GATE Exam  >  GATE Questions  >  A fully submerged infinite sandy slope has an... Start Learning for Free
A fully submerged infinite sandy slope has an inclination of 30° with the horizontal. The saturated unit weight and effective angle of internal friction of sand are 18 kN/m3 and 38°, respectively. The unit weight of water is 10 kN/m3. Assume that the seepage is parallel to the slope. Against shear failure of the slope, the factor of safety (round off to two decimal places) is _______.
    Correct answer is '0.60'. Can you explain this answer?
    Verified Answer
    A fully submerged infinite sandy slope has an inclination of 30° w...

    = 0.601
    View all questions of this test
    Most Upvoted Answer
    A fully submerged infinite sandy slope has an inclination of 30° w...
    Degrees with the horizontal. The density of sand is 1600 kg/m³ and the angle of internal friction is 35 degrees. What is the height of the slope at which the sand starts to slide?

    To determine the height at which the sand starts to slide, we need to calculate the critical height based on the angle of internal friction.

    The angle of internal friction (φ) is given as 35 degrees, which means the tangent of φ is equal to the coefficient of friction (μ).

    μ = tan(φ) = tan(35) ≈ 0.7002

    The weight of the sand column above a certain height h is given by the formula:

    W = γ * A * h

    Where:
    W = weight of the sand column
    γ = density of sand = 1600 kg/m³
    A = cross-sectional area of the sand column
    h = height of the sand column

    The critical height is the height at which the weight of the sand column is equal to the resisting force due to friction.

    Weight of the sand column (W) = Resisting force due to friction

    W = μ * N

    Where:
    N = Normal force acting perpendicular to the slope

    The normal force (N) can be calculated as:

    N = W * cos(θ)

    Where:
    θ = inclination of the slope = 30 degrees

    Substituting the value of N in the equation for W:

    W = μ * N = μ * W * cos(θ)

    Simplifying the equation:

    1 = μ * cos(θ)

    Substituting the value of μ:

    1 = 0.7002 * cos(30)

    Solving for cos(30):

    cos(30) = 0.866

    0.7002 * 0.866 = 0.606

    Therefore, the critical height at which the sand starts to slide is approximately 0.606 times the height of the sand column.

    Let's assume the height of the sand column is H.

    Critical height = 0.606 * H

    The inclination of the slope is 30 degrees. In a right-angled triangle formed by the slope, the critical height is the opposite side and the height of the sand column is the hypotenuse.

    Using the trigonometric ratio:

    sin(30) = opposite/hypotenuse

    sin(30) = critical height/H

    Solving for critical height:

    critical height = sin(30) * H

    critical height = 0.5 * H

    Therefore, the critical height at which the sand starts to slide is half the height of the sand column.

    Hence, the height of the slope at which the sand starts to slide is equal to twice the critical height.

    Height of slope = 2 * critical height
    Height of slope = 2 * (0.606 * H)
    Height of slope = 1.212 * H

    Therefore, the height of the slope at which the sand starts to slide is approximately 1.212 times the height of the sand column.
    Explore Courses for GATE exam

    Similar GATE Doubts

    A fully submerged infinite sandy slope has an inclination of 30° with the horizontal. The saturated unit weight and effective angle of internal friction of sand are 18 kN/m3 and 38°, respectively. The unit weight of water is 10 kN/m3. Assume that the seepage is parallel to the slope. Against shear failure of the slope, the factor of safety (round off to two decimal places) is _______.Correct answer is '0.60'. Can you explain this answer?
    Question Description
    A fully submerged infinite sandy slope has an inclination of 30° with the horizontal. The saturated unit weight and effective angle of internal friction of sand are 18 kN/m3 and 38°, respectively. The unit weight of water is 10 kN/m3. Assume that the seepage is parallel to the slope. Against shear failure of the slope, the factor of safety (round off to two decimal places) is _______.Correct answer is '0.60'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A fully submerged infinite sandy slope has an inclination of 30° with the horizontal. The saturated unit weight and effective angle of internal friction of sand are 18 kN/m3 and 38°, respectively. The unit weight of water is 10 kN/m3. Assume that the seepage is parallel to the slope. Against shear failure of the slope, the factor of safety (round off to two decimal places) is _______.Correct answer is '0.60'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A fully submerged infinite sandy slope has an inclination of 30° with the horizontal. The saturated unit weight and effective angle of internal friction of sand are 18 kN/m3 and 38°, respectively. The unit weight of water is 10 kN/m3. Assume that the seepage is parallel to the slope. Against shear failure of the slope, the factor of safety (round off to two decimal places) is _______.Correct answer is '0.60'. Can you explain this answer?.
    Solutions for A fully submerged infinite sandy slope has an inclination of 30° with the horizontal. The saturated unit weight and effective angle of internal friction of sand are 18 kN/m3 and 38°, respectively. The unit weight of water is 10 kN/m3. Assume that the seepage is parallel to the slope. Against shear failure of the slope, the factor of safety (round off to two decimal places) is _______.Correct answer is '0.60'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE. Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
    Here you can find the meaning of A fully submerged infinite sandy slope has an inclination of 30° with the horizontal. The saturated unit weight and effective angle of internal friction of sand are 18 kN/m3 and 38°, respectively. The unit weight of water is 10 kN/m3. Assume that the seepage is parallel to the slope. Against shear failure of the slope, the factor of safety (round off to two decimal places) is _______.Correct answer is '0.60'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A fully submerged infinite sandy slope has an inclination of 30° with the horizontal. The saturated unit weight and effective angle of internal friction of sand are 18 kN/m3 and 38°, respectively. The unit weight of water is 10 kN/m3. Assume that the seepage is parallel to the slope. Against shear failure of the slope, the factor of safety (round off to two decimal places) is _______.Correct answer is '0.60'. Can you explain this answer?, a detailed solution for A fully submerged infinite sandy slope has an inclination of 30° with the horizontal. The saturated unit weight and effective angle of internal friction of sand are 18 kN/m3 and 38°, respectively. The unit weight of water is 10 kN/m3. Assume that the seepage is parallel to the slope. Against shear failure of the slope, the factor of safety (round off to two decimal places) is _______.Correct answer is '0.60'. Can you explain this answer? has been provided alongside types of A fully submerged infinite sandy slope has an inclination of 30° with the horizontal. The saturated unit weight and effective angle of internal friction of sand are 18 kN/m3 and 38°, respectively. The unit weight of water is 10 kN/m3. Assume that the seepage is parallel to the slope. Against shear failure of the slope, the factor of safety (round off to two decimal places) is _______.Correct answer is '0.60'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A fully submerged infinite sandy slope has an inclination of 30° with the horizontal. The saturated unit weight and effective angle of internal friction of sand are 18 kN/m3 and 38°, respectively. The unit weight of water is 10 kN/m3. Assume that the seepage is parallel to the slope. Against shear failure of the slope, the factor of safety (round off to two decimal places) is _______.Correct answer is '0.60'. Can you explain this answer? tests, examples and also practice GATE tests.
    Explore Courses for GATE exam
    Signup for Free!
    Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
    10M+ students study on EduRev