Measuring the plastic limit of fine soils: an experimental study

an experimental study Proceedings of the Institution of Civil Engineers Geotechnical Engineering 8 February 15 Issue GE1 Pages 53 64 http://dx.doi.org/.80/geng..00004 Paper 00004 Received 03/01/ Accepted 01/08/ Published online // Keywords: codes of practice & standards/geotechnical engineering/strength & testing of materials ICE Publishing: All rights reserved Measuring the plastic limit of fine soils: j 1 j 2 VinayagamoorthySivakumar MSc,PhD,DSc,DIC,CEng,FICE Reader, School of Planning, Architecture and Civil Engineering, Queen s University Belfast, UK Brendan C. O Kelly PhD, FTCD, CEng, CEnv, MICE Associate Professor, Department of Civil, Structural and Environmental Engineering, Trinity College Dublin, Dublin, Ireland j 3 j 4 j 5 Laura Henderson PhD Research Engineer, Norwegian Geotechnical Institute, Oslo, Norway Catherine Moorhead MEng, PhD Teaching Assistant, Queen s University Belfast, Belfast, UK Shiao Huey PhD Assistant Professor, University of Western Australia, Perth, Australia j 1 j 2 j 3 j 4 j 5 The Casagrande thread-rolling method for determining the plastic limit of fine-grained soil is heavily dependent on operator judgement and can often give inconsistent or unreliable results. This paper presents an energy-based approach used in the development of an improved testing procedure for the plastic strength limit. A 0. 727 kg cone is allowed to fall freely through 0 mm before contacting the surface of the test specimen, with the plastic strength limit determined for a cone penetration depth of mm. For ten mineral clays of intermediate to very high plasticity tested, the plastic limits deduced using the cone were in good agreement with the measured Casagrande plastic limits. The values deduced using an 8 kg contacting cone were consistently lower than the Casagrande limits. Notation c u strength mobilised for quasi-static condition c ud dynamic strength c ud(f) strength mobilised for fast dynamic loading c u(ll) undrained strength at LL c u(pl) undrained strength at PL c u(pl) /c u(ll) strength variation over plastic range E (C@LL) energy released by falling cone at LL E (C@PL) energy released by falling cone at PL g gravitational constant h cone penetration depth K cone factor LL liquid limit m cone mass m LL cone mass used in fall-cone LL apparatus PL Casagrande plastic limit PL (0) plastic strength limit deduced for strength ratio of 0 V 0 velocity of cone with its tip just contacting the top surface of the test specimen V f at rest position _ª strain rate î strain rate effect on mobilised strength (¼ c u =c ud ) î F revised strain rate effect on strength (¼ c u =c ud(f) ) 1. Introduction The water content corresponding to the transition between the plastic and semi-solid states for fine-grained soil is defined as the Casagrande plastic limit (PL). Haigh et al. (13) postulated a more accurate definition for PL, based on the physical state of the soil as its water content reduces to PL. The Casagrande PL method involves rolling out wetted soil threads on a glass plate, with the Casagrande PL value corresponding to the water content at which crumbling of the soil thread first occurs in reducing the thread diameter from 6. 0mmto3. 0 mm (BS 1377-2, BSI, 1990) or to 3. 2 mm (ASTM D43-05, ASTM, 05). Although simple, this method is rather crude and often unreliable, being heavily dependent on operator judgement (Sherwood, 1970). For instance, Table 1 lists Casagrande PL values (determined independently by four site investigation laboratories in accordance with the British Standard) for 11 inorganic fine-grained soils. The maximum variation in the measured PL values was 8%, although Sherwood (1970) reported that the variation can be up to %. Such large variations have prompted many researchers to seek more reliable and repeatable methods of measuring the PL value. New techniques centred on the fall cone apparatus have been developed over the past three decades, with some notable contributions, including the following methods. (a) Harrison s approach (Harrison, 1988), which relies on the relationship between liquidity index and the logarithm of penetration depth (h) for an 80 g 8 fall cone over the range 5 mm. The PL value was defined by extrapolating this relationship to determine the water content value for h ¼ 2. 0 mm, implying that the shear strength at this water 53

Type of soil LL: % PL: % Average PL: % GSI CPD WF QUB Max difference: % Sleech (SL) 50 25 25 23.3 2 Belfast Clay (BC) 55 23.8 3 Oxford Clay (OX) 55 23.3 4 Canadian Clay (CC) 73 27 27. 5 3 Glacial till (GT) 36 17 17. 0 3 Tennessee (TN) 72 33 35 31. 5 7 Ampthill (AT) 77 31 32 33 31. 5 3 Donegal Clay (DC) 43 21. 3 1 London Clay (LC) 71 27 27.0 3 Enniskillin (EK) 36 19 17 17.5 3 Kaolin (KC) 70 33 36 37 29 33.8 8 GSI: Glover Site Investigation Ltd; CPD: Central Procumbent Division, NI; WF: Whiteford Geoservices; QUB: Queen s University Belfast. Table 1. Liquid limits (LLs) and plastic limits (PLs) of soils obtained through different laboratories operating in Northern Ireland to BS 1377 (BSI, 1990) content is 0 times that mobilised at its liquid limit (LL). In other words, Harrison (1988) defined a new limit for use in geotechnics, namely the PL (0). (b) Stone and Phan (1995) developed an instrumented 8 cone, which was allowed to penetrate the test specimen at a rate of 3. 0 mm/min. The PL (0) value was determined as the water content that produced a cone penetration depth of 11.55 mm under a cone force of 80 N. (c) Feng (00) performed a detailed investigation in which an 80 g cone was allowed to penetrate into test specimens prepared over a range of water contents. The data were analysed by plotting the cone penetration depth against water content in log log scale. Using this relationship, the PL (0) value was defined as the water content at which the cone penetration depth was estimated to be 2.0 mm. (d) Sivakumar et al. (09) proposed the fast static loading technique to apply a force of 55 N to the British Standard 80 g 8 fall cone in order to measure the PL. These techniques determine the PL value using a strength approach, which is arguabley a more sensible approach to use, as the fall-cone method is clearly more repeatable (mechanical test). Haigh et al. (13), in their assessment of PL for fine-grained soils, concluded that the Casagrande PL is a measure of soil brittleness, with deduced PL values not corresponding to a fixed strength. Hence they promoted a need for a strength approach (i.e. the PL (0) ) for geotechnical analysis, which is what the authors use in this paper through the new test methodology. However, the PL (0) does not necessarily have to correspond to the brittle transition that the Casagrande thread-rolling test implies. In other words, one should not expect the PL (0) to align with the results from the threadrolling method, as different mechanisms are at play in both tests (e.g. see Haigh et al. (13), O Kelly () and Stone and Phan (1995)). In considering the above fall-cone methods, each has its own advantages and disadvantages. The Stone and Phan (1995) approach requires a carefully instrumented cone and its use in standard commercial laboratories may prove difficult; however, it could be a useful device in research-led laboratories. The Feng (00) approach relies on a number of data points (as many as eight are required) collected for various water contents, which may not be economically viable in a commercial operation. The Sivakumar et al. (09) approach requires a compressed air supply in order to activate the piston force of 55 N, and also relies heavily on the calibration of the device (Sivakumar et al., 11). For these reasons, a more user-friendly, technically sound and simple approach is necessary to measure PL (0) with reasonable accuracy; hence the genesis of this research. 2. Basis to the proposed approach 2.1 Energy-based approach Wroth and Wood (1978), Wood (1990), Stone and Phan (1995) and Sharma and Bora (03), among others, have reported that for many inorganic fine-grained soils of low and intermediate plasticity, the saturated undrained strengths c u(ll) and c u(pl) at Casagrande LL and PL are approximately 1.7 and 170 kpa respectively. On this basis, the strength variation over the plastic range (cu(pl)/cu(ll)) is,0 for many inorganic fine-grained 54

soils. This has been demonstrated experimentally by Sharma and Bora (03) for 55 different soils. However, the measured strength variation over the plastic range can potentially be 170 (Wood, 1990). Regression analysis of reported water content undrained strength correlations for mineral soils performed by O Kelly (13) indicated a strength variation range of 43 1. However, in the authors view, much of the variation in strength ratios may result from inaccurate measurement of the strength mobilised at Casagrande LL. According to BS 1377-2 (BSI, 1990), the LL corresponds to the water content at which the free-falling 80 g 8 cone penetrates into the remoulded soil specimen to a depth (h) of mm before coming to rest. At LL, the energy released by the falling cone (E (C@LL) ) is the difference in potential energy of the cone before and after penetration (Figure 1(a)), which is given by 1: E (C@LL) ¼ m LL g h where m LL is the cone mass used in the fall-cone LL apparatus (i.e. 80 g in the present investigation) and g is the gravitational constant. With the PL (0) defined in the same fashion as the British Standard fall-cone LL (i.e. water content for h ¼ mm), the cone mass required for the measurement of the fall cone PL is 0 3 m LL. Similarly, at PL (0), the energy released by the heavier cone (E (C@PL) ) is the difference in the potential energy of the cone before and after penetration 2: E (C@PL) ¼ 0 3 m LL g h For identical cones in term of cone surface roughness and apex angle, the deformed shapes of the soil after penetration at LL and PL are similar. Under these conditions, the energy dissipated in the soil at PL (0) is 0 times that for LL. Since an 80 g cone is used in the British Standard fall-cone LL method, an 8 kg cone would therefore be required for measuring PL (0). Using this heavier cone in routine laboratory investigations is not practical since it may bring about health and safety issues during the testing. Instead, the required energy (i.e. 0 times that for the fall-cone LL) can be extracted by (a) increasing the falling distance of the cone while maintaining its mass of 80 g 80 g cone cone angle Total mass m g with cone angle of V 0 0 m/s Soil at liquid limit (a) mm V f 0 m/s Falling distance 0 mm V 0 1 98 m/s mm Soil close to plastic limit V f 0 m/s (b) Figure 1. Cone penetration at (a) liquid limit and (b) plastic limit 55

(b) increasing the cone mass and also incorporating a falling distance. If the cone mass of 80 g is to be maintained, the cone falling distance has to be 2.0 m, which is not a practical solution. Hence option (b) above is considered to be a more appropriate approach to achieve the required energy. Hook Platform for additional weight 2.2 Equipment The configuration adopted in the present study is shown in Figure 1(b). A cone of mass m is allowed to free fall from a stationary position through a clear distance of 0 mm before contacting the specimen surface. For the British Standard LL method, the cone penetrates the soil by mm at LL. In the proposed PL method, after free falling through 0 mm, the PL (0) condition is defined by the cone penetrating into the soil by mm before coming to rest; that is, the total falling distance is 2 mm. A simple calculation would show that the cone mass required for the proposed device is 0.727 kg; this means it generates 0 times the potential energy of the 80 g fall cone penetrating into soil prepared at LL. This is the premise on which the new apparatus was developed and evaluated. Figure 2 shows a schematic diagram of the new PL device in which a 8 cone is attached to a vertical spindle that is guided during free fall by linear bearings. An 80 mm diameter thin metal disc is located just above the cone and is held in position by a 0 N capacity electromagnet, which is mounted on a support frame. In the present set-up, the cone assembly (i.e. the cone itself, its spindle and metal disc) has a combined mass of 0. 727 kg. A displacement gauge mounted on a vertical support rod can be moved away during cone penetration testing and brought back into position above the metal disc when taking cone penetration depth readings. The electromagnet is operated using a two-way switch such that, when its polarity is reversed, the magnetic field changes from north to south or from south to north. In the proposed set-up, the option of turning off the power to the electromagnet in order to release the metal disc (cone assembly) was not chosen because it may leave the 0. 727 kg mass with some residual magnetic flux. In this case, the metal disc (cone assembly) may not immediately depart from the electromagnet on turning off its power. Photographs of the device are provided in Figure 3. 3. Experimental programme 3.1 Validation of energy concept Falling objects develop kinetic energy that increases with the falling distance in proportion to the square of the velocity, assuming aerodynamic effects are negligible. The kinetic energy that the object has at a particular location/elevation is equivalent to the potential energy that the object has released over its falling distance. As part of the present investigation, an 8 kg 8 cone (Figure 3(b)) was allowed to penetrate into BS3-type foam, with the cone tip initially just contacting the foam surface. Out of Total mass with cone angle of Displacement transducer Wing nut Linear bearings 0 mm Sample prepared close to plastic limit Clamp Cone spindle Magnet Figure 2. Schematic of proposed fall cone PL measuring device trials performed, the mean cone penetration depth was 11. 04 mm, with standard deviation (SD) of 0. 21 mm. Next, the 0. 727 kg cone was allowed to free fall from a height of 0 mm above the foam surface and the resulting mean cone penetration depth was 11.17 mm, with SD of 0. mm, again for trials. This observation generally confirms the energy conservation. Other factors that may affect the penetration depth, and which are discussed in greater detail later in the paper, include (a) magnetic repulsion acting when the polarity of the magnet is reversed in order to release the metal disc, allowing the cone assembly to fall under gravity (b) differences in strain rate (inertia) for different cones 56

Total mass with cone angle of Cup (a) Total mass 8 kg through the additional 0 mm fall height. This maximum velocity was calculated from the cone s kinetic energy at the moment of contact between the cone tip and the test-specimen surface, assuming its acceleration was 9. 81 m/s 2. This is one of the critical details for the estimation of the PL (0). In routine testing laboratories, there is the potential that without regular cleaning and lubrication, the guide bearings may not remain sufficiently well lubricated to guarantee exactly the same dynamics of fall. This can be assessed by measurement of the contact velocity. Similarly, if some aerodynamic or frictional resistance in the bearings is anticipated (i.e. the cone s acceleration is not exactly 9. 81 m/s 2 ), calibrations can be performed after determining the actual kinetic energy at contact. However, such frictional and aerodynamic resistances were not significant in the present investigation, evidenced by remarkably similar cone penetrations obtained for the 8 kg cone and 0. 727 kg cone falling through 0 mm before penetrating into the BS3 foam. The experimental research performed to validate the proposed new PL approach was performed in two stages. In the first stage of experiments, the 0.727 kg cone was allowed to free fall through 0 mm before contacting the horizontal surfaces of soil specimens prepared at close to the PL. The initial assessment was performed on kaolin and London Clay. As part of the crosscheck, an 8 kg cone was allowed to penetrate the soil specimens, although in this case, the falling distance was set at zero (Figure 3(b)). A 0 N capacity electromagnet was used to hold the cones in position before allowing them to free fall and penetrate into the test specimens. The potential effect of the magnetic field on the cone penetration response was investigated first. For instance, consider the magnet was under north pole influence, with the metal disc (attached to the cone spindle) under south pole influence (Figure 4(a)). The power to the electromagnet was then reversed, instantaneously changing the pole of the magnet to south (Figure 4(b)), thereby releasing the cone assembly, allowing it to fall under gravity. However, the metal disc (cone assembly) may hold some residual magnetic charge with south pole (b) Figure 3. New fall cone PL measuring devices: (a) 0.727 kg cone; (b) 8 kg cone (c) aerodynamic and frictional resistances that may develop over the additional 0 mm free-fall distance for the 0. 727 kg cone set-up. In the present set-up, frictional resistance was minimised by using smooth, linear bearings to guide the vertical movement of the cone spindle. Aerodynamic effects were considered insignificant since the cone accelerates from a stationary position, reaching a maximum velocity of only 2. 0 m/s after free fall had occurred (a) Magnet Cone N S Cone (b) Magnet Figure 4. Change of polarisation: (a) before reversing power; (b) after reversing power S S 57

influence for some finite time (Figure 4(b)) on account of its greater mass, compared with that of the magnet. This means that the cone assembly (which just departed from the magnet) and the magnet itself could have the same polarisation, potentially exerting some additional force (repulsion) on the departing cone assembly. In order to examine the significance of this, the 0.727 and 8 kg cones were allowed to free fall without using electromagnets in the experimental set-ups. This was not a particular problem for the 0. 727 kg 0 mm cone set-up. For the heavier 8 kg cone mass, the cone was hung from a beam located above the testing area using a thin wire and the cone was released by cutting the wire. In the second stage of experiments, fall cone tests were performed on a wide range of soils (see Table 1) using the 0. 727 kg 0 mm and 8 kg 0 mm cone set-ups. For both set-ups, an electromagnet was used to hold the cones in position before allowing them to free fall. 3.2 Specimen preparation The materials for LL and PL determinations were prepared by dry sieving through the 425 ìm sieve. Approximately 0 g of each soil was then thoroughly mixed with de-aired water to produce water contents somewhere close to the PL. The wetted soils were sealed in separate plastic bags and allowed to equilibrate over a h period. Although oven drying of soil in advance of consistency limit tests is not ideal (Mesri and Peck, 11), the fact that the test materials investigated for LL and PL determinations in this study had been prepared in exactly the same manner meant that the relative impact of oven drying on the experimental results was not significant. The soils were carefully compacted into British Standard fall-cone LL cups (BSI, 1990) using the procedure described by Sivakumar et al. (09). During compaction, a collar attachment to the cup allowed the formation of a specimen higher than the cup. This extra height was carefully trimmed back in line with the top rim of the cup before performing the penetration tests. For a given soil, the variation in bulk density between test specimens prepared at the same water content using this approach was only 0. 004 g/cm 3. Each specimen was placed in turn directly beneath the cone and initial depth readings were taken using the displacement gauge (see Figure 3). The cone was allowed to free fall, with the final penetration reading taken after 5 s, as specified in the British Standard fall-cone LL method, by which time the cone had come to its rest position. 4. Results and discussion 4.1 Experimental investigation stage 1 In order to ensure consistency, a strict procedure was adopted whereby the cone penetration depth for each water content value investigated was measured twice, with the average penetration reading used for further analysis. In almost every case, the difference in penetration readings from two repeat tests was below 0. 25 mm, well within the 0. 5 mm difference specified by the British Standard fall-cone LL method. Figure 5 shows the measured penetration depth (h) against water content relationship for kaolin, determined twice using the 0. 727 kg 0 mm cone set-up. This study proposes that the fall-cone PL is defined as the water content corresponding to h ¼ mm, which from regression analysis corresponded to.8 0.15% water content for this kaolin material. These observations show that the procedure adopted is repeatable when performed under similar conditions. The effect of using an electromagnet to hold the cone assembly in position before free fall was assessed for kaolin and London Clay materials. Figure 6(a) shows cone penetration depth plotted against water content relationships determined using the new PL device in which the 0.727 kg cone was allowed to free fall without the use of the electromagnet (i.e. 0.727 kg free-fall data points), and in repeat tests by reversing the magnet polarity to allow free fall to occur (i.e. 0. 727 kg magnet data points). When the electromagnet was used to hold the cone in position, the kaolin and London Clay had PLs (i.e. water contents for h ¼ mm) of. 8% and 27. 0% respectively. When the cone was allowed to free fall without using the magnet, the deduced PLs were.8% and 27.3%, respectively, demonstrating that the use of the electromagnet had no significant effect on the cone penetration. As explained earlier in the paper, in an ideal situation and as suggested by Wood (1990), one should use an 8 kg 8 fall cone to measure the PL (0), after determining the LL using an 80 g 8 fall cone. Koumoto et al. (07) have discussed in a similar manner the applicability of a 1.5 kg 608 fall cone to determine the PL (0), after determining the LL using a 60 g 608 fall cone. As a preliminary assessment, the 8 kg 8 cone set-up shown in Figure 3(b) was investigated in the present study, with this cone 25 23 21 19 17 15 Test 1 Test 2 13 27 29 31 32 33 34 35 Figure 5. Cone penetration plotted against water content (two repeat tests on kaolin) for 0.727 kg 0 mm cone set-up 58

free fall, KC magnet, KC free fall, LC magnet, LC 23 25 27 29 31 32 33 34 35 36 (a) 32 8 kg free fall, KC 8 kg magnet, KC 8 kg free fall, LC 8 kg magnet, LC 23 25 27 29 31 32 (b) Figure 6. Effect of electromagnet on 0. 727 and 8 kg cone setups: (a) 0.727 kg cone; (b) 8 kg cone held in position by an electromagnet, or alternatively hung using a thin wire, before allowing it to free fall and penetrate into the soil specimen. When the magnet was used to hold the 8 kg cone before falling, the kaolin and London Clay had PLs of 29. 6% and 25. 4% respectively ( 8 kg magnet data points in Figure 6(b)). When the cone was allowed to free fall by cutting the wire hanger, it did not make a significant difference in the PL estimations, again demonstrating that the electromagnet did not have a significant effect on the cone penetration. The experimental measurements also indicated that the PL values determined using the 8 kg 0 mm cone were less than those determined using the 0. 727 kg 0 mm cone (Figure 6). The gradients of the measured penetration depth against water content correlations were also distinctively different. Hence the rest of this study concentrated on examining the cone penetration depth against water content relationships for a wide range of soils, using the electromagnet as the mechanism to hold the cone assembly in position before free fall was allowed to occur. 4.2 Experimental investigation stage 2 Figure 7 shows the penetration depth against water content relationships for ten different soils (refer to Tables 1 and 2) determined using the 8 kg and 0. 727 kg cone set-ups. Table 2 lists the PL values determined for h ¼ mm using the two cone set-ups. Also included in this table are the Casagrande PL values determined independently by four geotechnical laboratories (value mass for a given soil is average of reported PLs) and in separate testing by the authors. In the authors study, uniform soil threads for the rolling-out procedure were formed by compacting the wetted soil in a metal cylinder (having an inner diameter of 4. 0 mm) before extruding the compacted soil from the cylinder by insertion of a 4. 0 mm diameter pin. The soil threads were carefully rolled out in accordance with BS 1377-2 (BSI, 1990), with the Casagrande PLs identified when the threads broke on reduction to 3.0 mm in diameter (witnessed and agreed by three individuals). The PL value ranges obtained by this method are given in Table 2. Referring to Table 2, for all ten soils investigated, the PL values determined using the 8 kg contacting cone were on a percentage basis,8. 8% (range 1. 8. 6%), and in absolute terms,2. 3% water content (range 0. 4 4. 2%), lower than the average of the Casagrande PL values reported by the four independent laboratories. Also note that the soil threads crumbled and disintegrated immediately on attempting to roll them out at water contents equal to the 8 kg PL values. Although the 8 kg PLs (i.e. PL (0) values) do not have to correspond to the brittle transition that the thread-rolling method implies, it was clear that for the ten clays investigated, the 8 kg fall cone set-up consistently underpredicted the Casagrande PLs. Similar findings have been reported by Feng (00), Kodikara et al. (06) and O Kelly (13), with experimental fall-cone PL (0) values underpredicting the Casagrande PLs. Compared with the 8 kg PLs, the PLs determined using the 0. 727 kg 0 mm cone set-up were, on average, approximately 1. 5% higher (range 0. 9 2. 5% water content, Table 2). When threads of the ten test soils were rolled out at the 0. 727 kg 0 mm PL values, they began to disintegrate as their diameters approached 3.0 mm. This suggested that the 0.727 kg 0 mm PLs agreed more favourably with the Casagrande PLs (see Figure 8 in which the averages of the Casagrande PLs reported by the four geotechnical laboratories have been used). However, it should be noted that one should not expect the PL (0) (i.e. the values obtained using the 8 kg or 0. 727 kg free-falling cone) to align with the results from the thread-rolling experiment, as different mechanisms are at play in both tests. Nevertheless, an attempt was made to explore other potential reasons for the different PL values obtained using the 8 kg and 0.727 kg freefalling cones. 59

EK, 8 kg EK, DC, 8 kg OX, 8 kg DC, OX, TN, 8 kg TN, 32 (a) 32 SL, 8 kg SL, LC, 8 kg LC, AT 8 kg AT, 32 34 (b) 32 CC, 8 kg KC, 8 kg BC, BC, 8 kg CC, KC, 32 34 36 (c) Figure 7. Penetration water content relationships (0. 727 and 8 kg cones): (a) EK, DC, OX and TN; (b) SL, LC and AT; (c) BC, CC and KC 5. Assessment of PLS measured using 8 kg and 0. 727 kg cones The next stage in the research was aimed at exploring the reason(s) for the difference in PLs determined using the 0.727 kg 0 mm and 8 kg 0 mm cone set-ups, especially arising from differences in strain rate, which affect the strengths mobilised and hence the strength ratio cu(pl)/ac(ll). The strain rate varies during the penetration of the fall cone into the soil specimen. Koumoto and Houlsby (01) reported an average strain rate of,1. 0 3 6 %/h for the 80 g 8 fall cone penetrating into soil prepared at LL. The estimated time period required for penetration of the 80 g cone into the soil by mm (i.e. at LL) was,0 ms. This was independently measured in the present study, as shown by the solid data points in Figure 9. Koumoto and Houlsby (01) also reported that a strain rate of,79%/h is typically adopted in measuring the undrained shear strength (c u ) in standard, unconsolidated, undrained, triaxial compression tests. Ladd and Foott (1974) stated that the undrained strength mobilised in triaxial compression increased with strain rate ( _ª) at 5% per log cycle. Kulhawy and Mayne (1990) showed statistically that the % increase in undrained strength per log-cycle of strain could be justified based on triaxial compression data for clays. Koumoto and Houlsby (01) also came to this conclusion based on regression analysis of triaxial strength data from three published sources. Based on the reported average strain rates, the ratio (î) between the dynamic undrained strength (c ud ) mobilised at the LL by the 80 g 8 fall cone and the quasi-static undrained strength (c u ) is,0. 74; that is, c ud 1.35 3 c u. Assuming the cone characteristics (apex angle and surface roughness) and soil deformation patterns are similar to that for the British Standard fall-cone LL test, the time period required by the 8 kg contacting cone to penetrate into soil prepared at PL should be similar to that for the 80 g cone penetrating into soil prepared at LL. This was independently validated using digital measurements taken during the penetration of the 8 kg cone at close to PL (see Figure 9). Hence the strength ratio î for these cones under dynamic and quasi-static conditions would be expected to be the same. In the present investigation, the 0. 727 kg cone was allowed to free fall through 0 mm, contacting the test specimen surface at a velocity of 2. 0 m/s (in agreement with the measured velocity at the time of impact, from Figure 9), before coming to rest at h ¼ mm the basis assumed for measuring the fall cone PL. Hence the strain rates are far higher compared with the 8 kg contracting cone. An approximate estimate of the strain rate was determined from the time period required for the 0.727 kg 0 mm cone to penetrate into soil prepared at PL (Figure 9). Compared with the 8 kg cone, the penetration time was found to reduce,-fold and ten-fold at the beginning and towards the end of penetration, respectively, with the strain rate increasing on average -fold. With an average strain rate of,1. 0 3 6 %/h for the 8 kg cone, the average strain rate for the 0.727 kg 0 mm cone set-up is,1.8 3 7 %/h. Based on the % average increase in undrained strength per log cycle increase in 60

Type of soil Average Casagrande PL by four laboratories: % PL (0. 727 kg cone): % PL (8 kg cone): % PL (by group of operators): % Difference in PL a Sleech (SL).3 23.3 21.9 23 1.0 Belfast Clay (BC).8 25.1 23.5 25 0.3 Oxford Clay (OX).3.8 21.9 21 0.5 Canadian Clay (CC). 5 29. 2. 7 27 0. 7 Tennessee (TN) 31. 5 29. 9. 2 31 1. 6 Ampthill (AT) 31. 5 31. 1 29. 8 31 0. 4 Donegal Clay (DC). 3. 1 19. 0 19 0. 2 London Clay (LC). 0 27. 2 25. 4 27 0. 8 Enniskillin (EK) 17.5.9 13.9 15 2.6 Kaolin (KC) 33.8.8 29.6 32 3.0 a Difference between Casagrande PL (average) and PL (0.727 kg). Table 2. Average of PLs for soils obtained through laboratories operating in Northern Ireland and PLs determined by the authors using the 0.727 kg 0 mm and 8 kg 0 mm cone set-ups Average plastic limits obtained through four laboratories: % 40 0 0 40 Plastic limit using cone: % Figure 8. Plastic limits obtained using 0.727 kg cone setup and Casagrande method 25 15 5 80 g cone (close to LL) cone (close to PL) 8 kg cone (close to PL) 0 0 0 02 0 04 0 06 0 08 Time: s Figure 9. Cone penetration depth plotted against time (for soil close to LL and PL) strain rate (Koumoto and Houlsby, 01; Kulhawy and Mayne, 1990; Ladd and Foott, 1974), the revised undrained strength ratio î F (¼ c u =c ud(f) ) for the 0.727 kg 0 mm cone set-up can be shown to be 0. 69, where c ud(f) is the strength mobilised for fast dynamic loading and c u is based on the strain rate of 79%/h; that is, c ud(f) 1. 44 3 c u. For the initial evaluation of the cone mass required in the new experimental set-up (i.e. 0.727 kg), an allowance was not made for the increased strain rate effects in moving from the 8 kg 0 mm to 0.727 kg 0 mm cone set-ups. Hence, if PLs measured using the 8 kg contacting cone are to be reproduced, then the cone mass has to be increased from 0.727 to 0.775 kg (i.e. [0. 727 3 (1. 44/1. 35)]). Figure shows the penetration depth against water content relationships determined for the kaolin clay using 0. 727 kg 0 mm, 0. 757 kg 0 mm and 8 kg 0 mm cone set-ups. The test was not performed using a cone mass of 0. 775 kg due to human error. As shown in Figure, the g increase in mass for the lighter cone shifts the correlation line towards the 8 kg cone trend line. However, the increase in the cone mass is counterproductive for the present investigation 61

Cone penetration: mm 35 25 15 0 757 kg 8 kg mm at PL), K is the cone factor and g is the gravitational constant. For the 8 cone free falling from at-rest position with its tip initially just contacting the test specimen surface, Koumoto and Houlsby (01) reported the theoretical cone factor as 1. 33. From Equation 3, the 8 kg 0 mm cone set-up would mobilise a dynamic strength of,1 kpa for h ¼ mm, equivalent to,193 kpa in triaxial compression at _ª ¼ 79%/h. This may explain why the experimental PL predictions for the ten test soils determined using the 8 kg cone were consistently lower compared with the Casagrande PL values (see Table 2). because the 8 kg PLs were not true representations of the soil behaviour, with the PLs obtained using the 0. 727 kg 0 mm cone set-up more realistic and in better overall agreement with the average of the five independent Casagrande PL measurements for a given clay. The proposed 0.727 kg 0 mm fall cone PL method is in essence a strength approach that assumes the saturated quasistatic undrained strength (c u ) mobilised at the PL in triaxial compression for _ª ¼ 79%/h is,170 kpa. This strength value has been reported by Sharma and Bora (03), Stone and Phan (1995), Wood (1990) and Wroth and Wood (1978) for many inorganic fine-grained soils of low and intermediate plasticity. The effect of the significantly higher strain rates for the fall cones on mobilised strength must be allowed for, with for example, a typical average strain rate for the 8 kg contracting cone of,1. 0 3 6 %/h. This value was deduced by Koumoto and Houlsby (01) from a very approximate global estimate of the actual strain rates in the test specimen. Based on the % average increase in undrained strength per log cycle increase in strain rate, a dynamic strength (c ud ) value of,2 kpa mobilised by the contacting 8 kg cone is equivalent to a c u value of 170 kpa mobilised in triaxial compression for _ª ¼ 79%/h. The undrained strength determined using the experimental relationship reported by Hansbo (1957) is given by 3: 5 0 27 29 31 32 33 34 35 Figure. Penetration depth plotted against water content relationships for 8, 0. 757 and 0. 727 kg cone set-ups (kaolin) c ud ¼ Kmg h 2 where m is the cone mass, h is the cone penetration depth (i.e. An equally valid and complementary explanation is obtained by considering the dynamic c ud(ll) value of 2.66 kpa (Koumoto and Houlsby, 01) mobilised at h ¼ mm for the British Standard 80 g 8 fall-cone LL apparatus (BSI, 1990). On this basis, the 8 kg 0 mm cone set-up would mobilise a dynamic c ud(pl) value of 6 kpa. Hence the 8 kg cone mass must be reduced by a factor of approximately 0. 87 (i.e. ¼ 2/6 and corresponding strength ratio c u(pl) /c u(ll) of 87) to 6. 948 kg in order to mobilise an equivalent c u(pl) value of 170 kpa in triaxial compression at _ª ¼ 79%/h. Limited tests were performed on kaolin using 8 kg 0 mm, 6. 948 kg 0 mm and 0. 727 kg 0 mm cone set-ups in order to confirm the above analysis. The kaolin material used in performing these tests was sourced from a different batch and was found to have slightly different index values, as investigated by Boyd and Sivakumar (11), including a slightly higher PL than the kaolin material used in the earlier studies reported in Table 2. The agreement between the PLs determined using the 6.948 kg 0 mm and 0. 727 kg 0 mm set-ups was extremely good (Figures 11(b) and 11(c)). The percentage difference in PLs determined for the 8 kg and 6. 948 kg cones was 4. 0% (in absolute terms 1. 3% water content). Based on the critical state framework (considering the necessary constitutive parameters for kaolin) and water content values at the PLs determined using the 8 kg and 6.948 kg cones, the undrained strength ratio can be calculated as 1.17, which agrees favourably with the cone mass ratio of 1.15 (i.e. ¼ 8/6. 948). It must be restated that the new PL method (0. 727 kg 8 cone with a clear free fall of 0 mm) is essentially strength based. Any argument is not scientifically justified to corroborate PL measurements determined using the new method with those obtained using the classical Casagrande approach. However, based on the observational point of view, the measurements obtained using both methods were found to be in reasonably close agreement, at least for the ten mineral clays of intermediate to very high plasticity examined in the present investigation. The new method was developed on the basis of an undrained strength ratio (c u(pl) /c u(ll) ) of 0, typically reported for many low- and intermediate-plasticity fine-grained soils (Sharma and Bora, 03; Stone and Phan, 1995; Wood, 1990; Wroth and Wood, 1978). However, by considering strain rate effects in the predicted 62

32 32 34 36 38 (a) 32 34 36 38 (b) 32 34 36 38 (c) Figure 11. Penetration depth plotted against water content relationships for (a) 8, (b) 6.948 and (c) 0.727 kg cone set-ups fall-cone strengths, we later postulated that the strength ratio for the quasi-static condition appeared to be approximately 87. Some limited evidence has been presented to support this claim, although further investigation is required to draw any firm conclusion. In essence, therefore, the plastic limit values obtained using the new 0.727 kg 0 mm fall cone set-up reported herein should be referred to as PL (0), which may be a preferred option as the strength ratio of 0 is more generally accepted within the geotechnical community. 6. Conclusion A new fall cone PL device has been developed using an energybased criterion, with the required energy achieved by allowing a 0.727 kg 8 cone to free fall through 0 mm before penetrating into the soil specimen by mm, thereby defining the plastic strength limit. An 8 kg contacting cone, recommended by other researchers for the determination of the PL (0), was also investigated. For all ten mineral clays of intermediate to very high plasticity tested, the 0. 727 kg 0 mm cone set-up produced PLs in good agreement with the measured Casagrande PLs. The 8 kg fall cone consistently underestimated the Casagrande PLs and limited experimental data indicated that a lighter cone of 6.948 kg mass would produce better overall agreement. Acknowledgement The authors also would like to thank Mr Vimalan Jeganathan (V J Tech Ltd, Reading, UK) and K V Senthilkumaran (P J Careys Contractors, UK) for their unconditional financial support for geotechnical research at Queen s University Belfast. REFERENCES ASTM (05) D43-05: Standard test methods for liquid limit, plastic limit, and plasticity index of soils. ASTM International, West Conshohocken, PA, USA. Boyd J and Sivakumar V (11) Experimental observation of stress regime in compacted fills when laterally confined. Géotechnique 61(4): 345 363. BSI (1990) BS 1377-2: Methods of test for soils for civil engineering purposes Part 2: Classification tests. BSI, London, UK. Feng TW (00) Fall cone penetration and water content relationship of clays. Géotechnique 50(2): 1 7. Haigh SK, Vardanega PJ and Bolton MD (13) The plastic limit of clays. Géotechnique 63(6): 435 440. Hansbo S (1957) A new approach to the determination of the shear strength of clay by the fall-cone test. Proceedings of the Royal Swedish Geotechnical Institute : 7 48. Harrison JA (1988) Using BS cone penetrometer for the determination of plastic limit of soils. Géotechnique 38(3): 433 438. Kodikara JK, Seneviratne HN and Wijekulasuriya CV (06) Discussion on using a small ring and fall-cone to determine the plastic limit. Geotechnical and Geoenvironmental Engineering 132(2): 276 278. 63

Koumoto T and Houlsby GT (01) Theory and practice of the fall cone test. Géotechnique 51(8): 701 7. Koumoto T, Kondo F and Houlsby GT (07) Applicability of the fall cone method to determine the plastic limit of clays. Proceedings of Plasticity 07, Ancorage, AK, USA, pp. 46 48. Kulhawy FH and Mayne PW (1990) Manual on Estimating Soil Properties for Foundation Design. Electric Power Research Institute, Palo Alto, CA, USA, Report No. EL-6800. Ladd CC and Foott R (1974) A new design procedure for stability of soft clays. Journal of Geotechnical Engineering Division, ASCE 0(7): 763 786. Mesri G and Peck RB (11) Discussion on a new method of measuring plastic limit of fine materials. Géotechnique 61(1): 88 92. O Kelly BC (13) Atterberg limits and remolded shear strength water content relationships. ASTM Geotechnical Testing Journal 36(6): 939 947. O Kelly BC () Closure to discussion by K Prakash and A Sridharan on Atterberg limits and remolded shear strength water content relationships. Geotechnical Testing Journal 37(4): 729 731. Sharma B and Bora PK (03) Plastic limit, liquid limit and undrained shear strength of soil reappraisal. Geotechnical and Geoenvironmental Engineering 9(8): 774 777. Sherwood PT (1970) The Reproducibility of the Results of Soil Classification and Compaction Tests. Road Research Laboratory, Crowthorne, UK, Report LR 339. Sivakumar V, Glynn D, Cairns P and Black JA (09) A new method of measuring plastic limit of fine materials. Géotechnique 59(): 813 823. Sivakumar V, Glynn D, Cairns P and Black JA (11) Discussion on a new method of measuring plastic limit of fine materials. Géotechnique 61(1): 88 92. Stone KJL and Phan CD (1995) Cone penetration tests near the plastic limit. Géotechnique 45(1): 155 158. Wood DM (1990) Soil Behaviour and Critical State Soil Mechanics. Cambridge University Press, Cambridge, UK. Wroth CP and Wood DM (1978) The correlation of index properties with some basic engineering properties of soils. Canadian Geotechnical Journal 15(2): 137 5. WHAT DO YOU THINK? To discuss this paper, please email up to 500 words to the editor at journals@ice.org.uk. Your contribution will be forwarded to the author(s) for a reply and, if considered appropriate by the editorial panel, will be published as a discussion in a future issue of the journal. Proceedings journals rely entirely on contributions sent in by civil engineering professionals, academics and students. Papers should be 00 5000 words long (briefing papers should be 00 00 words long), with adequate illustrations and references. You can submit your paper online via www.icevirtuallibrary.com/content/journals, where you will also find detailed author guidelines. 64