EARTH SURFACE PROCESSES AND LANDFORMS, VOL. 1 1 , 107-1 10 (1986)
SHORT COMMUNICATIONS
AN INDIRECT METHOD OF DETERMINING MAGNITUDES OF EROSION
USING THE c/p' RATIO
JOHN PI'ITS
School of Civil and Structural Engineering, Nanyang Technological Institute. Singapore 2263
Received 20 Jwte 1984
Revised I 1 January 1985
ABSTRACT
An approximate method is described for determining the maximum consolidating pressure in a hard, heavily
overconsolidated fissured clay. From this, the overburden thickness producing the observed degree of consolidation has
been calculated. The normal method of calculating preconsolidation pressure using an oedometer was not possible. The
ratio c/p' is used in conjunction with the undrained shear strength. Values of c/p' are determined using empirical
relationshipswith Atterberg Limit values. The results allow an overburden thickness to be calculated by assuming a value
for unit weight.
KEY WORDS c/p' ratio Undrained shear strength
Preconsolidation pressure Old Alluvium Pleistocene Singapore
INTRODUCTION
During an investigation of a Pleistocene braided river deposit in the east of Singapore island, channel infill
consisting entirely of hard silty clay was encountered. The clay was extensively fissured, sheared, and faulted,
structures which were limited exclusively to the individual bed. As part of the investigation,some impression of
the palaeogeographyat the time of deposition was required, and it was felt that information on the elevation up
to which deposition occurred would be useful.
Normally, the determination of preconsolidation pressure is carried out using a consolidation test. An
attempt was made to do this. However, on reaching the applied pressure limit of the oedometer, the reduction
in void ratio of the sample was only one third of that required to calculate the preconsolidation pressure. The
oedometer was a standard model found in most modern soil mechanics laboratories. It seemed therefore that
either a much larger, not locally available machine was required, or that a significant reduction in sample size
would be needed. Preparation of a good example in the hard fissured clay was a difficult task. Reducing the size
would not only lead to physical problems of preparation, but also reduce the reliability of the results.
THE c/p' METHOD
An alternative,although rather more approximate, method was therefore utilized. The basis of the idea was the
c/p' ratio which is the ratio of the undrained cohesive strength to the effective consolidation pressure for a
normally consolidated clay. Clearly, the clays in question are not normally consolidated, but a value would be
found providing a pressure (a,) producing a particular degree of consolidation. By using a value of unit weight
0 197 -9337/86/0 1 0 1 07 -04$0 1.OO
0 1986 by John Wiley & Sons, Ltd.
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a
a
C
P'
a
0.
0.
Figure 1. Relationship between c/p' and I p (after Bjerrum and Simons, 1960)
Figure 2. Relationship between c/p' and WL (after Karlsson and Viberg, 1967)
(y) in the equation uv = yh, where h is the thickness of overburden, a value of h can be determined.
The c/p' ratio is now widely recognized (Bowles, 1979). Empirical relationships have been evolved between
c/p' and the plasticity index shown in Figure 1 (Bjerrum and Simons, 1960) and c/p' and liquid limit shown in
Figure 2 (Karlsson and Viberg, 1967). These were used to decide on values of c/p' ratio to employ in these
determinations.
The Atterberg Limits and corresponding c/p' ratios for the samples tested are shown in Table I. Sample 1 is
from the Resources Development Board Mechanised Sand Quarry at Bedok and Sample 2 is from the Housing
and Development Board cut site at Tampines.
In a series of undrained direct shear tests, the average cohesive strength determined for the Sample 1 was
112 kN/m2 and 118 kN/m2 for Sample 2. Care was taken to ensure that failure occurred as far as possible
through intact material, avoiding the fissures present in the clay. Therefore, applying these strengths, the c/p'
values obtained from the empirical relationships, and an assumed unit weight of 175 kN/m3, the overburden
above the clay was calculated as being between 55 m and 59 m above Sample 1 and 60.5 m to 65.6 m above
Sample 2.
Table I. Values of Atterberg Limits and c/p' ratios
WL %
Ip%
Sample 1
58.4
33.4
Sample 2
56.7
30.7
ClP'
0.27
0.25
0,26
0.24
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The calculation of overburden thickness has been made on the assumption that the water table in the river
valley was high at the times of deposition of the sediment on top of the clay. This assumes that the effective
pressure applied to the clay is related to the submerged unit weight (y - y,), where y, is the unit weight of water,
throughout its thickness. It is difficult to know in the case of Singapore how realistic this assumption is, but it
would generally be expected that the water table in the bottom of a river valley in an area of humid climate may
be at no great depth.
DISCUSSION
The value of p- obtained using the method outlined will provide only the lower bound. The error involved
when applying the method to a heavily overconsolidated clay may be very large, given that cohesion is
primarily dependent on the void ratio. The greater the degree of overconsolidation,the larger the error in
is likely to be.
The current stress levels on the samples are estimated to be about 140 kN/m2 taking into account purely the
effect of overburden. The position of the water table throughout the history of the Old Alluvium is an
unknown quantity. However, assuming a continued near-surface position for it, the overconsolidation ratio,
utilizing the figures presented, would be at the very least 4.7. Using the graph of Ladd et al., 1977, (Figure 3),
this produces undrained strengths of 129.2 kN/mZfor Sample 1,and 124.3 kN/mZfor Sample 2, both of which
are in broad agreement with the test results.
Nevertheless, this would indicate levels of stress which should be within the range of an oedometer. That the
reduction in void ratio to 0-42of the original was not attainable may well be a reflection of stress relief effects,
and particularly so upon the level of undrained shear strength obtained.
nc
I
2
4
6
8
10
Figure 3. Relative increase in undrained strength ratio with OCR from direct simple shear tests for a range of non-varved organic and
inorganic clays (after Ladd et al., 1977)
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CONCLUSIONS
The method outlined of determining overburden thickness is an approximate one. It has been evolved largely
because the more usual technique could not be employed in this project. The techniques available also demand
that a fine grained soil is available for testing. The use of a c/p‘ ratio and undrained shear strength has provided
quite consistent results for two clays from infilled channels in two different localities. The choice of the c/p‘
ratio presented little problem as the empirical relationships with consistency limits provided very similar values
by each method. Nevertheless, the value obtained for erosion of overburden will be a minimum only.
ACKNOWLEDGEMENTS
I am grateful to Dr. Avijit Gupta of the National University of Singapore for his stimulating discussion and
help with fieldwork; and to the following members of NTI for their help: Professor Bengt Broms for
discussions on the subject, Wang Jee Gat and Vincent Heng for the soil mechanics testing, and Sherlene Lim
for typing the paper. An anonymous referee made some extremely helpful comments on the original
submission.
REFERENCES
Bjerrum, L. and Simons, N. E. 1960. ‘Comparison of shear strength characteristics of normally consolidated clays’, Shear strength of
Cohesive Soils. Proc. 1st A X E Speciality Conference, Boulder, Colorado, 71 1-726.
Bowles, J. E. 1979. Physical and Geotechnical Properties of Soils, International Student Edition, McGraw-Hill Kogakusha, Japan.
Karlsson, R. and Viberg, L. 1967. ‘Ratio c/p’ in relation to liquid limit and plasticity index with special reference to Swedish clays’, Proc.
Geotechnical Conf,Oslo, Norway, 1, 43-47.
Ladd, C. C, Foott, R., Ishihara, K., Schlosser,F.,and Poulos, H. G. 1977. ‘Stressdeformationand strength characteristics: state of the art
report’, Proc. 9th Int. Conf Soil Mechs. Foundn. Engng., Tokyo, 2 , 4 2 1 4 9 4 .