Simulations of Potential 

Runout and Deposition of the 

Ferguson Rockslide, Merced 

River Canyon, California 

By Roger P. Denlinger 

U.S. Geological Survey 

Open File Report 2007-1275 

2007 

U.S. Department of the Interior 

U.S. Geological Survey 
U.S. Department of the Interior 

DIRK KEMPTHORNE, Secretary 

U.S. Geological Survey 

Mark D. Myers, Director 

U.S. Geological Survey, Reston, Virginia 2007 

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Denlinger, Roger P., 2007, Simulations of potential runout and deposition of the 

Ferguson rockslide, Merced River Canyon, California: U.S. Geological Survey Open File 

Report 2007-1275 [http://pubs.usgs.gov/of/2007/1275]. 

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this report 
SIMULATIONS OF POTENTIAL RUNOUT AND DEPOSITION OF THE 

FERGUSON ROCKSLIDE 

MERCED RIVER CANYON, CALIFORNIA

By 

Roger P. Denlinger 

roger@usgs.gov

U.S. Geological Survey Open File Report 2007-1275 
INTRODUCTION 

 An active rockslide in Merced River Canyon was first noticed on April 29, 2006 

when a few rocks rolled onto Highway 140 between mileposts 103 and 104, 

compromising traffic on this highway and signaling the onset of renewed activity of the 

Ferguson rockslide. State highway 140 is one of the main entrances toYosemite National 

Park and is the primary road for large commercial trucks access into the park from the 

west. Continued rockslide activity during 2006 built a large talus cone that covered the 

highway and encroached into the Merced River below it. Observations by the US Forest 

Service (USFS), the California Department of Transportation (CALTRANS), and the 

U.S. Geological Survey (USGS) confirm that the rockslide remained active through 2006 

and represents a potential threat to traffic along the rerouted highway as well as to 

recreational users of the Merced River in the runout path below the rockslide. 

Delineation of the hazards posed by the Ferguson rockslide is a necessary prerequisite to 

mitigating them. 

 Field observations of the rockslide, shown in the photo of Figure 1, have 

constrained the geometry and structure of the slide mass (Beck, 2006; Gallegos and 

DeGraff, 2006). Based on initial estimates by geologists from USFS, CALTRANS and 

the USGS, the rockslide, active in 2006 and 2007, has an area of approximately 40,000 

square meters and a volume of approximately 800,000 cubic meters. Structural mapping 

suggests that the motion of the slide is translational along a planar bed, and that 

differential motion of the slide from the toe to the headwall has resulted in formation of 

large tension cracks that transect the slide across the slope (Beck, 2006). These 

indications of persistent movement were confirmed during 2006 and 2007 by GPS 

measurements made by the USGS at three points on the rockslide (Rick LaHusen, USGS, 

2
written communication). The larger of these cracks divide the slide into regions that 

moved at different rates in 2006, with the toe of the rockslide moving five to ten times 

faster than the middle portion or headwall part of the slide. Downslope of the main 

rockslide mass, a talus slope consistin of angular blocks ranging in size from 0.1 to 

greater than 10 meters (Gallegos and DeGraff, 2006), buries Highway 140. Both the 

main rockslide and the talus consist of angular blocks ranging in size from 0.1 to more 

than 10 meters and are composed of highly fractured phyllite, slate, and chert from the 

Phyllite and Chert of Hite Cove (Bateman and Krauskopf, 1987). 

 The purpose of this report is to assess the hazard posed by the Ferguson rockslide 

by simulating the runout and deposition of a portion of the slide if rapid failure occurs. 

As discussed by Gallegos and DeGraf (2006), a runout analysis is needed to delineate 

slide hazards. The report is restricted to calculations of potential runout and does not 

address the likelihood of rapid failure. Based on discussions with Allan Gallegos 

(USFS), two end-member initial slide volumes were chosen: (1) the toe of the slide along 

boundaries defined by Tim Beck (CALTRANS) in (Beck, 2006), and (2) the entire 

sliding rock mass, again along boundaries defined by Tim Beck. The simulated runout of 

these volumes during rapid failure uses granular flow mechanics developed by Iverson 

(1997) and the model developed by Denliner and Iverson, (2004). This model has been 

thoroughly tested against experimental data and provides plausible, defensible results. 

METHODS 

 The flow of blocky, rock debris down a slope is a form of dry granular flow and is 

expected to behave like granular flows despite large variations in block sizes such as 

3
those found in the Ferguson rockslide. Conservation of mass within flowing rock debris 

in cases where the square root of the planimetric area is larger than the average depth 

may be written 

0

A

h h dA

t

⎡ ⎤ ∂

+ ∇⋅ = ⎢ ⎥ ⎣ ⎦ ∂ ∫ u (1.1) 

with conservation of momentum given by 

( ) ( ) 1

A V

h

h dA dV h d

t ρ

⎡ ⎤ ∂

+∇⋅ =− ∇⋅ + ⎢ ⎥ ∂ ⎣ ⎦ ∫ ∫ uuu

A

A ∫ τ g (1.2) 

Here ρ is bulk density, u is horizontal velocity, V is incremental volume, is the stress 

tensor, and g is an enhanced gravitational acceleration vector that contains variations in 

vertical momentum as well as gravity, h is the thickness of the flow measured vertically, 

and A is an incremental area in map view, such that V A

τ

= ⋅ h . These equations are 

derived by integrating over the depth of the flow, with special care taken to approximate 

stresses and velocities in three dimensions. Stresses in dry granular flow, such as a 

rockslide, are derived from friction between the fragments or blocks making up the flow 

and from friction between the fragments and the bed as the flow slides along its bed. As 

shown in equation (1.2) the bulk density ρ normalizes the forces per unit volume 

resulting from gradients in stress∇τ : the heavier the slide material, the less a role stresses 

(such as those resulting from friction) play in determining flow behavior. The entire left 

hand side of equation (1.2) and the gravity term on the right are the same for any shallow 

flow and these equations can be used to model floods, avalanches, tsunamis, and debris 

flows. Mechanically, what distinguishes between these different types of flow is the 

stress term on the right hand side, which incorporates the physics embodied by the type 

of flow, whether it is rock debris, water, ice, or some mixture. At the onset of flow 

4
( =0), the gravity term on the right hand side is the driving force, and is resisted by the 

bed friction embedded in . For the Ferguson rockslide, any imbalance of initial forces 

represented by the right hand side of equation 

u

τ

(1.2) when the rockslide begins to move 

has a profound effect on the initial acceleration, the maximum velocity achieved, and 

therefore the final runout of the slide debris. 

These equations are derived and numerically solved in Denlinger and Iverson, 

(2004), where their method is rigorously tested against experimental data. Solutions for 

granular flow over three-dimensional terrain were compared with sand flows over scale 

models of topography. Unpublished comparisons have also been done with flows of 

gravel down an 80 m long, 2m wide flume built into a steep hillside in Oregon (Iverson et 

al., 1992), establishing that these flows have mechanics similar to sand. The successful 

simulation of sand and gravel flows lends confidence to the applicability of this model for 

simulation of the Ferguson rockslide. 

APPLICATION TO THE FERGUSON ROCKSLIDE 

The purpose of this study is to delineate the hazards posed by the potential rapid 

release of all or part of the Ferguson rockslide. The flow and deposition of rock debris is 

modeled using the conservation equations above and the numerical method of Denlinger 

and Iverson (2004), applied to the three dimensional grid shown in Figure 2. The 

topography was defined using LIDAR data obtained by CALTRANS for the Ferguson 

rockslide. The data were gridded in an old stateplane coordinate system, in meters, in 

Zone 3326 (labeled ‘zone 3’ on the LIDAR data sheet), using the NAD83 datum to create 

a terrain model. Using the grid formed from these data I defined the boundaries of two 

5
potential slide volumes: one of the entire slide and one of a portion of the slide at the toe. 

Both volumes are based on the map of Beck (2006). 

 Two initial volumes were chosen based upon discussions with Allan Gallegos 

(USFS), and are shown in Figures 2, 3, and 4. Figures 2 and 3 show the full slide mass 

on the discretized terrain model, both in perspective view with no vertical exaggeration 

(Figure 2) and in a map view (Figure 3). Figure 4 shows the perspective view of the 

portion of the slide (the toe) used for the second initial volume. This initial toe volume is 

small enough to be shown together with map views of the final deposits obtained for this 

toe failure. Both volumes are presumed to slide on a plane close to the one estimated by 

Tim Beck (CALTRANS), shown in map view in Figure 5, which is sloping at an angle of 

31 degrees towards the Merced River. If the basal sliding plane angle is greater than the 

bed friction angle, then their difference determines the initial acceleration of the rockslide 

and consequently, its runout. If the basal sliding plane angle is less than the bed friction 

angle, then the difference between the slope of the ground surface and the bed friction 

angle determine whether the rock debris will fail internally, forming a shear plane above 

the bed at some steeper angle than the basal sliding plane. 

 I estimated the sliding friction for two endmember scenarios: one based on the 

angle of repose of the talus slope below the rock mass, and the other estimate based on a 

minimum value of sliding friction to create two end-member scenarios. The existing 

talus slope, built by shedding rock debris, is at an angle of repose of 38 degrees. Thus 

one end member assumes that the friction angle between rock fragments within a 

potential flow, or the angle of internal friction, is 38 degrees, and that the friction angle 

between the rock fragments in the slide and the basal sliding plane, or bed friction angle, 

6
is also 38 degrees. The other set of conditions uses an internal friction angle of 38 

degrees and a bed friction angle of 25 degrees. The lower effective friction angle 

represents either reduction of normal loads from pore pressure buildup in the slide from 

rainfall or snowmelt infiltration, or from work softening in the rock debris along the basal 

slide plane during creep of the rock mass. The latter condition requires the rockslide to 

be active. In all cases, the rockslide will fail only where the surface slope or the basal 

sliding plane exceeds the angle of bed friction, and the resisting force of friction is 

reduced by pore fluid pressure along this plane. The two end members chosen here 

represent very different initial conditions and thereby cause large differences in initial 

acceleration of a potential rock mass, with significant consequences for the final 

distribution of the rock debris. 

 The bulk density and pore-fluid pressure from water at the base of the flow 

complete the assigned parameters for the flow of debris. Bulk density was estimated 

from the phyllite and slate composition of the debris to be about 2000 kg/m3

, and is listed 

in Table 1. Fluid pressure was assumed to be zero everywhere except in the Merced 

River channel, where it was assumed to be either zero or the pressure given by a layer of 

water 1 meter deep. Potential fluid pressure at the base of the rockslide mass is implicitly 

incorporated in the scenarios using a low bed friction of 25 degrees. 

Table 1. Properties of Ferguson Rockslide used in model 

Bulk composition Pervasively fractured phyllite, slate 

Internal friction angle 38o

Bed friction angles 25o, 38o

Bulk density 2000 kg/m3

Pore fluid pressure head 1 meter in Merced River 

7
RESULTS 

The results of the simulations indicate that the final distribution of rock debris is 

controlled primarily by the initial conditions at failure, particularly the initial volume, 

slope of the failure surface, and the value of bed friction along the basal slide plane. The 

results for these conditions are summarized in Table 2, including the times for all of the 

debris to come to rest and the depth of burial along the Merced River channel. Results 

using water depths up to 1 meter in the Merced River channel had little affect on the final 

distribution of slide debris and are not shown. 

The simulations for the toe volume in Figures 6 and 7 illustrate the pronounced 

difference in depositional pattern produced by the two end-member values chosen for bed 

friction. In Figure 6, given a conservative estimate of bed friction equivalent to the 

observed angle of repose for the debris, the rockslide forms a steep talus fan that 

encroaches on the river channel but does not cross it. In contrast, Figure 7 shows that the 

small volume will nonetheless fill the Merced River channel with debris to a maximum 

depth of 22 meters if bed friction is low enough at failure for all of the toe debris to be 

shed rapidly from the slope. 

The simulations for release of the full 780,000 m3 volume encompassing the 2006 

active slide, shown in Figures 8 and 9, repeat this pattern. If the bed friction at failure is 

approximated by the observed angle of repose (38o

), then the rockslide slowly fails and 

forms a steep talus cone extending back up to the position of the original slide debris. 

The final deposit extends about 2/3 of the way across the channel and part of the debris 

does not move from its initial position. In contrast, if bed friction at failure is low enough 

for rapid acceleration to occur, then all of the debris rapidly accelerates and fills the river 

8
valley to a minimum depth of 10 m and a maximum depth of 33 meters (Figure 9). These 

two contrasting results are shown in perspective views in Figures 10 and 11, and in 

Figure 12, which compares the deposit thicknesses in cross section for both a toe release 

and the release of the entire slide mass active in 2006. 

Thus the final results depend critically on conditions along the sliding basal plane 

of the rockslide as it is released. The angle of repose of the talus makes it unlikely that 

friction will be higher than 38o. At the lower end of the range of friction values 

investigated, mechanisms that reduce the influence of rock friction, such as a buildup of 

pore pressure along the base of the slide, are required to produce a resistance equivalent 

to a bed friction below 30o. A conservative estimate for a number of processes, including 

pore pressure buildup, gives the five degree reduction I used. Larger reductions, 

particularly at or near the onset of failure, will have correspondingly larger initial 

accelerations and thus larger consequences on the final distribution of slide debris. 

Table 2. Results of Ferguson Rockslide Simulations 

Figure 

Number 

Slide 

Volume 

(m3

) 

Bed 

Friction 

Angle 

Internal 

Friction 

Angle 

Range of 

Dam 

Thicknesses

(m) 

Percent 

Channel 

Obstruction 

Time to 

final 

deposition 

(s) 

6 128,000 38 38 0 – 15 30 320 

7 128,000 25 38 3 – 22 100 80 

8 780,000 38 38 0 – 22 66 515 

9 780,000 25 38 10 – 33 100 275 

10 780,000 38 38 0 – 22 66 515 

11 780,000 25 38 10 – 33 100 275 

9
CONCLUSIONS 

 If the Ferguson rockslide, which blocks Highway 140 between mileposts 103 and 

104 in Merced River Canyon in 2006, fails rapidly, then the resulting runout of debris 

will either completely or partially dam the Merced River. Two possible failure volumes 

derived from the boundaries of the active 2006 rockslide, one of the toe (128,000 m3

) and 

one of the full slide (780,000 m3

), represent two drastically different volumes that may be 

mobilized by rapid failure. With either volume, the extent of the final deposition depends 

primarily upon the conditions of slip along the base of the sliding rock debris (or bed) at 

the time of failure. If bed friction is about 25 degrees, then either volume will dam the 

river to heights of between 3 and 33 meters. If, on the other hand, bed friction is 

comparable to the angle of repose of the talus fans already formed, then both volumes 

build steep talus cones that only partially dam the river. In the latter scenario the river 

will flow around the final deposit. 

REFERENCES 

Bateman, P.C., and Krauskopf, K.B., 1987, Geologic Map of the El Portal Quadrangle, 

West-Central Sierra Nevada, California, U.S. Geological Survey Miscellaneous Field 

Studies Map. 

Beck, T. J. (2006), Ferguson Ridge Rockslide, Dept. of Transportation, State of 

California, revision September 16, 2006. 

Denlinger, R. P., and R. M. Iverson (2004), Granular avalanches across irregular threedimensional terrain: 1. Theory and computation, Journal of Geophysical Research, 109. 

10
Gallegos, A. J., and J. V. DeGraff (2006), Ferguson Rock Slide Geology Report, edited 

by U. S. Department of Agriculture, U.S. Forest Service, 23 p. 

Iverson, R. M. (1997), Physics of Debris Flows, Reviews of Geophysics, 35, 245-296. 

Iverson, R.M., J.E.Costa, and LaHusen, R.G., 1992, Debris flow flume at H.J. Andrews 

Experimental Forest, Oregon, in Interior, D.o., ed.: Open File Report, U.S. 

Geological Survey, p. 2. 

11
1. Photo, looking northwest, of the east-facing Ferguson Rockslide, Merced River, with the talus 

covering Highway 140 (Mark Reid, US Geological Survey). 

12
Figure 2. Model of terrain with location and depth (distance from surface to basal slide plane) of the 

main mass of the Ferguson rockslide estimated from geologic mapping. View looking NW as in 

Figure 1.

13
Figure 3. Map view of slide thickness on contoured map of terrain model, where the slide model 

coincides with the mapped outline of the active 2006 rockslide. Slide thickness is determined by 

subtracting surface elevation from the elevation of the basal slide plane shown in figure 5. 

14
Figure 4. Model of terrain, showing toe portion of Ferguson rockslide used for second scenario.

15
Figure 5. Outline of basal sliding plane elevations for the Ferguson Rockslide. The boundaries and 

the basal slide plane are estimated from structural mapping of the rockslide (Beck, 2006). 

16
Figure 6. Simulated final deposit for failure of toe volume (128,000 cubic meters) for a bed friction 

angle of 38 degrees. 

17
Figure 7. Simulated final deposit for failure of toe volume (128,000 cubic meters) for a bed friction 

angle of 25 degrees. 

18
Figure 8. Simulated final deposit of entire Ferguson rockslide (780,000 cubic meters) for a bed 

friction angle of 38 degrees. 

19
Figure 9. Simulated final deposit of entire Ferguson rockslide (780,000 cubic meters) for a bed 

friction angle of 25 degrees. 

20
Figure 10. Perspective view of simulated deposition using entire rockslide volume and a bed friction 

of 38o

, comparable to that given by the angle of repose. In this scenario, rock debris builds a steep 

talus cone that blocks 2/3 of the Merced river channel, diverting but not damming the flow. 

21
Figure 11. Perspective view of simulated deposition using entire rockslide volume and a low bed 

friction. In this scenario, rock debris fills the entire valley to a minimum depth of 10 m and a 

maximum depth of 33 meters. 

22
Figure 12. Comparison of the same channel cross section for four different simulated deposits. The 

combination of existing surface topography and estimated slide plane for the entire rockslide is 

shown in green. After failure, the profile of the toe deposits are shown in red and orange and the full 

slide deposits are shown in blue and cyan. In contrast with all of the other simulations, the toe 

deposit for high bed friction (shown in red) removes just part of the original toe mass from the 

rockslide and consequently the final ground surface profile overlaps with much of the existing 

ground surface profile. The toe deposit that is removed is added to the existing talus at the base of 

the slope (Figure 6). 

23