FE Civil · Chapter 13 · 9–14 exam questions

FE Civil Geotechnical Eng.

This chapter covers soil classification, phase relations, effective stress, consolidation, shear strength, permeability and seepage, slope stability, bearing capacity, lateral earth pressure, retaining walls, deep foundations, and soil improvement.

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What the FE tests in Geotechnical Eng.

Soil Properties & Classification

As a civil engineer, you classify soils using USCS and AASHTO systems, compute phase relations from lab data (water content, unit weight, void ratio), and construct effective stress profiles through layered soil with a water table. These fundamentals underpin every geotechnical design calculation.

Consolidation & Shear Strength

As a civil engineer, you predict how much a clay layer will settle under new loading using the consolidation e-log p curve, and you determine soil shear strength from triaxial tests to check foundation, slope, and retaining wall stability.

Seepage & Slope Stability

As a civil engineer, you use Darcy's law and flow nets to quantify seepage through dams and excavations, check the critical hydraulic gradient against quick (boiling) conditions, and compute the factor of safety of natural and engineered slopes — including the destabilizing effect of seepage after rainfall.

Foundations & Earth Pressures

As a civil engineer, you compute bearing capacity to size foundations, calculate lateral earth pressures to design retaining walls, and check walls for overturning, sliding, and bearing failure. These are the most common geotechnical design tasks in practice.

Deep Foundations & Soil Improvement

As a civil engineer, you turn to deep foundations (piles, drilled shafts) when surface soils are too weak — combining end bearing and skin friction for capacity — and you improve weak ground by compaction (verified against a Proctor maximum) and chemical stabilization (lime for clays, cement for granular soils).

Key Geotechnical Eng. formulas

$\sigma' = \sigma - u$
Effective StressFE Handbook p. 263
$Se = \omega G_s$
Phase Relation (master equation)FE Handbook p. 259
$\gamma_{sat} = \frac{(G_s + e)\gamma_w}{1 + e}$
Saturated Unit WeightFE Handbook p. 259
$\Delta H = \frac{H_0}{1+e_0} C_c \log \frac{p_0 + \Delta p}{p_0}$
NC Consolidation SettlementFE Handbook p. 261
$\tau_f = c' + \sigma' \tan \phi'$
Mohr-Coulomb FailureFE Handbook p. 263
$q_{ult} = cN_c + \gamma' D_f N_q + 0.5\gamma' BN_\gamma$
Terzaghi's Bearing CapacityFE Handbook p. 264
$K_a = \tan^2(45\degree - \phi/2)$
Rankine Active PressureFE Handbook p. 263
$FS_{\text{overturning}} = \Sigma M_R / M_O$
Retaining Wall OverturningFE Handbook p. 264
$q = k\,i\,A$
Darcy's LawFE Handbook p. 292
$q = k\,H\,N_f/N_d$
Flow-Net SeepageFE Handbook p. 292
$i_c = \frac{G_s - 1}{1 + e}$
Critical Hydraulic GradientFE Handbook p. 260
$FS = \frac{\tan\phi}{\tan\beta}$
Infinite Slope (dry, cohesionless)FE Handbook p. 265
$RC = \frac{\gamma_{d,field}}{\gamma_{d,max}} \times 100$
Relative CompactionFE Handbook p. 260
$D_r = \frac{e_{max} - e}{e_{max} - e_{min}} \times 100$
Relative DensityFE Handbook p. 260
$Q_{ult} = Q_p + Q_s$
Pile Capacity (end bearing + skin friction)

Sample Geotechnical Eng. problems

Q1. A soil sample has a void ratio $e = 0.65$ and specific gravity $G_s = 2.70$ . What is the porosity $n$ ?

Answer: $0.394$

Explain it simply

Porosity relates to void ratio by $n = e/(1+e) = 0.65/(1+0.65) = 0.65/1.65 = 0.394$ . Choice B (0.650) is the void ratio itself, not the porosity. Choice C (0.241) might come from $e/(1+G_s)$ . Choice D (0.606) might come from $1/(1+e)$ , which is the reciprocal relationship.

Q2. A soil sample is tested and found to have a degree of saturation $S = 100\%$ . Which of the following statements is correct?

Answer: All void space is filled with water, and $e = \omega G_s$

Explain it simply

When $S = 100\%$ , the voids are completely filled with water (no air phase). The master relationship $Se = \omega G_s$ simplifies to $e = \omega G_s$ . Choice A is backwards -- full saturation means all voids have water, not that the soil is completely dry. Choice C is wrong because $e$ depends on the soil structure, not saturation alone. Choice D mixes up the formula -- $\omega = e/G_s$ at full saturation, not $\omega = G_s$ .

These are 2 of 1,126 problems across all 15 chapters. The full bank, lessons, mastery tracking, and timed exam simulation live inside the app.

Common Geotechnical Eng. mistakes on the FE

Forgetting to subtract pore water pressure (u) to get effective stress — this is the single most tested concept.
Using total unit weight below the water table instead of buoyant (submerged) unit weight: γ’ = γsat − γw.
Confusing Cc (compression index) with Cr (recompression index) — use Cr when stress stays below preconsolidation.
Active vs. passive earth pressure: active is when the wall moves AWAY from soil, passive is when wall pushes INTO soil.
Not dividing ultimate bearing capacity by FS when the problem asks for allowable bearing pressure.
Discharge velocity v = ki is NOT the seepage velocity — divide by porosity (v_s = ki/n) for the real pore speed.
A quick (boiling) condition occurs when the upward exit gradient reaches the critical gradient i_c = (G_s−1)/(1+e), usually near 1.0.
Seepage parallel to a slope roughly halves the factor of safety (γ′/γ_sat ≈ 0.5) — never ignore it after rainfall.
Relative compaction (vs. Proctor maximum) and relative density (vs. e_max/e_min) are different measures — relative density is for cohesionless soils.
Negative skin friction (downdrag) ADDS load to a pile; it does not help support it.

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