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# Craig's Soil Mechanics 7th Edition

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skeleton. The values of k for different types of soil are typically within the ranges shown in Table 2.1. For sands, Hazen showed that the approximate value of k is given by k ¼ 10�2D210 ðm=sÞ ð2:3Þ where D10 is the effective size in mm. On the microscopic scale the water seeping through a soil follows a very tortuous path between the solid particles but macroscopically the flow path (in one dimension) can be considered as a smooth line. The average velocity at which the water flows through the soil pores is obtained by dividing the volume of water flowing per unit Permeability 31 time by the average area of voids (Av) on a cross-section normal to the macroscopic direction of flow: this velocity is called the seepage velocity (v0). Thus v0 ¼ q Av The porosity of a soil is defined in terms of volume: n ¼ Vv V However, on average, the porosity can also be expressed as n ¼ Av A Hence v0 ¼ q nA ¼ v n or v0 ¼ ki n ð2:4Þ Determination of coefficient of permeability Laboratory methods The coefficient of permeability for coarse soils can be determined by means of the constant-head permeability test (Figure 2.1(a)). The soil specimen, at the appropriate density, is contained in a Perspex cylinder of cross-sectional area A: the specimen rests on a coarse filter or a wire mesh. A steady vertical flow of water, under a constant total head, is maintained through the soil and the volume of water flowing per unit time (q) Table 2.1 Coefficient of permeability (m/s) (BS 8004: 1986) Clean gravels Clean sands and sand – gravel mixtures Very fine sands, silts and clay-silt laminate Unfissured clays and clay-silts (>20% clay) 1 10–1 10–2 10–3 10–4 10–5 10–6 10–7 10–8 10–9 10–10 Desiccated and fissured clays 32 Seepage is measured. Tappings from the side of the cylinder enable the hydraulic gradient (h/l ) to be measured. Then from Darcy’s law: k ¼ ql Ah A series of tests should be run, each at a different rate of flow. Prior to running the test a vacuum is applied to the specimen to ensure that the degree of saturation under flow will be close to 100%. If a high degree of saturation is to be maintained the water used in the test should be de-aired. For fine soils the falling-head test (Figure 2.1(b)) should be used. In the case of fine soils, undisturbed specimens are normally tested and the containing cylinder in the test may be the sampling tube itself. The length of the specimen is l and the cross-sectional area A. A coarse filter is placed at each end of the specimen and a standpipe of internal area a is connected to the top of the cylinder. The water drains into a reservoir of constant level. The standpipe is filled with water and a measurement is made of the time (t1) for the water level (relative to the water level in the reservoir) to fall from h0 to h1. At any intermediate time t the water level in the standpipe is given by h and its rate of change by �dh/dt. At time t the Figure 2.1 Laboratory permeability tests: (a) constant head and (b) falling head. Permeability 33 difference in total head between the top and bottom of the specimen is h. Then, applying Darcy’s law: �a dh dt ¼ Ak h l ; � a Z h1 h0 dh h ¼ Ak l Z t1 0 dt ; k ¼ al At1 ln h0 h1 ¼ 2:3 al At1 log h0 h1 Again, precautions must be taken to ensure that the degree of saturation remains close to 100%. A series of tests should be run using different values of h0 and h1 and/or standpipes of different diameters. The coefficient of permeability of fine soils can also be determined indirectly from the results of consolidation tests (see Chapter 7). The reliability of laboratory methods depends on the extent to which the test specimens are representative of the soil mass as a whole. More reliable results can generally be obtained by the in-situ methods described below. Well pumping test This method is most suitable for use in homogeneous coarse soil strata. The procedure involves continuous pumping at a constant rate from a well, normally at least 300mm in diameter, which penetrates to the bottom of the stratum under test. A screen or filter is placed in the bottom of the well to prevent ingress of soil particles. Perforated casing is normally required to support the sides of the well. Steady seepage is established, radially towards the well, resulting in the water table being drawn down to form a ‘cone of depression’. Water levels are observed in a number of boreholes spaced on radial lines at various distances from the well. An unconfined stratum of uniform thickness with a (relatively) impermeable lower boundary is shown in Figure 2.2(a), the water table being below the upper surface of the stratum.A confined layer between two impermeable strata is shown inFigure 2.2(b), the originalwater tablebeingwithin theoverlying stratum.Frequent recordings are made of the water levels in the boreholes, usually by means of an electrical dipper. The test enables the average coefficient of permeability of the soil mass below the cone of depression to be determined. Full details of the test procedure are given in BS 6316. Analysis is based on the assumption that the hydraulic gradient at any distance r from the centre of the well is constant with depth and is equal to the slope of the water table, i.e. ir ¼ dh dr where h is the height of the water table at radius r. This is known as the Dupuit assumption and is reasonably accurate except at points close to the well. In the case of an unconfined stratum (Figure 2.2(a)), consider two boreholes located on a radial line at distances r1 and r2 from the centre of the well, the respective water 34 Seepage levels relative to the bottom of the stratum being h1 and h2. At distance r from the well the area through which seepage takes place is 2 rh, where r and h are variables. Then applying Darcy’s law: q ¼ 2 rhk dh dr ; q Z r2 r1 dr r ¼ 2 k Z h2 h1 h dh ; q ln r2 r1 � � ¼ kðh22 � h21Þ ; k ¼ 2:3q logðr2=r1Þ ðh22 � h21Þ For a confined stratum of thickness H (Figure 2.2(b)) the area through which seepage takes place is 2 rH, where r is variable and H is constant. Then q ¼ 2 rHk dh dr ; q Z r2 r1 dr r ¼ 2 Hk Z h2 h1 dh r1 r2 r1 r2 q q Well Observation boreholes h1 h2 h2h1 H W.T. W.T. (a) (b) Figure 2.2 Well pumping tests: (a) unconfined stratum and (b) confined stratum. Permeability 35 ; q ln r2 r1 � � ¼ 2 Hkðh2 � h1Þ ; k ¼ 2:3q logðr2=r1Þ 2 Hðh2 � h1Þ Borehole tests The general principle is that water is either introduced into or pumped out of a borehole which terminates within the stratum in question, the procedures being referred to as inflow and outflow tests, respectively. A hydraulic gradient is thus established, causing seepage either into or out of the soil mass surrounding the bore- hole and the rate of flow is measured. In a constant-head test the water level is maintained throughout at a given level (Figure 2.3(a)). In a variable-head test the water level is allowed to fall or rise from its initial position and the time taken for the level to change between two values is recorded (Figure 2.3(b)). The tests indicate the permeability of the soil within a radius of only 1–2m from the centre of the borehole. Careful boring is essential to avoid disturbance in the soil structure. A problem in such tests is that clogging of the soil face at the bottom of the borehole tends to occur due to the deposition of sediment from the water. To alleviate the q hc h h1 h2 W.T. W.T. W.T. (a) (e) (d) (b) (c) Seepage B A i = hAB Figure 2.3 Borehole tests. 36 Seepage problem the borehole may be extended below the bottom of the casing, as shown in Figure 2.3(c),