Soil classification, phase relationships, effective stress, strength, bearing capacity, retaining walls and settlement.
NCEES lists these Geotechnical Engineering topics for the FE Civil: index properties and soil classification; phase relations; laboratory and field tests; effective stress; retaining structures: lateral pressure, overturning, sliding; shear strength and bearing capacity; foundation types, consolidation and settlement; slope stability, soil stabilization, drainage and erosion control.
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Soil is solids, water and air.
A 1,000 cm³ sample has a total mass of 1,900 g and an oven-dry mass of 1,600 g. What is its water content?
Water = 1,900 − 1,600 = 300 g. w = Ww/Ws = 300/1,600 = 18.8%.
Common trap: (B) Divides by the wet mass instead of the dry mass.
Phase RelationshipsVoid RatioWater ContentThat was 1 of 4 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
Atterberg limits describe fine-grained soil: PI = LL − PL, and the liquidity index LI = (w − PL)/PI.
A fine-grained soil has LL = 48 and PL = 22. Its plasticity index plots above the A-line. What is the USCS symbol?
PI = 48 − 22 = 26. The A-line at LL = 48 is 0.73(28) = 20.4, so the soil is above it. With LL under 50 it is CL.
Common trap: (B) LL is under 50, so it is low plasticity.
Atterberg LimitsUSCSCompactionThat was 1 of 4 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
Soil strength and settlement follow effective stress: σ′ = σ − u.
A 3 m layer of sand (γ = 17 kN/m³) lies above a clay (γsat = 19 kN/m³). The water table is at the sand–clay interface. What is the effective vertical stress 4 m into the clay?
σ = 3(17) + 4(19) = 127 kPa. u = 9.81(4) = 39.24 kPa. σ′ = 87.8 kPa.
Common trap: (B) That is the total stress.
Effective StressDarcy's LawFlow NetThat was 1 of 4 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
The Mohr–Coulomb failure criterion is τf = c′ + σ′ tan φ′ on the failure plane.
A drained triaxial test on a clean sand (c′ = 0) is run at a confining pressure σ3 = 100 kPa. The sample fails at a deviator stress of 200 kPa. What is the friction angle φ′?
σ1 = σ3 + Δσd = 100 + 200 = 300 kPa. sin φ′ = (σ1 − σ3)/(σ1 + σ3) = 200/400 = 0.500, so φ′ = 30.0°.
Common trap: (B) Uses tan φ′ = Δσd/σ1 instead of the sine relation.
Mohr-CoulombBearing CapacityTriaxialThat was 1 of 4 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
Rankine pressures for a level backfill: Ka = tan²(45° − φ/2) = (1 − sin φ)/(1 + sin φ) (active), Kp = 1/Ka (passive), and K0 ≈ 1 − sin φ (at rest).
A 6 m wall retains a level sand backfill (φ = 30°) with the water table 2 m below the top. The sand has γ = 18 kN/m³ above the water table and γsat = 20 kN/m³ below it. The wall does not drain. What is the total horizontal force (soil plus water) per meter of wall?
Ka = tan²30° = 1/3. Soil pressure at 2 m: (1/3)(18)(2) = 12.00 kPa. At 6 m: (1/3)[36 + 10.19(4)] = 25.59 kPa. Soil force = ½(12.00)(2) + 12.00(4) + ½(13.59)(4) = 87.17 kN/m. Water: ½(9.81)(4)² = 78.48 kN/m. Total = 165.7 kN/m.
Common trap: (B) Leaves out the water pressure.
RankineActive and Passive PressureRetaining WallsThat was 1 of 4 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
A saturated clay under a new load squeezes out water and settles.
A site has 3 m of sand (γ = 18 kN/m³) over a 6 m layer of normally consolidated clay (γsat = 19 kN/m³, Cc = 0.32, e0 = 0.95). The water table is at the top of the clay. A wide fill adds Δσ = 50 kPa. What is the primary consolidation settlement of the clay?
At mid-clay (6 m deep): σ′0 = 3(18) + 3(19 − 9.81) = 54 + 27.57 = 81.57 kPa. Sc = [0.32(6)/1.95] log[(81.57 + 50)/81.57] = 0.9846(0.2076) = 204 mm.
Common trap: (B) Uses γsat for the clay, which gives total stress, not effective stress.
ConsolidationSettlementPreconsolidationThat was 1 of 4 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
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