Unsaturated Soil Mechanics

Introduction

Most near-surface soils are neither completely dry nor fully saturated. Their pores contain both air and water, and the interfaces between these phases generate capillary forces that strongly influence stiffness, strength, volume change and fluid flow. Unsaturated soil mechanics is therefore essential to the analysis of slopes, embankments, pavement subgrades, earth dams, landfill covers, foundations on collapsible or expansive soils, and geo-environmental barriers.

Unlike saturated soil, whose mechanical state is commonly described using one effective-stress variable, unsaturated soil generally requires both net stress and suction. Its hydraulic behaviour is nonlinear and history-dependent: water content and hydraulic conductivity vary by several orders of magnitude as suction changes, while drying and wetting follow different paths.

Learning Objectives

After studying this chapter, readers should be able to:

1. distinguish matric, osmotic and total suction;

2. calculate unsaturated-soil phase relations correctly;

3. interpret and model soil-water retention curves;

4. explain hydraulic hysteresis and its engineering consequences;

5. formulate infiltration and evaporation boundary-value problems;

6. compare effective-stress alternatives for unsaturated soils;

7. derive and apply an extended shear-strength relationship;

8. evaluate collapse and swelling caused by wetting or drying; and

9. apply unsaturated-soil principles to geotechnical design and risk management.

1. Phases and State Variables

An unsaturated soil contains three material phases—solid, water and air—and interfaces between water and air. Under many engineering conditions, the masses of air and interfaces are negligible in phase-relation calculations, although their mechanical effects are not negligible.

Let:

• \(V_s,V_w,V_a\) = volumes of solids, water and air;
• \(V=V_s+V_w+V_a\) = total volume;
• \(M_s,M_w\) = dry-solid and water masses;
• \(e=(V_w+V_a)/V_s\) = void ratio;
• \(n=(V_w+V_a)/V=e/(1+e)\) = porosity;
• \(S_r=V_w/(V_w+V_a)\) = degree of saturation;
• \(w=M_w/M_s\) = gravimetric water content;
• \(\theta=V_w/V\) = volumetric water content;
• \(G_s=\rho_s/\rho_w\) = specific gravity of solids; and
• \(\rho_d=M_s/V\) = dry density.

The fundamental phase relationships are

\[

w=\frac{S_r e}{G_s},

\qquad

S_r=\frac{wG_s}{e},

\]

and

\[

\theta=nS_r=\frac{S_r e}{1+e}

=\frac{wG_s}{1+e}

=\frac{w\rho_d}{\rho_w}.

\]

Because

\[

\rho_d=\frac{G_s\rho_w}{1+e},

\]

volumetric water content is not generally equal to gravimetric water content. Equality occurs only for the special numerical condition \(\rho_d=\rho_w\).

Worked Example 1: Phase relations

A soil has \(w=0.12\), \(G_s=2.70\) and \(e=0.80\). Determine its degree of saturation, volumetric water content and dry density, taking \(\rho_w=1000\,\text{kg/m}^3\).

\[

S_r=\frac{0.12(2.70)}{0.80}=0.405.

\]

\[

\theta=\frac{0.12(2.70)}{1+0.80}=0.180.

\]

\[

\rho_d=\frac{2.70(1000)}{1.80}=1500\,\text{kg/m}^3.

\]

The soil is 40.5% saturated and water occupies 18.0% of its total volume. Verification gives \(w\rho_d/\rho_w=0.12(1500)/1000=0.180\).

2. Soil Suction

Suction represents the free-energy state of pore water relative to a reference state. It is commonly expressed as an equivalent positive pressure, usually in kilopascals or megapascals.

2.1 Components of suction

Matric suction is

\[

s=u_a-u_w,

\]

where \(u_a\) and \(u_w\) are pore-air and pore-water pressures. It results mainly from capillarity and adsorption.

Osmotic suction arises from dissolved salts and differences in solute concentration across water reservoirs.

Total suction is, under the usual additive convention,

\[

s_t=s+s_o,

\]

where \(s_o\) is osmotic suction. Matric suction dominates many mechanical problems, while total suction is important in highly saline soils, compacted clay barriers and expansive soils.

2.2 Capillary interpretation

For an ideal cylindrical capillary tube, the pressure difference across a curved air–water interface follows the Young–Laplace equation:

\[

u_a-u_w=\frac{2T_s\cos\alpha_c}{r},

\]

where \(T_s\) is surface tension, \(\alpha_c\) is the contact angle and \(r\) is the capillary radius. Real soils have irregular, interconnected pores, so this equation is conceptual rather than a direct pore-size model.

2.3 Thermodynamic relation with relative humidity

At equilibrium, total suction may be related to relative humidity by the Kelvin equation:

\[

s_t=-\frac{\rho_wRT}{M_w}\ln(RH),

\]

where \(R\) is the universal gas constant, \(T\) is absolute temperature, \(M_w\) is the molar mass of water, and \(RH\) is relative humidity expressed as a fraction. Suction is in pascals when SI units are used. Temperature control is critical because small humidity errors can cause large suction errors at high suction.

2.4 Measurement

Common methods include tensiometers, axis-translation pressure plates, filter-paper testing, chilled-mirror dew-point potentiometers, psychrometers and thermal-conductivity sensors. Tensiometers measure matric suction directly but have a limited range because of cavitation. Vapour-equilibrium methods cover much higher total suctions but require careful temperature and salt control.

3. Soil-Water Retention Behaviour

The soil-water retention curve, also called the soil-water characteristic curve, relates suction to water content or degree of saturation. It is central to both hydraulic and mechanical modelling.

A typical drying curve contains:

1. a near-saturated zone;

2. an air-entry region, where air first enters the largest interconnected pores;

3. a desaturation region with rapid water loss; and

4. a residual zone, where remaining water is strongly adsorbed and relatively immobile.

Grain-size distribution, pore-size distribution, density, compaction water content, mineralogy, fabric and stress history affect the curve. Fine-grained soils commonly retain more water at a given suction than coarse soils.

3.1 Effective saturation

Effective saturation is defined as

\[

S_e=\frac{\theta-\theta_r}{\theta_s-\theta_r},

\]

where \(\theta_s\) and \(\theta_r\) are saturated and residual volumetric water contents. These parameters are model-fitting quantities and do not always correspond exactly to physically unique states.

3.2 van Genuchten model

A widely used retention model is

\[

S_e=\left[1+(\alpha s)^N\right]^{-m},

\]

where \(\alpha\) has inverse-pressure units, \(N>1\) controls pore-size distribution and \(m\) is often constrained to \(m=1-1/N\). This equation is empirical; its fitted parameters depend on the suction units and hydraulic path.

Worked Example 2: Retention and conductivity

For a soil, \(\theta_s=0.42\), \(\theta_r=0.06\), \(\alpha=0.020\,\text{kPa}^{-1}\), \(N=1.60\) and \(m=0.375\). At \(s=100\,\text{kPa}\),

\[

S_e=[1+(0.020\times100)^{1.60}]^{-0.375}=0.593.

\]

Therefore,

\[

\theta=0.06+0.593(0.42-0.06)=0.273.

\]

For the Mualem–van Genuchten conductivity model,

\[

K=K_sS_e^{\ell}\left[1-\left(1-S_e^{1/m}\right)^m\right]^2,

\]

where \(\ell\) is commonly taken as 0.5 when independent calibration is unavailable. With \(K_s=10^{-6}\,\text{m/s}\),

\[

K\approx10^{-6}(0.593)^{0.5}

\left[1-\left(1-0.593^{1/0.375}\right)^{0.375}\right]^2

\approx7.9\times10^{-9}\,\text{m/s}.

\]

Thus, moderate desaturation reduces conductivity by more than two orders of magnitude. Extrapolation beyond the calibrated suction range is unsafe.

4. Hydraulic Hysteresis

At the same suction, a soil commonly has a higher water content during drying than during wetting. This hysteresis arises from:

• the ink-bottle effect, in which narrow pore throats control drainage while larger pore bodies control filling;
• different advancing and receding contact angles;
• entrapped air during wetting;
• pore-network connectivity;
• fabric changes, shrinkage and swelling; and
• nonuniform phase distributions.

Intermediate reversals produce scanning curves rather than immediate transfer between the main drying and wetting curves. Hysteresis also affects hydraulic conductivity because identical water contents can correspond to different distributions and connectivity of water-filled pores.

Ignoring hysteresis may misrepresent infiltration fronts, seasonal slope response, cover-system performance and cyclic wetting–drying. Advanced models track reversal points and domain states, but additional parameters and experimental evidence are required.

5. Water Flow in Unsaturated Soil

5.1 Darcy–Buckingham law and Richards equation

Let elevation \(z\) be positive upward, pressure head \(h=u_w/(\rho_wg)\), and total hydraulic head \(H=h+z\). The water-flux vector is

\[

\mathbf q=-K(\theta)\nabla(h+z),

\]

where \(K\) is the unsaturated hydraulic conductivity. For rigid soil with incompressible water, conservation of water gives

\[

\frac{\partial\theta}{\partial t}

=\nabla\cdot[K(\theta)\nabla(h+z)]-S,

\]

where \(S\) is a volumetric sink term, such as root-water uptake, with units of reciprocal time. This nonlinear equation is known as Richards equation.

The rigid-soil assumption may be inappropriate for strongly swelling or collapsing soils. In such cases, deformation, porosity change and water flow must be coupled.

5.2 Infiltration

Rainfall infiltration is governed by rainfall intensity, surface condition, antecedent suction, retention behaviour and hydraulic conductivity. Before ponding, the surface may be prescribed by a flux equal to rainfall intensity. Once rainfall exceeds the soil’s infiltration capacity, ponding or runoff occurs and the surface condition changes toward a prescribed pressure head.

For one-dimensional vertical flow, with upward flux positive,

\[

q_z=-K\left(\frac{\partial h}{\partial z}+1\right).

\]

A downward infiltration rate \(i\) corresponds to \(q_z=-i\).

Under restrictive assumptions—homogeneous soil, a sharp wetting front, negligible initial surface ponding and constant saturated conductivity—the Green–Ampt infiltration capacity is

\[

f_c=K_s\left(1+\frac{\psi_f\Delta\theta}{F}\right),

\]

where \(F\) is cumulative infiltration, \(\psi_f\) is the positive wetting-front suction head and \(\Delta\theta\) is the increase in volumetric water content. Under continuous ponding,

\[

F=K_st+\psi_f\Delta\theta

\ln\left(1+\frac{F}{\psi_f\Delta\theta}\right).

\]

The model is useful for screening calculations but cannot fully represent layered soils, diffuse wetting fronts or hydraulic hysteresis.

5.3 Evaporation as a coupled boundary condition

Evaporation is not merely a prescribed removal of water. It couples liquid flow in the soil to vapour transfer through the surface and atmosphere. A resistance-based atmospheric flux, expressed as an equivalent liquid-water velocity, is

\[

E=\frac{\rho_{v,s}-\rho_{v,a}}

{\rho_w(r_a+r_s)},

\]

where \(\rho_{v,s}\) and \(\rho_{v,a}\) are vapour mass densities at the soil surface and in ambient air, while \(r_a\) and \(r_s\) are aerodynamic and surface resistances in seconds per metre. Positive \(E\) denotes upward evaporation.

The surface vapour density can be represented by

\[

\rho_{v,s}=RH_s\rho_{v,\mathrm{sat}}(T_s),

\qquad

RH_s=\exp\left(-\frac{M_ws_{t,s}}{\rho_wRT_s}\right),

\]

where \(T_s\) and \(s_{t,s}\) are surface temperature and total suction. The hydraulic boundary condition during evaporation is

\[

q_z(0,t)=E,

\]

or, when rainfall infiltration \(i\) occurs simultaneously,

\[

q_z(0,t)=E-i.

\]

These equations must be solved consistently with Richards equation. If atmospheric demand exceeds the rate at which liquid water can reach the surface, surface suction rises and actual evaporation falls below potential evaporation.

During stage-one evaporation, the surface remains sufficiently wet and evaporation is mainly controlled by atmospheric demand. During stage-two evaporation, a dry surface layer develops and internal liquid and vapour transport control the flux. At very low water contents, vapour diffusion and coupled heat transport may become important. Cracking, vegetation and salt accumulation can substantially alter the boundary condition.

6. Stress State and Effective-Stress Alternatives

For saturated soils, Terzaghi’s effective stress is \(\boldsymbol\sigma'=\boldsymbol\sigma-u_w\mathbf I\). Direct extension to unsaturated soil is difficult because air and water pressures act over different and evolving portions of the pore system.

6.1 Independent stress variables

A widely used framework employs:

\[

\boldsymbol\sigma-u_a\mathbf I

\quad\text{and}\quad

u_a-u_w.

\]

The first is net stress and the second is matric suction. Constitutive relationships may therefore be written as functions of both variables. This approach does not assume that all behaviour can be reduced to one effective stress.

6.2 Bishop-type effective stress

Bishop proposed

\[

\boldsymbol\sigma'

=(\boldsymbol\sigma-u_a\mathbf I)+\chi(u_a-u_w)\mathbf I,

\]

where \(0\leq\chi\leq1\) is an effective-stress parameter. The equation correctly approaches net stress when \(\chi=0\) and saturated effective stress when \(\chi=1\) and \(u_a\) is taken as the reference gas pressure.

Taking \(\chi=S_r\) is convenient but not universally valid. Mechanical effectiveness depends on water continuity, pore-scale menisci, fabric, hydraulic history and saturation definition. Effective saturation or calibrated nonlinear functions may provide better results.

6.3 Suction-stress concept

An alternative writes

\[

\boldsymbol\sigma'=\boldsymbol\sigma-u_a\mathbf I-\sigma^s\mathbf I,

\]

where suction stress \(\sigma^s\) is generally negative in the capillary regime. In a Bishop-equivalent form, \(\sigma^s=-\chi(u_a-u_w)\). This framework links retention behaviour to stress but remains dependent on constitutive assumptions.

No single formulation is universally superior. Model choice should be consistent with the measured variables, constitutive law, saturation range and intended prediction.

7. Shear Strength of Unsaturated Soil

7.1 Derivation from Bishop effective stress

For a saturated or effective-stress frictional material, the Mohr–Coulomb criterion is

\[

\tau_f=c'+\sigma_n'\tan\phi',

\]

where \(c'\) is effective cohesion, \(\phi'\) is effective friction angle and \(\sigma_n'\) is effective normal stress.

Substituting Bishop’s normal effective stress,

\[

\sigma_n'=(\sigma_n-u_a)+\chi(u_a-u_w),

\]

gives

\[

\tau_f=c'+(\sigma_n-u_a)\tan\phi'

+\chi(u_a-u_w)\tan\phi'.

\]

If, over a limited suction range, the suction contribution is approximated as linear and

\[

\tan\phi^b=\chi\tan\phi',

\]

then

\[

\boxed{\tau_f=c'+(\sigma_n-u_a)\tan\phi'

+(u_a-u_w)\tan\phi^b.}

\]

Here \(\phi^b\) quantifies the rate of strength increase with matric suction. This derivation shows that a constant \(\phi^b\) implicitly assumes a constant effective contribution of suction over the fitted range. In reality, \(\chi\) and \(\phi^b\) often decrease during substantial desaturation, so the strength envelope becomes nonlinear.

Worked Example 3: Unsaturated shear strength

Given \(c'=10\,\text{kPa}\), \(\sigma_n-u_a=100\,\text{kPa}\), \(u_a-u_w=200\,\text{kPa}\), \(\phi'=30^\circ\) and \(\phi^b=12^\circ\),

\[

\tau_f=10+100\tan30^\circ+200\tan12^\circ.

\]

\[

\tau_f=10+57.74+42.51=110.25\,\text{kPa}.

\]

This result is valid only if the linear strength parameters were calibrated over a suction range that includes 200 kPa.

7.2 Testing and interpretation

Unsaturated strength may be measured using modified direct-shear, triaxial or ring-shear apparatus. Axis translation independently controls air and water pressures but requires high-air-entry ceramics and adequate equilibration time. Volume change, air diffusion and incomplete suction equalisation are important error sources.

8. Collapse, Swelling and Hydro-Mechanical Coupling

8.1 Wetting-induced collapse

Collapsible soils possess an open, metastable structure maintained by suction, weak cementation or clay bridges. Under sustained net stress, wetting reduces suction and interparticle bonding, producing irreversible compression.

A double-oedometer or controlled-wetting test may quantify collapse potential as

\[

CP=\frac{e_{ ext{before wetting}}-e_{ ext{after wetting}}}{1+e_0}\times100\%,

\]

where both void ratios are evaluated at the same vertical stress and \(e_0\) is the initial void ratio. The result depends on stress level, initial density, water content, fabric and wetting path.

Engineering controls include prewetting, dynamic compaction, replacement, grouting, deep foundations and drainage. Uncontrolled prewetting can cause damage to adjacent structures and requires careful planning.

8.2 Swelling and shrinkage

Expansive soils contain active clay minerals and swell when suction decreases. Mechanisms include adsorption, diffuse-double-layer interactions and fabric rearrangement. Swell pressure depends on dry density, mineralogy, stress state, initial suction, pore-water chemistry and confinement.

Drying causes shrinkage and may generate cracks. These cracks increase infiltration during later rainfall, making the hydro-mechanical response strongly path-dependent. Common mitigation measures include moisture barriers, drainage, lime treatment, controlled compaction and stiffened or deep foundations.

8.3 Constitutive modelling

Elastoplastic models for unsaturated soil commonly use net stress and suction, or an effective stress supplemented by a hardening variable. Wetting may reduce apparent preconsolidation stress and trigger plastic collapse. Sophisticated models can reproduce loading–collapse behaviour, hydraulic hysteresis and saturation-dependent compressibility, but parameter identification is demanding.

9. Illustrative Case: Rainfall-Induced Failure of a Compacted Fill Slope

Background

This fictional case concerns a 12 m high compacted silty fill slope in a tropical region. Construction occurred during the dry season. Routine saturated testing indicated adequate frictional strength, but no retention or unsaturated-strength tests were performed.

Problem

A prolonged storm followed several months of dry weather. Tension cracks near the crest admitted runoff. Shallow movement developed along a compacted lift interface.

Analysis

For a representative potential sliding plane, take net normal stress \(45\,\text{kPa}\), mobilised shear stress \(32\,\text{kPa}\), \(c'=5\,\text{kPa}\), \(\phi'=28^\circ\) and \(\phi^b=12^\circ\).

Before rainfall, suction was approximately 80 kPa:

\[

FS=\frac{5+45\tan28^\circ+80\tan12^\circ}{32}=1.44.

\]

After infiltration reduced suction to 10 kPa:

\[

FS=\frac{5+45\tan28^\circ+10\tan12^\circ}{32}=0.97.

\]

The loss of suction contribution reduced the factor of safety below unity even before positive pore-water pressure developed. Layering and cracks accelerated infiltration, invalidating a homogeneous one-dimensional interpretation.

Approach and solution

The remedial investigation combined field tensiometers, water-content sensors, rainfall records, retention testing and suction-controlled shear tests. A transient seepage analysis supplied pore-pressure and suction fields to a slope-stability model. Crest runoff was intercepted, cracks were sealed, subsurface drainage was installed, and critical areas were regraded and reinforced.

Outcome

Monitoring during later storms showed smaller and slower suction reductions. Calculated factors of safety remained above the project criterion, subject to continued drain maintenance.

Learning points

1. Apparent dry-season stability may rely heavily on suction.

2. Rainfall intensity alone does not determine infiltration; antecedent state and surface defects matter.

3. Saturated strength parameters do not capture transient suction loss.

4. Field monitoring and hydraulic–mechanical modelling should inform one another.

5. Drainage performance requires inspection and long-term governance.

10. Professional Practice, Limitations and Emerging Methods

Unsaturated analyses are sensitive to spatial variability, sample disturbance, hysteresis, boundary conditions and parameter non-uniqueness. Best practice includes using site-specific retention and conductivity data, matching laboratory stress and hydraulic paths to field conditions, conducting sensitivity analyses, and validating predictions against monitoring.

Climate change increases concern over intense rainfall, drought, desiccation cracking and repeated wetting–drying cycles. Remote sensing, distributed moisture sensors and automated suction monitoring improve data availability. Machine-learning models can estimate retention parameters or identify anomalous field response, but they should not be used outside their training domain without physical checks. Physics-informed models offer promise but do not remove the need for reliable measurements.

Professional and ethical obligations require transparent reporting of parameter uncertainty, model assumptions and failure consequences. Conservative treatment of suction may be appropriate when long-term wetting is credible. Conversely, ignoring suction entirely can misrepresent construction-stage behaviour and prevent rational design. Monitoring data, calibration records and design changes should be auditable, while safety-critical sensors require maintenance and independent verification.

Chapter Summary

Unsaturated soils contain interconnected solid, water and air phases. Their behaviour is governed by phase relations, suction, hydraulic history and stress state. Volumetric water content satisfies \(\theta=wG_s/(1+e)=w\rho_d/\rho_w\), rather than being generally equal to gravimetric water content.

The water-retention curve links suction with water content and provides a basis for estimating unsaturated conductivity. Drying and wetting paths differ because of pore geometry, contact-angle effects, entrapped air and fabric change. Richards equation governs transient water flow, while infiltration and evaporation require physically consistent surface boundary conditions.

Unsaturated mechanical behaviour may be described using independent net stress and suction variables, Bishop-type effective stress or suction stress. Substitution of Bishop effective stress into Mohr–Coulomb strength provides a rational derivation of the extended shear-strength equation. Wetting can remove suction-derived strength, cause collapse in metastable soils or produce swelling in expansive soils. Reliable engineering therefore requires coupled hydraulic–mechanical reasoning, appropriate testing, field monitoring and explicit treatment of uncertainty.

Key Terms

Air-entry value: Suction at which air begins to enter the largest interconnected water-filled pores.

Axis translation: Laboratory technique for controlling matric suction by elevating air and water pressures while maintaining their difference.

Bishop effective stress: Stress variable combining net stress and a suction contribution through parameter \(\chi\).

Collapse potential: Vertical strain index describing wetting-induced compression at a specified stress.

Degree of saturation: Ratio of water volume to total void volume.

Effective saturation: Normalised water content between fitted residual and saturated states.

Evaporation boundary: Coupled condition linking atmospheric vapour demand with soil water supply.

Hydraulic hysteresis: Dependence of water retention or conductivity on drying–wetting history.

Matric suction: Difference between pore-air and pore-water pressures.

Net stress: Total stress relative to pore-air pressure.

Osmotic suction: Suction associated with dissolved solutes.

Residual water content: Fitted low-water-content parameter of a retention model.

Richards equation: Nonlinear conservation equation for variably saturated water flow.

Scanning curve: Intermediate retention path generated after reversal between drying and wetting.

Soil-water retention curve: Relationship between suction and water content or saturation.

Suction stress: Effective internal stress contribution associated with capillarity and adsorption.

Total suction: Combined matric and osmotic suction.

Volumetric water content: Volume of water divided by total soil volume.

Wetting collapse: Irreversible compression caused by suction reduction under load.

Review Questions

Short Answer Questions

1. Distinguish matric suction from total suction.

2. State the correct relationship between gravimetric and volumetric water content.

3. What physical processes cause hydraulic hysteresis?

4. Why does unsaturated hydraulic conductivity decline during drying?

5. What is the purpose of the Bishop parameter \(\chi\)?

Long Answer Questions

1. Explain the principal zones of a soil-water retention curve and the factors affecting its shape.

2. Discuss the assumptions, strengths and limitations of the van Genuchten–Mualem framework.

3. Derive the extended unsaturated shear-strength equation from Bishop effective stress and explain when a constant \(\phi^b\) is inappropriate.

4. Explain the mechanisms of wetting collapse and swelling, including suitable investigation and mitigation methods.

5. Formulate the hydraulic and atmospheric boundary conditions needed to analyse infiltration and evaporation from a soil surface.

Analytical / Application Questions

1. A soil has \(w=0.16\), \(G_s=2.65\) and \(e=0.90\). Calculate \(S_r\), \(\theta\) and \(\rho_d\).

2. For \(c'=8\,\text{kPa}\), net normal stress \(75\,\text{kPa}\), suction \(120\,\text{kPa}\), \(\phi'=32^\circ\) and \(\phi^b=14^\circ\), calculate shear strength and assess the effect of reducing suction to 20 kPa.

3. Develop a monitoring and modelling plan for an expansive-soil embankment exposed to seasonal drought and intense rainfall.

Multiple Choice Questions with Answers

Question 1

A soil has gravimetric water content 0.10, specific gravity 2.70 and void ratio 0.80. What is its volumetric water content?

A. 0.100

B. 0.150

C. 0.216

D. 0.338

Correct Answer: B. 0.150

Question 2

Matric suction is defined as:

A. Pore-water pressure minus pore-air pressure

B. Total stress minus pore-air pressure

C. Pore-air pressure minus pore-water pressure

D. Osmotic suction minus total suction

Correct Answer: C. Pore-air pressure minus pore-water pressure

Question 3

Which process primarily explains why a pore may drain through a narrow throat but refill differently during wetting?

A. Ink-bottle effect

B. Consolidation drainage

C. Mineral dissolution

D. Elastic rebound

Correct Answer: A. Ink-bottle effect

Question 4

In the van Genuchten model, effective saturation is 0.50, saturated volumetric water content is 0.40 and residual water content is 0.08. What is the volumetric water content?

A. 0.16

B. 0.20

C. 0.24

D. 0.32

Correct Answer: C. 0.24

Question 5

With elevation positive upward, which surface flux represents downward infiltration at rate i?

A. q_z=i

B. q_z=-i

C. q_z=0

D. q_z=i/ρw

Correct Answer: B. q_z=-i

Question 6

During stage-two evaporation, the evaporation rate is primarily limited by:

A. Atmospheric demand alone

B. Saturated conductivity alone

C. Internal soil water and vapour transport

D. Pore-air pressure remaining exactly zero

Correct Answer: C. Internal soil water and vapour transport

Question 7

In Bishop's effective-stress equation, which value of χ recovers the saturated effective-stress limit?

A. 0

B. 0.25

C. 0.50

D. 1

Correct Answer: D. 1

Question 8

A soil has c′ = 5 kPa, net normal stress = 50 kPa, suction = 100 kPa, φ′ = 30° and φb = 10°. Its shear strength is approximately:

A. 33.9 kPa

B. 46.5 kPa

C. 51.5 kPa

D. 79.0 kPa

Correct Answer: C. 51.5 kPa

Question 9

Wetting-induced collapse most directly results from:

A. An increase in suction-supported interparticle bonding

B. Loss of suction or bonding in a metastable structure under load

C. Complete prevention of particle rearrangement

D. An increase in pore-air volume without deformation

Correct Answer: B. Loss of suction or bonding in a metastable structure under load

Question 10

Why may taking χ equal to degree of saturation be inaccurate?

A. Degree of saturation has pressure units

B. χ must always exceed unity

C. Mechanical water effectiveness also depends on continuity, fabric and hydraulic history

D. Degree of saturation can only be measured in saturated soil

Correct Answer: C. Mechanical water effectiveness also depends on continuity, fabric and hydraulic history