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).