1-1 1. BASIC SOIL AND ROCK CHARACTERISTICS 1.1. THE PHASE DIAGRAM Soils are normally composed of three constituents - solid soil particles, air and water. The air and water occupy the void spaces or pores between the solid particles. In the case of saturated soils the pore fluid is made up entirely of water. To facilitate calculations involving various amounts of the three constituents of a soil it is convenient to represent these constituents by means of a diagram, often known as a phase diagram , as illustrated in Fig.1.1. The symbols for the masses and volumes of the constituents are also shown on this figure. The mass of the air occupying the voids is ignored since it is negligible by comparison with the masses of water and solid. A number of definitions may now be given in terms of the symbols in Fig.1.1. M + M Bulk Density ρ = W S (1.1) VA + V W + V s (Sometimes referred to as total density ρt) Ms Dry Density ρd = (1.2) V A + V W + Vs MW Density of Water ρw = (1.3) VW 3 ρw is commonly taken as 1000 kg/m for convenience Volume of Voids Vv = V A + V W (1.4) V Void Ratio e = V (1.5) VS V e Porosity n = V = , (1.6) VV + V S 1 + e often expressed as a percentage. VW Degree of Saturation S or S r = . (1.7) VA + V W usually expressed as a percentage. 1-2 Volume Mass air VA water VW MW VS solid MS Fig.1.1 Phase diagram for a partly Saturated soil Volume Mass VW water MW VS solid MS Fig.1.2 Phase diagram for a Saturated soil Volume Mass air VA 3 VW water MW 0.025 m VS solid MS 45.0 kg Fig.1.3 1-3 Density of Solid Particles or Soil Particle Density Ms ρs = (1.8) Vs Specific Gravity of Solid Particles ρ G = s (1.9) ρw Water Content or Moisture Content M w = W , (1.10) MS usually expressed as a percentage. VA Air Voids Va = , (1.11) VA + V W + V S usually expressed as a percentage. With a saturated soil the volume of air becomes zero as illustrated in Fig.1.2. Referring to the figure a further definition can be given. MW + M S Saturated Density ρsat = (1.12) VW + V S Example A soil sample having a total volume of 0.025mm 3 and total mass of 45.0 kg. has been removed from the ground. If the water content and specific gravity of the soil are 20.0% and 2.68 respectively calculate: a) the dry density of the sample, b) the degree of saturation, c) the porosity. Referring to the phase diagram in Fig.1.3 the unknown terms M S, M W, V A, V W, VS can be calculated as follows: MW = w x M S = 0.20M S but MW + M S = 45.0 kg ∴ 1.20M S = 45.0 ∴ M S = 37.5 kg ∴ MW = 45.0 - 37.5 = 7.5 kg 1-4 The volumes can now be calculated MW 7.5 3 VW = = = .0075 m ρw 1000 MS 37.5 3 VS = = = 0.014 m Gρw 2.68 x 1000 3 ∴ VA = .025 - .014 - .0075 = .0035 m With these known quantitites the three items required can now be determined: MS a) dry density ρd = (1.2) VA + V W + V S 37.5 = 1500 kg/m 3 = .025 V b) degree of saturation S = W (1.7) VA + V W .0075 = 0.682 or 68.2% = .0035 + .0075 V + V c) porosity n = A W VA + V W + V S .0035 + .0075 = 0.440 or 44.0% = .025 1.2 IDENTIFICATION OF SOILS In addition to the techniques described in Geomechanics 2 for identification of the mineralogical components of soils, a number of relatively simple laboratory tests which are useful in identifying various soil types, has been developed. The presentation here will concentrate on grain size and plasticity characteristics, but reference should be made to books on soil testing for details of the testing procedures. (Bowles, 1970, Lambe, 1951, Kezdi, 1980). More sophisticated laboratory tests, which may be used for soil identification are used on occasions but these will not be discussed in this introductory presentation. 1.2.1 GRAIN SIZE DISTRIBUTION Soils are traditionally described by one or more of the names gravel, sand, silt or clay which indicate sizes of the soil particles. A number of slightly different 1-5 classification systems are in use relating size ranges to these four names but probably the most widely used is the M.I.T. system as follows: Gravel - grain size greater than 2mm Sand - 0.06 mm to 2 mm Silt - 0.002 mm to 0.06 mm Clay - grain size less than 0.002 mm Soils often consist of mixtures of these four ranges resulting in names such as silty sand, sandy clay, etc. The distribution of grain sizes in the gravel and sand ranges is found by sieving. A sample of dry soil is passed through a nest of sieves with the coarsest sieve at the top and the finest sieve at the bottom. The mass of soil retained on each sieve is measured as shown in the sample calculation in Table 1.1. From this information a histogram may be constructed as in Fig.1.4. Because of the large range of grain sizes encountered in soils a log scale is normally used. It has been found more convenient in soil engineering practice to integrate the histogram and to present the data as a cumulative distribution curve as illustrated by curve A in Fig.1.5. Table 1.1 Sieve Analysis of a Sand Soil _____________________________________________________________________ Sieve Mass Retained Percent Cumulative Percent Aperture gm Retained Percent Retained Finer _____________________________________________________________________ 2.36 mm 2.5 2.6 2.6 97.4 1.18 mm 9.3 9.8 12.4 87.6 600 µm 25.2 26.5 38.9 61.1 300 µm 28.7 30.2 69.1 30.9 150 µm 18.1 19.0 88.1 11.9 75 µm 6.4 6.7 94.8 5.2 Pan 5.0 5.2 100.0 95.2 100.0 For soil classification purposes two parameters which can be determined from the grain-size distribution curve are often quoted. These are: Effective Size which is the grain size corresponding to the 10 percent finer point on the curve. This can be referred to as D 10 . 1-6 Fig. 1.4 Histogram from a Sieve Analysis Fig. 1.5 Grain size distribution curves 1-7 Uniformity Coefficient (C u) which is a measure of the uniformity of grain size in the soil and is defined as the ratio of the 60% finer size (D 60 ) to D 10 . D60 that is Cu = (1.13) D10 For curve A in Fig.1.5 the uniformity coefficient is: 0.57 Cu = 0.14 = 4.1 which indicates a relatively uniform soil (sometimes referred to as poorly graded). A grain size distribution curve for a soil with a uniformity coefficient larger than that for soil A in Fig.1.5 is illustrated by curve B (well graded soil) in Fig.1.5. For the silty clay soil represented by curve C in Fig.1.5 it is not possible to determine the uniformity coefficient since the effective size is unknown. Coefficient of Cuvature (C c) is a value that can be used to identify a poorly graded soil. 2 (D30 ) Cc = (1.14) D10 .D60 A well graded soil has C c between 1 and 3 as long as C u is also greater than 4 for gravels and 6 for sands. The finer portions of the grain size curves B and C cannot be determined by sieving since a sieve with an aperture of about 75 µm is normally the finest sieve used in this type of test. For silt and clay size soils the grain size distributions are found by means of a sedimentation procedure in which a sample of the soil is allowed to settle in water. This procedure utilizes Stokes Law which relates the size of a sphere to its fall velocity in a fluid (usually water) by means of the expression: 18000 η v D2 = (1.15) g(Gs - G w) where D is the sphere diameter in mm η is the dynamic viscosity of water in N sec/m 2 v is the fall velocity of the sphere in cm/sec. g is the gravitational acceleration in cm/sec 2. Gs is the specific gravity of the sphere solid Gw is the specific gravity of the water. 1-8 The concentration of solids in the water at a particular time after the commencement of sedimentation is found by measuring the specific gravity of the suspension with an hydrometer. Alternatively the concentration may be found by taking a small volume of suspension from a particular depth by means of a pipette. The mass of solids is determined by drying off the water. During preparation of the suspension for a sedimentation (or hydrometer) test a deflocculating agent such as sodium hexametaphosphate or sodium silicate is customarily added to prevent the formation of soil flocs. Some clay soils behave in such a way that a variety of grain size distribution curves may be obtained depending upon the type and concentration of deflocculating agent that is used. Discussion of the recommended procedure for determining the grain size distribution of soils is given in the S.A.A.