Soil Dynamics and Earthquake Geotechnics

Introduction and Context

Soil dynamics examines the response of soil deposits to time-dependent loading. Unlike conventional geotechnical design, which often treats loads as static or slowly varying, soil-dynamics problems involve inertia, cyclic stress, wave propagation, damping, resonance, and degradation of soil stiffness or strength. Important applications include earthquake-resistant foundations, machine foundations, railway and traffic-induced vibration, offshore structures, earth dams, retaining walls, excavations, and assessment of liquefaction susceptibility.

Earthquake geotechnics applies these principles to the interaction between seismic waves, soil deposits, foundations, slopes, retaining structures, and groundwater. The engineering objective is not merely to estimate a ground acceleration. It is to predict how the soil–structure system modifies, amplifies, attenuates, or redistributes seismic demand.

The subject requires integration of soil mechanics, structural dynamics, engineering seismology, numerical modelling, field investigation, and risk-informed decision-making. At postgraduate level, the engineer must understand both the simplifying assumptions used in design methods and the circumstances in which advanced analysis is justified.

Learning Objectives

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

1. Explain vibration, wave propagation, dynamic stiffness, damping, and cyclic soil behaviour.

2. Determine basic dynamic soil parameters from field and laboratory data.

3. Distinguish one-dimensional site response from soil–structure interaction.

4. Assess the susceptibility and triggering of liquefaction.

5. Evaluate seismic effects on slopes, retaining walls, and foundations.

6. Select suitable analytical, numerical, and field-investigation methods.

7. Recommend practical mitigation measures and recognise their limitations.

1. Fundamentals of Dynamic Soil Behaviour

1.1 Vibration and dynamic loading

A dynamic load varies with time. It may be harmonic, transient, impulsive, random, or earthquake-generated. A single-degree-of-freedom idealisation is commonly written as

mü + cũ + ku = p(t)

where m is mass, c is viscous damping coefficient, k is stiffness, u is displacement, and p(t) is the applied force. Dots denote derivatives with respect to time. The equation assumes linear behaviour and a lumped mass, stiffness, and damping representation. It is a useful conceptual model, but real soils exhibit nonlinear, hysteretic, strain-dependent behaviour.

For free vibration without damping, the natural circular frequency and natural frequency are

ω_n = √(k/m), f_n = ω_n/(2π), T_n = 1/f_n

where ω_n is in radians per second, f_n is in hertz, and T_n is the period in seconds. Resonance may occur when the frequency of excitation approaches the natural frequency of the soil–foundation system. In practice, damping and nonlinear soil response limit the theoretical resonant amplitude.

1.2 Shear-wave propagation

The most important body wave for many geotechnical earthquake problems is the shear wave. In a homogeneous, isotropic, linear elastic soil, the shear-wave velocity is

V_s = √(G_max/ρ)

where G_max is the small-strain shear modulus and ρ is mass density. Equivalently, using unit weight γ and gravitational acceleration g, ρ = γ/g. The formula assumes elastic response and negligible material heterogeneity at the strain level considered.

The compressional-wave velocity is

V_p = √[(K + 4G/3)/ρ]

where K is the bulk modulus and G is the shear modulus. In saturated soils, P-wave velocity is strongly affected by the near-incompressibility of water, whereas S-wave velocity is mainly controlled by the soil skeleton. Consequently, S-wave measurements are especially valuable for site classification and dynamic analyses.

The wavelength of a harmonic wave is

λ = V/f

where V is the relevant wave velocity and f is frequency. If the layer thickness is small relative to wavelength, wave propagation may be approximated as nearly uniform; if it is comparable with wavelength, phase differences and resonance become important.

1.3 Dynamic stiffness and strain dependence

Soil stiffness is not constant. At very small cyclic strains, particle contacts undergo approximately recoverable deformation and the maximum shear modulus, G_max, applies. With increasing strain, the secant or equivalent shear modulus decreases and damping generally increases. Results are often represented by modulus-reduction and damping curves:

G/G_max versus γ_c, and ξ versus γ_c

where γ_c is cyclic shear-strain amplitude and ξ is equivalent viscous damping ratio.

These curves depend on soil type, plasticity, confining pressure, overconsolidation ratio, number of cycles, fabric, saturation, and loading history. Curves obtained from one site should not be transferred uncritically to another. For advanced projects, site-specific resonant-column, cyclic triaxial, or torsional shear tests are preferred, although empirical correlations remain useful for preliminary assessment.

A common small-strain relation for a soil layer of thickness H over a rigid base is the fundamental period

T_0 ≈ 4H/V_s

This is a one-dimensional, vertically propagating shear-wave approximation. It is most appropriate for a relatively uniform layer with a strong impedance contrast at depth. Layering, inclined interfaces, three-dimensional topography, and nonlinear response can significantly alter the actual period.

1.4 Damping and energy dissipation

Damping represents energy loss during cyclic loading. It includes radiation damping, material damping, and hysteretic energy dissipation. For a linear single-degree-of-freedom system, the damping ratio is

ξ = c/(2√km)

This definition applies to an equivalent viscous model. Real soil damping is commonly described by the area within a stress–strain hysteresis loop. A wider loop indicates greater energy dissipation. Excessive use of constant damping may be misleading when soil stiffness changes substantially during shaking.

2. Dynamic Soil Properties and Investigation

2.1 Essential parameters

The parameters required depend on the problem, but commonly include:

• small-strain shear-wave velocity, V_s;
• maximum shear modulus, G_max;
• strain-dependent modulus-reduction and damping curves;
• density, unit weight, and Poisson’s ratio;
• permeability and groundwater conditions;
• cyclic resistance and cyclic mobility characteristics;
• dynamic interface friction and adhesion;
• degradation of strength under repeated loading.

The choice of parameters must match the analysis strain range. Using G_max in an analysis that generates strains of 0.5% can substantially overestimate stiffness and underestimate deformation.

2.2 Field methods

Cross-hole and down-hole seismic tests directly measure travel times between boreholes or between the ground surface and a borehole. Seismic cone penetration testing provides a continuous V_s profile alongside cone resistance and sleeve friction. Multichannel analysis of surface waves and spectral-analysis-of-surface-waves methods infer stiffness from dispersive surface-wave propagation. These methods are economical for profiling but require careful interpretation, particularly where strong lateral variability exists.

Standard penetration testing and cone penetration testing are not direct dynamic tests, but their results are widely used in liquefaction correlations. Borehole logging, groundwater monitoring, geophysical imaging, and laboratory sampling should be integrated rather than treated as separate activities.

2.3 Laboratory methods

Resonant-column and torsional-shear tests are appropriate for small to moderate cyclic strains and can determine stiffness and damping. Cyclic triaxial and cyclic simple-shear tests are used to study pore-pressure generation, cyclic resistance, deformation, and liquefaction. Bender elements provide small-strain shear-wave velocity, but specimen disturbance, boundary effects, saturation quality, and anisotropy must be considered.

No laboratory test reproduces every feature of an earthquake. Stress-path differences, irregular loading, drainage conditions, sample disturbance, and scale effects introduce uncertainty. Laboratory results should therefore be checked against field measurements and geological interpretation.

3. Site Response and Soil–Structure Interaction

3.1 Seismic waves and site effects

Earthquake motion at a site is modified by source characteristics, travel through rock and soil, local stratigraphy, topography, groundwater, and nonlinear soil behaviour. A soft deposit over stiff rock may amplify motion over a range of periods, while strong shaking may cause modulus reduction and increased damping, shifting the response toward longer periods and reducing high-frequency amplification.

The simplest site-response model is one-dimensional equivalent-linear analysis. The soil column is divided into horizontal layers, each assigned a strain-compatible shear modulus and damping ratio. The input motion is applied at the base, and wave propagation is calculated in the vertical direction. Iterations update strain-compatible properties until convergence.

Equivalent-linear analysis is efficient and widely used, but it assumes cyclic properties can be represented by effective linear values. It may be unreliable for very large strains, strong pore-pressure generation, cyclic mobility, sharply nonlinear response, or significant permanent deformation. Nonlinear time-domain analyses update constitutive behaviour during shaking and are preferable when deformation and excess pore pressure are central design concerns.

3.2 Impedance contrast and resonance

At an interface between materials of different shear-wave impedance, part of the wave is reflected and part transmitted. Shear-wave impedance is

Z_s = ρV_s

A large contrast between soft soil and rock can produce amplification, especially when the layer thickness and wave velocity create a resonant condition. The fundamental site period is only a first indicator; higher modes and irregular layering may be important for tall or flexible structures.

3.3 Soil–structure interaction

The free-field ground motion is not necessarily the motion experienced by a foundation. Soil–structure interaction includes:

• inertial interaction caused by structural mass and foundation forces;
• kinematic interaction caused by foundation embedment and averaging of spatially varying motion;
• foundation compliance and radiation damping;
• nonlinear contact, uplift, sliding, and gapping.

A rigid foundation may filter high-frequency motion, while a flexible foundation may lengthen the system period. For ordinary low-rise structures on competent ground, simplified procedures may be sufficient. Nuclear facilities, bridges, tall buildings, deep basements, and structures on soft or liquefiable soils require more detailed analysis.

4. Liquefaction and Cyclic Softening

4.1 Mechanism

Liquefaction is a loss of effective stress and stiffness in saturated, loose, cohesionless or low-plasticity soils under cyclic loading. When cyclic shear strains cause contractive particle rearrangement, drainage is too slow to dissipate the resulting water pressure. Excess pore-water pressure rises, reducing effective stress:

σ′ = σ − u

where σ′ is effective normal stress, σ is total normal stress, and u is pore-water pressure. As u approaches the initial effective stress, the soil may experience very low effective stress, large deformation, flow-type instability, or cyclic mobility.

Liquefaction is not restricted to clean sands. Silty soils may liquefy or undergo cyclic softening depending on plasticity, fabric, structure, drainage, and stress history. Clay-like soils may experience cyclic degradation without satisfying the conventional definition of liquefaction.

4.2 Triggering assessment

The simplified procedure compares cyclic stress ratio, CSR, with cyclic resistance ratio, CRR. A commonly used stress-based approximation is

CSR = 0.65 (a_max/g)(σ_v0/σ′_v0) r_d

where a_max is peak horizontal ground acceleration, g is gravitational acceleration, σ_v0 is total vertical stress, σ′_v0 is initial effective vertical stress, and r_d is a depth-dependent stress-reduction coefficient. The factor 0.65 converts peak cyclic loading to an approximate equivalent uniform cyclic stress. This equation is empirical and is generally applied within the range for which the selected liquefaction correlation was developed.

The factor of safety against triggering is commonly expressed as

FS_liq = CRR/CSR

A value below unity indicates that the estimated demand exceeds the estimated resistance. In practice, CRR is corrected for magnitude, overburden stress, fines content, density, and, where appropriate, static shear stress. Cone penetration, SPT, and shear-wave-based correlations each have distinct databases and limitations.

The cyclic stress approach does not by itself predict post-liquefaction settlement, lateral spreading, or flow failure. Those require separate deformation analyses.

4.3 Consequences

Potential consequences include:

• bearing-capacity failure and foundation punching;
• excessive total and differential settlement;
• lateral spreading toward a free face or water body;
• flotation of buried tanks and pipelines;
• loss of pile lateral support;
• embankment deformation;
• flow slides where driving shear stress exceeds residual resistance.

Liquefaction risk is governed by hazard, susceptibility, triggering, and consequences. A site with high triggering potential may still have tolerable risk if vulnerable structures are absent; conversely, moderate susceptibility may be unacceptable for critical infrastructure.

4.4 Mitigation

Mitigation strategies include densification by vibrocompaction or dynamic compaction, stone columns, gravel drains, deep mixing, permeation or compaction grouting, drainage enhancement, replacement of susceptible soil, deep foundations, ground improvement beneath embankments, and structural isolation from lateral spreading. Selection depends on soil gradation, depth, groundwater, access, environmental constraints, construction vibration, and verification requirements.

A ground-improvement specification should define performance objectives, such as minimum post-treatment CPT resistance, allowable pore-pressure response, maximum settlement, or drainage capacity. Verification testing is essential; installation records alone do not demonstrate performance.

5. Seismic Response of Slopes and Retaining Structures

5.1 Slopes

Seismic slope stability may be assessed using pseudo-static, displacement-based, or fully dynamic methods. In a pseudo-static analysis, horizontal and sometimes vertical inertial coefficients are applied to the sliding mass. A simplified horizontal coefficient is

k_h = a_h/g

where a_h is the selected horizontal design acceleration. The method is convenient but does not represent the duration, frequency content, progressive strength loss, or accumulated displacement of real earthquakes.

Newmark sliding-block analysis improves interpretation by allowing displacement whenever the driving acceleration exceeds a yield acceleration. It requires a representative acceleration time history and a rational estimate of yield acceleration. It remains a simplified rigid-block model and does not account directly for progressive failure, pore-pressure generation, or changing geometry.

Dynamic finite-element or finite-difference analysis is justified for large dams, critical slopes, sensitive foundations, major transport corridors, and sites with strong nonlinearity or complex groundwater conditions. Constitutive calibration and uncertainty analysis are as important as mesh refinement.

5.2 Retaining walls

Earthquake loading increases wall pressure through transient inertia, wall–soil interaction, and possible loss of backfill strength. Mononobe–Okabe theory extends Coulomb earth-pressure theory using horizontal and vertical seismic coefficients. It assumes a planar failure wedge, homogeneous backfill, a sufficiently long wall, and a specified wall movement condition. It may become singular or inappropriate near limiting combinations of wall friction, backfill slope, and seismic coefficient.

The method should not be used blindly for rigidly restrained basement walls, highly cohesive or unsaturated backfills, liquefiable backfills, walls with complex geometry, or situations involving large permanent deformation. Drainage, sliding, overturning, bearing capacity, structural flexure, and global stability must all be checked.

If backfill liquefies, conventional active-pressure calculations may be unconservative. The design may require liquefaction mitigation, replacement of backfill, drainage, flexible detailing, or deformation-based analysis.

6. Machine Foundations and Vibration Control

Machine foundations are subjected to periodic or impulsive forces. Design requires compatibility between operating frequency, foundation natural frequencies, allowable amplitude, soil bearing resistance, settlement, and neighbouring equipment sensitivity.

For a simplified vertical system, the natural frequency is

f_n = (1/2π)√(k_z/m)

where k_z is vertical foundation stiffness and m is the vibrating mass. The model assumes a single degree of freedom and linear stiffness. In reality, rocking, horizontal translation, coupling between modes, soil radiation damping, and frequency-dependent impedance may be significant.

A sound design process includes:

1. identification of operating frequencies and force amplitudes;

2. dynamic soil investigation and groundwater assessment;

3. estimation of frequency-dependent foundation impedance;

4. checks for resonance and permissible displacement or velocity;

5. static bearing and settlement checks;

6. evaluation of vibration transmission to adjacent facilities.

Mitigation may involve increasing mass, changing foundation dimensions, increasing separation, improving soil, installing isolation trenches, using resilient pads, or modifying machine operation. Increasing stiffness is not automatically beneficial because it can move a natural frequency closer to the operating frequency.

7. Worked Example: Preliminary Liquefaction Screening

Consider a saturated sand layer at 8 m depth. The measured total vertical stress is σ_v0 = 150 kPa and the effective vertical stress is σ′_v0 = 90 kPa. The estimated peak horizontal acceleration is 0.20g, and a preliminary stress-reduction coefficient is r_d = 0.90. A corrected in-situ test correlation gives CRR_7.5 = 0.18 for magnitude 7.5 shaking. Assume the magnitude-scaling factor is 1.0 for this preliminary example.

The cyclic stress ratio is

CSR = 0.65(0.20)(150/90)(0.90)

CSR = 0.195.

The factor of safety is

FS_liq = CRR/CSR = 0.18/0.195 = 0.92.

The screening result is therefore FS_liq < 1.0, indicating possible triggering. This is not a final design conclusion. The engineer should verify groundwater level, stress corrections, fines and plasticity, earthquake magnitude and duration, static shear stress, spatial variability, and the reliability of the selected correlation. If triggering remains credible, post-liquefaction settlement, lateral spreading, foundation vulnerability, and mitigation alternatives must be evaluated.

8. Illustrative Case Study: Industrial Facility on a Soft Alluvial Deposit

Background

An illustrative industrial facility is proposed on 12 m of soft to medium-dense alluvial sand and silt over dense gravel. The groundwater table lies 2 m below ground level. The facility contains vibration-sensitive rotating equipment and supports a rigid steel frame.

Problem

Initial geotechnical exploration based only on conventional borings suggested adequate static bearing capacity. However, preliminary seismic assessment indicated a site period close to the anticipated fundamental period of the structure and possible liquefaction in loose sand lenses. The machine supplier also specified a strict operating vibration limit.

Analysis

A combined investigation was undertaken using CPT with pore-pressure measurement, down-hole V_s testing, groundwater monitoring, laboratory cyclic testing of representative samples, and surface-wave profiling. The results showed strong layering, with low V_s in the upper deposit and denser material at depth. One-dimensional equivalent-linear analysis indicated amplification in the structure’s period range. Liquefaction screening identified two thin but continuous loose sand layers. A foundation-only dynamic model underestimated response because it ignored soil–structure interaction and machine-induced rocking.

Approach and solution

The upper loose layers beneath the critical equipment zone were treated using deep compaction grouting, with acceptance based on post-treatment CPT resistance and settlement performance. The main structural foundation was separated from the machine block by a designed joint. The machine block was made heavier and wider, but its dimensions were selected through frequency analysis so that the revised natural frequencies did not approach the operating frequencies. A nonlinear site-response sensitivity study was performed using several compatible earthquake records. Drainage and groundwater monitoring provisions were incorporated, and construction-stage vibration limits were specified.

Outcome

Verification testing showed improved resistance in the treated zones. The final analysis predicted acceptable liquefaction triggering margins and machine vibration levels under the design operating condition. The project also retained a contingency plan for additional treatment if field acceptance criteria were not met.

Learning points

The case demonstrates that static bearing capacity does not establish seismic safety. Site response, liquefaction, machine vibration, foundation dynamics, construction effects, and verification must be considered as an integrated system. It also illustrates the value of staged investigation: inexpensive screening was followed by targeted testing where uncertainty affected decisions.

9. Challenges, Limitations, and Professional Judgement

The principal uncertainty in soil dynamics is often not numerical precision but the reliability and representativeness of input data. Major limitations include spatial variability, imperfect groundwater information, sample disturbance, uncertain earthquake records, empirical correlations outside their database, constitutive-model error, and poorly constrained post-liquefaction behaviour.

Engineers should report uncertainty explicitly. Sensitivity analyses may vary V_s, damping, groundwater level, triggering resistance, permeability, interface friction, and input-motion characteristics. Results should be expressed as decision-relevant ranges rather than false precision.

Regulatory requirements differ by jurisdiction and may refer to national seismic codes, geotechnical standards, dam-safety guidance, or infrastructure-owner criteria. The responsible engineer must use the legally applicable edition and document seismic hazard, site classification, design spectrum, liquefaction methodology, load combinations, and acceptance criteria. Critical facilities may require peer review, independent checking, quality assurance, and emergency planning.

Ethically, engineers must not conceal uncertainty or present a screening correlation as a site-specific prediction. Ground improvement claims must be supported by verification. Monitoring data that contradicts the design model should trigger reassessment rather than selective dismissal.

10. Numerical Modelling, Monitoring, and Emerging Practice

Finite-element and finite-difference methods can model nonlinear soil behaviour, coupled pore-pressure generation, contact, staged construction, and wave propagation. Effective-stress analysis is appropriate when excess pore pressure and drainage control the response, but it requires a constitutive model calibrated for the relevant soil. A sophisticated model with poor parameters is not necessarily more reliable than a simpler calibrated model.

High-quality practice increasingly combines distributed sensing, automated groundwater monitoring, seismic interferometry, digital elevation models, and probabilistic hazard analysis. Machine learning can assist with pattern recognition in CPT data, rapid surrogate modelling, anomaly detection, and damage classification. It should not replace physical interpretation, data-quality checks, uncertainty quantification, or engineering accountability. Training-data bias and poor extrapolation are particularly serious risks for rare earthquake conditions.

Best practice consists of: defining the performance objective; developing a geological and geotechnical model; selecting investigation methods that reduce decision-critical uncertainty; matching model complexity to the consequence of failure; calibrating parameters; validating predictions against field evidence; designing mitigation with measurable acceptance criteria; and monitoring construction and long-term performance.

Chapter Summary

Soil dynamics concerns the response of soil to time-varying loading, including vibration, wave propagation, resonance, damping, cyclic stiffness degradation, and soil–structure interaction. Shear-wave velocity and maximum shear modulus are fundamental parameters, but dynamic stiffness and damping must be selected for the strain range of interest.

Site response is controlled by impedance contrasts, layer thickness, wave frequency, nonlinear soil behaviour, and groundwater. Equivalent-linear methods are efficient for moderate strains, whereas nonlinear effective-stress analyses are more appropriate when large strains, pore-pressure generation, or permanent deformation govern.

Liquefaction involves cyclic pore-pressure generation and reduction of effective stress in susceptible saturated soils. Simplified CSR–CRR procedures are valuable screening tools, but triggering, settlement, lateral spreading, and flow failure require separate consideration. Seismic slopes and retaining walls may be assessed using pseudo-static, displacement-based, or dynamic methods, with careful attention to their assumptions. Machine foundations require frequency compatibility, dynamic impedance, damping, and vibration-control measures.

Reliable earthquake geotechnics integrates field investigation, laboratory testing, analytical and numerical modelling, uncertainty assessment, mitigation, verification, and monitoring. Professional judgement is essential because empirical relationships and models have finite ranges of applicability.

Key Terms

Dynamic loading: Loading that varies with time and produces inertia effects.

Shear-wave velocity: Velocity at which a shear wave propagates through soil.

Maximum shear modulus: Small-strain shear modulus, commonly denoted G_max.

Dynamic stiffness: Soil or foundation stiffness under cyclic or frequency-dependent loading.

Damping: Dissipation of vibration energy.

Resonance: Large dynamic response occurring when excitation approaches a natural frequency.

Impedance: Product of density and wave velocity for a propagating wave mode.

Site response: Modification of earthquake motion by local soil and geological conditions.

Soil–structure interaction: Mutual influence of structural and soil response during loading.

Equivalent-linear analysis: Frequency-domain analysis using strain-compatible linear properties.

Nonlinear analysis: Time-domain analysis in which soil properties evolve during loading.

Liquefaction: Severe loss of effective stress and stiffness caused by cyclic loading in susceptible saturated soil.

Cyclic stress ratio: Earthquake-induced cyclic shear stress normalised by initial effective stress.

Cyclic resistance ratio: Soil resistance to a specified level of cyclic loading.

Cyclic mobility: Repeated accumulation of deformation associated with cyclic stress and changing effective stress.

Lateral spreading: Ground movement toward a free face or gentle slope after liquefaction.

Pseudo-static analysis: Stability analysis using equivalent inertial forces.

Newmark sliding-block analysis: Displacement method based on acceleration exceeding a yield acceleration.

Dynamic impedance: Frequency-dependent relationship between foundation force and displacement.

Ground improvement: Treatment intended to increase stiffness, strength, drainage, or liquefaction resistance.

Review Questions

Short Answer Questions

1. Define dynamic soil behaviour and explain why static soil parameters may be inadequate for earthquake analysis.

2. What is the significance of shear-wave velocity in site characterization?

3. Distinguish equivalent-linear analysis from nonlinear time-domain analysis.

4. Explain how excess pore pressure reduces effective stress during liquefaction.

5. State two limitations of pseudo-static slope analysis.

Long Answer Questions

1. Explain the strain dependence of soil stiffness and damping, including the role of modulus-reduction and damping curves.

2. Describe a complete field and laboratory investigation programme for a potentially liquefiable site.

3. Discuss the mechanisms of site amplification and the limitations of one-dimensional site-response analysis.

4. Compare pseudo-static, Newmark, and fully dynamic approaches to seismic slope stability.

5. Explain the design principles for machine foundations subjected to periodic loading.

Analytical / Application Questions

1. A saturated sand layer has σ_v0 = 180 kPa, σ′_v0 = 110 kPa, a_max = 0.25g, and r_d = 0.85. Calculate CSR using the simplified expression CSR = 0.65(a_max/g)(σ_v0/σ′_v0)r_d. If CRR = 0.20, calculate FS_liq and interpret the result.

2. A 20 m soil layer has an average shear-wave velocity of 200 m/s. Estimate its fundamental period using T_0 ≈ 4H/V_s, and explain why the estimate may differ from the measured site period.

3. An industrial machine operates at 12 Hz on a foundation whose estimated natural frequency is 11 Hz. Evaluate the resonance risk and propose at least three engineering responses, explaining why simply increasing stiffness may not always solve the problem.

Multiple Choice Questions with Answers

Question 1

Which parameter is most directly related to the small-strain shear modulus of soil?

A. Shear-wave velocity

B. Liquid limit only

C. Coefficient of permeability only

D. Plasticity index only

Correct Answer: A. Shear-wave velocity

Question 2

For a homogeneous soil layer over a rigid base, the approximate fundamental period is

A. H/V_s

B. 2H/V_s

C. 4H/V_s

D. V_s/(4H)

Correct Answer: C. 4H/V_s

Question 3

If excess pore-water pressure increases while total stress remains constant, effective stress

A. Increases

B. Decreases

C. Remains necessarily unchanged

D. Becomes equal to total stress

Correct Answer: B. Decreases

Question 4

Using CSR = 0.65(a_max/g)(σ_v0/σ′_v0)r_d, with a_max/g = 0.20, σ_v0 = 150 kPa, σ′_v0 = 100 kPa, and r_d = 0.80, CSR is approximately

A. 0.078

B. 0.156

C. 0.195

D. 0.240

Correct Answer: B. 0.156

Question 5

A factor of safety against liquefaction triggering is commonly calculated as

A. CSR/CRR

B. CRR/CSR

C. CRR + CSR

D. CRR − CSR

Correct Answer: B. CRR/CSR

Question 6

Which method explicitly permits displacement accumulation when acceleration exceeds a yield acceleration?

A. Newmark sliding-block analysis

B. Simple bearing-capacity analysis

C. Elastic settlement analysis

D. Static Rankine analysis

Correct Answer: A. Newmark sliding-block analysis

Question 7

A major limitation of equivalent-linear site-response analysis is that it

A. Cannot use soil layers

B. Cannot represent any damping

C. May be unreliable at very large strains and strong pore-pressure generation

D. Requires no earthquake input motion

Correct Answer: C. May be unreliable at very large strains and strong pore-pressure generation

Question 8

For a single-degree-of-freedom machine-foundation model, increasing mass while stiffness remains constant generally

A. Increases natural frequency

B. Decreases natural frequency

C. Has no effect on natural frequency

D. Makes damping ratio exactly zero

Correct Answer: B. Decreases natural frequency

Question 9

Which condition is most directly associated with liquefaction susceptibility?

A. Dry, cemented rock

B. Saturated loose granular soil

C. Very dense uncemented gravel only

D. Unsaturated stiff clay only

Correct Answer: B. Saturated loose granular soil

Question 10

Mononobe–Okabe theory is primarily used to estimate

A. Seismic earth pressure on retaining walls

B. Shear-wave velocity from CPT data

C. Machine operating frequency

D. Pore-water pressure dissipation time

Correct Answer: A. Seismic earth pressure on retaining walls