Soil Mechanics III. SOIL COMPOSITION WEIGHT-VOLUME RELATIONSHIPS TERMINOLOGY AND DEFINITIONS

Soil

Basic Terminology

Basic Terminology Porosity. Porosity of a soil mass is the ratio of the volume of voids to the total volume of the soil mass. It is denoted by the letter symbol n and is commonly expressed as a percentage: n = V v V x 100 V v = V a + V w V = V a + V w + V s Void Ratio. Void ratio of a soil mass is defined as the ratio of the volume of voids to the volume of solids in the soil mass. It is denoted by the letter symbol e and is generally expressed as a decimal fraction: e = V v V s

Basic Terminology Degree of Saturation. Degree of saturation of a soil mass is defined as the ratio of the volume of water in the voids to the volume of voids. It is designated by the letter symbol S and is commonly expressed as a percentage: S = V w V v x 100 For a fully saturated soil mass, V w = V v Therefore, for a saturated soil mass, S = 100%. For a dry soil mass, V w = 0. Therefore, for a perfectly dry soil mass, S = 0. The soil is considered to be a two-phase system in these conditions.

Basic Terminology Percent Air Voids. Percent air voids of a soil mass is defined as the ratio of the volume of air voids to the total volume of the soil mass. It is denoted by the letter symbol n a and is commonly expressed as a percentage: n a = V a V x 100 Air Content. Air content of a soil mass is defined as the ratio of the volume of air voids to the total volume of voids. It is designated by the letter symbol a c and is commonly expressed as a percentage: a c = V a V v x 100

Basic Terminology Water (Moisture) Content. Water content or Moisture content of a soil mass is defined as the ratio of the weight of water to the weight of solids (dry weight) of the soil mass. It is denoted by the letter symbol w and is commonly expressed as a percentage: w = W w W s x 100 w = W W s W s x 100 In the field of Geology, water content is defined as the ratio of weight of water to the total weight of soil mass ; this difference has to be borne in mind.

Basic Terminology Bulk (Mass) Unit Weight. Bulk unit weight or Mass unit weight of a soil mass is defined as the weight per unit volume of the soil mass. It is denoted by the letter symbol γ. γ = W V W = W w + W s V = V a + V w + V s The term density is loosely used for unit weight in soil mechanics, although, strictly speaking, density means the mass per unit volume and not weight.

Basic Terminology Unit Weight of Solids. Unit weight of solids is the weight of soil solids per unit volume of solids alone. It is also sometimes called the absolute unit weight of a soil. It is denoted by the letter symbol γ s : γ s = W s V s Unit Weight of Water. Unit weight of water is the weight per unit volume of water. It is denoted by the letter symbol γ w : γ w = W w V w

Basic Terminology Submerged (Buoyant) Unit Weight. The Submerged unit weight or Buoyant unit weight of a soil is its unit weight in the submerged condition. In other words, it is the submerged weight of soil solid (W s ) sub per unit of total volume, V of the soil. It is denoted by the letter symbol γ : γ = (W s) sub V = γ sat γ w (W s ) sub = W s V s. γ w (W s ) sub = W W w V s. γ w (W s ) sub = W V w. γ w V s. γ w (W s ) sub = W γ w (V w V s ) (W s ) sub = W V. γ w (W s ) sub V = W V V. γ w V

Basic Terminology Saturated Unit Weight. The Saturated unit weight is defined as the bulk unit weight of the soil mass in the saturated condition. This is denoted by the letter symbol γ sat. Dry Unit Weight. The Dry unit weight is defined as the weight of soil solids per unit of total volume ; the former is obtained by drying the soil, while the latter would be got prior to drying. The dry unit weight is denoted by the letter symbol γ d and is given by: γ d = W s V

Basic Terminology Specific Gravity of Solids. The specific gravity of soil solids is defined as the ratio of the unit weight of solids (absolute unit weight of soil) to the unit weight of water at the standard temperature (4 C). This is denoted by the letter symbol G s and is given by: G s = γ s γ o This is also known as Absolute specific gravity and, in fact, more popularly as Grain Specific Gravity. Since this is relatively constant value for a given soil, it enters into many computations in the field of soil mechanics. γ o is the symbol used to denote the unit weight of water at 4 C.

Basic Terminology Specific Gravity of Water. Specific gravity of water is defined as the ratio of the unit weight of water to the unit weight of water at the standard temperature (4 C). It is denoted by the letter symbol, G w and is given by: G w = γ w γ o Since the variation of the unit weight of water with temperature is small, this value is very nearly unity, and in practice is taken as such. γ o is the symbol used to denote the unit weight of water at 4 C.

Basic Terminology Mass Specific Gravity. The Mass specific gravity of a soil may be defined as the ratio of mass or bulk unit weight of soil to the unit weight of water at the standard temperature (4 C). This is denoted by the letter symbol G m and is given by: G m = γ γ o This is also referred to as bulk specific gravity or apparent specific gravity. γ o is the symbol used to denote the unit weight of water at 4 C.

Certain Important Relationships

Unit-Phase Diagram

Certain Important Relationships

Problem 1 For a saturated soil, show that: γ sat = e w 1 + w 1 + e. γ w Problem Set 1

Problem 2 Problem Set 1 A moist soil has these values: V = 7.08x10-3 m 3, m = 13.95 kg, w = 9.8%, and Gs = 2.66. Determine the following: 2.1 moist density (1970.339 kg/m 3 ) 2.2 dry density (1794.492 kg/m 3 ) 2.3 void ratio (0.482) 2.4 porosity (0.325) 2.5 degree of saturation (54.036%) 2.6 volume occupied by water (1.245x10-3 m 3 )

Problem 3 Problem Set 1 In the natural state, a moist soil has a volume of 0.0093 m 3, and weighs 177.6 N. The oven dry weight of the soil is 153.6 N. If Gs = 2.71, calculate the: 3.1 moisture content (15.625%) 3.2 moist unit weight (19.097 kn/m 3 ) 3.3 dry unit weight (16.516 kn/m 3 ) 3.4 void ratio (0.61) 3.5 porosity (0.379) 3.6 degree of saturation (69.449%)

Problem 4 The dry density of a sand with a porosity of 0.387 is 1600 kg/m 3. Find: 4.1 the void ratio of the soil (0.631) 4.2 the specific gravity of the soil solids (2.61) Problem Set 1

Problem 5 For a saturated soil, given w = 40% and Gs = 2.71, determine: 5.1 the saturated unit weight (17.859 kn/m 3 ) 5.2 the dry unit weight (12.757 kn/m 3 ) Problem Set 1

Problem 6 Problem Set 1 The mass of a moist soil sample collected from the field is 465 g, and its oven dry mass is 405.76 g. The specific gravity of the soil solids was determined in the laboratory to be 2.68. If the void ratio of the soil in the natural state is 0.83, find the following: 6.1 the moist unit weight of the soil in the field (16.464 kn/m 3 ) 6.2 the dry unit weight of the soil in the field (14.367 kn/m 3 ) 6.3 the weight of water to be added per m 3 of soil in the field for saturation (2.352 kn/m 3 )

Problem 7 Problem Set 1 For a given sandy soil, the void ratio in its loosest and densest conditions are 0.75 and 0.46, respectively. What is the moist unit weight of compaction in the field if Gs = 2.68, Dr = 78%, and w = 9%? (18.804 kn/m 3 )

Relative Density The term relative density (or density index) is commonly used to indicate the in-situ denseness or looseness of granular soil (or the state of compactness of a soil mass). This is used in relation to coarse-grained soils or sands. D r = D r = e max e 0 e max e min 1 γ 1 d min γ d 1 γ 1 D r = d min γ d max γ d max γ d e max, void ratio of the soil in loosest state e min, void ratio of the soil in densest state e 0, void ratio of the soil deposit (in-situ state) γ d max, dry unit weight in densest state γ d min, dry unit weight in loosest state γ d, dry unit weight (in-situ state) γ d γ d min γ d max γ d min

Problem 8 Problem Set 1 The weight of the moist soil as excavated from a hole is 895 g with a volume of 426 cm 3. After drying its weight was only 779 g. Of the dried soil only 400 g was poured into a vessel in a very loose state, and its volume was subsequently determined to be 276 cm 3. That same 400 g dried soil was then vibrated and tamped to a volume of 212 cm 3. 8.1 Compute the minimum dry unit weight. (14.217 kn/m 3 ) 8.2 Compute the maximum dry unit weight. (18.509 kn/m 3 ) 8.3 Compute the relative density of the soil sample. (89.5%)