Note: Descriptions are shown in the official language in which they were submitted.
2 ~
The present invention relates to improve-
ments in the field of earth materials testing. More
particularly, the invention is concerned with an
improved method and device for determining in-situ
rheological propertles of earth materials.
, The knowledge of rheological properties of; earth materials is an essential condition for the
design of structural elements in contact with soils ; ~;
or rocks, to which they transfer the applied loads.
Typical rheological properties are the creep ;
properties of the material and its time or rate
~ dependent deformation or strength. The earth
I materials to which the invention pertains are soils,both frozen and unfrozen, ice, and weak rocks, such
as rocksalt and potash. Practical problems requiring ~ ;
the knowledge of rheological properties of such earth
materials are, for instance, the design of founda-
tions in frozen and unfrozen soils, the bearing
capacity of ice covers, and the design of tunnel and
shaft linings. ;~
For determining the above mentioned rheolo- - -
gical propert!ies,~both laboratory and in-situ methods ~
,,
are presently being used. In the former, undisturbed
soil samples are taken from borings at selected -
levels, and are subjected to certain tests pertinent
~¦ to the purpose at hand. The latter, in-situ methods ~1
do not require soil sampling, but they permit to
measure only a limited number of rheological proper-
.. . . .. . . ... . . .. . . . ..
2~3~9
ties. Their main advantages over the former are their
rapidity and ability to furnish a continuous picture
of the geotechnical profile of the site. ~ ;
Not considering the geophysical methods,
which measure only the physical properties of the
ground, principal geotechnical in-situ methods
presently in use are the Cone Penetration Test (CPT),
the Pressuremeter Test (PMT) and the Flat Dilatometer
Test (DMT).
10The CPT method is a standardized method in
which a pressure-sensitive cone having a diameter of
3.56 cm and an apex angle of 60, and fixed to the
end of a drill rod of the same diameter, is pushed
into the soil at a rate of 2 cm/sec. From the
recorded cone resistance ~both total and piezometric
pressure), certain mechanical properties of
penetrated soils can be deduced, using theoretical
models and statistical correlations. Although
electrical cone tests have been in geotechnical use
since 1950's, such tests have been introduced also to
frozen soils only in the 1970's (see Ladanyi, B.,
"Determination of Geotechnical Parameters of Frozen -
Soils by Means of the Cone Penetration Test", Proc.
2nd Europ. Symp. on Penetration Testing, Amsterdam
82), Vol. 1, pages 671-678). The CPT method,
although being based on a continuous penetration
mode, requires heavy penetration equipment and
furnishes only information on soil strength proper- -
ties, with no data on soil deformability and on
: ~ :
30stress-strain properties.
';`'''~
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The PMT method, introduced to geotechnical
practice by Ménard in the 1950's, consists in placing
an inflatable probe into a predrilled (or self-
drilled) borehole of the same diameter. The hole is ~ -
drilled down to a cer-tain level, and the test is made
at that level by keeping the probe fixed in place.
The test is performed by inflating the probe and by
recording the relationship between the applied ~- `
pressure, the hole enlargement and the time. For any
additional testing, the hole is drilled further, and
the test is performed at another fixed level. In
unfrozen soils, this method has been used essentially
for determining the short-term mechanical properties
of soils. The theoretical interpretation of the test
in ordinary soils and rocks is presently well
developed. In frozen soils, the method has been used
for creep properties determination since 1973 (see `
Ladanyi, B. and Johnston, G.H., "Evaluation of
In-Situ Creep Properties of Frozen Soils with the
Pressuremeter", Proc. 2nd Int. Permafrost Conf.,
Yakutsk, USSR, North Amer. Contribution, NAS,
Washington, D.C., ~1973), pages 310-318), Being basçd
on a discontinuous penetration mode, the PMT method
gives information limited only to certain previously
selected levels and thus does not provide a continu- ;~
ous soil profile. In addition, the method requires a
rather sophisticated apparatus and a skilled
personnel.
- 3 -
~,..... . . ::~
` 2~3~g :
In the DMT method, introduced by Marchetti
ln 1980 (see Marchetti, S., "In-Si-tu Tests by Flat
Dilatometer", J. of Geotech. Engrg. Div., ASCE, Vol.
~ 106, No. GT3, (1980), pages 299-321), use is made of
; a soil testing tool ressembling a thick spade, which
is pushed into the soil at the end of a drill rod.
The measurement is made by slightly inflating a
metallic diaphragm located at one side of the spade.
The test interpre-tation is based exclusively on
statistical correlations with soil properties deduced
from other, more advanced, types of tests, and thus
the information furnished is not clear and lac]cs
theoretical background.
, It is therefore an ob~ect of the present
invention to overcome the above dxawbacks and to
~ provide a method and device for in-situ determination
i of rheological properties of earth materials, which
~ do not xequire a skilled personnel and which are
: .
capable of furnishing a continuous soil profile and a
more complete rheological information. -~
According to one aspect of the invention,
there is provided ai method for determining in-situ
creep properties of earth materials, which comprises
the steps of~
a) providing a cone penetrometer having a
conical end portion with a central longitudinal axis
and a taper anyle ranging between about 1 and about
lO relative to the central longitudinal axis;
. . ,', .
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2~1~93l~9
b) drilling into an earth material a bore-
hole having a conical wall portion merging with a
concentric cylindrical wall portion of smaller
~ diameter at the bottom of the borehole, the conical
,' wall portion of the borehole corresponding in size and shape to the conical portion of the penetrometer;
c) inserting the penetrometer into the
borehole such that the conical portion of the
penetrometer abuts the conical wall portion of the
.' 10 borehole;
d) applying a constant load to the penetro-
! meter to cause axial displacement of the conical
;~ portion thereof into the borehole and widening of the
` conical and cylindrical wall portions;
e) continuously monitorin~ penetration of
j the conical portion of the penetrometer into the
borehole and recording the amount of axial
displacement of the conical portion as a function of
. time, to provide recorded data representative of
creep properties of the earth material; and
f) determining from the recorded data at
3 least one creep parameter property of the earth
material.
Applicant has found quite unexpectedly that
the creep properties of earth materials can be
determined by pushing a low-angle cone penetrometer
under a constant axial load into a pre-drilled
conical hole of the same shape at the bottom of a
borehole in the material, which ends with a pre-
i 30 drilled cylindrical pilot hole of smaller diameter,
3 - 5
~v
- 2~3'~
,.
and by observing the time--dependent axial displace~
ment of the cone, tending to enlarge both the conical
and pilot holes. The major part of deformation is
thus radial and occurs under plane strain conditions.
sy the expression "low-angle cone penetrome-ter" as
used herein is meant a penetrometer having a conlcal
portion with a taper angle ranging between about 1
and about 10.
The taper angle of the conical portion of
the penetrometer is selected as a function of the
type of material tested and preferably ranges from
about 1 to about 5. For example, a taper angle of
about 5 has been found suitable for testing ice and
frozen soil, while a taper angle of about 2 is
preferable for testing a much stronger rocksalt.
Generally, an axial load of up to about 20
MPa can be applied to the upper end of the penetro-
meter, when testing ice and frozen soil, but much
higher loads of up to 100 MPa are needed for testing
rocksalt. A load ranging between about 0.5 and about
3.0 MPa has been found adequate for testing ice. In
the case of froizen soil, however, a~load rangi!ng
between about 3.0 and about 15.0 MPa is preferable. -
In a preferred embodiment, steps (d), (e)
and (f) of the method according to the invention are
repeated a predetermined number of times with the
penetrometer remaining in the borehole to provide a
multi-stage testing of the earth material, and the ~ -
load applied to the penetrometer is increased at each
stage. The duration of each stage at constant load is
. ' ' ~:
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, - 6
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~ ~''~;' -' '
2~93~9 :
usually between 1 and 10 hours, but the longer the
'.! better, the only limltation beiny the depth of the
pilot hole. If the load is kept constant, a steady-
state penetration veloc:ity is attained only at
relatively high loads. Otherwise, the velocity keeps
decreasing with time. For example, in tests carried
out in ice, for a range of applied loads between 0.5
and 2.6 MPa, the recorded steady-state penetration
rates varied from 1.7 x 10 6 to 33.3 x 10 6 cm/sec.
The above method makes it possible to
perform hole expansion tests at high pressures,
, :
~i without requiring sophisticated and expensive equip-
ment, while furnishing creep properties of materials
such as ice, frozen soils and other strong creeping
~ materials, such as rocksalt.
.'1
Applicant has also found that the time or
rate dependent deformation and strength properties of
earth materials can be determined by holding constant
'1
either the load on the cone or the rate of
penetration into the pilot hole, and by recording the
`~ relationship between the penetration or the
penetration rate and the total lateral pressure
. ~, ,.
exerted by the earth material on the lateral surface
of the cone, which is related to the resistance of
the material against the enlargement of the pilot
hole.
`'-''',''' ~',
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:.
- Accordingly, the present invention pro-
vides, in another aspect thereof, a method for
determining in-situ time or rate dependent
. deformation and strenght properties of earth
materials, which comprises the steps of:
. a) providing a cone penetrometer having a
i conical end portion with a central longitudinal axis
and a taper angle ranging between about 1 and about
10 relative to the central longitudi.nal axis, the
conical portion having small and large diameter ends
and a lateral surface defined therebetween, and
comprising pressure sensing means including at least
. three longitudinally spaced sensor elements flush
i mounted on the lateral surface;
b) drilling into an earth material a pilot
hole having a diameter corresponding to the small
diameter end of -the conical portion of the penetro
meter;
, ~ ,
c) inserting the penetrometer into the
pilot hole;
d) applying a load to the penetrometer to
cause axial displacement of the conical portion
thereof into the pilot hole and enlargement of same; `
e) continuously monitoring penetration of
the conical portion of the penetrometer into the
pilot hole while simultaneously monitoring total ~ ~:
: lateral pressure exerted by the earth material on thelateral surface of the conical portion and sensed by
the sensor elements, and recording the sensed lateral ~ .
pressures as a function of axial displacement of the :~
~. ' :
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~ - 8 - i
. i: '
:~ 2~3l~9
conical portion, to provide recorded data representa-
tive of time or rate-dependent deformation and
~. . - -
. strength properties of the earth material; and .
.~ , . . .
f) determining from the recorded data at
. the time or rate-dependent deformation or strength
.~ proper-ty of the earth material.
According to a further aspect of the inven-
tion, there is also provided a device for carrying
. out the above method, which comprises a main
. 10 elongated body having a conical end portion with a
~` central longitudinal axis and a taper angle ranging
between about 1 and about 10 relative to the
central longitudinal axis, the conical portion having
I! small and large diameter ends and a lateral surface
~ defined therebetween, and pressure sensing~ means
,~ :
. including at least three longitudinally spaced sensor
elements flush mounted on the lateral surface~ The
-:
: device of the invention is insertable into a pilot
i , ~
hole formed in an earth material and having a
diameter corresponding to the small diameter end of
:3 the conical portion such that upon application of a
:1 load to the device, ~ t~he conical portion is axially !
9 displaced into the pilot hole thereby causing
enlargement of same, the sensor elements being
operative to sense total lateral pressure exerted by
the earth material on the lateral surface of the
conical portion, the sensed lateral pressures
correlated to the axial displacement of th~ conical
. ` ~
-- 9
portion being representative of time or
rate-dependent deformation and strength properties of
~ the earth material.
i, Preferably, the pressure sensing means
,,
;I comprise three flush diaphragm-type pressure trans-
ducers arranged at different levels in the conical
portion of the penetrometer, each pressure transducer
being operative to sense, at a given level of the
earth material, a different value of the total
lateral pressure exerted by the material, since at
each given level, the total amount of hole enlarge-
ment is different as each successive transducer
passes through that level. In other words, for each
l selected level, the method of the invention enables
¦ one to determine several polnts of a "pressuremeter
curve", that is, the relationship between lateral
¦ pressures and radial displacements, the interpreta~
¦ tion of which in terms of rheological properties is
j well known for different types of earth materials.
For testing saturated clays, it is prefer~
able to use a penetrometer of the above type having a
conical portion with a taper angle of about 1 to 2.
On the other hand, larger angles of up to and above
5 may be found more appropriate when testing very
compressible materials, such as loose sands and peat.
In the case of loose sand, taper angles of about 5
to 8 are preferred, whereas in the case of peat,
angles of about 8 to 10 are usually more adequate.
' 1 ' '; '
..
1 0
~ ~ ~ 9 3 L~ 9 ~ ~
Generally, a rapid rate of penetration of,
for example, 2 to 20 mm/sec. is recommended for
obtaining an undrained response of a satura-ted clay.
A much slower ra-te of penetration of, for example, 1
to 10 cm/hour is recommendecl for testing for instance
the effects of pore pressure dissipation on the soil
behavior. The easlest way to achieve such very slow
rates of penetration is to keep constant the axial
load applied to the cone, since at small applied
loads, the rate will be as slow as desired.
The method and device of the invention not
only furnish a continuous soil profile, but also a
substantially complete rheological information,
without requlring a skilled personnel. `~
Further features and advantages of the
invention will become more readily apparent from the
following description of preferred embodiments as
illustrated by way of examples in the accompanying
drawi.ngs, in which:
Figure 1 is a side view of a low-angle cone
penetrometer according to a preferred embodiment of
the invention, seen inserted into a pilot hole;
Figure 2 is a sectional view taken along
line 2-2 of Fig. l;
Figure 3 is a plot of recorded lateral
pressure against the relative enlargement of the
pilot hole resulting from cone penetration;
Figure 4 is a view similar to Fig. 1,
showing a low-angle cone penetrometer according to
another preferred embodiment of the invention;
, .
-- 11 --
". .. ~ . . ~ . ,
~ ' !'" . '
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~ 2~g3~
Figure 5 is a log-log plot of the relation-
.~ ship between the relative cone penetration and time, .
~; for -the determination of creep parameter b;
!,: Figure 6 is a log-log plot of the rela-
tionship between the load applied and the relative
cone penetration, for the determination of creep
paramaters n and C~c~; and
'J, Figure 7 is a log-log plot of the minimum
, relative penetration rate and the applied load, for ~ .
the determination of creep parameters n and C~c~ in
the case of minimum creep rate formulation.
Referring first to Fig. 1, there is
illustrated a low-angle cone penetrometer generally ~`
~ designated by reference numeral 10 and seen inserted
¦ into a pilot hole 12. The cone penetrometer 10 has an
elongated body 14 with a central longitudinal axis 16 ~ :
and comprises a cylindrical member 18 and a hollow, ~
truncated conical head 20 which is connected to the ~ ~ .
member 18 by means of a connector member 22. The
conical head 20 has small and large diameter ends 24
and 26 with respective diameters A and B, and a `:~:
lateral surface .28 defined therebetween, the head ~
. :. ::
having a taper angle ~ relative to the central longi-
tudinal axis 16. A concentric, truncated conical .
guide nose 30 terminating in a short pointed tip 32
is connected to the small diameter end 24 of the head ~;:.
20, the guide nose 30 has a taper angle ~ which is
slightly greater than the taper angle ~X of the head
20. In the embodiment illustrated, the angle Cx is
about 1 whereas the angle ~ is about 2.
"1
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~ - 12 -
,~ .. ..
2~3~
Three equldistantly spaced-apart flush
diaphragm-type pressure transducers 34 are arranged
in the head 20, each transducer having a pressure
diaphragm 36 flush mounted on the lateral surface 28
of the head. The pressure diaphragms 36 define sensor
elements operative to sense total lateral pressure
exerted by the surrounding earth material on the
lateral surface 28. As shown in Fig. 2, each trans~
ducer 34 is mounted by means of a threaded collar 38
engaging a threaded flange 40 inside the head 20.
Three o-rings 42,42' are arranged to ensure adequate
;1 .: . .
sealing. The transducer pins 44 are received into an
electrical socket 46 and are electrically connected
by a wire 48 to a readout unit 50 which itself is ~ I
connected to a recorde~ 52. The first or lowermost
transducer is disposed at a distance X from the small
diameter end 24 of the head, whereas the second
transducer is disposed at a distance C from the first `~
¦ and the third or uppermost transducer is disposed at
a same distance C from the second. -~
.'. i . . . '.
In operation, the cone penetrometer 10 is
' inserted into~,a pre,drilled pilot hole 12 having a
diameter 2r corresponding to the diameter A of the
small diameter end 24 of the conical head 20. If ;~
desired, for the start of the test, the upper portion
of the pilot hole can be enlarged to have a conical
configuration corresponding in size and shape to the -~
conical head 20. The pilot hole can be made either
before the test by pre-drilling, or simultaneously
with the cone penetration by means of a self-boring ;~
r ~ 1 3
~ 2~3~
.
device whlch is readily commercially available. An
axial load Q i5 then applied to the upper end of the
! penetrometer 10 to cause axial displacement of the
conical head 20 in-to the pilot hole 12 and enlarge- ;
ment of same. The to-tal lateral pressure exerted by
the earth material on the lateral surface 28 of the
.. .
head 20 and sensed by the sensor elements 36 is
continuously monitored and recorded by the recorder
52. Penetration of the head 20 into the pilot hole 12
is also continuously monitored at the same time by
suitable means (not shown) and recorded by recorder
52. The sensed lateral pressures are recorded as a
function of axial displacement of the head 20, there- ~
by providing recorded data representative of time ~ ;
or rate-dependent deformation and strength proper-
ties of the earth material. The time or rate- ;
dependent deformation or strength property of the `
material is then deduced from the recorded data.
As the conical head 20 is axially displaced
into the pilot hole 12, the pilot hole of diameter 2r
is gradually enlarged to the diameter 2R correspond-
ing to the diameter B of the large diameter end 26 of
the head. The three pressure transducers 34 also
traverse successively the distànces X, (X -~ C) and (X
+ 2C), so that total radial strains ~equal to shear
strains) at a fixed level I-I are equal to:
Penetration Radial Displacement Radial Strain
X rl r ln(rl/r)
X + Cr2 ~ r ln(r2/r)
X ~ 2Cr - r ln(r3/r)
.
~ 14 -
. ~, , .
:
3 ~1 9
,
where
rl = r + X tan C~
r2 = r + (X + C)tan d ~ ~ -
r3 = r + (X ~ 2C)tan
Taking, for example, a cone penetrometer 10
having a conical head 20 with ~ = 1, intended to
enlarge a pilot hole from r = 3.0 cm to R = 3.5 cm,
and pressure transducers 34 positioned at distances
of 5 cm, 15 cm and 25 cm, respectively, from the ;
small diameter end 24 of the head, for a penetration
of X = 5 cm, one would get at the level I-I in Fig. 1
:: :
a shear strain equal to ln (1 + S x 0.01746/3) =
0.0287, and the corresponding pressure sens~d by the
first or lowermost pressure transducer will be Pl- A
penetration of 15 cm gives the strain ln (1 + 15 x
0.01746/3) = 0.0837, and the corresponding pressure
sensed by the second pressure transducer will be P2.
Finally, a penetration of 25 cm leads to a strain of
ln (1 + 25 x 0.01746/3) = 0.1358, and the correspond~
ing pressure sensed by the third or uppermost
pressure transducer will be p3. Had, for example, an
angle ~ = 2 been selected for the conical head 20
instead of 1, the corresponding shear strains would
have been 0.057, Q.161 and 0.225, respectively.
The s-trains will remain the same as long as
the pilot hole 12 precedes the conical head 20, but
the recorded pressures will vary according to the
soil properties.
:
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2~33~9
",
., .
By relating the radial (or shear) strains :~
~ with the corresponding pressures sensed by the :~
pressure transducers at different levels of the pilot ::
hole, one thus obtains a number of "pressuremeter
curves", such as shown schematically in Fig. 3. These
curves can then be treated in a conventional manner,
described for instance in the aforementioned Ladanyi
and Johnston publication, to determine the time or ~-
i rate-dependent deformation and strength properties of ;
1 10 the material tested, such as the time or ;~
¦ rate-dependent stress-strain curve.
,.. ...
i In addition to the pressure transducers 34
.l . for sensing the total lateral pressure, some
piezometric transducers (not shown) can also be .~:~
installed on the conical head 20 for measuring
generation and dissipation of pore pressure around
the head 20.
Turning to Fig. 4, there is itllustrated
another type of low-angle cone penetrometer 54 ..
comprising a cylindrical member 56 to which is
connected a conical head 58 having a taper angle C~of
about 10 rélàtive to the central longitudinal axiis
60. As shown, the penetrometer 54 is seen inserted
into a borehole 62 having a conical portion 64 -~
merging with a concentric cylindrical portion 66 of ;
smaller diameter, the cylindrical hole portion 66 .;
defining a pilot hole. As opposed to the embodiment
illustrated in Fig. 1, testing with the penetrometer
,' ~'.',,''
! 16 -
,
3 ~ ~
', -
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54 requires starting from a pre-drilled conical hole
~! portion 64 corresponding in size and shape to the
;~ conical head 58.
~1
t:~ Generally, the pilot hole 66 is drilled
first and then, using a sharp conical tool having the
3 same taper angle ~ as the conical head 58, the upper
portion of the pilot hole is enlarged to the size and ~ ~
shape of the head 58. The penetrometer 54 is there- -
after inserted into the borehole such that the ~-
conical head 58 abuts the conical wall portion 68
defined by the conical hole portion 64. A constant ;
;, load Q is applied to the upper end of the penetro-
,, .
meter 54 to cause axial displacement of the head 58
into the borehole 62 and enlargement of the conical
and cylindrical hole portions 64 and 66. Penetration
of the head 58 into the cylindrical hole portion or
pilot hole 66 is continuously monitored by suitable
means tnot shown) and the amount of axial displace-
ment of the head 58 is recorded as a function of
time, thereby providing recorded data representative
of creep properties of the earth material tested. At
least one creep parameter (i.e. creep parameters b, n
and~or ~c~of the material is then deduced from the
recorded data.
`, The size and shape of the conical head 58
depend on the selection of the taper angle ~ and the
diameters D and d of the main and pilot holes 62 and
66, respectively. For selected values of ~, D and d,
the total length Lt of the head 58 is given by~
ht = (D/2) cot~
' - 17 -
}~
2~349
and the length L of the head 58 in contact with the -~
earth material is given by~
L = [(D - d)/2] cot~ (2)
For example, if C~= 5 , D = 3.556 cm and
d = 0.635 cm, one gets: Lt = 5.715 D = 20.32 cm and
L = 5.715 (D - d) = 16.70 cm. This means that the tip
of the head 58 having a length Lt ~ L = 20.32 cm -
i 16.70 cm = 3.62 cm will always remain in the pilot
,:' hole 66 without contact with the wall, and will serve
;;l 10 only a guide during penetration.
`' However, if the angle C~ is very small and
the two diameters D and d are large, such as ~ = 1,
D = 7.0 cm and d = 6.0 cm, one gets from the above
;'~ equations (1) and (2):
3 Lt = 28.6 D = 200.2 cm, and
L = 28.6 ~D - d) = 28.6 cm.
j Clearly, in that case, the total length of the
¦ conical head 58 is too large and it is preferable to
I cut the tip of the cone, so that only a reasonable `~
20 length of the cone is retained as a guiding portion
within the pilot hole 66.
The creep p'roperties of the earth materialf
tested with the penetrometer 54, can be determined by
finding the values of creep parameters in the creep ;-`
equation of the tested material. For example, for
ice, frozen soils and rocksalt, the creep equation
has usually the form:
e (ae/aC~ ce/b3b (3
". ~
- 18 ~
2 ~ 9
,.
`~where Cre and &e are von Mises equivalent stress and ~ ~;
strain, respectively, n and b are creep exponents, t :~
is the time, and crc9 is the reference stress at a
temperature 0 and at a reference strain rate ~c
The parameters to be determined by the test are n, b ~ .
~and Crc0. This can be done by performing, in a single
;~borehole, or in different parallel boreholes, a ~:
series of tests at different axial loads. Figs. 5 and
6 show the principle of determination of these ~ j
parameters in Eq. (3).
. The value of b can be found from a single
test by plotting the measured values of the ratio s/L
. against the time, t, in a log-log plot, where for
this type of behavior a creep curve linearizes. Here,
~ s denotes the axial displacement of the conical head
j 58 and L its length in contact with the borehole wall ~
i 68, as shown in Fig. 4. The value of b is the slope~.
of the line representing the experimental creep curve ~-
as shown in Fig. 5.
20The value of n can be found if either a ;~"~
~ stage-loaded test is performed in the hole, or if ~ .
i `several step-loaded tests at different loads are
~ performed in separate holes under nearly identical
¦ conditions. If Eq. (3) represents correctly the .
¦~ tested material behavior, then these tests will give
a set of nearly parallel straight lines, each of them
~; valid for a different net pressure q, as in Fig. 5.
¦ The value of n can be found by plotting in a log-log
` . ' .`.: '. .'
:~
- 1 9
i
: 2~349
.
plot the ~7alues of s/L, read at an arbitrary time t =
tc. This will result in a straight line, such as in
~, Fig. 6. The value of n is the slope of this line.
;~ Finally, the value of Crc~ can be found by
; taking the coordinates oE any point on the straight
1 line in Fig. 6 (which is valid for t = tc), say,
and (s/L)l, from which it is found that:
.;
~ a 3 = ql(r3/n)[A(~ t /b) (~-3/2)~(slL~il] (4)
;;l .
': 10
where A = { ~2 - l/n) 2- ~ d/D) 1
2(1 + tan C/tan )rl - (d/D) 1/~]
:.,,
with ~ being the angle of friction between the cone
and the earth material.
1 It ~is found sometimes that a minimum creep
rate formulation describes better the material
behavior than the primary rate formulation described
¦ above. For processing the test results in such a
' case, it is sufficient to put b = 1 in Eq. (3) and to
.
differentiate it with respect to time. This yields
.. ~ - . ., ~ :. .:
the basic creep rate equation:
n
e ~c(5e/~c~) (5)
As shown in Fig. 7, in order to find n in
Eq. (5), it is necessary to plot (s/L)min against q
in a log-log plot, giving a straight line with the
slope n = log(s/L)min/log q. In order to find the
value of Crc9, it is only necessary to read from that
line the coordinates of an arbitrary point, say,
( / )min,l at q = ql~ from which
'~
~ j - 20 -
~ .
2~93~9 ~;
~c~ = q1(~3/~) [A ~C(r3l~)l(slL)
series of tests performed in polycrystal~
line ice at a temperature of -5C, using a low-angle
cone penetrometer 54 having a conical head 58 with a
taper angle of 5, in which the head was made to
;l penetrate in a pilot hole with a diameter of d =
0.635 cm, gave the following results when interpreted
' according to the above minimum creep rate formula-
`~I 10 tion:
Table 1. Minimum Creep Rates
Test No. q (MPa) (S/L)min (in 10 min
1 0.48 1.00
t 2 1.13 ~ 3.83
3 1.61 9.50
4 2.10 13.70
2.58 20.00 `~
These values plotted in Fig. 7, are seen to
fall quite well on a straight line, the slope of ` ;
which gives n = 1.90, which is within the range of n
; values;usually,found for such ice (1.75 to 2.40). The
value of Crc~ can be found from any point on that
i~ line, say, (s/L)min = 3.46 x 10 min at q = 1 MPa.
` Taking into account the measured friction on the ~`
conical head 58, one finds from Eq. (6) the value:
crc~ = 4.76 MPa, for a reference creep rate of 10 5
min 1. The minimum creep rate equation found from the ;i~
tests is then~
e 10 (ae/4.76)1 9 (7 ;~
- 21 -
!
2~93~9
... . .
. ...
It is clear that the value of crce found in
the tests at a temperature of -5C should be modified
,` for other temperatures using empirical relationships
'' known in the literature.
Other similar tests made in frozen sand
have also given reasonable values of creep parame-ters
comparable to those determined by laboratory creep
tests.
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