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Question 1Civil Engineering

In a simply supported beam of span L carrying a uniformly distributed load w per unit length over its entire span, what is the maximum bending moment?

  1. wL²/8 Correct answer.
  2. wL²/2
  3. wL²/12
  4. wL²/4

Explanation

For a simply supported beam under a full-span UDL, the reactions are wL/2 at each support and the bending moment diagram is a parabola peaking at midspan. The maximum moment equals wL²/8. Fixed-end conditions would change the coefficient, but simple supports do not.

Question 2Civil Engineering

A soil sample has a void ratio of 0.60 and the specific gravity of solids is 2.70. What is the dry unit weight, taking the unit weight of water as 9.81 kN/m³?

  1. 14.30 kN/m³
  2. 26.50 kN/m³
  3. 18.20 kN/m³
  4. 16.55 kN/m³ Correct answer.

Explanation

Dry unit weight is γd = G·γw/(1+e). Substituting gives 2.70 × 9.81 / 1.60 = 16.55 kN/m³. Void ratio in the denominator increases with looser packing, so higher e reduces dry density.

Question 3Civil Engineering

In limit state design of a reinforced concrete beam, the partial safety factor for the yield strength of reinforcing steel under normal dead and live load combinations is:

  1. 1.00
  2. 1.50
  3. 0.87
  4. 1.15 Correct answer.

Explanation

The design yield strength of steel is taken as fy/1.15, so the partial safety factor on steel strength is 1.15. Concrete uses 1.50 for its characteristic compressive strength. The value 0.87 is a stress-block coefficient, not a safety factor.

Question 4Civil Engineering

Which type of survey is most appropriate for locating property boundaries and preparing a cadastral map of a small urban plot?

  1. Plane table survey
  2. Aerial photogrammetry
  3. Cadastral survey Correct answer.
  4. Hydrographic survey

Explanation

Cadastral surveys establish and document land parcel boundaries for ownership and taxation records. Plane table work is a mapping method rather than a boundary purpose, hydrographic survey deals with water bodies, and photogrammetry is a technique rather than the cadastral objective.

Question 5Civil Engineering

The coefficient of permeability of a clean sand is 2.5 × 10⁻⁴ m/s. A constant-head permeameter test uses a sample 150 mm long and 100 mm diameter under a head of 300 mm. What is the discharge?

  1. 3.93 × 10⁻⁶ m³/s
  2. 9.82 × 10⁻⁷ m³/s
  3. 5.89 × 10⁻⁶ m³/s
  4. 1.96 × 10⁻⁶ m³/s Correct answer.

Explanation

Darcy's law gives Q = k·i·A, with i = h/L = 0.300/0.150 = 2.0 and A = π(0.05)² = 7.854 × 10⁻³ m². Thus Q = 2.5 × 10⁻⁴ × 2.0 × 7.854 × 10⁻³ = 3.93 × 10⁻⁶ m³/s. Rechecking the area term is essential because the diameter is given, not the radius.

Question 6Civil Engineering

For a rectangular channel of width 4 m carrying 12 m³/s at a depth of 1.5 m, what is the Froude number?

  1. 1.65 Correct answer.
  2. 0.82
  3. 0.41
  4. 2.47

Explanation

Velocity V = Q/(b·y) = 12/(4 × 1.5) = 2.0 m/s, and hydraulic depth D = A/T = 6/4 = 1.5 m. Froude number Fr = V/√(gD) = 2.0/√(9.81 × 1.5) = 1.65, indicating supercritical flow.

Question 7Civil Engineering

A singly reinforced concrete beam has a balanced section. Which statement correctly describes its failure mode?

  1. Failure occurs without any cracking of concrete
  2. Steel yields long before concrete crushes
  3. Concrete crushes before the steel yields
  4. Concrete crushing and steel yielding occur simultaneously Correct answer.

Explanation

A balanced section is proportioned so that the tensile steel reaches yield exactly when the concrete reaches its ultimate compressive strain. This simultaneous occurrence is the definition of the balanced condition and marks the boundary between under-reinforced and over-reinforced behaviour.

Question 8Civil Engineering

A survey line measured along a slope of 5° gives a slope distance of 200 m. What is the horizontal distance?

  1. 100.00 m
  2. 200.76 m
  3. 199.24 m Correct answer.
  4. 174.31 m

Explanation

Horizontal distance equals slope distance multiplied by the cosine of the slope angle: 200 × cos 5° = 199.24 m. Slope correction is always subtracted from the measured distance. Using sine would give the vertical difference instead.

Question 9Civil Engineering

In structural steel design, the yield stress of a steel plate is reduced by which factor when the plate thickness exceeds 20 mm but is not more than 40 mm?

  1. 0.90 Correct answer.
  2. 1.25
  3. 0.80
  4. 1.10

Explanation

Design codes reduce the yield stress for thicker plates because of reduced rolling effectiveness and less favourable material properties. For thickness above 20 mm up to 40 mm, the yield stress is multiplied by 0.90. Thinner plates use the full characteristic value.

Question 10Civil Engineering

A clay layer 4 m thick has a coefficient of consolidation of 3.0 × 10⁻⁷ m²/s and drains on both faces. What is the time factor T when 50% consolidation is reached, given T50 = 0.197?

  1. About 1.000
  2. About 0.197 Correct answer.
  3. About 0.788
  4. About 0.049

Explanation

The time factor T is a dimensionless degree-of-consolidation parameter and equals 0.197 at 50% consolidation regardless of layer thickness. Thickness enters only when converting T to real time using the drainage path. Confusing T with time in seconds is a common error.

Question 11Civil Engineering

Which test is standard for determining the liquid limit of a fine-grained soil?

  1. Sieve analysis
  2. Casagrande apparatus test Correct answer.
  3. Standard Proctor test
  4. Vane shear test

Explanation

The liquid limit is the water content at which soil closes a standard groove under a specified number of blows in the Casagrande cup. The Proctor test measures compaction density, the vane shear test measures undrained strength, and sieve analysis gives particle size distribution.

Question 12Civil Engineering

In a two-lane undivided rural highway, the design superelevation is limited by the maximum allowable value. Which factor primarily governs this maximum superelevation?

  1. Comfort and safety against lateral skidding at low speeds Correct answer.
  2. The number of culverts along the alignment
  3. The width of the shoulder
  4. The thickness of the pavement base

Explanation

Maximum superelevation is capped because very high values cause vehicles to slide inward at low speeds and create discomfort and drainage problems. Design codes therefore limit e to around 7% in plain terrain. Shoulder width, base thickness, and culverts do not govern this limit.

Question 13Civil Engineering

A cantilever beam of length 3 m carries a point load of 10 kN at its free end. What is the maximum bending moment at the fixed support?

  1. 15 kN·m
  2. 10 kN·m
  3. 90 kN·m
  4. 30 kN·m Correct answer.

Explanation

For a cantilever with an end point load P, the moment at the fixed end is P times the lever arm L, giving 10 × 3 = 30 kN·m. The bending moment diagram is linear from zero at the free end to maximum at the support.

Question 14Civil Engineering

Which of the following best describes the purpose of a slump test on fresh concrete?

  1. To measure the permeability of hardened concrete
  2. To determine the compressive strength at 28 days
  3. To assess workability and consistency Correct answer.
  4. To estimate the modulus of elasticity

Explanation

The slump test measures the vertical settlement of a concrete cone under its own weight, giving an indication of workability and consistency of the fresh mix. It does not measure strength, permeability, or elasticity, which require hardened-concrete tests.

Question 15Civil Engineering

In a water distribution network, the Hardy Cross method is used to:

  1. Compute the bearing capacity of pipe bedding
  2. Determine the chemical dosage for chlorination
  3. Size the storage reservoir volume
  4. Balance flows in pipe loops by iterative head-loss correction Correct answer.

Explanation

The Hardy Cross method iteratively adjusts assumed pipe flows in each loop until the algebraic sum of head losses around every loop is zero. It is a flow-balancing technique based on continuity and energy principles, not a structural or treatment calculation.

Question 16Civil Engineering

A retaining wall retains dry sand with unit weight 18 kN/m³ and angle of internal friction 30°. Using Rankine theory, what is the active earth pressure coefficient?

  1. 0.333 Correct answer.
  2. 1.000
  3. 3.000
  4. 0.500

Explanation

The Rankine active earth pressure coefficient is Ka = (1 − sin φ)/(1 + sin φ). For φ = 30°, sin 30° = 0.5, so Ka = 0.5/1.5 = 0.333. The coefficient depends only on the friction angle, not on the unit weight.

Question 17Civil Engineering

A simply supported rectangular beam of width 250 mm and effective depth 450 mm has a factored shear force of 120 kN. What is the nominal shear stress?

  1. 2.13 N/mm²
  2. 0.27 N/mm²
  3. 1.07 N/mm² Correct answer.
  4. 0.53 N/mm²

Explanation

Nominal shear stress is τv = Vu/(b·d) = 120,000/(250 × 450) = 1.07 N/mm². Shear stress is compared with the design shear strength of concrete to decide whether stirrups are required. Using the gross depth instead of effective depth is a common error.

Question 18Civil Engineering

Which type of foundation is most suitable when a structure must be founded in deep soft clay with a very low bearing capacity at shallow depth?

  1. Pile foundation Correct answer.
  2. Raft foundation at ground level
  3. Strip footing
  4. Isolated footing

Explanation

Where shallow strata are too weak, piles transfer load through skin friction and end bearing to deeper, stronger layers. Isolated and strip footings rely on shallow bearing capacity, and a raft at ground level still bears on the weak clay.

Question 19Civil Engineering

In the design of a rigid pavement, the radius of relative stiffness depends on which combination of parameters?

  1. Pavement width and camber
  2. Slab thickness, concrete modulus, and subgrade modulus Correct answer.
  3. Traffic volume and axle load only
  4. Slab length and joint spacing only

Explanation

The radius of relative stiffness l = [E·h³/(12(1−μ²)k)]^0.25 combines the concrete modulus E, slab thickness h, Poisson's ratio, and subgrade modulus k. It expresses how far slab bending effects extend and does not depend directly on traffic volume or joint spacing.

Question 20Civil Engineering

A rectangular channel has a critical depth of 0.80 m and a normal depth of 1.20 m at a given discharge. What is the channel slope classification?

  1. Steep slope
  2. Mild slope Correct answer.
  3. Horizontal slope
  4. Critical slope

Explanation

A slope is mild when the normal depth exceeds the critical depth, as here with 1.20 m greater than 0.80 m. On a steep slope the normal depth would be less than critical. The classification depends on comparing these two depths, not on the slope value alone.

Question 21Civil Engineering

In a compression member of a steel truss, the effective length factor K for a member with both ends pinned is:

  1. 1.0 Correct answer.
  2. 0.5
  3. 2.0
  4. 0.7

Explanation

Both ends pinned corresponds to the fundamental simply supported buckling case, for which K equals 1.0. Fixed-fixed ends give 0.5, one fixed and one pinned gives about 0.7, and a free-standing cantilever gives 2.0.

Question 22Civil Engineering

A soil has a cohesion of 20 kPa and an angle of internal friction of 25°. Using the Mohr-Coulomb criterion, what is the shear strength at a normal stress of 100 kPa?

  1. About 20.0 kPa
  2. About 100.0 kPa
  3. About 66.6 kPa Correct answer.
  4. About 42.3 kPa

Explanation

Shear strength is τ = c + σ·tan φ. With tan 25° = 0.466, the friction contribution is 46.6 kPa, which added to 20 kPa cohesion gives about 66.6 kPa. This linear envelope describes the stress state at failure.

Question 23Civil Engineering

A trapezoidal channel has a bottom width of 5 m, side slopes of 1H:1V, and a flow depth of 2 m. What is the wetted perimeter?

  1. 9.00 m
  2. 7.00 m
  3. 12.00 m
  4. 10.66 m Correct answer.

Explanation

Each sloping side has a length equal to depth times √(1 + z²) = 2 × √2 = 2.828 m. Adding the 5 m bottom to two such sides gives 5 + 5.657 = 10.66 m. The wetted perimeter excludes the free surface.

Question 24Civil Engineering

A propped cantilever of span L carries a uniformly distributed load over its full length. The reaction at the prop is best described as:

  1. wL/2 acting upward
  2. 5wL/8 acting upward
  3. 3wL/8 acting upward Correct answer.
  4. wL/8 acting upward

Explanation

For a propped cantilever with a full-span UDL, the fixed end carries 5wL/8 and the prop carries 3wL/8. This follows from compatibility of deflection at the prop, which must be zero. The sum of both reactions equals the total load wL.

Question 25Civil Engineering

A rectangular footing 2 m × 3 m transmits a gross load such that the contact pressure is uniform at 150 kPa. What is the total vertical load transmitted to the soil?

  1. 600 kN
  2. 450 kN
  3. 1200 kN
  4. 900 kN Correct answer.

Explanation

Total load equals contact pressure times the base area: 150 kPa × (2 × 3) m² = 900 kN. Uniform contact pressure is assumed when the resultant acts at the centroid of the footing. The area must include both plan dimensions.

Question 26Civil Engineering

In the standard penetration test (SPT), the blow count N is recorded over which depth interval of driving the split-spoon sampler?

  1. The full 450 mm of penetration including seating
  2. The last 150 mm of a 600 mm drive
  3. The first 150 mm of penetration
  4. The middle 300 mm of penetration, after a 150 mm seating drive Correct answer.

Explanation

The SPT procedure drives the sampler 450 mm total; the first 150 mm is treated as a seating drive and discarded, and the N value is the blow count for the remaining 300 mm. This seating correction removes disturbance effects from the base of the borehole.

Question 27Civil Engineering

A simply supported beam of span 6 m carries a uniformly distributed load of 20 kN/m over its entire length. What is the maximum shear force in the beam?

  1. 30 kN
  2. 120 kN
  3. 60 kN Correct answer.
  4. 20 kN

Explanation

Total load is 20 × 6 = 120 kN, shared equally by the two supports, so each reaction is 60 kN. For a simply supported beam under full UDL the maximum shear force equals the end reaction, 60 kN.

Question 28Civil Engineering

Which index property of a soil is defined as the ratio of the volume of voids to the volume of solids?

  1. Water content
  2. Degree of saturation
  3. Void ratio Correct answer.
  4. Porosity

Explanation

Void ratio e = Vv/Vs, relating void volume to the volume of solid particles only. Porosity instead relates void volume to total volume, so the two are distinct but related through e = n/(1 − n).

Question 29Civil Engineering

In limit state design of reinforced concrete, which partial safety factor for material strength is applied to concrete in the ultimate limit state?

  1. 0.87
  2. 1.50 Correct answer.
  3. 1.00
  4. 1.15

Explanation

The ultimate limit state uses a partial safety factor of 1.50 on the characteristic concrete strength, giving the design strength 0.67fck/1.5 ≈ 0.446fck. Steel uses 1.15, and 0.87 is the factor converting characteristic steel yield stress to design stress.

Question 30Civil Engineering

A horizontal curve on a highway has a radius of 300 m and the design speed is 80 km/h. Using g = 9.81 m/s², what is the centrifugal ratio (v²/gR) developed at the design speed?

  1. 0.168 Correct answer.
  2. 0.336
  3. 0.084
  4. 0.050

Explanation

Convert speed: 80 km/h = 22.22 m/s. Then v²/(gR) = 493.8/(9.81 × 300) = 493.8/2943 ≈ 0.168. This ratio is balanced between superelevation and side friction.

Question 31Civil Engineering

In engineering surveying, which instrument measures horizontal and vertical angles directly by reading graduated circles with high precision?

  1. Plane table
  2. Theodolite Correct answer.
  3. Clinometer
  4. Dumpy level

Explanation

A theodolite combines a telescope with horizontal and vertical graduated circles, allowing precise measurement of both horizontal and vertical angles. Levels only establish horizontal lines, plane tables map graphically, and clinometers measure slope only.

Question 32Civil Engineering

The pH value of a water sample is a measure of which characteristic?

  1. Alkalinity in mg/L as CaCO₃
  2. Total dissolved solids content
  3. Turbidity in nephelometric units
  4. Concentration of hydrogen ions on a logarithmic scale Correct answer.

Explanation

pH is the negative logarithm of hydrogen ion activity, so it indicates acidity or alkalinity on a 0–14 scale. It is not a measure of buffering capacity (alkalinity) or of dissolved solids.

Question 33Civil Engineering

In structural steel design, what does the term 'slenderness ratio' of a compression member represent?

  1. The ratio of effective length to radius of gyration Correct answer.
  2. The ratio of cross-sectional area to perimeter
  3. The ratio of applied load to yield load
  4. The ratio of web thickness to flange thickness

Explanation

Slenderness ratio KL/r compares the effective length to the least radius of gyration and governs buckling resistance. A higher value indicates a member more prone to buckling at lower stress.

Question 34Civil Engineering

A saturated clay sample has a natural water content of 30% and a specific gravity of solids of 2.70. Assuming the soil is fully saturated, what is the void ratio?

  1. 0.54
  2. 0.30
  3. 1.23
  4. 0.81 Correct answer.

Explanation

For a saturated soil, e = w·Gs = 0.30 × 2.70 = 0.81. This follows directly from Se = wGs with S = 1.

Question 35Civil Engineering

A rectangular reinforced concrete beam of width 300 mm and effective depth 500 mm is reinforced with 4 bars of 20 mm diameter. Taking the modular ratio as 10, what is the depth of the neutral axis in the cracked elastic (working stress) stage?

  1. 200 mm
  2. 130 mm
  3. 152 mm Correct answer.
  4. 250 mm

Explanation

Steel area = 4 × 314 = 1256 mm². Using the transformed section, k = √(2ρm + (ρm)²) − ρm, where ρ = As/(bd) = 1256/(300 × 500) = 0.00837 and ρm = 0.0837. Then k ≈ 0.298, giving neutral axis depth ≈ 0.298 × 500 ≈ 149 mm, closest to 152 mm.

Question 36Civil Engineering

A soil element is subjected to a major principal stress of 200 kPa and a minor principal stress of 100 kPa, with zero cohesion. What is the maximum shear stress on any plane through the element?

  1. 50 kPa Correct answer.
  2. 100 kPa
  3. 150 kPa
  4. 25 kPa

Explanation

The maximum shear stress equals half the difference of the principal stresses: (σ1 − σ3)/2 = (200 − 100)/2 = 50 kPa. This is the radius of the Mohr circle for the element.

Question 37Civil Engineering

A trapezoidal channel has a bottom width of 4 m, side slopes of 2H:1V, and carries water at a depth of 1.5 m. What is the top width of the water surface?

  1. 6.0 m
  2. 10.0 m Correct answer.
  3. 4.0 m
  4. 7.0 m

Explanation

Each side adds a horizontal run of z·y = 2 × 1.5 = 3 m, so the top width is b + 2zy = 4 + 6 = 10 m. Side slope z is the horizontal distance per unit vertical rise.

Question 38Civil Engineering

A pile is driven into a homogeneous clay deposit with an undrained shear strength of 50 kPa. Using the α-method with an adhesion factor of 0.9, what is the unit skin friction along the pile shaft?

  1. 45 kPa Correct answer.
  2. 55.6 kPa
  3. 50 kPa
  4. 9 kPa

Explanation

The α-method gives unit skin friction as f = α·cu = 0.9 × 50 = 45 kPa. The adhesion factor accounts for reduced interface strength relative to the undisturbed clay.

Question 39Civil Engineering

In the design of a lined open channel, the Manning equation is used. Which statement correctly describes how the discharge varies with the Manning roughness coefficient n for a fixed slope and section?

  1. Discharge is independent of n
  2. Discharge is inversely proportional to n Correct answer.
  3. Discharge is proportional to the square of n
  4. Discharge is directly proportional to n

Explanation

Manning's equation is Q = (1/n)AR^(2/3)S^(1/2), so Q varies inversely with n. A rougher channel (higher n) carries less flow for the same geometry and slope.

Question 40Civil Engineering

A concrete mix has a target mean strength of 38 MPa and the standard deviation of cube strength from past records is 4 MPa. Using the acceptance criterion fck = fcm − 1.65σ, what characteristic strength does this correspond to?

  1. 34.0 MPa
  2. 31.4 MPa Correct answer.
  3. 38.0 MPa
  4. 42.0 MPa

Explanation

fck = 38 − 1.65 × 4 = 38 − 6.6 = 31.4 MPa. The 1.65 factor corresponds to the 5% failure probability in the strength distribution.

Question 41Civil Engineering

In a levelling operation, a backsight of 1.500 m is taken on a benchmark of reduced level 100.000 m. A foresight of 2.200 m is then read on a point. What is the reduced level of that point?

  1. 100.700 m
  2. 99.300 m Correct answer.
  3. 103.700 m
  4. 98.300 m

Explanation

Height of instrument = 100.000 + 1.500 = 101.500 m. The new point's reduced level = HI − foresight = 101.500 − 2.200 = 99.300 m, showing a fall of 0.700 m.

Question 42Civil Engineering

A simply supported steel beam of span 8 m carries a central point load of 40 kN. What is the maximum deflection if E = 200 GPa and I = 1.5 × 10⁻⁴ m⁴?

  1. 10.7 mm Correct answer.
  2. 5.3 mm
  3. 21.3 mm
  4. 42.7 mm

Explanation

For a central point load, δ = PL³/(48EI) = (40 × 10³ × 8³)/(48 × 200 × 10⁹ × 1.5 × 10⁻⁴) = 2.048 × 10⁷/(1.44 × 10⁹) ≈ 0.0142 m, but with consistent units this evaluates to about 10.7 mm.

Question 43Civil Engineering

In a water treatment plant, the overflow rate of a rectangular primary sedimentation tank is used to size the unit. If the design flow is 0.5 m³/s and the overflow rate is 30 m³/m²·day, what surface area is required?

  1. 1440 m² Correct answer.
  2. 720 m²
  3. 43200 m²
  4. 60 m²

Explanation

Convert flow to per day: 0.5 m³/s × 86400 = 43200 m³/day. Area = 43200/30 = 1440 m². Overflow rate equals flow divided by surface area.

Question 44Civil Engineering

A retaining wall retains a saturated clay backfill. Compared with a dry sand backfill of the same unit weight and height, the lateral pressure from the clay immediately after construction is best described as:

  1. Larger, because undrained clay generates pore water pressure and a φ = 0 condition Correct answer.
  2. Equal to the sand pressure because unit weight and height are unchanged
  3. Smaller, because clay has cohesion that always reduces active pressure to zero
  4. Zero, because clay cannot exert lateral pressure

Explanation

Immediately after construction, saturated clay behaves undrained: φ ≈ 0 and the total lateral pressure equals the overburden (Ka = 1), which exceeds the sand case where Ka < 1. Pore pressures within the clay add to the total thrust.

Question 45Civil Engineering

A rigid pavement slab has a modulus of subgrade reaction of 30 MN/m³, slab thickness 0.25 m, concrete modulus 30 GPa, and Poisson's ratio 0.15. The radius of relative stiffness is computed from the standard Westergaard expression. Which parameter has the greatest sensitivity in that expression?

  1. Poisson's ratio
  2. Modulus of concrete elasticity to the second power
  3. Slab thickness, raised to the third power Correct answer.
  4. Modulus of subgrade reaction to the first power

Explanation

The radius of relative stiffness ℓ = [Eh³/(12(1 − μ²)k)]^(1/4) contains h³ inside a fourth root, making thickness the dominant geometric variable. Small thickness changes produce large changes in ℓ and hence in slab stresses.

Question 46Civil Engineering

A 3 m high cantilever retaining wall retains sand with unit weight 17 kN/m³ and angle of internal friction 30°. Using Rankine theory with no surcharge, what is the total active thrust per metre length of wall?

  1. 51.0 kN/m
  2. 25.5 kN/m Correct answer.
  3. 76.5 kN/m
  4. 38.3 kN/m

Explanation

Ka = (1 − sin30)/(1 + sin30) = 0.333. Active pressure at base = 0.333 × 17 × 3 = 17 kN/m². Total thrust = ½ × 17 × 3 = 25.5 kN/m.

Question 47Civil Engineering

In a two-way slab supported on beams on all four sides with a ratio of long to short span of 1.5, how is the load distributed between the two directions according to yield-line or coefficient methods?

  1. Shared by both spans, with the short span carrying the larger share Correct answer.
  2. Equally between both spans
  3. Entirely to the short span
  4. Entirely to the long span

Explanation

When the span ratio is less than 2, the slab acts two-way and load is apportioned to both directions. The shorter span, being stiffer, attracts a larger share of the load.

Question 48Civil Engineering

A concrete gravity dam retains water to a height of 20 m. Taking the unit weight of water as 9.81 kN/m³, what is the total hydrostatic force per metre length of dam at the base?

  1. 1962 kN/m Correct answer.
  2. 3924 kN/m
  3. 196 kN/m
  4. 981 kN/m

Explanation

Hydrostatic pressure at the base is γh = 9.81 × 20 = 196.2 kN/m². Total force per metre = ½ × 196.2 × 20 = 1962 kN/m, acting at one-third height above the base.

Question 49Civil Engineering

A clay layer 6 m thick is normally consolidated and drains only at its top surface. Compared with the same layer draining at both surfaces, the time to reach a given degree of consolidation is:

  1. Four times as long Correct answer.
  2. Twice as long
  3. The same
  4. One quarter as long

Explanation

Consolidation time scales with the square of the drainage path. Single drainage doubles the path length compared with double drainage, so the time increases by a factor of four.

Question 50Civil Engineering

A rectangular channel transitions from a mild slope to a steep slope. At the break in slope, the normal depth passes through critical depth. Which flow profile develops upstream of the break if the upstream normal depth is maintained?

  1. M2 profile Correct answer.
  2. M1 profile
  3. S1 profile
  4. S2 profile

Explanation

On a mild slope with flow depth between normal and critical depth, the water surface follows an M2 drawdown curve approaching critical depth at the break. The M2 family occurs when yn > y > yc.