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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
751
DOI: 10.4408/IJEGE.2011-03.B-082
THE 2005 LA CONCHITA LANDSLIDE, CALIFORNIA:
PART 2 - MODELING
P
aRmesHwaR
L. SHRESTHA
(*)
, P
HiliP
J. SHALLER
(**)
, m
aCan
DOROUDIAN
(***)
,
David W. SYKORA
(****)
& d
ouGlas
L. HAMILTON
(*****)
(*)
Institute of Mountain Risk Engineering, University of Natural Resources and Life Sciences, Vienna, Austria
(**)
Grup d’Allaus (RISKNAT), Dept. Geodinàmica i Geofisica, Fac. de Geologia, Universitat de Barcelona, Spain
(***)
Institute of Mountain Hazards and Environmnent, Chinese Academy of Sciences and Ministery of Water Ressources, Chengdu, China
(****)
Mechanics College, Southwest Jiao Tong University, Chengdu, China
(*****)
Swiss Federal Institute for Forest, Snow and Landscape Research WSL, Birmensdorf, Switzerland
viscosity by ± 20% had a minor effect on the extent
of debris flow runout. Sensitivity analyses were also
performed by varying the debris volume by one-half
and 1.5 times the original volume. Model results show
a significant difference in debris runout as a result of
these inputs. Two lobes of debris formed during the
transport phase. The spatial distribution of the main
lobe of the debris flow was similar to actual conditions
in all of the simulations performed. The spatial distri-
bution of the minor lobe, however, generally differed
from that predicted by the analysis.
K
ey
words
: Debris flow, Landslide, FLO-2D, Numerical mo-
deling, La Conchita
INTRODUCTION
Debris flows are very viscous hyperconcentrated
sediment-laden flows that are non-homogenous, tran-
sient, and exhibit non-Newtonian behaviour. Prop-
erties such as density, viscosity and yield stress are
functions of the sediment concentration in the sedi-
ment-water mixture. The high viscosity of debris flow
results in slow velocities as compared to water flow on
the same slope. The yield stress, which is a measure
of the internal fluid resistance to flow, will affect both
flow initiation and cessation. FLO-2D has the capa-
bility to simulate many of the complex behaviours of
debris flow, and has been used to model debris flows
at various sites (flo-2d u
seRs
m
anual
, 2007).
A two-dimensional finite difference model (FLO-
ABSTRACT
This is Part II of a two-part causation analysis of
the January 10, 2005 La Conchita landslide. This paper
describes the development and application of a two-
dimensional finite difference model (FLO-2D) model
to simulate the debris flow over a fixed substrate. The
model domain consisted of 25,614 square grid cells,
each measuring 1.52 m on a side, and was developed
using digitized pre- and post-event topographic maps.
An inflow hydrograph, representing the volume of
displaced material, was specified as a line input at the
base of the headscarp area. The sediment concentra-
tion in the input hydrograph was varied (from zero to
0.7) over the 14-second duration of the hydrograph.
Samples of debris collected from test pits in the debris
flow provided a saturated density of 1,762 kg m-3. An
initial estimate of the yield stress (stress) of the debris
of 5,257 Pa was calculated using parameters derived
from pre- and post-event topographic maps of the
area. Because no independent means of calculation
was available, the dynamic viscosity of the debris was
adopted from values contained in the FLO-2D Users
Manual. The Manning’s bottom roughness coefficient
for each grid cell was based on estimates of the sur-
face and vegetation characteristics of the area. A series
of simulations were performed to evaluate travel path
variations for three differing wall and slope configura-
tions present in the area between 1995 and 2005. Sen-
sitivity analyses performed for each of the simulations
by varying the yield stress (strength) and dynamic
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P.L. SHRESTHA, P.J. SHALLER, M. DOROUDIAN, D.w. SYkORA, & D.L. HAMILTON
752
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
grid boundary. The flow velocity across the bound-
ary is computed from the solution of the momentum
equation. The time step is limited by the Courant-Frie-
drich-Lewy (CFL) criterion for numerical stability.
For debris flows, the total friction slope in equa-
tion (2) is modified as follows:
where S
f
= total friction slope (S
fx
); S
y
= yield slope; S
v
= viscous slope; and S
td
= turbulent-dispersive slope.
Equation (3) can be written in the following form:
where τ
y
= yield stress; γ
m
= specific weight of the de-
bris flow mixture = γ
w
+ C
v
s
– γ
w
); C
v
= sediment
concentration by volume; γs = specific weight of sedi-
ment; γw = specific weight of water; K = resistance
parameter for laminar flow; η = dynamic viscosity; V
= depth-averaged velocity; and n
td
= flow resistance
(i.e., equivalent Manning’s n-value) of the turbulent
and dispersive shear stress components.
The dynamic viscosity (η) and yield stress (τ
y
) are
functions of the sediment concentration, and are ex-
pressed as follows:
where α
1
, α
2
, β
1
, and β
2
are empirical coefficients de-
termined from laboratory experiments (o’b
Rien
&
J
ulien
, 1988). The FLO-2D Users Manual (2007) pro-
vides a library of dynamic viscosity and yield stress
that can be used if these values cannot be independ-
ently established.
The assumptions and limitations of the FLO-2D
model include (FLO-2D Users Manual, 2007): (1)
steady flow for the duration of the time step; (2) hy-
drostatic pressure distribution; (3) hydraulic rough-
ness is based on steady, uniform flow; (4) grid ele-
ments are represented by single values for elevation,
flow depth, and Manning’s roughness; (5) channel
elements are represented by uniform channel geom-
etry and roughness; and (6) rapidly-varying flows are
not simulated.
2D Version 2006.01) was utilized to simulate the La
Conchita landslide as a debris flow. The FLO-2D
model is a commercial software package that was de-
veloped originally in 1988 to conduct a Federal Emer-
gency Management Agency (FEMA) flood insurance
study (FIS) of an urbanized alluvial fan in Colorado
(flo-2d u
seRs
m
anual
, 2007). The model imple-
ments the Diffusive Hydrodynamic Model (DHM)
of H
Romadka
& y
en
(1987) to predict the spatial
and temporal values of the attributes such as the flow
depth and velocity at each grid element. The software
package includes a grid developer system (GDS) that
interpolates elevations from digital elevation model
(DEM) data onto a square grid system; and a post-
processor program (MAPPER) that depicts the model
results as two- and three-dimensional graphical output
and animation of results.
MODEL DESCRIPTION
FLO-2D is a volume conservation model that sim-
ulates overland flow in eight directions. The flow is
controlled by topography and resistance to flow. The
governing equations include the equations for con-
servation of fluid volume and the dynamic wave mo-
mentum equations. For completeness, the equations
are summarized below. The reader is referred to the
FLO-2D u
seR
m
anual
(2007) and J
ulien
& o’b
Rien
(1997) for a more detailed description of the model
features and computational procedure.
Continuity equation:
Momentum equation:
where h = flow depth; V
x
= depth-averaged velocity
component; i = excess rainfall intensity; S
fx
= friction
slope based on Manning’s equation; S
ox
= bed slope;
the other terms represent the pressure gradient, the
convective acceleration, and local acceleration terms.
The above equations are solved with a central, finite
difference scheme. The computational procedure in-
volves computation of discharge across each of the
boundaries in the eight potential flow directions and
begins with a linear estimate of the flow depth at the
(1)
(2)
(3)
(4)
(5)
(6)
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THE 2005 LA CONCHITA LANDSLIDE, CALIFORNIA: PART 2 - MODELING
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
753
areas (Fig. 2). The high resolution unit grid cell size
was selected to provide the level of detail required to
resolve the key issues related to the study. Once the
topographic elevations were rendered onto the grid el-
ements, the height of the temporary wall was entered
manually based on as-built drawings of the structure.
INFLOw HYDROGRAPH
The inflow hydrograph represents one of the key
pieces of input data for model simulations. For flood
events, the inflow hydrograph represents the discharge
entering the model domain through the inflow grids.
For simulation of debris flows, the volumetric sedi-
ment concentration is introduced as an additional in-
put. The sediment concentration may be varied over
the duration of the inflow hydrograph.
Four key elements were required to generate the
inflow hydrograph for simulating the La Conchita
event: 1) the volume of water and sediment; 2) the du-
ration of the hydrograph; 3) the variation of sediment
concentration as a function of the simulation period;
and 4) the initial lateral distribution of debris emerg-
ing from the headscarp area.
The volume of debris input into the simulations
MODEL DEVELOPMENT
The key steps in the development of the FLO-2D
model for the La Conchita event included: construc-
tion of a model grid using digital terrain data and sup-
plementary elevation data for structures such as the
temporary wall; development of an inflow hydrograph
with corresponding volumetric sediment concentra-
tions; delineation of surface roughness (Manning’s n
value) for grid elements; and estimation of the weight,
dynamic viscosity and yield stress of the debris.
FLO-2D GRID
A model grid was created for the project site using
the GDS program. Topographic elevations were based
on the minimum topography resulting from the 2002
(pre-event) and 2006 (post-event) topographic maps
(Fig. 1). This topography was selected to represent
conditions experienced by the majority of the debris
flow that occurred over the simulation period. The
model domain consisted of 25,615 1.52 m square grid
cells that cover the source and potential debris runout
Fig. 1 - Topographic map of the 2005 La Conchita land-
slide showing elevation differences reported in
2002 (pre-event) and 2006 (post-event) topo-
graphic maps. Areas of net accumulation and net
depletion are shown in red and blue, respectively.
The gray shaded area near the toe of the deposit
was modified by grading activities in the immedi-
ate aftermath of the event
Fig. 2 - The limits of the FLO-2D model grid, with the lo-
cation of the input grid cells, and the spatial dis-
tribution of the surface roughness (Manning’s n)
values
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P.L. SHRESTHA, P.J. SHALLER, M. DOROUDIAN, D.w. SYkORA, & D.L. HAMILTON
754
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
the toe of the upper depletion area. Based on the surface
topography in this area, it was assumed that the initial
landslide accelerated from rest to ~10 m s
-1
The dense, coherent appearance of the moving
debris captured on video implies that the debris flow
had a very high sediment concentration. Based on
suggested parameters contained in the FLO-2D u
seRs
m
anual
(2007), the sediment concentration in the in-
put hydrograph was therefore rapidly increased from
a value of zero to 0.5, then ramped up more slowly to
a peak value of 0.7 over the 14-second duration of the
hydrograph as shown in Figure 3.
The upper zone of depletion exhibits a spoon-like
shape, indicating that the debris did not exhibit a uni-
form lateral distribution at the initiation of the event.
This geometric effect was modeled by subdividing
the source area into seven parallel chutes (Fig. 4),
with each of the 1-7 chutes supplying 2%, 8%, 14%,
26.5%, 24%, 18%, and 7.5% of the total debris vol-
ume, respectively. The input from each of the seven
chutes was distributed between four grid cells. For
example, as shown in Figure 3, Cells 1-4 represent the
four grid cells for chute 1.
was taken as the total volume of both the upper and
lower depletion zones, since this represented the ulti-
mate mass of debris moved in the event. This volume
was added into the inflow hydrograph and input into
the model along a series of 28 inflow grid cells distrib-
uted across the upper zone of depletion. The input grid
cells were placed at a central location within the upper
depletion zone to average out the effects created by the
distributed nature of the debris in the source landslide.
Evidence from the television videotape indicates
that the debris flow was moving as fast as ~10 m s
-1
near
Fig. 3 - Inflow hydrograph and volumetric sediment con-
centration used for the FLO-2D simulations
Fig. 4 - Shaded relief map of the 2005 La Conchita land-
slide. Black dots show approximate locations of
main lobe lateral levees; 107 m radius circle in-
dicates radius of curvature of levees. Transverse
sections a-a’ and b-b’ show locations of profiles
used for superposition calculations. Numbered
area at top of page shows subdivision of head-
scarp area used for input hydrograph calcula-
tions. Tw indicates location of temporary wall
Fig. 5 - Dynamic viscosity (top) and yield stress (bottom)
relationships adopted for the FLO-2D simulations
plotted against literature values reported in the
FLO-2D U
SerS
m
ANuAl
(2007)
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THE 2005 LA CONCHITA LANDSLIDE, CALIFORNIA: PART 2 - MODELING
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
755
SURFACE ROUGHNESS
Examination of the 2002 aerial photography for
land cover indicated that a variety of surface roughness
values (Manning’s n) were appropriate for input to the
FLO-2D simulations. As shown on Fig. 2, roughness
values ranging from 0.016 to 0.25 were used in the
analysis. Low surface roughness values were used for
streets in the development (0.016) and to model the
portion of the headscarp area located downslope from
the inflow grid cells (0.02). High roughness values
were added for the residential area (0.2) and for the
area of dense chaparral located just upslope (0.25).
Intermediate values (0.05) were used for the remain-
der of the undeveloped slope area, which supported a
moderate vegetation cover.
MODELING OF TEMPORARY wALL
Three cases were considered to model the poten-
tial effects of the temporary wall on the debris flow.
The first was to run the simulation with the wall as
it existed prior to the failure (termed “With Wall”).
Because there is no mechanism within FLO-2D to
simulate the destruction of a structure, this simulation
case assumes that the wall exhibits infinite stress. In
the second case, the FLO-2D grid was manually mod-
ified to remove the topographic effect of the wall in
areas where it was observed to have been overtopped
and/or breached by the debris flow (termed “Breached
Wall”). Elsewhere the wall continued to be treated as
if it exhibited infinite stress. In the third case, the FLO-
2D grid was modified to remove the temporary wall
entirely and restore the topography present before the
construction of the wall (termed “Without Wall”). A
1996 topographic map was utilized to establish the to-
pography of the area to the earlier, pre-wall condition.
DISCUSSION OF MODEL RESULTS
GENERAL OBSERVATIONS
Figure 6 presents the results of the base-line FLO-
2D simulations for the three cases. The three simula-
tions consistently predict the formation of a large main
(eastern) lobe, a smaller, more irregular minor (west-
ern) lobe, and a finger of material filling the pre-exist-
ing drainage channel in the mid-slope area.
MAIN (EASTERN) LOBE
The three base-line simulations predict very simi-
lar behavior for the main (eastern) lobe of the debris.
MATERIAL PROPERTIES
UNIT wEIGHT
Samples of debris collected from test pits in the
western lobe of the debris flow were tested to assess
the moisture content and dry density of this material.
These results were used to estimate a saturated density
of 1,762 kg m
-3
for the debris at the time of the event.
This value was used in all subsequent calculations.
DYNAMIC VISCOSITY
Because no independent means was available to
estimate the dynamic viscosity of the debris, an inter-
mediate value was adopted from values contained in
the FLO-2D u
seRs
m
anual
(2007). The dynamic vis-
cosity parameters α
1
and β
1
shown in equation (5) were
assigned values of 0.000602 and 22.5, respectively.
Figure 5 shows a comparison of the dynamic viscosity
using the above α
1
and β
1
values with other published
values from the FLO-2D u
seRs
m
anual
(2007).
YIELD STRESS
An initial estimate of the yield stress of the debris
was calculated using parameters derived from the pre-
and post-event topographic maps of the area by means
of the following relationship (J
oHnson
, 1970):
τ= T
c
γ
d
sin δ
where τ = yield stress (Pa); T
c
= critical thickness (m);
γ
d
= unit weight of debris (kg m
-3
); and δ = slope angle
(degrees).
The yield stress of the debris flow was calculated
for each 1.52 m grid in the zone of accumulation us-
ing the calculated thickness of the debris (see Figure
1), the pre-event (2002) slope angle, and a unit weight
of 1,762 kg m
-3
. Because this approach produced un-
realistically high stress values for debris captured in
narrow channels, the median (rather than mean) value
of the calculated yield stress of 5,257 Pa was adopted.
This stress was taken to be equivalent to the yield
stress of the debris at a volume concentration of sol-
ids of 0.59, considered representative of the average
debris at the time of emplacement. The yield stress
parameters α
2
and β
2
shown in equation (6) were as-
signed values of 1.75 and 17.475, respectively. Figure
5 shows a comparison of the yield stress using the
above α2 and β2 values with published values from
the FLO-2D u
seRs
m
anual
(2007).
(7)
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P.L. SHRESTHA, P.J. SHALLER, M. DOROUDIAN, D.w. SYkORA, & D.L. HAMILTON
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
The simulations consistently show that the modeled
wall condition exercised a minimal effect upon the dis-
tribution of the main lobe of debris. The visible effects
of the wall were limited to the extreme western margin
of the main lobe near Vista del Rincon Avenue.
All three simulations consistently predict debris
in the main lobe spreading one row of houses farther
to the east than actually occurred. At least four factors
likely contributed to the over prediction of debris inun-
dation in this area: (i) incorporation of the full deple-
tion volume in the inflow hydrograph, thereby raising
the average potential energy of the debris in the simu-
lation relative to the actual conditions; (ii) using the
scoured topography in the FLO-2D input grid, result-
ing in a less-restrained travel path for the debris than
under actual conditions, resulting in less material over-
flowing into the minor lobe; (iii) conceptual difficul-
ties in modeling the interaction of the debris flow with
houses and other large obstacles in the community; and
(iv) simulation of the final stages of movement.
With respect to the final point, all the FLO-2D sim-
ulations predicted very slow movement of the debris
upon reaching the vicinity of Santa Barbara Avenue.
Such slow movement may be unrealistic because the
elevated pore pressures required to keep the debris in a
fluid state are maintained by the agitation of the mov-
ing debris, which is in turn a function of its velocity. As
the velocity and agitation of the debris diminishes, the
pore pressures will diminish in kind, ultimately falling
below that needed to keep the debris in a fluid condi-
tion. A “critical velocity” necessary to maintain fluidity
was not, however, determined in this analysis.
MINOR (wESTERN) LOBE
The most significant differences among the FLO-
2D simulations and between the simulations and the
actual behavior of the debris flow occur in the area of
the minor (western) lobe. At the western end of the
temporary wall (left-hand circled area on Fig. 6), the
“With Wall” and “Breached Wall” simulations show a
lobe of debris spilling out from behind the wall that did
not occur in the actual event. The model results appear
to be related to the remobilization of material that ac-
cumulates behind the wall. In the actual event, the de-
bris that accumulated behind the wall arrived in pulses
and came to rest. Evidently, this allowed the elevated
pore pressures in the debris to dissipate, increasing its
stress and viscosity such that it did not remobilize as
predicted in the simulations.
The FLO-2D simulations also differ from each
other and from the actual behavior of the debris flow
near the center of the temporary wall (right-hand cir-
cled area on Fig. 6). The small lobe associated with the
“With Wall” simulation is consistent with the anticipat-
ed behavior of the debris where the wall was present
and indestructible; only a small amount of debris spills
over the wall at a local low spot.
In the “Breached Wall” simulation, debris flows
through the breach, but extends somewhat farther than
it did in the actual event. Again, this can probably be
ascribed to the pulse-like arrival of debris to the wall
in the actual event and the interaction between the wall
and the debris. Although the wall was breached by the
impacting debris, the movement of the material would
have slowed sufficiently to modify its rheology and di-
minish its mobility.
In the “Without Wall” simulation, the debris in the
minor lobe is predicted to travel considerably farther
than occurred in the other simulations and in the actual
event. This simulated behavior appears to reasonably
approximate the distribution of debris that would have
occurred had the event occurred prior to 2000 (i.e., ab-
sent the temporary wall and the removal of debris from
Vista del Rincon Avenue). This result suggests that the
installation of the wall and the removal of debris from
the roadway, though not intended to mitigate landslide
hazards, protected one or two houses from the impact
of debris that would likely have occurred in the ab-
Fig. 6 - Results of FLO-2D simula-
tionof debris flow depths (shad-
ed colors) for the “with wall,”
“Breached wall,” and “No
wall” conditions
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THE 2005 LA CONCHITA LANDSLIDE, CALIFORNIA: PART 2 - MODELING
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
757
the debris in the simulations, with changes to the yield
stress having the larger effect. A 20% reduction in the
yield stress resulted in a maximum of 12 m of addi-
tional runout of the main lobe compared to the baseline
case, whereas a 20% increase in stress reduced the ru-
nout by up to about 9 m. By comparison, variation of
the dynamic viscosity by ± 20% resulted in a change of
about ± 3 m in the runout distance. Figure 7 shows the
model results of debris flow depth for dynamic viscos-
ity ± 20% for the “Breached Wall” condition. A plot
of the base case is provided for comparison. Figure 8
shows the model results of debris flow depth for yield
stress ± 20% for the “Breached Wall” condition. Again,
a plot of the base case is provided for comparison.
Sensitivity analyses were also carried out for the
“No Wall” condition for debris input volumes equal
to one-half and 1.5 times the original input. Figure 9
shows a plot of the model results of this sensitivity anal-
yses. When the input is one-half of the original volume,
the debris runout does not approach the actual limits;
whereas if the input is 1.5 times the original volume, the
debris runout extends beyond the actual limits.
CONCLUSIONS
The La Conchita landslide was simulated as a de-
bris flow using the FLO-2D model. Of interest was to
assess the mechanics of the debris flow and the role,
if any, played by a temporary wall in altering the path
taken by the debris flow as it traversed the community.
sence of this work.
Finally, the simulations all predict the occurrence
of a small clear area between the main and minor lobes
that was in fact mantled by the debris flow. This differ-
ence between actual and predicted behavior was prob-
ably related to the incorporation of the lower depletion
zone into the FLO-2D simulation grid. In the actual
event, early arriving material in the main lobe was at
a higher elevation and, as a result, could more readily
spill over into this area due to superelevation as the
debris flow curved to the left.
CHANNEL FILL
All of the FLO-2D simulations predict a finger of
debris extending down the incised channel in the mid-
slope area. Review of the simulation output indicates
that this is early, water-rich material mobilized in the
early stages of the landslide. Later-arriving material ex-
hibiting a higher sediment concentration subsequently
clogs the steep-sided channel, resulting in avulsion of
debris from the channel. This behavior is generally
consistent with field observations of the channel down-
stream from the portion choked by the debris flow.
SENSITIVITY ANALYSES
A sensitivity analysis was conducted for each of the
FLO-2D simulations, in which the yield stress and dy-
namic viscosity were independently varied by ± 20%.
These variations had a minor effect on the behavior of
Fig. 7 - Results of sensitivity analyses
of the dynamic viscosity values
of ± 20% of the original for the
"Breached wall" condition. The
base case is provided for com-
parison
Fig. 8 - Results of sensitivity analyses of
the yield stress values of ± 20%
of the original for the "Breached
wall" condition. The base case is
provided for comparison
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P.L. SHRESTHA, P.J. SHALLER, M. DOROUDIAN, D.w. SYkORA, & D.L. HAMILTON
758
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
rain over which the flow was routed, the behavior of
the debris at low velocities and the remobilization of
stopped material. The different model runs provided
useful insights into the behavior of the debris flow as
it descended the hillside, as well as its interaction with
the temporary retaining wall. Model response to vari-
ation of the dynamic viscosity and yield stress param-
eters by ± 20 % did not significantly change the model
results. Varying the inflow debris volume by on-half
and 1.5 times the original debris volume caused large
differences in debris runout.
To the best of our knowledge, this investigation is the
most detailed application of the FLO-2D model for
analysis of a debris flow with a high grid resolution
of 1.52 m. The model simulations offered a good ap-
proximation of the actual behavior of the debris flow.
Based on the modeling results, the destructiveness
of the event can be attributed to the large volume of
debris mobilized, the geometry of the flow path, and
the yield stress and viscosity of the flowing debris.
Differences between the model and actual behavior
principally resulted from the fixed character of the ter-
Fig. 9 - Results of sensitivity
analyses of the debris in-
put volume as one-half
and 1.5 times the original
debris volume for the "No
wall" condition. The base
case (original volume) re-
sult is provided for com-
parison
REFERENCES
FLO-2D u
seRs
m
anual
(2007) - Nutrioso, Arizona, U.S.A.
H
Romadka
t.v. & y
en
C.C. (1987) - Diffusive hydrodynamic model. U.S. Geological Survey Water Resources Investigations
Report 87-4137.
J
oHnson
a.m. (1970) - Physical processes in geology. Freeman, Cooper & Co., San Francisco, Calif., 433-459.
J
ulien
P.y. & o’b
Rien
J.s. (1997) - On the importance of mud and debris flow rheology in structural design. In Debris-Flow
Hazards Mitigation: Mechanics, Prediction and Assessment, Chen C.-I., ed., ASCE, New York, N.Y., 350-359.
o’b
Rien
J.s. & J
ulien
P.y. (1988) - Laboratory analysis f mudflow properties. Journal of Hydraulic Engineering, ASCE, 114(8):
877-887.
Statistics