data
  from significant storms in N years

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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, m 10-min rainfall (in)
1 0.66
2 0.60
3 0.55
4 0.50

28 0.12
29 0.11
30 0.09
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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, m 10-min rainfall (in) Tr (yrs) ( N/m)
1 0.66 30.0
2 0.60 15.0
3 0.55 10.0
4 0.50 7.5

28 0.12 1.071
29 0.11 1.034
30 0.09 1.000
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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, m 10-min rainfall (in) Tr (yrs) ( N/m)
1 0.66 30.0
2 0.60 15.0
3 0.55 10.0
4 0.50 7.5

28 0.12 1.071
29 0.11 1.034
30 0.09 1.000
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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, m 10-min rainfall (in) Tr (yrs) ( N/m)
1 0.66 30.0
2 0.60 15.0
3 0.55 10.0
4 0.50 7.5

28 0.12 1.071
29 0.11 1.034
30 0.09 1.000
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
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Rainfall Records

• Repeat for other durations
• As duration increases, rainfall amount (in) goes
  up

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Rainfall Records

• Repeat for other durations
• As duration increases, rainfall amount (in) goes
  up

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Rainfall Records

• Repeat for other durations
• As duration increases, rainfall amount (in) goes
  up

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Rainfall Records

• Repeat for other durations
• As duration increases, rainfall amount (in) goes
  up

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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-retu
  rn period triples
• Common to plot contours of constant Tr on
  intensity-duration plot

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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-retu
  rn period triples
• Common to plot contours of constant Tr on
  intensity-duration plot

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1 hr
Every 2 yrs, can expect more than 1.2 inches of
rainfall in one hour
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1 hr
Every 3 yrs, can expect more than 1.6 inches of
rainfall in one hour
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1 hr
Every 10 yrs, can expect more than 2.0 inches of
rainfall in one hour
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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
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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
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Rainfall Records

• Can use to plot rainfall maps

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
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Rainfall Records

• Can use to plot rainfall maps

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
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Rainfall Records

• Can use to plot rainfall maps

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
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Rainfall Records

• Can use to plot rainfall maps

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
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Slope Stability Analysis
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Slope Stability Evaluation

• Involved, multi-disciplinary process (to do it
  right)
• Identification of problem
• Maps topographic and geologic

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Slope Stability Evaluation

• Involved, multi-disciplinary process (to do it
  right)
• Identification of problem
• Maps topographic and geologic

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Slope Stability Evaluation

• Involved, multi-disciplinary process (to do it
  right)
• Identification of problem
• Maps topographic and geologic

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Slope Stability Evaluation

• Involved, multi-disciplinary process (to do it
  right)
• Identification of problem
• Maps topographic and geologic
• Airphotos stereo-paired photograph
  interpretation

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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

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Slope Stability Evaluation

• Involved, multi-disciplinary process (to do it
  right)
• Field reconnaissance
• Cracks in ground
• Differences in vegetation
• Seepage

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Slope Stability Evaluation

• Involved, multi-disciplinary process (to do it
  right)
• Field reconnaissance
• Cracks in ground
• Differences in vegetation
• Seepage
• Hummocky terrain

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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.

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Slope Stability Evaluation

• Involved, multi-disciplinary process (to do it
  right)
• Subsurface exploration
• Geophysical methods (e.g., seismic refraction)

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Slope Stability Evaluation

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

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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

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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.

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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

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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

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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
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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
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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
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Slope Stability Analysis
Limit equilibrium analyses used Consider infinite
slope in frictional soil
W
T
N
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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
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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
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Slope Stability Analysis
Limit equilibrium analyses used Consider infinite
slope in frictional soil
W
T
N
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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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Slope Stability Analysis
Limit equilibrium analyses used For more general
conditions
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Slope Stability Analysis
Limit equilibrium analyses used For more general
conditions
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Slope Stability Analysis
Limit equilibrium analyses used For more general
conditions
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Slope Stability Analysis
Limit equilibrium analyses used For more general
conditions
jth slice
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
Vj
Ej
Ej1
Wj
Vj1
Tj
Nj
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Slope Stability Analysis
Compute FS values for multiple potential failure
surfaces
Limit equilibrium analyses used For more general
conditions
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Slope Stability Analysis
Compute FS values for multiple potential failure
surfaces Identify critical failure surface one
with lowest FS
Limit equilibrium analyses used For more general
conditions
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Slope Stability Analysis
How well do we know the parameters that go into a
slope stability analysis?
Cohesion, c Water table depth, zw Unit weights,
gm, gsat, gb Friction angle, f Slope angle,
b Depth of failure surface, z
COV 0.3 Varies case-by-case COV 0.05 COV
0.1 Varies case-by-case Varies case-by-case
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Slope Stability Analysis
How does the uncertainty in these inputs affect
the factor of safety?
FS f (c, zw, z, gm, gb, gsat, b, f)
Y f (X) f (x1, x2, x3, , xN)
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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
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Slope Stability Analysis
How does the uncertainty in these inputs affect
the factor of safety?
In vicinity of mean, (Xi-mXi) 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
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Slope Stability Analysis
How does the uncertainty in these inputs affect
the factor of safety?
Separating out the variances (diagonal of
covariance matrix),
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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
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Slope Stability Analysis
Shear strength of partially saturated
soils Principle of effective stress s
s u
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Slope Stability Analysis
Shear strength of partially saturated
soils Principle of effective stress
Saturated soil
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Slope Stability Analysis
Shear strength of partially saturated
soils Principle of effective stress
Saturated soil
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Slope Stability Analysis
Shear strength of partially saturated
soils Principle of effective stress
Partially saturated soil
Air
Menisci
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Slope Stability Analysis
Shear strength of partially saturated
soils Principle of effective stress
Partially saturated soil
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Slope Stability Analysis
Shear strength of partially saturated
soils Principle of effective stress
Partially saturated soil
Porewater suction
Zero total stress
Zero total stress
Intergranular forces
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Slope Stability Analysis

• Shear strength of partially saturated soils
• Principle of effective stress
• s u
• 0 s (-u)

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
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Infinite Slope
Root zone
Unsaturated zone
Saturated zone
H
Bedrock
Bedrock
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Infinite Slope
Precipitation
Root zone
Unsaturated zone
Saturated zone
Bedrock
Bedrock
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Infinite Slope
Evapotranspiration
Root zone
Unsaturated zone
Saturated zone
Bedrock
Bedrock
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Infinite Slope
Evapotranspiration
Root zone
Unsaturated zone
Saturated zone
Unsaturated flow
Saturated flow
Bedrock
Bedrock
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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
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Shallow Sliding
Simple model for saturated zone thickness
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Shallow Sliding
Simple model for saturated zone thickness
Instantaneous unit hydrograph
Rainfall intensity
flow
intensity
Return period
time
duration
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Shallow Sliding
Simple model for saturated zone thickness
Permeability
Slope angle
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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
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Shallow Sliding
0.05 cm/yr creep
Soil thickness (m)
no creep
-0.05 cm/yr creep
Simple model
Soil age (yrs)
Rainfall is time-dependent, thickness of
saturated zone is time-dependent, soil thickness
is time-dependent, and uncertainty exists in all
parameters and relationships
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Shallow Sliding

• Preceding equations can be used with Monte Carlo
  approach to simulate many years of rainfall,
  infiltration, evapotranspiration, soil
  accumulation, etc.
• Steps
• 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
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Shallow Sliding

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

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Shallow Sliding
Results
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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.