Soil Compressibility and Consolidation Cheat Sheet

This cheat sheet covers the fundamental principles of soil compressibility and consolidation, focusing on how soil volume changes under load and the factors influencing settlement over time. It details key concepts, calculation methods, and experimental procedures.

Core Principles

Consolidation is the gradual reduction in volume of a saturated soil due to effective stress changes.
Total settlement comprises immediate, consolidation, and secondary compression components.
Soil behavior under load is visco-elastic and highly non-linear.
Terzaghi's theory of one-dimensional consolidation is a foundational model.
The oedometer test is crucial for determining soil compressibility parameters.
Overconsolidation Ratio (OCR) indicates a soil's stress history.
The rate of consolidation depends on soil permeability and drainage conditions.

Action Steps

Understand the concept of consolidation and its components.
Perform laboratory oedometer tests to determine consolidation parameters.
Analyze e-log σ' curves to identify normally consolidated (NC) and overconsolidated (OC) states.
Calculate the Overconsolidation Ratio (OCR) to assess stress history.
Apply Terzaghi's theory and relevant formulas to predict consolidation settlement.
Determine the coefficient of consolidation ($c_v$) using time-settlement data.
Use the U-T$_v$ relationship to estimate the time required for a certain degree of consolidation.

Formulas

$S_t = S_i + S_c + S_s$ (Total Settlement)
$OCR = \frac{\sigma'_p}{\sigma'_{vo}}$
$c_v = \frac{k}{m_v \gamma_w}$ (Coefficient of Consolidation)
$T_v = \frac{c_v t}{d^2}$ (Time Factor)
$U_z = \frac{e_0 - e}{e_0 - e_1}$ (Degree of Consolidation - Void Ratio)
$U_z = \frac{\sigma'_1 - \sigma'_0}{\sigma'_1 - \sigma'_0}$ (Degree of Consolidation - Effective Stress)
$U_z = 1 - \frac{u_e}{u_i}$ (Degree of Consolidation - Pore Pressure)
$S_c = \frac{H_0}{1+e_0} C_c \log\frac{\sigma'_1}{\sigma'_0}$ (Settlement for NC Clay)
$S_c = \frac{H}{1+e_0} C_r \log\frac{\sigma'_1}{\sigma'_0}$ (Settlement for OC Clay, Case 1)
$S_c = \frac{H}{1+e_0} [C_r \log\frac{\sigma'_p}{\sigma'_0} + C_c \log\frac{\sigma'_2}{\sigma'_p}]$ (Settlement for OC Clay, Case 2)

Key Terms

Consolidation: Gradual reduction in soil volume due to effective stress increase, primarily driven by pore water dissipation.
Oedometer Test: Laboratory test to measure soil volume change under controlled vertical loading and drainage.
Effective Stress: The stress carried by the soil skeleton, calculated as total stress minus pore water pressure.
Void Ratio (e): Ratio of the volume of voids to the volume of solids in a soil sample.
Compression Index (Cc): Slope of the virgin compression curve on an e-log σ' plot, representing compressibility in the NC state.
Recompression Index (Cr): Slope of the recompression curve on an e-log σ' plot, representing compressibility in the OC state.
Preconsolidation Pressure (σ'p): The maximum effective stress the soil has experienced in its history.
Overconsolidation Ratio (OCR): Ratio of preconsolidation pressure to the current effective overburden pressure.
Coefficient of Consolidation (cv): Parameter indicating the rate at which consolidation occurs.
Time Factor (Tv): Dimensionless number relating time, drainage path, and coefficient of consolidation.

Timeline

t < 0: Before consolidation: Soil at equilibrium with overburden pressure.
t = 0: Surcharging: Load applied; excess pore pressure increases, carrying the entire load.
t > 0: Consolidation begins: Pore water drains, excess pore pressure dissipates, effective stress increases.
t >> 0: After consolidation: Pore pressure returns to hydrostatic; effective stress equals total stress.
Completion: Excess pore pressure is zero; settlement is complete (primary consolidation).