Chartered Civil Engineer (ICE) Geotechnical and Foundation Engineering Flashcards

24 sample cards from the Geotechnical and Foundation Engineering deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. Define net bearing pressure, allowable bearing capacity and factor of safety for a shallow foundation.

   Net pressure = applied pressure minus original overburden at founding level. Allowable bearing capacity $$q_a = \frac{q_{nu}}{F} + q_0,$$ where $q_{nu}$ = net ultimate, $F$ = factor of safety (typically 3 for total stress) and $q_0$ = overburden. The lower of bearing-capacity and settlement criteria governs.

2. Give the elastic (immediate) settlement formula for a flexible foundation on a deep elastic layer.

   $$s_i = q B \frac{(1-\nu^2)}{E}\,I_f,$$ where $q$ = net bearing pressure, $B$ = width, $\nu$ = Poisson's ratio, $E$ = undrained or drained Young's modulus, and $I_f$ = influence factor depending on shape and rigidity.

3. Distinguish end-bearing piles and friction (shaft) piles, and write the ultimate pile capacity equation.

   End-bearing piles transmit load through the toe to a competent stratum; friction piles transfer load via shaft friction along their length. $$Q_u = Q_b + Q_s = q_b A_b + \sum f_s A_s,$$ where $Q_b$ = base resistance, $Q_s$ = shaft resistance, $A_b$ = base area, $A_s$ = shaft area, $f_s$ = unit skin friction.

4. Compare driven (displacement) and bored (replacement) piles.

   Driven piles: pre-formed and hammered/vibrated in, displace and densify surrounding soil, no spoil, but cause noise/vibration; good in granular soils. Bored (cast-in-place) piles: a hole is augured/excavated and filled with concrete, low vibration, allow large diameters and inspection of strata, but generate spoil and can suffer base relaxation/softening.

5. For piles in clay, what is the alpha method, and for sands the typical base/shaft resistance approach?

   Alpha (total stress) method: unit shaft friction $f_s = \alpha\,c_u$, with adhesion factor $\alpha \approx 0.4$–1.0 (lower for stiff clays). Effective stress (beta) method: $f_s = \beta\,\sigma'_v$. In sands, shaft $f_s = K\,\sigma'_v \tan\delta$ and base $q_b = N_q\,\sigma'_v$ (capped for displacement piles).

6. Define active, passive and at-rest earth pressure states.

   At-rest ($K_0$): wall does not move; soil in its in-situ state. Active ($K_a$): wall moves away from the soil, which expands and reaches minimum lateral pressure. Passive ($K_p$): wall moves into the soil, which compresses to maximum lateral pressure. Order of magnitude: $K_a < K_0 < K_p$.

7. Give the Rankine earth pressure coefficients for a smooth vertical wall with horizontal backfill.

   $$K_a = \frac{1-\sin\phi'}{1+\sin\phi'} = \tan^2\!\left(45^\circ - \tfrac{\phi'}{2}\right),$$ $$K_p = \frac{1+\sin\phi'}{1-\sin\phi'} = \tan^2\!\left(45^\circ + \tfrac{\phi'}{2}\right),$$ and $K_a = 1/K_p$. The at-rest coefficient (Jaky) is $K_0 = 1 - \sin\phi'$ for normally consolidated soil.

8. How are active and passive pressures computed for a $c'$–$\phi'$ soil (Rankine with cohesion)?

   $$\sigma'_a = K_a \sigma'_v - 2c'\sqrt{K_a}, \qquad \sigma'_p = K_p \sigma'_v + 2c'\sqrt{K_p}.$$ Cohesion reduces active pressure (causing a tension crack to depth $z_0 = \dfrac{2c'}{\gamma\sqrt{K_a}}$) and increases passive resistance.

9. What stability checks are required for a gravity/cantilever retaining wall, and the typical factors of safety?

   Check: (1) sliding along the base — $F = \dfrac{\text{resisting (friction + passive)}}{\text{driving (active thrust)}} \geq 1.5$; (2) overturning about the toe — $F = \dfrac{\text{restoring moments}}{\text{overturning moments}} \geq 2.0$; (3) bearing capacity of foundation soil (with eccentricity); (4) overall/global slope stability; (5) settlement. EC7 uses partial factors instead of lumped FoS.

10. For a smooth vertical wall retaining dry cohesionless soil of height $H$, what is the total active thrust and its point of application?

    $$P_a = \tfrac{1}{2} K_a \gamma H^2,$$ acting horizontally at $H/3$ above the base (triangular pressure distribution). If a uniform surcharge $q$ acts, add $K_a q H$ acting at $H/2$. Water pressure (if present) is added separately as a full hydrostatic triangle.

11. Compare embedded retaining wall types: cantilever, propped/anchored, and how they resist earth pressure.

    Cantilever embedded walls (e.g. sheet/secant piles) rely solely on passive resistance of the embedded depth — economical only for shallow retained heights. Propped or anchored walls add support near the top (prop, raking shore or ground anchor), reducing bending moments and embedment depth, enabling deeper excavations.

12. Describe the method of slices for slope stability and define the factor of safety.

    The potential failure mass above a slip surface is divided into vertical slices; equilibrium of each slice gives the resisting vs disturbing forces/moments. $$F = \frac{\text{available shear strength}}{\text{mobilised shear stress}} = \frac{\sum (c'l + (N - ul)\tan\phi')}{\sum W \sin\alpha}.$$ Methods include Fellenius (Swedish), Bishop's simplified, and Janbu.

13. For an undrained ($\phi_u = 0$) circular slip analysis, how is the factor of safety expressed?

    $$F = \frac{c_u\,L_a\,R}{\sum W\,x} = \frac{c_u\,L_a\,R}{M_d},$$ where $c_u$ = undrained strength, $L_a$ = arc length of the slip circle, $R$ = circle radius, $W$ = weight of slice, $x$ = horizontal lever arm to the centre, and $M_d$ = disturbing moment. Taylor's stability number charts can also be used.

14. What is the infinite slope stability solution for a cohesionless slope, with and without seepage?

    Dry/no seepage cohesionless slope: $$F = \frac{\tan\phi'}{\tan\beta},$$ so the slope is stable while slope angle $\beta < \phi'$. With steady seepage parallel to the slope (fully saturated): $$F = \frac{\gamma'}{\gamma_{sat}}\cdot\frac{\tan\phi'}{\tan\beta},$$ roughly halving the factor of safety.

15. Name common ground improvement techniques and the soil conditions each suits.

    Vibro-compaction (clean granular soils — densifies); vibro stone columns (soft cohesive/mixed soils — reinforce and drain); dynamic compaction (loose fills/granular); preloading/surcharge with vertical (band) drains (soft clays — accelerate consolidation); deep soil mixing/grouting (weak/contaminated soils); compaction grouting and jet grouting (localised strengthening/sealing).

16. Explain how vertical (band) drains accelerate consolidation and their effect on the time factor.

    Vertical drains shorten the drainage path by providing radial (horizontal) drainage to closely spaced vertical wicks, so excess pore pressure dissipates much faster (radial consolidation governed by $c_h$ and drain spacing). Because consolidation time $\propto d^2$, reducing the drainage path dramatically reduces settlement time, often used with a surcharge preload.

17. Define optimum moisture content (OMC) and maximum dry density (MDD) from a compaction test, and why they matter in earthworks.

    In a Proctor compaction test, dry density is plotted against moisture content; the peak gives the maximum dry density (MDD) at the optimum moisture content (OMC). Compacting fill at around OMC achieves the densest, strongest, least compressible state. Field compaction is controlled to a percentage of MDD (e.g. 95%) within an acceptable moisture range.

18. What is the coefficient of uniformity $C_u$ and coefficient of curvature $C_c$ (gradation), and what indicates well-graded soil?

    $$C_u = \frac{D_{60}}{D_{10}}, \qquad C_c = \frac{(D_{30})^2}{D_{60}\,D_{10}},$$ where $D_{10}, D_{30}, D_{60}$ are particle sizes at 10/30/60% passing. Well-graded: $C_u > 4$ (gravel) or $>6$ (sand) and $1 \le C_c \le 3$. A low $C_u$ indicates uniform (poorly graded) soil.

19. Define relative density (density index) of a granular soil and its formula.

    $$I_D = \frac{e_{max} - e}{e_{max} - e_{min}}\times100\%,$$ where $e$ = in-situ void ratio, $e_{max}$/$e_{min}$ = loosest/densest void ratios. $I_D$: 0–15% very loose, 15–35% loose, 35–65% medium dense, 65–85% dense, 85–100% very dense. Describes packing state of sands/gravels.

20. What is liquefaction and which conditions make a soil susceptible?

    Liquefaction is the sudden loss of shear strength when undrained cyclic loading (e.g. earthquake) generates excess pore pressure that rises to equal total stress, reducing effective stress to zero. Most susceptible: loose, saturated, uniform (poorly graded) fine sands and silts with low relative density below the water table.

21. Distinguish total stress and effective stress analysis and state when each is appropriate.

    Total stress (undrained) analysis uses $c_u$, $\phi_u = 0$ and total stresses — appropriate for short-term stability in low-permeability clays immediately after loading (no drainage). Effective stress (drained) analysis uses $c', \phi'$ with pore pressures — appropriate for long-term conditions and for free-draining granular soils where excess pore pressure dissipates quickly.

22. For consolidation settlement using the coefficient of volume compressibility $m_v$, what is the formula?

    $$s_c = m_v\,\Delta\sigma'\,H,$$ where $m_v$ = coefficient of volume compressibility ($\mathrm{m^2/MN}$), $\Delta\sigma'$ = increase in effective stress, and $H$ = thickness of the compressible layer. $m_v$ is obtained from oedometer test results over the relevant stress range.

23. What is negative skin friction (downdrag) on a pile and when does it occur?

    Negative skin friction occurs when the soil around a pile settles more than the pile (e.g. consolidating soft clay, fill placed over compressible ground, lowered water table). The settling soil drags the pile downward, imposing an additional axial load and reducing net capacity rather than supporting the pile. It is added as a load, not a resistance.

24. Explain the difference between peak, critical-state and residual shear strength of clay.

    Peak strength: maximum shear resistance, mobilised at small strain, associated with dilation/structure (higher $c', \phi'_p$). Critical-state (constant volume): strength at large strain with no volume change ($c'=0$, $\phi'_{cv}$). Residual strength: minimum strength after large displacement with particle re-orientation along a slip surface ($\phi'_r < \phi'_{cv}$) — governs reactivated landslides.

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