Terrain Stability Mapping Using the
ArcView SINMAP extension
David G Tarboton, Robert T Pack,
Craig N Goodwin
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Acknowledgements
The SINMAP software was developed
through a collaboration of Terratech
Consulting Ltd., Utah State University,
and Canadian Forest Products.
Funding was provided by Forest Renewal
B.C., Canada.
Key points
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An example of the combination of
GIS and engineering analysis.
Hydrology, Geology, Geomorphology
and Geotechnical Engineering.
Extendibility of ArcView.
Programming to provide integration
of modeling into ArcView.
Key points continued
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Synthesis of GIS based digital elevation
data with field observations.
Interactive calibration to combine fitting
to data with engineering judgement.
Recognition of parameter uncertainty
through probability distributions.
Free – In the public domain at
http://www.engineering.usu.edu/dtarb
Outline
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The Problem
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Theory
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Inputs and Outputs
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Implementation
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Demonstration
The Problem
Norrish Watershed, BC.
Norrish Watershed, BC.
SINMAP Does:
Geographic Information System Based
Mapping of Slope Stability with Uncertain
Parameters
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Is based on an objective physical model
Can be quantitative or qualitative
Is expressed in terms of stability indices
Can be combined with geomorphic and
statistical analysis
Where is it Used
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Forest and watershed management,
forestry and forest engineering.
Determine volume of harvestable
timber in annual allowable cut
calculations.
Better plan timber development to
minimize occurrence of landslides and
resulting impacts.
Lardeau Creek, BC
Contour Map
Slope Map
22.5°- 33°
33°- 45°
0 - 22.5°
Specific Catchment Area Map
The first SINDEX map
The SINMAP Formulation
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Based on the Infinite Plane Slope Stability model
with wetness (pore pressure) obtained from a
topographically based steady state hydrology model
(e.g. Montgomery and Dietrich, 1994, WRR p1153)
Uses Grid DEM data format
Spatial distributions rely on shallow subsurface
groundwater flow convergence and topographic
slope
Parameter uncertainty incorporated through ranges
of soil and hydrology parameters
Limitations
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Applies only to shallow transitional landsliding
controlled by shallow groundwater flow convergence.
Not applicable to deep seated instability such as
deep earthflows or rotational slumps.
Maps potential landslide initiation zones - not runout
or hazard areas.
Constrained by DEM resolution.
Theoretical Basis
Infinite Plane Slope Stability Model
h
D
hw
Dw
 = atan S
Factor of safety
1. Relative Wetness
C  cos  [1  wr ] tan 
FS 
sin 
where
Dw
Ra 

w
 Min 
,1
D
 T sin  
2. Dimensionless Cohesion C  (Cr  Cs ) /(hs g)
Density Ratio
r   w / s
(assumed a constant of 0.5)
1. Relative Wetness Defined
Specific catchment area a [m2/m  m]
(per unit coutour length)
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Slope angle 
D
q
.
Dw
Assumes lateral depth integrated flux
q is proportional to specific catchment
area a
q = R·a
[L2/T]
Soil transmission capacity = T·sin 
where T is the soil transmissivity and
 is the topographic slope
“Relative Wetness” is defined as
W = Min{(R·a / T·sin ),1}
Specific Catchment Area “a”
Upslope catchment area divided by unit contour width
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AREA 2
3
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AREA 1
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12
Uses GRID structure
Calculated for each
grid cell
Grid cell size depends
on original DEM grid
cell size
Expressed as the
variable “a” with units
of m2/m  m
The D Algorithm
Steepest direction
downslope
Proportion flowing to
neighboring grid cell 3
is 2/(1+2)
Proportion
flowing to
neighboring
grid cell 4 is
1/(1+2)
3
4
2
1
2
Flow
direction.
5
1
6
8
7
Tarboton, D. G., (1997), "A New Method for the Determination of Flow Directions and
Contributing Areas in Grid Digital Elevation Models," Water Resources Research,
33(2): 309-319.) (http://www.engineering.usu.edu/cee/faculty/dtarb/dinf.pdf)
Specific catchment area a is the upslope area per unit
contour length [m2/m  m]
2. Dimensionless Cohesion Defined
(includes both soil and root effects)
h
Combined Cohesion
Cr+Cs [N/m2]
(independent of soil
thickness)
h
Soil weight
h s g [N/m2]
Dimensionless cohesion is the cohesive restoring force
relative to soil weight [C = (Cr+Cs)/(h s g)], illustrated
here on a vertical face to remove the effect of the
normal and friction forces.
Topographic Slope “” Defined
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SLOPE 2
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SLOPE 1
Uses GRID structure
Calculated for each
grid cell
Expressed as the
variable  with angle
units in radians or
degrees
Example slope map
Area-Slope Plot
FS > 1
w=1
FS < 1
Stable,
Saturated
Unstable
FS > 1
w<1
Stable,
Unsaturated
But
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Soil parameters, C, , T are uncertain and spatially
variable.
Recharge parameter R is spatially and temporally
variable.
Assume Uniform Probability Distributions
C ~ U(C1, C2)
R/T ~ U(x1, x2)
tan ~ U(t1, t2)
range
P
C1
C2
Definition of Stability Index SI
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SI = Prob(FS > 1)
If FS > 1 using most conservative
end of each parameter range
SI = FS
A
r
e
a
10 50 10 50 50
Area-Slope plot with uncertainty
Most conservative
parameter limits
Most destabilizing
parameter limits
R
e
g
i
o
n
1
.
S
a
t
u
r
a
t
e
d
SI = Prob(FS >1)
R
e
g
i
o
n
2
.
M
i
x
e
d
S
a
t
/
U
n
s
a
t
FS < 1
for all possible
parameters
SI = 0
FS* > 1
SI = FS*
*(using most
conservative end of
each parameter
range)
R
e
g
i
o
n
3
.
U
n
s
a
t
u
r
a
t
e
d
0 .00 .51 .01 .52
S l ope
SI derived analytically for each region
in Slope vs Contributing Area plot
e.g. for region 2
SI  1 

x 2 a / sin   1
C
C
cos (1  r ) t1 cos (1  r ) t1
F2s ( 1 , 2 ,
,
,1)
x 2 a / sin   x1a / sin 
sin  sin 
sin 
sin 
1  x1a / sin 
C
C
cos 
a
F3s ( 1 , 2 ,
(1  x 2
),
x 2 a / sin   x1a / sin 
sin  sin  sin 
sin 
cos 
a
(1  x1
), t1 , t 2 ;1)
sin 
sin 
Stability Class Definitions
Condition
Class
Predicted State
SI > 1.5
1
Stable slope zone
1.5 > SI > 1.25
2
1.25 > SI > 1.0
3
1.0 > SI > 0.5
4
0.5 > SI > 0.0
5
0.0 > SI
6
Moderately stable
zone
Quasi-stable slope
zone
Lower threshold
slope zone
Upper threshold
slope zone
Defended slope
zone
Parameter Range
Range cannot model
instability
Range cannot model
instability
Range cannot model
instability
Pessimistic half of range
required for instability
Optimistic half of range
required for stability
Range cannot model
stability
Possible Influence of Factors
Not Modeled
Significant destabilizing factors are
required for instability
Moderate destabilizing factors are
required for instability
Minor destabilizing factors could
lead to instability
Destabilizing factors are not
required for instability
Stabilizing factors may be
responsible for stability
Stabilizing factors are required for
stability
Summary of SINMAP Inputs
Topography (dictated by DEM)
a - specific catchment area
θ - slope angle
Soil Parameters (given as a range)
C - dimensionless cohesion
tan Φ- tan of soil internal friction angle
R/T - soil hydraulic parameter
Summary of SINMAP Outputs
1. Specific Catchment Area Map
2. Stability Index Map
3. Soil Wetness Map
4. Calibration Plot
5. Statistical Tables
Stability Index Map
Soil Wetness Map
Calibration Plot
SI = minimum
safety factors
SI indicates lower than average potential instability
SI indicates higher than average potential instability
SI < 0 indicates instability
Possibly Saturated
Slope-Area plot interactive calibration
Percentage of Average Landslide Density
1000.0%
Percentage of Average
900.0%
Kilpala
Rose
Burnt River
800.0%
700.0%
600.0%
500.0%
400.0%
300.0%
200.0%
100.0%
0.0%
Stable
Moderately
Stable
QuasiStable
Lower
Upper
Defended
Threshold Threshold
Stability Class
Implementation Exploiting ArcView 3.2
Extendability
Customization of the Graphical User
Interface
• Avenue Script Programming Language
• Core computations in C++ DLL for speed
and supportability
• Access ESRI grid data using grid
application programmers interface
(GRIDIO)
• Result: Tight integration between
hydrologic modeling and GIS
Conclusions
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Extended the infinite plane slope
stability model with topographically
based wetness to account for parameter
uncertainty.
Successfully mapped potentially
unstable terrain. 56% of landslides in
8.5% of area classified as “upper
threshold”.
Implementation is an interactive ArcView
© extension, named SINMAP.
Available from
http://www.engineering.usu.edu/dtarb/
Are there any questions ?
AREA 2
3
AREA 1
12
Demo of the Software