Q: Sedimentation (hydrometer) analysis assumptions: Stokes-law based grain-size analysis assumes which of the following about particles and the settling environment?

Introduction / Context: Hydrometer and pipette analyses estimate fine-grained soil size distribution from sedimentation velocity. The interpretation relies on Stokes’ law, which links particle diameter to terminal settling velocity under laminar flow. Understanding the idealizing assumptions behind Stokes’ law is essential for correct test application and limitations. Given Data / Assumptions: Spherical, smooth particles. Laminar flow with negligible inertia (low Reynolds number). Independent settling without particle interaction. Infinite or sufficiently large fluid domain with negligible wall effects. Concept / Approach: Stokes’ law expresses v = (g (ρ_s − ρ_f) d^2) / (18 μ) for a single rigid sphere settling in a viscous fluid. Wall proximity, particle concentration, shape irregularity, and flocculation violate the assumptions and bias diameter estimates. Laboratory procedures attempt to mitigate these effects by dilution, dispersants, and selecting appropriate cylinder sizes. Step-by-Step Solution: Identify which statements directly reflect Stokes’ assumptions.All of (a), (b), (c) are standard assumptions → choose “All the above”. Verification / Alternative check: Corrections exist for wall effects and non-sphericity, confirming that these are indeed simplifying assumptions, not always realities. Why Other Options Are Wrong: (e) omits the important wall-effect assumption; (a)–(c) alone are incomplete; therefore the aggregate is correct. Common Pitfalls: Applying Stokes’ law at high concentrations or with flocculated clays; ignoring temperature-viscosity corrections. Final Answer: All the above

Q: Identifying cohesive soils: Which of the following is most appropriately classified as a cohesive soil for geotechnical design purposes?

Introduction / Context: Cohesive soils exhibit significant plasticity and apparent cohesion due to clay mineral surfaces and adsorbed water. Correctly identifying a soil as cohesive versus cohesionless guides the choice of laboratory tests (e.g., Atterberg limits) and strength parameters (c, φ) for analysis. Given Data / Assumptions: Cohesive soils: clays and some silts with plasticity. Cohesionless soils: sands and gravels with little to no plasticity. Naming should refer to a soil type, not a construction condition. Concept / Approach: “Clay” is the canonical cohesive soil, often showing plasticity, shrink–swell, and low permeability. Black cotton soil is an expansive clay, also cohesive, but the option set requests a single best identification. “Compacted ground” is not a soil type, and lateritic red earth can vary widely, sometimes behaving as granular or weakly cohesive depending on cementation and fines. Step-by-Step Solution: Match definition: cohesive soil → clay minerals dominate behavior.Select the unambiguous choice: Clay. Verification / Alternative check: USCS classes CL, CI, CH describe cohesive clays with plastic fines; expansive variants (black cotton soils) fall within CH/CI categories but the general term “clay” is the baseline cohesive descriptor. Why Other Options Are Wrong: (a) Red earth may be lateritic and not consistently cohesive; (c) is cohesive but is a specific sub-type causing ambiguity; (d) is not a soil type; (e) well-graded sand is cohesionless. Common Pitfalls: Equating color names with engineering behavior; treating construction state (“compacted”) as a classification. Final Answer: Clay

Question 1

Seepage Beneath Hydraulic Structures – Streamline Shape Without a Floor If there is no impervious floor or boundary provided at the bottom of a hydraulic structure (e.g., a weir without a floor), the seepage streamlines tend to follow which idealize…

Accepted Answer

Introduction / Context: Design of hydraulic structures on permeable foundations requires understanding seepage patterns. Classical flow approximations (e.g., Bligh’s creep theory and potential flow analogies) provide intuitive shapes for flow lines when structural floors or cutoffs are absent. Given Data / Assumptions: Homogeneous, isotropic pervious foundation. No impervious floor at the structure's base. Two-dimensional seepage under the structure is considered. Concept / Approach: Without a floor, the equipotential and streamlines under a narrow obstruction approximate circular arcs due to symmetry and boundary conditions. The idealized streamline beneath the structure tends toward a semi-circular path connecting upstream and downstream faces, a result consistent with potential flow solutions for obstacles on a pervious half-space. Step-by-Step Solution: Model the base as a line obstruction on a pervious medium.Apply symmetry and boundary conditions → potential lines and streamlines form orthogonal families.Recognize that streamlines wrap around the toe tracing semi-circular trajectories beneath the structure. Verification / Alternative check: Flow nets drawn for structures without floors show nearly circular flow tubes under the base, while adding floors or cutoffs distorts these into elongated paths. Why Other Options Are Wrong: Straight or parabolic paths do not satisfy boundary conditions; semi-elliptical forms are more representative when floors/cutoffs exist and geometry is elongated, not for a bare base. Common Pitfalls: Confusing idealized streamline shapes with actual, more complex patterns when anisotropy or layered foundations are present. Final Answer: A semi-circle

Question 2

Boussinesq Solution – Vertical Stress on the Axis Beneath a Point Load For a point load Q acting at the ground surface of a homogeneous, isotropic, elastic half-space, the vertical stress at depth z directly below the load (on the axis of loading) i…

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Introduction / Context: The Boussinesq elastic solution provides closed-form expressions for stress distribution in a semi-infinite, homogeneous, isotropic, linear-elastic half-space due to a surface point load. The axial stress beneath the load is frequently used in settlement and stress distribution calculations below footings and embankments. Given Data / Assumptions: Point load Q applied at the surface. Elastic, homogeneous, isotropic half-space. Interest is the vertical stress σ_z at a depth z directly beneath the load (r = 0 along the axis). Concept / Approach: From Boussinesq’s equations, the vertical stress at a general point is σ_z = (3 Q / (2 π)) * (z^3 / R^5), where R = (r^2 + z^2)^(1/2) and r is radial distance from the load axis. On the axis (r = 0), R = z, so σ_z simplifies to σ_z = (3 Q) / (2 π z^2). This elegant result shows that the axial vertical stress decays with the square of depth and is independent of Poisson’s ratio for the axial point. Step-by-Step Solution: Start with σ_z = (3 Q / (2 π)) * (z^3 / R^5).Set r = 0 on axis → R = z.Obtain σ_z = (3 Q) / (2 π z^2). Verification / Alternative check: The same expression can be recovered by integrating the axisymmetric stress influence factor I_z = 3/(2π) * 1/(1 + (r/z)^2)^(5/2) at r = 0, which equals 3/(2π). Why Other Options Are Wrong: (a), (d), and (e) have incorrect coefficients. (c) writes a general form that reduces to (b) only when the correct power of R is used; with R^3 the units are wrong. Common Pitfalls: Forgetting that on-axis stress is independent of Poisson’s ratio; mixing up depth dependence (1/z^2) with off-axis expressions. Final Answer: σ_z = (3 Q) / (2 π z^2)

Question 3

Plate load test for ultimate bearing capacity: For determining the ultimate bearing capacity of soil, a square steel bearing plate of size 30 cm to 75 cm is recommended. What should be the minimum plate thickness to ensure rigidity and avoid flexure…

Accepted Answer

Introduction / Context: In a field plate load test, a thick, rigid steel plate is used to simulate the foundation contact area and to obtain a realistic load–settlement curve. If the plate is too thin, it can bend under load, corrupting settlement readings and leading to an unsafe estimate of bearing capacity. This question checks knowledge of the standard minimum plate thickness used in geotechnical practice. Given Data / Assumptions: Square plate size typically between 30 cm and 75 cm on a side. Objective: measure load–settlement behavior to infer ultimate bearing capacity. Plate must behave as a rigid body (no flexural distortion). Soil reaction assumed uniform beneath a sufficiently rigid plate. Concept / Approach: The plate must be thick enough that its flexural stiffness greatly exceeds the soil reaction induced curvature. Field guidance and codal practices widely adopt a nominal minimum thickness so that the plate response remains essentially rigid under commonly applied jack loads in granular or cohesive soils. Among practical choices, 25 mm thickness has become a conventional baseline that prevents noteworthy bending for the plate sizes mentioned. Step-by-Step Solution: Identify the governing requirement: rigid plate to avoid flexural deflection.Check practical standard: 25 mm is widely adopted for 30–75 cm plates.Thinner plates (e.g., 5–20 mm) risk bending and measurement error. Verification / Alternative check: Empirical practice and many test setups use 25 mm thick plates successfully without measurable flexure, validating settlement readings. Heavier loading or larger plates sometimes use even thicker plates, but 25 mm is the accepted minimum for the stated size range. Why Other Options Are Wrong: 5–20 mm thicknesses are insufficient for rigidity over 30–75 cm spans under high jack pressures; they can bend and distort settlements. Common Pitfalls: Using thin plates due to convenience; not accounting for bending that masks true soil deformation; ignoring plate roughness and seating corrections. Final Answer: 25 mm

Question 4

Circular slip (Swedish circle) concept: The shearing force acting along the slices of a curved surface of slippage in an earth slope tends to make the soil mass slide in which direction?

Accepted Answer

Introduction / Context: Limit equilibrium analysis of slopes often assumes a circular slip surface (Swedish or Fellenius method). The potential sliding mass above this surface is subdivided into vertical slices. The mobilized shear along the base of each slice drives movement toward the slope face and toe. Understanding the direction of this driving component is fundamental to setting up force and moment equilibrium. Given Data / Assumptions: Curved (approximately circular) slip surface with a center of rotation. Vertical slices used to compute interslice forces and base reactions. Smooth slip surface with mobilized shear aligned tangentially. Weight of slices acts vertically; driving component acts downslope. Concept / Approach: At every point on the circular arc, the base shear acts in the tangential direction consistent with potential motion of the sliding mass. For typical concave-up slip circles in an earth embankment, the resultant effect of gravity on the mass produces a tangential downslope component that pushes the mass toward the open face, culminating at the toe region. Thus, the net tendency is to slide downward toward the toe, which is why resisting moments are commonly summed about a point near the circle center while checking factor of safety. Step-by-Step Solution: Resolve weight of a typical slice into components normal and tangential to the slip surface.Tangential component drives motion in the downslope direction.Across the mass, these tangential components collectively drive sliding toward the toe. Verification / Alternative check: In Fellenius/Ordinary method of slices, driving moment is the sum of W * r * sin α over all slices (α being the local inclination), which is maximum near the toe side of the slip surface. Why Other Options Are Wrong: (a) and (c) suggest centrally directed or upward motion, inconsistent with gravity-driven sliding. (d) and (e) do not represent the tangential downslope nature of the driving shear. Common Pitfalls: Confusing local shear direction with the radial line to the circle center; assuming uniform motion everywhere rather than net downslope tendency toward the toe. Final Answer: Down at the toe of the slope

Question 5

Aeolian deposits: “Loess” is a predominantly silt-sized soil (often called silty clay in older texts) formed primarily by which transporting agency?

Accepted Answer

Introduction / Context: Loess is a widespread geologic deposit consisting mainly of silt-sized particles that are loosely cemented, collapsible when wetted, and often metastable. Identifying its mode of formation is important because depositional processes control structure, fabric, and engineering behavior such as collapsibility and erodibility. Given Data / Assumptions: Loess is dominantly silt-sized with minor clay and sand fractions. It is typically homogeneous, porous, and capable of standing in vertical faces when dry. Often shows carbonate nodules and open, metastable structure. Concept / Approach: The hallmark of loess is its aeolian (wind-blown) origin. During glacial and periglacial periods, fine particles were lifted and transported by strong winds from outwash plains and floodplains, then deposited over large areas. The resulting low-density, open fabric explains its high sensitivity to wetting and potential collapse, features that are key in geotechnical design. Step-by-Step Solution: Identify defining traits: widespread, uniform silt; metastable open structure.Link to process: transportation and deposition by wind → aeolian deposit.Therefore, select wind as the primary agency. Verification / Alternative check: Global maps show extensive loess belts (e.g., China, Central Europe, Midwestern USA) associated with ancient wind patterns downwind of glacial outwash sources. Why Other Options Are Wrong: (a) Fluvial deposits typically form alluvium with layering; (b) glacial tills are mixed and dense; (d) gravity alone does not produce extensive, uniform silt blankets; (e) volcanic ash differs mineralogically and morphologically. Common Pitfalls: Confusing loess with silt derived from rivers; assuming its apparent cohesion indicates clay-rich origin. Final Answer: Wind (aeolian action)

Question 6

Slope stability condition: Failure of an earth slope will occur only when the total driving shear force acting along the potential slip surface is how related to the total available shearing strength?

Accepted Answer

Introduction / Context: Slope stability in soil mechanics is evaluated by comparing the total mobilized (driving) shear along a potential failure surface with the total available shearing strength (resisting) along that surface. The safety margin is commonly summarized by the factor of safety. This item tests the fundamental failure criterion. Given Data / Assumptions: Potential slip surface (often circular for simple analyses). Shear strength follows Mohr–Coulomb: τ_f = c + σ′ tan φ. Driving shear arises from self-weight, surcharge, and seepage forces. Concept / Approach: Failure occurs when the mobilized shear equals or exceeds the available strength. In practice, failure is identified when the driving shear slightly exceeds strength and progressive failure ensues. The factor of safety FS is defined as Strength / Mobilized shear. Stability requires FS > 1; incipient failure corresponds to FS ≈ 1; failure corresponds to FS < 1 (i.e., driving > strength). Step-by-Step Solution: Set criterion: Driving shear ≥ Shear strength.Translate to factor of safety: FS = Strength / Driving < 1 at failure.Therefore, failure when driving shear is greater than total shearing strength. Verification / Alternative check: Limit equilibrium methods (Fellenius, Bishop, Janbu) all pivot on this comparison. Numerical analyses also use a “shear strength reduction” method to find the state where mobilized shear just exceeds strength. Why Other Options Are Wrong: (a) Equality indicates incipient failure (limit state), not general stability. (c) If driving is less than strength, slope is stable. (d) and (e) ignore the full Mohr–Coulomb strength. Common Pitfalls: Confusing equality with actual observed failure; overlooking pore pressure effects that reduce σ′ and therefore strength. Final Answer: Greater than total shearing strength

Question 7

Sedimentation (hydrometer) analysis assumptions: Stokes-law based grain-size analysis assumes which of the following about particles and the settling environment?

Accepted Answer

Introduction / Context: Hydrometer and pipette analyses estimate fine-grained soil size distribution from sedimentation velocity. The interpretation relies on Stokes’ law, which links particle diameter to terminal settling velocity under laminar flow. Understanding the idealizing assumptions behind Stokes’ law is essential for correct test application and limitations. Given Data / Assumptions: Spherical, smooth particles. Laminar flow with negligible inertia (low Reynolds number). Independent settling without particle interaction. Infinite or sufficiently large fluid domain with negligible wall effects. Concept / Approach: Stokes’ law expresses v = (g (ρ_s − ρ_f) d^2) / (18 μ) for a single rigid sphere settling in a viscous fluid. Wall proximity, particle concentration, shape irregularity, and flocculation violate the assumptions and bias diameter estimates. Laboratory procedures attempt to mitigate these effects by dilution, dispersants, and selecting appropriate cylinder sizes. Step-by-Step Solution: Identify which statements directly reflect Stokes’ assumptions.All of (a), (b), (c) are standard assumptions → choose “All the above”. Verification / Alternative check: Corrections exist for wall effects and non-sphericity, confirming that these are indeed simplifying assumptions, not always realities. Why Other Options Are Wrong: (e) omits the important wall-effect assumption; (a)–(c) alone are incomplete; therefore the aggregate is correct. Common Pitfalls: Applying Stokes’ law at high concentrations or with flocculated clays; ignoring temperature-viscosity corrections. Final Answer: All the above

Question 8

Identifying cohesive soils: Which of the following is most appropriately classified as a cohesive soil for geotechnical design purposes?

Accepted Answer

Introduction / Context: Cohesive soils exhibit significant plasticity and apparent cohesion due to clay mineral surfaces and adsorbed water. Correctly identifying a soil as cohesive versus cohesionless guides the choice of laboratory tests (e.g., Atterberg limits) and strength parameters (c, φ) for analysis. Given Data / Assumptions: Cohesive soils: clays and some silts with plasticity. Cohesionless soils: sands and gravels with little to no plasticity. Naming should refer to a soil type, not a construction condition. Concept / Approach: “Clay” is the canonical cohesive soil, often showing plasticity, shrink–swell, and low permeability. Black cotton soil is an expansive clay, also cohesive, but the option set requests a single best identification. “Compacted ground” is not a soil type, and lateritic red earth can vary widely, sometimes behaving as granular or weakly cohesive depending on cementation and fines. Step-by-Step Solution: Match definition: cohesive soil → clay minerals dominate behavior.Select the unambiguous choice: Clay. Verification / Alternative check: USCS classes CL, CI, CH describe cohesive clays with plastic fines; expansive variants (black cotton soils) fall within CH/CI categories but the general term “clay” is the baseline cohesive descriptor. Why Other Options Are Wrong: (a) Red earth may be lateritic and not consistently cohesive; (c) is cohesive but is a specific sub-type causing ambiguity; (d) is not a soil type; (e) well-graded sand is cohesionless. Common Pitfalls: Equating color names with engineering behavior; treating construction state (“compacted”) as a classification. Final Answer: Clay

Soil Mechanics and Foundation Engineering Questions