PAPER THE CONE FACTOR FOR A
"ie cone
'Wah~~ccicaaae'oll
'acI:or
'or a.'ll',I'cone
No.1
No.2
PJ BrownLMAHuxley
~ n his paper considers the influence of a number of factors on the
measured values for the cone factor as proposed by Hansbo. A
series of fall cone and laboratory vane tests was conducted on
soils of varying plasticity. The data obtained indicated that the cone
factor was not constant over a wide range of penetrations. However, for
the penetrations associated with the liquid limit a constant cone factor
of 0.76 was indicated. Data are also presented to indicate an increase in
cone factor with increasing plasticity and it is further suggested that
additional work will be required to confirm this trend. Although the
available data are biased towards low shear strength, they indicate a
cone factor of 0.33 at an undrained vane shear strength of 100kPa. It
may also be concluded that further testing will be required to investigate the influence of cone roughness on measured k values, and that
the current criterion used in the liquid limit test for acceptable cone
penetrations may not be stringent enough for the determination of
cone factors.
lnlroduclon
Since 1975 the fall cone, or cone penetrometer, method has been preferred by the British Standards Institution as the method of determining the liquid limit of fine grained soils. Essentially, fall cone tests are
strength tests and Hansbo, 1957, in particular carried out an investigation of cones of differing weights and geometries and suggested the following relationship:
c„=k.W giving k =
c„.d'2
Where:
30'ONE
c„=the undrained shear strength
k = the cone factor
W = the weight of the cone
d = the depth of cone penetration when allowed to
fall from rest from a position of touching the
No.3
No.4
No.5
No.6
No.7
No.8
No.9
W,
W,
I,
SSCS
Clay
Sfe
Sand
A
98
99
75
78
64
53
37
35
106
33
34
65
65
46
46
CE
24
25
3
41
CH
31
23
17
18
30
MH/CM
38
CI
19
18
38
36
43
62
29
3
CV
73
73
59
59
0.894
0.890
0.792
0.781
1.319
0.610
0.900
1.017
29
32
23
30
20
17
76
CE
CV
Cl/CL
10
2
5
26
0
52
72
OE
Note: w, liquid limit obtained from the standard 80g cone tests described above.
wp plastic limit obtained from the thread rolling method.
I plasticity
index obtained using Brown's plastic limit results.
-Activity
Clay, silt and fine sand content percentage
by dry weight from hydrometer analysis.
Umits quoted to nearest integer, Activities derived from unrounded limit values.
BSCS-British Soils Classification System, BS 5930:1981.
tors are in addition to any variation in measured undrained shear
strength imposed by the test method used and rate of shear.
The inference is, therefore, that for a given cone, k will not be constant over a wide range of penetrations and moisture contents, and
may vary with soil type.
To investigate the influence of some of the factors a series of laboratory tests was conducted on nine different soils using fall cone equipment as used to measure liquid limits, the standard 55mm diameter by
40mm deep liquid limit cup and a laboratory vane.
By carrying out fall cone and shear vane tests in a standard liquid
limit cup, remoulded soil could be tested under the same conditions in
terms of approximate density and moisture content. Hence by carrying out three tests at a given moisture content, namely two cone tests at
different weights and a laboratory vane test, direct correlation is possible since there will be little variation in the moisture content
between tests.
soil surface
Wroth & Wood, 1978, derived the same expression from dimensional
analysis while Terzaghi, 1927, also suggested a similar relationship.
In his original paper Hansbo suggested that k depended mainly on the
cone angle but is also influenced by the rate of shear, while Karlsson,
1961, further suggested that k varied not only with soil type but to a certain extent with moisture content for the same soil. Although investigating the undrained shear strength at the liquid limit using a theoretical analysis, Houlsby, 1982, discusses the influence of such factors as
the surface properties of the cone and heave of the soil surface during
cone penetration —issues which may have equal bearing on determined
values for the cone factor. Finally, the values obtained by Wood, 1985,
were determined using cones wiped with an oily cloth in an attempt to
keep the friction between the soil and cone as uniform as possible.
Reported values are summarised in Table 1.
Accepting Hansbo's relationship then, for a given cone geometry,
measured values for k will be influenced by a number of factors. It
seems likely that the interaction between the soil and cone will depend
not only on cone roughness but also on the soil type and depth of penetration.
Additionally there may be dynamic effects associated with the penetration of the
Saaraa
Caaalasfa( )
k
Wood,1985
Hansbo,1957
Karlsson,1961
Wood,1985
Wood,1985
Karlsson,1961
75
60
60
60
45
30
30
30
30
30
0.19
0.3
Houlsby,1982
Houlsby,1982
Wood(Hansbo),1982
Wood,1985
0.25-0.35
0.29
0.49
0.7-0.86
0.96-Smooth
0.51-Rough
1.2
0.85
cone, (Wroth &
Wood,
1978)
which will also
vary with the
depth of penetration as will
heave
any
around
the
cone. Such facPJ Ihawa,
Sample preparation andmethod
For the investigation, soil pastes ranging in moisture content from
above their liquid to below their plastic limit were used. The soil pastes
were prepared by hand mixing with distilled water and stored in air
tight containers for a minimum period of 24 hours to equilibrate.
The testing procedures adopted were generally in accordance with
BS1377:Part 2: 1990, the notable exceptions being that the range of cone
penetrations was extended beyond the normal range of 15-25mm associated with the liquid limit and that two cone weights were used.
For this investigation a single 30'one as used for British Standard
Liquid limit determinations was used weighing 80g, (0.785N) and 230g,
(2.256N). The heavier weight was achieved using the additional weights
supplied with the liquid limit equipment. For any given test the cone
was clean, dry and unlubricated.
The vane used during the laboratory work was 12.7mm by 12.7mm
and was positioned to be coincident with the centre of the liquid limit
cup. Brown, 1993, Brown and Huxley, 1996, suggest that the measurement of the undrained shear strength at the centre of the liquid limit
cup, using a vane of this size, is not affected by boundary conditions.
Testing
During the testing programme cone penetrometer tests were carried out
using both the standard (80g), and heavy (230g) cones. After the cone tests,
and without changing the moisture content, the liquid limit cup was
refilled and the remoulded soil subjected to a laboratory vane test with
the blade centrally placed in the cup. This procedure was repeated three
times, the shear strength being taken as the mean of the three readings.
The whole process was repeated using increasing paste moisture
content until the standard cone achieved a penetration of at least
25mm. The use of the heavy cone was terminated when it achieved similar or slightly higher penetrations. This, naturally, occurred at lower
moisture contents.
Built Environment
Faculty, Southampton
Institute.
MA Himfey, Department of Civil Engineering, University of Surrey.
Soils used
The soils used were the same as
those used for a parallel investiGROUND ENGINEERING DECEMBER
1996
PAPER THE CONE FACTOR FOR A
30'ONE
250-
0.9-
u 250o
r
250-
nq
I 250-
o07
> 250250
0.8-
0.6-
'
1000
500
1500
0.5
10
2500
2000
20
W/d*2 (kPa)
Rgure1.Polynomial
30
40
PlasMly
curse thnmgh full thdn test
indimt
Rguro 3.gaifagonIn cone factor at the gguhl emit
tion or weight.
10-
ro
~
CL
fn
6.
~
s
c
~
~
Cio
4~
o
c
~
~
l5
2-
~
~
ceo
'tolo
~o %sr ~
~ ~
~
~
~
~ ~
~
~ o
~~
~ ~
os
o
80g cone
230g cone
Poiynominai fit
Linear fit wL
0
Flgmo
0
2. Cone penetragons
ooo
4
2
I
ttN'@%:~:-..I=
In the range assotdatedniHh
squid emit test
gation by Brown and Huxley, 1996, into the undrained shear strength
between the liquid and plastic limit. The characteristics of the materials used are summarised in Table 2.
Cone factor k at the llftnht limit
Using Hansbo's proposed relationship, the cone factor k may be investigated over a range of penetrations by plotting the vane shear
strength, c„,against W/d2. Clearly such a plot would be linear if k were
constant over the whole range of penetrations.
During the investigation the cone achieved penetrations ranging
between 0.55mm and 28.1mm. A polynomial best fit through the results
from all the tests made on the nine soils used is given as Figure 1.
From this plot it is clear that the relationship between c„and W/d'as
not linear over the full range of cone penetrations. It should be noted,
however, that due to the difficulties of working with very stiff soil
pastes in the vicinity of the plastic limit, limited data were obtained in
the higher strength/lower cone penetration regions.
If the available data for both cone weights are considered over the
range of penetrations normally associated with the fall cone determination of the liquid limit, namely 15-25mm, the resulting values for
W/d'ie between 1.26 and 10.0 for the two cone weights used. Over this
range the polynomial curve is virtually straight and a linear regression analysis of the data in this region produces a line which is almost
coincident with this best fit curve. Figure 2, The slope of the straight
line, and hence cone factor for this range, was founded to be 0.76.
Beyond the range of penetrations associated with the determination
of liquid limit, it may be seen that the polynomial curve diverges significantly from linearity Figure 1.
If a similar analysis is carried out on the nine soils individually then
the influence of soil type on measured cone factors may be investigated. Plotting the cone factor obtained in the region of the liquid limit for
each soil against plasticity index, Figure 3, shows a general trend of
increasing cone factor with increasing plasticity although the correla-
tion is poor (R'=0.537).
During the analysis it was noted that when using Hansbo's equation
to determine the cone factor k, the expression displayed a certain sensitivity to changes in the three possible variables of strength, penetraGROUND ENGINEERING DECEMBER
1996
c, hPa
dmm
ng
h
1.50
1.50
1.60
1.40
1.50
1.50
20.5
80
80
80
80
85
75
0.80
0.73
0.82
0.71
0.72
0.82
19.5
20
20
20
20
the criterion
used to measure cone penetrations
was
that defined by
BS 1377. This
effectively
gives an acceptable range of
1mm. If this range is considered at the liquid limit the influence of the
possible variation in cone penetrations on the resulting k values may
be ascertained. Taking an assumed undrained shear strength of 1.5
kPa at the liquid limit, (Brown and Huxley, 1996, Atkinson 1993), and
cone penetrations of 19.5mm and 20.5mm results in factors of 0.73 and
0.80 respectively for an 80g cone (Table 3).
A similar variation is noted for arbitrary changes in cone weight and
vane shear strength. For this investigation it may be assumed that
changes in cone weights were negligible, hence only the cone penetration and measured shear strength were prone to the experimental variability. The sensitively of Hansbo's expression and the known difficulties of measuring shear strength using a vane may account for some of
the data scatter.
Cone factor at the phtsttc limit
To determine a cone factor at the plastic limit, this empirical boundary
will also need to be redefined in terms of undrained shear strength. A
of values have been suggested, notably 170kPa (Wroth and
Wood, 1978), 110kPa (Whyte, 1982 and Harrison, 1988) and 150kPa
(Atkinson, 1993). However, it may be argued that, due to the noted variability of plastic limit results obtained from the thread rolling method,
number
and the sensitivity of the undrained shear strength at this limit to small
changes in moisture content, it may be acceptable to assume an arbitrary undrained shear strength of 100kPa, (Brown and Huxley, 1996).
The data here suggest that for a strength of 100kPa, W/d's 305 and
hence the cone factor is 0.33. However, since the available data are
biased towards low strength and high cone penetrations there may be
some doubt as to the validity of the polynomial curve in this region.
Accepting this caveat the data suggest cone factors of 0.30, 0.22 and 0.18
at shear strengths of 100kPa, 150kPa and 170kPa respectively.
Conctnslons
By considering the data obtained from fall cone and shear vane tests
carried out on remoulded soils of differing plasticities under similar
conditions a number of conclusions may be drawn.
From the graph of vane shear strength against W/d2 it is apparent
that the cone factor, k, is not constant over a wide range of penetrations
but the relationship may be considered linear and hence k a constant,
below values of about 10 for W/d'. For the cone used in this study it is
suggested that a suitable cone factor for values in this range, which
approximates to penetrations of between 15mm and 25mm, is 0.76. This
is in general agreement with previously published data.
Below such values it may be seen that there is considerable divergence between the linear model at low shear strengths and the polynomial curve through the full data set. It is suggested that additional
data are collected in the vicinity of the plastic limit to investigate further the cone factor at this limit.
The available data here suggest a cone factor of 0.33 at an undrained
shear strength of 100kPa.
PAPER THE CONE FACTOR FOR A
Furthermore, it is uncertain how these data would have been influenced by variations in surface roughness of the cone. To this end it
may be advisable in future studies to use lightly oiled cones as proposed by Houlsby, 1982 and practised by Wood, 1985.
Data here suggest that stricter criteria in terms of acceptable cone
penetrations may be required when determining cone factors.
Consistent penetrations within a maximum of 0.25mm may be appropriate. Similarly, despite its appeal as a rapid and simple form of
strength measurement, vane shear strength values may give rise to
errors especially at low and high strength values.
Finally, any further test programmes will need to investigate the
influence of plasticity on cone factors.
The authors would like to thank M Burgess, Southampton Institute,
and D Brown, University of Portsmouth, for their assistance with the
laboratory work.
30'ONE
Atkinson, J (1993) 'An introduction to the mechanics of soils and foundations'. McGrawHill, International Series in Civil Engineering, 52-54.
Brown, P J (1993) 'A review of the index testing of soi1s with particular reference to the
use of the fall cone in the determination
of the plastic limit'. MSc dissertation,
University of Surrey.
Brown, P J & Huxley, MA 'The undrained shear strength of remoulded soil in the plastic
range'. In preparation.
Hansbo, S (1957) 'A new approach to the determination of the shear strength of clay by
the fall cone test'. Proc. Royal Swedish Geotechnical Inst., No 14. 7-14.
Harrison, JA (1988) 'Using the BS cone penetrometer for the determination of the plastic
limit of soils'. Geotechnique 38, No. 3, 433-438.
Houlsby, GT (1982) 'Theoretical analysis of the fall cone test'. Geotechnique 32, No.2, 111-118.
Karlsson, R (1961) 'Suggested improvements tn the liquid limit test, with reference to the
flow properties of remoulded clays'. Proceedings 5th Int. Conf. Soil Mech. Found. Eng.
Paris, 171-184.
TerzaghL K (1927) 'Determination of consistency of soils by means of penetration tests".
Public Roads, Vol. 7, No.12, 240-247.
Whyte, I.L (1982) 'Soil plasticity and strength —a new approach using extrusions', Ground
Engineering, 15, No. 1, 16-24.
Wood, DM 'Cone Penetrometer and Liquid Limit', Geotechnique, 32, No.2. 152-157. 1982.
Wood, DM (1985) 'Some fall cone tests'. Geoiechni que, 35, No 1, 64-68.
Wroth, CP & Wood, DM (1978) 'The correlation of index properties with some basic engineering properties of soils'. Canadian Geotechnical Journal, Vol 15, No. 137.
Ground &efneering welcomes papers on geotechnics,
geo-environmental engineering and engineering geology.
Payeri should be topical, practically orientated andpreferably of
international interest. Case studies describing innovative
geotechnical work are particularly encouraged. All original papers
are refereed. Authors should aim for a maximum overall length of no
more than 3500words, although shorter payers are particularly
welcome.
Ground Engineering aims to publish papers within six months of
receipt offering authors rapid and widespread dissemination of
information throughout the world's geotechnical community.
Prospective authors should contact: Paul Wheeler.
Tel:+44 1715056647;
Fax: +441715056642;
e-mail:[email protected]
GROI)ND ENGINEERING Dl.'CEMBER
1996