Soil Dynamics, Cyclic Loading and Earthquake Effects

Introduction and Context

Soil dynamics examines the response of soil deposits and geotechnical systems to time-varying loads. These loads may arise from earthquakes, machine foundations, traffic, blasting, wave action, pile driving, or repeated construction activity. Unlike conventional static analysis, dynamic analysis must consider inertia, wave propagation, strain-rate effects, damping, cyclic degradation, resonance, and the interaction between soil and structures.

Earthquake loading is particularly important because it can impose thousands of irregular stress cycles within a short period. The consequences range from tolerable vibration and small stiffness reduction to excessive settlement, lateral spreading, cyclic mobility, and complete bearing-capacity failure. Reliable assessment therefore requires integration of soil mechanics, elastodynamics, laboratory testing, field investigation, seismology, numerical modelling, and engineering judgement.

At postgraduate level, the engineer must distinguish between the mechanisms that control wave transmission, the parameters measured in laboratory tests, and the empirical procedures used for design. No single index or analysis method is universally adequate. The appropriate method depends on soil type, strain level, groundwater conditions, loading duration, seismic demand, and the performance objective.

Learning Objectives

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

1. Explain wave propagation in soil and derive the principal body-wave velocities.

2. Distinguish small-strain stiffness, modulus degradation, damping, and hysteretic behaviour.

3. Select and interpret laboratory and field methods for dynamic soil characterization.

4. Evaluate cyclic stress, cyclic resistance, liquefaction triggering, cyclic mobility, and post-cyclic deformation.

5. Explain one-dimensional and nonlinear site-response analysis and its limitations.

6. Integrate empirical, analytical, and numerical methods in earthquake geotechnical engineering.

7. Recognize uncertainty, ethical responsibilities, and appropriate professional safeguards in seismic design.

1. Dynamic Soil Behaviour

1.1 Stress, strain and time scale

For static loading, soil response is often represented by a stress–strain curve under monotonic loading. Under cyclic loading, the path is repeatedly reversed. The response depends on strain amplitude, number of cycles, loading frequency, drainage condition, initial stress state, fabric, saturation, and overconsolidation history.

At very small strains, soil behaviour is approximately elastic and the shear modulus is close to its maximum value, denoted by G_max. As shear strain increases, particle contacts rearrange and the secant or tangent modulus decreases. Simultaneously, energy dissipation increases. Thus a realistic constitutive description generally requires both modulus-reduction and damping relationships.

Dynamic soil problems are often classified by shear-strain level:

• Very small strain, typically below about 10^-5: nearly linear response; G_max and wave velocity are appropriate.
• Small to intermediate strain, approximately 10^-5 to 10^-3: nonlinear modulus reduction and increasing damping.
• Large strain, above approximately 10^-3: pronounced hysteresis, irreversible strain, pore-pressure generation, fabric change, and possible instability.

These ranges are indicative rather than universal. Clean sands, plastic clays, sensitive soils, and cemented materials can exhibit substantially different thresholds.

1.2 Effective stress and dynamic loading

The effective-stress principle remains central to saturated soil dynamics:

σ′ = σ − u

where σ′ is effective normal stress, σ is total normal stress, and u is pore-water pressure. Under rapid undrained cyclic loading, total stress may vary while the generated excess pore pressure Δu reduces effective stress. Because shear strength and stiffness depend strongly on σ′, pore-pressure generation can cause progressive softening and, in extreme cases, liquefaction.

For a saturated soil element, cyclic shearing tends to alter the soil fabric. Contractive soils generate positive excess pore pressure; dilative soils may generate negative pore pressure during part of the cycle. The net response depends on density, confining stress, stress reversal, and state relative to the critical state line.

2. Wave Propagation in Soil

2.1 Elastic waves

An ideal homogeneous, isotropic, linear-elastic soil supports compression waves (P waves) and shear waves (S waves). The P-wave velocity is

V_p = √[(K + 4G/3)/ρ]

and the S-wave velocity is

V_s = √(G/ρ)

where K is the bulk modulus, G is the shear modulus, and ρ is mass density. These equations assume small strain, homogeneous isotropic elasticity, and negligible attenuation over the distance considered. In saturated soil, V_p may be high because the nearly incompressible pore water contributes substantially to the bulk response, whereas V_s is governed mainly by the soil skeleton and is therefore more useful for site characterization.

For an isotropic elastic material, Poisson’s ratio can be related to wave velocities by

ν = [V_p^2 − 2V_s^2]/[2(V_p^2 − V_s^2)]

provided the assumptions of isotropic elasticity are reasonable. Near-surface soil commonly has V_p much greater than V_s under saturated conditions, but interpretation must account for drainage, frequency, and layering.

The shear-wave travel time through a horizontally layered profile is

t = Σ (h_i/V_{s,i})

where h_i is layer thickness and V_{s,i} is the representative shear-wave velocity of layer i. The average velocity to depth H is therefore

V_{s,avg} = H / Σ(h_i/V_{s,i}).

This is a travel-time or harmonic-type average, not an arithmetic average. It is important in classifying sites and estimating fundamental period.

2.2 Reflection, refraction and impedance contrast

At an interface between materials of different wave impedance, part of the incident wave is reflected and part transmitted. For shear waves, impedance is commonly represented by Z_s = ρV_s. Large impedance contrasts can amplify motion in a soft layer and create strong reflections. Layering, dipping interfaces, topography, and two- or three-dimensional geometry can produce effects that cannot be represented by a simple vertical-column model.

A simplified estimate of the fundamental period of a soil layer over a stiff base is

T_0 ≈ 4H/V_s

for a uniform layer with a compliant surface and approximately rigid base. This equation is a first-mode approximation and should not be used without considering the actual velocity profile, damping, impedance contrast, and input-motion definition.

2.3 Attenuation and damping

Wave amplitude decreases with distance because of geometric spreading and material damping. Geometric spreading is associated with wavefront expansion; material damping converts mechanical energy into heat and microstructural rearrangement. Scattering from heterogeneity can add further attenuation. The damping ratio is not a universal soil constant: it depends on strain amplitude, frequency, confining stress, density, saturation, and loading history.

3. Dynamic Soil Properties and Their Measurement

3.1 Maximum shear modulus

The small-strain shear modulus is related to shear-wave velocity by

G_max = ρV_s^2.

If unit weight γ is used instead of mass density, ρ = γ/g, so G_max = γV_s^2/g. Units must be consistent: with γ in N/m³ and V_s in m/s, G_max is in Pa.

G_max is particularly valuable because it can be measured in situ without imposing large strains. It does not, however, represent the modulus during strong shaking. The operational modulus at a given strain is often expressed as

G = G_max (G/G_max)

where G/G_max is obtained from laboratory curves, published correlations, or calibrated constitutive models.

3.2 Laboratory tests

Important laboratory methods include:

• Resonant-column tests: determine small- to intermediate-strain shear modulus and damping under controlled cyclic excitation.
• Torsional shear tests: measure cyclic shear response, including modulus degradation and pore-pressure generation.
• Cyclic triaxial tests: assess cyclic strength and liquefaction resistance under specified stress paths.
• Cyclic simple-shear tests: reproduce approximately horizontal shear stresses and are often more representative of level-ground earthquake loading.
• Bender-element tests: measure very small-strain wave velocity, provided signal interpretation and boundary effects are controlled.

Sample disturbance, reconsolidation procedures, membrane compliance, end restraint, anisotropy, drainage control, and stress-path differences can substantially affect results. Laboratory data should therefore be interpreted with the field fabric and stress history in mind.

3.3 Field methods

Downhole and crosshole seismic tests directly estimate shear-wave velocity. Seismic cone penetration testing provides a continuous profile when properly calibrated. Surface-wave methods, including spectral analysis of surface waves and multichannel analysis of surface waves, infer velocity profiles from dispersion. Standard penetration resistance, cone resistance, density, fines content, and geological history are used in empirical liquefaction procedures, but they are indirect measures of dynamic behaviour.

A robust investigation commonly combines geophysical velocity measurements with borings, sampling, groundwater observations, in situ penetration tests, and laboratory cyclic testing where consequences are significant.

4. Cyclic Loading, Hysteresis and Degradation

4.1 Hysteretic response

A cyclic stress–strain curve forms a loop. The energy dissipated per unit volume in one cycle is the enclosed area:

W_d = ∮ τ dγ

where τ is shear stress and γ is shear strain. For a sinusoidal cycle, an equivalent viscous damping ratio may be defined as

D = W_d/(4πW_s)

where W_s = (1/2)τ_aγ_a is the maximum strain energy for a linear equivalent system, and τ_a and γ_a are representative stress and strain amplitudes. The definition is an equivalent parameter; real soil damping may be amplitude-dependent, frequency-dependent, and non-viscous.

4.2 Modulus-reduction and damping curves

The normalized modulus G/G_max generally decreases with increasing cyclic strain, while damping increases. Curves developed by Darendeli, Vucetic–Dobry, Seed-type procedures, and other researchers are useful only within their calibration ranges. Plasticity index, mean effective stress, overconsolidation ratio, loading frequency, and number of cycles influence the curves.

Equivalent-linear analysis uses a strain-compatible modulus and damping to approximate nonlinear response. It is efficient for moderate nonlinearity, but it may become unreliable when strong shaking causes large stiffness changes, significant pore-pressure generation, or sharp yielding.

4.3 Cyclic degradation

Repeated loading can reduce stiffness and strength through fabric rearrangement, bond breakage, pore-pressure accumulation, particle crushing, or progressive strain localization. Degradation is not necessarily monotonic for all soils. Dense dilative sands can harden after initial cycles, while loose contractive sands may soften rapidly. Clays can show cyclic degradation, rate effects, and reconsolidation settlement after excess pore pressure dissipates.

5. Liquefaction and Cyclic Mobility

5.1 Conceptual distinction

Liquefaction is a broad term for loss of strength or stiffness in saturated, loose or contractive soil under cyclic loading. Flow liquefaction occurs when the available static shear stress exceeds the post-triggering shear resistance and large, rapidly developing deformation follows. Cyclic mobility occurs when cyclic loading produces transient loss of effective stress and repeated deformation, but the soil may regain strength during parts of the loading history and may not undergo uncontrolled flow.

The term “initial liquefaction” is sometimes used when excess pore pressure reaches the initial effective overburden stress, so that the mean effective stress approaches zero. This condition is a useful laboratory indicator but is not by itself a complete field-failure criterion.

5.2 Stress-based triggering framework

The cyclic stress ratio is commonly defined as

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 overburden stress, σ′_v0 is initial effective vertical stress, and r_d is a depth-dependent stress-reduction coefficient. The factor 0.65 converts a variable earthquake shear-stress history into an equivalent uniform cyclic stress representation. This expression is empirical and is normally applied within the depth and earthquake ranges for which it was calibrated.

The cyclic resistance ratio, CRR, is estimated from corrected cone penetration resistance, corrected penetration resistance, shear-wave velocity, or laboratory testing. A factor of safety against triggering is commonly expressed as

FS_liq = CRR/CSR.

Values greater than unity indicate resistance exceeding the estimated demand under the adopted model; they do not guarantee absence of damaging deformation. Magnitude scaling, overburden correction, fines correction, aging, cementation, and stress-history effects must be treated explicitly.

5.3 Empirical procedures

The simplified procedure based on SPT uses corrected blow count, often denoted (N_1)₆₀cs, where corrections account for energy, borehole diameter, rod length, sampler configuration, overburden, and fines content. CPT procedures use normalized cone resistance and sleeve friction. Shear-wave procedures use corrected V_s. Each method has uncertainty and should not be extrapolated blindly to gravelly soils, unusual silts, cemented soils, organic deposits, or non-level ground.

5.4 Post-liquefaction deformation

Triggering analysis answers whether significant pore-pressure generation is likely. It does not directly predict settlement or lateral spreading. Post-liquefaction settlement depends on density, thickness, drainage, reconsolidation compressibility, and stress redistribution. Differential settlement is usually more damaging than uniform settlement.

Lateral spreading requires a free face or gentle slope, a liquefiable layer, and a mechanism for downslope or toward-free-face movement. Empirical displacement models may be used, but their uncertainty can be large. Where consequences are high, numerical effective-stress analysis and ground-improvement verification may be necessary.

6. Site Response Analysis

6.1 One-dimensional wave equation

For vertically propagating shear waves in a horizontally layered soil profile, the small-strain equation of motion is

ρ ∂²u/∂t² = ∂τ/∂z

with τ = G ∂u/∂z for linear elasticity. Combining these gives

∂²u/∂t² = V_s² ∂²u/∂z².

Boundary conditions include the input motion at the base and a free-surface condition, or an appropriate compliant-base formulation. The soil profile is discretized into layers, and transfer functions can be calculated in the frequency domain.

6.2 Equivalent-linear and nonlinear methods

Equivalent-linear analysis iteratively selects modulus and damping compatible with calculated strain. It is economical and widely used for one-dimensional site response. Its weaknesses include reliance on strain-compatible averages, inability to represent permanent deformation directly, and possible over-damping or inaccurate response under very strong motion.

Nonlinear time-domain analysis updates stress, strain, stiffness, damping, and possibly pore pressure at each time step using a constitutive model. It can represent cyclic degradation, strength limits, and irreversible strain more directly, but results depend heavily on model calibration, numerical integration, boundary conditions, and input-motion selection.

6.3 Input motions and uncertainty

Input motions must be compatible with the selected boundary condition and hazard level. Recorded motions may require scaling or spectral matching, but excessive modification can distort duration, phasing, and cyclic content. Multiple records should normally be used because a single accelerogram cannot represent the uncertainty in amplitude, frequency content, duration, and phase.

Important sources of uncertainty include:

• spatial variability in soil and groundwater;
• uncertainty in V_s, density, and dynamic curves;
• epistemic uncertainty in constitutive models;
• aleatory variability in earthquake records;
• uncertainty in pore-pressure response and drainage;
• interaction between soil, foundation, and structure.

7. Worked Example: Wave Velocity and Fundamental Period

Consider a soil layer 20 m thick with unit weight γ = 18 kN/m³ and measured shear-wave velocity V_s = 200 m/s. Estimate its small-strain shear modulus and approximate fundamental period over a stiff base.

Mass density is

ρ = γ/g = 18,000/9.81 = 1,835 kg/m³.

Therefore,

G_max = ρV_s² = 1,835(200)² = 73,400,000 Pa ≈ 73.4 MPa.

Using the uniform-layer approximation,

T_0 ≈ 4H/V_s = 4(20)/200 = 0.40 s.

The result is a preliminary estimate. If the velocity increases substantially with depth, the actual period will differ from the uniform-layer value, and a layered site-response analysis is preferable.

8. Applied Case: Illustrative Liquefaction Assessment for a Port Reclamation

Background

An illustrative port expansion is planned on 12 m of hydraulically placed sand over dense native sand. The groundwater table is 1.5 m below ground level. A nearby active fault produces a design peak ground acceleration of 0.25g. CPT soundings indicate loose to medium-dense sand between depths of 3 and 10 m, with corrected cone resistance suggesting variable liquefaction resistance.

Problem

The owner must determine whether earthquake shaking could cause triggering, excessive settlement, or lateral spreading toward the harbour edge. A simple factor of safety alone is insufficient because the site contains a free face and high-value crane rails.

Analysis

The investigation team first established groundwater levels, stratigraphy, density, fines content, V_s, and the geometry of the harbour slope. CPT-based CRR values were calculated with corrections for overburden and fines, while SPT data and selected cyclic laboratory tests provided independent checks. CSR was estimated using the adopted acceleration, vertical stresses, effective stresses, and a depth-reduction coefficient. The strongest concern occurred in the loose saturated reclamation sand, where estimated FS_liq values were below unity in several layers.

The team then performed one-dimensional effective-stress site-response analyses using several compatible earthquake records. Results indicated substantial pore-pressure generation, temporary stiffness reduction, and post-shaking reconsolidation settlement. A separate lateral-spreading assessment predicted that deformation would concentrate near the free face. Because the consequence classification was high, the analysis included sensitivity cases for groundwater rise, lower density, and alternative earthquake duration.

Approach and solution

The selected mitigation combined densification of the upper reclamation sand, gravel drains to accelerate pore-pressure dissipation, and a locally reinforced quay-edge zone. Improvement was verified through post-treatment CPT and shear-wave measurements. Drain design was checked for clogging, filter compatibility, installation disturbance, and drainage capacity. Structural tolerances were incorporated into the performance criteria rather than relying solely on a binary liquefaction/no-liquefaction decision.

Outcome

Post-improvement testing showed increased penetration resistance and shear-wave velocity. Reanalysis produced factors of safety above the project criterion over most of the treated zone and materially reduced predicted settlement and lateral displacement. Residual uncertainty remained in the untreated transition zone, which was addressed through monitoring and a contingency plan.

Learning points

1. Liquefaction triggering, settlement, and lateral spreading are different design questions.

2. Field correlations should be checked using independent measurements and geological interpretation.

3. High-consequence sites require sensitivity analysis and performance-based criteria.

4. Ground improvement must be verified after construction, not assumed from installation records alone.

5. Drainage, maintenance, monitoring, and emergency procedures are part of geotechnical risk management.

9. Professional Practice, Governance and Emerging Methods

Seismic geotechnical decisions have public-safety consequences. Engineers must state assumptions, disclose uncertainty, use current local codes and standards, and avoid presenting empirical correlations outside their validated domain. Data quality, chain of custody for samples, calibration of instruments, and transparent software verification are essential. Independent peer review is appropriate for major dams, nuclear facilities, hospitals, ports, lifeline corridors, and dense urban developments.

Artificial intelligence and machine learning can assist with velocity-profile inversion, anomaly detection in CPT data, record selection, and probabilistic surrogate modelling. They do not remove the need for geological judgement. Training-data bias, extrapolation, explainability, and unsafe automated decisions are significant risks. AI-generated correlations should be benchmarked against independent field and laboratory data and documented sufficiently for audit.

Contemporary practice is moving toward probabilistic seismic hazard analysis, performance-based earthquake engineering, three-dimensional and coupled effective-stress modelling, distributed sensing, and digital site characterization. Research continues on fabric-sensitive constitutive models, microbial and chemical ground improvement, robotics for rapid post-earthquake assessment, and physics-informed machine learning. These developments should complement—not replace—mechanics-based interpretation and professional accountability.

Best-Practice Workflow

A defensible dynamic soil assessment generally follows these steps:

1. Define the hazard, performance objectives, geometry, and consequences of failure.

2. Develop a geological and hydrogeological model before selecting correlations.

3. Measure V_s and penetration resistance using appropriate field methods.

4. Obtain representative samples and perform cyclic laboratory tests where needed.

5. Select modulus-reduction, damping, pore-pressure, and strength models consistent with the soil and strain range.

6. Choose and validate earthquake input motions and boundary conditions.

7. Conduct screening analyses before advanced numerical modelling.

8. Evaluate triggering, deformation, settlement, lateral spreading, and foundation interaction separately.

9. Quantify uncertainty through sensitivity studies or probabilistic analysis.

10. Verify ground improvement and establish inspection, monitoring, and emergency procedures.

Challenges and Limitations

Dynamic soil assessment is limited by incomplete knowledge of subsurface variability, disturbance of samples, scale effects, uncertain groundwater conditions, and the difficulty of reproducing earthquake stress paths in the laboratory. Empirical liquefaction methods are powerful screening tools but are not universal constitutive laws. One-dimensional site response can miss basin effects, topographic amplification, inclined layering, and structural interaction. Numerical models can create false confidence when parameters are poorly calibrated. Finally, post-earthquake performance depends not only on soil response but also on foundation flexibility, utilities, adjacent structures, and the time required for repair.

Chapter Summary

Soil dynamics concerns the response of soil to time-varying loading and requires consideration of inertia, wave propagation, damping, nonlinear stiffness, cyclic degradation, pore-pressure generation, and irreversible deformation. Shear-wave velocity provides a primary measure of small-strain stiffness, with G_max = ρV_s². P- and S-wave velocities depend on the elastic moduli and density, while impedance contrasts control reflection and amplification.

Cyclic loading produces hysteresis and energy dissipation. Modulus-reduction and damping curves allow approximate nonlinear analysis, but their validity depends on strain level, soil type, stress history, and calibration. Liquefaction assessment distinguishes triggering from the resulting settlement, lateral spreading, or flow failure. CSR–CRR methods are useful empirical tools, but corrections, uncertainty, and applicability limits must be explicitly considered.

Site-response analysis ranges from equivalent-linear one-dimensional procedures to nonlinear effective-stress simulations. The chosen method must match the level of shaking and the performance objective. A reliable professional workflow integrates geological interpretation, field testing, laboratory data, analytical modelling, sensitivity analysis, independent review, and post-construction verification. The central engineering principle is that seismic safety is a performance and uncertainty-management problem, not merely a calculation of one factor of safety.

Key Terms

Dynamic soil mechanics: Study of soil response to time-dependent loading.

Shear-wave velocity: Velocity of an S wave through soil, commonly used to characterize stiffness.

Maximum shear modulus: Small-strain shear modulus, G_max, associated with the initial soil stiffness.

Wave impedance: Product of mass density and wave velocity governing reflection and transmission.

Hysteresis: Stress–strain behaviour in which loading and unloading paths differ.

Damping ratio: Equivalent measure of energy dissipated during cyclic loading.

Cyclic degradation: Progressive reduction of stiffness or strength under repeated loading.

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

Cyclic resistance ratio: Soil resistance to a specified cyclic loading demand.

Liquefaction: Cyclic loss of soil stiffness or strength caused mainly by excess pore-pressure generation.

Flow liquefaction: Uncontrolled large deformation after loss of resistance in a contractive soil.

Cyclic mobility: Repeated transient softening and deformation without necessarily producing flow failure.

Site response: Modification of bedrock motion by the overlying soil profile.

Equivalent-linear analysis: Approximation using strain-compatible modulus and damping.

Nonlinear analysis: Time-domain analysis that updates constitutive response as loading proceeds.

Lateral spreading: Ground displacement toward a free face or downslope after liquefaction.

Stress path: Sequence of stresses followed by a soil element during loading.

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

Performance-based design: Design linked to specified deformation or damage objectives.

Review Questions

Short Answer Questions

1. Why is shear-wave velocity generally more useful than compressional-wave velocity for characterizing the stiffness of near-surface soil?

2. Define hysteretic damping and explain how energy dissipation is represented on a stress–strain loop.

3. Distinguish liquefaction triggering from post-liquefaction settlement.

4. State two principal limitations of equivalent-linear site-response analysis.

5. Why must groundwater conditions be established carefully in liquefaction assessment?

Long Answer Questions

1. Derive the expressions for P-wave and S-wave velocity in an isotropic linear-elastic soil and discuss their assumptions.

2. Explain how cyclic loading changes soil modulus, damping, pore pressure, and strength for contractive and dilative soils.

3. Compare SPT-, CPT-, shear-wave-, and laboratory-based liquefaction assessment methods, including their limitations.

4. Describe a complete one-dimensional site-response analysis workflow, from site characterization to interpretation of surface motion.

5. Discuss the professional and ethical responsibilities associated with seismic geotechnical design at a high-consequence facility.

Analytical / Application Questions

1. A 25 m uniform soil layer has V_s = 250 m/s, unit weight 19 kN/m³, and is underlain by stiff rock. Calculate G_max and estimate the fundamental period using T_0 ≈ 4H/V_s. Explain why the estimate may differ from an actual site-response result.

2. At a depth in saturated sand, a simplified analysis gives CSR = 0.18 and CRR = 0.23. Calculate the triggering factor of safety and explain why this result does not by itself predict settlement or lateral spreading.

3. Develop a decision framework for a reclaimed port site where liquefaction triggering is possible, including investigation, analysis, mitigation, verification, monitoring, and residual-risk communication.

Multiple Choice Questions with Answers

Question 1

Which equation relates maximum small-strain shear modulus to shear-wave velocity?

A. G_max = ρV_s²

B. G_max = ρ/V_s²

C. G_max = V_s/ρ

D. G_max = ρgV_s

Correct Answer: A. G_max = ρV_s²

Question 2

For a uniform soil layer over a stiff 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

Which condition most directly promotes liquefaction in saturated sand?

A. Positive excess pore pressure reducing effective stress

B. Complete drainage during every cycle

C. Increasing effective stress during cyclic loading

D. Very high cementation of particle contacts

Correct Answer: A. Positive excess pore pressure reducing effective stress

Question 4

In the simplified CSR expression, r_d represents the

A. density correction factor

B. depth-dependent stress-reduction coefficient

C. damping ratio

D. record scaling factor

Correct Answer: B. depth-dependent stress-reduction coefficient

Question 5

If CRR = 0.24 and CSR = 0.16, the simplified liquefaction factor of safety is

A. 0.67

B. 1.00

C. 1.50

D. 2.40

Correct Answer: C. 1.50

Question 6

The area enclosed by a cyclic stress–strain loop represents

A. elastic modulus

B. energy dissipated per unit volume in one cycle

C. initial effective stress

D. wave travel time

Correct Answer: B. energy dissipated per unit volume in one cycle

Question 7

Equivalent-linear site-response analysis primarily uses

A. constant zero damping and zero stiffness

B. strain-compatible modulus and damping

C. only compressional-wave velocity

D. static bearing-capacity equations

Correct Answer: B. strain-compatible modulus and damping

Question 8

Cyclic mobility differs from flow liquefaction because cyclic mobility

A. always occurs only in dry soil

B. involves transient softening and does not necessarily cause uncontrolled flow

C. requires no cyclic loading

D. cannot produce ground deformation

Correct Answer: B. involves transient softening and does not necessarily cause uncontrolled flow

Question 9

For layered soil, the travel-time average shear-wave velocity to depth H is calculated as

A. ΣV_s,i/n

B. H/Σ(h_i/V_s,i)

C. Σ(h_iV_s,i)/H

D. HΣ(h_iV_s,i)

Correct Answer: B. H/Σ(h_i/V_s,i)

Question 10

A major limitation of empirical liquefaction correlations is that they

A. are universal constitutive laws for every soil

B. cannot be affected by groundwater level

C. may be unreliable outside their calibration range

D. directly predict all post-liquefaction displacement

Correct Answer: C. may be unreliable outside their calibration range