Some fall-cone
tests
D. M. WOOD*
INTRODUCTION
Fall-cone tests have been used for many decades
in Scandinavia for the estimation of the strength
(and sensitivity) of cohesive soils. Different standard fall-cone tests have been adopted in Scandinavian countries and in the UK for the determination of the liquid limit of cohesive soils.
Association of strengths with penetrations of
any particular cone has been made using correlations with other strength measurements. Recent theoretical analyses have, however, opened
the way to a direct estimation of strength from
fall-cone tests.
In this Note, the results of some fall-cone tests
performed with cones of different angles are
presented together with the results of some vane
strength tests. The link between cone penetration and strength is compared with theoretical
predictions and with earlier experimental correlations.
FALL-CONE TESTS
The geometry of the fall-cone test is shown in
Fig. 1. A cone of angle CY and weight W is
allowed to fall from rest touching the surface of
the soil of strength c, and penetrates a distance
d. The parameters of the fall-cone test may be
linked by dimensional analysis to give the relation (Hansbo, 1957; Wood & Wroth, 1978)
g
= k(a, x)
where x is a measure of the friction between the
soil and the cone, e.g. the ratio of adhesion to
undrained strength as used by Houlsby (1982) in
his analyses. Though Houlsby shows that the
degree of adhesion is an important factor controlling the penetration of the cone this adhesion
was not varied in the present tests and the
function k(a, x) will be replaced by k, with k,
expected to take a different value for each value
of cone angle (Y.
Fall-cone tests have been performed with
cone angles cy of 30”, 45”, 60” and 75”. In the
majority of the tests the cone weight was set to
100 gf (0.981 N). For some of the tests on
Discussion OU this Technical
Note closes on
July
1985. For further details see inside back cover.
* Cambridge University Engineering Department.
Drammen Clay (Gardiner, 1982) other cone
weights were used but the validity of expression
(1) was assumed to convert the measured penetrations to the penetrations that would have
been observed with a cone weight of 100 gf. For
constant c, and (Y, d is proportional to W”‘.
The procedure for the fall-cone tests was similar to that outlined in BS 1377 (British Standards Institution, 1975) for the determination of
the liquid limit of soils. The fall-cone equipment
was the cone penetrometer apparatus illustrated
there. Penetrations were measured after 5 s. The
soils tested-Drammen
Clay (I, = 0.14), speswhite kaolin (I, = 0.26) and Cambridge Gault
Clay (I, = 0.41)-were
reconstituted from dry
powder and mixed with distilled water to give
different water contents. To try to keep the
soil-cone friction as uniform as possible the
cones were wiped with an oily cloth just before
performing each fall-cone test. The penetrations
presented here are the averages of several
penetrations in each soil mix.
The variations in cone penetration with water
content for each cone angle are shown in Figs
2(a), 2(b) and 2(c) for Drammen Clay, speswhite
kaolin and Cambridge Gault Clay respectively.
VANE
TESTS
Vane tests were performed
on the reconstituted soils using the miniature
vane shown in
Fig. 3. This vane has three triangular blades
each of rhomboidal section. The tips of the
blades lie at radius 12.5 mm; the shaft is of
radius 2.5 mm. With this configuration of blades
a simple plasticity analysis can be made to relate
blade force P per unit length to soil strength for
the two cases of no adhesion between soil and
blade (Fig. 4(a)) and full adhesion between soil
and blade (Fig. 4(b)). The variation in Plhc,, with
blade angle 0, where h is the height of the
blade, for these two cases is shown in Fig. 5.
The relation between vane torque and soil
strength can then be deduced. For the tests
performed here it has been assumed that the
blades of the vane are fully rough so that
P//K, = 11.4. When the vane is rotated in a soil
of strength c, = 100 kN/m’ a torque of 0.5 N m
is generated.
The variations in vane strength with water
content for the three clays are shown in Fig. 6.
64
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65
TECHNICAL NOTES
I
Fig. 1. Diagram
CONE
of fall-cone
test
5
It is often convenient to assume a linear relation between water content and logarithm of
undrained strength (e.g. Wroth & Wood, 1978).
However, the results of the vane tests shown in
Fig. 6 imply significant curvature of this relation
and this curvature has to be taken into account
if the results of the cone and vane tests are to be
fitted into a common picture.
If it is assumed that expression (1) is correct
then
k,W
(2)
lnc,+2lnd=ln(k,W)
(3)
c,d2=
and
5
12.5
:::--
Inc,=f(w)
(4)
lnd =iln(k,W)-$j(w)
(5)
3. Laboratory
(c) typical
millimetres)
vane: (a) plan; (b) radial section;
section though
blade (dimensions
in
has been fitted simultaneously to the vane
strength and cone penetration data for each clay
by a least-squares process. The resulting curves
are shown in Figs 2 and 6. It will be noted that
this process has forced an independence of cone
factor k, from water content or strength for
each clay.
The values of k, that have emerged from
these fall-cone and vane tests are plotted against
cone angle OLin Fig. 7(a). For comparison the
ranges of values of k,, and k,, obtained by
Karlsson (1961) with fall-cone tests on a number
of different clays using 30” and 60” cones are
A simple form for f(w),
f(w)=aw2+bw+c
(C)
(b)
Fig.
Hence if
then
(_-__-
5
FACTORS
23"
(6)
75" 60-45" 30"
75" 60"45" 30"
0.70-
0.65-
0,40-
0.60-
0.380.36-
30.55
s 0.34 0.50 0-320.45-
0.30-
0.4or
I
5
10
20
d mm
(4
I
I
50
2
I
10
5
20
2
d mm
(b)
5
1
I
10
20
d mm
CC)
2. Variation in penetration d with water content w for cones of weight 100 gf with angles 30”, 45”, 60” and
75”: (a) Drammen Clay; @) speswhite kaolin; (c) Cambridge Gault clay
Fig.
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66
TECHNICAL
NOTES
12Rough
ll-
lo-
9-
I
8
0
I
20
I
I
I
40
60
80
0: deg
I
0
I
0.6
I
0.8
I
1.0
Fig. 5. Variation ia P/he, with blade angle for smooth
and rough blades pushed through soil
Fig. 4. Plasticity mechanismsfor (a) smooth and (b)
rough blades pashed through soil
shown. The present data lie broadly within
Karlsson’s ranges.
From
information
provided by Houlsby
(1984), using the analysis described by Houlsby
(1982), the theoretical variations in cone factor
k, with cone angle for the extreme cases of fully
rough and fully smooth cones can be deduced.
These are also plotted in Fig. 7(a). Particularly
for the smaller cone angles, the theoretical
values of k,, even assuming a fully rough
soil-cone interface, are considerably higher than
those observed.
Houlsby (1982) presents some of his theoretical results in terms of a bearing capacity factor
0
I
0.4
blh
(b)
(4
I
0.2
v,:
NC=
Q
(7)
c,-rrD2 tan2 (o/2)
Ihe quantity D tan o/2 is the radius of the inden:ation at the soil surface. It must be noted that
Houlsby’s analysis is a quasi-static analysis relati ng cone force Q to indentation D. It can be
shown that, in the absence of dynamic effects
:ausing a change in the strength of the soil, if
:he quasi-static cone force is Q for an indenta-ion D then a cone of weight W = Q will pene.rate a distance d = D& when allowed to drop
‘reely from the surface of the soil (Houlsby,
0.70-
0.75.
o
0.65-
0.70-
0
0.65-
0.60-
0.380.36 I
3
cl
Cl
0.34-
0.50-
0.32-
0.28
0.401
2
5
cu. kN/m’
@I
0
0,55-
0.50-
0.45-
0
0.30-_A,
0.40
-
Fig.
' 0.60-
0.55-
10
,\,
12
0.455
10
20
,J,
0
1
cu. kN/m’
(W
2
5
cu
10
20
kN/m’
(Cl
6. Variation in vane shear strength with water content: (a) Drammen Clay; (b) speswldte kaolin; (c)
Cambridge Gaalt clay
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TECHNICAL
68
In the UK the definition is similar (BS 1377,
1975) but requires a 20mm penetration of a
cone of weight 80 gf (0.785 N) and angle 30”.
Accepting Karlsson’s value for k,,, = 0.8 this implies c, = 1.57 kN/m*.
Karlsson’s (1961) data suggest that k,, rises
and k,, falls for lower plasticity soils (1,<0.2).
The data from the present tests support the rise
in k,, at low I, but do not support a fall in k,,.
Average values of cone factor from the present
tests are
kzO = 0.85
k,, = 0.49
kc0 = 0.29
k,, = 0.19
With these values of k,, and k,,, the liquid limit
values of strength are 1.67 kN/m’ according to
the UK definition and 1.71 kN/m’ according to
the Swedish definition.
From studies of strength data of soils at water
contents close to their liquid limit (as determined by the Casagrande liquid limit device)
Wroth & Wood (1978) suggested that the undrained strength of remoulded soils at water
contents equal to the liquid limit is about
1.7 kN/m’.
The comparison of theoretical and experimental results suggests that as a description of the
mechanics of the fall-cone test the theoretical
analysis may not be entirely satisfactory. As
already mentioned, one factor that has certainly
been omitted is the influence of undrained
strength on rate of shearing. However, Houlsby
(1982) compares predicted cone velocities with
cone velocities measured by Hansbo (1957) and
concludes that at least for the soil being tested
NOTES
by Hansbo ‘viscous slowing
significant’.
A more detailed
of the mechanism
cones of different
of the cone is not
experimental
study
of quasi-static
penetration
of
angles is perhaps called for.
ACKNOWLEDGEMENTS
Some of the data presented
here were obtained by undergraduates
in Cambridge
University Engineering
Department
in the course of
second- and third-year projects.
REFERENCES
British Standards Institution (1975). Methods of test for
soils for civil engineering purposes. BS 1377 : 1975.
London: BSI.
Gardiner, E. 0. (1982). Part II project report, Cambridge University Engineering Department.
Hansbo, S. (1957). A new approach to the determination of the shear strength of clay by the fall-cone
test. Proc. R. Swed. Geotech. Inst., No. 14.
Houlsby, G. T. (1982). Theoretical analysis of the fall
cone test Giotechnique 32, No. 2, 111-118.
Houlsby, G. T. (1984). Private communication.
Houlsby, G. T. & Wood, D. M. (1983). Discussion on
Wood. Gtotechnique 33, No. 4, 463.
Karlsson, R. (1961). Suggested improvements in the
liquid limit test, with reference to flow properties
of remoulded clays. Proc. 5th Int. Conf. Soil Mech.
Fdn Engng, Paris 1, 171-184.
Karlsson, R. (1977). Consistency limits: a manual for
the performance and interpretation of laboratory inuestigations, part 6. Stockholm: Statens rid f6r
byggnadsforskning.
Wood, D. M. & Wroth, C. P. (1978). The use of the
cone penetrometer to determine the plastic limit of
soils. Ground Engng 11,No. 3,37.
Wroth, C. P. & Wood, D. M. (1978). The correlation
of index properties with some basic engineering
properties of soils. Can. Geotech. J. 15, No. 2,
137-145.
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