Geotechnical Engineering

Soil classification systems categorize soils based on their physical properties. The Unified Soil Classification System (USCS) and the AASHTO system are commonly used.

Key soil properties include:

• Grain size distribution
• Atterberg limits (liquid limit, plastic limit, plasticity index)
• Moisture content
• Specific gravity
• Void ratio and porosity
• Unit weight

Basic soil relationships:

Where:

• e = void ratio
• n = porosity
• w = moisture content
• S = degree of saturation
• V_v = volume of voids
• V_s = volume of solids
• V = total volume
• V_w = volume of water
• W_w = weight of water
• W_s = weight of solids

Soil strength is a critical parameter for geotechnical design. The Mohr-Coulomb failure criterion is commonly used to describe soil strength:

Where:

• τ_f = shear strength (kPa)
• c = cohesion (kPa)
• σ = normal stress (kPa)
• φ = angle of internal friction (degrees)

For saturated soils, the effective stress principle applies:

Where:

• σ' = effective stress (kPa)
• σ = total stress (kPa)
• u = pore water pressure (kPa)

The shear strength in terms of effective stress is:

Where c' and φ' are effective cohesion and effective friction angle, respectively.

Foundations transfer loads from structures to the underlying soil or rock. The bearing capacity of a shallow foundation can be calculated using Terzaghi's equation:

Where:

• q_ult = ultimate bearing capacity (kPa)
• c = cohesion (kPa)
• γ = unit weight of soil (kN/m³)
• D_f = depth of foundation (m)
• B = width of foundation (m)
• N_c, N_q, N_γ = bearing capacity factors (functions of φ)

The allowable bearing capacity is:

Where FS is the factor of safety (typically 2.5 to 3 for shallow foundations).

Settlement of foundations can be estimated using:

Where:

• S = settlement (m)
• H = thickness of soil layer (m)
• Δe = change in void ratio
• e_0 = initial void ratio