Compression & Consolidation of Soils | Soil Mechanics - Civil Engineering (CE) PDF Download

Compression and Consolidation of Soils

When a soil layer is subjected to an increase in vertical stress, the arrangement of soil grains may change and some grain crushing can occur. The volume of the solid grains themselves remains essentially constant; therefore any change in the total volume of the soil mass is due to change in the volume of voids (air and water). In saturated soils this change in void volume can occur only if pore water is expelled from the voids. The movement of pore water out of the soil mass takes time and is controlled by the permeability of the soil and by the location and number of free-draining boundaries.

Mechanism of Settlement and Consolidation

Two questions are important when a soil is loaded: (a) what is the magnitude of the volume change (or settlement) and (b) how long will it take for this volume change to occur? The magnitude of settlement depends on the applied stress, the thickness of the compressible soil layer, and the compressibility properties of the soil. The time required depends primarily on soil permeability and drainage conditions.

When a saturated soil is loaded faster than pore water can escape (undrained loading), the extra load is initially carried by an increase in pore water pressure. As time passes, the excess pore pressure dissipates by seepage and the effective stress in the soil increases; deformation (settlement) then occurs. The rate of settlement therefore decreases with time.

Coarse soils (sands and gravels) are highly permeable and excess pore pressures dissipate rapidly, so most volume change is essentially immediate. Fine soils (silts and clays) have low permeability and show slow dissipation; for these soils consolidation is the dominant time-dependent settlement mechanism.

Components of Total Settlement

• Immediate (or elastic) settlement: Deformation that occurs at constant volume (undrained) due to elastic strain of the soil skeleton immediately after loading. It is associated with shape change (vertical compression and lateral expansion) and is significant for coarse soils or rapid loading.
• Primary consolidation: Settlement due to flow of pore water out of the voids as excess pore pressure dissipates. This is time-dependent and governed by soil permeability and compressibility.
• Secondary compression (creep): Long-term settlement occurring after primary consolidation is essentially complete, due to viscous or rearrangement effects in the soil skeleton.

One-Dimensional Consolidation and Its Use

For many practical problems (wide foundations, fills and embankments), the soil beneath the loaded area far from edges undergoes essentially vertical strain with negligible horizontal strain. Under these conditions the deformation and seepage can be approximated as one-dimensional consolidation in the vertical direction. The one-dimensional assumption greatly simplifies analysis and is adequate for most settlement estimates in geotechnical engineering.

Compressibility Characteristics: Void Ratio versus Effective Stress

The compressibility of a soil under one-dimensional loading is conveniently described by the relation between void ratio, e, and effective vertical stress, σ'. This relation can be presented either as an arithmetic plot (e versus σ') or as a semi-log plot (e versus log σ').

On an arithmetic plot, as effective stress increases by the same increment, Δσ', the void ratio reduces by decreasing increments (smaller Δe at higher stresses) because particle packing becomes denser as pore water is expelled. Thus the soil becomes less compressible as effective stress increases.

Coefficient of Compressibility and Volume Compressibility

The slope of the e - σ' relationship is a measure of compressibility. For a small range of effective stress the coefficient of compressibility a_v may be defined as the change in void ratio per unit change in effective stress (with a negative sign introduced to make the coefficient positive):

Another useful parameter is the coefficient of volume compressibility, m_v, which represents the compression of the soil per unit original thickness per unit increase of effective pressure. If e₀ is the initial void ratio of the consolidating layer, then

Equivalently, m_v can be written in terms of change in void ratio Δe and change in effective stress Δσ' as

m_v = Δe / [(1 + e₀) · Δσ']

Using m_v, the settlement of a layer of original thickness H under an increase in effective stress Δσ' may be written as

ΔH = m_v · H · Δσ'

Normally Consolidated and Over-Consolidated Clays

The behaviour of clays is commonly represented on an e - log σ' semi-log plot. The soil response on such a plot shows different paths for loading, unloading and reloading.

On the figure, O→P represents initial (virgin) loading; P→Q represents unloading; and Q→F→R represents reloading. The point P corresponds to the maximum past effective stress experienced by the deposit and is called the preconsolidation stress σ'_pc. The current state of stress is represented by σ'.

If the current effective stress σ' equals the preconsolidation stress σ'_pc (σ' = σ'_pc), the clay is said to be normally consolidated (NC). If the current effective stress σ' is less than σ'_pc (σ' < σ'_pc), the clay is over-consolidated (OC).

For the same increase in effective stress, the compression of an over-consolidated soil (path Q→F) is smaller than that of a normally consolidated soil (path O→P). On unloading the soil swells but the increase in void ratio is less than the prior decrease for the same stress difference.

Overconsolidation Ratio (OCR)

The overconsolidation ratio (OCR) quantifies the degree of overconsolidation and is defined as the ratio of preconsolidation stress to the current effective stress:

OCR = σ'_pc / σ'

When OCR = 1 the soil is normally consolidated. Settlements are generally smaller for structures built on overconsolidated soils. Typical causes of overconsolidation include desiccation (drying), changes in groundwater level, past higher loading followed by unloading (for example by erosion of overlying strata), or glaciation.

Compression Index and Recompression Index

For normally consolidated clays the e - log σ' plot can be approximated by a straight line over a range of stresses. The slope of this line is the compression index, C_c, usually determined from oedometer test data:

The recompression index C_r (also called swelling or recompression index) is the slope of the e - log σ' curve in the unloading/reloading range. Typical values: C_r < C_c.

Terzaghi's One-Dimensional Consolidation Theory (Practical Points)

Terzaghi's 1-D consolidation theory provides a practical framework to estimate the rate of consolidation in saturated soils under one-dimensional conditions. The governing differential equation for dissipation of excess pore pressure u (excess above hydrostatic) is

∂u/∂t = C_v · ∂²u/∂z²

where C_v is the coefficient of consolidation, z is vertical coordinate and t is time. The coefficient of consolidation relates permeability and compressibility as

C_v = k / (m_v · γ_w)

where k is permeability and γ_w is the unit weight of water. For practical settlement calculations the concept of degree of consolidation U(t) is used, representing the fraction of primary consolidation completed at time t. The classical solution uses a dimensionless time factor T_v given by

T_v = C_v · t / H_dr²

where H_dr is the maximum drainage path length (half the thickness H if drainage occurs at both top and bottom; equal to H if drainage is from one side only). For many practical purposes the relation between U and T_v is obtained from standard charts or series solutions. Inverting the relation gives the time required for a chosen degree of consolidation:

t = T_v · H_dr² / C_v

Typical approximate values from charts: U ≈ 50% corresponds to T_v ≈ 0.197; U ≈ 90% corresponds to T_v ≈ 0.848 (for double drainage). Engineers use these values with measured or estimated C_v to compute consolidation times.

Laboratory and Field Determination

• Oedometer (consolidation) test: A standard laboratory test in which a soil sample is loaded in increments and deformation and pore pressure dissipation are recorded. From the test one determines e - log σ' behaviour, C_c, C_r, σ'_pc (Casagrande method often used to estimate preconsolidation stress) and C_v by consolidation curve analysis.
• Permeability tests: k measured in the laboratory (constant head or falling head) or estimated from particle size and index properties; permeability is essential to estimate rate of consolidation via C_v.
• Field measurements: Plate load tests, settlement gauges, piezometers, and in-situ tests (e.g., pressuremeter) give supplementary information on compressibility and rate parameters.

Settlement Estimation - Practical Formulas

For a compressible layer of original thickness H subject to an increase in effective vertical stress Δσ', the primary consolidation settlement may be estimated by either of the equivalent expressions:

ΔH = m_v · H · Δσ'

or, when using e - log σ' relations for normally consolidated clays,

ΔH = H · (e₀ - e_f) / (1 + e₀)

where e_f is the void ratio after loading corresponding to σ' + Δσ'. Using the compression index C_c for normally consolidated clay,

e₀ - e_f = C_c · log(σ' + Δσ')/σ'

so

ΔH = H · C_c · log(σ' + Δσ')/σ' / (1 + e₀)

These relations are widely used in foundation settlement calculations. Immediate settlement must be estimated separately (for example using elastic theory) and secondary compression estimated using a secondary compression index C_α with a logarithmic time law:

S_secondary = C_α · H · log(t₂ / t₁)

Practical Considerations and Applications

• Consolidation analysis is essential for design of foundations, embankments, ground improvement works and for prediction of long-term settlements that may affect serviceability of structures.
• Drainage conditions (single or double drainage) control consolidation time: double drainage halves the maximum drainage path and so markedly reduces consolidation time.
• Estimating preconsolidation stress and OCR is important because overconsolidated soils compress much less on future loading than normally consolidated soils.
• Improvement measures (prefabricated vertical drains, staged construction, surcharging) are used to accelerate consolidation in low-permeability deposits.

Summary

Consolidation is the process by which saturated soils decrease in volume as pore water is expelled under increased effective stress. The magnitude of settlement depends on soil compressibility (described by parameters such as m_v, C_c and e - log σ' relations), while the rate depends on permeability and drainage (through C_v and H_dr). Distinguishing between normally consolidated and overconsolidated soils and measuring the relevant parameters in the laboratory and field are the practical steps required for reliable settlement prediction and design.