Nigerian Journal of Technology, Vol. 24, No. 2, September 2005 Obasi and Anyaegbunam 1
CORRELATION OF THE UNDRAINED SHEAR STRENGTH AND PLASTICITY INDEX OF TROPICAL CLAYS
OBASI, N. L. Department of Civil Engineering, Enugu State University of Science and Technology Enugu, Nigeria
and ANYAEGBUNAM, A. J. Department of Civil Engineering, University of Nigeria, Nsukka.
ABSTRACT This paper attempts to establish a relationship between the undrained strength and plasticity index of tropical clays. Its theoretical basis lies with the previous works of Skempton and Northey [1] and Atkinson and Bransby [2]. The data obtained from independent laboratory tests on so some clay samples sourced from several actual project locations in Eastern Nigeria, were subjected to statistical least squares regression analysis after the samples had been grouped into CL, CI and CH using the Unified System of Soil Classification. The derived regression equations are shown to have high correlation coefficients thereby proving their viability. These equations can be used to estimate the undrained strength of clays encountered in Eastern Nigeria in lieu of the very expensive triaxial compression tests.
NOTATION Cu = Undrained Cohesion Cc = volumetric compression index CL = clay of low plasticity CI = clay of intermediate plasticity CH = clay of high plasticity e = void ratio Gmax = initial tangent shear modulus Gs = specific Gravity of soil particles Ko, = coefficient of lateral earth pressure at rest LI = Liquidity Index LL = liquid limit P = total mean stress (= ( + 23)/3 for axis-symmetric compression) Po = initial total mean stress or preconsolidation pressure (= 3 for isotropic compression) PI = plasticity index PL = plastic limit qu, = undrained shear strength Sr = degree of saturation U = pore pressure w = moisture content or natural moisture content (%) = total normal stress 1 = effective normal stress 1 = major principal stress 3 = cell pressure in the triaxial test (or minimum principal stress) Nigerian Journal of Technology, Vol. 24, No. 2, September 2005 Obasi and Anyaegbunam 2
1 vo = initial effective vertical stress (or effective overburden pressure) u = undrained angle of internal friction =Unit Weight (with subscript 'w' for water)
INTRODUCTION It should be noted that correlation Soil Mechanics arose to meet the need between soil properties and the Atterberg of a means of evaluating in a rational limits had been initiated more than an half manner such soil engineering problems as: a century ago and some of these will now the bearing capacity of a foundation; the be mentioned. stability of natural slopes, embankments Terzaghi and Peck [3] had tabulated a and excavations; the magnitude and the correlation between the unconfined time-rate of settlement of a footing; the compressive strength of clays and their quantity of seepage through an earth dam standard penetration resistances. But when or beneath a concrete dam or into an the exhorbitant cost of the standard excavation; the force on a retaining wall. penetration test is considered no advantage For each of the above purpose it is is gained therefrom. For a truly cohesive necessary for the soil engineer to furnish soil the undrained shera strength is half the himself with the necessary soil parameters unconfined compressive strength. which he must then employ in some There exists in the technical literature a empirical or analytical formulae in order to number of empirical correlations between 1 get the desired solution. The needed soil qu/ vo (the normalised undrained shear parameters, invariably, must be obtained strength) and the Atterberg indices for either through careful laboratory normally consolidated clays, namely: measurements or some other in-situ tests. Skempton and Henkel [1] presented a 1 The shear strength parameters viz., the curve for the variation of qu/ vo with cohesion and angle of internal friction are plasticity index which was later needed for the following purposes: the approximated by the linear equation. evaluation of the bearing capacity of a 푞 /휎 푣 = 0.11 + 0.37(푃퐼/100) (1) foundation; the assessment of the stability of a slope Bjerrum and Simons (1960) gave the Accurate measurement of shear following regression equations as fitting strength parameters, coefficient of their experimental data best. consolidation, and compressibility can be / difficult, time consuming and costly. As a 푞 /휎 푣 = 0.45(푃퐼/100) (2) result of this there is now a tendency in For PI > 50%; which had a deviation range countries all over the world towards (or scatter) of ± 25% Or building up correlation equations between the above soil properties and the so-called / 푞 /휎 푣 = 0.18(퐿퐼/100) (3) soil indices in order to speed-up the design process. This is most pertinent in third For LI > 50%; which had a deviation range world countries where up-to-date testing of±30% equipment are lacking together with the trained manpower needed to operate them. Karlson and Viberg (1967) obtained the For the plastic, clayey soils the Atterberg simple formula limits (which are indices of soil behaviour) 푞 /휎 푣 = 0.5(퐿퐿/100) (4) have been found useful for this application. This is because the For LL > 20%; with a deviation range of ± measurement of the Atterberg limits 30% requires very simple apparatuses and takes up comparatively short periods of time. Osterman [4] presented of graphical Nigerian Journal of Technology, Vol. 24, No. 2, September 2005 Obasi and Anyaegbunam 3 correlation – but no regression equation. engineer is the undrained shear strength of 1 between qu/ vo and PI for normally fine- grained soils. The shear strength of consolidated soils. His plot indicated that soils is required for the design of 1 qu/ vo varied along a concave downward foundations and retaining walls and for curve with PI for the soils he designed as calculating the stability of embankments, special clays but increased almost linearly cuttings and natural slopes. It is common with PI for marine clays. An inspection of in Geotechnical engineering practice to use his plot indicated a substantial deviation the undrained shear strength to evaluate (scatter) of the data points from the best-fit the stability of a slope, or the bearing lines. capacity of a foundation, in the short term From the above it is obvious that all the excess pore pressures, generated in the the listed researchers proposed a linear soil as a result of the surcharge loads, are still high and have not had the time to variation of qu with 휎 and by implication with depth in a stratum of normally dissipate. consolidated clay in accordance with field Skempton and Northey [1], and observations. The constant of Atkinson and Bransby [2] showed that the proportionality in their equations is a undrained shear strength and liquidity function of either PI, or LI or LL. They did index of remoulded saturated clays are not give any explanations for the relatively related. In particular, Atkinson and high scatter of their regression equations Bransby investigated the behaviour of four from the data points. These authors hereby different samples of clay soils and the suggest that it may have arisen because results of the tests on three of the samples they did not distinguish between CL, CI are listed below in Table 1. and CH clays in their analyses. A few of the correlation equations Table 1 developed for the other soil parameters Clay type LL (%) PL (%) PI (%) include: Terzaghi and peck [3] suggested Horten 30 16 14 that for virgin compression of normally London 73 25 48 consolidated soils shellhaven 97 32 65 For remolded soil By varying the moisture content of each 퐶 = 0.007 (퐿퐿 − 10%) (5) For undisturbed soil clay sample the liquidity index is made to 퐶 = 0.009(퐿퐿 − 10%) (6) vary and the undrained shear strength corresponding to the different values of Alpan [5] recommended that of normally liquidity index were measured with the consolidated clay. triaxial apparatus. The test results were K = 0.19 + 0.233 log(PI%) (7) presented graphically by plotting the More recently, Vucetic and Dobry [6] liquidity index against the logarithm of the have shown that the shapes of the curves undrained shear strength. It this G/Gmax (the modulus ratio) versus C (the worthwhile at this stage to point out that cyclic shear strain amplitude) and (the the upper limits of the water contents used equivalent damping ratio) for a soil are in these experiments were unrealistically primarily influenced by the plasticity high, being frequently in excess of 100%, index. They produced design curves which while in reality the in-situ saturated can be used for evaluating the dynamic moisture contents were usually in the response of a foundation soil under cyclic range of 28 to 35%. loading from such varied causes as The plots of Atkinson and Bransby machine vibration, earthquakes, pile [2] indicated that for a remoulded soil driving, explosions etc. sample log (qu) varies inversely as the Of particular interest to the soil liquidity index. That is Nigerian Journal of Technology, Vol. 24, No. 2, September 2005 Obasi and Anyaegbunam 4
effective stress has the value log q = a + (8) σ = σ − U (11)
which, to an extent, is not influenced by Where a and are constants are for a the actual moisture content. In an particular soil (which will not be the same undrained test the pore pressure, U will for another soil) increase as the deviator stress, increases But LI = (W = PL)/PI but for saturated specimens
=> log q = a + (9) ( ) Of the same soil U will be independent of the actual moisture contents. If now /(w-PL) is a assumed to be a Consequently, the undrained shear constant for a set of soils then strength of saturated soils can be expected to be independent of their actual moisture log 푞 푎 + 푏푃퐼 where b = /(w − PL) (10) contents (provided of -course that particle contacts still subsist). If the moisture and a and b are constants which will be content becomes so large as to prevent shown later to be functions of 3. particle contact then the undrained strength Subsequently if / (W-PL) could also be expected to vary with approximates a constant then, a plot of log moisture content. This leads to the concept qu versus plasticity index (P.I.) will be of an upper threshold value of water straight line in accordance with eqn. (6). content below which strength is moisture- Hence in this study a correlation was content independent. The lower threshold sought between the log of qu, and the P.I. value is somehow below the saturated in accordance with eqn. (6). moisture content. This proposition awaits The correlation of undrained shear further investigation. strength (qu) with plasticity index (PI) In partially saturated soils (with appears to be spurious as soon as it is moisture contents below the saturation realized that the PI is obtained from tests value), the effective stress is a variable on fully disturbed and remoulded soil. But quantity defined by Bishop et.al. [7] as the manner in which qu varies with PI can σ = σ − U + χ(U − U ) (12) be anticipated as follows: It is known that soils of high plasticity Where Uw = pore water pressure are composed of very small particles, Ua = pore air pressure which having relatively high surface area = the ratio of area of water cross- per unit weight, possess a large number of section to the total area of cross-section particles contact points. On the other hand, taken along the points of contact. soils of low plasticity, which have larger The quantity Ua _ Uw is a measure of particles, possess a fewer number of inter- soil suction and is related primarily to particle contact points. Under an externally the degree of saturation of the soil. applied load, it is not difficult to visualize For a saturated soil (Sr = 1), = 1 that for the soil with numerous contact For a completely dry soil (Sr =0), = 0 points the average inter-particle contact The behaviour of a partially stress will be relatively lower. As such, the saturated soil is quite complex. As the void shear stress that can be mobilized to resist ratio,e, of such a soil is reduced under sliding would also be lower. In that case a loading, the pore air becomes compressed soil with higher P.I. (numerous contact and its pressure increases (i.e. Ua points) will have a lower undrained shear increases). Also, increases as the degree strength than a soil with lower P.I. (fewer of saturation increases as can be seen from contact points). the relations
So-far-as a soil is saturated the 푆 = (13a)
Nigerian Journal of Technology, Vol. 24, No. 2, September 2005 Obasi and Anyaegbunam 5
χ = χ(S ) (13b) membrane to a confinement cell pressure (variable). since the moisture content remains Subsequently, a deviator stress is applied constant in an undrained test. through a proving ring at a constant rate of Depending on the relative strain until the soil sample fails in shear. magnitudes of Ua and the effective This test is performed on each sample at a stress can increase or decrease under minimum of three different initial cell increased loading in accordance with eqn pressures of 70, 140 and 210KN/m2. From (8). As can be seen from eqns. (9) is a the results so obtained a series of Mohr's function of the moisture content. As a circles of stress are drawn from which the consequence, the final value of effective shear strength parameters of each sample stress in a sample of partially saturated soil are obtained i.e. the cohesion and internal will depend on its moisture content friction angle. (through the factory). Since the shear For the determination of the Atterberg resistance of a particulate system caries limits the Casangrande device was used to with the effective stress it becomes obtain the liquid limits of the various obvious that a partially saturated soil will samples. The usual criterion was used to have an undrained shear strength which is obtain the plastic limits. These tests were dependent on its moisture content (or carried out on the samples in accordance initial degree of saturation). with B.S. 1377 (1975). Other tests carried out on the samples SAMPLING OF MATERIALS AND were the particle size distribution analyses LABOURATORY TEST METHODS and the determination of their natural The data used in this study were those moisture contents. obtained by Kabia Engineering Services The various samples were then Ltd. And Geoprobe Geological and classified into CL, CI and CH soils based Engineering Services Ltd. from the sites of on the following three soil characteristics: actual projects executed in several particles size distribution, liquid limit and localities in Eastern Nigeria. The samples plasticity index. Casangrande's plasticity used for the test were obtained by means chart containing the A- line plays a major of hollow cylindrical cutters attached to role in the classification. boring rods. These samples were then It is relevant at this point to list the trimmed to cylindrical shapes with height project sites from which the tested samples to diameter ratios of 2:1 and thereafter were obtained. They are as follows: tested for undrained shear strengths in the 1. Federal Mortgage Bank, Enugu triaxial test apparatus as per B.S. 1377 2. NNPC, Emene (1975). 3. PRODA, Staff Housing Complex, Emene In each case the test sample was 4. Secretariat Complex, Owerri. enclosed in a rubber membrane with 5. Federal School of Arts and Science, Aba impervious plates at both ends and placed in the Perspex cell of the triaxial 6. Eziorsu - Oguta Road apparatus. The cell was then sealed up and 7. Eziorsu Bridge water pumped in to fill the cell and thereby 8. Eastern Highway By-Pass, Port- Harcourt subject the samples in the rubber
Nigerian Journal of Technology, Vol. 24, No. 2, September 2005 Obasi and Anyaegbunam 6
EXPERIMENTAL RESULTS AND ANALYSIS Table 2 (CL soils): shear strength parameters Cu and u Site location Bore Hole Depth s C (KN/m ) u Number (meters) u (degrees) 1 Secretariat Complex, Owerri 2 3.00 28 25 2 Eastern Highway By-pass, 1 7.00 33 24 Port Harcourt 3 Eziorsu Bridge Site 1 4.50 75 15 4 Federal School of Arts and 1 3.00 40 18 Science, Aba
Table 3: (CI soils): shear strength parameters Cu and u S/no Site location Bore Hole Depth s C (KN/m ) u Number (meters) u (degrees) 5 Eziorsu - Oguta Road 3 4.50 78 10 6 Secretariat Complex Owerri 3 3.50 65 11 7 Federal Mortgage Bank, Enugu 2 3.00 60 12 8 Eziorsu Bridge 3 3.00 45 13 9 NNPC, Emene 29 4.50 50 11 10 PRODA Staff Housing, Emene 3 1.50 45 12 11 PRODA Staff Housing, Emene 5 1.50 46 11 Table 4: (CH soils): shear strength parameters Cu and u
S/NO Site location Bore Hole Depth Cu u s Number (meters) (KN/m ) (degrees) 12 NNPC, Emene 27 4.50 25 10 13 PRODA Staff Housing, Emene 3 4.50 26 9 14 NNPC, Emene 32 4.50 34 7 15 PRODA Staff Housing, Emene 5 6.00 24 8.5 16 PRODA Staff Housing, Emene 6 3.00 18 8
/ The test results, obtained by the 휎 휎 푁휙 + 2퐶 (푁휙) (15) aforementioned soil testing companies, are reproduced above in Tables 2 to 4. The Where N, called the flow factor, is given natural moisture contents and Atterberg by ( ) limits have been omitted in these tables to 푁휙 = tan (45 + 휙 /2) (16) avoid duplication of Tables 5 to 7 where ( ) they have been included. It should be noted that some authors Evaluation of Undrained Shear Strength propose that qu be calculated from The undrained shear strength, qu is 푞 = 1(휎 − 휎 ) calculated from 푞 = 1(휎 − 휎 ) cos 휙푢 (14) but these authors have preferred the formula given in eqn. (14) because, in the The minimum principal stress, 3 is known first instance it accords with theory and and corresponds to the triaxial cell secondly it gives a conservation value. confinement pressure. The major principal In Tables 5 to 7 are presented the stress,1, is calculated from the well relevant data which were used for the known Bell's formula viz: regression analysis. The undrained shear Nigerian Journal of Technology, Vol. 24, No. 2, September 2005 Obasi and Anyaegbunam 7 strengths were evaluated for cell pressures 210KN/ m2 and these are seen to be 2 of 3 = 70, 140 and 210 KN/m . In Fig. 1 matched by the straight line - regression the experimental data have been presented equations within the limits of experimental as log qu versus PI plots for the case of 3 error.
Table 5: (CL Soils): Atterberg Limits and undrained shear strengths. 2 qu (KN/m ) S/NO W LL PL PI W-PL 3 3=140 3 (%) (%) (%) (%) (%) =70KN/m2 KN/m2 =(KN/m2) 1 15.2 31.0 21.0 10.0 -5.8 86.3 132.7 179.1 2 16.9 31.0 17.0 14.0 -0.1 90.3 134.1 177.9 3 16.0 34.0 17.0 17.0 -1.0 118.0 141.6 165.2 4 10.7 34.0 14.4 -19.6 -3.7 82.1 111.9 141.6
Table 6: (CL Soils): Atterberg Limits and undrained shear strengths. 2 Qu (KN/m ) S/NO W LL PL PI W-PL (%) 3=70 3=140 3 =201 (%) (%) (%) (%) KN/m2 KN/m2 (KN/m2) 5 16.7 38.0 22.0 16.0 +0.7 106.0 120.5 135.0 6 13.0 37.0 19.6 17.4 -6.6 93.6 109.8 126.0 7 20.0 44.0 25.5 18.5 -5.5 90.4 108.4 126.4 8 11.9 41.0 22.0 19.0 -10.1 74.9 94.7 114.4 9 19.7 48.0 28.0 20.0 -83 75.8 92.0 108.2 10 22.0 45.0 23.0 22.0 -1.0 72.3 90.3 108.3 11 20.7 45.0 21.0 24.0 -0.3 71.0 87.2 103.4
Table 7: (CL Soils): Atterberg Limits and undrained shaer strengths 2 qu (KN/m ) S/NO W LL (%) PL (%) PI (%) W-PL 3=70 3=140 3 201 (%) (%) KN/m2 KN/m2 (KN/m2) 12 17.8 50.0 27.0 23.0 -9.2 43.8 58.3 72.8 13 26.5 55.0 28.0 27.0 -1.5 42.9 55.7 68.5 14 29.0 62.0 33.0 29.0 -4.0 47.8 57.5 67.1 15 24.7 58.0 25.0 33.0 -0.3 39.6 51.6 63.6 16 26.4 64.0 30.0 34.0 -3.6 31.7 42.9 54.1
The least squares analyses of the data With a correlation coefficient of - 88.2% in Tables 5 to 7 yielded the following For the CH group: regression equations: log q = 1.911 − 1.028 (PI/100) (19) For σ = 70KN/m With a correlation coefficient of -68.3% For the CL group: For σ = 140KN/m log q = 1.930 + 0.263 (PI/100) (17) For the CL group: With a correlation coefficient of + 15.4% log 푞 = 2.196 − 0553 (푃퐼/100) (20) For the CI group: With a correlation coefficient of -51.6% log 푞 = 2.342 − 2.175(푃퐼/100) (18) Nigerian Journal of Technology, Vol. 24, No. 2, September 2005 Obasi and Anyaegbunam 8
For the CL group: With a correlation coefficient of -87.8% log q = 2.345 − 1.767 (PI/100) (21) For the CI group: log 푞 = 2.356 − 1.472(PI/100) (24) With a correlation coefficient of-91.0% For σ = 140KN/m With a correlation coefficient of -92.5%
For the CL group: For the CH group: log q = 2.011 − 0.986(PI/100) (22) log q = 2.093 − 0.961(PI/100) (25)
With a correlation coefficient of-81.2% With a correlation coefficient of-88.4% For σ = 210KN/m
For the CL group: log 푞 = 2.371 − 1.008(PI/100) (23)
The coefficients of the above correlation log 푞 = 1.725 + 0.315 + (0.834 − equations (17) to (25) can be seen to vary 0.906 ) (27) with the confinement pressure 3. Consequently the constants 'a' and 'b' in which has a correlation coefficient of - eqn. (10) are functions of 3. On the basis 92.7%, a mean standard % deviation of ± of a linear variation of a and b with 3 a more general regression equation was 9.5% and maximum % deviations of -19.3 assumed to hold, namely: to 17.5%. For the CI soil group 푎2 휎3 푃퐼 푎1 log 푞 = 2.334 + 0. 0.0094 + log 푞 = + (푏
+ ) (2.508 − 0.504 ) (28) 푏
(26) On analysis the data in Tables 5 to 7 via which has a correlation coefficient of - the least square method the more useful 96.0%, a mean standard % deviation of ± and general regression equations below 5.3% and maximum % deviations of -6.6 were obtained: to 13.9%. For the CL soil group For the CH soil group
log 푞 = 1.821 + 0.131 σ + (1.054 −
0.0457 ) (29)
Nigerian Journal of Technology, Vol. 24, No. 2, September 2005 Obasi and Anyaegbunam 9
2 which has a correlation coefficient of - of 3 =210KN/m there is a greater 94.0%, a mean standard % deviation of ± likelihood for most of the samples to be 7.7% and maximum % deviations of -13.6 saturated at failure than at the lower cell 2 to 16.1 %. pressure of 3 =70K N / m . As postulated Also, an analysis of the data in earlier samples which are saturated at Tables 5 to 7 shows that (w-PL) varied failure should have undrained strengths from +0.7 to - 10.1 % and as such is far that are independent of their moisture constant. The mean value of (w-PL) = contents while those which are not will 3.77%. The standard deviation = 3.50%. behave contrariwise. This partially On the basis of a normal distribution for explains the higher correlation of the loq 2 (w-PL) the 90% confidence interval for qu versus PI plots for 3 =210KN / m than (w-PL) is -3.77 ±-1.645*3.50 [i e. -9.53 % 2 for 3=70KN/m . (w-PL) + 1.99%]. The behaviour of the CL soils at 3 =70KN/ m2 may be attributable to two DISCUSSION OF RESULTS more reasons. First, they are frictional- An examination of the initially derived cohesive soils, that is granular material regression equations (17) to (25) reveals with plastic properties, as an examination the following facts: The three regression of Table 2 will reveal that they have higher equations for the CI group have very high u which range from 15 to 25°. Secondly, correlation coefficients in excess of -88%. as explained above, because of their low Those for the CH group also have very water contents, they are very unlikely to be high correlation coefficients except for 3 saturated at the failure in which case their =70KN/m2 which is medium/high at - 68.4 qu, would also depend on their water %. The CL group displays the least level of contents. The partial saturation of the correlation except for the equation for 3 granular CL soils can actually make them 2 2 =210KN/m . In fact for 3 =70KN/m the to have a higher than expected qu Thssis is CL group exhibits an unusually small and because negative pore pressures may be positive correlation of +15.4%. Also all generated which according to eqn. (11) three soil groups exhibit a high correlation will result in increased effective stress and 2 at 3 =210KN/ m . To further mystify the increased undrained strength. whole situation the general regression From the plots of Fig. 1, which are for 2 equations (27) to (29) all have excellent 3 =210KN/m , it is shown that the correlation coefficients. behaviours of the different classes of soils The above observations are not easy to viz. CL, CI and CH are different. It is seen explain but it appears that one of the that for all classes of soils the undrained reasons for the excel1ent correlation of the shear strength decreases with increasing CI group was the greater number of value of plasticity index. Also, in general, samples in that group: 7 of them versus 4 for the range of plasticity index increases for the CL and 5 for the CH. This same in the following order CH, CI, and CL. reason appears responsible for the That is at any value of plasticity index, the improved correlation of the general CI. soil class possesses a higher undrained equations in that the data used for their shear strength than the CI soil which in evolution are thrice those used previously. turn attains a higher undrained shear Another reason is the saturation or non- strength than the CH soil class. This result saturation of the samples at failure. was earlier anticipated. Also a curious Unfortunately, due to lack of data, the thing can be observed: the slope of the degrees of saturation cannot be reliably regression line for the CI soil class is quantified. Estimates only are made in greater than the slopes of the regressions Appendix 1. In Appendix 1 it is lines for the CL and CH soil classes which demonstrated that at a higher cell pressure are approximately equal. This indicates Nigerian Journal of Technology, Vol. 24, No. 2, September 2005 Obasi and Anyaegbunam 10 that the CI soils undergo greate: decrease conservatively estimated using eqn (7). in strength with increasing plasticity index However, as had been pointed out above than they do the CI, and CH soils. No the soils that were investigated were at reasons can be readily put forth to explain water contents that were mainly below this observation. their plastic limits. Therefore the authors A question that arises is, "were the clay recommend that the derived equations be used samples considered normally consolidated with confidence only when the natural or overconsolidated In the absence of a moisture content of a soil sample is equal volume versus log(P) diagram such a to or not more than 8% below the plastic question would be difficult to answer. An limit. Should this condition not be met, overconsolidated sample has a volume- log then any evaluation of the undrained shear (p) diagram which consists of strength from the plasticity index using the approximately two straight lines with above regression equations must be different slopes while a normally regarded as only an approximate guide. consolidated sample has a single straight Ultimately, recourse must be made to the line diagram. triaxial apparatus for the determination of the As suggested above and also proved in true undrained strength of a soil. Appendix 1 a majority of the soil samples Notwithstanding the deficiencies of this would be saturated at the failure state even study the authors believe that the formulae though they might have been unsaturated that have been presented would be found at the beginning of the tests (especially at to be very useful for preliminary estimates 2 of undrained shear strength of the tropical 3 =210KN/m ). Since pore water is prevented from escaping in an undrained clays of Eastern Nigeria. Of course, it test, this will result in increasing degree of should be recognized that any correlation saturation as the sample is compressed between a particular soil property and the under increasing pressure, until at 100% Atterberg limits can only be approximate. saturated the sample can no more undergo To improve the reliability of the volume change, and is thereby described to correlation equations, research is being carried out on the incorporation of more variables be in a critical state. which may significantly influence the undrained shear strength of saturated tropical CONCLUSION AND clays namely; initial void ratio, RECOMMENDATIONS overconsolidation ratio and crystalline In this paper the relationship between structure. the undrained shear strength and the plasticity index of saturated tropicals clays Appendix 1: Minimum Water Content of Eastern Nigeria has been investigated. It For Sample To Become Saturated At has been shown that the logarithm of the Failure. undrained shear strength is related to the A contention of this paper is that if a plasticity index via the regression soil sample is nearly saturated or saturated equations (27) to (29) for the three classes then the undrained shear strength may be of soil considered with correlation expected to be independent of the actual coefficients of - 92.7%, -96.0% and - water contents. This is because, though the 94.0% for the CL, CI and CH soils stress path used to approach failure may be respectively. These high values of complex, once the sample becomes correlation coefficient strongly confirm the saturated the failure pattern is likely to be suggested relationships. For the evaluation independent of the initial approach path. of the strength of a soil in-situ it is Proof is hereby given that most of the soil suggested that po=vo (l + 2Ko)/3 be samples in this paper could have achieved 2 substituted for 3 in eqns.(27) to (29) as is saturated at failure when 3 =210KN/ m usual in Soil Mechanics. Ko could be thereby explaining the high correlation Nigerian Journal of Technology, Vol. 24, No. 2, September 2005 Obasi and Anyaegbunam 11 coefficients of eqns. (23) to (25). Note respectively. again that in the standard triaxial test a3 is Based on the above, since the kept constant while 1 is increased. Also in actual moisture content was 20%, the the undrained test the moisture content simple reconsolidated at a3 = 210KN/m2 remains constant while the degree of would have become saturated at failure saturation varies. while that at 3 =70KN/m2 would still The subscript '0' shall designate the remain partially saturated at failure: This initial state while 'f’ will represent the analysis is of course only approximate final/ failure state. It can be derived that since the actual Cc and y are not available. the minimum water content. Wmin, for a partially saturated sample to become REFERENCES saturated at failure is Skempton , A. W. and Nor they, R.D. The ( ) sensitivity of days, Geotechnique, Vol,3, 푊 = (30) 1952 PI' 30 - 53 ( ) where Atkinson, J. H. and Bransby, P.I. The Mechanics, 푒 − 푒 ≅ 퐶 log(푃푓/휎 ) (31) of soils: An Introduction to critical state soil Mechanics, M,c Craw _ HILL BOOK Company LtD., London. 1978. 푃푓 = (휎 + 2휎 )/3 = 휎 + (32) Terzaghi, and peck, R. R Soil Mechanics in 2푞 /(3 cos 휙 Cc is given by equ. (6) namely Engineering practice, 1st ed., John Wiley 퐶 ≅ 0.009(퐿퐿 − 10%) and Sons, New York, 1948.
Osterman, J. Notes on the shearing Resistance of Also, o = the unit weight at void ration of Soft Clays, Acta Polytechnica, eo and mean stress po = 3 In addition the following relationship will Skempton, A.W and Henkel, D.J. The post Glacial hold clays of the thames Estuary at Tilbury and Shell haven, Proc .3rd ICSMFF, Zurich, 푆 = 푤퐺푠/푒 (13a) Vol. 1,1953,302-308
푒 = 푒 = 푤퐺푠/100 (33) Alpan I. The Empirical Evaluation of the Coefficient Kor, and soil and foundation, ( ) 훾 = (34) Journal of Jap. Sec. Soil Mech. Found. ( ) Eng., Vol. VII (I), 1967, PP, 31.
푒 ≅ 푒표 − 퐶푐 log(푃/푃 ) (35) Atterberg, A Uber die PhySicalische Bodenuntersuchuug und uber die Where eo and e are the void ratios at mean plastizitat der tone, Internationale stress of p and p respectively. Mnteilungen fur Rodenkunde, Vol. 1,1911, Illustrative example: consider sample S/ PP. 2 – 7 No .7 for which LL = 44%, w = 20%, 2 2 Vucetic, M. and Dobry, R. Effect of soil plasticity =12°. At 3 =70KN/m qu, = 90. KN/m on Cyclic Response, J. Grotech. Eng. Div., 2 2 and at 3= 210KN/m qu, = 126.4KN/ m ASCEC, 117, Vol. 1, 1991, PI', 89-107. Eqn. (6) gives Cc =0.306. Let it be assumed that Gs = 2.7 and that = 20. Bishop, A.. W., Alpan, I. Et, Al Factors 3 2 Controlling the Strength of partially 5KN/m at =210KN /m . Then from eqn . Saturated soils, proc ASCE Research conf (34) eo =0. 5505. Using eqns. (35) and (34) On Shear Strength of Cohesive soils, 2 at 3 =70KN/m eo = 0.6965 and =18 Boulder, Col orado.I960, pP.503-532. .7KN/ m3 by using eqn. (30) it can be calculated that Wmin = 25.9% and 17.5% at 2 2 a3 =70KN/m and 210 KN/m respectively. The corresponding initial degrees of saturation are 89.3% and 91 .2%