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Lecture 2 grain size distribution

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Dr.Abdulmannan Orabi

This document discusses the origin and classification of soil particles based on grain size. It begins by explaining that the grain size distribution of a soil is important for soil classification, filter design, and predicting engineering properties. It then describes various particle size classification systems used by different organizations. The main soil types - gravel, sand, silt, and clay - are defined based on particle diameter ranges. Factors like mineral composition, shape, and texture are also discussed. Common soil structures such as single-grained, honeycomb, and flocculated are summarized. Finally, the document notes that mechanical and hydrometer analyses are the typical methods used to determine grain size distribution.

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INTERNATIONAL UNIVERSITY FOR SCIENCE & TECHNOLOGY ‫وا‬ ‫م‬ ‫ا‬ ‫و‬ ‫ا‬ ‫ا‬ CIVIL ENGINEERING AND ENVIRONMENTAL DEPARTMENT 303322 - Soil Mechanics Origin of soil & Grain Size Dr. Abdulmannan Orabi Lecture 2
Das, B., M. (2014), “ Principles of geotechnical Engineering ” Eighth Edition, CENGAGE Learning, ISBN-13: 978-0-495-41130-7. Knappett, J. A. and Craig R. F. (2012), “ Craig’s Soil Mechanics” Eighth Edition, Spon Press, ISBN: 978- 0-415-56125-9. References Dr. Abdulmannan Orabi IUST 2
Origin of Soil and Grain Size The knowledge of sizes of solid particles comprising a certain soil type and their relative proportion is useful because it is used in; Soil classification Soil filter design Predictions the behavior of a soil with respect to shear strength, settlement and permeability Dr. Abdulmannan Orabi IUST 3
The classification of soils for engineering purposes requires the distribution of grain sizes in a given soil mass. Soil can be range from boulders or cobbles of several centimeters in diameter down to ultrafine-grained colloidal materials. Grain Size Distribution Dr. Abdulmannan Orabi IUST 4
Soils generally are called gravel, sand, silt, or clay, depending on the predominant size of particles within the soil. Soil – Particle Size The standard grain size analysis test determines the relative proportions of different grain size as they are distributed among certain size range. Dr. Abdulmannan Orabi IUST 5
To describe soils by their particle size, several organizations have developed particle-size classifications. Soil – Particle Size Particle-Size Classifications Name of organization Grain size (mm) Gravel Sand Silt Clay MIT >2 2 to 0.06 0.06 to 0.002 < 0.002 USDA >2 2 to 0.05 0.05 to 0.002 < 0.002 AASHTO 76.2 to 2 2 to 0.075 0.075 to 0.002 < 0.002 USCS 76.2 to 4.75 4.75 t0 0.075 < 0.075 6Dr. Abdulmannan Orabi IUST
Gravels are pieces of rocks with occasional particles of quartz, feldspar, and other minerals. Sand particles are made of mostly quartz and feldspar. Soil – Particle Size Silts are the microscopic soil fractions that consist of very fine quartz grains and some flake-shaped particles that are fragments of micaceous minerals. Clays are mostly flake-shaped microscopic and submicroscopic particles of mica, clay minerals, and other minerals. Dr. Abdulmannan Orabi IUST 7
Soils can be divided into cohesive and non-cohesive soils. Cohesive soil contains clay minerals and posses plasticity. Non-cohesive means the soil has no shear strength if no confinement .Sand is non-cohesive and non-plastic. Soil – Particle Size Furthermore, gravel and sand can be roughly classified as coarse textured soils, wile silt and clay can be classified as fine textures soils. Dr. Abdulmannan Orabi IUST 8
Soil – Particle Size GravelsSand Dr. Abdulmannan Orabi IUST 9
Coarse –grained soilsFine –grained soils GravelClay Medium Gravel Coarse Sand Silt Soil – Particle Size Dr. Abdulmannan Orabi IUST 10
• Angular particles are those that have been freshly broken up and are characterized by jagged projections, sharp ridges, and flat surfaces. • Subangular particles are those that have been weathered to the extent that the sharper points and ridges have been worn off. Soil – Particle Size Angular Subangular Shape of bulky particles Dr. Abdulmannan Orabi IUST 11
• Subrounded particles are those that have been weathered to a further degree than subangular particles. • Rounded particles are those on which all projections have been removed, with few irregularities in shape remaining. • Well rounded particles are rounded particles in which the few remaining irregularities have been removed. Soil – Particle Size RoundedSubrounded Well Rounded Shape of bulky particles Dr. Abdulmannan Orabi IUST 12
A soil particle may be a mineral or a rock fragment. A mineral is a chemical compound formed in nature during a geological process, whereas a rock fragment has a combination of one or more minerals. Based on the nature of atoms, minerals are classified as silicates, aluminates, oxides, carbonates and phosphates. Structure of Clay Minerals Out of these, silicate minerals are the most important as they influence the properties of clay soils. Dr. Abdulmannan Orabi IUST 13
Structure of Clay Minerals Clay minerals are very tiny crystalline substances evolved primarily from chemical weathering of certain rock forming minerals, they are complex alumino – silicates plus other metallic ions. Clay minerals Dr. Abdulmannan Orabi IUST 14
Different arrangements of atoms in the silicate minerals give rise to different silicate structures. Structure of Clay Minerals Clay minerals are composed of two basic units: (1) silica tetrahedron and (2) alumina octahedron. These units are held together by ionic bonds. Clay minerals Dr. Abdulmannan Orabi IUST 15
Silica Unit consists of a silicon ion surrounded by four oxygen ions arranged in the form of a tetrahedron. A combination of tetrahedrons forms a silica sheet. The basic units combine in such a manner as to form a sheet. Hydroxyl Aluminum Silica sheetSilica Tetrahedron si Structure of Clay Minerals Dr. Abdulmannan Orabi IUST 16
Aluminium (or Magnesium) Octahedral Unit The octahedral unit has an aluminium ion or a magnesium ion endorsed by six hydroxyl radicals or oxygen arranged in the form of an octahedron. In some cases, other cations (e.g. Fe) are present in place of Al and Mg. Structure of Clay Minerals Alumina sheetAlumina Octahedron Hydroxyl Aluminum Dr. Abdulmannan Orabi IUST 17
The combination of tetrahedral silica units gives a silica sheet (Figure b). Three oxygen atoms at the base of each tetrahedron are shared by neighboring tetrahedra. Structure of Clay Minerals Dr. Abdulmannan Orabi IUST 18
The octahedral units consist of six hydroxyls surrounding an aluminum atom (Figure c), and the combination of the octahedral aluminum hydroxyl units gives an octahedral sheet. This also is called a gibbsite sheet (Figure d.) Structure of Clay Minerals Dr. Abdulmannan Orabi IUST 19
From an engineering point of view, three clay minerals of interest are - Kaolinite, - Illite, and - Montmorillonite Types of Clay Minerals Dr. Abdulmannan Orabi IUST 20
Kaolinite consists of repeating layers of elemental silica- gibbsite sheets in a 1:1 lattice. The atoms in a crystal are arranged in a definite orderly manner to form a three dimensional net-work, called a “lattice.” Kaolinite Silica sheet Gibbsite sheet Silica sheet Gibbsite sheet H bond 7.2Å Types of Clay Minerals Dr. Abdulmannan Orabi IUST 21
Kaolinite Mineral The basic kaolinite unit is a two-layer unit that is formed by stacking a gibbsite sheet on a silica sheet. These basic units are then stacked one on top of the other to form a lattice of the mineral. Kaolinite Silica sheet Gibbsite sheet Silica sheet Gibbsite sheet H bond 7.2Å Types of Clay Minerals Dr. Abdulmannan Orabi IUST 22
Kaolinite Mineral The layers are held together by hydrogen bonding . The strong bonding does not permit water to enter the lattice. Thus, kaolinite minerals are stable and do not expand under saturation. Kaolinite is the most abundant constituent of residual clay deposits. Kaolinite Silica sheet Gibbsite sheet Silica sheet Gibbsite sheet H bond 7.2Å Types of Clay Minerals Dr. Abdulmannan Orabi IUST 23
• Each layer is about 7.2 ( 0.72 Nm)thick.Å • A kaolinite particle may consist of over 100 stacks. •Si4Al4O10(OH)8 Platy shape •There is no interlayer swelling Kaolinite Silica sheet Gibbsite sheet Silica sheet Gibbsite sheet H bond 7.2Å Types of Clay Minerals Dr. Abdulmannan Orabi IUST 24
Kaolinite The surface area of the kaolinite particles per unit mass is about 15 m^2/g. The surface area per unit mass is defined as specific surface Joined by strong hydrogen bond….no easy separation Types of Clay Minerals Dr. Abdulmannan Orabi IUST 25
Illite consists of a gibbsite sheet bonded to two silica sheets—one at the top and another at the bottom. It is sometimes called clay mica. The illite layers are bonded by potassium ions. Potassium 10 Å Silica sheet Gibbsite sheet Silica sheet Silica sheet Gibbsite sheet Silica sheet Illite Types of Clay Minerals 26
The negative charge to balance the potassium ions comes from the substitution of aluminum for some silicon in the tetrahedral sheets. Potassium 10 Å Silica sheet Gibbsite sheet Silica sheet Silica sheet Gibbsite sheet Silica sheet Illite Types of Clay Minerals Dr. Abdulmannan Orabi IUST 27
The bond with the non-exchangeable K+ ions are weaker than the hydrogen bond in the Kaolite but is stronger than the water bond of montmorillonite. The illite crystal does not swell so much in the presence of water as does in montmorillonite particles. Illite Types of Clay Minerals Dr. Abdulmannan Orabi IUST 28
Montmorillonite has a structure similar to that of illite—that is, one gibbsite sheet sandwiched between two silica sheets. Montmorillonite 10 Å Silica sheet Gibbsite sheet Silica sheet Silica sheet Gibbsite sheet Silica sheet nH2O and exchangeable Types of Clay Minerals Dr. Abdulmannan Orabi IUST 29
In montmorillonite there is isomorphous substitution of magnesium and iron for aluminum in the octahedral sheets. Montmorillonite 10 Å Silica sheet Gibbsite sheet Silica sheet Silica sheet Gibbsite sheet Silica sheet nH2O and exchangeable The specific surface is about 800 m^2/g. Types of Clay Minerals Dr. Abdulmannan Orabi IUST 30
Potassium ions are not present as in illite, and a large amount of water is attracted into the space between the layers. There exists interlayer swelling, which is very important to engineering practice (expansive clay). Montmorillonite 10 Å Silica sheet Gibbsite sheet Silica sheet Silica sheet Gibbsite sheet Silica sheet nH2O and exchangeable Types of Clay Minerals Dr. Abdulmannan Orabi IUST 31
When water is added to clay, these cations and a few anions float around the clay particles. This configuration is referred to as a diffuse double layer The cation concentration decreases with the distance from the surface of the particle Clay Minerals Larger negative charges are derived from larger specific surfaces. The clay particles carry a net negative charge on their surfaces. Dr. Abdulmannan Orabi IUST 32
The force of attraction between water and clay decreases with distance from the surface of the particles. All the water held to clay particles by force of attraction is known as double-layer water. The innermost layer of double-layer water, which is held very strongly by clay, is known as adsorbed water This water is more viscous than free water is . Clay Minerals Dr. Abdulmannan Orabi IUST 33
Water molecules are polar. Hydrogen atoms are not axisymmetric around an oxygen atom; instead, they occur at a bonded angle of 105° . As a result, a water molecule has a positive charge at one side and a negative charge at the other side. It is known as a dipole. Dipolar water is attracted both by the negatively charged surface of the clay particles and by the cations in the double layer. The cations, in turn, are attracted to the soil particles. Clay Minerals Dr. Abdulmannan Orabi IUST 34
There is usually a negative electric charge on the crystal surfaces and electro – chemical forces on these surfaces are therefore predominant in determining their engineering properties. Clay Minerals Dr. Abdulmannan Orabi IUST 35
Clay Minerals Diffuse double layer Distance from the clay particle Concentrationofions Anions Cations Surface of clay particle Dr. Abdulmannan Orabi IUST 36
For all particle purpose , when the clay content is about 50% or more. The sand and silt particles float in clay matrix and the clay minerals primarily dictate the engineering properties of the soil. Clay Minerals Dr. Abdulmannan Orabi IUST 37
Types of Soil Structures • Single grained structure. • Honeycomb structure. • Flocculated structure and dispersed structure – in the case of clay deposits. • Course-grained skeleton structure and matrix structure – in the case of composite soils. Soil Structures Dr. Abdulmannan Orabi IUST 38
1) Single grained structure Found in the case of coarse-grained soil deposits. When such soils settle out of suspension in water, the particles settle independently of each other. Major force causing their deposition is gravitational and the surface forces are too small to produce any effect. There will be particle-to-particle contact in the deposit. The void ratio attained depends on the relative size of grains. Soil Structures Dr. Abdulmannan Orabi IUST 39
2) Honeycomb structure Associated with silt deposits. When silt particles settle out of suspension, in additional to gravitational forces, the surface forces also play a significant role. When particles approach the lower region of suspension they will be attracted by particles already deposited as well as the neighbouring particles leading to formation of arches. The combination of a number of arches leads to the honey comb structure. Soil Structures Dr. Abdulmannan Orabi IUST 40
3) (a) Flocculated structure There will be edge-to-edge and edge-to-face contact between particles. Soil Structures Dr. Abdulmannan Orabi IUST 41
3) (b) Flocculated structure The particles will have face to face contact as shown below: Soil Structures Dr. Abdulmannan Orabi IUST 42
4) (a) Course-grained skeleton The course-grained skeleton structure can be found in the case of composite soils in which the course-grained fraction is greater in proportion compared to fine-grained fraction. The course- grained particles form the skeleton with particle to particle contact and the voids between these particles will be occupied by the fine-grained particles. Soil Structures Dr. Abdulmannan Orabi IUST 43
4) (b) Cohesive matrix structure The cohesive matrix structure can be found in composite soils in which the fine-grained fraction is more in proportion compared to course grained fraction. In this case the course-grained particles will be embedded in fine-grained fraction and will be prevented from having particle-to-particle contact. This type of structure is relatively more compressible compared to the more stable course grained structure. Soil Structures Dr. Abdulmannan Orabi IUST 44
Two types of grain size analyses are typically performed 1) Mechanical analysis also know as sieve analysis. Sieving is generally used for coarse-grained soils. (for particle sizes larger than 0.075 mm in diameter) 2) Hydrometer analysis ( sedimentation ) Sedimentation procedure is used for analyzing fine- grained soils.( for particle sizes smaller than 0.075 mm in diameter). Grain Size Distribution Dr. Abdulmannan Orabi IUST 45
Grain Size Distribution Mechanical Analysis (Sieve Analysis) Using sieve analysis one can determine the grain size distribution of soils and classify the soil into sands and gravels. Sieves are made of woven wires with square openings which decrease in size as the sieve number increases; this allows the grains to be sorted by size. Table in the slide No 6 gives a list of the U.S. standard sieve numbers with their corresponding size of openings; most commonly used sieves are highlighted in red. Dr. Abdulmannan Orabi IUST 46
Mechanical Analysis (Sieve Analysis ) U.S. standard sieves Sieve No. Opening (mm) Sieve No. Opening (mm) - 25 0.71 3/8” - 30 0.60 4 4.75 35 0.500 5 4.00 40 0.425 6 3.35 45 0.355 7 2.80 50 0.300 8 2.36 60 0.250 10 2.00 70 0.212 12 1.70 80 0.180 14 1.40 100 0.150 16 1.18 120 0.125 18 1.00 140 0.106 20 0.85 200 0.075 Dr. Abdulmannan Orabi IUST 47
Mechanical Analysis (Sieve Analysis ) The method of sieve analysis described here is applicable for soils that are mostly granular with some or no fines. Sieve analysis only classifies soils into sizes and does not provide information as to shape or type of particles. The U.S. No. 200 sieve (0.075mm) is the smallest sieve size typically used in practice Small size of sample is 500g Dr. Abdulmannan Orabi IUST 48
For coarse-grained soil, a sieve analysis is performed in which a sample of dry soil is shaken mechanically openings since the total mass of sample is known, the percentage retained or passing each size sieve can be determined by weighing the a mount of soil retained on each sieve after shaking. Mechanical Analysis (Sieve Analysis ) Dr. Abdulmannan Orabi IUST 49
Mechanical Analysis (Sieve Analysis ) In the sieve analysis, a series of sieves having different sized openings are stacked with the large sizes over the smaller( a pan is placed below the stack). Pan Dr. Abdulmannan Orabi IUST 50
For measuring the distribution of particle sizes in a soil sample, it is necessary to conduct different particle-size tests. Wet sieving is carried out for separating fine grains from coarse grains by washing the soil specimen on a 75 micron sieve mesh. Dry sieve analysis is carried out on particles coarser than 75 micron. Mechanical Analysis (Sieve Analysis ) Dr. Abdulmannan Orabi IUST 51
Samples (with fines removed) are dried and shaken through a set of sieves of descending size. The weight retained in each sieve is measured. The cumulative percentage quantities finer than the sieve sizes (passing each given sieve size) are then determined. Mechanical Analysis (Sieve Analysis ) Dr. Abdulmannan Orabi IUST 52 To conduct a sieve analysis, one must first oven- dry the soil and then break all lumps into small particles.
The resulting data is presented as a distribution curve with grain size along x-axis (log scale) and percentage passing along y-axis (arithmetic scale). Mechanical Analysis (Sieve Analysis ) Dr. Abdulmannan Orabi IUST 53 100 20 40 60 80 0 0.0010.010.1110 Particle diameter (mm) Percentfiner
Percent(%)FinerbyWeight 0.6 0.0754.75 2.0 0.425 0.150. 25 Particle Diameter (mm) (mm) Particle-size Distribution Curve Dr. Abdulmannan Orabi IUST 54
Particle-size Distribution Curve 1010.01 0.850.075 4.752.00.4250.15 0. 25 #200 #100 #60 #40 #20 #10 #4 Particle Diameter (mm) 0.1 Percent(%)FinerbyWeight Dr. Abdulmannan Orabi IUST 55
Dr. Abdulmannan Orabi IUST 56
For materials finer than 150 µm, dry sieving can be significantly less accurate. This is because the mechanical energy required to make particles pass through an opening and the surface attraction effects between the particles themselves and between particles and the screen increase as the particle sizes decreases. Dr. Abdulmannan Orabi IUST 57 Limitations of Sieve Analysis
Wet sieving analysis can be utilized where the material analysed is not affected by the liquid – except to disperse it. Suspending the particles in a suitable liquid transports fine material through the sieve much more efficiently than shaking the dry material. Dr. Abdulmannan Orabi IUST 58 Limitations of Sieve Analysis
Sieve analysis assumes that all particles will be round – and will pass through the square openings Particle size reported assumes that the particles are spherical, Elongated particle might pass through the screen end-on, but would be prevented from doing so if it presented itself side-on. 59 Limitations of Sieve Analysis Dr. Abdulmannan Orabi IUST
Hydrometer analysis is a widely used method of obtaining an estimate of the distribution of soil particle sizes from the No. 200 (0.075 mm) sieve to around 0.01 mm. The data are presented on a semi- log plot of percent finer vs. particle diameters and may be combined with the data from a sieve analysis of the material retained (+) on the No.200 sieve. Sedimentation Analysis (Hydrometer) Dr. Abdulmannan Orabi IUST 60 Hydrometer analysis is based on the principle of sedimentation of soil grains in water.
Sedimentation Analysis (Hydrometer) In this method, the soil is placed as a suspension in a jar filled with distilled water to which a deflocculating agent is added. Sodium hexametaphosphate generally is used as the dispersing agent. Soil particles are allowed to settle from a suspension. The decreasing density of the suspension is measured at various time intervals. Dr. Abdulmannan Orabi IUST 61
Sedimentation Analysis (Hydrometer) The procedure is based on the principle that in a suspension, the terminal velocity of a spherical particle is governed by the diameter of the particle and the properties of the suspension. The concentration of particles remaining in the suspension at a particular level can be determined by using a hydrometer. Dr. Abdulmannan Orabi IUST 62
Hydrometer analysis is based on the principle of sedimentation of soil grains in water. When a soil specimen is dispersed in water, the particles settle at different velocity, depending on their shape, size and weight and the viscosity of the water. Sedimentation Analysis (Hydrometer) The lower limit of the particle size determined by this procedure is about 0.001mm The sample size is 50g passing #10 Dr. Abdulmannan Orabi IUST 63 Sometimes 100-g samples also can be used.
Sedimentation Analysis (Hydrometer) This method is based on Stoke’s law: = − 18 = !, #/% = % % ! & '( ) = * +% ! & % * ,() %, -/ #. = * +% ! & '( ), -/ #. = * (# ) & % ,() %, # where: Dr. Abdulmannan Orabi IUST 64 (2 − 1)
Sedimentation Analysis (Hydrometer) = 18 − = 18 0 − 1 × 2 3 From Stoke’s law, the diameter can be given as or If the units of η are g.sec/cm^2 , L is in cm , t is in min, and D is in mm, then (##) 10 = 18 (-. % / # 0 − 1 (-/ #. × 2 3(min) × 60 Dr. Abdulmannan Orabi IUST 65
Sedimentation Analysis (Hydrometer) The grain diameter can be calculated from a knowledge of the distance and time of fall. = 30 0 − 1 × 2 3 For computational purpose, equation can be simplified even further to = 8 2 3 8 = 30 0 − 1 where, T = time (min) recorded from the beginning of the sedimentation. Dr. Abdulmannan Orabi IUST 66 (2 − 2)
Sedimentation Analysis (Hydrometer) where = the length of the hydrometer stem = the length of the hydrometer bulb = volume of the hydrometer bulb A = cross-sectional area of the sedimentation cylinder L2 VB L1 L = Distance between water surface and center of gravity of hydrometer bulb Dr. Abdulmannan Orabi IUST 67 2 = 29 + 1 2 2 − ;< = (2 − 3)
L1 L2 L RRc .......... .......... ..... .......... .... .... ..... .......... .......... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . L1 L2 Center of gravity of hydrometer bulb Sedimentation Analysis (Hydrometer) Definition of L in Hydrometer Dr. Abdulmannan Orabi IUST 68
The values of K as function of specific gravity and temperature are given in table (ASTM2004): Sedimentation Analysis (Hydrometer) Dr. Abdulmannan Orabi IUST 69
In the laboratory, the hydrometer test is conducted in a sedimentation cylinder usually with 50 g of oven-dried sample. The soil is mixed with water and a dispersing agent, stirred vigorously, and allowed to settle to the bottom of a measuring cylinder. Sedimentation Analysis (Hydrometer) Dr. Abdulmannan Orabi IUST 70
The length of the hydrometer projecting above the suspension is a function of the density , so it is possible to calibrate the hydrometer to read the density of the suspension at different time. The calibration of the hydrometer is affected by temperature and the specific gravity of the suspended solids. Sedimentation Analysis (Hydrometer) Dr. Abdulmannan Orabi IUST 71
Sedimentation Analysis (Hydrometer) Reading the density of the suspension at different time. .... .... .......... .......... ... . . . . . . . . . . . .. . . . . . . . . . . . ... .... ....... ....... ...... . . . . . . . . . . . . . . . . . . . . . . . . .... .... .......... ............ . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .... .... .......... ........... . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. L L L Start T1 T2 T3 Dr. Abdulmannan Orabi IUST 72
By knowing the amount of soil in suspension, L, and t, we can calculate the percentage of soil by weight finer than a given diameter. The hydrometer should float freely and not touch the wall of the sedimentation cylinder. Sedimentation Analysis (Hydrometer) Dr. Abdulmannan Orabi IUST 73
For Type 152H hydrometers, the effective depth can be given as L = 16.3 – 0.164 R where R is the reading on the hydrometer in grams of solids per liter of suspension. The effective depth is the distance that the soil has settled that can then be used to calculate velocity. Sedimentation Analysis (Hydrometer) Dr. Abdulmannan Orabi IUST 74 (2 − 4)
The equation for the percentage of the soil remaining in suspension is Sedimentation Analysis (Hydrometer) ?@ = ( AB C 100% AB = AEBFGEH − I ) )) + + JK ( = 1.650 2.65 0 − 1 a = correction factor required when the specific gravity of the soil grains is not equal to 2.65 and given by the following equation where: Dr. Abdulmannan Orabi IUST 75 (2 − 5) (2 − 6)
C = *)! #(%% & M & + % N% * + M M!*) # ) (+( !% % Sedimentation Analysis (Hydrometer) JK = )) + &( )& ) #, )( N) Finally, the percent passing for the fines taken for the hydrometer analysis (N’) and for the total soil sample (N) were computed by: ? = ?@ O PP 100 F200 = % finer of #200 sieve as a percent Dr. Abdulmannan Orabi IUST 76 (2 − 7)
Sedimentation Analysis (Hydrometer) For soils with both fine and coarse grained materials a combined analysis is made using both the sieve and hydrometer procedures. Dr. Abdulmannan Orabi IUST 77
Sieve analysis Hydrometer analysis #10 #200#60 20 40 60 80 100 0 0.0010.010.1110 Particle diameter (mm) Percentfiner Particle size distribution curve Sieve analysis and hydrometer analysis Dr. Abdulmannan Orabi IUST 78
Curve I represent a soil in which most of the soil grains are the same size. This is called poorly graded soil. I II III Data obtained from Sieve Analysis Dr. Abdulmannan Orabi IUST 79
Curve II represents a soil in which the particle size distributed over a wide range termed well graded. Curve III represents a soil might have a combination of two or more uniformly graded fraction. This type of soil is termed gap graded. Data obtained from Sieve Analysis Dr. Abdulmannan Orabi IUST 80
Data obtained from Sieve Analysis Particle size distribution curve can be used to determine the following parameters for a given soil 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. The higher the D10 value, the coarser the soil and the better the drainage characteristic. Dr. Abdulmannan Orabi IUST 81
Particle diameter (mm) Percentfiner Particle size distribution curve #10 #200#60 10 20 30 40 100 0 0.01110 50 60 70 80 90 D30 D10D60 Dr. Abdulmannan Orabi IUST 82
Data obtained from Sieve Analysis Uniformity coefficient (Cu); This parameter is defined as where = diameter corresponding to 60 % finer. Coefficient of gradation (CC ); This parameter is defined as JG = XP 9P JB = .P 9P∗ XP XP .P = diameter corresponding to 30 % finer. The grading characteristics are then determined as follows: Dr. Abdulmannan Orabi IUST 83 (2 − 8) (2 − 9)
The percentage of gravel, sand, silt and clay size particles present in soil can be obtained from the particle distribution curve. Data obtained from Sieve Analysis Dr. Abdulmannan Orabi IUST 84 Sieve analysis Hydrometer analysis #10 #200#60 20 40 60 80 100 0 0.0010.010.1110 Particle diameter (mm) Percentfiner Sand FinesGravel
A sieve analysis is used to determine the grain size distribution of coarse-grained soils. For fine-grained soils, a hydrometer analysis is used to find the particle size distribution. Particle size distribution is represented on a semilogarithmic plot of % finer versus particle size Summary Dr. Abdulmannan Orabi IUST 85
The particle size distribution plot is used to determine the different soil textures ( percentage of gravel, sand, silt, and clay ) in soil. The effective size is the diameter in the particle size distribution curve corresponding to 10 % finer. Two coefficients – the uniformity coefficient and the coefficient of curvature are used to characterize the particle size distribution. Summary Dr. Abdulmannan Orabi IUST 86
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: Sieve No. Opening , mm Mass retained, g 4 4.75 0 10 2.00 14.8 20 0.85 98 40 0.425 90.1 100 0.15 181.9 200 0.075 108.8 pan 6.1 Worked Example Dr. Abdulmannan Orabi IUST 87
Solution Worked Example Tabulate data to obtain % finer Sieve No. Mass retained , g % Retained On each sieve ∑( %Retained) % Finer 4 0 0 0 100-0 =100 10 14.8 3.0 3.0 100-3=97 20 98.0 19.6 22.6 100-22.6=77.4 40 90.1 18 40.6 100-40.6=59.4 100 181.9 36.4 77.0 100-77=23 200 108.8 21.8 98.8 100-98.8=1.2 pan 6.1 1.2 100 Total mass M = 499.7 g Dr. Abdulmannan Orabi IUST 88
Worked Example Solution Effective size= 0.1mm Dr. Abdulmannan Orabi IUST 89
Calculate Cu and Cc D60= 0.45 D30 = 0.18 Cu = 0.45/0.1 = 4.5 Cc = 0.72 Extract percentage of gravel, sand, silt, and clay. Gravel = 0 % Sand = 98.8 % Silt and Clay = 1.2 % Worked Example Solution Dr. Abdulmannan Orabi IUST 90
Relative Density Relative density ( Dr ) is sometimes used to describe the state condition in cohesionless soil. Relative density ( Dr ) is an index that quantifies the degree of packing between the loosest and densest possible state of coarse-grained soils as determined by experiments: ^ = _E` − P _E` − _ab Dr. Abdulmannan Orabi IUST 91 (2 − 10)
Relative Density where: is the maximum void ratio ( loosest condition), is the minimum void ratio ( densest condition ), and is the current void ratio. ^ = _E` − P _E` − _ab Dr. Abdulmannan Orabi IUST 92 _E` _ab c
Relative Density The relative density can also be written as: Dr. Abdulmannan Orabi IUST 93 ^ = de − de(_ab) de fgh − de(_ab) × de fgh de de fgh = d ∗ 0 1 + _ab de fij = d ∗ 0 1 + _E` de = d ∗ 0 1 + c (2 − 11)
Relative Density A description of sand based on relative density is given in the following table: Dr ( % ) Approximate Angle of internal friction , Ф Description 0 – 15 25 – 30 Very loose 15 – 35 27 – 32 Loose 35 – 65 30 – 35 Medium dense or firm 65 – 85 35 – 40 Dense 85 – 100 38 – 43 Very dense Dr. Abdulmannan Orabi IUST 94
Lecture 2 grain size distribution

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Lecture 2 grain size distribution

  • 1. INTERNATIONAL UNIVERSITY FOR SCIENCE & TECHNOLOGY ‫وا‬ ‫م‬ ‫ا‬ ‫و‬ ‫ا‬ ‫ا‬ CIVIL ENGINEERING AND ENVIRONMENTAL DEPARTMENT 303322 - Soil Mechanics Origin of soil & Grain Size Dr. Abdulmannan Orabi Lecture 2
  • 2. Das, B., M. (2014), “ Principles of geotechnical Engineering ” Eighth Edition, CENGAGE Learning, ISBN-13: 978-0-495-41130-7. Knappett, J. A. and Craig R. F. (2012), “ Craig’s Soil Mechanics” Eighth Edition, Spon Press, ISBN: 978- 0-415-56125-9. References Dr. Abdulmannan Orabi IUST 2
  • 3. Origin of Soil and Grain Size The knowledge of sizes of solid particles comprising a certain soil type and their relative proportion is useful because it is used in; Soil classification Soil filter design Predictions the behavior of a soil with respect to shear strength, settlement and permeability Dr. Abdulmannan Orabi IUST 3
  • 4. The classification of soils for engineering purposes requires the distribution of grain sizes in a given soil mass. Soil can be range from boulders or cobbles of several centimeters in diameter down to ultrafine-grained colloidal materials. Grain Size Distribution Dr. Abdulmannan Orabi IUST 4
  • 5. Soils generally are called gravel, sand, silt, or clay, depending on the predominant size of particles within the soil. Soil – Particle Size The standard grain size analysis test determines the relative proportions of different grain size as they are distributed among certain size range. Dr. Abdulmannan Orabi IUST 5
  • 6. To describe soils by their particle size, several organizations have developed particle-size classifications. Soil – Particle Size Particle-Size Classifications Name of organization Grain size (mm) Gravel Sand Silt Clay MIT >2 2 to 0.06 0.06 to 0.002 < 0.002 USDA >2 2 to 0.05 0.05 to 0.002 < 0.002 AASHTO 76.2 to 2 2 to 0.075 0.075 to 0.002 < 0.002 USCS 76.2 to 4.75 4.75 t0 0.075 < 0.075 6Dr. Abdulmannan Orabi IUST
  • 7. Gravels are pieces of rocks with occasional particles of quartz, feldspar, and other minerals. Sand particles are made of mostly quartz and feldspar. Soil – Particle Size Silts are the microscopic soil fractions that consist of very fine quartz grains and some flake-shaped particles that are fragments of micaceous minerals. Clays are mostly flake-shaped microscopic and submicroscopic particles of mica, clay minerals, and other minerals. Dr. Abdulmannan Orabi IUST 7
  • 8. Soils can be divided into cohesive and non-cohesive soils. Cohesive soil contains clay minerals and posses plasticity. Non-cohesive means the soil has no shear strength if no confinement .Sand is non-cohesive and non-plastic. Soil – Particle Size Furthermore, gravel and sand can be roughly classified as coarse textured soils, wile silt and clay can be classified as fine textures soils. Dr. Abdulmannan Orabi IUST 8
  • 9. Soil – Particle Size GravelsSand Dr. Abdulmannan Orabi IUST 9
  • 10. Coarse –grained soilsFine –grained soils GravelClay Medium Gravel Coarse Sand Silt Soil – Particle Size Dr. Abdulmannan Orabi IUST 10
  • 11. • Angular particles are those that have been freshly broken up and are characterized by jagged projections, sharp ridges, and flat surfaces. • Subangular particles are those that have been weathered to the extent that the sharper points and ridges have been worn off. Soil – Particle Size Angular Subangular Shape of bulky particles Dr. Abdulmannan Orabi IUST 11
  • 12. • Subrounded particles are those that have been weathered to a further degree than subangular particles. • Rounded particles are those on which all projections have been removed, with few irregularities in shape remaining. • Well rounded particles are rounded particles in which the few remaining irregularities have been removed. Soil – Particle Size RoundedSubrounded Well Rounded Shape of bulky particles Dr. Abdulmannan Orabi IUST 12
  • 13. A soil particle may be a mineral or a rock fragment. A mineral is a chemical compound formed in nature during a geological process, whereas a rock fragment has a combination of one or more minerals. Based on the nature of atoms, minerals are classified as silicates, aluminates, oxides, carbonates and phosphates. Structure of Clay Minerals Out of these, silicate minerals are the most important as they influence the properties of clay soils. Dr. Abdulmannan Orabi IUST 13
  • 14. Structure of Clay Minerals Clay minerals are very tiny crystalline substances evolved primarily from chemical weathering of certain rock forming minerals, they are complex alumino – silicates plus other metallic ions. Clay minerals Dr. Abdulmannan Orabi IUST 14
  • 15. Different arrangements of atoms in the silicate minerals give rise to different silicate structures. Structure of Clay Minerals Clay minerals are composed of two basic units: (1) silica tetrahedron and (2) alumina octahedron. These units are held together by ionic bonds. Clay minerals Dr. Abdulmannan Orabi IUST 15
  • 16. Silica Unit consists of a silicon ion surrounded by four oxygen ions arranged in the form of a tetrahedron. A combination of tetrahedrons forms a silica sheet. The basic units combine in such a manner as to form a sheet. Hydroxyl Aluminum Silica sheetSilica Tetrahedron si Structure of Clay Minerals Dr. Abdulmannan Orabi IUST 16
  • 17. Aluminium (or Magnesium) Octahedral Unit The octahedral unit has an aluminium ion or a magnesium ion endorsed by six hydroxyl radicals or oxygen arranged in the form of an octahedron. In some cases, other cations (e.g. Fe) are present in place of Al and Mg. Structure of Clay Minerals Alumina sheetAlumina Octahedron Hydroxyl Aluminum Dr. Abdulmannan Orabi IUST 17
  • 18. The combination of tetrahedral silica units gives a silica sheet (Figure b). Three oxygen atoms at the base of each tetrahedron are shared by neighboring tetrahedra. Structure of Clay Minerals Dr. Abdulmannan Orabi IUST 18
  • 19. The octahedral units consist of six hydroxyls surrounding an aluminum atom (Figure c), and the combination of the octahedral aluminum hydroxyl units gives an octahedral sheet. This also is called a gibbsite sheet (Figure d.) Structure of Clay Minerals Dr. Abdulmannan Orabi IUST 19
  • 20. From an engineering point of view, three clay minerals of interest are - Kaolinite, - Illite, and - Montmorillonite Types of Clay Minerals Dr. Abdulmannan Orabi IUST 20
  • 21. Kaolinite consists of repeating layers of elemental silica- gibbsite sheets in a 1:1 lattice. The atoms in a crystal are arranged in a definite orderly manner to form a three dimensional net-work, called a “lattice.” Kaolinite Silica sheet Gibbsite sheet Silica sheet Gibbsite sheet H bond 7.2Å Types of Clay Minerals Dr. Abdulmannan Orabi IUST 21
  • 22. Kaolinite Mineral The basic kaolinite unit is a two-layer unit that is formed by stacking a gibbsite sheet on a silica sheet. These basic units are then stacked one on top of the other to form a lattice of the mineral. Kaolinite Silica sheet Gibbsite sheet Silica sheet Gibbsite sheet H bond 7.2Å Types of Clay Minerals Dr. Abdulmannan Orabi IUST 22
  • 23. Kaolinite Mineral The layers are held together by hydrogen bonding . The strong bonding does not permit water to enter the lattice. Thus, kaolinite minerals are stable and do not expand under saturation. Kaolinite is the most abundant constituent of residual clay deposits. Kaolinite Silica sheet Gibbsite sheet Silica sheet Gibbsite sheet H bond 7.2Å Types of Clay Minerals Dr. Abdulmannan Orabi IUST 23
  • 24. • Each layer is about 7.2 ( 0.72 Nm)thick.Å • A kaolinite particle may consist of over 100 stacks. •Si4Al4O10(OH)8 Platy shape •There is no interlayer swelling Kaolinite Silica sheet Gibbsite sheet Silica sheet Gibbsite sheet H bond 7.2Å Types of Clay Minerals Dr. Abdulmannan Orabi IUST 24
  • 25. Kaolinite The surface area of the kaolinite particles per unit mass is about 15 m^2/g. The surface area per unit mass is defined as specific surface Joined by strong hydrogen bond….no easy separation Types of Clay Minerals Dr. Abdulmannan Orabi IUST 25
  • 26. Illite consists of a gibbsite sheet bonded to two silica sheets—one at the top and another at the bottom. It is sometimes called clay mica. The illite layers are bonded by potassium ions. Potassium 10 Å Silica sheet Gibbsite sheet Silica sheet Silica sheet Gibbsite sheet Silica sheet Illite Types of Clay Minerals 26
  • 27. The negative charge to balance the potassium ions comes from the substitution of aluminum for some silicon in the tetrahedral sheets. Potassium 10 Å Silica sheet Gibbsite sheet Silica sheet Silica sheet Gibbsite sheet Silica sheet Illite Types of Clay Minerals Dr. Abdulmannan Orabi IUST 27
  • 28. The bond with the non-exchangeable K+ ions are weaker than the hydrogen bond in the Kaolite but is stronger than the water bond of montmorillonite. The illite crystal does not swell so much in the presence of water as does in montmorillonite particles. Illite Types of Clay Minerals Dr. Abdulmannan Orabi IUST 28
  • 29. Montmorillonite has a structure similar to that of illite—that is, one gibbsite sheet sandwiched between two silica sheets. Montmorillonite 10 Å Silica sheet Gibbsite sheet Silica sheet Silica sheet Gibbsite sheet Silica sheet nH2O and exchangeable Types of Clay Minerals Dr. Abdulmannan Orabi IUST 29
  • 30. In montmorillonite there is isomorphous substitution of magnesium and iron for aluminum in the octahedral sheets. Montmorillonite 10 Å Silica sheet Gibbsite sheet Silica sheet Silica sheet Gibbsite sheet Silica sheet nH2O and exchangeable The specific surface is about 800 m^2/g. Types of Clay Minerals Dr. Abdulmannan Orabi IUST 30
  • 31. Potassium ions are not present as in illite, and a large amount of water is attracted into the space between the layers. There exists interlayer swelling, which is very important to engineering practice (expansive clay). Montmorillonite 10 Å Silica sheet Gibbsite sheet Silica sheet Silica sheet Gibbsite sheet Silica sheet nH2O and exchangeable Types of Clay Minerals Dr. Abdulmannan Orabi IUST 31
  • 32. When water is added to clay, these cations and a few anions float around the clay particles. This configuration is referred to as a diffuse double layer The cation concentration decreases with the distance from the surface of the particle Clay Minerals Larger negative charges are derived from larger specific surfaces. The clay particles carry a net negative charge on their surfaces. Dr. Abdulmannan Orabi IUST 32
  • 33. The force of attraction between water and clay decreases with distance from the surface of the particles. All the water held to clay particles by force of attraction is known as double-layer water. The innermost layer of double-layer water, which is held very strongly by clay, is known as adsorbed water This water is more viscous than free water is . Clay Minerals Dr. Abdulmannan Orabi IUST 33
  • 34. Water molecules are polar. Hydrogen atoms are not axisymmetric around an oxygen atom; instead, they occur at a bonded angle of 105° . As a result, a water molecule has a positive charge at one side and a negative charge at the other side. It is known as a dipole. Dipolar water is attracted both by the negatively charged surface of the clay particles and by the cations in the double layer. The cations, in turn, are attracted to the soil particles. Clay Minerals Dr. Abdulmannan Orabi IUST 34
  • 35. There is usually a negative electric charge on the crystal surfaces and electro – chemical forces on these surfaces are therefore predominant in determining their engineering properties. Clay Minerals Dr. Abdulmannan Orabi IUST 35
  • 36. Clay Minerals Diffuse double layer Distance from the clay particle Concentrationofions Anions Cations Surface of clay particle Dr. Abdulmannan Orabi IUST 36
  • 37. For all particle purpose , when the clay content is about 50% or more. The sand and silt particles float in clay matrix and the clay minerals primarily dictate the engineering properties of the soil. Clay Minerals Dr. Abdulmannan Orabi IUST 37
  • 38. Types of Soil Structures • Single grained structure. • Honeycomb structure. • Flocculated structure and dispersed structure – in the case of clay deposits. • Course-grained skeleton structure and matrix structure – in the case of composite soils. Soil Structures Dr. Abdulmannan Orabi IUST 38
  • 39. 1) Single grained structure Found in the case of coarse-grained soil deposits. When such soils settle out of suspension in water, the particles settle independently of each other. Major force causing their deposition is gravitational and the surface forces are too small to produce any effect. There will be particle-to-particle contact in the deposit. The void ratio attained depends on the relative size of grains. Soil Structures Dr. Abdulmannan Orabi IUST 39
  • 40. 2) Honeycomb structure Associated with silt deposits. When silt particles settle out of suspension, in additional to gravitational forces, the surface forces also play a significant role. When particles approach the lower region of suspension they will be attracted by particles already deposited as well as the neighbouring particles leading to formation of arches. The combination of a number of arches leads to the honey comb structure. Soil Structures Dr. Abdulmannan Orabi IUST 40
  • 41. 3) (a) Flocculated structure There will be edge-to-edge and edge-to-face contact between particles. Soil Structures Dr. Abdulmannan Orabi IUST 41
  • 42. 3) (b) Flocculated structure The particles will have face to face contact as shown below: Soil Structures Dr. Abdulmannan Orabi IUST 42
  • 43. 4) (a) Course-grained skeleton The course-grained skeleton structure can be found in the case of composite soils in which the course-grained fraction is greater in proportion compared to fine-grained fraction. The course- grained particles form the skeleton with particle to particle contact and the voids between these particles will be occupied by the fine-grained particles. Soil Structures Dr. Abdulmannan Orabi IUST 43
  • 44. 4) (b) Cohesive matrix structure The cohesive matrix structure can be found in composite soils in which the fine-grained fraction is more in proportion compared to course grained fraction. In this case the course-grained particles will be embedded in fine-grained fraction and will be prevented from having particle-to-particle contact. This type of structure is relatively more compressible compared to the more stable course grained structure. Soil Structures Dr. Abdulmannan Orabi IUST 44
  • 45. Two types of grain size analyses are typically performed 1) Mechanical analysis also know as sieve analysis. Sieving is generally used for coarse-grained soils. (for particle sizes larger than 0.075 mm in diameter) 2) Hydrometer analysis ( sedimentation ) Sedimentation procedure is used for analyzing fine- grained soils.( for particle sizes smaller than 0.075 mm in diameter). Grain Size Distribution Dr. Abdulmannan Orabi IUST 45
  • 46. Grain Size Distribution Mechanical Analysis (Sieve Analysis) Using sieve analysis one can determine the grain size distribution of soils and classify the soil into sands and gravels. Sieves are made of woven wires with square openings which decrease in size as the sieve number increases; this allows the grains to be sorted by size. Table in the slide No 6 gives a list of the U.S. standard sieve numbers with their corresponding size of openings; most commonly used sieves are highlighted in red. Dr. Abdulmannan Orabi IUST 46
  • 47. Mechanical Analysis (Sieve Analysis ) U.S. standard sieves Sieve No. Opening (mm) Sieve No. Opening (mm) - 25 0.71 3/8” - 30 0.60 4 4.75 35 0.500 5 4.00 40 0.425 6 3.35 45 0.355 7 2.80 50 0.300 8 2.36 60 0.250 10 2.00 70 0.212 12 1.70 80 0.180 14 1.40 100 0.150 16 1.18 120 0.125 18 1.00 140 0.106 20 0.85 200 0.075 Dr. Abdulmannan Orabi IUST 47
  • 48. Mechanical Analysis (Sieve Analysis ) The method of sieve analysis described here is applicable for soils that are mostly granular with some or no fines. Sieve analysis only classifies soils into sizes and does not provide information as to shape or type of particles. The U.S. No. 200 sieve (0.075mm) is the smallest sieve size typically used in practice Small size of sample is 500g Dr. Abdulmannan Orabi IUST 48
  • 49. For coarse-grained soil, a sieve analysis is performed in which a sample of dry soil is shaken mechanically openings since the total mass of sample is known, the percentage retained or passing each size sieve can be determined by weighing the a mount of soil retained on each sieve after shaking. Mechanical Analysis (Sieve Analysis ) Dr. Abdulmannan Orabi IUST 49
  • 50. Mechanical Analysis (Sieve Analysis ) In the sieve analysis, a series of sieves having different sized openings are stacked with the large sizes over the smaller( a pan is placed below the stack). Pan Dr. Abdulmannan Orabi IUST 50
  • 51. For measuring the distribution of particle sizes in a soil sample, it is necessary to conduct different particle-size tests. Wet sieving is carried out for separating fine grains from coarse grains by washing the soil specimen on a 75 micron sieve mesh. Dry sieve analysis is carried out on particles coarser than 75 micron. Mechanical Analysis (Sieve Analysis ) Dr. Abdulmannan Orabi IUST 51
  • 52. Samples (with fines removed) are dried and shaken through a set of sieves of descending size. The weight retained in each sieve is measured. The cumulative percentage quantities finer than the sieve sizes (passing each given sieve size) are then determined. Mechanical Analysis (Sieve Analysis ) Dr. Abdulmannan Orabi IUST 52 To conduct a sieve analysis, one must first oven- dry the soil and then break all lumps into small particles.
  • 53. The resulting data is presented as a distribution curve with grain size along x-axis (log scale) and percentage passing along y-axis (arithmetic scale). Mechanical Analysis (Sieve Analysis ) Dr. Abdulmannan Orabi IUST 53 100 20 40 60 80 0 0.0010.010.1110 Particle diameter (mm) Percentfiner
  • 54. Percent(%)FinerbyWeight 0.6 0.0754.75 2.0 0.425 0.150. 25 Particle Diameter (mm) (mm) Particle-size Distribution Curve Dr. Abdulmannan Orabi IUST 54
  • 55. Particle-size Distribution Curve 1010.01 0.850.075 4.752.00.4250.15 0. 25 #200 #100 #60 #40 #20 #10 #4 Particle Diameter (mm) 0.1 Percent(%)FinerbyWeight Dr. Abdulmannan Orabi IUST 55
  • 57. For materials finer than 150 µm, dry sieving can be significantly less accurate. This is because the mechanical energy required to make particles pass through an opening and the surface attraction effects between the particles themselves and between particles and the screen increase as the particle sizes decreases. Dr. Abdulmannan Orabi IUST 57 Limitations of Sieve Analysis
  • 58. Wet sieving analysis can be utilized where the material analysed is not affected by the liquid – except to disperse it. Suspending the particles in a suitable liquid transports fine material through the sieve much more efficiently than shaking the dry material. Dr. Abdulmannan Orabi IUST 58 Limitations of Sieve Analysis
  • 59. Sieve analysis assumes that all particles will be round – and will pass through the square openings Particle size reported assumes that the particles are spherical, Elongated particle might pass through the screen end-on, but would be prevented from doing so if it presented itself side-on. 59 Limitations of Sieve Analysis Dr. Abdulmannan Orabi IUST
  • 60. Hydrometer analysis is a widely used method of obtaining an estimate of the distribution of soil particle sizes from the No. 200 (0.075 mm) sieve to around 0.01 mm. The data are presented on a semi- log plot of percent finer vs. particle diameters and may be combined with the data from a sieve analysis of the material retained (+) on the No.200 sieve. Sedimentation Analysis (Hydrometer) Dr. Abdulmannan Orabi IUST 60 Hydrometer analysis is based on the principle of sedimentation of soil grains in water.
  • 61. Sedimentation Analysis (Hydrometer) In this method, the soil is placed as a suspension in a jar filled with distilled water to which a deflocculating agent is added. Sodium hexametaphosphate generally is used as the dispersing agent. Soil particles are allowed to settle from a suspension. The decreasing density of the suspension is measured at various time intervals. Dr. Abdulmannan Orabi IUST 61
  • 62. Sedimentation Analysis (Hydrometer) The procedure is based on the principle that in a suspension, the terminal velocity of a spherical particle is governed by the diameter of the particle and the properties of the suspension. The concentration of particles remaining in the suspension at a particular level can be determined by using a hydrometer. Dr. Abdulmannan Orabi IUST 62
  • 63. Hydrometer analysis is based on the principle of sedimentation of soil grains in water. When a soil specimen is dispersed in water, the particles settle at different velocity, depending on their shape, size and weight and the viscosity of the water. Sedimentation Analysis (Hydrometer) The lower limit of the particle size determined by this procedure is about 0.001mm The sample size is 50g passing #10 Dr. Abdulmannan Orabi IUST 63 Sometimes 100-g samples also can be used.
  • 64. Sedimentation Analysis (Hydrometer) This method is based on Stoke’s law: = − 18 = !, #/% = % % ! & '( ) = * +% ! & % * ,() %, -/ #. = * +% ! & '( ), -/ #. = * (# ) & % ,() %, # where: Dr. Abdulmannan Orabi IUST 64 (2 − 1)
  • 65. Sedimentation Analysis (Hydrometer) = 18 − = 18 0 − 1 × 2 3 From Stoke’s law, the diameter can be given as or If the units of η are g.sec/cm^2 , L is in cm , t is in min, and D is in mm, then (##) 10 = 18 (-. % / # 0 − 1 (-/ #. × 2 3(min) × 60 Dr. Abdulmannan Orabi IUST 65
  • 66. Sedimentation Analysis (Hydrometer) The grain diameter can be calculated from a knowledge of the distance and time of fall. = 30 0 − 1 × 2 3 For computational purpose, equation can be simplified even further to = 8 2 3 8 = 30 0 − 1 where, T = time (min) recorded from the beginning of the sedimentation. Dr. Abdulmannan Orabi IUST 66 (2 − 2)
  • 67. Sedimentation Analysis (Hydrometer) where = the length of the hydrometer stem = the length of the hydrometer bulb = volume of the hydrometer bulb A = cross-sectional area of the sedimentation cylinder L2 VB L1 L = Distance between water surface and center of gravity of hydrometer bulb Dr. Abdulmannan Orabi IUST 67 2 = 29 + 1 2 2 − ;< = (2 − 3)
  • 68. L1 L2 L RRc .......... .......... ..... .......... .... .... ..... .......... .......... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . L1 L2 Center of gravity of hydrometer bulb Sedimentation Analysis (Hydrometer) Definition of L in Hydrometer Dr. Abdulmannan Orabi IUST 68
  • 69. The values of K as function of specific gravity and temperature are given in table (ASTM2004): Sedimentation Analysis (Hydrometer) Dr. Abdulmannan Orabi IUST 69
  • 70. In the laboratory, the hydrometer test is conducted in a sedimentation cylinder usually with 50 g of oven-dried sample. The soil is mixed with water and a dispersing agent, stirred vigorously, and allowed to settle to the bottom of a measuring cylinder. Sedimentation Analysis (Hydrometer) Dr. Abdulmannan Orabi IUST 70
  • 71. The length of the hydrometer projecting above the suspension is a function of the density , so it is possible to calibrate the hydrometer to read the density of the suspension at different time. The calibration of the hydrometer is affected by temperature and the specific gravity of the suspended solids. Sedimentation Analysis (Hydrometer) Dr. Abdulmannan Orabi IUST 71
  • 72. Sedimentation Analysis (Hydrometer) Reading the density of the suspension at different time. .... .... .......... .......... ... . . . . . . . . . . . .. . . . . . . . . . . . ... .... ....... ....... ...... . . . . . . . . . . . . . . . . . . . . . . . . .... .... .......... ............ . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .... .... .......... ........... . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. L L L Start T1 T2 T3 Dr. Abdulmannan Orabi IUST 72
  • 73. By knowing the amount of soil in suspension, L, and t, we can calculate the percentage of soil by weight finer than a given diameter. The hydrometer should float freely and not touch the wall of the sedimentation cylinder. Sedimentation Analysis (Hydrometer) Dr. Abdulmannan Orabi IUST 73
  • 74. For Type 152H hydrometers, the effective depth can be given as L = 16.3 – 0.164 R where R is the reading on the hydrometer in grams of solids per liter of suspension. The effective depth is the distance that the soil has settled that can then be used to calculate velocity. Sedimentation Analysis (Hydrometer) Dr. Abdulmannan Orabi IUST 74 (2 − 4)
  • 75. The equation for the percentage of the soil remaining in suspension is Sedimentation Analysis (Hydrometer) ?@ = ( AB C 100% AB = AEBFGEH − I ) )) + + JK ( = 1.650 2.65 0 − 1 a = correction factor required when the specific gravity of the soil grains is not equal to 2.65 and given by the following equation where: Dr. Abdulmannan Orabi IUST 75 (2 − 5) (2 − 6)
  • 76. C = *)! #(%% & M & + % N% * + M M!*) # ) (+( !% % Sedimentation Analysis (Hydrometer) JK = )) + &( )& ) #, )( N) Finally, the percent passing for the fines taken for the hydrometer analysis (N’) and for the total soil sample (N) were computed by: ? = ?@ O PP 100 F200 = % finer of #200 sieve as a percent Dr. Abdulmannan Orabi IUST 76 (2 − 7)
  • 77. Sedimentation Analysis (Hydrometer) For soils with both fine and coarse grained materials a combined analysis is made using both the sieve and hydrometer procedures. Dr. Abdulmannan Orabi IUST 77
  • 78. Sieve analysis Hydrometer analysis #10 #200#60 20 40 60 80 100 0 0.0010.010.1110 Particle diameter (mm) Percentfiner Particle size distribution curve Sieve analysis and hydrometer analysis Dr. Abdulmannan Orabi IUST 78
  • 79. Curve I represent a soil in which most of the soil grains are the same size. This is called poorly graded soil. I II III Data obtained from Sieve Analysis Dr. Abdulmannan Orabi IUST 79
  • 80. Curve II represents a soil in which the particle size distributed over a wide range termed well graded. Curve III represents a soil might have a combination of two or more uniformly graded fraction. This type of soil is termed gap graded. Data obtained from Sieve Analysis Dr. Abdulmannan Orabi IUST 80
  • 81. Data obtained from Sieve Analysis Particle size distribution curve can be used to determine the following parameters for a given soil 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. The higher the D10 value, the coarser the soil and the better the drainage characteristic. Dr. Abdulmannan Orabi IUST 81
  • 82. Particle diameter (mm) Percentfiner Particle size distribution curve #10 #200#60 10 20 30 40 100 0 0.01110 50 60 70 80 90 D30 D10D60 Dr. Abdulmannan Orabi IUST 82
  • 83. Data obtained from Sieve Analysis Uniformity coefficient (Cu); This parameter is defined as where = diameter corresponding to 60 % finer. Coefficient of gradation (CC ); This parameter is defined as JG = XP 9P JB = .P 9P∗ XP XP .P = diameter corresponding to 30 % finer. The grading characteristics are then determined as follows: Dr. Abdulmannan Orabi IUST 83 (2 − 8) (2 − 9)
  • 84. The percentage of gravel, sand, silt and clay size particles present in soil can be obtained from the particle distribution curve. Data obtained from Sieve Analysis Dr. Abdulmannan Orabi IUST 84 Sieve analysis Hydrometer analysis #10 #200#60 20 40 60 80 100 0 0.0010.010.1110 Particle diameter (mm) Percentfiner Sand FinesGravel
  • 85. A sieve analysis is used to determine the grain size distribution of coarse-grained soils. For fine-grained soils, a hydrometer analysis is used to find the particle size distribution. Particle size distribution is represented on a semilogarithmic plot of % finer versus particle size Summary Dr. Abdulmannan Orabi IUST 85
  • 86. The particle size distribution plot is used to determine the different soil textures ( percentage of gravel, sand, silt, and clay ) in soil. The effective size is the diameter in the particle size distribution curve corresponding to 10 % finer. Two coefficients – the uniformity coefficient and the coefficient of curvature are used to characterize the particle size distribution. Summary Dr. Abdulmannan Orabi IUST 86
  • 87. 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: Sieve No. Opening , mm Mass retained, g 4 4.75 0 10 2.00 14.8 20 0.85 98 40 0.425 90.1 100 0.15 181.9 200 0.075 108.8 pan 6.1 Worked Example Dr. Abdulmannan Orabi IUST 87
  • 88. Solution Worked Example Tabulate data to obtain % finer Sieve No. Mass retained , g % Retained On each sieve ∑( %Retained) % Finer 4 0 0 0 100-0 =100 10 14.8 3.0 3.0 100-3=97 20 98.0 19.6 22.6 100-22.6=77.4 40 90.1 18 40.6 100-40.6=59.4 100 181.9 36.4 77.0 100-77=23 200 108.8 21.8 98.8 100-98.8=1.2 pan 6.1 1.2 100 Total mass M = 499.7 g Dr. Abdulmannan Orabi IUST 88
  • 89. Worked Example Solution Effective size= 0.1mm Dr. Abdulmannan Orabi IUST 89
  • 90. Calculate Cu and Cc D60= 0.45 D30 = 0.18 Cu = 0.45/0.1 = 4.5 Cc = 0.72 Extract percentage of gravel, sand, silt, and clay. Gravel = 0 % Sand = 98.8 % Silt and Clay = 1.2 % Worked Example Solution Dr. Abdulmannan Orabi IUST 90
  • 91. Relative Density Relative density ( Dr ) is sometimes used to describe the state condition in cohesionless soil. Relative density ( Dr ) is an index that quantifies the degree of packing between the loosest and densest possible state of coarse-grained soils as determined by experiments: ^ = _E` − P _E` − _ab Dr. Abdulmannan Orabi IUST 91 (2 − 10)
  • 92. Relative Density where: is the maximum void ratio ( loosest condition), is the minimum void ratio ( densest condition ), and is the current void ratio. ^ = _E` − P _E` − _ab Dr. Abdulmannan Orabi IUST 92 _E` _ab c
  • 93. Relative Density The relative density can also be written as: Dr. Abdulmannan Orabi IUST 93 ^ = de − de(_ab) de fgh − de(_ab) × de fgh de de fgh = d ∗ 0 1 + _ab de fij = d ∗ 0 1 + _E` de = d ∗ 0 1 + c (2 − 11)
  • 94. Relative Density A description of sand based on relative density is given in the following table: Dr ( % ) Approximate Angle of internal friction , Ф Description 0 – 15 25 – 30 Very loose 15 – 35 27 – 32 Loose 35 – 65 30 – 35 Medium dense or firm 65 – 85 35 – 40 Dense 85 – 100 38 – 43 Very dense Dr. Abdulmannan Orabi IUST 94