Sensitivity Analysis of a Physically-based Landslide Model
From evaluating sensitivity to reporting probability
A Review of Project Goals
• Identify landslide susceptible areas on the watershed scale: zones with a low Stability Index (SI). • Evaluate the impacts of roads, structures, and vegetation on slope stability. • Develop recommendations for slide-prone locations and for the stabilization of open scars.
Infinite Slope Stability Model
D
Dw
W T
N f q
Infinite Slope Stability Model
(Hammond et al. 1992): FS = Cr + Cs + cos2q[rsg(D - Dw) + (rsg - rwg)Dw]tanf Drsgsinqcosq
Cr = Cohesion due to roots Cs = Cohesion due to soil q = Slope angle rs = Wet soil density rw = Density of Water
f = Angle of Internal Friction D = Depth below soil surface Dw = Depth below water table
SINMAP
Stability INdex MAPing (Pack, Tarboton, Goodwin)
Environment: ArcView extension Language: C and Avenue Theoretical basis: Infinite Plane Slope Stability Model Required Data: Digital Elevation Model, Parameter Calibration Regions, User-Defined Parameters Stochastic Element: Parameters are allowed to be uncertain following uniform distribution between specified limits
Why Perform Sensitivity Analysis?
1. Evaluate the precision required of future field measurements. 2. Assess the stability of model outcome • Report predictions in probabilistic terms
Implemented Formula
C + cosq[1 - min
FS =
(
R a T sinq ,1
) r]tanf
sinq
C = dimensionless Cohesion T = Transmissivity R = Rate of Recharge (steady state) r = density ratio (rw/rs) a = specific catchment area (flow calculated using D method)
Sensitivities of SINMAP UserDefined Parameters
• • • • Water input (R) = Rainfall*Throughfall Transmissivity(T) = Conductivity*Depth Flow Cohesion(C) = Sc / (Depth Failure*gsat) Angle of Internal Friction (f) = f(Porosity)
A Statistical Approach
c ~ N(m,s2) C n ~ N(m,s2) f log Ksat ~ N(m,s2) T rsat ~ N(m,s2) C Dflow = Dfailure ~ ?? T, C R = constant
Sensitivity Response
What constitutes sensitivity? •Changes in the global mean.
•Variability in FS at a range of selected points.
•Total number of grid cells that lie below the instability threshold.
Ksat
0.3
Angle of Friction
0.3
0.25
cohesive intercept
0.2 0.3 <1 1-1.25 1.25-1.5
<1 1-1.25
0.25
fractional change
0.2
0.15 0.3 0.1 0.25 0.05
change from bestbet
depth
0.25 0.2
0.15 0.1
Ksat and Angle of Friction 1.25-1.5
<1 1-1.25 100 1.25-1.5 <1 1-1.25
d 1s 2s d
0.05
-100
-50
0
d 2s 1s us us
0.2 0 0 0.15
0.45 0.4 0.35
fractional change b
t tb e
0.15 50 0.1
hf sd
d
hf sd
1.25-1.5
in
in
pl
m
m
in
pl
pl
0.1
0.3
es
0.05
us
us
us
us
-100
0.05
0.25 0.2 0.15
Deep
0 0 50 100
<1 1-1.25 1.25-1.5
Average Shallow
m
-50
0
0.1 0.05 0
sd sd 0 d d +1 s sd sd d .5 s +0 .2 5 -0 .2 5 +2 s .5 s -2 -1 d
+0
-0
Friction and Ksat
1 0.9 0.8 0.7
probability
<1 <1.25 <1.5
0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.2 0.4 0.6
0.8
1
fraction of watershed area
Assessment
1. Precision required of future field measurements. Ksat and f require careful measurement, while depth, bulk density, and soil cohesion (in non-cemented soils) can be estimated.
Assessment
2. Stability of model outcome The locations of zones of predicted instability are not sensitive to changes in calibration parameters. The fraction of total area predicted to be unstable, however, changes significantly at the outer range of cumulative parameter distribution.
Assessment
3. Reporting predictions in probabilistic terms Sensitivity Analysis has allowed us to generate an “Expected Probability of Failure” map. This is a considerable improvement over binary instability maps.
General Conclusions
• The SA was pursued in order to reveal the hidden instabilities of the model, and it does achieve this end. • Additionally, a rigorous SA gives the modeler insight to the variables that truly drive a model. • In this case the SA has become a useful component of results presentation, presenting the end-user with more complete information on landslide risk in the watershed.
Thank you