Stress Distribution, Compressibility and Consolidation

Introduction and Context

Soil is a three-phase material whose engineering response depends on the interaction of solids, water, and air. When a load is applied to a soil mass, the resulting stress is not transmitted uniformly with depth, and the resulting deformation may occur immediately or over an extended period. These processes govern the performance of foundations, embankments, retaining structures, pavements, tunnels, and reclamation projects.

This chapter examines stress distribution in soil, compressibility, immediate settlement, one-dimensional consolidation, multidimensional consolidation, secondary compression, and allowable settlement. The treatment combines classical analytical methods with constitutive concepts used in contemporary geotechnical practice.

Learning Objectives

After studying this chapter, the reader should be able to:

1. Distinguish total stress, pore-water pressure, and effective stress.

2. Estimate stress increments beneath loaded areas using analytical and approximate methods.

3. Explain soil compressibility and obtain settlement parameters from laboratory tests.

4. Calculate immediate, primary consolidation, and secondary compression settlement.

5. Apply one-dimensional consolidation theory and interpret time-rate relationships.

6. Recognize the limitations of one-dimensional assumptions and assess multidimensional consolidation.

7. Select appropriate constitutive models and evaluate allowable settlement in design.

1. Stress in Soil Masses

1.1 Total, pore, and effective stress

For saturated soil under static conditions, Terzaghi’s effective stress principle is

σ′ = σ − u

where σ is total normal stress, u is pore-water pressure, and σ′ is effective normal stress. Total stress and pore pressure have units of force per unit area, commonly kPa. Effective stress is the stress carried by the soil skeleton and controls shear strength, compressibility, and volume change.

For a soil layer of saturated unit weight γ_sat and depth z below the ground surface, if the groundwater table is at the surface,

σ_v = γ_sat z

u = γ_w z

σ′_v = (γ_sat − γ_w)z = γ′z

where γ_w is the unit weight of water and γ′ is the submerged unit weight. Above the water table, pore pressure may be negative because of capillarity; however, the simple hydrostatic equations should not be applied without considering suction and the position of the phreatic surface.

A change in total stress does not necessarily produce an equal immediate change in effective stress. In saturated low-permeability clay under rapid loading, the initial stress increment is carried largely by pore water. As drainage occurs, pore pressure dissipates and effective stress increases. In freely draining sand, pore pressure dissipates rapidly and the effective stress increase is approximately immediate.

1.2 Initial stresses and stress paths

The initial vertical effective stress is often written σ′_v0. The horizontal effective stress at rest is

σ′_h0 = K_0 σ′_v0

where K_0 is the coefficient of earth pressure at rest. For normally consolidated soils, the commonly used approximate relationship is

K_0 ≈ 1 − sin φ′

where φ′ is the effective friction angle. This relationship is empirical and should not be applied uncritically to overconsolidated, cemented, structured, or heavily fissured soils. A stress path describes the changes in mean effective stress and deviator stress during loading; it is essential when evaluating yielding, undrained response, and strength under complex loading.

2. Distribution of Applied Stress

2.1 Conceptual behavior

A foundation load produces a three-dimensional stress increment beneath the loaded area. The increment is greatest near the loaded surface and decreases with depth. Its spread depends on the geometry of the loaded area, soil stiffness, boundary conditions, and whether the soil behaves as an elastic, plastic, or layered medium.

Stress distribution calculations are used to identify the depth of significant influence, estimate settlement, assess stress changes in compressible layers, and evaluate interaction between adjacent foundations.

2.2 Boussinesq solution

For a vertical point load Q applied at the surface of a homogeneous, isotropic, linearly elastic, semi-infinite soil, the vertical stress increment at depth z and radial distance r is

Δσ_z = (3Q / 2πz²) [1 + (r/z)²]^(−5/2)

The equation assumes elastic behavior, a homogeneous and isotropic soil, a horizontal ground surface, small strains, and a semi-infinite medium. At the point directly below the load, r = 0, so

Δσ_z = 3Q / (2πz²)

The point-load solution is integrated over finite loaded areas. For a uniformly loaded rectangular area, influence-factor methods are usually more convenient:

Δσ_z = q I_z

where q is the applied uniform pressure and I_z is a dimensionless influence factor dependent on plan geometry, depth, and position. Charts, tables, numerical integration, and software may be used to determine I_z.

2.3 Approximate 2:1 method

A simple preliminary method assumes that load spreads with depth at a ratio of 2 vertical units to 1 horizontal unit. For a rectangular area of width B and length L carrying uniform pressure q, the stress increment at depth z below the center is approximated by

Δσ_z ≈ qBL / [(B + z)(L + z)]

This method is useful for preliminary estimates and rapid checks. It is not a substitute for elastic influence factors or numerical analysis where geometry, layering, interaction, or accuracy is important.

2.4 Stress distribution in layered and nonuniform soil

The classical elastic solutions assume uniform stiffness. In real profiles, a stiff layer may attract load and a soft layer may deform disproportionately. The calculated stress increment is therefore an approximation whose accuracy depends on the contrast in stiffness and the location of boundaries. Three-dimensional finite-element analysis can represent layered stiffness, nonlinear constitutive behavior, groundwater conditions, staged construction, and structural interaction, but the quality of the result remains dependent on the soil model and parameters.

3. Compressibility and Settlement Mechanisms

Settlement is the vertical downward movement of the ground or a structure. It is commonly divided into:

• immediate settlement, caused mainly by elastic distortion and, in partly saturated soils, rapid volume change;
• primary consolidation settlement, caused by drainage and dissipation of excess pore-water pressure; and
• secondary compression, caused by gradual deformation of the soil skeleton after primary consolidation is substantially complete.

The distinction is conceptual rather than perfectly chronological. Immediate and consolidation responses can overlap, particularly in soils of intermediate permeability.

3.1 Void ratio, strain, and compressibility

Void ratio is

e = V_v / V_s

where V_v is the volume of voids and V_s is the volume of solids. For one-dimensional compression with constant area, vertical strain is related to the change in void ratio by

ε_v = Δe / (1 + e_0)

where e_0 is the initial void ratio and Δe is the decrease in void ratio. If a layer thickness is H, settlement is

S = H Δe / (1 + e_0)

For a stress increment within a relatively narrow stress range, constrained compressibility may be described by the coefficient of volume compressibility, m_v:

m_v = Δe / [(1 + e_0)Δσ′]

and the corresponding one-dimensional settlement is

S = m_v Δσ′ H

The units of m_v are inverse stress, such as m²/kN when stress is in kPa. The parameter is stress-dependent and should not be treated as a universal soil constant.

3.2 Oedometer test

The oedometer test applies incremental vertical loads to a laterally confined specimen. It provides the e–log σ′_v relationship, compression index, recompression index, preconsolidation stress, coefficient of consolidation, and information about secondary compression.

The compression index is the slope of the virgin compression line:

C_c = Δe / Δlog_10 σ′_v

The recompression index C_r, also called the swelling or recompression index in some contexts, is the slope of the overconsolidated portion. The preconsolidation stress σ′_p is the approximate maximum past vertical effective stress. It separates recompression from virgin compression, although its determination is subject to sampling disturbance and interpretation uncertainty.

The coefficient of consolidation is

c_v = k / (m_v γ_w)

where k is hydraulic conductivity, m_v is coefficient of volume compressibility, and γ_w is unit weight of water. The units of c_v are area per time. Since both k and m_v vary with stress, c_v is also stress-dependent.

3.3 Normally consolidated and overconsolidated soils

A normally consolidated soil has not previously experienced a vertical effective stress greater than its current value. An overconsolidated soil has experienced a higher past stress. The overconsolidation ratio is

OCR = σ′_p / σ′_v0

For a normally consolidated layer, settlement caused by an increase from σ′_v0 to σ′_v0 + Δσ′ is

S_c = H C_c/(1 + e_0) log_10[(σ′_v0 + Δσ′)/σ′_v0]

For an overconsolidated layer that remains below σ′_p,

S_c = H C_r/(1 + e_0) log_10[(σ′_v0 + Δσ′)/σ′_v0]

If the final stress exceeds σ′_p, settlement is calculated in two parts:

S_c = H/(1 + e_0) {C_r log_10(σ′_p/σ′_v0) + C_c log_10[(σ′_v0 + Δσ′)/σ′_p]}

These equations assume one-dimensional compression, a representative constant layer thickness and parameters, and stresses expressed in the same units. For thick or highly variable deposits, the layer should be subdivided and the calculation integrated numerically.

4. Immediate Settlement

Immediate settlement is commonly estimated using elastic theory:

S_i = q B (1 − ν²) I_s / E_s

where q is net foundation pressure, B is foundation width, ν is Poisson’s ratio, E_s is an appropriate soil Young’s modulus, and I_s is a dimensionless influence factor accounting for foundation shape, rigidity, embedment, and depth of observation. The exact form of I_s depends on the selected elastic solution.

This equation is most defensible for small strains and soils that can be represented by a reasonably uniform elastic modulus. In layered soils, a strain-influence method may be preferable. The modulus may be obtained from laboratory tests, pressuremeter tests, seismic measurements, or correlations, but the strain range and drainage condition must be compatible with the design problem.

For saturated clay under undrained loading, an undrained modulus and an appropriate undrained Poisson’s ratio may be used. For drained sands, stress-dependent stiffness and strain level are particularly important. Elastic settlement calculations should be checked against empirical observations and settlement records where available.

5. One-Dimensional Consolidation Theory

5.1 Physical mechanism

When a saturated clay is loaded rapidly, drainage is initially negligible. The applied increment produces excess pore pressure. With time, water flows toward drainage boundaries, excess pore pressure decreases, and effective stress increases. The soil skeleton contracts, producing settlement.

Terzaghi’s one-dimensional consolidation theory assumes saturated soil, incompressible soil grains and water, one-dimensional strain, one-dimensional drainage, Darcy flow, constant properties over the increment, and a linear relationship between effective stress and strain for the selected range. The governing equation is

∂u/∂t = c_v ∂²u/∂z²

where u is excess pore-water pressure, t is time, and z is the vertical coordinate. The equation describes diffusion of excess pore pressure rather than direct settlement alone.

5.2 Degree of consolidation and time factor

The average degree of consolidation is

U = (S_t / S_∞) × 100%

where S_t is settlement at time t and S_∞ is ultimate primary consolidation settlement. The time factor is

T_v = c_v t / H_d²

where H_d is the maximum drainage path: the layer thickness for single drainage and half the thickness for double drainage.

For one-dimensional consolidation, the exact relationship between U and T_v is represented by a series solution. Common approximations are:

For U ≤ about 60%,

T_v ≈ (π/4)U²

where U is expressed as a decimal.

For U greater than about 60%,

T_v ≈ −0.933 log_10(1 − U) − 0.085

These approximations are applicable to the classical theory with uniform initial excess pore pressure and the stated drainage conditions.

5.3 Consolidation settlement at time t

For a soil layer undergoing primary consolidation,

S_t = U S_c

where S_c is ultimate primary consolidation settlement. This relation is appropriate when the degree of consolidation is defined consistently with the settlement calculation and secondary compression is treated separately.

5.4 Worked example: consolidation settlement and time

A 6 m thick saturated normally consolidated clay layer has e_0 = 1.20, C_c = 0.30, initial vertical effective stress σ′_v0 = 100 kPa, and an average stress increment Δσ′ = 80 kPa. The coefficient of consolidation is 2 m²/year. Drainage occurs at both the top and bottom boundaries. Estimate ultimate primary settlement and the time for 90% primary consolidation.

Ultimate settlement is

S_c = [6(0.30)/(1 + 1.20)] log_10(180/100)

= 0.8182 log_10(1.8)

= 0.8182(0.2553) = 0.209 m

Thus, S_c is approximately 209 mm.

For double drainage, H_d = 6/2 = 3 m. At U = 0.90,

T_v = −0.933 log_10(0.10) − 0.085

= 0.848 approximately.

Therefore,

t = T_v H_d²/c_v = 0.848(3²)/2 = 3.82 years.

The result assumes constant c_v and uniform properties. In practice, permeability and compressibility change as consolidation proceeds, so the predicted time should be regarded as an engineering estimate.

6. Multidimensional Consolidation

One-dimensional theory is appropriate when the loaded area is wide relative to the thickness of the compressible layer, lateral strain is restrained, and drainage is predominantly vertical. Many field problems violate these conditions. Narrow embankments, isolated footings, excavations, slopes, and deposits with horizontal drainage paths exhibit two- or three-dimensional consolidation.

In multidimensional consolidation, settlement and pore-pressure dissipation depend on the coupled deformation and seepage fields in several directions. Horizontal drainage may greatly accelerate consolidation, especially in deposits containing sand seams, prefabricated vertical drains, or natural fissures. Conversely, horizontal deformation may transfer load and produce lateral movements that are not captured by one-dimensional analysis.

Biot’s theory of poroelasticity provides a general coupled framework. In simplified notation, equilibrium of the soil skeleton is combined with fluid mass conservation and Darcy’s law. Numerical finite-element programs implement such formulations using coupled displacement–pore-pressure calculations. Advanced analyses may include nonlinear elasticity, elastoplastic yielding, anisotropic permeability, destructuration, creep, and staged construction.

6.1 Vertical drains and radial consolidation

Prefabricated vertical drains shorten the drainage path by providing highly permeable artificial outlets. The resulting response involves radial consolidation, vertical consolidation, smear effects around the drain, and well resistance. Design requires estimates of horizontal permeability, drain spacing, drain diameter or equivalent diameter, smear-zone properties, and surcharge history. Barron-type idealizations and subsequent extensions are commonly used, but field verification is important because natural soil fabric and installation disturbance can dominate performance.

7. Secondary Compression and Creep

After excess pore pressure has substantially dissipated, some soils continue to deform at approximately constant effective stress. This is called secondary compression or creep. It is significant in organic soils, peat, highly plastic clays, sensitive soils, and some fills.

The secondary compression index is

C_α = Δe / Δlog_10 t

where t is time measured consistently from a defined reference point, often the end of primary consolidation. The secondary settlement over a time interval from t_1 to t_2 is commonly estimated as

S_s = H C_α/(1 + e_p) log_10(t_2/t_1)

where e_p is the void ratio at the beginning of the secondary compression interval. The equation assumes approximately linear behavior on an e–log time plot over the selected interval. The reference time must be clearly defined; changing it changes the apparent division between primary and secondary settlement.

Modern constitutive models often represent creep through a time-dependent yield surface or viscoplastic strain rate. The Modified Cam Clay model, for example, describes critical-state elastoplastic behavior but does not by itself fully represent time-dependent creep unless supplemented by a viscous formulation. Soft Soil Creep and related models are more suitable where long-term deformation is central to the problem.

8. Allowable Settlement and Design Decisions

Allowable settlement is not a universal soil property. It depends on structural type, stiffness, frame action, foundation geometry, serviceability requirements, utilities, finishes, drainage, and the distinction between total and differential settlement.

Design checks should consider:

1. total settlement under serviceability loads;

2. differential settlement and angular distortion;

3. rate of settlement and construction schedule;

4. tilt, lateral movement, and rotation;

5. effects on adjacent structures and buried services;

6. uncertainty in soil parameters and groundwater conditions; and

7. monitoring and contingency measures.

A foundation may tolerate substantial uniform settlement but very little differential settlement. Conversely, a flexible structure may accommodate some distortion that would be unacceptable for a brittle masonry system. Numerical limits should therefore be taken from the applicable building code, project performance specification, and structural assessment rather than copied from a generic table.

Settlement predictions should include uncertainty. A useful professional approach is to report a central estimate, a plausible range, the parameters controlling that range, and the observations required to update the prediction. Observational methods may involve staged loading, settlement plates, piezometers, inclinometers, and survey monitoring. Preloading or surcharge, staged construction, vertical drains, lightweight fill, deep foundations, and ground improvement are possible mitigation measures.

9. Constitutive Models and Computational Practice

The constrained modulus, elastic models, and e–log σ′ relationships are useful for routine design, but they have limitations. Linear elasticity cannot reproduce yield, stress-path dependence, anisotropy, destructuration, or creep. The Modified Cam Clay model represents critical-state concepts using parameters such as λ, κ, and the critical-state stress ratio, but parameter quality and stress-history interpretation remain crucial. Hardening Soil-type models use stress-dependent stiffness and separate loading and unloading behavior, often giving more realistic settlement predictions for excavations and foundations.

Model selection should follow the engineering question. A one-dimensional settlement estimate may require only reliable oedometer parameters. A staged embankment on soft clay may require coupled consolidation, nonlinear stiffness, strength anisotropy, and construction sequencing. A finite-element model should not be used merely because it is sophisticated; verification, sensitivity analysis, mesh assessment, boundary selection, and comparison with hand calculations are essential.

Artificial intelligence and data-driven methods can assist parameter interpretation, anomaly detection in monitoring data, surrogate modelling, and probabilistic prediction. They do not remove the need for physical understanding. Training data may be site-specific, biased, or sparse, and an apparently accurate prediction outside the calibration domain can be unsafe. Professional judgement, traceability, and independent verification remain mandatory.

10. Illustrative Case Study: Embankment on Soft Clay

Background

An illustrative project involves a 5 m highway embankment proposed over 8 m of normally consolidated soft clay. The clay is underlain by dense sand. The embankment must be completed within 18 months, but predicted primary consolidation under rapid construction would continue for several years.

Problem

A preliminary oedometer assessment indicates an ultimate primary settlement of approximately 0.65 m. The low coefficient of consolidation suggests that rapid construction could generate high excess pore pressures and reduce short-term stability. Differential settlement near the transition to the sand layer is also a concern.

Analysis

The design team subdivides the clay into stress-increment layers and calculates settlement using the e–log σ′ relationship. A coupled consolidation analysis is then performed for staged embankment construction. Sensitivity analyses vary C_c, σ′_p, c_v, horizontal permeability, and undrained shear strength. The analysis shows that construction faster than the drainage capacity permits would produce unacceptable pore pressure and a low factor of safety.

Approach and solution

The adopted solution uses a temporary surcharge, staged filling, and prefabricated vertical drains. Instrumentation includes settlement plates, vibrating-wire piezometers, and lateral-displacement inclinometers. Filling is paused when piezometer readings approach the predefined trigger level. Observed settlement and pore-pressure data are used to update the construction schedule.

Outcome

The drains accelerate pore-pressure dissipation and allow much of the primary settlement to occur before surfacing. Monitoring confirms that the observed response is within the predicted range, although the measured horizontal permeability is lower than initially assumed. The surcharge duration is extended before removal.

Learning points

The case demonstrates that settlement magnitude and settlement rate are separate design issues. It also shows the value of staged construction, observational control, parameter updating, and independent hand calculations. A model that predicts ultimate settlement adequately may still predict the wrong construction-time pore pressure or lateral movement.

11. Challenges, Limitations and Best Practice

The greatest sources of error are often not algebraic. They include disturbed samples, incorrect groundwater assumptions, unrecognized sand seams, uncertain stress history, inappropriate modulus selection, and failure to distinguish net from gross foundation pressure. Settlement calculations should use effective stress increments, account for foundation embedment and excavation unloading, and consider the actual construction sequence.

Best practice includes conducting an adequate site investigation; identifying drainage boundaries; testing representative samples; checking laboratory data for disturbance; subdividing thick layers; comparing multiple methods; performing sensitivity analysis; documenting assumptions; and monitoring critical projects. Calculations should preserve unit consistency, especially when converting kPa, m, years, and logarithmic relationships. Independent review is particularly important for soft-ground projects and structures sensitive to differential movement.

Chapter Summary

Stress distribution determines how an applied load affects soil at depth. Total stress is divided between pore-water pressure and effective stress, with effective stress controlling soil skeleton behavior. Classical Boussinesq solutions, influence factors, and the 2:1 method provide increasingly approximate tools for estimating vertical stress increments.

Compressibility is described through void ratio, constrained strain, m_v, C_c, C_r, and stress-history parameters. Settlement is commonly separated into immediate settlement, primary consolidation, and secondary compression. Terzaghi’s one-dimensional theory relates excess pore-pressure dissipation to time through c_v and T_v, but its assumptions must be checked. Multidimensional consolidation, radial drainage, and coupled numerical analyses are required where lateral flow or deformation is important.

Secondary compression may control long-term performance in organic and highly plastic soils. Allowable settlement is a project-specific serviceability criterion involving total settlement, differential settlement, angular distortion, time, and uncertainty. Reliable design combines analytical calculations, constitutive modelling, monitoring, and professional judgement.

Key Terms

Effective stress: Stress carried by the soil skeleton, equal to total stress minus pore-water pressure.

Total stress: Overall stress imposed on a soil mass, including the portion carried by water and solids.

Pore-water pressure: Pressure exerted by water within soil voids.

Stress increment: Change in stress caused by loading, excavation, groundwater change, or other action.

Boussinesq solution: Elastic solution for stress caused by a point load on a semi-infinite medium.

Compressibility: Tendency of soil to undergo volume reduction when effective stress increases.

Void ratio: Ratio of void volume to volume of soil solids.

Coefficient of volume compressibility: Change in void ratio per unit effective stress increment, normalized by one plus initial void ratio.

Compression index: Slope of the virgin compression line on an e–log effective stress plot.

Recompression index: Slope of the overconsolidated portion of the compression curve.

Preconsolidation stress: Maximum previous effective vertical stress inferred from soil history.

Overconsolidation ratio: Ratio of preconsolidation stress to current effective vertical stress.

Immediate settlement: Settlement occurring primarily through rapid elastic or undrained deformation.

Primary consolidation: Volume change caused by dissipation of excess pore-water pressure.

Coefficient of consolidation: Parameter describing the rate of one-dimensional consolidation.

Degree of consolidation: Ratio of settlement completed at a given time to ultimate primary settlement.

Drainage path: Maximum distance water must travel to reach a drainage boundary.

Secondary compression: Time-dependent deformation after substantial primary consolidation.

Allowable settlement: Project-specific settlement limit compatible with structural and functional performance.

Constitutive model: Mathematical representation of stress–strain, strength, and time-dependent soil behavior.

Review Questions

Short Answer Questions

1. Define effective stress and explain its importance in soil behavior.

2. State the assumptions of Terzaghi’s one-dimensional consolidation theory.

3. Distinguish normally consolidated soil from overconsolidated soil.

4. What is the significance of the drainage path in consolidation calculations?

5. Define secondary compression and the secondary compression index.

Long Answer Questions

1. Explain the mechanisms of immediate settlement, primary consolidation, and secondary compression, including their typical time scales.

2. Derive or explain the use of the e–log σ′ relationship for settlement of normally consolidated and overconsolidated clay.

3. Discuss the Boussinesq stress-distribution solution, its assumptions, and its practical limitations.

4. Explain one-dimensional consolidation theory and the use of c_v, T_v, and degree of consolidation.

5. Compare analytical settlement methods with constitutive finite-element modelling for a staged embankment.

Analytical / Application Questions

1. A 4 m normally consolidated clay layer has e_0 = 1.0, C_c = 0.25, initial effective stress of 80 kPa, and a final stress of 160 kPa. Calculate its primary consolidation settlement.

2. A 5 m clay layer drains from both surfaces and has c_v = 1.5 m²/year. Estimate the time for 50% consolidation using T_v ≈ (π/4)U².

3. An embankment is planned on soft clay with uncertain horizontal permeability and low undrained strength. Propose a design and monitoring strategy that addresses both settlement rate and short-term stability.

Multiple Choice Questions with Answers

Question 1

Which stress is carried primarily by the soil skeleton?

A. Total stress

B. Effective stress

C. Hydrostatic pressure

D. Atmospheric pressure

Correct Answer: B. Effective stress

Question 2

For a 6 m layer draining from both its top and bottom surfaces, the maximum drainage path is:

A. 1.5 m

B. 3 m

C. 6 m

D. 12 m

Correct Answer: B. 3 m

Question 3

The coefficient of consolidation is expressed as:

A. k m_v γ_w

B. k/(m_v γ_w)

C. m_v/(k γ_w)

D. γ_w/(k m_v)

Correct Answer: B. k/(m_v γ_w)

Question 4

For a normally consolidated soil, primary consolidation settlement is commonly calculated using:

A. The compression index C_c

B. The friction angle only

C. The permeability alone

D. The liquid limit only

Correct Answer: A. The compression index C_c

Question 5

If U = 0.50, the approximate time factor using T_v = (π/4)U² is:

A. 0.079

B. 0.196

C. 0.393

D. 0.785

Correct Answer: B. 0.196

Question 6

Secondary compression is most directly associated with:

A. Immediate elastic rebound only

B. Gradual deformation after substantial primary consolidation

C. Instantaneous pore-pressure generation only

D. Failure of soil particles by crushing in every soil

Correct Answer: B. Gradual deformation after substantial primary consolidation

Question 7

The Boussinesq point-load solution assumes the soil is:

A. Homogeneous, isotropic, and linearly elastic

B. Always normally consolidated and saturated

C. Rigid and perfectly plastic

D. Layered with zero permeability

Correct Answer: A. Homogeneous, isotropic, and linearly elastic

Question 8

If the final effective stress remains below the preconsolidation stress, settlement is generally evaluated using:

A. The virgin compression index C_c

B. The recompression index C_r

C. The coefficient of permeability only

D. The undrained shear strength only

Correct Answer: B. The recompression index C_r

Question 9

Vertical drains primarily accelerate consolidation by:

A. Increasing the soil unit weight

B. Reducing the drainage distance through radial flow

C. Eliminating all settlement

D. Increasing pore-water viscosity

Correct Answer: B. Reducing the drainage distance through radial flow

Question 10

Allowable settlement should primarily be selected according to:

A. A universal value independent of the structure

B. The soil color

C. Structural and functional performance requirements

D. The foundation concrete strength alone

Correct Answer: C. Structural and functional performance requirements