Soil mechanics miscellaneous

Soil mechanics miscellaneous

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Soil Mechanics

Soil mechanics miscellaneous
  1. Two soil specimens with identical geometric dimensions were subjected to falling head permeability tests in the laboratory under identical conditions. The fall of water head was measured after an identical time interval. The ratio of initial to final water heads for the test involving the first specimen was 1.25. If the coefficient of permeability of the second specimen is 5-times that of the first, the ratio of initial to final water heads in the test involving the second specimen is








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    Let coeff. of permeability of first specimen be k
    ∴ coeff of permeability of second specimen = 5 k
    For falling head permeability test,

    k = 2.303
    aL
    		log10
    h1
    Ath2

    For indential specimen,
    k ∝ log10
    h1
    h2


    ∴
    h1
    		= 3.05
    h2

    Correct Option: A

    Let coeff. of permeability of first specimen be k
    ∴ coeff of permeability of second specimen = 5 k
    For falling head permeability test,

    k = 2.303
    aL
    		log10
    h1
    Ath2

    For indential specimen,
    k ∝ log10
    h1
    h2


    ∴
    h1
    		= 3.05
    h2

  1. The range of void ratio between which quick sand conditions occurs in cohesion less granular soil deposits is








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    For cohesion less soil, G = 2.65 to 2.68
    For quick sand condition, iC ≈ 1

    iC =
    (G - 1)
    (1 + e)

    Substituting the values, e = G – 2 is, 0.65 – 0.68
    ≈ 0.6 to 0.7

    Correct Option: B

    For cohesion less soil, G = 2.65 to 2.68
    For quick sand condition, iC ≈ 1

    iC =
    (G - 1)
    (1 + e)

    Substituting the values, e = G – 2 is, 0.65 – 0.68
    ≈ 0.6 to 0.7

  1. To provide safety against piping failure, with a factor of safety of 5, what should be he maximum permissible exit gradient for soil with specific gravity of 2.5 and porosity of 0.35?








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    iC =
    (G - 1)
    		= (G- 1)(1 - η)
    (1 + e)

    = (2.5 – 1) (1– 0.35) = 0.975
    max. possible exit gradient, = 0.975/5 = 0.195 (F. S = 5)

    Correct Option: C

    iC =
    (G - 1)
    		= (G- 1)(1 - η)
    (1 + e)

    = (2.5 – 1) (1– 0.35) = 0.975
    max. possible exit gradient, = 0.975/5 = 0.195 (F. S = 5)

  1. For a saturated sand deposit, the void ratio and the specific gravity of solids are 0.70 and 2.67, respectively. The critical (upward) hydraulic gradient for the deposit would we








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    iC =
    (G - 1)
    (1 + e)

    iC =
    2.67 - 1
    		= 0.98
    1 + 0.7

    Correct Option: B

    iC =
    (G - 1)
    (1 + e)

    iC =
    2.67 - 1
    		= 0.98
    1 + 0.7

  1. Steady state seepage is taking place through a soil element at Q, 2 m below the ground surface immediately downstream of the toe of an earthen dam as shown in the sketch. The water level in a piezometer installed at P, 500 mm above Q is at the ground surface. The water level in a piezometer installed at R, 500 mm below Q, is 100 mm above the ground, surface. The bulk saturated unit weight of the soil is 18 kN/ m3 and the unit weight of water is 9.81 kN/m3. The vertical effective stress (in kPa) at Q is.








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    Pore water pressure, µ = γw. h.
    µP = γw × 1.5 m
    µR = γw × (2.5 + 0.1) = γw × 2.6

    µ varies linearly with depth. As P & R are at equal distance from θ, µQ will be average of UP and UR.

    Effective stress, σ = σ – U
    at Q = γsat. h – UQ.
    = 18 × 2 – 2.05 × 9.81 = 15. 89 kPa

    Correct Option: B

    Pore water pressure, µ = γw. h.
    µP = γw × 1.5 m
    µR = γw × (2.5 + 0.1) = γw × 2.6

    µ varies linearly with depth. As P & R are at equal distance from θ, µQ will be average of UP and UR.

    Effective stress, σ = σ – U
    at Q = γsat. h – UQ.
    = 18 × 2 – 2.05 × 9.81 = 15. 89 kPa