Question 1

Terzaghi’s one-dimensional consolidation — basic assumptions: Which set of assumptions correctly represents Terzaghi's classical 1D consolidation theory for saturated soils?

Accepted Answer

Introduction / Context: Terzaghi’s one-dimensional consolidation theory provides a practical framework to predict time-dependent settlement of saturated clays under vertical loading. The theory simplifies complex soil behavior through a set of assumptions that enable a diffusion-type equation linking excess pore pressure and time. Given Data / Assumptions: Clay layer is homogeneous, isotropic, and fully saturated. Flow is one-dimensional and vertical. Water and soil grains are taken as incompressible relative to the voids volume change. Darcy’s law holds for flow at the prevailing gradients. Concept / Approach: These assumptions lead to the classical consolidation equation where the coefficient of consolidation governs the rate of excess pore-pressure dissipation. Deformation results from a decrease in void ratio as water is expelled; lateral strains are constrained in the 1D idealization, focusing on vertical strains and settlement. Step-by-Step Solution: Define vertical drainage path(s) and boundary conditions (single or double drainage).Adopt Darcy’s law to relate discharge to hydraulic gradient.Apply continuity to link volume change to pore-pressure decay.Obtain diffusion-type equation and solve for u(z, t) and settlement vs. time. Verification / Alternative check: Oedometer tests are interpreted using this framework to estimate the coefficient of consolidation and preconsolidation pressure for design. Why Other Options Are Wrong: Each listed statement is one of the required assumptions; none is incorrect when viewed within the simplified 1D framework. Common Pitfalls: Applying the model to heavily overconsolidated clays or structured soils without judgment; ignoring secondary compression which the basic theory does not capture explicitly. Final Answer: All the above

Question 2

Hydrometer test in soil classification: Which corrections are typically applied to hydrometer readings in a sedimentation analysis of fine-grained soils?

Accepted Answer

Introduction / Context: Hydrometer analysis estimates the particle-size distribution of fine soils (typically silt and clay sizes) by measuring suspension density at depth versus time. Accurate interpretation requires several standard corrections to the hydrometer readings before converting to equivalent particle diameter using sedimentation theory. Given Data / Assumptions: Hydrometer measures relative density of suspension at a reference depth. Readings are influenced by instrument geometry and test conditions. Chemical dispersant is used to prevent flocculation. Concept / Approach: Three key corrections are usually necessary: (1) Temperature correction to account for water viscosity and density changes; (2) Meniscus correction because reading is taken at the top of the meniscus in opaque suspensions; (3) Dispersing agent correction to subtract the effect of the solution’s specific gravity from the reading. Applying all three yields corrected hydrometer values for calculating particle diameters and percentages finer. Step-by-Step Solution: Record raw hydrometer reading at time t.Apply meniscus correction (instrument-specific constant).Apply dispersant correction based on blank test.Apply temperature correction using standard tables. Verification / Alternative check: Perform a blank test (water + dispersant) to quantify the dispersant effect; compare viscosity–temperature tables to confirm applied temperature corrections. Why Other Options Are Wrong: Any subset omits at least one required correction, leading to biased results. Common Pitfalls: Ignoring flocculation (insufficient dispersant or agitation); not maintaining isothermal conditions; misreading the meniscus in turbid suspensions. Final Answer: Temperature, meniscus, and dispersing agent corrections

Question 3

Mohr–Coulomb (Mohr’s straight line) failure concept: Which statements correctly characterize the basis of the Mohr's straight theory used in soil and rock strength?

Accepted Answer

Introduction / Context: The Mohr–Coulomb failure criterion represents shear failure by a straight line envelope in shear-normal stress space: τ = c + σ′ tan φ. It is widely applied to geomaterials due to its simplicity and reasonable approximation of strength behavior in many practical problems. Given Data / Assumptions: Material fails along a plane when shear stress reaches a critical combination with normal stress. Criterion is defined by two parameters: cohesion intercept c and friction angle φ. Intermediate principal stress is ignored in the basic form. Concept / Approach: Mohr’s circles represent stress states; failure is predicted when the circle touches the straight-line envelope. The theory assumes shear-dominated failure, with the envelope calibrated from tests such as triaxial compression where principal stresses are controlled and the critical plane is inferred from the Mohr representation. Step-by-Step Solution: Construct Mohr’s circle for the stress state at failure.Draw the linear envelope τ = c + σ′ tan φ.Intersection indicates the shear stress and normal stress on the slip plane at failure.Predict strength on other planes or stress paths using the same two parameters. Verification / Alternative check: Comparison with triaxial data at varying confining pressures shows approximate linearity for many soils within practical ranges. Why Other Options Are Wrong: Each statement A–C is a defining feature of the Mohr–Coulomb model; dismissing any one would misstate the criterion. Common Pitfalls: Applying the linear envelope at very low or very high confining pressures where curvature exists; neglecting the role of intermediate principal stress addressed by more advanced criteria (e.g., Drucker–Prager). Final Answer: All the above

Question 4

Principal stresses and planes: Through a point in a loaded soil mass, how many mutually orthogonal planes exist on which the stress is purely normal (no shear stress acts)?

Accepted Answer

Introduction / Context: Stress at a point in a continuous medium can be represented by a second-order tensor. On certain planes passing through that point, called principal planes, shear stresses vanish and only normal stresses act. Understanding this concept is foundational for failure criteria and stress transformations in soil mechanics. Given Data / Assumptions: Three-dimensional stress state in a continuum. Real, symmetric Cauchy stress tensor at a point. Materials considered are classical continua without couple stresses. Concept / Approach: The stress tensor has three real eigenvalues (principal stresses) with associated mutually orthogonal eigenvectors (principal directions). Planes normal to these principal directions are the principal planes. On each principal plane, shear stress is zero and only the corresponding principal normal stress acts. Step-by-Step Solution: Write the traction vector on an arbitrary plane.Set shear component to zero to identify extremal normal stresses.Solve the eigenvalue problem for the symmetric stress tensor → three eigenvalues/eigenvectors.Conclude there are three mutually orthogonal principal planes. Verification / Alternative check: Mohr’s circles (3D) also reflect three principal stresses where the circles intersect the normal-stress axis; shear is zero at these points. Why Other Options Are Wrong: One or two planes would be incomplete; four mutually orthogonal planes cannot exist in 3D Euclidean space. Common Pitfalls: Confusing 2D plane stress (two principal planes) with the full 3D case, which has three. Final Answer: 3

Question 5

Atterberg limits — indices and definitions: Choose the correct combined statement about plasticity index, consistency index, liquidity index, and toughness index for fine-grained soils.

Accepted Answer

Introduction / Context: Atterberg limits and derived indices describe the consistency and plasticity of cohesive soils. These parameters are widely used for classification, correlation with engineering properties, and specification compliance in earthworks and foundations. Given Data / Assumptions: Liquid limit (LL), plastic limit (PL), and natural water content (w) are known or measurable. Flow index (If) is the slope of the flow curve in the liquid limit determination. Concept / Approach: Definitions: Plasticity index (PI) = LL − PL.Consistency index (Ic) = (LL − w) / PI.Liquidity index (LI) = (w − PL) / PI.Toughness index (It) = PI / If.These indices help compare soils with different Atterberg limits and evaluate field consistency relative to the plastic range. Step-by-Step Solution: State each definition and confirm dimensional consistency.Note that LI + Ic = (LL − PL)/PI = 1, showing their complementarity.Recognize that higher PI often implies higher plasticity and potential swelling. Verification / Alternative check: Worked examples with typical values (e.g., LL = 60, PL = 25, w = 35) confirm the indices and their ranges. Why Other Options Are Wrong: Each of A–D correctly states standard definitions; therefore the combined correct answer is “All the above”. Common Pitfalls: Using percentages without consistent units; confusing consistency index with liquidity index; misreading the flow curve slope units when computing It. Final Answer: All the above

Question 6

Soil Index Property – Definition of Water Content (Moisture Content) In geotechnical engineering, the ratio of the weight of water to the weight of dry solids in a given mass of soil is known as what?

Accepted Answer

Introduction / Context: Correctly defining the basic index properties of soils is essential for laboratory testing, quality control, and design calculations in foundation engineering, earthworks, and pavement subgrades. Water content (also called moisture content) directly affects compaction, strength, and compressibility of soils and is therefore measured frequently in practice. Given Data / Assumptions: The question asks for the name of a ratio: weight of water divided by weight of dry soil solids. Standard geotechnical terminology is assumed. No numerical calculation is required. Concept / Approach: By definition, water content w is the mass (or weight) of water divided by the mass (or weight) of dry soil solids, usually expressed as a percentage. It is distinct from porosity n (volume-based) and void ratio e (also volume-based). It is also distinct from specific gravity Gs (ratio of densities) and does not by itself give the phase volumes without additional information. Step-by-Step Solution: Identify the requested ratio: W_water / W_solids.Recall the standard definition: water content w = (W_w / W_s) * 100% (often reported in %).Match this definition to the correct term among the options → 'Water content'. Verification / Alternative check: Laboratory methods such as oven-drying at 105–110 °C, the alcohol method, and pycnometer-based methods for coarse soils all determine water content consistent with the same definition. Why Other Options Are Wrong: Porosity and void ratio are volume ratios, not weight ratios. Specific gravity compares densities, not water mass to dry mass. Common Pitfalls: Confusing volume-based indices with mass-based moisture content; reporting w as a fraction when the specification expects a percentage. Final Answer: Water content

Question 7

Flow Net Applications in Seepage Analysis A properly constructed flow net for a homogeneous, isotropic soil can be used to determine which of the following quantities in seepage problems?

Accepted Answer

Introduction / Context: Flow nets are graphical solutions to Laplace’s equation for two-dimensional steady seepage in saturated soils. They are widely used beneath sheet pile walls, around cutoffs, and through earth dams to evaluate safety against boiling, piping, and uplift, and to estimate seepage quantities for drainage design. Given Data / Assumptions: Soil domain is treated as homogeneous and isotropic. Steady-state conditions with well-defined boundary conditions. The constructed net forms approximate curvilinear squares with orthogonal flow lines and equipotentials. Concept / Approach: From a flow net, discharge per unit thickness is computed by q = k * (N_f / N_d) * Δh, where k is coefficient of permeability, N_f is the number of flow channels, and N_d is the number of potential drops. The pore-water pressure at any point is u = γ_w * h, where h is the hydraulic head read from equipotential lines. Seepage pressure equals γ_w * i along a flow line, while exit gradient at the downstream toe is obtained from the head loss across the last potential drop divided by the flow path length at the exit element. Step-by-Step Solution: Count N_f and N_d → compute q.Read head at a node → compute u = γ_w * h.Estimate local hydraulic gradient i from potential spacing → get seepage pressure γ_w * i.At the exit, compute i_exit and compare to critical gradient to check piping risk. Verification / Alternative check: Finite element seepage analysis reproduces similar results when boundary conditions and anisotropy treatments are equivalent. Why Other Options Are Wrong: Each listed quantity legitimately comes from a correct flow net; omitting any would be incomplete. Hence 'All the above' is the comprehensive choice. Common Pitfalls: Using distorted grids that are not curvilinear squares; miscounting N_f or N_d; applying the method without transforming axes for anisotropic soils. Final Answer: All the above

Question 8

Effective Stress Concept – Meaning of Neutral Stress in Soils In a saturated soil mass, the term 'neutral stress' refers to which quantity?

Accepted Answer

Introduction / Context: The effective stress principle (σ′ = σ − u) is fundamental in soil mechanics. It separates total stress σ into effective stress σ′ carried by the soil skeleton and neutral stress u carried by the pore water. Many soil behaviors—strength, compressibility, and volume change—depend primarily on σ′, not on σ alone. Given Data / Assumptions: Saturated soil; static conditions. Pore-water pressure u is well-defined. Neutral stress is a commonly used synonym in classical texts. Concept / Approach: Neutral stress is another name for pore-water pressure u. It acts equally in all directions within the water phase and does not contribute to shear resistance of the soil skeleton. The soil solids carry the effective stress. Understanding the split between u and σ′ is vital for predicting consolidation, shear strength, and stability under changing groundwater conditions. Step-by-Step Solution: Write σ′ = σ − u.Identify neutral stress with u (pore pressure).Conclude that neutral stress is 'stress taken up by pore water'. Verification / Alternative check: Field measurements using piezometers directly read u, confirming it is distinct from the stress carried by the soil skeleton read indirectly through deformation and strength. Why Other Options Are Wrong: (a) and (b) are not standard definitions; (d) describes effective stress, not neutral stress. Common Pitfalls: Assuming total stress controls strength; ignoring changes in u during rapid loading or drawdown. Final Answer: Stress taken up by the pore water (pore-water pressure)

Question 9

Why the Triaxial Shear Test is Preferred Over Direct Shear Which statement best explains why the triaxial test is generally preferred to the direct shear test for determining soil shear strength?

Accepted Answer

Introduction / Context: Laboratory shear tests aim to measure strength parameters under controlled stress and drainage conditions. The triaxial test apparatus allows flexible control and measurement compared with the simpler direct shear box, providing more reliable parameters for design of foundations, slopes, and retaining structures. Given Data / Assumptions: Specimen is cylindrical and jacketed (triaxial cell). Drainage and pore pressure can be controlled/monitored. Failure plane is not pre-imposed, allowing natural failure to develop. Concept / Approach: Triaxial testing supports undrained–unconsolidated (UU), consolidated–undrained (CU with pore pressure measurement), and consolidated–drained (CD) conditions. It permits measurement of volume change and pore pressure (in CU) and yields well-defined stress paths and principal stress states. In contrast, the direct shear test enforces a horizontal failure surface and suffers from stress non-uniformity along the plane, offering limited drainage control. Step-by-Step Solution: Identify the key advantage: drainage and stress control in triaxial testing.Recognize ability to measure/monitor u and ΔV in CU/CD modes.Conclude option (a) best captures these advantages. Verification / Alternative check: Design manuals recommend triaxial parameters (CU with pore pressure; CD for sands) when accurate undrained/drained strengths are needed. Why Other Options Are Wrong: (b) is false—triaxial enables such measurements; (c) describes a drawback of the direct shear test, not a benefit. Common Pitfalls: Using direct shear results for conditions requiring pore pressure control; misinterpreting UU results for long-term behavior. Final Answer: It can be performed under all three drainage conditions (UU, CU, CD) with good control of stresses and drainage

Question 10

Natural Slope of Cohesionless Soil – Names for the Limiting Plane at Angle φ A plane inclined at an angle equal to the soil’s angle of internal friction φ to the horizontal is the inclination at which loose cohesionless soil can stand without latera…

Accepted Answer

Introduction / Context: In stockpiles and embankments of cohesionless soil, the steepest stable slope under self-weight is characterized by the angle of repose, very close to the angle of internal friction φ for clean, dry sand. The corresponding plane at angle φ to the horizontal is referred to by several synonymous terms in practice. Given Data / Assumptions: Cohesionless soil, dry or drained condition. Stability governed by frictional resistance. Small-scale surface effects (fabric, particle shape) may cause minor deviations. Concept / Approach: The limiting natural slope occurs when the downslope component of weight is balanced by frictional resistance with no lateral support. In routine usage, the terms 'natural slope line', 'repose line', and 'φ line' all describe this limiting plane. While precise definitions may vary across texts, they point to the same physical concept: the slope at or near the friction angle. Step-by-Step Solution: Recognize the physical condition: marginal stability without lateral support.Associate the angle with φ (internal friction angle) or angle of repose.Identify that all three listed names refer to this same limiting plane. Verification / Alternative check: Photography of dry sand heaps shows faces at a nearly constant angle, and shear box tests quantify φ to which the repose angle is closely related. Why Other Options Are Wrong: 'None of these' is incorrect because the listed terms are acceptable synonyms for the concept. Common Pitfalls: Confusing angle of repose with compacted slope design angles that include stability factors and drainage considerations. Final Answer: All of the above

Question 11

Grouting in Ground Improvement – Effects and Definition Which of the following statements about grouting in coarse-grained soils is/are correct?

Accepted Answer

Introduction / Context: Grouting is a common ground improvement technique used to reduce permeability, control seepage, and enhance strength/stiffness of soils and weak rocks. It is frequently applied below dams, around shafts, and beneath foundations to mitigate piping or settlement and to improve bearing capacity locally. Given Data / Assumptions: Target soils are typically coarse-grained or fissured media where grout penetration is feasible. Grout types include cementitious, chemical, microfine, and polyurethane, among others. Objective may be seepage control, void filling, or structural improvement. Concept / Approach: By injecting grout under pressure, interconnected voids are partially or fully filled, thereby reducing the hydraulic conductivity and increasing interparticle bonding. This often elevates the small-strain stiffness and shear strength. The process definition itself is the injection of grout into the pore space or fractures to achieve the desired performance outcomes. Step-by-Step Solution: Relate grouting to permeability reduction through void filling and sealing.Define grouting precisely as injection of fluid grout into pores/fractures.Recognize strength gain due to bonding and reduced defects. Verification / Alternative check: Permeability tests before/after grouting and in-situ shear/penetration tests typically show reduced k and enhanced strength/stiffness. Why Other Options Are Wrong: Each of (a)–(c) is correct; 'All the above' captures the complete picture. Common Pitfalls: Attempting to grout very fine silts/clays with coarse cement grouts; inadequate pressure/volume control causing hydrofracture or heave. Final Answer: All the above

Question 12

Bearing Capacity – Factors That Influence a Soil’s Load-Carrying Ability The ultimate bearing capacity of a soil deposit depends primarily on which characteristics of the constituent particles and their interaction?

Accepted Answer

Introduction / Context: Bearing capacity refers to the ability of soil to support loads from foundations without undergoing shear failure or excessive settlement. It is governed by both the intrinsic characteristics of the particles and the structure (fabric) of the soil mass, as well as drainage and loading conditions. Given Data / Assumptions: General shallow foundation context, drained behavior emphasized for sands; undrained behavior for clays considered separately. Homogeneous near-surface layer for simplicity. Other influences (water table, shape/depth factors) are secondary to intrinsic strength parameters. Concept / Approach: Particle size and gradation influence packing density and stiffness. Particle shape affects interlocking and friction. Cohesion (true cementation or apparent cohesion in clays) contributes to shear strength at low normal stresses. Internal friction is represented by φ in Mohr–Coulomb and is central to resistance against shear. Together these properties determine c and φ, which appear in classical bearing capacity equations (e.g., Terzaghi, Meyerhof) through N_c, N_q, N_γ factors. Step-by-Step Solution: Relate particle size/shape to packing and friction.Relate cohesion and friction to shear strength parameters c and φ.Link c, φ, and γ to ultimate bearing capacity through standard equations. Verification / Alternative check: Laboratory shear tests and in-situ tests (SPT, CPT) correlate with bearing capacity charts where φ and density dominate for sands and undrained su dominates for clays. Why Other Options Are Wrong: Each factor contributes; choosing only one would be incomplete. Hence 'All the above' is correct. Common Pitfalls: Ignoring groundwater and foundation geometry effects; over-reliance on a single parameter without considering fabric and density. Final Answer: All the above

Question 13

Stress–Deformation Trends Under Changing Effective Stress Which statement correctly describes how key soil indices respond when effective stress increases (loading) in a typical compressible soil?

Accepted Answer

Introduction / Context: Understanding qualitative trends under changes in effective stress is vital for consolidation, settlement prediction, and permeability assessment. As soils are loaded, their structure compresses, affecting void ratio, hydraulic conductivity, and compressibility parameters in predictable ways for most natural soils. Given Data / Assumptions: Normal consolidation or general compressible behavior (not cemented rock-like materials). Drainage permitted over time so that effective stress increases. Comparisons are qualitative trends with increasing effective stress. Concept / Approach: With increasing effective stress, soil particles pack more closely, so void ratio e decreases. Reduced void space typically leads to decreased permeability k. The coefficient of volume change m_v, which relates volumetric strain to stress increment, generally decreases as stress level grows (soil stiffens). Therefore the only universally correct statement among the options is that void ratio decreases as effective stress increases. Step-by-Step Solution: Start from consolidation mechanics: Δe = − m_v * Δσ′ * (1 + e) (trend illustrates compression).Increasing σ′ → e decreases; structure densifies.Permeability correlates with e and n → tends to decrease as soil densifies.m_v often reduces with stress because the soil becomes less compressible at higher stresses. Verification / Alternative check: e–log σ′ curves and k–e relationships measured in oedometer tests show these monotonic trends for most clays and silts. Why Other Options Are Wrong: (b), (c), and (d) contradict typical observed behavior; permeability and compressibility do not increase with increasing effective stress. Common Pitfalls: Confusing immediate total-stress changes with long-term effective-stress changes; extrapolating trends outside the tested stress range. Final Answer: When effective stress increases, void ratio decreases

Question 14

Critical Hydraulic Gradient for Boiling (Quicksand) in Terms of Porosity If G is the specific gravity of sand particles (Gs) and e denotes porosity (n) of the soil, write the expression for the critical hydraulic gradient i_c for onset of boiling (q…

Accepted Answer

Introduction / Context: The critical hydraulic gradient i_c indicates when upward seepage causes effective stress to vanish (boiling or quick condition) in cohesionless soils. Designers compare exit gradients against i_c to assess piping risk beneath hydraulic structures and at excavation bottoms under dewatering. Given Data / Assumptions: Specific gravity of soil solids G (i.e., Gs). Porosity is denoted here by e (note: many texts use n for porosity and e for void ratio). Saturated, homogeneous soil; upward seepage. Concept / Approach: The familiar expression in terms of void ratio is i_c = (Gs − 1) / (1 + e_void), where e_void is the void ratio. If porosity n is used instead, recall the relation e_void = n / (1 − n) → 1 + e_void = 1 / (1 − n). Substituting into the standard formula gives i_c = (Gs − 1) * (1 − n). Since the problem denotes porosity as e, we write i_c = (G − 1) * (1 − e). This directly connects i_c to the fraction of solids by volume (1 − n). Step-by-Step Solution: Start with i_c = (Gs − 1) / (1 + e_void).Use e_void = n / (1 − n) ⇒ 1 + e_void = 1 / (1 − n).Therefore i_c = (Gs − 1) * (1 − n).Rename n as e (given as porosity in the stem) ⇒ i_c = (G − 1) * (1 − e). Verification / Alternative check: For typical values G ≈ 2.65 and porosity e (n) ≈ 0.40, i_c ≈ (1.65)*(0.60) ≈ 0.99, consistent with standard ranges. Why Other Options Are Wrong: (b) is the correct form if the symbol e meant void ratio, but the stem explicitly says e is porosity. (c), (d), and (e) are dimensionally or physically inconsistent with the boiling condition. Common Pitfalls: Mixing symbols: many texts use e for void ratio and n for porosity; always translate before applying formulas. Final Answer: i_c = (G − 1) * (1 − e)

Question 15

Minimum depth of foundation as per Rankine’s concept: According to Rankine’s formulation for cohesionless backfill with unit weight γ and friction angle φ, the minimum embedment depth D_f (to prevent shear failure at ground level under net foundatio…

Accepted Answer

Introduction / Context: Designing a shallow foundation requires a sufficient embedment to prevent shear failure and to develop adequate passive resistance near the ground surface. Rankine’s earth pressure theory leads to a practical expression for the minimum depth of foundation in cohesionless soil in terms of soil unit weight γ, friction angle φ, and the net contact pressure q at the base. Given Data / Assumptions: Cohesionless soil (c = 0), homogeneous and horizontal ground surface. Foundation base loaded with net pressure q at depth D_f. Rankine active/passive states with no wall friction, planar ground. Unit weight of soil = γ, friction angle = φ. Concept / Approach: At minimum embedment, the available passive resistance near the surface must balance the driving tendency from foundation pressure. Using Rankine’s coefficients, K_a = (1 − sin φ)/(1 + sin φ) and K_p = (1 + sin φ)/(1 − sin φ), and equating forces, the limiting embedment is expressed in terms of K_a (or K_p). Rearrangement gives the standard Rankine depth formula. Step-by-Step Solution: Use Rankine: K_a = tan^2(45° − φ/2) = (1 − sin φ)/(1 + sin φ).Minimum depth arises when overburden γ D_f produces enough lateral confining effect.Solving for D_f yields D_f = (q/γ) * [ (1 − sin φ) / (1 + sin φ) ]^2. Verification / Alternative check: Dimensional check: q/γ has units of length. The bracketed ratio is dimensionless; squaring preserves units. As φ increases (denser sand), the bracket decreases, giving smaller D_f, which is physically consistent. Why Other Options Are Wrong: (b) inverts the ratio, predicting larger D_f for stronger sands—unrealistic. (c) and (d) use tan half-angle forms unrelated to D_f here. (e) inverts q/γ, giving wrong dimensions. Common Pitfalls: Confusing gross vs. net pressure q; applying the expression to cohesive or sloping backfills without modification. Final Answer: D_f = (q / γ) * [ (1 − sin φ) / (1 + sin φ) ]^2

Question 16

Moisture (water) content from wet and dry masses: An unsaturated soil sample (volume 100 cm³) weighs 190 g in the field. After oven drying, it weighs 160 g. What is the water content w of the soil?

Accepted Answer

Introduction / Context: Water content (also called moisture content) is a fundamental index property in soil mechanics, needed for compaction control, shear strength correlations, and consolidation predictions. It compares the mass of water in a soil to the mass of dry soil solids. Given Data / Assumptions: Wet (natural) mass M_wet = 190 g. Dry mass M_dry = 160 g (after oven drying). Standard definition w = (mass of water) / (mass of dry solids). Sample volume is provided but not required for w. Concept / Approach: Water content w is the ratio of the mass of water removed by drying to the mass of soil solids left after drying. It is commonly expressed as a decimal or percentage. Use simple subtraction to find water mass, then divide by dry mass. Step-by-Step Solution: Mass of water M_w = M_wet − M_dry = 190 − 160 = 30 g.Water content w = M_w / M_dry = 30 / 160 = 0.1875.Rounded to three decimals, w ≈ 0.188 (18.8%). Verification / Alternative check: A result under 0.20 is typical for an unsaturated compacted soil. If expressed in percent, w ≈ 18.8%. Why Other Options Are Wrong: 0.288, 0.388, 0.488, and 0.588 imply much more water relative to solids than given by the mass difference. Common Pitfalls: Dividing by wet mass instead of dry mass, or forgetting to subtract to find water mass. Final Answer: 0.188

Question 17

Air content definition in phase relationships: The ratio of the volume of air voids to the volume of total voids of a soil mass is called:

Accepted Answer

Introduction / Context: Describing the state of a soil requires several volumetric ratios. Besides void ratio and porosity, technicians often report how much of the void space is air versus water. This question targets the correct name for the ratio involving air voids and total voids. Given Data / Assumptions: Three-phase soil system: solids, water, and air. V_v = V_a + V_w (total voids = air + water volume). We seek the ratio V_a / V_v. Concept / Approach: By definition: air content a = V_a / V_v. Related but different terms include porosity n = V_v / V_t, percentage air voids = (V_a / V_t) * 100%, and degree of saturation S = V_w / V_v. Distinguishing these prevents misinterpretation of lab results and compaction targets. Step-by-Step Solution: Identify target ratio: V_a / V_v.Match name: “air content”. Verification / Alternative check: Check companion definitions to ensure no confusion with porosity or saturation. Why Other Options Are Wrong: (b) Percentage air voids uses V_a / V_t, not V_a / V_v. (c) Percentage voids is V_v / V_t. (d) Porosity is also V_v / V_t. (e) Degree of saturation is V_w / V_v. Common Pitfalls: Interchanging “air content” with “percentage air voids”; confusing void-based ratios with total-volume ratios. Final Answer: Air content

Question 18

Void ratio from mass specific gravity and water content: A soil has mass specific gravity G_m = 1.92 and water content w = 30%. If the specific gravity of solids G_s = 2.75, determine the void ratio e.

Accepted Answer

Introduction / Context: Relating mass specific gravity G_m, water content w, and specific gravity of solids G_s to the void ratio e is a common task in soil phase-relationship problems. Using two standard equations allows elimination of degree of saturation S and solution for e directly. Given Data / Assumptions: G_m = γ/γ_w = 1.92. w = 0.30 (30%). G_s = 2.75. Water unit weight/ density normalization is implied. Concept / Approach: Key relations: 1) G_m = (G_s + S e) / (1 + e). 2) w = (S e) / G_s. Use (2) to substitute S e = w G_s into (1), then solve for e. Step-by-Step Solution: Compute S e from w: S e = w * G_s = 0.30 * 2.75 = 0.825.Substitute in G_m: (G_s + S e) / (1 + e) = 1.92 → (2.75 + 0.825) / (1 + e) = 1.92.Sum numerator: 3.575 / (1 + e) = 1.92.Solve: 1 + e = 3.575 / 1.92 = 1.86198 → e ≈ 0.86198.Round suitably: e ≈ 0.862. Verification / Alternative check: Back-calculate S from w = S e / G_s → S = (w G_s) / e ≈ 0.825 / 0.862 ≈ 0.957 (reasonable near full saturation), confirming consistency. Why Other Options Are Wrong: 0.858, 0.860, 0.864 are close but reflect rounding beyond justified precision; 0.880 deviates from the derived e. Common Pitfalls: Using bulk unit weight formula for saturated soil; forgetting to eliminate S correctly; rounding too early. Final Answer: 0.862

Question 19

Indices from Atterberg limits: A soil has natural water content w = 30.5%, liquid limit LL = 42.5%, and plastic limit PL = 22.5%. What is the ratio (Liquidity index / Plasticity index)?

Accepted Answer

Introduction / Context: Atterberg limits quantify fine-grained soil consistency. The liquidity index I_L places the in-situ water content within the plastic range, while the plasticity index PI measures the width of that range. Their ratio helps compare state to plastic range width. Given Data / Assumptions: w = 30.5%. LL = 42.5%. PL = 22.5%. Definitions: PI = LL − PL; I_L = (w − PL)/PI. Concept / Approach: Compute PI, then I_L, and finally the requested ratio I_L / PI. Keep units consistent (percent values are used as numbers in the formulae). Step-by-Step Solution: PI = LL − PL = 42.5 − 22.5 = 20.0.Liquidity index I_L = (w − PL) / PI = (30.5 − 22.5) / 20.0 = 8.0 / 20.0 = 0.40.Required ratio = I_L / PI = 0.40 / 20.0 = 0.02. Verification / Alternative check: Note that I_c = (LL − w)/PI = (42.5 − 30.5)/20 = 0.60, and I_c + I_L = 1.0, confirming internal consistency. Why Other Options Are Wrong: 0.20 and 0.04 result from misplacing numerator/denominator; 0.50 and 2 contradict the computed I_L and PI values. Common Pitfalls: Confusing I_L with I_c; dividing by 100 unnecessarily; mixing percent and decimal forms inconsistently. Final Answer: 0.02

Question 20

Meaning of plastic equilibrium in soils: A soil mass is said to be in plastic equilibrium when which condition holds?

Accepted Answer

Introduction / Context: Limit equilibrium methods in geotechnical engineering evaluate stability by assuming that along a potential surface the soil is at “plastic equilibrium.” Understanding this phrase is crucial for interpreting slope stability and bearing capacity analyses. Given Data / Assumptions: Mohr–Coulomb shear strength criterion governs failure: τ_f = c + σ′ tan φ. Plastic equilibrium implies critical conditions along a failure plane. Small-strain elasticity elsewhere is not the focus. Concept / Approach: Plastic equilibrium means the mobilized shear stress τ equals the available shear strength τ_f. The soil is neither safely below failure nor post-failure flowing; it is exactly at the threshold—“on the verge of failure.” This is the state assumed on slip surfaces in limit equilibrium analyses. Step-by-Step Solution: Define condition: τ_mobilized = τ_f.Interpretation: any further load increment or reduction in strength will cause failure.Hence, choose the option describing verge-of-failure state. Verification / Alternative check: In bearing capacity solutions (Prandtl–Terzaghi) and slope stability, yield lines or slip circles are taken at plastic equilibrium. Why Other Options Are Wrong: (a) is vague and not tied to strength; (c) “in plastic stage” does not guarantee limit state; (d) describes post-failure flow; (e) refers to elastic behavior, not plasticity. Common Pitfalls: Equating plastic range with plastic equilibrium; confusing onset of flow with limit state. Final Answer: It is on the verge of failure (mobilized shear stress equals shear strength)

Soil Mechanics and Foundation Engineering Questions