Steady Movement of Landslides 

In Fine-Grained Soils 

A Model for Sliding Over an 

Irregular Slip Surface

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Chapter D

Steady Movement of Landslides 

In Fine-Grained Soils 

A Model for Sliding Over an 

Irregular Slip Surface

By REX L. BAUM and ARVID M. JOHNSON

Analysis of a possible mechanism for 

sliding of landslides on irregular 

slip surfaces shows how surface 

roughness can retard movement of 

landslides in fine-grained soils

U.S. GEOLOGICAL SURVEY BULLETIN 1842

LANDSLIDE PROCESSES IN UTAH OBSERVATION AND THEORY
U.S. DEPARTMENT OF THE INTERIOR 

MANUEL LUJAN, JR., Secretary

U.S. GEOLOGICAL SURVEY 

Dallas L. Peck, Director

Any use of trade, product, or firm names in this publication is fordescriptive purposes only and 

does not imply endorsement by the U.S. Government

UNITED STATES GOVERNMENT PRINTING OFFICE: 1993

For sale by

USGS Map Distribution 

Box 25286, Building 810 

Denver Federal Center 

Denver, CO 80225

Library of Congress Cataloging-in-Publication Data

Baum, Rex L.

Steady movement of landslides in fine-grained soils : a model for sliding over an 

irregular slip surface / by Rex L. Baum and Arvid M. Johnson, 

p. cm. (U.S. Geological Survey bulletin ; 1842-D) 

(Landslides processes in Utah observation and theory ; ch. D)

Includes bibliographical references.

Supt.ofDocs.no.: I 19.3: 1842-D

1. Landslides Utah. I. Johnson, Arvid M. II. Title.

III. Series. IV. Series: Landslide processes in Utah observation and theory ; ch. D. 

QE75.B9 no. 1842-D 

[QE599.U5]

557.3 s dc20 92-19448 

[551.3'07] CIP
CONTENTS

Abstract Dl 

Introduction Dl

Acknowledgments D2 

Slip surfaces in landslides D3

Slip surface irregularities D5

Equilibrium of a landslide mass on an irregular slip surface D8 

The role of forced circulation in the equilibrium of a landslide D13 

Preliminary analysis of the effect of forced circulation on the movement of 

landslides D14

Perturbation analysis of equations governing stress and pore-water

movement D15

Derivation of boundary conditions for sliding and forced circulation D17

Solution for the stresses and velocities in the porous-elastic material D20

Resistance to sliding due to forced circulation D22 

Discussion and conclusion D23 

References cited D26

FIGURES

Dl. Photographs showing displacement across a slip surface exposed in a pipeline

trench in West Virginia D4 

D2. Photograph showing cross-section of a shear (or kneaded) zone in bank of

Ephraim Creek, near Ephraim, Utah D5 

D3. Sketch and photograph showing shear zones and intruded layers of clay in the

bank of Ephraim Creek D6 

D4. Photograph showing slip surface on a thrust fault within the Thistle landslide,

Thistle, Utah D7

D5. Sketches showing profiles of stepped slip surfaces of landslides D8 

D6. Photographs showing slip surface of a landslide near Indianola, Utah D9 

D7. Photograph of a lateral slip surface of the Cottonwood Spring landslide, Ephraim

Canyon, Utah DIG 

D8. Sketch showing the stresses acting at the ground surface, at the slip surface, and

within a typical landslide Dll 

D9. Sketch showing features of the model used to analyze the resistance to sliding due

to forced circulation D15 

Dl 0. Graph showing relationship between shear strength, shear stress, the resistance to

sliding due to roughness, mean height of the water table, and the velocity of the

landslide D24

Dll. Graphs showing resistance to sliding due to forced circulation D25 

D12. Cross section showing contours of total head in a hypothetical landslide D26

Contents III
LIST OF SYMBOLS

.c6 

etc.

A

a

B

b

c

c'

Ci,

EX

e

G

h

H 

K

/

L

n

n, s

O

P

qx, qz

R

5

t

7^, etc.

ux, uz

v.x' vz 

x, z

Amplitude of sine wave

A constant

Skempton's pore-pressure coefficient

A constant

Diffusion coefficient

Cohesion of soil in effective stress

Constants

Strain components

Volumetric strain

Elastic shear modulus

Pressure head at the slip surface, and height of

water table above slip surface

Static head (pressure head plus elevation head)

Hydraulic conductivity

Wave number (2n/L)

Wavelength

Porosity

Coordinates normal and tangential to a surface

On the order of

Pore pressure

Specific discharge components

Resistance to sliding due to roughness

Shear strength of a slip surface

Time

Stress components

Displacement components

Velocity components

Cartesian coordinates

Y0

z

a

P 

It

0

6

v

V2 

V4

Elevation of origin of x-z coordinates above

some arbitrary datum

Thickness of a landslide

Elevation of the wavy slip surface above the xaxis

Elevation of the ground surface above the jc-axis

Counterclockwise angle from the jt-axis to the

horizontal

Compressibility of water

Unit weight of saturated soil

Unit weight of water

Viscosity of glacier ice

Time, in quasi-static coordinate system

Local angle between the jc-axis and the wavy slip

surface

Counterclockwise angle from the jc-axis to a line

tangent to the ground surface

Poisson's ratio (drained)

Poisson's ratio (undrained)

x -vxt, a coordinate parallel to jc-axis

Airy's stress function

Friction angle of a soil in effective stress

The divergence operator,

The Laplacian operator,

The biharmonic operator, d4/9jt4+294/

CONVERSION FACTORS

For the convenience of readers, the metric units used in this report may be converted to inch-pound units 

by using the following factors:

Multiply metric units

micrometers ((im)

millimeters (mm)

centimeters (cm)

meters (m)

pascals (Pa)

kilopascals (kPa)

kilonewtons per cubic meter (kN/m3)

By

3.937xlQ-5

0.03937

0.3937

3.281

0.02089

20.89

6.367

To obtain inch-pound units

inches

inches

inches

feet

pounds per square foot

pounds per square foot

pounds per cubic foot

IV Contents
Steady Movement of Landslides in Fine-Grained SoilsA Model for Sliding Over an Irregular Slip Surface

By Rex L. Baum1 and Arvid M. Johnson"

Abstract

Slip-surface roughness can control the velocity of landslides in soils. Field observations indicate that many landslides 

in soils move by gliding on slip surfaces. Slip surfaces have 

asperities, including broad steps, depressions, and bumps that 

can obstruct landslide movement. Landslides typically deform 

at the asperities in order to stay in contact with the slip surface. 

Slip-surface asperities can retard the movement of landslides in 

soils, as asperities retard the movement of temperate glaciers 

sliding on bedrock surfaces.

An irregular slip surface can control the velocity of a 

landslide by causing redistribution of pore water near the slip 

surface. In order to study the effects of this redistribution, we 

have modeled a landslide, moving over an irregular slip surface, as a porous-elastic solid sliding past a wavy rigid surface. 

According to our model, water is forced to flow from zones of 

high pressure at the proximal sides of bumps and is sucked into 

zones of low pressure on the distal sides of bumps. Resistance 

to sliding resulting from the irregularity of the surface augments 

the shear strength of the slip surface. The analysis indicates that 

the resistance to sliding depends on the roughness of the slip 

surface, the velocity of the landslide, the hydraulic conductivity of the landslide debris, and the wavelength of the bumps. 

Other things being equal, landslides in soils having low 

hydraulic conductivity should move more slowly than landslides in soils having moderate or high hydraulic conductivity.

Our model is consistent with the observations of other 

workers who found that the velocity of a landslide increases 

gradually as the water level in the landslide rises. An increasing 

water level generally results in decreased shear strength at the 

slip surface. For example, it is known from the infinite slope 

analysis that the strength of the landslide debris decreases as 

the water table rises, but the driving force is constant. According to our model, the resistance to sliding (due to roughness of 

the slip surface) increases to compensate for the loss in 

strength. For the mechanism of sliding we have analyzed, the 

resistance due to roughness is proportional to the velocity of 

the landslide. Thus, as the water table rises, the landslide

Approved for publication February 26,1992. 

1 U.S. Geological Survey, Box 25046, MS 966, Denver, CO 80225. 

2Dept. of Earth and Atmospheric Sciences, Purdue University, West 

Lafayette, IN 47907.

accelerates until the resistance to sliding over the irregular surface increases sufficiently that it, combined with the strength of 

the slip surface, balance the driving force.

INTRODUCTION

Surface roughness has been recognized as a source of 

sliding resistance in rock slopes (Patton, 1966), glaciers 

(Kamb, 1970) and faults (Byerlee, 1970). However, surface 

roughness has only recently been recognized as a source of 

significant sliding resistance for landslides in soils (Baum, 

1988; Dounias and others, 1988; Mizuno, 1989). The basal 

and lateral slip surfaces of landslides in soils are irregular; 

they have bumps, steps, depressions, and other features. The 

roughness of these surfaces can retard movement of a landslide so as to control its velocity.

Observations show that many landslides move for 

weeks, months, or even longer at rates ranging from less than 

a millimeter per day to a few meters per day. Keefer and 

Johnson (1983, p. 44, 45) compiled data from many sources 

on the maximum and average velocities of landslides in 

soils. The average velocities range from 10~5 to 10 m/d 

(meters per day), and the maximum velocities range from 

10~3 to 104 m/d (maximum velocities ranging from 102 to 10 

4 m/d were attained during surges).

Landslides commonly move at constant rates for periods of several days. These periods are interrupted by shorter 

periods (lasting perhaps several minutes) of acceleration and 

deceleration. However, sustained acceleration resulting in 

very rapid movement rarely occurs (Keefer and Johnson, 

1983, p. 46-48).

Steady movement of landslides cannot be explained in 

terms of slope stability theory, which predicts that a landslide will accelerate indefinitely as soon as the driving forces 

exceed the frictional and cohesive resisting forces on the slip 

surface (Keefer and Johnson, 1983, p. 48, 49). For example, 

according to slope-stability theory, a slight increase of porewater pressure at the slip surface of a landslide at limiting

Steady Movement of Landslides in Fine-Grained Soils D1
equilibrium ought to cause the landslide to accelerate without bound.

Field measurements show that velocities of landslides 

increase gradually with increasing pore-water pressures. 

Terzaghi (1950, p. 120) observed a linear relationship 

between water level and velocity in a landslide that was 

about 40 m deep. The velocity increased from about 60 

mm/d when the water level was 3.0 m below the ground surface to about 200 mm/d when the water level was only 1.0m 

below the ground surface. Rybdr (1968, p. 140) observed 

that a landslide, 5.4 m deep, accelerated from rest to about 8 

mm/d as water levels increased by 1 m. The velocity of a 

landslide in Japan increased from about 1 mm/d to 13 mm/d 

as the water level in a borehole rose about 2 to 2.5 m (Japan 

Society of Landslide, 1980, p. 9). Similar findings were 

reported by Iverson (1986).

A popular model used to explain the steady movement 

of landslides is inconsistent with some field observations. In 

the model, the velocity at the basal boundary of the landslide 

is assumed to be zero, and flow of soil is assumed to occur in 

a layer of material above the basal boundary (Ter-Stepanian, 

1965; Yen, 1969; Keefer, 1977; Suhayda and Prior, 1978; 

Craig, 1981; Savage and Chleborad, 1982; Iverson, 1986; 

and others). This model is usually justified on the basis of 

inclinometer profiles; however, deformation of an inclinometer tube might not bear a close resemblance to the deformation of the soil containing the tube. In fact, field observations 

(Keefer and Johnson, 1983; Hutchinson, 1970; Prior and 

Stephens, 1972; Niigata Laboratory, 1973) indicate that the 

main body of a landslide moves primarily by sliding. Furthermore these observations show that the velocity at the 

basal slip surface nearly equals the velocity at the ground 

surface, and deformation is concentrated near the slip 

surface.

A possible explanation for the steady movement of 

landslides in soils is that strength of material at the slip surface is velocity dependent, although this explanation is discounted by several investigators. Keefer and Johnson (1983) 

determined that the shear strength of a sample of landslide 

slip surface increased linearly with the log of the velocity, so 

that the strength of the material tested increased only 2.5 percent for each tenfold increase in velocity. They concluded 

that such an increase is too small to account for the steady 

movement of landslides. Similar results were obtained by 

Kenney (1968), Ramiah and Purushothamaraj (1971), and 

Mitchell (1976, p. 292), who indicate that shear strength of 

soils generally increases 5 to 10 percent for each tenfold 

increase in rate of deformation. Recently, however, Skempton and others (1989) have argued that this small velocity 

dependence of the strength could explain the movements of 

the Mam Tor landslide in England.

In this study, we investigated how roughness might 

control the rate of movement of a landslide that moves 

mainly by sliding on a basal slip surface as an alternative to 

models that attempt to explain steady movement by means of 

viscous flow or rate-dependent shear strength.

Similarities between the movement of glaciers and the 

movement of landslides in soils indicate that the mechanisms 

that control the rate of sliding of temperate glaciers may be 

analogous to that of landslides (Keefer and Johnson, 1983, p. 

53). Both glaciers and landslides move slowly and steadily, 

and some temperate glaciers are known to move by sliding 

over irregular bedrock surfaces (Kamb and LaChapelle, 

1964). Surface roughness (unevenness of the bedrock surface) has been shown to retard movement of temperate glaciers; regelation and plastic deformation of the ice make 

sliding on the rough surfaces possible (Kamb and 

LaChapelle, 1964; Lliboutry, 1968; Budd, 1970a; Kamb, 

1970; Nye, 1969, 1970; Morland, 1976a, 1976b). In regelation, water moves around asperities by melting of ice at the 

proximal sides and refreezing at the distal sides of asperities. 

The rate of regelation is controlled by the rate of heat transfer 

in the ice and in the bedrock. In plastic deformation, solid ice 

flows around asperities. The rate of plastic deformation is 

controlled by the rheological properties of the ice.

Similarly, surface roughness could retard movement 

of landslides. Sliding over a rough surface might cause 

movement of pore fluid, due to consolidation and swelling, 

as well as plastic deformation of landslide debris. Consolidation at the proximal sides and swelling at the distal sides of 

asperities might play a role corresponding to that of regelation in glaciers. The rate of consolidation and swelling is 

controlled by the movement of water, which is related to the 

permeability of the soil. Henceforth, this mechanism is 

called forced circulation, because volume change of the soil 

forces water to circulate from places of high pressure to 

places of low pressure. Plastic deformation around the obstacles might be distributed as plastic flow, or localized on slip 

surfaces that form within the landslide debris. In either case, 

plastic deformation will resist sliding. No matter what the 

mechanism of deformation during sliding, the asymmetric 

pressure distribution that occurs at the slip surface during 

sliding results in a net force opposing sliding of the soil. 

Mizuno (1989) analyzed a possible mechanism of plastic 

deformation by assuming that deformation in an active landslide is analogous to deformation that occurs during 

undrained triaxial creep tests, and derived an equation for 

predicting the velocities of landslides in clayey soils. Forced 

circulation of pore fluid around asperities is the model investigated here, as an alternative rate-dependent process to 

explain the steady movement of landslides. We cannot couple forced circulation and plastic flow in a simple way, and 

we have neglected plastic deformation in order to make our 

analysis as simple as possible.

Acknowledgments

Robert Fleming of the U.S. Geological Survey 

(USGS) shared useful insights and criticism as we were 

writing this paper. William Z. Savage, Richard M. Iverson, 

and David J. Varnes (all USGS) provided critical reviews

D2 Landslide Processes in Utah
that resulted in improvements. David J. Varnes shared ideas 

and references needed to help document the fact that landslides in soils move by sliding on slip surfaces.

SLIP SURFACES IN LANDSLIDES

The analogy we proposed between the mechanisms 

that control the rate of movement of landslides and the mechanisms that control the rate of movement of some temperate 

glaciers is reasonable if landslides move by gliding over 

irregular surfaces, as do the glaciers. We describe slip surfaces of landslides in clayey soils in order to show that the 

slip surfaces of many such landslides could be sufficiently 

bumpy to retard landslide movement.

Slip surfaces in clayey materials form in thin layers of 

parallel clay particles where deformation has been concentrated. Hutchinson (1983, p. 243) noted that layers containing slip surfaces are often paper thin, making them difficult 

to locate in samples and exploratory trenches. Mary Riestenberg (College of Mount St. Joseph, oral commun., 1987) 

observed that the slip surfaces of shallow landslides in 

Cincinnati occur in paper-thin layers. Observations made 

using a polarizing microscope (Skempton and Petley, 1968; 

Morgenstern and Tchalenko, 1968) indicate that slip surfaces are in layers of strongly oriented clay particles from 

100 to 500 micrometers thick. Typically, the clay within a 

few centimeters of the slip surfaces is deformed or remolded, 

but deformation is concentrated on the slip surfaces.

The existence of slip surfaces in landslides has been 

recognized for more than a century. Collin (1846) was the 

first to document and accurately describe slip surfaces of 

landslides that occurred in clay embankments and cuts in 

clay slopes. During the course of repairing the landslides, the 

debris was cleared away, exposing the basal slip surfaces. 

They were "smooth, slippery and soapy" surfaces.

Summarizing observations of many landslides, 

Skempton and Petley (1968, p. 33) indicated that slip surfaces occur in the majority of landslides. They indicate that 

slip surfaces extend over large areas beneath a landslide and 

are polished subplanar surfaces, striated parallel with the 

direction of movement.

Observations and measurements indicate that landslides move primarily by gliding on their slip surfaces. Collin (1846, p. 36, 37) was able to show that the basal slip 

surfaces formed as a result of landslide movement and that 

movement occurred primarily by sliding on the basal slip 

surface. He observed that the bedding or layering was tilted 

and offset across the basal slip surface of a landslide.

A sequence of time-lapse photographs by the Niigata 

Laboratory (1973) shows that displacement of the Sarukuyoji landslide occurred primarily on a slip surface. The photographs show the face of a trench in the landslide. At time 

zero, no slip surface is visible, but after five minutes, the

trace of the slip surface is visible as a faint line across the 

face of trench. After 35 minutes, the shadow cast by the 

overhanging edge of the block of soil above the slip surface 

makes a broad black stripe across the photograph. The photographs show clearly that the movement of the landslide is 

concentrated on a slip surface. The photographs show no evidence that any other deformation occurred at the face of the 

trench during the 35-minute period.

Similarly, photographs of the face of a pipeline trench 

show that sliding occurred on a surface (fig. Dl). The light 

band of soil in the middle of figure D LA contains the slip surface. Colluvium overlying the slip surface slid 1-2 mm 

downslope after the trench was opened, and the shadow of 

the overhanging material (narrow black line through the center of the white band of soil in figure DIB) clearly shows that 

deformation was concentrated at the slip surface.

At a shallow earthflow in California, experiment 

showed that deformation was concentrated on the basal slip 

surface (Keefer and Johnson, 1983, p. 31, 32). A stack of 

wooden disks, shaped like poker chips, was placed in a borehole that penetrated the basal slip surface of the main body 

of the landslide. After the landslide had moved about 0.4 m, 

the disks were recovered by digging a trench next to the 

borehole, and the positions of the disks were mapped. At 

least 94 percent of the movement occurred within 1.3 cm 

(the thickness of one disk) of the basal slip surface. Little 

evidence of deformation outside the slip surface was 

observed.

Ter-Stepanian (1965, p. 577) performed a similar 

experiment with wooden blocks, each 0.2 m high, stacked in 

a borehole. The profile of the blocks was exposed in a trench 

after 5 yr of movement. Total displacement at the ground 

surface was 2.8 m. The block just above the basal slip surface (3.8 m deep) was displaced 2.2 m. The upper 3 m of the 

stack of blocks leaned several degrees downslope, and 

blocks in the lower 0.8 m of the stack were offset or rotated. 

Although part of the displacement was due to internal deformation of the landslide debris, most of the displacement (78 

percent) was concentrated on the basal slip surface.

Displacement at the lateral boundaries of many landslides also occurs on slip surfaces. Strike-slip faults having 

slickensided surfaces constituted the lateral boundaries of 

the Aspen Grove landslide in central Utah. Displacement 

measurements at three transverse lines of stakes on the landslide showed that displacement at the boundaries was from 

85 to 95 percent of the displacement at the axis of the landslide. David Varnes (USGS, oral commun., 1988) reported 

similar findings for the Slumgullion landslide in southern 

Colorado.

Several investigators have reported that some deep 

landslides move on "thick kneaded zones," layers of clay, 

several decimeters thick, that have been strongly sheared and 

remolded (Zaruba and Mencl, 1982, p. 161; Gould, 1960; 

Brunsden, 1984). However, even the kneaded zones are 

bounded by or contain slip surfaces that accommodate most

Steady Movement of Landslides in Fine-Grained Soils D3
Figure D1. Displacement on a slip surface exposed in a pipeline trench in West Virginia. (A) Overview showing location 

of slip surface (in white layer of clay) in the side of the trench. (6) Close-up of slip surface. Displacement of overhanging 

block toward the camera shown by shadow across middle of light-colored layer of clay. Knife handle in both photographs 

is 9 cm long. (Photographs by Robert W. Fleming, U.S. Geological Survey.)

D4 Landslide Processes in Utah
of the displacement. A horizontal layer of black plastic clay 

(1m thick, thinly laminated and schistose) within less plastic, stony, brown colluvium, was exposed at the base of the 

eroded toe of the Twin Lake landslide (about 30 m deep), 

near Mayfield, Utah. The black clay, evidently part of the 

basal slip zone of the landslide, was divided into almondshaped pieces by a family of anastomosing, subhorizontal 

slip surfaces. A layer of "kneaded" clay exposed in a landslide in the south bank of Ephraim Creek, near Ephraim, 

Utah, was bounded at its top by slip surfaces (fig. D2). Several meters away, at another exposure, polished slip surfaces 

formed the boundaries between layers of plastic clay and the 

gravel-rich colluvium that they had intruded (figs. D3A and 

B). Thus, movement by gliding on slip surfaces appears to be 

almost universal in landslides.

Slip Surface Irregularities

Slip surfaces deviate from the idealized cylindrical or 

planar shapes assumed in most stability analyses. Steps, 

bumps, depressions, grooves, striations, and other irregularities have been observed on slip surfaces of landslides in 

California, Utah, France, Norway, and Japan (Collin, 1846; 

Stout, 1971; Mizuno, 1989).

Striations and grooves are commonly observed on slip 

surfaces (fig. D4). They form as a result of deformation at 

small irregularities in the slip surface that might retard landslide movement slightly. Striations and grooves are parallel 

to the direction of movement of the landslide, so they cannot 

cause significant deformation of the landslide debris; rather, 

they merely increase the area of the slip surface.

Steps, depressions, and bumps are other types of irregularities on a slip surface and they can obstruct movement. 

Such irregularities are termed asperities. Asperities are 

oblique to the direction of movement so that they can cause 

interlocking or deformation (either distributed or localized 

on faults) of the landslide debris. (See Savage and Smith, 

1986, for a discussion of one style of deformation that can 

occur in landslides.)

Slip surfaces of some landslides in France had streamlined bumps that caused them to deviate from idealized 

cycloidal shapes (Collin, 1846, pi. VI, VII, VIII, and others). 

Accurate surveys showed that the bumps were a few meters 

long and a few decimeters high.

The slip surfaces of two landslides in California had 

steps that consisted of rounded treads (flats) and risers 

(ramps) (Stout, 1971). The treads had slopes as low as 4°, 

and the risers had slopes as steep as 41°. The average slope

«**? * *--

Figure D2. Cross-sectional view of a shear (or kneaded) zone exposed in bank of Ephraim Creek near Ephraim, Utah. Dark lensshaped area, A, is part of a slip surface exposed in an overhang and is approximately 30 cm across.

Steady Movement of Landslides in Fine-Grained Soils D5
LU

D6 Landslide Processes in Utah
Figure D4. Slip surface on a thrust fault within the Thistle landslide, Thistle, Utah. The slip surface is covered with grooves and 

striations. (Photograph by IrvingJ. Witkind, U.S. Geological Survey.)

of each slip surface was about 14°. Measured relative to a 

smoothly curving, average slip surface, the steps were from 

3 to 6 m high and tens of meters long (fig. D5).

Steps were also observed in the basal slip surface of a 

quick-clay landslide in Norway (Stout, 1971). About one 

third of the slip surface was exposed, including parts of the 

steps. The steps had rounded noses that separated broad, 

gently sloping treads from steep risers. The treads sloped 

about 0.5° to 2.0°, and the risers sloped as steeply as 50°. The 

risers were from 5 to 7 m high, and the average slope of the 

slip surface (not including the headscarp) was about 5°.

Streamlined bumps are common on the slip surface of 

the Indianola landslide in central Utah. The slip surface is 

roughly a U-shaped (fig. D6A) or V-shaped (fig. D6Z?), 

slightly sinuous channel. Grooves and striations on the sides 

of the channel are approximately parallel to the channel bottom (figs. D6A and E). Larger bumps on the sides of the 

channel are a few meters long and small bumps, each less 

than a meter long, are superimposed on the larger bumps 

(fig. D6A). Many of the smaller bumps are relatively narrow 

features oriented approximately parallel to the direction of 

movement.

Elongate, asymmetrical ridges resembling roches 

moutonnees are exposed in a lateral slip surface of a landslide at Cottonwood Spring in Ephraim Canyon, Utah (fig.

D7). All are 15 to 40 cm long, 5 to 15 cm wide, and a few 

centimeters high, and are superimposed on a larger bump 

that is about 1 to 1.5 m long. There are other larger bumps 

nearby.

To summarize, several general observations can be 

made about slip surfaces of landslides. The main body of a 

landslide moves principally by sliding on a single slip surface within a thin (usually less than 1 mm thick) layer of 

strongly oriented clay particles. In many landslides, from at 

least 90 to 95 percent of the displacement observed at the 

ground surface occurs on the basal slip surface; minor deformation occurs in the ground adjacent to the slip surface of 

the main body of a slide; however, significant deformation 

may occur throughout the thickness of the slide in the vicinity of the head, toe, and major asperities in the failure 

surface.

Slip surfaces of landslides in clayey materials are 

irregular. Asperities on slip surfaces comprise bumps that 

resemble flattened domes or roches moutonnees, broad steps 

having steep risers and gently sloping treads, and perhaps 

other forms. Lengths of asperities range from decimeters to 

tens of meters. Generally, the amplitudes or heights are small 

compared to the lengths of the asperities. Mizuno (1989) 

reports that the average ratio of height to length is 0.065. 

Asperities tend to be asymmetrical; distal slopes are generally steeper than proximal slopes.

Steady Movement of Landslides in Fine-Grained Soils D7
40

30

20

10

30

20

£ io

50

40

30

20

10

0

Sulphur Creek, California

Original ground surface

30 METERS

San Juan Creek, California 

Original ground surface

30 METERS

Hekseberg landslide, Norway

Original ground surface

Slip surface

30 METERS 

j___i

Figure D5. Profiles of stepped slip surfaces of landslides. (Modified from Stout, 1971.)

EQUILIBRIUM OF A LANDSLIDE MASS ON 

AN IRREGULAR SLIP SURFACE

Resistance to sliding on an irregular slip surface is 

determined by the stresses acting on the landslide mass (fig. 

D8). In the following derivation we separate sliding resistance into a shear stress and a normal stress acting on an 

irregular slip surface. The normal stress that acts on the 

irregular slip surface can oppose sliding, as does the shear 

stress of the slip surface. To demonstrate this, we integrate 

the differential equation for equilibrium in the jc-direction,

methods used by several glaciologists (Collins, 1968; Budd, 

1970b; and Kamb, 1986), we integrate with respect to z, 

between the elevation of the basal slip surface, Z=ZQ(X), and 

the elevation of the ground surface, z=z\(x):

dx

fz zx. fz i I ~^ dz+ Y, 

Jz0 dz Jzo f

, 1UX since dz = 0. (Ib)

dT~a?z: + Y, since = 0 '

(la)

(See "List of symbols" on p. IV for definitions of terms.) We 

assume that normal stresses are positive in tension (the notation for stresses is after Malvern, 1969). Following the

In equations la and Ib, the unit weight of soil, assumed constant with respect to x and z, is Yt, and the counterclockwise 

angle from the Jt-axis to the horizontal is a. We have used the 

convention that normal stresses are positive in tension. Txx is 

the normal component of stress acting parallel to jc, and Tzx 

is the shear stress acting parallel to x.

Equation Ib is related to integrated forms of the equilibrium equation used to study longitudinal stress and strain 

gradients in glaciers (Collins, 1968; Budd, 1970b; Kamb, 

1986). However, the following analysis differs in that we 

work with the total stresses, whereas the glaciologists cast

D8 Landslide Processes in Utah
Figure D6. Slip surface of a landslide near Indianola, Utah. (A) The landslide occupied a V-shaped channel or trough. 

Striations on channel wall are parallel to the transport direction. Elongated bumps are transverse to direction of movement. 

(6) Curvature of channel and rounded shapes of bumps on the slip surface are evident in this view.

Steady Movement of Landslides in Fine-Grained Soils D9
itf IIf ' " ' ' ' » ,

^*^i^V

Figure D7. A lateral slip surface of the Cottonwood Spring landslide, Ephraim Canyon, Utah. Features resembling roches 

moutonnees are visible near center of photograph. Lens cap is about 5 cm in diameter. Arrow shows direction of landslide movement.

their equations in terms of deviatoric stresses. This is 

because the flow of glacier ice is considered to be independent of the hydrostatic or mean stress (Collins, 1968), 

whereas deformation of landslide debris is known to depend 

on the mean stress (Lambe and Whitman, 1969). Consequently, equation Ib is closely related to one of the equations 

of equilibrium used in stability analysis of landslides (Morgenstern and Price, 1965; Janbu, 1973). Mizuno (1989) also 

analyzed equilibrium on a wavy slip surface; however, his 

derivation differs from ours in several ways, so his results 

cannot be readily applied to part of our analysis.

When we evaluate the last two integrals in equation 

Ib, the equation simplifies to

A "\'T1 >»

r r . C/y ^7 T7. llrr c/ll -^ dz = I

J Z0 OJf <3A^ J Z0

dzl

- [Txx] i * * z\ dx 7 z0

(Id)

In equation Id, dz\/dx and dzo/dx denote the slope (dzfdx) of 

a line tangent to the ground surface, or slip surface, respectively.

We substitute equation Id into Ic, and move terms 

evaluated at the slip surface, Z=ZQ, to the right side of the 

equation,

^0

dc)

Note that the second term in equation Ib integrates readily 

(Wylie and Barrett, 1982, p. 795-797).

The remaining integral in equation Ib can be evaluated by means of Leibnitz's rule,

dzG

- \T 1 - . l J

^1 f/JC

(le)

We assume that the stresses acting normal, Tnn, and 

tangential, Tns, to the ground surface are zero. Equilibrium

D10 Landslide Processes in Utah
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Steady Movement of Landslides in Fine-Grained Soils D11
parallel to the jc-direction at the ground surface (fig. D8, 

stresses for X>0) requires that

cosx-[rn j z = [T]

z\

(2a)

In equation 2a, Ss, 8jt, and 8z are small increments parallel to s, x, and z, respectively. Note that 8jt/8s=cos X and 

8z/8s=sin X in the limit as 8s, 8*, and 8z become infinitesimals. We divide equation 2a by 8s cos X to obtain

= [T (2b)

In equation 2b, tan X equals (dzi/dx), in the limit as Sue 

becomes infinitesimal. The reader can verify that equation 

2b is correct, whether X is greater or less than zero, by 

observing how the normal stresses change their orientation 

as X changes sign. All stresses shown in figure D8 are positive, according to the sign convention adopted previously. 

For X>0 (tan X>0), the jc-components of the normal stress act 

in the opposite direction to the ^-components of the corresponding shear stresses. For X<0 (and tan X<0), the jc-components of the normal stresses act in the same direction as the 

^-components of the corresponding shear stresses (fig. D8).

The left side of equation 2b is zero because the stresses 

at the ground surface, [Tnn ]Zl and [Tns]Z{ , are zero. By substituting this result into equation le, we determine that

-Zn) sina =

dzQ

IT 1 1 xx*zodx (3)

Equation 3 is an exact statement of the requirements 

for equilibrium at any position along the slip surface. We 

need an expression for the overall equilibrium of the landslide mass. If we assume that the waviness of the slip surface 

of the landslide is periodic, with wavelength L;, that the 

ground surface is stress-free and parallel to the Jt-axis; and 

that the slope has an infinite extent, then we can derive such 

an expression by integrating equation 3 with respect to x, 

over one wavelength, L, and dividing by L,

1

D12

1 CL

T \ t^rr ] dXLj o z* zo 

Landslide Processes in Utah

*

-T-dx. (4a) 

zo dx

The first term on the left side of equation 4a is zero. The grad fz i

dient of longitudinal force per unit width, I Trrdz (the dxjz0 xx

integrand of the first term), is a periodic function of jc. The

1 PL d fz, 

average value of the gradient, - \ \ Trrdz dx, must be '[*'(":

^ J 0 dxj z0

zero so that the longitudinal force per unit width does not 

become infinite at large values of*. For example, if the average value of the gradient were a (non-zero) constant, then the 

absolute value of the longitudinal force would increase without bound in proportion to x. The second integral on the left 

side can be evaluated explicitly, so that equation 4a simplifies to

j PL i PL dz0 

y(Z sina = - ^ Tz^^dx ~"l\ [T^ ZQ ~^ dx - (4b)

In equation 4b, Z is the average thickness of the landslide 

mass. For convenience, we let

R = (4c)

Equation 4b is an expression for overall equilibrium of 

an infinite slope having a wavy, periodic slip surface. It 

shows that the average shear stress due to weight of the landslide debris (left side of equation 4b) is balanced by the average shear stress at the slip surface (first term on right side of 

equation 4b) and the average resistance (acting parallel to jc) 

due to roughness of the slip surface, R. If the slip surface is 

perfectly smooth, such that (dzo/dx)=0, then the second integral on the right side of equation 4b, R vanishes, and the 

equation reduces to the well-known expression of equilibrium for an infinite slope. Thus, R can be thought of as a correction term for the effect of roughness.

Roughness can increase the resistance to sliding only 

if the material above the slip surface is stronger than the slip 

surface. Baum (1988) has shown analytically, for a von 

Mises plastic, that resistance to sliding is greater on a rough 

(bumpy) slip surface than on a smooth one, provided that the 

strength of the material is greater than the adhesion of the 

material to the slip surface. Laboratory experiments, in 

progress (Baum, unpub. data) corroborate this analysis. 

However, if strength of the material equals the adhesion to 

the rough slip surface, then sliding must occur on a smooth 

surface within the material because the resistance to sliding 

on the rough surface will exceed the strength of the material.

Roughness of the slip surface contributes to equilibrium of a landslide mass because the distribution of normal 

force on the slip surface is asymmetrical. The compressive 

normal stress, Txx, is greater (in absolute value) on the proximal sides of bumps than on the distal sides. The resultant 

force due to the action of the normal stress on the bumps 

opposes downslope movement of the landslide mass.
Thus, in a landslide, normal stress on the slip surface 

contributes to equilibrium in two distinct ways. First, it contributes to equilibrium by determining the shear strength, 5, 

as indicated by the Coulomb-Terzaghi yield criterion,

S = c'-{[Tn (5a).

and second, it contributes to equilibrium through roughness. 

In equation 5a, P is the pore pressure (negative in tension), 

c is the cohesion for effective stress and tan 0' is the coefficient of friction for effective stress. We assume, hereafter, 

that the average shear stress at the slip surface equals the 

average shear strength when the landslide is active.

The two contributions of normal stress to equilibrium 

can be seen clearly in the equation of equilibrium by transforming stresses at the slip surface in equation 4b to local 

coordinates tangent and normal to the slip surface, and by 

substituting the yield criterion for the slip surface (equation 

5a) into equation 4b. The equation for transformation of 

stress to local coordinates (see fig. D8 and equations 2a and 

2b)is

dzn dzo

r f i f T "\ ___ _ f T 1 f T 1 /<K\ L'nr-L ~ L' ]., ~T~ - L^ 7rJ. ~ I* rrJ . ~3~ (->*>)

Equations 5a and 5b are substituted into equation 4b to 

show the two ways that normal stress at the slip surface contributes to equilibrium

sina = i fV~

(5c)

The first term on the right side of equation 5c determines the shear strength, and the second term determines the 

resistance to sliding due to roughness. Significantly, the 

effective normal stress (Tnn+P) enters the shear strength 

term, whereas the total normal stress enters the roughness 

term.

The contribution of normal stress to equilibrium, 

through the roughness of the slip surface, may seem unfamiliar to some readers. Perhaps it can be visualized by considering the action of one gear driving another gear in a 

machine. Torque is transferred from one gear to the other 

through the normal stresses acting on the faces of gear teeth 

that are in contact. The gears are lubricated so that shear 

stress on the faces of the teeth is small. Compressive normal 

stress on the leading faces of these gear teeth is greater than 

on the trailing faces. This asymmetrical distribution of stress 

on the gear teeth is similar to the asymmetrical stress distribution that we expect to occur at asperities on the slip surface 

of a landslide.

THE ROLE OF FORCED CIRCULATION IN 

THE EQUILIBRIUM OF A LANDSLIDE

Within the framework of the general theory of slope 

equilibrium just described, we wish to focus on a possible 

mechanism that can explain the observed rate dependence of 

the forces that resist sliding. We have already noted that the 

rate dependence of the shear strength of slip surfaces is too 

weak to explain the steady movement of landslides, because 

the shear strength increases only about 5-10 percent for each 

tenfold increase in the rate of shearing, within the range of 

rates tested (Kenney, 1968; Ramiah and Purushothamaraj, 

1971; Mitchell, 1976; Keefer and Johnson, 1983). Thus, to 

explain the steady movement, we examine a possible mechanism of sliding in which R is rate dependent.

The mechanism we propose, in order to explain the 

rate dependence of /?, is forced circulation of pore fluid 

through the landslide debris. As the landslide moves over its 

bumpy slip surface, high compressive normal stress on the 

proximal sides of bumps forces fluid to flow away from the 

proximal sides. Concurrently, low compressive normal 

stress on the proximal sides of bumps allows the soil there to 

swell, causing pore fluid to be drawn toward the distal sides 

of bumps. As we have shown, the distribution of normal 

stress on the slip surface determines R. Energy is dissipated 

by means of the flow process during forced circulation. Sliding by the mechanism of forced circulation is rate dependent, 

because forced circulation is a diffusive and hence a ratedependent process that depends on the hydraulic conductivity of the soil and the path length of diffusion.

Our model for forced circulation applies to landslides 

that fail in a ductile manner (without sudden loss of 

strength), such as landslides on natural slopes that fail by a 

gradual rise of the water table. Landslides having slip surfaces are very common and observations indicate that slip 

surfaces of landslides in clayey materials commonly are 

wavy (Mizuno, 1989, p. 96, 105). Thus, we believe our 

model applies to most landslides that have relatively steady 

motion. Driving forces in natural slopes tend to be near equilibrium with the residual strength of the soil (Skempton, 

1964). Any strength that is lost in the failure of such slopes 

generally is lost progressively (Bjerrum, 1967; Palmer and 

Rice, 1973). However, in slopes that fail in a brittle manner 

(a sudden or abrupt loss of strength accompanies failure), 

such as rock slopes or slopes underlain by quick clay, driving 

forces are sufficient to overcome the peak strength of the 

material and roughness of the failure surface cannot retard 

sliding to a degree sufficient to prevent acceleration of the 

failed mass.

We have solved a boundary-value problem that models forced circulation as the deformation and fluid flow 

occurring in a porous elastic solid that is sliding over a wavy, 

impermeable, rigid surface (details of the solution follow in 

succeeding sections of this paper). Solving this problem

Steady Movement of Landslides in Fine-Grained Soils D13
allowed us to determine the normal stress on the slip surface 

and thus compute a formula for R due to forced circulation,

(6)

In equation 6, vx is the mean velocity of the landslide, 

parallel to x; yw is the unit weight of water, A is the amplitude 

of the bumps, K is the hydraulic conductivity of the landslide 

debris, / is the wave number, equal to 2n/L; L is the wavelength of sinusoidal bumps on the slip surface; (A/), the product of the amplitude and the wave number, is the maximum 

local slope of the slip surface with respect to x;, and [I is 

Poisson's ratio for drained deformation of the soil. Hereafter, 

Al is called the roughness.

Equation 6 helps to explain how a landslide can maintain equilibrium even when shear strength at the basal slip 

surface decreases due to an increase in the average porewater pressure at the basal slip surface. If equation 6 is substituted into equation 5c, the following is obtained:

R = - In

na

(8b)

where a and b are constants to be determined from field data, 

a has units of velocity, and b has units of inverse stress.

Mizuno's (1989) corresponding formula for predicting velocity of a landslide from R is

(8c)

Note that Mizuno's (1989) formula indicates an exponential 

relationship between R and vx, whereas our formula (equation 6) indicates a linear relationship between R and vx.

y Z sina = (cf - { [Tnn ] + [P] } tanf) dx

LjO "" ZQ ZQ

(7)

According to equation 7, if the average shear strength of the 

slip surface (the integral on the right side of equation 7) 

decreases, due to a decrease in effective stress, the landslide 

can stay in equilibrium if R increases. Thus, R can increase 

if the velocity, v^, increases, because other parameters that 

determine R are nearly constant in a given landslide.

Our formula (equation 6) for resistance to sliding of a 

landslide, by the mechanism of forced circulation, is similar 

to the result Kamb (1970) obtained for a temperate glacier 

sliding on a wavy bedrock surface by a mechanism of ratedependent plastic deformation (viscous flow). Kamb's 

(1970) formula for /?, in our notation, is

PRELIMINARY ANALYSIS OF THE EFFECT OF 

FORCED CIRCULATION ON THE 

MOVEMENT OF LANDSLIDES

We model a landslide as a deformable body that slides 

at a constant velocity past a rigid body (fig. D9). The boundary (that is, interface) between the bodies undulates. It is 

assumed that variation of stresses generated by acceleration 

is negligible near the interface and that no cavitation occurs 

at the interface. The undulations are assumed to be wide, 

symmetrical, low-amplitude steps. Movement is assumed 

parallel to the jc-axis, and the undulations are assumed to be 

periodic in x, and independent of y. Consequently, plane 

deformation is assumed to occur. The landslide is represented as an infinite strip bounded by Z=ZQ and z=z\, and 

moving parallel to the Jt-axis with a mean velocity of vx (fig. 

D9). The basal slip surface, z0, is a sinusoidal perturbation of 

the x-y plane:

R = - 2' (8a) = A sin Ix.

where T| is the viscosity of glacier ice.

However, our equation 6 differs in basic form from the 

formula derived by Mizuno (1989) for resistance to sliding. 

Mizuno (1989) assumed that landslide debris slides over an 

uneven slip surface by the mechanism of soil creep. Creep is 

used in the sense of undrained plastic deformation of a triaxial specimen subject to a constant load that is a fraction of the 

static load needed to cause failure. Mizuno's (1989) formula 

for resistance to sliding (in our notation) is

(9)

In order to investigate the resistance to sliding generated by forced circulation of pore water in a landslide, and 

the effect of that resistance on the velocity of the landslide, 

we assume that the landslide debris behaves like a fluid-infiltrated, porous-elastic solid (Biot, 1941; Rice and Cleary, 

1976). We have chosen such a model for material behavior 

because the movement of pore water is considered the primary cause of time-dependent effects in fine-grained soils 

(Terzaghi, 1925; Wroth and Houlsby, 1985, p. 6).

D14 Landslide Processes in Utah
Ground surface, z=Zj

Direction of landslide movement

Water is squeezed out 

of soil on upstream 

sides of bumps

Water is sucked into 

swelling soil on downstream sides of bumps

Local coordinates

Slip surface, Z= 

zo=A sin (/x)

Figure D9. Features of the model used to analyze the resistance to sliding due to forced circulation. The ground surface is 

a plane, and the x- and z-axes are parallel and perpendicular to 

the ground surface, respectively. Sinusoidal undulations of the 

slip surface have wavelength L and amplitude A. The maximum 

local slope of the slip surface with respect to the x-axis is Al,

where / is the wave number, 2n/L The landslide is moving 

toward the right so that the compressive stress, Tnn (shown by 

heavy arrows), is greater on the upstream sides of the bumps 

than on the downstream sides. The small curved arrows indicate 

that water is flowing away from the upstream sides of the bumps 

and is flowing toward the downstream sides of the bumps.

Perturbation Analysis of Equations Governing 

Stress and Pore-Water Movement

Stress and pore-water movement in the landslide are 

governed by the following equations:

ar ar

r ox dz since = 0 ,

V2 [r

_Y cosa = 0 ,

~

= o,

(la)

(10a)

(10b)

and

2TO(l-iQ 2

Yw d-2n)

(10c)

Equations la and lOa are the equilibrium equations, 

equation lOb is the compatibility equation for stress diffusion (Rice and Cleary, 1976), and equation lOc is the stressdiffusion equation (Rice and Cleary, 1976). In equations lOb

and lOc, P is the pore-water pressure, Kis the hydraulic conductivity, YW is the unit weight of water, G is the shear modulus, and n is Poisson's ratio for drained deformation. We 

assume that the soil skeleton is incompressible, so the coefficients appearing in lOb and lOc are simpler than their counterparts in Rice and Cleary (1976).

We use perturbation expansions of the field variables 

to determine the stresses and pore pressure caused by deformation near the wavy slip surface. The expansions are in 

powers of Al, which is the maximum local slope of the slip 

surface (with respect to x); Al, is small compared to unity. 

Then (Al)2 must be small compared to Al. The pressure, P,

and the stress components; T 

by the following expansions:

P =

, T, ^, and T; are determined

(Ha) 

(lib) 

(He)

and

ZZ ~ ZZ ' * ZZ ' '-'v**/ » V-I--I-W

Steady Movement of Landslides in Fine-Grained Soils D15
where O(Al)2 is the remainder term on the order of (A/)2 .

The zero-order components of the stresses are known 

from the infinite slope analysis and solutions for problems in 

elasticity (Lambe and Whitman, 1969, p. 353-356; Jaeger 

and Cook, 1969, p. 356),

(12a) 

(12b)

* *

\.i 

Txx - T\ rY,U-£i) cosa. (12c)

= y/ (z 1 -z)sina, 

H

Likewise, the zero-order pore pressure for slope-parallel 

flow (we assume that the slip surface is impermeable) is 

determined by the following:

P = ,cosa; z<h. (13a)

The pore pressure is part of the head, //, that drives groundwater flow. The complete expansion for the head is

; z<h. (13b)

In equation 13b, 70 is the elevation of the origin of the x-z 

coordinate system above some arbitrary datum, and h is the 

height of the water table above the x axis.

We note that the zero-order stresses and pore pressure 

are independent of x and t. By substituting equations lla, 

lib, lie, lid, 12a, 12b, 12c, and 13a into equations la and 

lOa, lOb, and lOc, we derive the following for the first-order 

variables:

(14a) 3z

(14d)

To simplify our analysis of the mechanism of forced 

circulation, we assume the landslide is moving at a steady 

rate, vx, and introduce a new system of coordinates that 

moves parallel with x in order to make the problem independent of time (Rosenthal, 1946). Only two independent variables, ^ and z, remain after transforming the coordinates. Let

(15a)

and

0 = t. (15b)

We use the chain rule for partial differentiation to obtain formulas for transforming partial derivatives to the £-z coordinate system,

dx

30

"37 J30' (15c)

and

__ 

31 3/ 3r J30- (15d)

The partial derivatives of £ and 0, appearing in equations 15c and 15d, are obtained by differentiating equations 

15a and 15b with respect to x and t. The derivatives are 

3£/3jt=l, 3£/3r=- vx, 30/3jt=0, and 30/3r=l. Note that 

3/30=0, because a steady state of deformation is observed in 

the new coordinate system. Equations 15c and 15d reduce to 

the following when the values of the derivatives are substituted into the equations:

37_ 

3* 3z (14b)

(15e)

and

= 0, (14c)

and

31 = ~^3T (15f)

The field equation, 14d, for stress diffusion can be 

rewritten as

D16 Landslide Processes in Utah
c V2 ( Tx = ( Txx 2P), (16a) a2;

(17c)

(Rice and Cleary, 1976, p. 230).

The diffusion constant, c, in equation 16a is determined by

2GK

l-2n (16b)

where 7^=9.8 kN/m3 (Freeze and Cherry, 1979).

The field equation for stress diffusion in the new £- 

coordinate system is

(16c)

The term on the right side of equation 16c accounts for 

advection (conveyance) of water by the landslide debris.

If the absolute value of the coefficient, vx/c, is small 

compared to 1, then advection can be neglected (Kamb, 

1970). For steady landslides in which vx/K<\OQ and the 

debris has typical values for G and (j (G=107 Pa, |a=0.3; 

Lambe and Whitman, 1969), the coefficient on the right side 

of equation 16c is small compared to 1; |-v,/c| <0.03. 

Advection causes a small phase shift in the solution 

for (7^ + T,. + 2P) that has a negligible effect on the 

magnitude of (7^ + 7^ + 2P). Thus, Laplace's equation 

is a good approximation of the diffusion equation (16c):

= 0. (16d)

Equation 16d, together with the compatibility equation, the equilibrium equations, the constitutive equations, 

and the boundary conditions govern the problem in the new 

coordinate system. Transformation of equations 14a, 14b, 

and 14c is accomplished by simply replacing the x's with £'s.

Airy's stress function (Malvern, 1969) facilitates solution of equations 14a, 14b, 14c, and 16d. The stress function 

automatically satisfies the equilibrium equations; the following relationships hold between the stress components and the 

stress function:

(17a)

a

When the stress function is substituted into the simplified 

diffusion equation (16d) and the compatibility equation 

(14c), two equations relating the stress function and the porepressure function are obtained,

and

V2 [V2 <j>

V2 <j>

= 0 (18a)

2uv~l 

~ l = (18b)

The Laplacian, V2, is a linear operator and the quantities in square brackets in equations 18a and 18b satisfy 

Laplace's equation; therefore, any linear combination of 

these quantities also satisfy Laplace's equation. Equations 

18a and 18b can be combined algebraically to show that P 

satisfies Laplace's equation and <j> satisfies the biharmonic 

equation:

= 0

V4ij> = 0

(18c) 

(18d)

Thus, we solve equations 18c and 18d subject to boundary 

conditions at the slip surface, in order to determine the relationship between the rate of movement and the resistance to 

sliding due to forced circulation.

Derivation of Boundary Conditions for 

Sliding and Forced Circulation

We have made several assumptions in setting up a 

boundary value problem that describes forced circulation of 

water as a landslide moves over its slip surface. Many of the 

assumptions are embodied in the boundary conditions.

A boundary condition on ZQ is that sliding is tangential

(19a)

and

3

= T-- (17b) This assumption is consistent with our observations of slip 

surfaces and with the observations of others (for example, 

Lambe and Whitman, 1969) that soil subject to constant normal load shears at constant volume once the residual strength

Steady Movement of Landslides in Fine-Grained Soils D17
is attained. This assumption (equation 19a) would be violated if our model included (Coulomb-type) plastic deformation, because dilation would occur at the slip surface (Savage 

and Smith, 1986)

The velocity, vn, can be written in terms of the x and z 

components of velocity, vx and vz,

sin9+[vz ] cos9. (19b)

In equation 19b, 9 is the counterclockwise angle between the 

x-axis and a line tangent to ZQ\ thus,

tan9 = ~dx (19c)

If we set vn equal to zero in equation 19b and solve for vz, we 

determine that

tone. (19d)

We can expand the components of the velocity in a 

perturbation series as we have done for the stresses,

the mean slope of the slip surface. The term Vx(dzQ/dx) is 

second order because it is the product of two first order quantities, Vx and (dzo/dx). By dropping terms higher than first 

order, the relationship between [vj, and [vz], reduces to

[vz ], = v,(~r). 

z zo x dx (21)

Formulas similar to equation 21 have been used by Nye 

(1969), Kamb (1970), and Morland (I976a). The geometry 

of the slip surface enters the solution of equations 18c and 

18d through equation 21.

A second boundary condition concerns the shear stress 

at the slip surface. The obvious assumption is that the shear 

stress is determined by the yield criterion (equation 5a). The 

normal stress [T^J^, shear stress [T^]^ and pore water 

pressure [P],, can be expanded (as in equations lla, lib, 

1 Ic, and 1 Id) in the yield criterion,

= c - 0 (A/) 2 ] Zo tanf . (22a)

and

(20a) Equation 22a can be resolved into two equations by collecting terms of zero and first order and deleting terms of second 

order,

V = V + V

z z vz O(A/) (20b) (22b)

but and

vx = constant, (20c) (22c)

and

vz = 0, (20d)

where vx is the constant rate of sliding in the absence of slipsurface irregularities; vz is zero because sliding is assumed 

to be parallel to the x-axis.

When equations 19c, 20a, and 20b are substituted into 

equation 19d, a boundary condition for Vz results:

(v

z0

= [v -. 

zo dx

We previously defined vz and v^ to be constants, 

independent of x and z (equations 20c, 20d); vz is zero 

because the average movement is parallel to the jc-axis and

The zero-order shear stress is a constant. In the zeroorder approximation, the slip surface is a plane parallel to the 

x-axis so (? ],= [Ty]^ and [^^=[7^. Thus, the zeroorder shear stress is determined by substituting equations 13 

and 17a into equation 22b,

(cosa) ') . (22d)

We have analyzed and attempted to solve a boundaryvalue problem that models forced circulation with Coulomb 

friction at the boundary (first-order shear stress determined 

by equation 22c). However, we were unable to determine an 

appropriate boundary condition to replace equations 19a or 

21, because Coulomb friction at the boundary would cause 

dilation and contraction at the slip surface.

D18 Landslide Processes in Utah
In order to overcome the difficulties connected with 

using equation 22c as a boundary condition, we have 

assumed that the first-order shear stress is zero everywhere 

on the boundary,

In equation 26, qn is the component of the specific discharge 

that is normal to the slip surface. We can rewrite equation 26 

in terms of qx and qz by expanding them in terms of perturbation series,

=0. (23) (27a)

This assumption is equivalent to letting the coefficient of 

friction in equation 22c be zero. The coefficient of residual 

friction of clayey materials ranges from 0.08 to 0.36 

(Skempton, 1964; Lambe and Whitman, 1969). This 

assumption results in the constants being determined by a 

system of linear equations that are readily solved.

We use the standard equations for transformation of 

stress (Hill, 1950, p. 347) to put equation 23 in terms of

and

47 = (27b)

By following steps similar to those used in deriving equation 

21 from equation 19a, we determine that

Tns ~ (Tzz -Txx)sinQ cos9

(24a)

Leading terms in the Taylor series expansions of cos 9, sin 

9, and tan 9 are 1,9, and 9, respectively. If we neglect higher 

order terms in the Taylor expansions, we can write

7x'' (27c)

In equations 27a and 27b

q = -K tana, a constant, (27d)

and

Recall that tan 9=A/ cos (/jc), and that for small 9, 9= tan 9; 

thus 9 = A/ cos (Ix). Making this substitution of tan 9 for 9 

shows that the right side of equation 24b consists of one firstorder term, 71r, and some second-order terms,

(24c)

Thus, we replace equation 23 with

(25a)

or in the moving coordinate system,

q? = 0, (27e)

because mean flow is assumed to be parallel to the slope. For 

landslides on gentle to moderate slopes (a<15°), tan o= 

O(A/). Thus, substituting equation 27d into 27c, shows that 

[<7Z], = O(A/)2, so that it can be neglected in the continuity 

equation, thus

(270

To relate the components of flow to the volumetric 

strains at the slip surface, we use a form of the continuity 

equation derived by combining equations A2.9, A2.10, and 

A2.12 of Freeze and Cherry (1979, p. 532).

[Tz$] = 0. (25b)

The velocity of the landslide also enters the solution of 

equations 18c and 18d through the flow at the wavy boundary. We assume that the slip surface is impermeable to water, 

so that

=0, (26)

Dt dz (28)

In equation 28, P represents the compressibility of water, n 

represents the porosity of the soil, qx and qz are components 

of the specific discharge vector or Darcy velocity vector of 

the fluid relative to the grains, vx and vz are components of 

the velocity vector of the solid, and DPIDt is the total-time 

or material-time derivative,

Steady Movement of Landslides in Fine-Grained Soils D19
DP = dP_ 

Dt Vx dx ^

dz

Equation 28 is a mathematical statement of the law of conservation of mass for the fluid and solids that constitute the 

landslide material. The equation ensures that the change in 

mass of fluid within a representative elemental volume of the 

material is balanced by flow of water and solids into or out 

of the element.

When equations 1 la, 13a, 20a, 20b, 20c, 20d, and 27a, 

27b, 27d, 27e, and 27f are substituted into equation 28 and 

terms of O(A/)2 are dropped, the expression becomes

equation 33 into equation 32 and neglect the first term on the 

right side to derive

(34)

Equation 34 relates fluid flow to volume change at the 

slip surface. Equations 21,25b, and 34 determine the boundary conditions needed to solve the boundary-value problem 

that models forced circulation.

Solution for the Stresses and Velocities in the 

Porous-Elastic Material

dx

3P _ n I "" ~ "' I A ~ £

- "P I V r + VZ + ^7 I + "gj + -5^

We use the first-order approximations of the boundary 

conditions (equations 21, 25b, and 34) to guess the form of 

the pore-pressure function, P, which satisfies equation 18c 

and the stress function, <j>, which satisfies equation 18d,

because the x and t derivatives of the zero-order quantities 

qx, qz, P, Vj, and vz, are zero (the zero order quantities are 

all constants with respect to x and r.) 

Let

dv de

(30)

for small strains, where e is the volumetric strain, and 

is the rate of volumetric strain. In equation 30,

e = (31)

where f^. and ^ are the normal components of strain.

When equations 30, 15c, and 15f are combined with 

equation 29, it simplifies to

. oP _ de

- n\jV? -=: ^ r '=\K f1^\

z dz x ot (32)

However, the quantity «P is small compared to A/, so that the 

first term on the right side of equation 32 can be neglected in 

a first-order analysis.

The specific discharge, q^, is determined by Darcy's 

law,

3P

(33)

The elevation head does not appear in equation 33, because 

the elevation head is a zero-order quantity. We substitute

and

P = exp(-/z) [cj

= (c3 + c4/z) exp (-/z) [c5 cos

(35a)

(35b)

Note that equation 35b is an incomplete solution of equation 

18d. In a complete solution., exp(-/z) would be replaced by 

[exp(-/z)+c7 exp(/z)]. We can neglect the exp(/z) part of the 

solution because the effects of forced circulation are greatest 

near the slip surface and we expect them to be undetectable 

at heights above the slip surface where z is greater than L.

We proceed to solve equations 35a and 35b together 

with the boundary conditions for the velocities, stresses, and 

the pore pressure. Then we compute the resistance to sliding 

from the solution for the normal stress, 7W.

The free-slip boundary condition (equation 25) in 

terms of <j> and the quasi-static coordinate system is,

= 0, (36)

where 32(j>/3£3z is determined by

c4 (/z-l)]exp(-/z)

(-c5 sin (37)

D20 Landslide Processes in Utah
When equation 36 is substituted into equation 37, and 

z is set equal to zero, we determine that (41)

c, = CA (38)

Thus, c3 and c4 can be set equal to unity and their numerical 

value can be absorbed into c5 and c6.

To apply the velocity boundary condition, equation 

21, we use the definition of vz and transform coordinates; 

thus,

v, = 3 df

= -v

du

We compute MZ by integrating the constitutive equation 

relating Tzz and EK.

The constitutive equations that govern the behavior of 

the porous-elastic solid are listed in Rice and Cleary (1976). 

We have assumed that the soil particles are incompressible, 

so that the pore-pressure coefficient, B (Skempton, 1954; 

Lambe and Whitman, 1969), is equal to one, and Poisson's 

ratio for undrained loading, nu, is 0.5. For this assumption, 

the constitutive equations of Rice and Cleary (1976, p. 229) 

simplify to the following equations (in terms of the new 

coordinate system, equations 31):

, (39a)

<39b)

and

2GEZZ = Tzz - . (39c)

After making the appropriate substitutions for the 

stress function into equation 39c, we integrate to derive an 

expression for vz:

(l-2\i)P \dz

(40)

In equation 40, fit) must be zero, because vz-»0 as 

. We perform the operations indicated in equation 40 to 

obtain an expression for vz,

-exp(-/z) {- /z)c5 -2/nc5

In equation 41, z is set equal to zero, and the velocity 

boundary condition (equation 21) is used to solve for the 

constants; thus, by collecting sine and cosine terms, two 

expressions relating the constants are obtained

0 = 2/c5 -2/jic5-(l-2ji) j (42a)

and

v// = -

Equations 42a and 42b simplify to

. (42b)

(43a)

and

(43b)

Now we use the boundary condition given by equation 

34 to solve for c5 and c6. To compute £, we use equations 

39a and 39c, and the definition of e:

Thus,

and

(44)

[-c5 sin

+ c6 cos /£] +21 exp(-/z) [-CjSi

+ c2 cos (45)

We differentiate equation 35a to compute an expression for

Steady Movement of Landslides in Fine-Grained Soils D21
- = -/ exp(-/z) {c,cos (46) R = -

(50)

Equations 45 and 46 are substituted into equation 34, 

the no-flow condition at the boundary, to obtain two more 

equations relating the unknown constants. When z is set 

equal to zero and the sine and cosine terms are collected, the 

following expressions are obtained.

v v (l-2n) x'w

KG (47)

[rcs - Cl ] . (48)

Equations 43a, 43b, 47, and 48 constitute a system of four 

algebraic equations that can be solved simultaneously for the 

unknown constants, ct , c2, c5, and c6.

The constant c5 is determined by solving equations 

43a, 43b, 47 and 48 simultaneously:

. (51)

1+

The formula for R can now be written out fully by substituting equation 51 into 50:.

R =

-vx (Al)\(l-2\i) 2

1 +

\2KGl(I-\i)

. (52)

Resistance to Sliding Due to 

Forced Circulation

We can now compute the resistance to sliding due to 

forced circulation, using equations 4c, 12b, 17a, and35b. 

Resistance to sliding due to roughness results only from the 

first order normal stress. The resistance to sliding due to the 

zero-order normal stress is zero, because (dzQldx) is periodic, 

\TXX\ZQ is a constant, and the average value of (dzjdx) is zero,

0 =

1 PL _ (zQ 

= 7 [7«] - \7T- £>JO ^{dx

Thus, the resistance to sliding, /?, is determined by substituting equations 3 1 into equation 4c

L ~

(49b)

On the boundary, the normal stress, [7^.]^, due to forced circulation is determined by substituting equations 35b and 38 

into 17a,

ZQ = -I2 [c5 cos . (49c)

Equations 49c and 9 are substituted into equation 49b to 

compute R,

An approximate formula for R that applies when 

vr/A"<100 is derived by neglecting part of equation 52.

For combinations of vx, \i, G, and K typical for silty

and clayey soils, the term (in the denomi- \2KGl (\ -\i) J 

nator of equation 52) is small compared to 1. The resistance, 

/?, is approximately

R ~

-v, (A/) \Q-2n) 2 

4*7(1-n) 2

(53)

The corresponding expression for resistance to sliding 

due to plastic deformation at the base of a glacier (Kamb, 

1970) is

R = -±vx (Al) 2 lr\. (54)

In equation 54, T| is the viscosity of glacier ice. The negative 

sign in the right hand side of equations 50, 51, 52,53, and 54 

are a result of the sign convention used in computing the 

stresses. When R is substituted into equation 4b, it is clear 

that the resistance to sliding due to forced circulation augments the shear strength of the slip surface, because the negative sign preceding R in equation 4b cancels the negative 

sign in the formula for R.

For short wavelengths, the resistance due to forced circulation is small, and it increases with increasing wavelength, so that forced circulation will occur at short (perhaps

D22 Landslide Processes in Utah
less than 10 m) wavelength bumps on the slip surface. This 

result is consistent with the fact that diffusion becomes more 

difficult as the path length, which is proportional to the 

wavelength, increases. At sufficiently long wavelengths, the 

resistance to sliding caused by forced circulation might 

become so great that some other mechanism of deformation 

becomes active near the slip surface, in much the same way 

that regelation gives way to viscous drag as the wavelength 

increases (Kamb, 1970). In glaciers, viscous drag is active at 

long wavelengths, because the viscous drag decreases with 

increasing wavelength (at constant roughness, equation 55). 

We do not know what mechanism in landslides might correspond to viscous drag in glaciers. One possibility is the creep 

deformation analyzed by Mizuno (1989); however, it 

appears to be independent of wavelength.

Equations 52 and 54 were derived for the case where 

the boundary is impermeable. If the boundary is permeable, 

pore-fluid diffusion is active at asperities having longer 

wavelengths (other things being equal), because the water 

flows through material beneath the landslide as well as 

through the slide, effectively reducing the resistance to flow 

of water. A permeable boundary has the same effect on the 

resistance to sliding, or the velocity of the landslide, as does 

increasing the permeability of the soil above the slip surface.

DISCUSSION AND CONCLUSION

Roughness of slip surfaces can affect the velocity of 

landslides. We have shown that forced circulation of water 

around asperities can control the velocity of a landslide.

We have not observed forced circulation occurring in 

landslides, but forced circulation is a plausible mechanism 

for the slow movement of landslides in clayey soils because 

most rate-dependent properties of soils have been attributed 

to the movement of pore water, and landslides move by sliding on uneven slip surfaces. Consolidation is considered the 

primary cause of time-dependent effects in fine-grained soils 

(Terzaghi, 1925; Wroth and Houlsby, 1985, p. 6). This suggests that movement of pore water might play an important 

role in controlling the velocities of landslides.

The mechanism of forced circulation is consistent 

with the observed linear relationship between landslide 

velocity and the average height of the water table (Terzaghi, 

1950). In a wide, thin landslide where the water table is 

unconfined and flow is parallel to the ground surface, R is 

proportional to the mean pressure head at the slip surface, h 

cos a. The velocity dependent resistance to sliding, /?, 

needed to maintain equilibrium is determined by the difference between the shear stress due to weight of the debris and 

the shear strength at the slip surface. An expression for R is 

determined by substituting equations 4c, 22d, and 49b into 

4b and rearranging:

R = Zy{ { since- !- h^ ( cosa) (fcnf)} -c'.

(55)

Equation 55 indicates that as the average pore pressure 

(/ryw) at the slip surface rises, the shear strength due to friction on the slip surface decreases in proportion to the change 

in h, but the driving forces remain constant. Consequently, R 

must increase linearly as h increases, in order to provide 

enough resistance at the slip surface to compensate for the 

loss of shear strength and balance the driving forces acting 

on the landslide. This increase in R causes a corresponding 

increase in the velocity of the landslide.

For the mechanism of forced circulation, the velocity 

of the landslide, vx, is proportional to R. Rearranging equation 53 yields

(56)

(A/)\(l-2|a) 2

In equation 56, R is determined by equation 55. Thus, 

according to the mechanism of forced circulation (equations 

55 and 56), the steady velocity increases linearly with the 

mean height of the water table. Furthermore, equations 55 

and 56 indicate that the maximum velocity of a given landslide is determined by the maximum height attained by the 

average pressure head at the slip surface.

The relationship between velocity, shear stress, available shear strength, and resistance to sliding due to forced 

circulation are shown in figure DIG. The shear stress tending 

to cause sliding is approximately constant, as indicated by 

the horizontal line in figure DIG (assuming that the total unit 

weight of soil does not change significantly through time). 

Sliding occurs when the water table exceeds its critical 

height, hcr. When the critical height is exceeded, the shear 

stress exceeds the available shear strength, and sliding 

begins. However, the resistance to sliding due to forced circulation, R, augments the shear strength to exactly balance 

the shear stress and maintain equilibrium. If the average 

water table reaches some steady height, ~h (fig. D10), the 

slide will reach a steady velocity, vx, consistent with R.

The amount of resistance to sliding that can result 

from forced circulation is shown in figure Dl 1. Figure Dl 1A 

shows R graphed as a function of vx/K for typical values of 

L, Al, n, and yw. The graph shows R only for values 

of vx/K<\00 because we have neglected advective transport 

of water in deriving equation 54. Errors in R, due to neglecting advection, should become significant when vxIK is 

greater than a few hundred. Figure Dl 1A indicates that R is 

less than 5 kPa if vx/K<lQQ.

We expect the steady velocities of landslides in clayey 

soils to be correlated with the average hydraulic conductivity 

of the landslide material. Figure D11B shows /?/Zyf sin a 

(where Zyt sin a is the shearing stress due to the weight of the

Steady Movement of Landslides in Fine-Grained Soils D23
CO CO Q LU

z z

< I

. o

I D

H O

O QC

cc f

I- LU

CO D

oc Q

CO Q

CO d

CO w

iii O

CO CJ

CO

LU

cc

0

HEIGHT OF WATER TABLE ABOVE SLIP SURFACE

her

h=z

Shear stress, Zyf sin (a)

No movement

Shear stress

T

Shear strength

Velocity

Figure D10. Relationship between shear strength, 

shear stress, the resistance to sliding due to roughness 

(R), mean height of water table above the slip surface 

(h), and the velocity of a landslide ( ~vx). No movement 

occurs when h<hcr, because the available shear 

strength exceeds the average shear stress. Movement

occurs at velocity vx when the water table is at a height, 

h, between the critical height and the maximum height 

(hc^h<Z)t so that R plus the shear strength equals the 

average shear stress. The height of the shaded triangular 

area along any vertical line h - vx is R.

landslide material) graphed as a function of vx/K. Of course, 

R must be less than or equal to the shear stress, Zyr sin a, and 

we expect it to be less than 10 percent of the shear stress in 

most cases. Figure Dl 15 indicates that the maximum steady 

velocities of landslides should range from about one tenth to 

a few thousand times the hydraulic conductivity, assuming 

that R/Zyt sin a rarely exceeds 0.1. Thus, a scatter plot of 

velocity versus hydraulic conductivity for various landslides 

should show a trend of landslides with higher hydraulic conductivity having greater velocities than those with lower 

conductivity.

The large range of velocities of steady landslides 

might be explained by the mechanism of forced circulation. 

The velocity of the landslide is proportional to the hydraulic 

conductivity, K, of the soil (equation 50). The conductivity 

of fine-grained soils ranges over several orders of magnitude, from 10~12 to 10~5 m/s (Freeze and Cherry, 1979, p. 

29). The average velocities of steadily moving landslides in 

fine-grained soils also range over several orders of

magnitude, from 10~ 10 to 10 3 m/s (Keefer and Johnson, 

1983). A few landslides in clayey soils may actually move 

much faster than 10~3 m/s (R.M. Iverson, USGS, written 

commun., 1988). However, observations indicate that most 

landslides in clay soils, which have very low permeability, 

move steadily and slowly. For example, debris of the Aspen 

Grove landslide, near Ephraim, Utah, was clay and silty clay 

that presumably had a low permeability. The peak velocity 

of the landslide (Baum, 1988), which occurred when the 

water table was at the ground surface, was only 20 cm/day 

(2.3X10"6 m/s). The peak velocity of the Thistle landslide 

(Duncan and others, 1986, p. 11) was 48 m/day (5.6x10^ 

m/s). Of landslides in clayey soils that were active in central 

Utah during 1983 and 1984, the Thistle landslide moved 

faster than any others we know of and the Aspen Grove landslide moved at a speed we consider typical of the landslides 

in central Utah.

Forced circulation will produce a complicated pattern 

of seepage within a moving landslide. For example, figure

D24 Landslide Processes in Utah
0.01

0.1

VX/K (dimensionless)

Figure D11. Graphs showing resistance to sliding due to 

forced circulation, R (computed using equation 53). (A) R is 

plotted against vx/Kfor typical field values of the parameters; 

H=0.3, 7^=9.80 kN/m3 (Lambe and Whitman, 1 969); values of 

Al and L indicated on the graph are from Mizuno (1989). (B) R

D12 shows contours of total head in a landslide in which 

flow, due to forced circulation, is superposed on flow 

parallel to the slope with the water table at the ground surface. Total head, H, in figure D12, is determined by the 

formula,

H = cos a-x sin

A

exp(-/z)cos Ix, (57)

which is derived by substituting equation 35a into equation 

13b. In equation 57, H is the head, z\ is the height of the 

water table (and the ground surface) above the x-axis, a is 

the slope of the ground surface, and v^A/Kis the constant q 

(equation 35a) divided by the unit weight of water, yw, for 

the case where (a is zero. The following parameters were 

used in equation 57 to determine the contours of head shown 

in figure D12: vx/K is unity, / is 1 nT1 , A is 0.1 m, and z\ is 

2 m. For this combination of parameters, c2 in equation 35a 

is approximately 0.0005 q, and, therefore, is negligible.

Although the details of the flow pattern resulting from 

forced circulation vary with the choice of parameters, some 

general features are illustrated by figure D12. Upwarddirected flow, emanating from the proximal sides of the sinusoidal bumps, fans outward and some of the water seeps out 

of the ground surface along roughly horizontal flow lines 

(flow lines are perpendicular to contours of head). A small 

amount of water, emanating from the proximal side of a 

bump, flows upslope toward the zone of suction and dilation 

at the distal side of the neighboring bump. However, flow 

directed upslope might not occur in all cases. Flow near the

10 

(dimensionless)

100 1000

divided by the shear stress, Zyf sin a, is plotted against vx//Cfor 

typical field values of the parameters: Z ranges from 1 to 30 m, 

yf=18.8 kN/m3, 7^=9.8 kN/m3, ^1=0.3 (Lambe and Whitman, 

1969), cc=15°, A/=0.2, and L ranges from 1 to 10 m.

distal sides of bumps is directed downward, and some water 

infiltrates from the ground surface in these areas.

The water level in observation wells (open tubes), or 

the pore pressure measured by piezometers, will depend on 

the position of the instrument with respect to the slip surface. 

The pore pressure near the distal sides of bumps ought to be 

lower than average, whereas the pore pressure near proximal 

sides of the bumps ought to be higher than average. However, testing the hypothesis of forced circulation by measuring pore pressure in an active landslide might have 

ambiguous results, because one needs to know the shape of 

the failure surface and the general pattern of groundwater 

flow in the slope in order to interpret the measurements.

We do not have enough field data to verify the mechanism of forced circulation, but at the Minor Creek landslide 

in northern California, the hydraulic conductivity is known 

well enough to use equation 53 to estimate the velocity. This 

landslide has an average hydraulic conductivity, K, of 

5x10~8 m/s (Iverson and Major, 1987) and a maximum 

velocity of a few decimeters per month (Iverson, 1986), or 

from about 4xlO~8 to 2xlO~7 m/s. Using data from a stability 

analysis by Iverson and Major (1987), we calculate that R 

equals 0.13 kPa when the landslide is moving at its maximum velocity. Using this value for R and assuming that the 

wavelength, L, is between 1 and 10m (range of wavelengths 

reported by Mizuno, 1989); the roughness, A/, is 0.2 (the 

average field value determined by Mizuno, 1989), and (a is 

0.3; we calculate a maximum velocity for the Minor Creek 

landslide of 1.3xlO~7 m/s (for L=l m) or 1.3xlO~8 m/s (for 

L=10 m). Our calculated velocities are of the same order of

Steady Movement of Landslides in Fine-Grained Soils D25
-1

-2

EXPLANATION

0.5

Contour of static headNumber indicates head, in meters

Ground surface

345 

HORIZONTAL DISTANCE, IN METERS

Figure D12. Cross section showing contours of total head, H, in a hypothetical landslide. The pattern of head results from 

the superposition of slope-parallel flow and forced circulation due to sliding on the uneven slip surface.

magnitude as the maximum velocity observed by Iverson 

(1986).

We expect our analysis of the mechanism of forced 

circulation to poorly represent operation of the mechanism in 

landslides that have been displaced less than one wavelength, and to represent the operation of forced circulation 

with acceptable accuracy in landslides that have been displaced at least a few wavelengths. Nonlinear deformation of 

soil, such as irreversible deformation that results in hysteresis during repeated cycles of loading and unloading, was not 

considered in our analysis. However, permanent deformation is greatest during the first cycle of loading and unloading, which would correspond to displacement of the 

landslide over one wavelength. Hysteresis diminishes during 

repeated cycles of loading and unloading of clay samples, or 

in other words, loading and unloading curves tend toward 

each other (Lambe and Whitman, 1969, p. 321) so that the 

modulus for unloading (swell index) approximately equals

the modulus for loading (compression index). Thus, after a 

landslide has been displaced several wavelengths, hysteresis 

should be negligible, and equation 53 should determine the 

resistance due to forced circulation with fair accuracy.

REFERENCES CITED

Baum, R.L., 1988, The Aspen Grove landslide, Ephraim Canyon, 

central Utah: Cincinnati, Ohio, University of Cincinnati, 

Ph.D. thesis, 363 p.

Biot, M.A., 1941, General theory of three-dimensional consolidation: Journal of Applied Physics, v. 12, p. 155-164.

Bjerrum, Laurits, 1967, Progressive failure in slopes of over-consolidated plastic clay and clay shales: Journal of the Soil 

Mechanics and Foundations Division of the American Society of Civil Engineers, v. 93, no. SM5, p. 3-49.

Brunsden, Denys, 1984, Mudslides, in Brunsden, Denys, and Prior, 

D.B., eds., Slope instability: New York, Wiley, p. 363-418.

D26 Landslide Processes in Utah
Budd, W.F., 1970a, Ice flow over bedrock perturbations: Journal of 

Glaciology, v. 9, no. 55, p. 29^18.

___1970b, The longitudinal stress and strain-rate gradients in ice 

masses: Journal of Glaciology, v. 7, no 55., p. 19-27.

Byerlee, J.D., 1970, The mechanics of stick-slip: Tectonophysics, 

v. 19, no. 5, p. 475^486.

Collin, Alexandre, 1846, Recherches expe"rimentales sur les glissements spontane's des terrains argileux: Paris, Corps Royal des 

Fonts et Chausdes and Corps des Mines. Translation by W.R. 

Schriever, 1956, Landslides in clays: Toronto, University of 

Toronto Press, 160 p.

Collins, I.F., 1968, On the use of the equilibrium equations and 

flow law in relating the surface and bed topography of glaciers and ice sheets: Journal of Glaciology, v. 7, no. 50, p. 

199-204.

Craig, D., 1981, Mudslide plug flow within channels: Engineering 

Geology, v. 17, p. 273-281.

Dounias, G.T., Potts, D.M., and Vaughn, P.R., 1988, The shear 

strength of soils containing undulating shear zones A 

numerical study: Canadian Geotechnical Journal, v. 25, p. 

550-558.

Duncan, J.M., Fleming, R.W., and Patton, F.D., 1986, Report of the 

Thistle Slide Committee to State of Utah, Department of Natural Resources, Division of Water Rights: U.S. Geological 

Survey Open-File Report 86-505, 95 p.

Freeze, R.A., and Cherry, J.A., 1979, Groundwater: Englewood 

Cliffs, N.J., Prentice-Hall, 604 p.

Gould, J.P., 1960, A study of shear failure of certain Tertiary 

marine sediments, in Research conference on shear strength 

of cohesive soils, Boulder, Colorado: New York, American 

Society of Civil Engineers, p. 615-641.

Hill, Rodney, 1950, The mathematical theory of plasticity: Oxford, 

Clarendon Press, 356 p.

Hutchinson, J.N., 1970, A coastal mudflow on the London clay 

cliffs at Beltinge, North Kent [England]: Ge'otechnique, v. 

20, no. 4, p. 412-438.

____1983, Methods of locating slip surfaces in landslides: Bulletin of the Association of Engineering Geologists, v. 20, no. 

3, p. 235-252.

Iverson, R.M., 1986, Dynamics of slow landslides A theory for 

time-dependent behavior, in Abrahams, A.D., ed., Hillslope 

processes: Winchester, Mass., Alien & Unwin, p. 297-317.

Iverson, R.M., and Major, J.J., 1987, Rainfall, groundwater flow, 

and seasonal movement at Minor Creek landslide, northwestern California Physical interpretation of empirical 

relations: Geological Society of America Bulletin, v. 99, p. 

579-594.

Jaeger, J.C., and Cook, N.G.W., 1969, Fundamentals of rock 

mechanics: London, Methuen and Co., Ltd., 513 p.

Janbu, N., 1973, Slope stability computations, in Hirschfield, R.C., 

and Poulos, S.J., eds., Embankment-dam engineering 

Casagrande volume: New York, Wiley, p. 47-86.

Japan Society of Landslide, 1980, Landslides in Japan: Tokyo, The 

Japan Society of Landslide National Conference on Landslide Control, 44 p.

Kamb, Barclay, 1970, Sliding motion of glaciers theory and 

observation: Reviews of Geophysics and Space Physics, v. 8, 

no. 4, p. 673-728.

____1986, Stress-gradient coupling in glacier flow HI. Exact 

longitudinal equilibrium equation: Journal of Glaciology, v. 

32, no. 112, p. 335-341.

Kamb, Barclay, and LaChapelle, E., 1964, Direct observation of the 

mechanism of glacier sliding over bedrock: Journal of Glaciology, v. 5, no. 38, p. 159-172.

Keefer, D.K., 1977, Earthflow: Stanford, Calif., Stanford University, Ph.D. thesis, 317 p.

Keefer, D.K., and Johnson, A.M., 1983, Earth flows Morphology, mobilization and movement: U.S. Geological Survey 

Professional Paper 1264, 56 p.

Kenney, T.C., 1968, The influence of mineral composition on the 

residual strength of natural soils: Proceedings of the Geotechnical Conference, Oslo, Norway, 1967, v. 1, p. 123-129.

Lambe, T.W., and Whitman, R.V., 1969, Soil mechanics: New 

York, Wiley, 553 p.

Lliboutry, L., 1968, General theory of subglacial cavitation and 

sliding of temperate glaciers: Journal of Glaciology, v. 7, no. 

49, p. 21-58.

Malvern, L.E., 1969, An introduction to the mechanics of a continuous medium: Englewood Cliffs, N.J., Prentice-Hall, 713 p.

Mitchell, J.K., 1976, Fundamentals of soil behavior: New York, 

Wiley, 422 p.

Mizuno, Keiji, 1989, Landsliding of clayey slopes with a wavy slip 

surface Model and its application: Japan, Science Reports 

of the Institute of Geosciences, University of Tsukuba, sec. 

A,v. 10, p. 87-151.

Morgenstern, N.R., and Price, V.E., 1965, The analysis of the stability of general slip surfaces: Ge'otechnique, v. 15, p. 79-93.

Morgenstern, N.R., and Tchalenko, J.S., 1968, Microstructural 

observations on shear zones from slips in natural clays: Proceedings of the Geotechnical Conference, Oslo, Norway, 

1967, v. 1, p. 147-152.

Morland, L.W., 1976a, Glacier sliding down an inclined wavy bed: 

Journal of Glaciology, v. 17, no. 77, p. 447-462.

____1976b, Glacier sliding down an inclined wavy bed with friction: Journal of Glaciology, v. 17, no. 77, p. 463-477.

Niigata Laboratory, 1973, Sarukuyoji landslide: Niigata, Japan, 

Public Works Research Institute of Japan, 15 p. Nye, J.F., 

1969, A calculation on the sliding of ice over a wavy surface 

using a Newtonian viscous approximation: Proceedings of 

the Royal Society of London, series A, v. 311, p. 445-467.

Nye, J.F., 1969, A calculation on the sliding of ice over a wavy surface using a Newtonian viscous approximation: Proceedings 

of the Royal Society of London, series A, v. 311, p. 445-467.

____1970, Glacier sliding without cavitation in a linear viscous 

approximation: Proceedings of the Royal Society of London, 

series A, v. 315, p. 381-403.

Palmer, A.C., and Rice, J.R., 1973, The growth of slip surfaces in 

the progressive failure of over-consolidated clay: Proceedings of the Royal Society of London, series A, v. 332, p. 

527-548.

Patton, F.D., 1966, Multiple modes of shear failure in rock and 

related materials: Urbana, University of Illinois Ph.D. thesis, 

293 p.

Prior, D.B., and Stephens, N., 1972, Some movement patterns of 

temperate mudflows Examples from northeastern Ireland: 

Geological Society of America Bulletin, v. 83, no. 8, p. 

2533-2543.

Ramiah, B.K., and Purushothamaraj, P., 1971, Influence of strain 

rate on the residual strength of a kaolinitic clay: Geotechnical 

Engineering, v. 2, no. 2, p. 151-158.

Rice, J.R. and Cleary, M.P., 1976, Some basic stress diffusion solutions for fluid saturated elastic porous media with compressible constituents: Reviews of Geophysics and Space Physics, 

v. 14, no. 2, p. 227-241.

Rosenthal, D., 1946, The theory of moving sources of heat and its 

application to metal treatments: Transactions of the American Society of Mechanical Engineers, v. 68, p. 849-866.

Steady Movement of Landslides in Fine-Grained Soils D27
Rybdf, Jan, 1968, Bin Beispiel von Bewegsungsmessungen an Rutschungen: Zeitschrift fiir angewandte Geologic, v. 14, p. 

138-141.

Savage, W.Z., and Chleborad. A.F., 1982, A model for creeping 

flow in landslides: Bulletin of the Association of Engineering 

Geologists, v. 19, no. 4, p. 333-338.

Savage, W.Z., and Smith, W.K., 1986, A model for the plastic flow 

of landslides: U.S. Geological Survey Professional Paper 

1385. 32 p.

Skempton, A.W., 1954, The pore-pressure coefficients A and B: 

Gdotechnique, v. 4, p. 143-147.

____1964, Long-term stability of clay slopes: Gdotechnique, v. 

14, p. 77-102.

Skempton, A.W., Leadbeater, A.D., and Chandler, R.J., 1989, The 

Mam Tor landslide. North Derbyshire: Philosophical Transactions of the Royal Society of London, series A, v. 329, no. 

1607, p. 503-547.

Skempton, A.W., and Petley, D.J., 1968, The strength along structural discontinuities in stiff clays: Proceedings of the Geotechnical Conference, Oslo, Norway, 1967, v. 2, p. 29-48.

Stout, M.L., 1971, Slip surface geometry in landslides, southern 

California and Norway: Association of Engineering Geologists Bulletin, v. 8, no. 1, p. 59-78.

Suhayda, J.N., and Prior, D.B., 1978, Explanation of submarine 

landslide morphology by stability analysis and Theological

models: Offshore Technology Conference, Proceedings, no. 

10, v. 2, p. 1075-1082.

Ter-Stepanian, G., 1965, In-situ determination of the rheological 

characteristics of soils on slopes, in Proceedings of the Sixth 

International Conference on Soil Mechanics and Foundation 

Engineering, Montreal, Canada, 1965: Toronto, University 

of Toronto Press, v. 2, p. 575-577.

Terzaghi, K.V., 1925, Erdbaumechanik auf Bodenphysicalischer 

Grundlage: Vienna, Franz Deuticke, 399 p.

____1950, Mechanism of landslides, in Paige, Sidney, ed.. 

Application of geology to engineering practice: Geological 

Society of America, Berkey Volume, p. 83-123.

Wroth. C.P., and Houlsby, G.T., 1985, Soil mechanics Property 

characterization and analysis procedures, in Proceedings of 

the Eleventh International Conference on Soil Mechanics 

and Foundation Engineering, San Francisco, 1985: Rotterdam/Boston, A.A. Balkema, v. 1, p. 1-55.

Wylie, C.R., and Barrett, L.C., 1982, Advanced engineering mathematics: New York, McGraw-Hill, 1,103 p.

Yen, B.C.. 1969, Stability of slopes undergoing creep deformation: 

American Society of Civil Engineers Proceedings, v. 95, no. 

SM4, p. 1075-1096.

Zaruba, Quido, and Mencl, Vojtech, 1982, Landslides and their 

control: New York, Elsevier Publishing Co., 324 p.

D28 Landslide Processes in Utah

irU.S. GOVERNMENT PRINTING OFFICE: 1993-774-049/66029
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