EARTH SURFACE PROCESSES AND LANDFORMS, VOL. 1 1 , 107-1 10 (1986)

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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 relationships with 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 palaeogeography at 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 1 97 -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 a

0.

0.

P'

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 % C l P '

0.27 0.25 0,26 0.24

Sample 1 58.4 33.4

Sample 2 56.7 30.7

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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/mZ for Sample 1, and 124.3 kN/mZ for 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 0-42 of 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

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.

Ladd, C. C, Foott, R., Ishihara, K., Schlosser, F., and Poulos, H. G. 1977. ‘Stressdeformation and strength characteristics: state of the art

Cohesive Soils. Proc. 1st A X E Speciality Conference, Boulder, Colorado, 71 1-726.

Geotechnical Conf, Oslo, Norway, 1, 43-47.

report’, Proc. 9th Int. Conf Soil Mechs. Foundn. Engng., Tokyo, 2 ,421494.