Geotechnical Engineering

3.6 PARTICLE SIZE DISTRIBUTION (MECHANICAL ANALYSIS) This classification test determines the range of sizes of particles in the soil and the percentage of particles in each of these size ranges. This is also called ‘grain-size distribution’; ‘mechanical analysis’ means the separation of a soil into its different size fractions. The particle-size distribution is found in two stages: (i) Sieve analysis, for the coarse fraction. (ii) Sedimentation analysis or wet analysis, for the fine fraction. ‘Sieving’ is the most direct method for determining particle sizes, but there are practical lower limits to sieve openings that can be used for soils. This lower limit is approximately at the smallest size attributed to sand particles (75 or 0.075 mm). Sieving is a screening process in which coarser fractions of soil are separated by means of a series of graded mesh. Mechanical analysis is one of the oldest test methods for soils.

Where mr = mass of soil retained mr = cumulative mass retained on any sieve m = total soil mass r = sum of percentages retained on all coarser sieves

1. USDA (United States – Department of Agriculture) Particle size diameter

Sand

mm

Silt

2.0

Clay

0.05

0.002

2. ASTM D422 or D653 (American Society for Testing and Materials) Sand Cobble

Boulder

Gravel

Silt Coarse

300

75

4.75

Medium 2.0

Clay

Colloids

Fine 0.075

0.425

0.005

0.001

Fine

Fines (Silt, clay)

3. USCS (Unified Soil Classification System) Gravel

Sand

Cobble

Boulder

Coarse 300

Coarse

Fine 19

75

Figure 3.1 Different types of Particle-Size distribution Curves A particle-size distribution curve can be used to determine the following four parameters for a given soil: 1. Effective Size (D10): This parameter is the diameter in the particle-size distribution curve corresponding to 10% finer. The effective size is a good measure to estimate the hydraulic conductivity and drainage through soil. 2. Uniformity coefficient (Cu): This parameter is defined as

Medium 2.0

4.75

3.

0.075

0.425

4. AASHTO (American Association of State Highway and Transportation Officials) 4. Sand Boulder

Gravel

Silt Coarse

75

2.0

Clay

Colloids

Fine 0.425

0.005

0.075

Where D60 = diameter corresponding to 60% finer. Coefficient of gradation (Cc): This parameter is defined as

Where D30 = diameter corresponding to 30% finer. Sorting Coefficient (So): This parameter is another measure of uniformity and is generally encountered in geologic works expressed as

0.001

Comparison of 4 systems for describing soils based on particle size

√ Where

D75 = diameter corresponding to 75% finer D25 = diameter corresponding to 25% finer.

Additional parameter: 5. Average grain size (D50): This parameter is the diameter in the particle-size distribution curve corresponding to 50% finer.

3.6.1 SIEVE ANALYSIS US Standard Sieves Designation 2 in 1-1/2 in 3/4 in 3/8 in 4 8 10 14 16 18 20 30

Opening mm 50.80 38.10 19.00 9.51 4.75 2.36 2.00 1.40 1.18 1.00 0.85 0.60

Designation 35 40 50 60 70 80 100 120 170 200 270

Calculations needed: 99. Percentage retained on any sieve, r 2. Cumulative percentage retained on any sieve, R ∑ ∑ 3. Percentage finer than any sieve, F (

∑

)

Opening mm 0.50 0.425 0.355 0.250 0.212 0.180 0.150 0.125 0.090 0.075 0.052

EXAMPLE 3.3 A sieve analysis test was conducted on 650 grams of soil. The results are as follows. Mass of soil retained on each Sieve No. sieve (g) 3/8 in 0 4 53 10 76 20 73 40 142 100 85 200 120.5 Pan 99.8 Determine the following: a. The amount of coarse-grained and fine-grained soils. b. Amount of each soil type based on ASTM system. c. Particle size distribution (gradation) curve d. Effective size e. Average particle size f. Uniformity coefficient g. Coefficient of curvature h. Description of gradation curve i. Classification of soil using USDA chart, AASHTO-CS and USCS EXAMPLE 3.4 A sample of a dry, coarse-grained material of mass 500 grams was shaken through a nest of sieves, and the following results were obtained:

a. b. c.

Plot the particle size distribution (gradation) curve Determine (1) the effective size, (2) the average particle size, (3) the uniformity coefficient, and (4) the coefficient of curvature Determine the textural composition of the soil (i.e., the amount of gravel, sand, etc.).

, EXAMPLE 3.5 Classify the soil using AASHTO-CS and USCS.

3.7 CONSISTENCY OF CLAY SOILS ‘Consistency’ is that property of a material which is manifested by its resistance to flow. In this sense, consistency of a soil refers to the resistance offered by it against forces that tend to deform or rupture the soil aggregate; in other words, it represents the relative ease with which the soil may be deformed. Consistency may also be looked upon as the degree of firmness of a soil and is often directly related to strength. This is applicable specifically to clay soils and is generally related to the water content.

Figure 3.2 Variation of volume of soil mass with variation of water content

EXAMPLE 3.6 Classify the soil using AASHTO-CS and USCS.

CONSISTENCY LIMITS (Atterberg Limits) and INDECES a. Liquid Limit ‘Liquid limit’ (LL or wL) is defined as the arbitrary limit of water content at which the soil is just about to pass from the plastic state into the liquid state. At this limit, the soil possesses a small value of shear strength, losing its ability to flow as a liquid. In other words, the liquid limit is the minimum moisture content at which the soil tends to flow as a liquid. Laboratory Definition 1 (ASTM D 4318): Using Cup Device or the Casagrande Apparatus, the moisture content corresponding to 25 blows from the flow curve is taken as the liquid limit of the soil. From the figure, LL = 31.5%.

Figure 3.3 Flow Curve (x – No. of blows, y – moisture contents) Flow Index (FI) – slope of the flow curve

(

)

(

)

One-Point Method

Laboratory Definition 2: Using cone penetrometer (fall cone method) with two masses of cone (80 g and 240 g), PL can be determined by this equation:

Where Δw = separation in terms of moisture content between liquid state lines of two cones M1 = 80-g cone M2 = 240-g cone

50% < LL < 120%, N: from 20 to 30 blows or drops LL < 50%, N: from 15 to 35 blows or drops Where N = number of drops required to close the groove at the moisture content, wN x = 0.092 for soils with LL less than 50% x = 0.120 for soils with LL more than 50%

Laboratory Definition 3: By Feng, 2000

Where Laboratory Definition 2: Using Fall Cone penetrometer, the water content corresponding to a 80-g cone penetration of 20 mm defines the liquid limit.

m = slope (taken as positive) of the best-fit straight line. If you use a spreadsheet program, you can obtain C and m from a power trend line function that gives the best-fit equation

c. Shrinkage Limit ‘Shrinkage limit’ (SL or ws) is the arbitrary limit of water content at which the soil tends to pass from the semi-solid to the solid state. It is that water content at which a soil, regardless, of further drying, remains constant in volume. Laboratory Definition: SL can be calculated from this equation (

)

Where m1 = mass of wet soil m2 = mass of oven-dried soil V1 = volume of wet soil V2 = volume of oven-dried soil d. Plasticity Index ‘Plasticity index’ (PI or Ip) is the range of water content within which the soil exhibits plastic properties; that is, it is the difference between liquid and plastic limits. Flow Index (FI) – slope of the flow curve

(

)

Where w1, w2 = moisture contents at cone penetrations of d1 and d2, respectively b. Plastic Limit ‘Plastic limit’ (PL or wp) is the arbitrary limit of water content at which the soil tends to pass from the plastic state to the semi-solid state of consistency. Thus, this is the minimum water content at which the change in shape of the soil is accompanied by visible cracks, i.e., when worked upon, the soil crumbles. Laboratory Definition 1: By rolling on glass through bare hands, the moisture content at which the soil crumbles when rolled into threads of 3.2 mm (1/8 in) in diameter is taken as the plastic limit of the soil.

Most probable value of PL

∑

Table: Plasticity Characteristics e. Shrinkage Index ‘Shrinkage index’ (SI or Is) is defined as the difference between the plastic and shrinkage limits of a soil; in other words, it is the range of water content within which a soil is in a semisolid state of consistency.

f. Consistency Index ‘Consistency index’ or ‘Relative consistency’ (CI or Ic) is defined as the ratio of the difference between liquid limit and the natural water content to the plasticity index of a soil: Where

w = natural moisture content of the soil (water content of a soil in the undisturbed condition in the ground If CI = 0, w = LL CI = 1, w = PL CI > 1, the soil is in semi-solid state and is stiff CI < 0, the natural water content is greater than LL, and the soil behaves like liquid g. Liquidity Index ‘Liquidity index (LI or IL)’ or ‘Water-plasticity ratio’ is the ratio of the difference between the natural water content and the plastic limit to the plasticity index: If LI = 0, w = PL LI = 1, w = LL LI > 1, the soil is in liquid state LI < 0, the soil is in the semi-solid state and is stiff Table: Consistency Classification

h. Toughness Index ‘Toughness Index’ (TI) is defined as the ratio of the plasticity index to the flow index:

EXAMPLE 3.7 A liquid limit test, conducted on a soil sample in the cup device, gave the following results: Number of blows 10 19 23 27 40 Water Content (%) 60.0 45.2 39.8 36.5 25.2 Four determinations for the plastic limit gave water contents of 20.3% 20.55%, 20.8% and 11.26%.

EXAMPLE 3.9 The following results were recorded in a shrinkage limit test using mercury.

Initial volume of saturated soil = 32.4 cc Determine the following: a. Shrinkage limit of soil b. Specific gravity of grains c. Bulk unit weight of soil d. Initial and final dry unit weight of soil e. Void ratio EXAMPLE 3.10 The Atterberg limits of a clay soil are: Liquid limit = 75%; Plastic limit = 45%; and Shrinkage limit = 25%. If a sample of this soil has a volume of 30 cm 3 at the liquid limit and a volume 16.6 cm3 at the shrinkage limit, determine the specific gravity of solids. Determine the following: a. LL and PL (in %) b. Plasticity Index c. Liquidity index and Consistency Index, if the natural water content is 27.4%. Describe the consistency. d. Void ratio at the LL if Gs = 2.7 e. Shrinkage limit of the soil if the void ratio of this soil is at the minimum volume reached on shrinkage is 0.405 If the soil were to be loaded to failure, would you expect a brittle failure? EXAMPLE 3.8 A fall cone test was carried out on a soil to determine liquid limit and plastic limit using cones of masses 80 g and 240 g. The following results were obtained. 80-g cone Penetration (mm) Moisture Content %

EXAMPLE 3.11 The mass specific gravity of a saturated specimen of clay is 1.84 when the water content is 38%. On oven drying the mass specific gravity falls to 1.70. Determine the specific gravity of solids and shrinkage limit of the clay. EXAMPLE 3.12 A saturated soil sample has a volume of 23 cm3 at liquid limit. The shrinkage limit and liquid limit are 18% and 45%, respectively. The specific gravity of solids is 2.73. Determine the minimum volume which can be attained by the soil. EXAMPLE 3.13 Two soils S1 and S2 are tested in the laboratory for the consistency limits. The data available is as follows:

240-g cone

8

15

19

28

9

18

22

30

43.1

52

56.1

62.9

37

47.5

51

55.1

a. b. c. d. e.

Which soil is more plastic? Which soil is better foundation material when remolded? Which soil has better strength as a function of water content? Which soil has better strength at the plastic limit? Could organic matter be present in these soils?