For a friction angle of 30 degrees, the bearing capacity factor N_q can be approximated using the formula N_q = e^(π * tan(φ)) * tan(45 + φ/2). For φ = 30 degrees, N_q is approximately 3.5.

The Cone Penetration Test (CPT) is widely used in site investigations to assess the bearing capacity of soil.

Using Terzaghi's equation for cohesive soils, q_u = c*N_c + q, where c = 75 kPa, N_c = 5, and assuming q = 0, q_u = 75 kPa * 5 = 375 kPa.

The primary mode of failure for a foundation subjected to vertical loads is typically bearing capacity failure, which occurs when the soil can no longer support the applied load.

For sandy soil, the bearing capacity factor Nq is typically around 3.0, which is used in calculating the ultimate bearing capacity.

A high water table can decrease the effective stress in the soil, thereby reducing its bearing capacity.

Bearing pressure (q) is calculated as q = Load / Area. The area of the foundation is 2 m * 1 m = 2 m². Therefore, q = 400 kN / 2 m² = 200 kPa.

The time required for 50% consolidation can be calculated using the formula t = H²/Cv, where H is the thickness of the layer. For H = 5 m, t = (5²)/0.01 = 250 years, but for 50% consolidation, we use a factor of 0.1, leading to approximately 1 year.

The bearing capacity is independent of the footing width when the load remains constant; it is a function of the soil properties and the load applied.

Soil stratigraphy is crucial for deep foundation design as it affects load transfer and bearing capacity.

Using deep foundations is an effective method to mitigate settlement in clay, as it transfers loads to deeper, more stable soil layers.

High compressibility of the soil can lead to excessive settlement under load, which is a common issue in foundation failures.

The backfill angle significantly affects the lateral earth pressure acting on the retaining wall, impacting its stability.

A plate load test is specifically designed to evaluate the bearing capacity of soil under a given load.

Consolidation involves volume change due to the expulsion of pore water, leading to settlement over time.

The coefficient of consolidation (Cv) represents the rate at which a soil volume changes under applied load, reflecting the speed of consolidation.

The consolidation test measures the volume change of soil over time under a constant load, which is critical for understanding settlement behavior.

The presence of a low permeability layer decreases the settlement rate as it restricts the flow of pore water.

The presence of a weak layer generally decreases the overall bearing capacity because it can lead to shear failure at lower loads than would be expected from the stronger layers.

The primary parameter measured in a one-dimensional consolidation test is the settlement over time as the soil consolidates under a given load.

Primary consolidation refers to the settlement that occurs due to the expulsion of pore water from the soil, leading to a decrease in volume over time.

Surcharge refers to an additional load applied to the soil surface, which can increase the effective stress and lead to consolidation settlement.

Terzaghi's one-dimensional consolidation theory is widely used to estimate settlement in saturated clay due to its simplicity and effectiveness.

Terzaghi's theory provides a framework for estimating the time rate of consolidation in saturated soils, taking into account the soil's permeability and compressibility.

The coefficient of permeability is crucial for determining the time rate of consolidation, as it affects how quickly pore water can escape from the soil.

The vane shear test is specifically designed to measure the in-situ shear strength of cohesive soils.

The purpose of applying confining pressure in a triaxial test is to simulate in-situ conditions and assess the strength of the soil under controlled stress.

Overburden pressure refers to the pressure exerted by the weight of the soil above the foundation, which contributes to the effective stress.

The rate of consolidation is primarily affected by the permeability of the soil, as it determines how quickly pore water can escape from the soil.

Cohesion refers to the bonding between soil particles that contributes to the shear strength of the soil.