GATE Civil Engineering (CE) Flashcards

24 sample cards from the Civil Engineering (CE) deck

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

1. Define slenderness ratio for a compression member and its significance.

   Slenderness ratio $\lambda = \frac{KL}{r}$, where $KL$ is the effective length and $r=\sqrt{I/A}$ is the radius of gyration. A higher slenderness ratio means greater tendency to buckle and lower compressive (buckling) strength. IS 800 limits it (e.g., $\leq 180$ for members carrying loads).

2. Compare bolted and welded connections in steel structures.

   Bolted connections: faster site assembly, easily dismantled/inspected, but reduce net section (holes) and may loosen under vibration. Welded connections: full member section is effective, neater appearance and lighter joints, but require skilled labour, are sensitive to fatigue and residual stresses, and are hard to inspect.

3. Write the strength of a fillet weld and define throat thickness.

   Design strength of a fillet weld $= \frac{f_u}{\sqrt{3}\,\gamma_{mw}}\times (\text{throat thickness} \times \text{effective length})$. Effective throat thickness $t = 0.7s$ for a $90^\circ$ weld, where $s$ is the leg/weld size; $\gamma_{mw}=1.25$ (shop) or $1.5$ (site).

4. State the three-phase (block) diagram quantities used in soil and the basic phase relation.

   Soil is a three-phase system: solids, water, and air, with total volume $V = V_s + V_w + V_a$ and void volume $V_v = V_w + V_a$. Fundamental relation: $$Se = wG$$ where $S$ = degree of saturation, $e$ = void ratio, $w$ = water content, $G$ = specific gravity of solids.

5. Define void ratio and porosity, and give the relation between them.

   Void ratio $e = \frac{V_v}{V_s}$ (volume of voids to volume of solids). Porosity $n = \frac{V_v}{V}$ (volume of voids to total volume). Relation: $$n = \frac{e}{1+e}, \qquad e = \frac{n}{1-n}.$$

6. Write the expressions for bulk (total), dry, and saturated unit weights of soil.

   $$\gamma_{bulk} = \frac{(G + Se)\gamma_w}{1+e}, \quad \gamma_{dry} = \frac{G\gamma_w}{1+e}, \quad \gamma_{sat} = \frac{(G+e)\gamma_w}{1+e}.$$ Submerged unit weight $\gamma' = \gamma_{sat} - \gamma_w$.

7. Define the Atterberg limits and the plasticity index.

   Atterberg limits mark water-content boundaries between consistency states of fine soil: Liquid Limit ($w_L$, liquid-plastic boundary), Plastic Limit ($w_P$, plastic-semisolid boundary), and Shrinkage Limit ($w_s$). Plasticity Index $I_p = w_L - w_P$ is the range of water content over which soil is plastic.

8. State the equation of the A-line used in the plasticity chart for soil classification.

   $$I_p = 0.73\,(w_L - 20)$$ Soils plotting above the A-line are clays (C); below are silts (M) or organic soils (O). It is used in the Unified Soil Classification System / IS classification.

9. In the Unified Soil Classification System, what do the symbols W, P, M, and C denote?

   For coarse soils: W = well graded, P = poorly graded. For fine soils/secondary: M = silt, C = clay. Prefixes G = gravel and S = sand; e.g., GW = well-graded gravel, CH = high-plasticity clay, ML = low-plasticity silt.

10. Define the coefficient of uniformity $C_u$ and coefficient of curvature $C_c$ for gradation.

    $$C_u = \frac{D_{60}}{D_{10}}, \qquad C_c = \frac{(D_{30})^{2}}{D_{10}\,D_{60}}$$ Well-graded sand requires $C_u > 6$ and $1 \leq C_c \leq 3$; for gravel $C_u > 4$. $D_{10}$ is the effective size.

11. State Darcy's law for laminar flow of water through soil.

    $$q = k\,i\,A \quad\text{or}\quad v = k\,i$$ where $q$ = discharge, $k$ = coefficient of permeability, $i = \frac{h}{L}$ = hydraulic gradient, $A$ = cross-sectional area, and $v$ = discharge (Darcy) velocity. Valid for laminar flow (Reynolds number low).

12. Define effective stress and write Terzaghi's effective stress equation.

    Effective stress is the stress carried by the soil skeleton (grain-to-grain contact) that governs strength and deformation. $$\sigma' = \sigma - u$$ where $\sigma$ = total stress, $u$ = pore water pressure, $\sigma'$ = effective stress.

13. What is a flow net and what two families of lines compose it?

    A flow net is a graphical grid representing two-dimensional steady seepage, consisting of flow lines (paths of water particles) and equipotential lines (lines of equal total head). The two families intersect at right angles forming approximately square fields.

14. Write the formula for seepage discharge through a flow net.

    $$q = k\,H\,\frac{N_f}{N_d}$$ where $k$ = permeability, $H$ = total head loss, $N_f$ = number of flow channels, and $N_d$ = number of equipotential drops.

15. Define critical hydraulic gradient and the condition for quick sand (boiling).

    Critical hydraulic gradient is the upward gradient at which effective stress becomes zero: $$i_c = \frac{\gamma'}{\gamma_w} = \frac{G-1}{1+e}.$$ When the seepage gradient reaches $i_c$ (typically $\approx 1$), the soil loses all shear strength and behaves as a quick (boiling) condition.

16. State the assumptions of Terzaghi's one-dimensional consolidation theory.

    Key assumptions: soil is homogeneous and fully saturated; soil grains and water are incompressible; flow and compression are one-dimensional (vertical); Darcy's law is valid; coefficient of permeability $k$ and compressibility are constant; and there is a unique linear relationship between effective stress and void ratio.

17. Write the governing differential equation of Terzaghi's 1-D consolidation and define $c_v$.

    $$\frac{\partial u}{\partial t} = c_v \frac{\partial^{2} u}{\partial z^{2}}, \qquad c_v = \frac{k}{m_v \gamma_w}$$ where $u$ = excess pore pressure, $c_v$ = coefficient of consolidation, $k$ = permeability, and $m_v$ = coefficient of volume compressibility.

18. Write the formula for primary consolidation settlement of a normally consolidated clay.

    $$S_c = \frac{C_c\,H}{1+e_0}\,\log_{10}\!\left(\frac{\sigma'_0 + \Delta\sigma'}{\sigma'_0}\right)$$ where $C_c$ = compression index, $H$ = layer thickness, $e_0$ = initial void ratio, $\sigma'_0$ = initial effective stress, and $\Delta\sigma'$ = stress increment.

19. Define the degree of consolidation and give the time factor relations for $U \leq 60\%$.

    Degree of consolidation $U$ is the ratio of settlement at time $t$ to ultimate settlement. Time factor $T_v = \frac{c_v t}{d^{2}}$ ($d$ = drainage path). For $U \leq 60\%$: $$T_v = \frac{\pi}{4}U^{2};$$ for $U > 60\%$: $T_v = 1.781 - 0.933\log_{10}(100 - U\%)$.

20. State the Mohr-Coulomb failure criterion for soil shear strength.

    $$\tau_f = c + \sigma_n \tan\phi$$ where $\tau_f$ = shear strength at failure, $c$ = cohesion, $\sigma_n$ = normal stress on the failure plane, and $\phi$ = angle of internal friction. In effective stress terms: $\tau_f = c' + \sigma'\tan\phi'$.

21. For the Mohr-Coulomb criterion, what is the inclination of the failure plane to the major principal plane?

    The failure plane is inclined at an angle $\theta = 45^\circ + \frac{\phi}{2}$ to the major principal plane (i.e., to the plane on which $\sigma_1$ acts).

22. Compare cohesive (clay) and cohesionless (sand) soils in terms of shear strength parameters.

    Cohesionless soils (sand, gravel): shear strength comes only from friction, $c \approx 0$, so $\tau_f = \sigma_n\tan\phi$. Cohesive soils (clay): strength comes mainly from cohesion; for saturated clay under undrained (UU) conditions $\phi_u \approx 0$ and $\tau_f = c_u$ (undrained cohesion).

23. Name the common laboratory tests used to measure shear strength of soil.

    Direct shear (shear box) test, triaxial compression test (UU, CU, CD types), unconfined compression test (for saturated clay, giving $q_u = 2c_u$), and the laboratory/field vane shear test (for soft clays).

24. Write the relationship between coefficient of permeability $k$, coefficient of consolidation $c_v$, and compressibility.

    $$k = c_v\,m_v\,\gamma_w$$ where $m_v = \frac{a_v}{1+e_0}$ is the coefficient of volume compressibility and $a_v = -\frac{de}{d\sigma'}$ is the coefficient of compressibility.

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