Smith's Elements of Soil Mechanics. Ian Smith

76.5 – 68.7 = 7.8% and the percentage of clay (<0.002 mm) is 68.7%.

      1.5.5 Cohesive soils – liquid and plastic limit tests

      The results of the grading tests described above can only classify a soil with regard to its particle size distribution. They do not indicate whether the fine grained particles will exhibit the plasticity generally associated with fine grained soils. Hence, although a particle size analysis will completely define a gravel and a sand, it is necessary to carry out plasticity tests in order to fully classify a clay or a fine silt.

These tests were evolved by Atterberg (1911) and determine the various values of water content at which changes in a soil's strength characteristics occur. As an introduction to these tests, let us consider the volume of a soil as the amount of water within it is varied (Fig. 1.5).

      As the water is added to the dry clay, there is no immediate increase in volume. However, as the amount of water is gradually increased, the volume increases too. Also, as the water content changes, the soil behaves differently: when dry, the soil is brittle but when extremely wet, the soil is a liquid (referred to as a slurry). There is a stage in between the brittle and liquid states and the soil in this range of water contents behaves as a plastic material.

      The boundaries to the four states in which a soil may exist are defined:

       liquid limit, wL: the boundary between the liquid and the plastic state;

       plastic limit, wP: the boundary between the plastic and the semi‐solid state;

       shrinkage limit, wS: the boundary between the semi‐solid and the solid state.

      The limits are defined as the water contents of the soil at each boundary, as indicated in Fig. 1.5.

       Liquid limit (wL) and plastic limit (wP)

      The water content at which the soil stops acting as a liquid and starts acting as a plastic solid is known as the liquid limit (w_L). If the soil is dried from the liquid limit, it passes through the plastic state. When plastic, the soil can be moulded in the fingers akin to working with modelling clay. But as further water is driven from the soil, the soil no longer behaves as a plastic material and instead acts as a brittle solid. The limit at which plastic behaviour changes to brittle failure is known as the plastic limit (w_P).

Fig. 1.5 Changes in volume against water content.

       Plasticity index (IP)

      The plasticity index is the range of water content within which a soil is plastic; the finer the soil the greater its plasticity index.

      (1.5)

       Liquidity index

      The liquidity index enables a comparison to be made of a soil's plasticity with its natural water content (w).

      (1.6)

      If I_L = 1.0 the soil is at its liquid limit. If I_L = 0 the soil is at its plastic limit.

       Shrinkage limit (wS)

      If the drying process is prolonged after the plastic limit has been reached, the soil will continue to decrease in volume until a certain value of water content is reached. This value is known as the shrinkage limit and at values of water content below this level the soil is partially saturated. In other words, below the shrinkage limit the volume of the soil remains constant with further drying, but the weight of the soil decreases until the soil is fully dried.

       Determination of liquid and plastic limits

      The test procedures are given in BS EN ISO 17892‐12 (BSI, 2018).

       Liquid limit test

      BS EN ISO 17892‐12 specifies two methods for determining the liquid limit of soil.

      1 Fall cone method (preferred method)This is typically referred to as the cone penetrometer test. Details of the apparatus are shown in Fig. 1.6. The soil to be tested is air dried and thoroughly mixed. At least 200 g of the soil is sieved through a 425 μm sieve and placed on a glass plate. The soil is then mixed with distilled water into a paste.A metal cup, approximately 55 mm in diameter and 40 mm deep, is filled with the paste and the surface struck level. The cone, of mass 80 g, is next placed at the centre of the smoothed soil surface and level with it. The cone is released so that it penetrates into the soil and the amount of penetration, over a time period of five seconds, is measured.The test is now repeated by lifting the cone clear, cleaning it and filling up the depression in the surface of the soil by adding a little more of the wet soil.If the difference between the two measured penetrations is less than 0.5 mm then the tests are considered valid, else a third penetration test is done. The average penetration is noted, and a water content determination is carried out on the soil.The procedure is repeated at least four times with increasing water contents. The amount of water used throughout should be such that the penetrations obtained lie within a range of 15–25 mm.Fig. 1.6 Fall cone apparatus.To obtain the liquid limit, the variation of cone penetration is plotted against water content and the best straight line is drawn through the experimental points. The liquid limit is taken to be the water content corresponding to a cone penetration of 20 mm, expressed as a whole number.

      2 Casagrande apparatusAlthough still used worldwide, the Casagrande test has now been largely superseded by the fall cone method because the latter achieves more repeatable results. In the UK, the fall cone test is adopted as the first‐choice test method.

       Plastic limit test

      About 20 g of soil prepared as in the liquid limit test is used. The soil is mixed on the glass plate with just enough water to make it sufficiently plastic for rolling into a ball, which is then rolled out between the hand and the glass to form a thread. The soil is judged to be at its plastic limit when it just begins to crack at a thread diameter of 3 mm. At this stage, several pieces of the thread are taken for water content determination. The test is repeated until two water content tins contain an adequate mass of soil threads – approximately 10–15 g in each tin.

It is interesting to note that in some countries, the fall cone penetrometer is used to determine both w_L and w_P. The apparatus uses a 30° angle cone of mass 76 g. The procedure is the same as the fall cone described above, only this time w_L is taken at a penetration of 17 mm and w_P is taken as the water content at a penetration of 2 mm.

Example 1.4 Consistency