3 (1990) 45-55
Geomorphology,
Elsevier SciencePublishers 8.V., Amsterdam -
^Ê
Printed in The Netherlands
A ComparisonbetweenTheoreticaland Measured
CreepProfilesof Landslides
Th.J.W.VAN ASCH andP.M.B.VAN GENUCHTEN
Department of PhysicalGeography,IJtrecht lJniuersity, P.O. Box 80 115, 3508TC Utrecht (The Netherlands)
(ReceivedMarch 24, 198?;acceptedafter revision April 20, 1989)
Abstract
Van Asch, Th.J.W. and Van Genuchten,P.M.B., 1990.A comparisonbetweentheoretical and measuredcreepprofiles
of landslides.Geomorphology,3: 45-55.
Continuous creep contributes to the movementsof a landslide in varved clays.The creepmodelsdevelopedin this
paper are basedon the Bingham rheologicalbehaviour of the soil. In this Bingham model the yield strength value and
the viscosity coefficient can be defined in different ways,as was done by Ter Stepanian ( 1963) and Yen ( 1969). The
yield strength can be defined as a residualstrength value for overconsolidatedclays (Yen ) or as a fixed fraction of the
peak strength parametersCo,and Qp,(Ter Stepanian), and the viscosity coefficient can be consideredas a constant
(Yen) or as a flow factor which dependson the effectivenormal stress (Ter Stepanian).
Creep tests, (reversal) direct shear tests and triaxial tests were carried out on varved clay samplesin order to
determineyield strength valuesand the viscosity parameteraccordingto different definitions. Four creepmodelshave
been evaluated;these are based on four possiblecombinations of the different definitions of yield strength and the
viscosity parameter. Yen's definition of the yield strength in combination with a flow factor which dependson the
effectivestress ( Ter Stepanian) is found to give the best prediction of the creepvelocity data that were measuredin
the field.
1. Introduction
Recording of landslide displacement over
about ten years has revealedthat sliding along
distinct slip surfacesis not the only mechanism
of movement involved. As mentioned by several authors (Dysli and Recordon, 1982;Manfredini et al., 1982; Van Asch, 1984; Iverson,
1985) an additional movement mechanism is
continuous creep,which can occur at a certain
depth in the landslide shear zone. The creep
processmay be of $eat importance in the development of landslides becauseinitial movement of the slope may start with creep processesat stress values that Iie far below the peak
strength of the soil material (Terzaghi, 1936).
These slow creep movements can also lead to
0169-555X/90/$03.50
acceleratedcreepand shear failure (Murayama
and Shibata, 1961; Singh and Mitchell, 1969;
Campanella and Vaid, 1974;Vyalov et al., 1976;
Ting, L982).
In this paper four models are presented which
describethis so-calleddepth creep.The models
are based on different definitions of the yield
strength and viscosity parameter. Theoretical
creep velocity profiles were calculated with
these models and compâred with measured
creep profiles from varved clay slopes in the
French AIps. The input parameters of these
models based on different definitions were determined in the Iaboratory by means of creep
tests, (reversal) direct shear tests and triaxial
tests. In the modelswhich are developedin this
paper the soil rheological behaviour is consid-
@ 1990ElsevierSciencePublishersB.V.
46
Th. J.W.ASCHAND P.M.B.VAN GENUCHTEN
ered to be described by the following simple
stress-strain rate relationship:
, /d"\
r:ro*kl , |
\oy,/
(1)
the yield strength 16in eqn. (1) has a physical
meaning and correspondsto the Mohr's envelope of the residual strength of the material
(Yen, 1969;Suhaydu and Prior, 1978;Iverson,
1985). This yield strength line can be described
by the following equation:.:
where: T:shear stress; To:â cr€€p threshold
shearstrength (yield strength); k:a flow fac10:C" * O'tanQ!,
e)
tor; and du/dy:shear strain rate (-velocity
where: ?o:the yield strength; ci:the residual
gradient).
cohesion (usually c',x0); o' :the effective norStress-strain rate relationships can be meamal stress;and @i:the residual friction angle.
sured in a direct shear apparatus, where under
Figure 2a depictsin the plane of Mohr a yield
constant effective normal stress a relationship
strength line. In the stressfield, which lies becan be found betweenthe deformationrate du/
low this line the body is assumed to be rigid
dy andthe applied shear stress z. Fig. 1 gives a
(comparewith Fig. 1). AccordingtoYen (1969)
schematicexample.
line correspondsto the residual strength
this
The curve in Fig. 1 can be approximated by a
envelope. Above the yield strength line lies a
vertical line (du/dy-O up to ?:?o) and a
stressfield where the material is in a creepphase
straight line (tan V: k'for r > ro) . In this ïvay a
( s e eF i g . 2 a ) .
rigid phase du/dy:0 is assumedfor 0<z<16
Ter Stepanian (1963) used a different defiand a creepphasefor r> zoaccordingto a linear
nition
for the yield strength line. He stated that
model, seeeqn. ( 1 ). In reality Ë is mostly time
the yield strength line can be describedby the
dependent.However, time dependency can be
following equation (Fig. 2b):
built into the models discussedbelow. It will be
(3 )
shown below that creeptests done with a direct -à to:co * o'tan 0o
shear apparatus show stress-strain rate relawhere: ro:the yield strength; c6-a reduced
tionshipswhich correspondto the model given
peak cohesion;and 0o:a reducedpeakfriction
i n e q n .( 1 ) .
angle.
In this paper two problems connected with
Ter Stepanian (1963) stated that to, c6 and
this rheologicalmodel will be discussed:( 1) the
96are fixed fractions of the peak shear strength
definition of ro;and (2 ) the question of whether
?i,peak cohesionci and peak friction angle /i:
or not È is dependent on the existing isotropic
stressesin the soil. It is generally assumedthat
ç )To cç tan 0s
(4)
^/ /r-:.--;
Tç
du
oy
Fig. 1. An example of a simple stress-strainrate relationship of a soil sample.
cp
tAnQp
Figure 2b showsa yield strength line according to the definition of Ter Stepanian (1963),
eqn. (4). The line has the same origin as the
Mohr's peak strength envelop but shows a reduced internal friction angle ( 0o).
The secondproblem that will be discussedin
this paper is the factor È in eqn. (1 ). Yen (1969)
consideredthis factor as a viscosity coefficient
which is independent of the existing isotropic
stress in the soil as in a Bingham fluid. In a
number of publications about rheologicalcreep
behaviourofsoils, Ter Stepanian (1975,7977,
47
CREEP PROFILES OF LANDSLIDES
t o Y e n ( 19 6 9 )
creep
, _
_/
tan 6o-line:
yield strength
according to TerS t e p a n i a n( 1 9 6 3 )
normalstress
Fig. 2 Two different interpretations ofthe apparent creepthreshold value (yield strength) ofsoil material; do and copeak
strength parameters;c, and @,residual strength parameters;coand 9oyield strength parametersaccordingto Ter Stepanian;
to yield stressvalue; t' effective shear stress. (a) Shows a yield strength line which correspondsto the residual strength of
the material. In (b ) the yield strength line givesvaluesof ro, coand 0owhich are fixed fractions of rç,co and Q..
1980)explainedthat the soil "viscosity" is positively related to a soil structure deformability
coefficient: F /R, where F and .R are vectorial
sums of the normal and shear forces respectively working in a plane through the contact
zone between the particles. The distance between the particles is also positively related to
the viscosity of the diffuse layers in this contact
zone.Since the F /R ratio and the distance between the contact zone are directly propor-
tional to the effective normal stress at work in
a soil sample,Ter Stepanian (1963) assumed
that the A-factor, eqn. (1), generally increases
with increasing modified effective stress:
k,: (o' * oo)/À
(ô,
where:
d' : normal
effective
stress;
oo:cpcot{p (see Fig. 2b); and l:the coefficient of flow which is assumedto be a constant.
In the next section creep velocity models in
Th. J.W.ASCHAND P.M.B.VAN GENUCHTEN
48
terms of effective stresswill be developed;these
models will incorporate different definitions of
zoand È, as discussedabove.
As stated in section 1, Ter Stepanian assumed a linear relationship between the flow
factor k and the modified effective normal stress
o'. This relationship can be written as follows:
2. Models for calculating creep velocity
7: (oo* o' )/k
The creep modelsthat will be developedhere
incorporate the following assumptions: (1) a
flat slip surface with an infinitely long and wide
slope; (2 ) an isotropic normal consolidatedmaterial and no volume changes; (3) no changes
in stressdistribution arising from creep;and (4 )
the viscosity of the material is not time
dependent.
First a creep model will be developedwhich
incorporatesthe definitions of t6 and h Iseesection 1, equation (1) I as formulated by Ter Stepanian ( 1963). For all the models an r-y coordinate system will be used as given in Fig. 3. A
shear stressparallel to the slope is given by:
t:fy.(y-t*)*y*J,"lsinB+S
(6)
where: J:soil depth measuredperpendicular
from the soil surfacely*: depth ofphreatic surface perpendicular from slope surface; B:lhe
slopeangle;7. : unit weight of unsaturated soil;
/": unit weight of saturated soil; and S: shear
stressof overburden.
If groundwater flows parallel to the slopethe
effectivenormal stresso' at depth y is given by:
o':l(y-y*)y'*y*y,lcosB*P
(7)
(8a)
where .tr:coefficient of flow which is assumed
to be a constant, and:
oo:c'pcob/i (seeFig. 2b)
(8b)
Substituting eqn. (8a) into eqn. (1) gives:
duldy:l(r-rù
/(o6*o')
(9)
From Fig. 2b Ter Stepanian's threshold value
for creep can be describedas follows:
tan96: rof (oo * o' )
(10)
A combinationof eqns. (9) and (10) gives:
duldy:f,Ir/ (oo* o') -tanqsl
(11)
Substituting eqns. (6) and (7) into eqn. (11)
gives:
duldy:7 [y"ysinB-y*sin f (y,- y") +S]/
[y'ycosB-y*cos f (y' -y")
*P*ool-tan 96
(r2)
If one integrateseqn. (12) and takesinto accountthe boundaryconditionthat u : 0 fory : fu
(seeFig.3 ) oneobtains(for y)y*):
uy: 7f (h - y) (y"tanB/ y' - tan 0s)
* (S/sinf -y,Pr/y' -y*y,y*/y')
( t a nB / y ' ) l n ( / 'h * y * ( y . - y ' )
where P is normal stress of overburden,and y'
is the submergedunit weight of soil ( l" - y* ) .
+ Pr)/ (y'y * y*(y" - t' ) * Pr)l
(13a)
where
4:
Fig. 3. The coôrdinate systemused for the creepmodels.
(P + oo)/cosB
(13b)
Without any problem one can develop from
eqn. (13) a secondcreep model which incorporates a threshold definition fot 16,as formulated by Yen (1969) and others, seeeqn. (2).
The model can be made by substituting Q, for
dsineqn. (13a) and oo:c',cot@i(whichr0becausec'.is usually = 0 ) in eqn. ( 13b).
49
CREEP PROFILES OF LANDS]
In the next model the definitions of z6and À
as formulated by Yen are used. The model is in
fact the model presented by Yen ( 1969) . However Yen did not use effective stressesin his
derivation. Therefore a derivation of Yen's
model in terms of effective stressesis given here.
Using the threshold definition given in eqn.
(2) and the eqns. (6) and (7) for ? and o', respectively, and using the Bingham rheological
model [eqn. ( 1 ) , Ë: constant ] one can formulate the following equation for steady state
creep:
-kdu/dy:c|*
Ptan dl -S+cos É[ (y
-y*) (/'tan Q',-y,tan Ê) *y*y"(tan Qt
(14)
-tanÉ) l
Taking into account the boundary condition of
u:0 when y: h, integration of eqn. ( 14) yields
( f o ry 2 y * ) :
tt o) : | (h -y) / kl{ (c,,*Ptan 0| - S)
*cos B[ (ih+ iy - y*) (y' tan Q|
-7"tanf)l-y,,y,(tanQ|-tanB)lj
(15)
The fourth model has been obtained by the
introduction into eqn. (15) of the threshold
definition as defined by Ter Stepanian. For this
model ci and tan Q| have to be replaced by c6
[:cotan 06/Lan@i; see eqn. (4)] and tan 0e,
respectively.In all these models the rigid zone
y- (seeFig. 3 ) measuredperpendicularfrom the
soil surface ends at a depth where t: ro. Using
Yen'sthreshold definition for ?o,eqn. (2), and
substituting o' by eqn. (7), in eqn. (2), and
equalizing this expression for z6with eqn. (6)
for t, y(:y*) can be solved:
Jm-
Y * [ ( Y " - Y ' ) t a nQ | *
().,"tanÊ-y'tan Q|)
X
(/" -;l")tan fl+ (c',-S+P tan Q',)lcosB
( y " t a nB - y ' t a n Q t )
(16)
By means of the threshold definition of Ter
Stepanianone can also use eqn. (16) to calcu-
late the depth of the rigid zone (y-). In that
caseQ',and ci have to be replaced by 06 and c6,
respectively.
The minimum groundwater depth Jw,mi.
needed for starting the creep process (i.e.
can be obtained by rearranging eqn.
!^:h)
( 16) and replacing y* by h.:
Jw,min
-
lh(y,tan B-y'tan Q',)[ ( Y " - Y ' ) t a nQ t* ( 1 "- Y " ) t a n f ]
X
(cl - S+P tan Qt")
/cosf)
y")tanÉl
(
1
"
l ( y , - y ' ) t a nQ | *
(17)
The above describedcreep models are based
on four combinations of different definitions of
"viscosity" ofthe soil.
the yield strength and the
Before the theoretical results of these models
are compared with measuredvelocity profiles,
a description is given of the study area. Then
the laboratory results are given for the yield
strength and viscosity parameters according to
different definitions.
3. Description of the site and its
environment
The investigated area is situated in the
French Alps in the drainage basin of the River
Drac near its confluencewith the River Bonne.
Duringthe post-Wiirm periodthe rivers incised
into a basin filled mainly with varved clays
which had been deposited in a former glacial
lake (Monjuvent, 1973). The slopes in these
varved clays are partly unstable. The landslide
under investigation is situated in the sourcearea
of a small intermittent stream above a steep
secondaryvalley on the northwestern slope of
the River Drac. The landslide complex consists
of the following units (Fig. 4 ):
(1) A slide area with a concaveform (slopes
between 12 and 40" ) and heavily vegetatedwith
grass,shrub and sometrees. It is divided into a
number of soil blocks by large fissures and
scarpsup to 2 m high.
(2) A largeslump bowl (30 m diameter) with
Th. J.W.ASCHAND P.M.B.VAN GENUCHTEN
TABLE 1
The total andcreepdisplacement
for the flexibletubesbetweenMay 1981and March1982
Tube
no.
Displacement
at the surface
(m,
Mean velocity
at the surface
(ms-t)
Displacement
due to creep
(m)
Creep
velocity
(, m s_ ]' \ ,
Thickness
of the
creepzone
tm,
165
166
167
168
2
1.6
1.1
0.4
7.7xl0-8
6 x10 8
4 . 2x 1 0 - 8
1 . ?x 1 0 - 8
0.06
0.0?
0.03
0
4 . 0x 1 0 - e
3 . 5x 1 0 - e
1 . 0x 1 0 - e
0
t 1.8
t 1.8
0.5
0
ô
N
m
1
2
3
4
5
Depth to
the slip
plane
(m)
^ q
ll
.,
^
4
(3) An accumulation tongue on the thalweg
of the secondary valley built up by the clay
masseswhich have slid through the bowl. The
tongueis about 30" steep,100 m long,20-40 m
wide and some 5 m thick.
Geodeticmeasurementsshowedthat in general the blocks move in a direction perpendicular to the contour lines. The blocks move at
different velocities;in the period 1980-1988the
displacementsof the down-slopeblocks next to
the bowl were found to be the largest. The displacements of the blocks are concentrated in
spring and autumn. The mean displacementof
the fastest moving blocks is some 2 m per year
(Van Genuchtenand Van Asch, 1988).
Monitoring the deformation with an inclinometer of four flexible tubes inserted into the
sliding mass (seeFigs. 4 and 5) revealedthat
creep contributes about 5% to the displacements of the slide (seeTable 1 ).
t)
Irf.- 7
B
4. The threshold for creep of varved clay
material
15m
Fig. 4. The landslide complex: 1 : scarp< 40 cm;
cm;
2:scarp>40 cm and <80 cm;3:scarp>80
4: fissures; 5 : intermittent streams; 6 = slide; 7: bowl;
8 = tongue.
bare concavesides (10-60" ) which are partly
coveredwith slid material and are also marked
with erosion rills and small gullies.
Stress-strain rate tests were carried out to
determine the creepthreshold of the varved clay.
These tests were run in a direct shear box on
nine cylindrical samples (diameter 56 mm,
height 26 mm) at a constant effective normal
stressof 20.3kPa. The shear stresses(between
7.8 and 17 kPa) were applied with dead loads
on a hanger connected to the upper confining
ring with a line led over a pulley to convert the
vertical force into a horizontal one. The hori-
CREEP PROFILES OF LANDSLIDES
51
ESE
A
-----ll6
or.
P-----165
DT,fp
^
--i168
I
1
1 - l
=
-=
-: 4 - - !
-
234
H
: t
-
=
--
t
167
t
t
I
L
=
::
_
|
166
_
I
J
I
F
240
.
I
|
-
-
I
l
165
.
1
!-J
=
=
:
-i
:
-- l
------I
+
-\\
I
I
Izlùollrucron
rmdlenal
5
6
7
.-.''',,'..8
D T s
:
P 1 0
EP
11
Fig. 5. Cross-sectionprofile through the central part of slide (seeFig. 4 ) with position of flexible tubes and detectedslip
surfaces.1-rootzone; 2:clayey material, with few stones;3:stoney, clayey material; 4:varved clays; 5:phreatic level;
6 = displacementvectorperiod April 1981-April 1985;7:topographic surfacewith major fissure;8 = slip plane;9: deformation
tube; .10: standpipe piezomeLe4 11 :piezo-resistive piezometer.
zontal displacement (s) was measured with a
dial gauge sensitive to 0.01 mm. All samples
were shearedalong the lamination of the varved
clay. The pore water in the sample could not
evaporatebecauseof a surrounding water bath
and saturated porous stones above and below
the sample.
The mean shear strain rate for each test was
calculated,using the relation:
y: (ds/dt) /z
(18)
where:i:the shear strain rate (s -t); ds:the
horizontal displacementin the period dt (s);
and z: height of the sample.
Figure 6 gives the shear strain rates versus
the various effective shear stressesfor the various tests with a constant effective normal stress
(o' :20.3 kPa). As can be seenfrom this figure
the shear strain rate seemsto show a linear relation with the applied shear stress. This implies a simple linear-viscousmodel as described
by eqn. (1) and Fig. 1. The interception of the
linear fit with the y-axis in Fig. 6 givesthe value
5.2+0.2 kPa. This can be consideredas the
creep threshold value z6at an effective normal
stressof 20.3 kPa for varved clay. From this z6
value andthe appliedeffectivenormal stressTer
Stepanian's c6and 0o can be calculated accordingto eqns. (3) and (4). Forthis it is necessary
to know the peak strength parameters of the
material, seeeqn. (4). Table 2 gives a survey of
the soil mechanical and mineralogical characteristics. Within this table the peak strength
along the lamination is used to calculate c6and
9owhich are 1.37 kPa and L0.75,respectively.
Using Yen's creep threshold definition, eqn.
(2), and assumingc'.:0, one can also deduce
the residual friction angle from the apparent
threshold value (ro:5.2+0.2 kPa at o' =20.3
kPa) measured by means of the direct shear
creeptests:Q,:L4.4 + 0.5o.
In the laboratory the residual strength ofthe
varved clay material was determined also by
multireversal direct shear tests. The samoles
Th. J.W.ASCHAND P,M.B.VAN GENUCHTEN
<t
TABLE 2
propertiesof the varvedclay
Somephysicalandmineralogical
S t rength char acter ist ics
d ' o ( P e a k)
c'o (peak)
c'or(Peak)
c'. (residual)
@'. (residual)
c" (undrained)
c, (undrained)
Bulk d.ensity
Dry specific weight
Wet specificweight
23' + 2"
30 + 10kPa
180 + 50 kPa
0 kPa
l.q 70 +
360 + 60 kPa
570 + 110kPa
1 6 . 0+
20.0t
Atterberg limits
LL
PI
32-38%
1 3 ' - 1 8"
Mineral content of clay fraction
Quartz* calcite
Plagioclase* albite
Chlorite, elite vermiculite smectite
60 -70%
t0%
20 307o
both along and acrosslaminae
along laminae
acrosslaminae
both along and across laminae, reversal shear tests
both along and acrosslaminae, reversalsheartests
along laminae
acrosslaminae
0 . 8k N m - 3
0.8 kNm-3
Iiquid limit
plasticity index
Grainsize(wt.7o)
< 2 1t:49%; 2 8 p: 15%; 8- 16 7-r:73%; 32-50 1t:37o;50 p: l%
were shearedalong the lamination until a mrnimum strength was obtained; this strength was
assumedto be the residual strength. Five different effective normal stressesbetween 17 and
175 kPa were applied. A consolidation of 24l'r
was allowed for each sample before the straincontrolled, consolidated drained direct shear
tests were run. In order to check whether the
consolidation was complete the vertical adjustment was regularly measured with a dial gauge
sensitiveto 0.01mm. The samplesweresheared
at 0.2 mm h-r. The applied shear stresswas
measuredwith a dynamometer ring sensitiveto
1 N. These re-shear tests yield an effective residual cohesion (c'") of 0.0 kPa and an effective
residualfriction angle (@,)of 18.7t 1'.
The friction angle found in multi reversal
shear tests is some 4" higher than the one estimated from the creep tests. This difference
may be due to the fact that a direct shear box
was used to determine residual strength prop-
erties of soils.Residual friction anglesobtained
in direct shear tests (whether multireversal or
on cut planesor natural slip planes) were found
to be up to 7' higher than those obtained in ring
shear tests (cf. Bishop et al., 1971;Hutchinson
et al., 1980) and those estimated from back
analysis (Hutchinson et al., 1973). Therefore
it is expectedthat the multireversal direct shear
tests yield too high a friction angle' Another explanation for this difference might be that Yen's
assumption about the creepthreshold is wrong.
From Fig. 6 it is possible to determine the flow
factor k (:tanry):2.42x108 kPa s' Yen assumesthis to be constant, seeeqn. (15). The
coefficient of flow, according to Ter Stepanian
can be calculatedby eqn. (15), where coand /o
are known (Table 2) and o'-20.3 kPa. This
givesa valuefor A-37.6 X 10-8. In the next section the different values for yield strength and
flow characteristics, will be used to calculate
theoretical velocity profiles. These theoretical
53
CREEP PROFILES OF LANDSLIDES
TABLE 3
T
levelsfor the variouscreepthreshold
Minimumgroundwater
(kPa)
values, according to eqn. ( f 7 ) , y*, -r" is measured in the direction as indicated in Fig. 3
Threshold values determined from:
Creep tests
Reversal shear
Peak strength
lesis
c'(kPa)
a
Y*.-r. (m)
w
r=tnsÉ
5
0
i ho-8s-r]
Fig. 6. The relation between the applied shear stress and
the relative rate of shear deformation for varved clay samples.The effectivenormal stress:o' :20.3 kPa.
results will be comparedwith the creepprofiles
measuredin the field.
5. Comparison between measured and
theoretical creep velocity profiles
Four flexible tubes were placed in the central
part of the slide (seeFigs. 4 and 5). Their surface displacementswere measuredwith a theodolite in combination with an electronic distance meter (Van Genuchten and Van Asch,
1988). The deformationsof the tube profiles due
to creep were measured with an inclinometer
sensitiveto 0.1'. The inclinometer measurements revealeda slip plane at a depth of 4-4.5
m and a curved profile in an approx. 1 m thick
zoneabovethis plane (seeTable 1).
Table 1 shows the total displacementsmonitored at the surface and the displacement
0
14.4"
0
18.7'
3.38
r.60
1.37
10.75'
causedby creepfor the blocks during the period
May l98l-March 1982.The table indicates that
the displacementby creepis approximately 5%
of the total displacement.From Table 1 it also
appearsthat creepvelocity and the thickness of
the creep zone increase downslope despite the
decreasingslope angle in that direction (seeFig.
5). This can be explained by the fact that the
phreatic level increasesdown-slope,as couldbe
monitored from open standpipe piezometers.
Accordingto eqn. (18) the creepzoneincreases
with increasing pore water pressure.
The displacementsin tubes 165 and 166 over
the period May 198l-March 1982 were significantly beyond the range of the measuring errors in the inclinometer technique. In addition
the pore pressurescould be measuredin the vicinity of these tubes. Therefore the measurement results for these tubes are comparedwith
the theoretical displacement profiles as calculated with the models.
Three threshold values are introduced into
the models:the first basedon the creep test result and Yen's definition, the secondbased on
the creeptest result, the peak strength and Ter
Stepanian's definition, and the third based on
the reversal direct shear test results and Yen's
definition.
It was assumed that maximum pore water
pressure (in March) decreasedlinearly over
time towards zeropore pressureas measuredin
late August-September. The total displace-
Th. J.W.ASCHAND P.M.B,VAN GENUCHTEN
54
0.65
. f l e x i b l et u b e 1 6 6
' f l e x i b l et u b e 1 6 5
0.2
0 . 15
0.1
0.05
0
d i s p l a c e m e n tr a t e ( m / Y e a r )
Fig. 7. A comparisonbetweenthe displacementprofiles measuredfrom the flexible tubes 165and 166betweenMay 1981and
March 1982 (seefig. ) and the calculateddisplacementaccordingto four models (curve o-d) using different combinations
of yield strength definitions and definitions for viscosity. a:Ter Stepanian'sdefinitions of yield strength and viscosity;
ô = Yen's definition of yield strength and Ter Stepanian'sdefinition of viscosity; c: Yen's definitions of yield strength and
viscosity;d: Ter Stepanian'sdefinition of yield strength and Yen's definition of viscosity.
ment over the period May 1981-March 1982was
calculated by summing the monthly displacements on the assumptionthat the phreatic level
for that particular month was constant.
Table 3 gives the minimum groundwater
depth needed for creep for the various thresholds. The models give zero-creepdisplacements for the actual field situation (slope angle, slip plane depth and pore pressure
variations ) when the threshold value deduced
from the reversal shear tests (c':0 and
A' :I8.7" ) is insertedinto the models.
Figure 7 givesthe velocity profiles estimated
from the four modelsr curve a is the model incorporating Ter Stepanian's definitions of the
yield strength and the flow factor; curve b is
basedon Yen's definition of the yield strength
(determined by the creep tests) and Ter Stepanian's definition of the flow factor; curve c is
basedon Yen's definitions of the yield strength
(determined by the creep tests) and the flow
factor; and curve d is the model that uses Ter
Stepanian'sdefinition of the yield strength and
Yen's definition of the flow factor. T'he figure
showsthat introduction into the model of a re-
sidual strength value determined by the creep
tests in which ci is assumedto be zero and a flow
factor which depends on the normal effective
stressgivesthe nearest estimate to the data obtained in the field. The differencesbetweencalculated and monitored profiles rnight be due to
the anisotropic and overconsolidatedcharacter
of the varved clay. Overconsolidationis not one
of the assumptionsmentioned in section 3. Furthermore, pore pressure might not diminish
linearly over time.
Acknowledgements
The authors would like to thank Mrs. H.
Brinkhorst, H. Buist, and J. Weijers for their
assistancein the field. The technical assistance
given by Mr. W. Haak (soil tests) and Mrs. J.
Van Barneveld and Th. Tiemissen (field equipment) is gratefully acknowledged.Miss S.M.
McNab is thanked for her linguistic advice and
Miss. M. Tiemeijer is thanked for drawing the
figures.
CREEP PROFILES OF LANDSLIDES
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