CE 240 Soil Mechanics & Foundations Lecture 1.3. Soil Particles (Das, Ch. 2)

Transcription

1 CE 240 Soil Mechanics & Foundations Lecture 1.3 Soil Particles (Das, Ch. 2)

2 Outline of this Lecture 1.Engineering consideration of soil particles 2.Sieve test 3.Hydrometer test 4.Particle distribution 5.Shape of soil particles

3 Definitions for SOIL Engineering definitions: Civil Engineering: Soil is the earth material that can be disaggregated in water by gentle agitation. Construction: Soil is material that can be removed by conventional means without blasting. similar to the definition of regolith in geological terms. Agronomy definition: Soil consists of the thin layers of the earth s crust formed by surface weathering that are able to support plant life.

4 Soil particles The description of the grain size distribution of soil particles according to their texture (particle size, shape, and gradation). Major textural classes include: gravel (>2 mm); sand (0.1 2 mm); silt ( mm); clay (< 0.01 mm). Furthermore, gravel and sand can be roughly classified as coarse textured soils, wile silt and clay can be classified as fine textures soils.

5 For engineering purposes, soils can also be divided into cohesive and non-cohesive soils. Non-cohesive means the soil has no shear strength if no confinement. Cohesive soil contains clay minerals and posses plasticity. In engineering practice, plasticity is defined as the ability to be rolled into thin thread before breaking into pieces. Clay is cohesive and plastic. For example, mud sticking on shoes in a rainy day when one walk in a field. Sand is non-cohesive and non-plastic.

6 Procedure for grain size determination Sieving - used for particles > 75 µm Hydrometer test - used for smaller particles (φ < 75 µm) Analysis based on Stoke s Law, velocity proportional to diameter

7 A sieve test apparatus in a soil mechanics laboratory, (Das, Fig. 2.15)

8 Sieves and scale A set of soil test sieves

9 Sieve Test First of all, let s discuss the sieve that is the essential tool to study particle size distribution for the grain size greater than mm (75 microns). U.S. Standard Sieve Sizes sieve # Sieve opening (mm)

10 Sieve test procedure: 0, the total mass of the soil sample (ΣM) under sieve test; 1, determine the mass of soil retained on each sieve and the pan at last (i.e., M 1, M 2, M 3,. M n, and M p ). 2, the sum of soil mass retained on each sieve plus the mass in the pan should be equal to the total mass (ΣM= M 1 +M 2 +M M n +M p ). 3, determine the cumulative mass of soil retained above each sieve, for the ith sieve we have ΣM i = M 1 +M 2 +M M i. 4, the mass of soil passing the ith sieve is ΣM - ΣM i = ΣM (M 1 +M 2 +M M i ). 5, the percent of soil passing the ith sieve (percent finer) is F ΣM ΣM = i 100 ΣM

11 Example: If you have a soil sample with a weight of 150 g, after thorough sieving you get the following result. sieve# size(mm) W(g) % accum% 100-accum% The last column shows the percentage of material finer than that particular sieve size by weight.

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13 Gradation: Gradation is a measure of the distribution of a particular soil sample. Larger gradation means a wider particle size distribution. Well graded poorly sorted (e.g., glacial till) Poorly graded well sorted (e.g., beach sand) The range of grain size distribution is enormous for natural soils. E.g., boulder can be ~1 m in diameter, and the colloidal mineral can be as small as mm = 0.01 micron => It has a tremendous range of 8 orders of magnitude.

14 Fine-grained soil The hydrometer test uses Stokes equation (for the velocity of a free falling sphere in suspension) to determine grain size distribution smaller than #200 sieve. The grain size distributions of soils are commonly determined by sieve (smallest being #200) and hydrometer procedures. In the hydrometer analysis the soil smaller than #200 sieve is placed in suspension and by use of Stokes' equation for the velocity of a free falling sphere the equivalent particle size and percent of soil in suspension are computed. For soils with both fine and coarse grained materials a combined analysis is made using both the sieve and hydrometer procedures.

15 Procedure for grain size determination Hydrometer test - used for smaller particles Analysis based on Stoke s Law, velocity proportional to diameter Figure 1 Schematic diagram of hydrometer test

16 Procedure for grain size determination Hydrometer test - used for smaller particles Analysis based on Stoke s Law, velocity proportional to diameter Figure 1 Schematic diagram of hydrometer test

17 Stokes Law A sphere falling freely through a liquid of infinite extent will accelerate rapidly to a certain maximum velocity and will continue at that velocity as long as conditions remain the same. The relationship of the terminal velocity to the physical properties of the sphere and the liquid are expressed by Stokes' Equation as shown in the following page.

18 v = ρ s ρ w D 2 18 η where v: velocity of the particle settlement ρ s : density of soil particles ρ w : density of soil particles η: viscosity of water D: diameter of soil particles

19 From the Stokes equation, rearranging the factors we can get D 18η 18η = v = ρ ρ ρ ρ s w s w L t ρ = G ρ with s s w where G s is the specific gravity of the soil particle, We get D = 18η ( G 1) ρ s w L t

20 With the use of the SI units and choose g-sec/cm 2 for viscosity h, and 1 g/cm 3 for the density of water ρ w, and the length L in cm, and time t in minute, and D in mm, we can get Dmm ( ) 30 η L L( cm) = = K G 1 t t(min) s Since both viscosity and specific gravity of soil particles are temperature dependent, so does parameter K. Table 2.6 in the textbook gives the K value as the function of temperature.

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22 ASTM 152H Hydrometer and the definition of L (Das, Fig and Fig. 2.18)

23 V B 1 L= L + ( L ) A where L 1 : the length of the hydrometer stem; L 2 : the length of the hydrometer bulb; V b : the volume of the hydrometer bulb; D: cross-section area of the cylinder;

24 7, The test is actually used for diameters as large as 0.07 mm. Stokes' Law is applicable to spheres varying from 0.02 mm to mm in diameter. As applied to soil particles falling through water, inaccuracies for using the Stokes equation to determine the particle size occur due to the following factors: 1, Soil particles are not spheres; 2, The fluid is not of infinite extent; 3, The specific gravity of individual particles may vary; 4, Turbulence caused by larger particles falling; 5, Brownian movement of smaller particles; 6, Disturbance due to insertion and removal of the hydrometer;

25 Scanning electron micrograph of soil composed of fine sand, silt and clay 100 µ m Sandstone

26 However, by proper sample and laboratory technique all except Item 1 (soil particles are not always spherical) in the 7 factors can be controlled or minimized so that the resulting inaccuracies can be ignored in normal testing. The shape of soil particles will vary from cubes to flakes with each of the shapes between these limits having different influence. Nevertheless, the results of the hydrometer analysis are valid if they are considered equivalent grain diameter rather than actual grain diameter.

27 Useful links for hydrometer test

28 The particle distribution curves for 3 soil samples (West, Fig. 7.1)

29 There are a number of ways to characterize the particle size distribution of a particular soil sample. D 10 : D 10 represents a grain diameter for which 10% of the sample will be finer than it. Using another word, 10% of the sample by weight is smaller than diameter D 10. It is also called the effective size and can be used to estimate the permeability. Hazen s approximation (an empirical relation between hydraulic conductivity with grain size) k (cm/sec) = 100D 10 D 10 Where D 10 is in centimeters. It is empirical because it is not consistent in dimension (cm/sec vs cm 2 ).

30 Uniformity coefficient C u : C u = D 60 /D 10 where D 60 is the diameter for which 60% of the sample is finer than D 60. The ratio of two characteristic sizes are the uniformity coefficient C u. Apparently, larger C u means the size distribution is wider and vice versa. C u = 1 means uniform, all grains are in the same size, such as the case of dune sands. On the other extreme is the glacial till, for which its C u can reach 30. from C u = D 60 /D 10, then D 60 = C u D 10

31 Coefficient of gradation Curvature C c Another shape parameter, as the second moment of grain size distribution curve, is called the coefficient of curvature, and defined as C c = (D 30 D 30 )/(D 10 D 60 ) A soil is thought to be well graded if the coefficient of curvature C c between 1 and 3, with C u greater than 4 for gravels and 6 for sands.

32 Sorting Coefficient S 0 Another parameter for measruing uniformity used mostly by geologists, and defined as S 0 = sqrt(d 75 /D 25 ) It is not frequently used by geotechnical engineers.

33 D10 D10 D10 D60 West, Figure 7.1 D60 D60

34 Preliminary Soil Classification There are six (6) classification systems, each one is designed for a particular field. 1) Wentworth Scale For Geology, not engineering geology; 3) USDA Scale Agriculture; 3) BPR Scale Road construction 4) ASTM Scale Ceramic industry; 5) AASHTO Scale Highway engineering; 6) USC Scale Civil Engineering, construction; We go through briefly of the first 3 systems and leave the last 2 to a more detailed discussion in 2 weeks.

35 (West, Figure 8.8)

36 Soil Classification (cont.) 1) Wentworth Scale For Geology, not engineering geology. Wentworth scale uses 2 as the base and mm as the primary unit. The subdivisions are based on a ratio of 2. φ-scale /8 ¼ ½ φ 2φ 1φ 0φ -1φ -2φ -3φ

37 (West, Figure 8.9)

38 Soil Classification (cont.) 2) USDA Scale USDA scale intentionally sets silt/clay boundary lower than the Wentworth scale (0.004 mm) and ASTM scale (0.005 mm), it is mm. The reason behind this classification is: Fine-sized quartz and feldspar grains may occur at mm, but definitely not smaller than mm. However, quartz and feldspar are not plastic at all. Inclusion of these quartz grains into clay complicates many problems. USDA intends to coincide clay size with clay minerals.

39 clay clay sand silt sand silt (West, Figures 8.10 and 8.11)

40 Reading Assignment: Das, Ch. 2 Homework: 2.3, 2.8, 2.9