GEOTECHNICAL ENGINEERING
What is Geotechnical Engineering?
Geotechnical engineering is a branch of civil engineering that studies the engineering behavior of earth materials. Geotechnical engineering entails investigating existing subsurface conditions and materials, determining their physical/mechanical and chemical properties relevant to the project under consideration, assessing risks posed by site conditions, designing earthworks and structure foundations, and monitoring site conditions, earthwork and foundation construction.
Geotechnical engineering is a civil engineering discipline concerned with the behavior of earth materials and the application of soil and rock mechanics. Geotechnical engineers design foundations, retaining structures, and earthwork based on their understanding of soil and rock properties.
Geotechnical engineers design above and below-ground foundations and plan, direct, and conduct survey work to analyze the likely behavior of soil and rock when subjected to pressure from proposed structures.
GEOTECHNICAL ENGINEERING FORMULAS
SYMBOLS AND NOTATION
e = void ratio
n = porosity
w = moisture content, water content
s = specific gravity of any substance
G = specific gravity of solids
S = degree of saturation
V = volume of soil mass
Va = volume of air
Vw = volume of water
Vs = volume of solids
Vv = volume of voids
W = total weight of soil
Ww = weight of water
Ws = weight of solids
Dr = relative density
γs = unit weight of soil solids
γw = unit weight of water
γb = γ′ = buoyant unit weight, submerged unit weight
γd = γdry = dry unit weight
γsat = saturated unit weight
LL = liquid limit
PL = plastic limit
LI = liquidity index
PI = plasticity index
GI = group index
γm = unit weight of soil mass, moist unit weight, bulk unit weight
ATTERBERG or CONSISTENCY LIMITS
Consistency is a term used to define the degree of hardness of a soil in a qualitative manner using terms like soft medium, firm stiff, and hard.
Liquid Limit (LL): The moisture content, in percent, at the point transition from plastic to liquid.
Plastic Limit (PL): The moisture content, in percent, at the point transition from semisolid to plastic state.
Shrinkage Limit (SL): The moisture content, in percent, at the point transition from solid to semi solid state.
LIQUID, PLASTIC, and SHRINKAGE LIMITS DETERMINATION
Liquid Limit Test- Limit can be determined using the Casagrande cup method or a cone penetrometer. The soil paste is placed in the Casagrande cup, and a groove is formed in the center of it. The limit is defined as the moisture content, in percent, necessary to close a distance of 0.5 inch at the bottom of a groove after 25 blows in a liquid limit device.
The water content w1 and w2 correspond to the number of blows N1 and N2, respectively.
Plastic Limit Test-The Plastic limit test is carried out by hand rolling an ellipsoidal-sized soil mass over a non-porous surface many times. The plastic limit, according to Casagrande, is the water content at which a thread of soil merely crumbles when carefully rolled out to a diameter of 3 mm (1/8″).
The soil is too wet if the thread collapses at a diameter less than 3 mm. If the thread crumbles at a diameter higher than 3 mm, the soil is dry enough to break. The test can then be performed once the sample has been remolded. Following the production of the proper size rolls, the moisture content is determined using the previously described process.
The plastic limit is computed using the following formula:
Shrinkage Limit Test- The following formula is used to calculate the shrinkage limit. M1 is a mass of moist soil that is placed in a porcelain dish with a diameter of 44.5 mm and a height of 12.5 mm and dried in the oven. The volume of oven-dried soil is calculated by filling the empty areas created by shrinkage with mercury. The mass of mercury is computed, and the volume loss due to shrinking is calculated using the density of mercury.
The shrinkage limit is computed using the following formula:
where:m1 = mass of wet soil
m2 = mass of oven-dried soil,
V1 = volume of wet soil
V2 = volume of oven-dried soil,
ρw = density of water.
Shrinkage ratio: 
Specific gravity of solid:
PHYSICAL PROPERTIES OF SOIL
Soil contains solids, liquids, and gases. Water and air are the two most common liquids and gases. These two elements (water and air) are known as voids, and they exist between soil particles. The diagram below depicts an idealized soil divided into solid, water, and air phases.
The Weight-Volume Relationship from the Soil Phase Diagram
Properties of Soil
Void ratio, e
It is defined as the ratio of the volume of voids to the volume of solids.
Porosity, n
It is defined as the ratio of the volume of voids to the total volume.
Degree of Saturation, S
The ratio of the volume of water to the volume of voids is the degree of saturation.
Water Content or Moisture Content, w
Water content is defined as the ratio of the mass of water to the mass of soil.
Unit Weight, γ
The weight of soil per unit volume is referred to as its unit weight. Bulk unit weight (γ) and moist unit weight (γm) are two different terms for the same thing.
Dry Unit Weight, γd
The weight of dry soil per unit volume is expressed as “dry unit weight.”
Saturated Unit Weight, γsat
The weight of saturated soil per unit volume is known as saturated unit weight.
Effective Unit Weight, γ‘
The weight of solids in a submerged soil per unit volume is known as effective unit weight. Also known as buoyant unit weight (γb) or buoyant density.
Specific Gravity of Solid Particles, G
The ratio of the unit weight of solids (γs) to the unit weight of water (γw) determines the specific gravity of soil solid particles.
Formulas for Properties of Soil
Atterberg Limits
Basic Formulas
Relationship between voids and porosity
Relationship between specific gravity of solid particles (G), water content or moisture content (w), degree of saturation (S), and void ratio( e)
Gw = Se
