Practice Problems: Soil Mechanics
Question 1
A geotechnical engineer is analyzing a soil sample from a proposed building site. Laboratory tests on a saturated soil sample provide the following data:
Total unit weight of saturated soil = 19.8 kN/m³
Specific gravity of soil solids (Gs) = 2.68
Unit weight of water = 9.81 kN/m³
What is the void ratio of this saturated soil?
(a) 0.58
(b) 0.66
(c) 0.74
(d) 0.82
Question 2
A civil engineer is designing a foundation for a water tank. A consolidation test is performed on a clay sample from the site. The following data are obtained:
Initial height of specimen = 25 mm
Final height after consolidation = 23.5 mm
Initial void ratio = 0.95
What is the final void ratio after consolidation?
(a) 0.78
(b) 0.83
(c) 0.89
(d) 0.92
Question 3
A geotechnical consultant is evaluating the permeability of a sandy soil layer for a dewatering project. A constant head permeability test yields the following results:
Length of soil specimen = 150 mm
Cross-sectional area = 7500 mm²
Constant head difference = 400 mm
Water collected in 3 minutes = 360 cm³
What is the coefficient of permeability in cm/s?
(a) 0.020 cm/s
(b) 0.030 cm/s
(c) 0.040 cm/s
(d) 0.050 cm/s
Question 4
A foundation engineer is analyzing effective stress conditions at a construction site. A soil profile consists of:
0 to 4 m depth: Sand with γ = 18 kN/m³
4 to 10 m depth: Clay with γsat = 19.5 kN/m³
Groundwater table is at 4 m below ground surface
What is the effective vertical stress at 10 m depth? (γw = 9.81 kN/m³)
(a) 115.0 kPa
(b) 125.4 kPa
(c) 129.1 kPa
(d) 135.6 kPa
Question 5
A project engineer is conducting direct shear tests on a cohesionless sand sample for slope stability analysis. The test results show:
Normal stress = 100 kPa, Shear stress at failure = 58 kPa
Normal stress = 200 kPa, Shear stress at failure = 116 kPa
Normal stress = 300 kPa, Shear stress at failure = 174 kPa
What is the angle of internal friction for this sand?
(a) 28°
(b) 30°
(c) 32°
(d) 35°
Question 6
A geotechnical engineer is designing a sheet pile wall for an excavation. The soil behind the wall is cohesionless sand with the following properties:
Unit weight γ = 17.5 kN/m³
Angle of internal friction φ = 32°
Height of wall H = 6 m
What is the Rankine active earth pressure coefficient (Ka)?
(a) 0.253
(b) 0.307
(c) 0.354
(d) 0.412
Question 7
A foundation designer is analyzing settlement for a new office building. A normally consolidated clay layer has the following properties:
Initial void ratio e0 = 1.10
Compression index Cc = 0.35
Initial effective stress σ'0 = 80 kPa
Final effective stress σ'f = 150 kPa
Layer thickness H0 = 4 m
What is the primary consolidation settlement?
(a) 0.112 m
(b) 0.142 m
(c) 0.178 m
(d) 0.204 m
Question 8
A highway engineer is analyzing a soil sample for pavement design. The particle size distribution analysis shows:
Gravel content = 15%
Sand content = 55%
Silt content = 20%
Clay content = 10%
D60 = 0.8 mm, D30 = 0.35 mm, D10 = 0.15 mm
What is the coefficient of uniformity (Cu) for this soil?
(a) 3.2
(b) 4.5
(c) 5.3
(d) 6.1
Question 9
A structural engineer is designing a shallow foundation on clay soil. Unconfined compression tests on saturated clay samples yield an average unconfined compressive strength of 96 kPa. The foundation dimensions are:
Width B = 2.5 m
Length L = 2.5 m (square footing)
Depth of foundation Df = 1.5 m
Unit weight of soil γ = 18.5 kN/m³
What is the undrained cohesion (cu) of the clay?
(a) 24 kPa
(b) 36 kPa
(c) 48 kPa
(d) 72 kPa
Question 10
A geotechnical consultant is performing a falling head permeability test on a clayey soil sample. The following data are recorded:
Standpipe cross-sectional area a = 5 cm²
Soil sample cross-sectional area A = 50 cm²
Soil sample length L = 10 cm
Initial head h1 = 80 cm
Final head h2 = 30 cm
Time interval t = 6 minutes
What is the coefficient of permeability?
(a) 1.1 × 10⁻⁴ cm/s
(b) 2.5 × 10⁻⁴ cm/s
(c) 3.8 × 10⁻⁴ cm/s
(d) 5.2 × 10⁻⁴ cm/s
Question 11
A construction manager is evaluating soil compaction for a highway embankment. A standard Proctor test yields the following results:
Maximum dry density = 18.2 kN/m³
Optimum moisture content = 12%
Specific gravity of soil solids Gs = 2.70
What is the degree of saturation at optimum moisture content?
(a) 62%
(b) 68%
(c) 74%
(d) 80%
Question 12
A foundation engineer is analyzing a retaining wall for a commercial development. The wall retains 5 m of dry cohesionless backfill with the following properties:
Unit weight γ = 18 kN/m³
Angle of internal friction φ = 35°
Wall is frictionless and vertical
What is the total active lateral force per meter length of wall using Rankine theory?
(a) 60.3 kN/m
(b) 74.8 kN/m
(c) 89.5 kN/m
(d) 105.2 kN/m
Question 13
A project engineer is designing a drainage system and needs to evaluate seepage through a soil layer. The soil profile consists of three horizontal layers:
Layer 1: thickness = 2 m, k1 = 4 × 10⁻⁴ cm/s
Layer 2: thickness = 3 m, k2 = 2 × 10⁻⁴ cm/s
Layer 3: thickness = 5 m, k3 = 1 × 10⁻⁴ cm/s
Flow is perpendicular to the layers (vertical flow). What is the equivalent vertical permeability?
(a) 1.43 × 10⁻⁴ cm/s
(b) 1.67 × 10⁻⁴ cm/s
(c) 2.00 × 10⁻⁴ cm/s
(d) 2.33 × 10⁻⁴ cm/s
Question 14
A geotechnical engineer is evaluating a triaxial compression test on a saturated clay sample under consolidated-undrained conditions. The test results show:
Cell pressure σ3 = 150 kPa
Deviator stress at failure (σ1 - σ3) = 180 kPa
Pore pressure at failure u = 90 kPa
What is the effective minor principal stress at failure?
(a) 45 kPa
(b) 60 kPa
(c) 75 kPa
(d) 90 kPa
Question 15
A civil engineer is designing a foundation on an overconsolidated clay deposit. Laboratory testing provides the following data:
Present effective overburden pressure σ'0 = 100 kPa
Preconsolidation pressure σ'p = 250 kPa
Compression index Cc = 0.40
Recompression index Cr = 0.08
What is the overconsolidation ratio (OCR)?
(a) 1.5
(b) 2.0
(c) 2.5
(d) 3.0
Question 16
A project manager is evaluating slope stability for a roadway cut. The slope consists of cohesive soil with the following properties:
Unit weight γ = 19 kN/m³
Cohesion c = 25 kPa
Angle of internal friction φ = 20°
Slope height H = 8 m
Slope angle β = 30°
Using the infinite slope analysis for a potential failure plane parallel to the slope surface at depth z = 4 m, what is the normal stress on the failure plane?
(a) 58.7 kPa
(b) 65.7 kPa
(c) 72.3 kPa
(d) 76.0 kPa
Question 17
A geotechnical consultant is conducting plate load tests for a commercial building foundation. A 0.3 m × 0.3 m square plate settles 10 mm under a load of 45 kN. For a prototype foundation 3 m × 3 m carrying the same bearing pressure, what is the expected settlement using elastic theory? (Assume same contact pressure)
(a) 65 mm
(b) 80 mm
(c) 100 mm
(d) 120 mm
Question 18
A foundation engineer is analyzing bearing capacity for a continuous strip footing on sandy soil. The following conditions exist:
Width of footing B = 2 m
Depth of foundation Df = 1.5 m
Unit weight of soil γ = 18 kN/m³
Angle of internal friction φ = 30°
Cohesion c = 0
Using Terzaghi's bearing capacity factors: Nc = 37.2, Nq = 22.5, Nγ = 19.7
What is the ultimate bearing capacity? (Shape factors = 1.0 for strip footing)
(a) 608 kPa
(b) 719 kPa
(c) 823 kPa
(d) 962 kPa
Question 19
A construction engineer is monitoring consolidation settlement of a clay layer beneath a large storage tank. Time-settlement measurements show:
Settlement at t = 100 days: 80 mm
Settlement at t = 400 days: 120 mm
Ultimate consolidation settlement = 200 mm
What is the average degree of consolidation at t = 400 days?
(a) 45%
(b) 52%
(c) 60%
(d) 68%
Question 20
A highway engineer is evaluating the California Bearing Ratio (CBR) test results for subgrade soil. The test data shows:
Load at 2.5 mm penetration = 1100 lbs
Load at 5.0 mm penetration = 1650 lbs
Standard load at 2.5 mm = 3000 lbs
Standard load at 5.0 mm = 4500 lbs
What is the CBR value of this soil?
(a) 32%
(b) 37%
(c) 41%
(d) 45%
