Unit Weight

Unit Weights and Densities of Soil

Symbols and Notations
γ, γm = Unit weight, bulk unit weight, moist unit weight
γd = Dry unit weight
γsat = Saturated unit weight
γb, γ' = Buoyant unit weight or effective unit weight
γs = Unit weight of solids
γw = Unit weight of water (equal to 9810 N/m3)
W = Total weight of soil
Ws = Weight of solid particles
Ww = Weight of water
V = Volume of soil
Vs = Volume of solid particles
Vv = Volume of voids
Vw = Volume of water
S = Degree of saturation
w = Water content or moisture content
G = Specific gravity of solid particles

Physical Properties of Soil

Phase Diagram of Soil
Soil is composed of solids, liquids, and gases. Liquids and gases are mostly water and air, respectively. These two (water and air) are called voids which occupy between soil particles. The figure shown below is an idealized soil drawn into phases of solids, water, and air.



Weight-Volume Relationship from the Phase Diagram of Soil
total volume = volume of soilds + volume of voids
$V = V_s + V_v$

volume of voids = volume of water + volume of air
$V_v = V_w + V_a$

total weight = weight of solids + weight of water
$W = W_s + W_w$

Problem 01 - Buoyancy

Problem 01
A piece of wood 305 mm (1 ft) square and 3 m (10 ft) long, weighing 6288.46 N/m3 (40 lb/ft3), is submerged vertically in a body of water, its upper end being flush with the water surface. What vertical force is required to hold it in position?

02-001-wood-submerged-in-water.gif           02-001-wood-submerged-in-water-english-units.gif


014 Review Problem - Weight of concrete surge chamber when full of water

Problem 14
A concrete surge chamber with circular cross section and vertical inner walls has an inside diameter of 100 ft. The outer walls taper uniformly. The outer walls taper uniformly ¼ in. to 1 ft. of rise, and at the base the thickness is 5 ft. The height of the surge chamber is 150 ft. above the pressure tunnel, and the material used in its construction weighs 150 lb. per cu. ft. Find the total weight of the chamber when full of water.

005 Review Problem - Weight of gravity dam

Problem 5
If the gravity whose cross section is shown in the figure weighs 150 lb. per cu. ft., find the total weight of a section of a dam 50 ft. long.



Properties of common materials

Material Unit weight
Aluminum 26.095 2660 2.66
Brass 81.423 8300 8.3
Brick 19.62 2000 2.0
Cast iron 70.632 7200 7.2
Concrete 23.544 2400 2.4
Copper 87.407 8910 8.91
Earth (dry) 12.557 1280 1.28
Earth (wet) 17.266 1760 1.76
Glass 25.408 2590 2.59
Ice 8.829 900 0.9
Lead 111.540 11,370 11.37
Mercury 133.416 13,600 13.6
Oil 8.829 900 0.9
Water (fresh) 9.81 1000 1.0
Water (sea) 10.104 1030 1.03
Wood (hard) 7.848 800 0.8
Wood (soft) 4.709 480 0.48

010 Volume of snow blocks in an igloo

Example 010
An igloo or Eskimo hut is built in the form of a hemispherical shell with an inside diameter of 12 ft. If the igloo is constructed of snow block having a uniform thickness of 2 ft and weighing 40 lb/ft3, find the weight of the igloo, neglecting the entrance. Also, if fresh air contains 0.04% carbon dioxide, find the amount of this gas in the igloo when freshly ventilated.

005 Weight of ivory billiard balls

Example 005
A cubic foot of ivory weighs 114 lb. Find the weight of 1000 ivory billiard balls 2½ inch in diameter.

003 Weight of an iron shell

Example 003
An iron ball 10 cm in diameter weighs 4 kg. Find the weight of an iron shell 5 cm thick whose external diameter is 50 cm.

002 Weight of snow ball

Problem 002
Find the weight of the snowball 1.2 m in diameter if the wet compact snow of which this ball is made weighs 480 kg/m3


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