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Soil - Basic Definitions & Relationships

The document provides a comprehensive overview of soil properties, focusing on definitions and relationships between soil components, including weight, volume, density, and water content. It details the methods for determining water content and specific gravity of soil, along with formulas for calculating various soil parameters such as void ratio, porosity, and degree of saturation. Various laboratory and field methods are discussed for practical applications in soil engineering and analysis.

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Arbaz Mubarak Kazi, B.E, M.E (Civil Engineering) Email: arbaazkazi91@gmail.com https://gtearchives.wordpress.com www.linkedin.com/in/arbaz-kazi-20747570 SOIL - BASIC DEFINITIONS & RELATIONSHIPS “Everyday is an Adventure When you are Civil Engineer”
BASIC DEFINITIONS AND RELATIONSHIPS Soil has two principle components: solid particles and voids. Voids are the empty spaces in between the solid particles that may be filled with air or liquid or both. These components make solid a complex matter and difficult to study about. Therefore, with a view to simplify the study, these particles are segregated and shown in different layers (like a block diagram). The diagram which shows solid, water and air of soil separately is known as 3-phase diagram (figure shown) Three Phase Diagram:
Here, W = Total Weight = Weight of solid particles + Weight of water (Weight of air can be neglected because of its low density) V = Total Volume = Volume of solid particles + Volume of water + Volume of air Ws = Weight of solid particles Wa = Weight of air Vs = Volume of solid particles Vw = Volume of water Vv = Volume of voids = Total volume (V) - Volume of solid particles (Vs)
TWO PHASE DIAGRAM FOR FULLY SAURATED SOIL • In this case two phases, solid, water is present. • Air is absent. Voids are filled with water only.
• Moisture Content: It is defined as the ratio of mass of water to mass of solids. It is denoted by (w) and expressed in percentage. 𝑤 = 𝑀𝑤/𝑀𝑠 x 100 • Void ratio: It is defined as the ratio of the volume of voids to the volume of solids. It is denoted by (e). For coarse grained soil, void ratio is larger and for fine grained soil it is vice-versa 𝑒 = 𝑉𝑣/𝑉𝑠 • Porosity: It is defined as the ratio of the volume of voids to the total volume. It is denoted by (n). n = Vv/V FUNDAMENTAL DEFINITION:
Relationship 1: Between Void ratio and Porosity We Know, V = Vs + Vv 𝑛 = 𝑉 𝑣 𝑉 = 𝑉 𝑣 𝑉 𝑠 + 𝑉 𝑣 = 𝑉 𝑣/𝑉 𝑠 𝑉 𝑠 𝑉 𝑠 + 𝑉 𝑣 𝑉 𝑠 = 𝑒 1 + 𝑒 𝑒 = 𝑉 𝑣 𝑉 𝑠 = 𝑉 𝑣 𝑉 − 𝑉 𝑣 = 𝑉 𝑣/𝑉 𝑉 𝑉 − 𝑉 𝑣 𝑉 = 𝑛 1 − 𝑛
• Degree of saturation: It is the ratio of the volume of water to the volume of voids and is generally expressed as a percentage and denoted by (S). S= 𝑉𝑤/𝑉𝑣 In case of fully saturated soil, voids are completely filled with water. There is no air. Vw = Vv, Hence S = 1. In case of fully dry soil, voids are completely filled with air. There is no water i.e. Vw = 0, Hence S = 0. • Air Content: It is defined as volume of air to volume of voids. It is denoted by (ac) ac= 𝑉𝑎/𝑉𝑣
• Percentage air content: It is defined as volume of air to total volume. It is denoted by (na). It is expressed as percentage. Relationship 2: Between Percentage Air content, Air content & Porosity na= 𝑉𝑎/𝑉= 𝑉𝑎/𝑉𝑣 * 𝑉𝑣/𝑉= n*ac • Density: It is the ratio of the total mass to the total volume of the soil. It is denoted by (ρ) and is also referred as bulk density (ρb) or mass density. ρ or ρb = M/V
• Unit weight: It is the ratio of the total weight to the total volume of the soil. It is denoted by (ϒ) and is also referred as bulk unit weight(ϒb) or weight density. ϒ or ϒb = W/V • Dry Density: The dry density is defined as the ratio of the mass of soil solids to the total volume. It is denoted by (ρd). ρd = MS/V • Dry Unit weight: The dry unit weight is defined as the ratio of the weight of soil solids to the total volume. It is denoted by (ϒd). ϒd = WS/V
• Density of Solids: The density of solids is defined as the ratio of the mass of soil solids to the total volume of soil solids. It is denoted by (ρs). ρs = MS/VS • Unit weight of Solids: The dry unit weight is defined as the ratio of the weight of soil solids to the total volume of soil solids. It is denoted by (ϒS). ϒS = WS/VS • Saturated Density: The saturated density is defined as the ratio of the saturated mass of soil to the total volume. It is denoted by (ρsat). ρsat = Msat/V
• Saturated Unit weight: The saturated unit weight is defined as the ratio of the saturated weight of soil to the total volume. It is denoted by (ϒsat). ϒsat = Wsat/V • Submerged Unit weight: The submerged unit weight is the effective mass per unit volume when the soil is submerged below standing water or below the ground water table. It is denoted by (ϒ’) 𝛾′ = (𝛾𝑠𝑎𝑡 − 𝛾𝑤) 𝑉
Explanation of Submerged Unit Weight
• Specific Gravity: It is defined as the ratio of the weight of a given volume of soil solids to the weight of an equal volume of distilled water. G = ϒS/ϒw or ρs/ρw Typical values of specific gravity for different soils are given below: Type of Soil Sp. Gravity Type of Soil Sp. Gravity GRAVEL 2.65 - 2.68 SILTS 2.66 – 2.70 SAND 2.65 - 2.68 INORGANIC CLAY 2.68 – 2.80 SILTY SAND 2.66 – 2.70 ORGANIC SOILS below 2.0
• Mass Specific Gravity: The specific gravity of a mass of soil (including air, water and solids) is termed as bulk or mass specific gravity Gm. It is expressed as 𝐺𝑚 = 𝛾 𝛾𝑤 𝑜𝑟 𝜌 𝜌𝑤
Relationship 3: Between 𝒏𝒂,𝒆 & 𝐒 We Know, 𝑉 𝑣 − 𝑉𝑤 = 𝑉 Also, 𝑆 = / 𝑉 𝑤 𝑉𝑣 Hence, 𝑆∗ 𝑉 𝑣 = 𝑉𝑤 𝑛𝑎= 𝑉 𝑣 − 𝑆 ∗ 𝑉 𝑣 𝑉 𝑎 𝑉 𝑣*(1 − 𝑆) 𝑛 = 𝑉 𝑎 𝑛 = 𝑛∗(1 − 𝑆) Also, 𝑛 = e / 1 + e Hence, 𝑎 𝑒∗ (1 − 𝑆) 𝑛 = 1 + 𝑒 𝑛𝑎 = ൗ 𝑉 𝑎 𝑉 𝑤
Relationship 4: Between e, G, w and S Take Vs = 1, But e = Vv/Vs and Vv = e, therefore V = 1+e
𝑤 = 𝑊 𝑤 𝑊 𝑠 = 𝛾𝑊 ∗ 𝑉 𝑤 𝛾𝑠 ∗ 𝑉 𝑠 Also, S = VW/VV and G = ϒS/ϒW 𝐻𝑒𝑛𝑐𝑒, 𝑤 = 𝑊 𝑤 𝑊 𝑠 = 𝛾𝑊 ∗ 𝑉 𝑤 𝛾𝑠 ∗ 𝑉 𝑠 = 𝛾𝑊 ∗ 𝑉 𝑣 ∗ 𝑆 𝐺 ∗ 𝛾𝑤 ∗ 𝑉 𝑠 ………………. (1) But Vv/Vs = e, so equation (1) becomes 𝑤. 𝐺 = S. 𝑒
We know that, ϒ = = 𝑊 𝑊𝑠+ 𝑊𝑤 𝑉 𝑉 𝑉 ϒ = ϒ𝑠*𝑉𝑠+ϒ𝑤*𝑉𝑤 …… (1) (ϒ𝑠 = Ws/Vs and ϒ𝑤=Ww/Vw) From Fig. Vs = 1 and Vv = e ϒ = 𝐺*ϒ𝑤*1+ϒ𝑤*𝑆*𝑒 𝑉 …….. (G = ϒs/ϒw) and (Vw = S*Vv) 1+𝑒 ϒ = 𝐺+𝑆*e *ϒ𝑤 ……………….(2) Relationship 5: Between ϒ, G, e and S
If soil is fully dry eq. (2) becomes, 𝐺.ϒ𝑤 ϒsat = ϒd = 1 + 𝑒 If soil is fully saturated eq. (2) becomes, 𝐺 + 𝑒 *ϒ𝑤 1 + 𝑒 Relationship 6: Between 𝒂𝒄 andS 𝑐 𝑎 = / 𝑉 𝑎 𝑉 𝑣 1 − 𝑆 = 𝑉 𝑣 = ൗ 𝑉 𝑣 − 𝑉 𝑤 𝑉 𝑣
We know that, ϒ = 𝑊 𝑉 ϒ = 𝑊𝑠+ 𝑊𝑤 𝑉 𝑉 ϒ = 𝑊𝑠 + 𝑤*𝑊𝑠 ……………. (w = Mw/Ms) ϒ = 𝑊𝑠*(1 + 𝑤) 𝑉 ϒ = ϒ𝑑* 1 + 𝑤 ………….. (Ws/V = ϒd) ϒ ϒd = (1 + 𝑤) Relationship 7: Between ϒd, ϒand w
Relationship 8: Between ϒd, G, w and 𝒏𝒂 𝑉=𝑉 𝑎+ 𝑉𝑤+ 𝑉 𝑠 𝑉=𝑉 𝑎+ 𝛾𝑤 + 𝑊 𝑤 𝑊𝑠 𝛾 𝑠 1 = 𝑉 𝑎 𝑉 + 𝑊 𝑤 𝛾𝑤 ∗ 𝑉 + 𝑊 𝑠 𝛾𝑠 ∗ 𝑉 1 = 𝑉 𝑎 𝑉 + 𝑊 𝑠 ∗ 𝑤 𝛾𝑤 ∗ 𝑉 + 𝑊 𝑠 𝛾𝑠 ∗ 𝑉 1 = 𝑉 𝑎 𝑉 + 𝛾𝑑 ∗ 𝑤 𝛾𝑤 + 𝛾𝑑 𝛾𝑠 1 − 𝑛𝑎 = 𝛾𝑑 𝛾𝑤 ∗ ( 1 + 𝑤 𝐺 ) 𝛾𝑑 = 1 − 𝑛𝑎 ∗ 𝛾𝑤 ∗ 𝐺/(1 + 𝑤𝐺)
d We know that, ϒ = 𝐺∗𝛾𝑤 (1+𝑒) …… from Relationship 7 d ϒ = 𝐺 ∗𝛾𝑤 1 − 𝑛 (1 + 𝑛 ) ϒd = 𝐺 ∗𝛾𝑤 ( 1 − 𝑛 + 𝑛 1 − 𝑛 ) ϒd = 𝐺 ∗𝛾𝑤*(1 - n) Relationship 9: Between ϒd, G and n
ϒsat = We know that, from Relationship 5 1 + 𝑒 𝐺 ∗ ϒ𝑤 𝑒∗ϒ𝑤 ϒsat = (1 + 𝑒) + (1 + 𝑒) ∗(1 − 𝑛) 𝐺 ∗ ϒ𝑤 𝑛 ∗ϒ𝑤 ϒsat = (1 − 𝑛 + 𝑛/1 − 𝑛) + (1 − 𝑛 + 𝑛/1 − 𝑛) ϒsat = 𝐺∗ϒ𝑤∗ 1 − 𝑛 + 𝑛 ∗ϒ𝑤 Relationship 10: Between ϒ, G, and n (𝐺+ 𝑒)*ϒ𝑤
ϒsat = We know that, from Relationship 5 1 + 𝑒 𝛾′ = 1 + 𝑒 𝐺 + 𝑒 .ϒ𝑤 − 𝛾 𝛾′ = 𝐺 ∗ ϒ𝑤 ∗ 𝑒 ∗ ϒ𝑤 − 𝛾𝑤 + 𝑒 ∗ 𝛾𝑤 (1 + 𝑒) 𝛾′ = (𝐺 − 1) ∗ ϒ𝑤 (1 + 𝑒) Relationship 11: Between 𝜸′, G, andn (𝐺 + 𝑒).ϒ𝑤
We know that, from Relationship 11 𝛾′ = (𝐺 − 1) ∗ ϒW 𝛾′ = 𝐺 ∗ϒ𝑤 − (1 + 𝑒) (1 + 𝑒) 𝛾′ = 𝛾𝑑 − 𝛾𝑤 ∗ (1 − 𝑛) 𝛾𝑤 Relationship 12: Between 𝜸′, ϒ, andn (1 + 𝑒)
Relationship 13: Between ϒsat, ϒd, ϒ, and S We know that, from Relationship 5 𝛾 = 𝐺 + 𝑆 ∗ 𝑒 .ϒ𝑤 1 + 𝑒 𝛾 = 𝐺 ∗ϒ𝑤 + 𝑆 ∗( 𝑒∗ ϒ𝑤 (1 + 𝑒) 1 + 𝑒 ) 𝛾 = 𝛾𝑑 + 𝑆 ∗( − (𝐺 + 𝑒) ∗ ϒ𝑤 𝐺 ∗ϒ𝑤 1 + 𝑒 1 + 𝑒 ) 𝛾 = 𝛾𝑑 + 𝑆 ∗(𝛾𝑠𝑎𝑡 − 𝛾𝑑)
INDEX PROPERTIES OF SOIL: Those properties of soil which are used in the identification and classification of soil are known as Index Properties. Various index properties of soils are: - a. Water content b. In-situ density c. Specific gravity d. Particle size e. Consistency f. Density index
a) Oven drying method b) Pycnometer method c) Sand bath method d) Alcohol method e) Calcium carbide method f) Radiation method Methods of Water Content Determination Laboratory Methods Field Methods Following are the methods used for water content determination:
OVEN DRYING METHOD This method employs use of thermostatically controlled oven for water content determination. This is the most accurate method of water content determination. Thermostatically controlled oven Vacuum Desiccator Weighing Balance Containers with Lid
The following procedure is adopted as per IS 2720: Part 2 1. Clean the container, dry it and weight it with lid (M1). 2. Take the required quantity of the wet specimen in the container and close it with lid. Take the mass (M2) 3. Place the container with its lid removed in the oven till mass becomes constant (normally for 24 hours). 4. When the soil has dried, remove the container from the oven using tongs. Replace the lid on the container. Cool it in a desiccator. 5. Find the mass (M3) of the container with lid and dry soil sample. After all parameters are found out, find water content using following relation w = M2 - M3/M3 – M1
 In This method, the soil sample is taken in a evaporating dish. Sample is then mixed with methylated spirit.  Quantity of methylated spirit required is one milli litre for every gram of soil.  The methylated spirit is then ignited. The mixture is then stirred with spatula.  After the methylated spirit has burnt away completely dish is allowed to be cooled and mass of dry soil is obtained. ALCOHOL METHOD
DISADVANTAGES:  Cannot be used if soil contain large proportion of clay, organic matter.  Methylated spirit is volatile so extra care is required.  Not accurate.  After all parameters are found out, find water content using following relation. w = M2 - M3/M3 – M1
SAND BATH METHOD • Sand Bath Method for the determination of soil water content is a quick field method which is employed when an electric oven is not available for drying of wet soil. • Sand is kept on a tray to a height of about 3 cm. • A container is filled with wet soil and dried by keeping on the sand bath and heating with stirring. Few white papers are kept on top of the wet soil in the container. • The soil is said to be dry when these white papers turn brown. Finally, dry soil is obtained, and the water content can be determined with the help of the equation obtained for oven drying method.
This method of the determination of water content makes use of fact that when water reacts with calcium carbide, acetylene gas is produced. This test is performed as per IS 2720:Part 2 (1973). CALCIUM CARBIDE METHOD
1. Set up the balance, place the sample in the pan till the mark on the balance arm matches with the index mark. 2. Check that the cup and the body are clean. 3. Hold the body horizontally and gently deposit the levelled, scoop-full of the absorbent (Calcium Carbide) inside the chamber. 4. Transfer the weighed soil from the pan to the cup. 5. Hold cup and chamber horizontally, bringing them together without disturbing the sample and the absorbent. 6. Clamp the cup tightly into place. If the sample is bulky, reverse the above placement, that is, put the sample in the chamber and the absorbent in the cup. 7. In case of clayey soils, place all the 4 steel balls (3 smaller and 1 bigger) in the body along with the absorbent.
8. Shake the unit up and down vigorously in this position for about 15 seconds. 9. Hold the unit horizontally, rotating it for 10 seconds, so that the balls roll around the inner circumference of the body. 10. Rest for 20 seconds. 11. Repeat the above cycle until the pressure gauge reading is constant and note the reading. Usually it takes 4 to 8 minutes to achieve constant reading. This is the water content (m) obtained on wet mass basis. 12. Finally, release the pressure slowly by opening the clamp screw and taking the cup out, empty the contents and clean the instrument with a brush. 13. The water content on dry mass basis, w = m/[100-m] * 100%
Methods of Specific Gravity Determination The specific gravity of solids is frequently required for computation of several soil properties such as void ratio, degree of saturation, unit weight of solids, fine soil particle size, etc. Methods used for determination are:- 1. Pycnometer bottle method 2. Density bottle method 3. Measuring flask method 4. Gas jar method 5. Shrinkage limit method
Density Bottle Method PROCEDURE: (As per IS 2720: Part 3) • Firstly, Weigh the bottle, with stopper to the nearest 0.001g (M1). • Take the oven dried soil sample and transfer it the density bottle. Weigh the bottle with the stopper and the dry sample (M2). • Add de-aired distilled water to the density bottle just enough to cover the soil. • Shake gently to mix the soil and water. Place the bottle containing the soil and water after removing the stopper in the vacuum desiccator. • Take out the bottle from the water bath and determine the mass of the bottle and its contents (M3). • Atlast fill the bottle with water and weigh as (M4) and using the relation below find specific gravity of soil sample. G = 𝑀2 − 𝑀1 ) 𝑀2 − 𝑀1 − (𝑀3 − 𝑀4
Stepwise procedure to determine Specific Gravity • Density Bottle of 50ml capacity, provided with nose. • The nose has a small opening on the top to help escape of air. Density Bottle
Pycnometer Method PROCEDURE: (As per IS 2720: Part 3) • The procedure for finding specific gravity using pycnometer is same as that of density bottle. • The capacity of bottle is different, which is 1000 ml. • This method is widely adopted for finding the specific gravity of coarse grained soil usually having size greater than 4.75 mm • Pycnometer Bottle of 1000ml capacity, provided with lid. • The lid has a small opening on the top (2mm) to help escape of air. Pycnometer Bottle
A measuring flask of 250 ml capacity, with a graduation marked at that level .It is fitted with an adaptor for connecting it to a vacuum line for removing entrapped air. This method is similar to density bottle method. About 80-100 g of oven drying sample is taken. Suitable for fine grained and medium grained soil. Measuring Flask Method Gas Jar Method In this method, a gas jar of about 1 litre capacity is used. The jar is fitted with rubber bung. The gas jar serve as pycnometer. The method is similar to pycnometer method.
Methods of Unit Weight Determination The Unit Weight of soil is frequently required for computation of several soil properties such as void ratio, degree of saturation, unit weight of solids, etc. Apart this also helpful when finding the bearing capacity of soil and compaction effort Methods used for determination are:- 1. Core Cutter method 2. Sand Replacement method 3. Water Displacement method 4. Rubber balloon method.
1. Measure the inside dimensions of the core cutter 2. Determine empty weight of core cutter (M1) 3. Level the surface, about 300 mm square in area. 4. Place the dolly over the top of the core cutter and press the core cutter into the soil mass using the rammer. 5. Stop the process of pressing when about 15 mm of the dolly protrudes above the soil surface. 6. Remove the soil surrounding the core cutter and take out the core cutter. 7. Remove the dolly. Trim the top and bottom surface of the core cutter carefully using a straight edge. 8. Weight the core cutter filled with the soil (M2). 9. Remove the core of the soil from the cutter. Determine the water content Core Cutter Method
Steps involved in core cutter test Core Cutter details
M1 M2 Firstly Bulk density, is computed using following relation: 𝛒 = 𝑴𝟐 − 𝑴𝟏 𝑽 Secondly dry density, is computed using following relation: 𝛒d = 𝛒 𝟏 + 𝒘
Relative Density  Relative density is the measure of compactness of cohesionless soil. Relative density or density index is the ratio of the difference between the void ratios of a cohesionless soil in its loosest state and existing natural state to the difference between its void ratio in the loosest and densest states.  Determination of relative density is helpful in evaluating compaction state of coarse grained soils and also assessing the safe bearing capacity in case of sandy soils. The density index is defined as, ID = (emax – e / emax – emin) Where, emax = void ratio in the loosest state emin = void ratio in the densest state e = natural void ratio of the deposit
Relationship between Density Index and Void Ratio Source: https://i1.wp.com/civilengineering.blog/wp content/uploads/2020/02/SmartSelect_20200214-183420_Amazon-Kindle.jpg?resize=400%2C400&ssl=1
The slope of the straight line AB, representing the relationship between ID and e is given by tanθ =1/(emax – emin) cotθ = (emax – emin) Now, for an intermediate value e we have, (emax – e) = ID*cotθ or ID= emax− e*cotθ Substituting the value of cotθ from equation ii, we get ID= emax− e/emax− emin From fig., we observe that when e = emax, ID = 0 and when e = emin, ID = 1. Now from equation, we have e = G*γw/γd−1 emax= G*γw/γdmin− 1 emin= G*γw/γdmax − 1 [ID= γd − γdmin/ γdmax − γdmin]*[γdmax/γd]
 “Soil Mechanics & Foundation Engineering”, Dr. K.R.Arora  “Basic & Applied Soil Mechanics”, Gopal Ranjan & A.S.R. Rao  “Soil Mechanics & Foundation”, B.C.Punmia, Ashok Kumar Jain, Arun Kumar Jain  “Soil Mechanics”, T.William Lambe  “Geotechnical Engineering Hand Book”, Ernst and Sohn  “Methods of Test for Soils (IS : 2720)”, Bureau of Indian Standards References

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Soil - Basic Definitions & Relationships

  • 1.
    Arbaz Mubarak Kazi, B.E,M.E (Civil Engineering) Email: arbaazkazi91@gmail.com https://gtearchives.wordpress.com www.linkedin.com/in/arbaz-kazi-20747570 SOIL - BASIC DEFINITIONS & RELATIONSHIPS “Everyday is an Adventure When you are Civil Engineer”
  • 2.
    BASIC DEFINITIONS ANDRELATIONSHIPS Soil has two principle components: solid particles and voids. Voids are the empty spaces in between the solid particles that may be filled with air or liquid or both. These components make solid a complex matter and difficult to study about. Therefore, with a view to simplify the study, these particles are segregated and shown in different layers (like a block diagram). The diagram which shows solid, water and air of soil separately is known as 3-phase diagram (figure shown) Three Phase Diagram:
  • 3.
    Here, W = TotalWeight = Weight of solid particles + Weight of water (Weight of air can be neglected because of its low density) V = Total Volume = Volume of solid particles + Volume of water + Volume of air Ws = Weight of solid particles Wa = Weight of air Vs = Volume of solid particles Vw = Volume of water Vv = Volume of voids = Total volume (V) - Volume of solid particles (Vs)
  • 4.
    TWO PHASE DIAGRAMFOR FULLY SAURATED SOIL • In this case two phases, solid, water is present. • Air is absent. Voids are filled with water only.
  • 5.
    • Moisture Content:It is defined as the ratio of mass of water to mass of solids. It is denoted by (w) and expressed in percentage. 𝑤 = 𝑀𝑤/𝑀𝑠 x 100 • Void ratio: It is defined as the ratio of the volume of voids to the volume of solids. It is denoted by (e). For coarse grained soil, void ratio is larger and for fine grained soil it is vice-versa 𝑒 = 𝑉𝑣/𝑉𝑠 • Porosity: It is defined as the ratio of the volume of voids to the total volume. It is denoted by (n). n = Vv/V FUNDAMENTAL DEFINITION:
  • 6.
    Relationship 1: BetweenVoid ratio and Porosity We Know, V = Vs + Vv 𝑛 = 𝑉 𝑣 𝑉 = 𝑉 𝑣 𝑉 𝑠 + 𝑉 𝑣 = 𝑉 𝑣/𝑉 𝑠 𝑉 𝑠 𝑉 𝑠 + 𝑉 𝑣 𝑉 𝑠 = 𝑒 1 + 𝑒 𝑒 = 𝑉 𝑣 𝑉 𝑠 = 𝑉 𝑣 𝑉 − 𝑉 𝑣 = 𝑉 𝑣/𝑉 𝑉 𝑉 − 𝑉 𝑣 𝑉 = 𝑛 1 − 𝑛
  • 7.
    • Degree ofsaturation: It is the ratio of the volume of water to the volume of voids and is generally expressed as a percentage and denoted by (S). S= 𝑉𝑤/𝑉𝑣 In case of fully saturated soil, voids are completely filled with water. There is no air. Vw = Vv, Hence S = 1. In case of fully dry soil, voids are completely filled with air. There is no water i.e. Vw = 0, Hence S = 0. • Air Content: It is defined as volume of air to volume of voids. It is denoted by (ac) ac= 𝑉𝑎/𝑉𝑣
  • 8.
    • Percentage aircontent: It is defined as volume of air to total volume. It is denoted by (na). It is expressed as percentage. Relationship 2: Between Percentage Air content, Air content & Porosity na= 𝑉𝑎/𝑉= 𝑉𝑎/𝑉𝑣 * 𝑉𝑣/𝑉= n*ac • Density: It is the ratio of the total mass to the total volume of the soil. It is denoted by (ρ) and is also referred as bulk density (ρb) or mass density. ρ or ρb = M/V
  • 9.
    • Unit weight:It is the ratio of the total weight to the total volume of the soil. It is denoted by (ϒ) and is also referred as bulk unit weight(ϒb) or weight density. ϒ or ϒb = W/V • Dry Density: The dry density is defined as the ratio of the mass of soil solids to the total volume. It is denoted by (ρd). ρd = MS/V • Dry Unit weight: The dry unit weight is defined as the ratio of the weight of soil solids to the total volume. It is denoted by (ϒd). ϒd = WS/V
  • 10.
    • Density ofSolids: The density of solids is defined as the ratio of the mass of soil solids to the total volume of soil solids. It is denoted by (ρs). ρs = MS/VS • Unit weight of Solids: The dry unit weight is defined as the ratio of the weight of soil solids to the total volume of soil solids. It is denoted by (ϒS). ϒS = WS/VS • Saturated Density: The saturated density is defined as the ratio of the saturated mass of soil to the total volume. It is denoted by (ρsat). ρsat = Msat/V
  • 11.
    • Saturated Unitweight: The saturated unit weight is defined as the ratio of the saturated weight of soil to the total volume. It is denoted by (ϒsat). ϒsat = Wsat/V • Submerged Unit weight: The submerged unit weight is the effective mass per unit volume when the soil is submerged below standing water or below the ground water table. It is denoted by (ϒ’) 𝛾′ = (𝛾𝑠𝑎𝑡 − 𝛾𝑤) 𝑉
  • 12.
  • 13.
    • Specific Gravity:It is defined as the ratio of the weight of a given volume of soil solids to the weight of an equal volume of distilled water. G = ϒS/ϒw or ρs/ρw Typical values of specific gravity for different soils are given below: Type of Soil Sp. Gravity Type of Soil Sp. Gravity GRAVEL 2.65 - 2.68 SILTS 2.66 – 2.70 SAND 2.65 - 2.68 INORGANIC CLAY 2.68 – 2.80 SILTY SAND 2.66 – 2.70 ORGANIC SOILS below 2.0
  • 14.
    • Mass SpecificGravity: The specific gravity of a mass of soil (including air, water and solids) is termed as bulk or mass specific gravity Gm. It is expressed as 𝐺𝑚 = 𝛾 𝛾𝑤 𝑜𝑟 𝜌 𝜌𝑤
  • 15.
    Relationship 3: Between𝒏𝒂,𝒆 & 𝐒 We Know, 𝑉 𝑣 − 𝑉𝑤 = 𝑉 Also, 𝑆 = / 𝑉 𝑤 𝑉𝑣 Hence, 𝑆∗ 𝑉 𝑣 = 𝑉𝑤 𝑛𝑎= 𝑉 𝑣 − 𝑆 ∗ 𝑉 𝑣 𝑉 𝑎 𝑉 𝑣*(1 − 𝑆) 𝑛 = 𝑉 𝑎 𝑛 = 𝑛∗(1 − 𝑆) Also, 𝑛 = e / 1 + e Hence, 𝑎 𝑒∗ (1 − 𝑆) 𝑛 = 1 + 𝑒 𝑛𝑎 = ൗ 𝑉 𝑎 𝑉 𝑤
  • 16.
    Relationship 4: Betweene, G, w and S Take Vs = 1, But e = Vv/Vs and Vv = e, therefore V = 1+e
  • 17.
    𝑤 = 𝑊 𝑤 𝑊 𝑠 = 𝛾𝑊 ∗𝑉 𝑤 𝛾𝑠 ∗ 𝑉 𝑠 Also, S = VW/VV and G = ϒS/ϒW 𝐻𝑒𝑛𝑐𝑒, 𝑤 = 𝑊 𝑤 𝑊 𝑠 = 𝛾𝑊 ∗ 𝑉 𝑤 𝛾𝑠 ∗ 𝑉 𝑠 = 𝛾𝑊 ∗ 𝑉 𝑣 ∗ 𝑆 𝐺 ∗ 𝛾𝑤 ∗ 𝑉 𝑠 ………………. (1) But Vv/Vs = e, so equation (1) becomes 𝑤. 𝐺 = S. 𝑒
  • 18.
    We know that, ϒ= = 𝑊 𝑊𝑠+ 𝑊𝑤 𝑉 𝑉 𝑉 ϒ = ϒ𝑠*𝑉𝑠+ϒ𝑤*𝑉𝑤 …… (1) (ϒ𝑠 = Ws/Vs and ϒ𝑤=Ww/Vw) From Fig. Vs = 1 and Vv = e ϒ = 𝐺*ϒ𝑤*1+ϒ𝑤*𝑆*𝑒 𝑉 …….. (G = ϒs/ϒw) and (Vw = S*Vv) 1+𝑒 ϒ = 𝐺+𝑆*e *ϒ𝑤 ……………….(2) Relationship 5: Between ϒ, G, e and S
  • 19.
    If soil isfully dry eq. (2) becomes, 𝐺.ϒ𝑤 ϒsat = ϒd = 1 + 𝑒 If soil is fully saturated eq. (2) becomes, 𝐺 + 𝑒 *ϒ𝑤 1 + 𝑒 Relationship 6: Between 𝒂𝒄 andS 𝑐 𝑎 = / 𝑉 𝑎 𝑉 𝑣 1 − 𝑆 = 𝑉 𝑣 = ൗ 𝑉 𝑣 − 𝑉 𝑤 𝑉 𝑣
  • 20.
    We know that,ϒ = 𝑊 𝑉 ϒ = 𝑊𝑠+ 𝑊𝑤 𝑉 𝑉 ϒ = 𝑊𝑠 + 𝑤*𝑊𝑠 ……………. (w = Mw/Ms) ϒ = 𝑊𝑠*(1 + 𝑤) 𝑉 ϒ = ϒ𝑑* 1 + 𝑤 ………….. (Ws/V = ϒd) ϒ ϒd = (1 + 𝑤) Relationship 7: Between ϒd, ϒand w
  • 21.
    Relationship 8: Betweenϒd, G, w and 𝒏𝒂 𝑉=𝑉 𝑎+ 𝑉𝑤+ 𝑉 𝑠 𝑉=𝑉 𝑎+ 𝛾𝑤 + 𝑊 𝑤 𝑊𝑠 𝛾 𝑠 1 = 𝑉 𝑎 𝑉 + 𝑊 𝑤 𝛾𝑤 ∗ 𝑉 + 𝑊 𝑠 𝛾𝑠 ∗ 𝑉 1 = 𝑉 𝑎 𝑉 + 𝑊 𝑠 ∗ 𝑤 𝛾𝑤 ∗ 𝑉 + 𝑊 𝑠 𝛾𝑠 ∗ 𝑉 1 = 𝑉 𝑎 𝑉 + 𝛾𝑑 ∗ 𝑤 𝛾𝑤 + 𝛾𝑑 𝛾𝑠 1 − 𝑛𝑎 = 𝛾𝑑 𝛾𝑤 ∗ ( 1 + 𝑤 𝐺 ) 𝛾𝑑 = 1 − 𝑛𝑎 ∗ 𝛾𝑤 ∗ 𝐺/(1 + 𝑤𝐺)
  • 22.
    d We know that,ϒ = 𝐺∗𝛾𝑤 (1+𝑒) …… from Relationship 7 d ϒ = 𝐺 ∗𝛾𝑤 1 − 𝑛 (1 + 𝑛 ) ϒd = 𝐺 ∗𝛾𝑤 ( 1 − 𝑛 + 𝑛 1 − 𝑛 ) ϒd = 𝐺 ∗𝛾𝑤*(1 - n) Relationship 9: Between ϒd, G and n
  • 23.
    ϒsat = We knowthat, from Relationship 5 1 + 𝑒 𝐺 ∗ ϒ𝑤 𝑒∗ϒ𝑤 ϒsat = (1 + 𝑒) + (1 + 𝑒) ∗(1 − 𝑛) 𝐺 ∗ ϒ𝑤 𝑛 ∗ϒ𝑤 ϒsat = (1 − 𝑛 + 𝑛/1 − 𝑛) + (1 − 𝑛 + 𝑛/1 − 𝑛) ϒsat = 𝐺∗ϒ𝑤∗ 1 − 𝑛 + 𝑛 ∗ϒ𝑤 Relationship 10: Between ϒ, G, and n (𝐺+ 𝑒)*ϒ𝑤
  • 24.
    ϒsat = We knowthat, from Relationship 5 1 + 𝑒 𝛾′ = 1 + 𝑒 𝐺 + 𝑒 .ϒ𝑤 − 𝛾 𝛾′ = 𝐺 ∗ ϒ𝑤 ∗ 𝑒 ∗ ϒ𝑤 − 𝛾𝑤 + 𝑒 ∗ 𝛾𝑤 (1 + 𝑒) 𝛾′ = (𝐺 − 1) ∗ ϒ𝑤 (1 + 𝑒) Relationship 11: Between 𝜸′, G, andn (𝐺 + 𝑒).ϒ𝑤
  • 25.
    We know that,from Relationship 11 𝛾′ = (𝐺 − 1) ∗ ϒW 𝛾′ = 𝐺 ∗ϒ𝑤 − (1 + 𝑒) (1 + 𝑒) 𝛾′ = 𝛾𝑑 − 𝛾𝑤 ∗ (1 − 𝑛) 𝛾𝑤 Relationship 12: Between 𝜸′, ϒ, andn (1 + 𝑒)
  • 26.
    Relationship 13: Betweenϒsat, ϒd, ϒ, and S We know that, from Relationship 5 𝛾 = 𝐺 + 𝑆 ∗ 𝑒 .ϒ𝑤 1 + 𝑒 𝛾 = 𝐺 ∗ϒ𝑤 + 𝑆 ∗( 𝑒∗ ϒ𝑤 (1 + 𝑒) 1 + 𝑒 ) 𝛾 = 𝛾𝑑 + 𝑆 ∗( − (𝐺 + 𝑒) ∗ ϒ𝑤 𝐺 ∗ϒ𝑤 1 + 𝑒 1 + 𝑒 ) 𝛾 = 𝛾𝑑 + 𝑆 ∗(𝛾𝑠𝑎𝑡 − 𝛾𝑑)
  • 27.
    INDEX PROPERTIES OFSOIL: Those properties of soil which are used in the identification and classification of soil are known as Index Properties. Various index properties of soils are: - a. Water content b. In-situ density c. Specific gravity d. Particle size e. Consistency f. Density index
  • 28.
    a) Oven dryingmethod b) Pycnometer method c) Sand bath method d) Alcohol method e) Calcium carbide method f) Radiation method Methods of Water Content Determination Laboratory Methods Field Methods Following are the methods used for water content determination:
  • 29.
    OVEN DRYING METHOD Thismethod employs use of thermostatically controlled oven for water content determination. This is the most accurate method of water content determination. Thermostatically controlled oven Vacuum Desiccator Weighing Balance Containers with Lid
  • 30.
    The following procedureis adopted as per IS 2720: Part 2 1. Clean the container, dry it and weight it with lid (M1). 2. Take the required quantity of the wet specimen in the container and close it with lid. Take the mass (M2) 3. Place the container with its lid removed in the oven till mass becomes constant (normally for 24 hours). 4. When the soil has dried, remove the container from the oven using tongs. Replace the lid on the container. Cool it in a desiccator. 5. Find the mass (M3) of the container with lid and dry soil sample. After all parameters are found out, find water content using following relation w = M2 - M3/M3 – M1
  • 31.
     In Thismethod, the soil sample is taken in a evaporating dish. Sample is then mixed with methylated spirit.  Quantity of methylated spirit required is one milli litre for every gram of soil.  The methylated spirit is then ignited. The mixture is then stirred with spatula.  After the methylated spirit has burnt away completely dish is allowed to be cooled and mass of dry soil is obtained. ALCOHOL METHOD
  • 32.
    DISADVANTAGES:  Cannot beused if soil contain large proportion of clay, organic matter.  Methylated spirit is volatile so extra care is required.  Not accurate.  After all parameters are found out, find water content using following relation. w = M2 - M3/M3 – M1
  • 33.
    SAND BATH METHOD •Sand Bath Method for the determination of soil water content is a quick field method which is employed when an electric oven is not available for drying of wet soil. • Sand is kept on a tray to a height of about 3 cm. • A container is filled with wet soil and dried by keeping on the sand bath and heating with stirring. Few white papers are kept on top of the wet soil in the container. • The soil is said to be dry when these white papers turn brown. Finally, dry soil is obtained, and the water content can be determined with the help of the equation obtained for oven drying method.
  • 34.
    This method ofthe determination of water content makes use of fact that when water reacts with calcium carbide, acetylene gas is produced. This test is performed as per IS 2720:Part 2 (1973). CALCIUM CARBIDE METHOD
  • 35.
    1. Set upthe balance, place the sample in the pan till the mark on the balance arm matches with the index mark. 2. Check that the cup and the body are clean. 3. Hold the body horizontally and gently deposit the levelled, scoop-full of the absorbent (Calcium Carbide) inside the chamber. 4. Transfer the weighed soil from the pan to the cup. 5. Hold cup and chamber horizontally, bringing them together without disturbing the sample and the absorbent. 6. Clamp the cup tightly into place. If the sample is bulky, reverse the above placement, that is, put the sample in the chamber and the absorbent in the cup. 7. In case of clayey soils, place all the 4 steel balls (3 smaller and 1 bigger) in the body along with the absorbent.
  • 36.
    8. Shake theunit up and down vigorously in this position for about 15 seconds. 9. Hold the unit horizontally, rotating it for 10 seconds, so that the balls roll around the inner circumference of the body. 10. Rest for 20 seconds. 11. Repeat the above cycle until the pressure gauge reading is constant and note the reading. Usually it takes 4 to 8 minutes to achieve constant reading. This is the water content (m) obtained on wet mass basis. 12. Finally, release the pressure slowly by opening the clamp screw and taking the cup out, empty the contents and clean the instrument with a brush. 13. The water content on dry mass basis, w = m/[100-m] * 100%
  • 37.
    Methods of SpecificGravity Determination The specific gravity of solids is frequently required for computation of several soil properties such as void ratio, degree of saturation, unit weight of solids, fine soil particle size, etc. Methods used for determination are:- 1. Pycnometer bottle method 2. Density bottle method 3. Measuring flask method 4. Gas jar method 5. Shrinkage limit method
  • 38.
    Density Bottle Method PROCEDURE:(As per IS 2720: Part 3) • Firstly, Weigh the bottle, with stopper to the nearest 0.001g (M1). • Take the oven dried soil sample and transfer it the density bottle. Weigh the bottle with the stopper and the dry sample (M2). • Add de-aired distilled water to the density bottle just enough to cover the soil. • Shake gently to mix the soil and water. Place the bottle containing the soil and water after removing the stopper in the vacuum desiccator. • Take out the bottle from the water bath and determine the mass of the bottle and its contents (M3). • Atlast fill the bottle with water and weigh as (M4) and using the relation below find specific gravity of soil sample. G = 𝑀2 − 𝑀1 ) 𝑀2 − 𝑀1 − (𝑀3 − 𝑀4
  • 39.
    Stepwise procedure todetermine Specific Gravity • Density Bottle of 50ml capacity, provided with nose. • The nose has a small opening on the top to help escape of air. Density Bottle
  • 40.
    Pycnometer Method PROCEDURE: (Asper IS 2720: Part 3) • The procedure for finding specific gravity using pycnometer is same as that of density bottle. • The capacity of bottle is different, which is 1000 ml. • This method is widely adopted for finding the specific gravity of coarse grained soil usually having size greater than 4.75 mm • Pycnometer Bottle of 1000ml capacity, provided with lid. • The lid has a small opening on the top (2mm) to help escape of air. Pycnometer Bottle
  • 41.
    A measuring flaskof 250 ml capacity, with a graduation marked at that level .It is fitted with an adaptor for connecting it to a vacuum line for removing entrapped air. This method is similar to density bottle method. About 80-100 g of oven drying sample is taken. Suitable for fine grained and medium grained soil. Measuring Flask Method Gas Jar Method In this method, a gas jar of about 1 litre capacity is used. The jar is fitted with rubber bung. The gas jar serve as pycnometer. The method is similar to pycnometer method.
  • 42.
    Methods of UnitWeight Determination The Unit Weight of soil is frequently required for computation of several soil properties such as void ratio, degree of saturation, unit weight of solids, etc. Apart this also helpful when finding the bearing capacity of soil and compaction effort Methods used for determination are:- 1. Core Cutter method 2. Sand Replacement method 3. Water Displacement method 4. Rubber balloon method.
  • 43.
    1. Measure theinside dimensions of the core cutter 2. Determine empty weight of core cutter (M1) 3. Level the surface, about 300 mm square in area. 4. Place the dolly over the top of the core cutter and press the core cutter into the soil mass using the rammer. 5. Stop the process of pressing when about 15 mm of the dolly protrudes above the soil surface. 6. Remove the soil surrounding the core cutter and take out the core cutter. 7. Remove the dolly. Trim the top and bottom surface of the core cutter carefully using a straight edge. 8. Weight the core cutter filled with the soil (M2). 9. Remove the core of the soil from the cutter. Determine the water content Core Cutter Method
  • 44.
    Steps involved incore cutter test Core Cutter details
  • 45.
    M1 M2 Firstly Bulk density,is computed using following relation: 𝛒 = 𝑴𝟐 − 𝑴𝟏 𝑽 Secondly dry density, is computed using following relation: 𝛒d = 𝛒 𝟏 + 𝒘
  • 46.
    Relative Density  Relativedensity is the measure of compactness of cohesionless soil. Relative density or density index is the ratio of the difference between the void ratios of a cohesionless soil in its loosest state and existing natural state to the difference between its void ratio in the loosest and densest states.  Determination of relative density is helpful in evaluating compaction state of coarse grained soils and also assessing the safe bearing capacity in case of sandy soils. The density index is defined as, ID = (emax – e / emax – emin) Where, emax = void ratio in the loosest state emin = void ratio in the densest state e = natural void ratio of the deposit
  • 47.
    Relationship between DensityIndex and Void Ratio Source: https://i1.wp.com/civilengineering.blog/wp content/uploads/2020/02/SmartSelect_20200214-183420_Amazon-Kindle.jpg?resize=400%2C400&ssl=1
  • 48.
    The slope ofthe straight line AB, representing the relationship between ID and e is given by tanθ =1/(emax – emin) cotθ = (emax – emin) Now, for an intermediate value e we have, (emax – e) = ID*cotθ or ID= emax− e*cotθ Substituting the value of cotθ from equation ii, we get ID= emax− e/emax− emin From fig., we observe that when e = emax, ID = 0 and when e = emin, ID = 1. Now from equation, we have e = G*γw/γd−1 emax= G*γw/γdmin− 1 emin= G*γw/γdmax − 1 [ID= γd − γdmin/ γdmax − γdmin]*[γdmax/γd]
  • 49.
     “Soil Mechanics& Foundation Engineering”, Dr. K.R.Arora  “Basic & Applied Soil Mechanics”, Gopal Ranjan & A.S.R. Rao  “Soil Mechanics & Foundation”, B.C.Punmia, Ashok Kumar Jain, Arun Kumar Jain  “Soil Mechanics”, T.William Lambe  “Geotechnical Engineering Hand Book”, Ernst and Sohn  “Methods of Test for Soils (IS : 2720)”, Bureau of Indian Standards References