BASIC QUANTITIES - SATURATED UNIT MASS, SATURATED UNIT WEIGHT, SUBMERGED UNIT MASS, SUBMERGED UNIT WEIGHTS - SOIL MECHANICS (StudyCivilEngg.com)

SATURATED UNIT MASS, SATURATED UNIT WEIGHT, SUBMERGED UNIT MASS, SUBMERGED UNIT WEIGHTS

SUBJECT : SOIL MECHANICS

SATURATED UNIT MASS OR SATURATED MASS DENSITY

What is Saturated Unit Mass or Saturated Mass Density?

Saturated unit mass or Saturated mass density of a soil mass is defined as the bulk unit mass of the soil mass in  saturated condition. In other words saturated unit mass or saturated mass density of a soil mass is the total mass of  the soil mass in saturated condition per unit of total volume of the soil mass. It is denoted by symbol ρ_sat. Thus 

ρ_sat  =  M_sat/V

SATURATED UNIT WEIGHT OR SATURATED WEIGHT DENSITY

What is Saturated Unit Weight or Saturated Weight Density?

Saturated unit weight or Saturated weight density of a soil mass is defined as the bulk unit weight of the soil mass  in saturated condition. In other words saturated unit weight or saturated weight density of a soil mass is the total  weight of the soil mass in saturated condition per unit of total volume of the soil mass. It is denoted by symbol γsat.  Thus

γ_sat  =  W_sat/V

SUBMERGED UNIT MASS OR SUBMERGED MASS DENSITY

What is Submerged Unit Mass or Submerged Mass Density?

Submerged unit mass or Submerged mass density of a soil mass is defined as the bulk unit mass of the soil mass in  submerged condition. In other words submerged unit mass or submerged mass density of a soil mass is the submerged mass of solids or solid particles of the soil mass per unit of total volume of the soil mass. It is denoted by symbol ρ′ or ρ_sub. Thus

ρ′ or ρ_sub = M_s(sub)/V

When the soil mass is submerged the mass of the solids or solid particles of the soil mass is reduced due to buoyancy. The submerged mass M_s(sub) of the solids or solid particles of the soil mass is therefore equal to the mass of the solids or solid particles in air minus the mass of water displaced by the solids or solid particles. Thus

M_s(sub) = M_s - V_sρ_w

Since a submerged soil mass is invariably saturated,

M_s = M_sat - M_w

Thus, M_s(sub) = M_sat - M_w- V_sρ_w = M_sat - V_wρ_w- V_sρ_w = M_sat - (V_w+V_s)ρ_w

Since the soil mass is submerged the voids must be full of water, the total volume V, then, must be equal to (V_w+V_s). Thus M_s(sub) may be written as  M_s(sub) = M_sat - Vρ_w

Dividing throughout by V, the total volume of the soil mass,

M_s(sub)/V = M_sat/V = ρ_w

or ρ′ or ρ_sub = ρ_sat - ρ_w

SUBMERGED UNIT WEIGHT OR SUBMERGED WEIGHT DENSITY

Submerged unit weight or Submerged weight density of a soil mass is defined as the bulk unit weight of the soil mass in submerged condition. In other words submerged unit weight or submerged weight density of a soil mass is the submerged weight of solids or solid particles of the soil mass per unit of total volume of the soil mass. It is denoted by symbol γ´ or γ_sub. Thus 

γ′ or γ_sub= W_s(sub)/V

The submerged unit weight is also known as ‘buoyant unit weight’. When the soil mass is submerged the weight of the solids or solid particles of the soil mass is reduced due to buoyancy. The submerged weight W_s(sub) of the solids or solid particles of the soil mass is therefore equal to the weight of the solids or solid particles in air minus the weight of water displaced by the solids or solid particles. Thus 

 W_s(sub) = W_s – V_sγ_w 

Since a submerged soil is invariably saturated, 

W_s = W_sat - W_w

Thus 

W_s(sub) = W_sat - W_w – V_sγ_w = W_sat – V_wγ_w – V_sγ_w = W_sat – (V_w + V_s)γ_w

Since the soil mass is submerged the voids must be full of water, the total volume V, then, must be equal to (V_w + V_s). Thus W_s(sub) may be written as 

W_s(sub) = W_sat – Vγ_w

Dividing throughout by V, the total volume of the soil mass, 

W_s(sub)/V= W_sat/V – γ_w

or γ′ or γ_sub =  γ_sat – γ_w

Equations (ρ′ or ρ_sub = ρ_sat - ρ_w and γ′ or γ_sub =  γ_sat – γ_w) may also be obtained directly on the basis of Archimedes’ Principle which state that the apparent loss of mass or weight of a substance when held submerged in water is equal to the mass or weight of the water displaced by it.

FAQs COVERED IN THIS POST

What is Saturated Unit Mass?
What is the equation for Saturated Unit Mass?

What is Saturated Unit Weight?

What is the equation for Saturated Unit Weight?

What is Submerged Unit Mass?
What is the equation for Submerged Unit Mass?

What is Submerged Unit Weight?

What is the equation for Submerged Unit Weight?

What is Saturated Mass Density?
What is the equation for Saturated Mass Density?

What is Saturated Weight Density?

What is the equation for Saturated Weight Density?

What is Submerged Mass Density?
What is the equation for Submerged Mass Density?

What is Submerged Weight Density?

What is the equation for Submerged Weight Density?

RELATED POSTS

• WATER CONTENT OR MOISTURE CONTENT
• POROSITY, VOID RATIO, DEGREE OF SATURATION
• BULK UNIT MASS, BULK WEIGHT DENSITY
• DRY UNIT MASS, DRY WEIGHT DENSITY
• AIR CONTENT, PERCENTAGE AIR VOIDS
• RESIDUAL AND TRANSPORTED SOILS
• COMPOSITION OF SOILS
• INTRODUCTION & BASIC DEFINITIONS IN SOIL MECHANICS
• SOIL GROUPS IN INDIA
• FORMATION OF SOILS
• DIFFERENT TYPES OF SOILS

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