CE-701 Geotechnical Engineering - Dec 2024 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 7 Marks
   aA rectangular area of $2m \times 4m$ carries a uniformly distributed load $80\text{ kN/sq.m}$ at ground surface. Find the vertical pressure at $5m$ below the center and corner of the loaded area. Solve the problem by :

   1. i)dividing the rectangle into four equivalent rectangles
   2. ii)2:1 method
   How to answer

   • Rectangular loaded area $2m \times 4m$, $q=80 kN/m^2$, depth $z=5m$.
   • Center: divide into 4 rectangles, use Fadum/Newmark influence factor $I$, $\sigma_z = 4 I q$.
   • Corner: use whole $L/B$, $z$ influence factor $I$, $\sigma_z = I q$.
   • 2:1 method: $\Delta\sigma = Q / [(B+z)(L+z)]$ for center/corner discussion.
2. 7 Marks
   bDescribe the direct shear test. What are its merits and demerits compared to Triaxial test?
   How to answer

   • Apparatus and procedure of direct shear box test.
   • Mohr-Coulomb envelope to get c and phi.
   • Merits: simple, quick, drained, direct.
   • Demerits vs triaxial: forced plane, non-uniform stress, no pore pressure, drainage uncontrolled.
   • Comparison table with triaxial test.
3. 7 Marks
   aA partially saturated clay weighs $113.4\text{ gm}$ in its natural state and $93.4\text{ gm}$ in its dry state. If specific gravity is $2.65$, find out the void ratio, porosity, degree of saturation, $\gamma_{wet}$, $\gamma_d$ and $\gamma_{sat}$. Size of the clay is $3.7\text{ cm}$ in dia. and $7.5\text{ cm}$ ht.
   How to answer

   • Find volume $V = \pi d^2 h/4$ and masses.
   • Water content $w = (W-W_d)/W_d$.
   • Void ratio $e = G_s \gamma_w V/W_s -1$.
   • Porosity $n=e/(1+e)$, $S_r = w G_s/e$.
   • Unit weights $\gamma_{wet}, \gamma_d, \gamma_{sat}$ formulas.
4. 7 Marks
   bDefine the following terms.

   1. i)Critical hydraulic gradient
   2. ii)Quick sand condition.
   How to answer

   • Define critical hydraulic gradient $i_c = (G_s-1)/(1+e)$.
   • Condition of zero effective stress.
   • Define quick sand condition and where it occurs.
   • Relation $i_c \approx 1$ for typical sands.
5. 6 Marks
   aExplain in detail about three clay minerals.
   How to answer

   • Structure: 1:1 vs 2:1 minerals.
   • Kaolinite: fixed, low swelling, low CEC.
   • Montmorillonite: expanding, high swelling, high shrinkage.
   • Illite: intermediate behaviour, potassium bond.
6. 8 Marks
   bA soil profile consists of a surface layer of sand $3m$ thick ($\gamma=16\text{ kN/m}^3$), an intermediate clay layer $2m$ thick ($\gamma_{sat}=19.25\text{ kN/m}^3$) and a bottom layer of gravel $4m$ thick ($\gamma_{sat}=19\text{ kN/m}^3$). The water table is at the top of the clay layer. Determine the effective stress at various interfaces. There is a surcharge of $50\text{ kN/m}^2$ on the ground surface.
   How to answer

   • Draw soil profile with water table and surcharge.
   • Compute total stress $\sigma$ at each interface.
   • Compute pore pressure $u$ below water table.
   • Effective stress $\sigma' = \sigma - u$ at interfaces.
   • Show variation diagram.
7. 10 Marks
   aAn oedometer test is performed on a $3\text{ cm}$ thick clay sample. After $5$ minutes, $50\%$ consolidation is reached. After how long a time would the same degree of consolidation is achieved in the field where the clay layer is $6\text{ m}$ thick? Assume the sample and the clay layers have the same drainage boundary conditions (double drainage).
   How to answer

   • Time factor $T_v$ same for same $U$; $T_v = C_v t/d^2$.
   • For double drainage $d = H/2$.
   • $t_{field}/t_{lab} = (d_{field}/d_{lab})^2$.
   • Lab $d=1.5cm$, field $d=3m$, $t_{lab}=5 min$ for $50\%$.
   • Compute field time in days/years.
8. 4 Marks
   bExplain Flow nets, their characteristics and uses.
   How to answer

   • Definition of flow net: flow lines and equipotentials.
   • Characteristics: orthogonal, curvilinear squares.
   • Uses: seepage, uplift, exit gradient.
   • Neat sketch of flow net.
9. 10 Marks
   aIn a direct shear test on a specimen of clean dry sand, a normal stress of $180\text{ kPa}$ was applied and failure occurred at a shear stress of $100\text{ kPa}$. Determine analytically the angle of shearing resistance, the principal stresses during failure and directions of the principal planes with respect to the direction of the plane of shearing.
   How to answer

   • Given $\sigma_n=180 kPa$, $\tau_f=100 kPa$ on failure plane.
   • For sand $c=0$, $\phi = \tan^{-1}(\tau/\sigma)$.
   • Mohr circle: centre and radius to get $\sigma_1, \sigma_3$.
   • Orientation $\theta = 45+\phi/2$ from principal plane.
   • Report principal stresses and directions.
10. 4 Marks
    bExplain standard proctor test to determine MDD and OMC of soil.
    How to answer

    • Apparatus: mould, 2.5kg rammer, 3 layers, 25 blows.
    • Procedure and water content variation.
    • Plot dry density vs water content.
    • MDD as peak and OMC as corresponding water content.
11. 7 Marks
    aWhat are various field compaction methods?
    How to answer

    • Rollers: smooth, pneumatic, sheepsfoot, vibratory.
    • Suitability for sands, clays, gravels.
    • Field control: layers, passes, moisture.
12. 7 Marks
    bDefine over consolidated, under consolidated and normally consolidated clays.
    How to answer

    • Define OCR = pc / present stress.
    • Over-consolidated: OCR>1, precompressed.
    • Normally consolidated: OCR=1.
    • Under-consolidated: OCR<1, still consolidating.
13. 7 Marks
    aWrite a short note on the pipette method.
    How to answer

    • Principle: sedimentation, Stokes law.
    • Apparatus and sampling at depth-time.
    • Calculation of % finer.
    • Advantages for fine soils.
14. 7 Marks
    bDefine 'preconsolidation pressure'. In what ways is its determination important in soil engineering practice? Describe a suitable procedure for determining the preconsolidation pressure.
    How to answer

    • Definition of preconsolidation pressure $p_c$.
    • Importance: settlement, OCR, strength, design.
    • Casagrande method steps on e-log p curve.
    • Determine point of max curvature, tangents.
15. 7 Marks
    aWith the help of a sketch of a flow net, derive the formula to determine the quantity of seepage through an earth dam.
    How to answer

    • Draw flow net with $N_f$ channels, $N_d$ drops.
    • Head loss per drop $\Delta h = H/N_d$.
    • Discharge per channel $\Delta q = k \Delta h$.
    • Total $q = k H N_f/N_d$ per unit length.
    • Apply to earth dam section.
16. 7 Marks
    bWhat are the methods of soil stabilization? Explain functions and applications of geo synthetic in detail.
    How to answer

    • Methods: mechanical, chemical, thermal, electrical.
    • Stabilizers: cement, lime, bitumen.
    • Geosynthetics functions: separation, reinforcement, filtration, drainage.
    • Applications in roads, slopes, retaining walls.