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A 20m thick clay layer is aandwiched between gravelly layer at the top and impermeable layer at the bottom. The layer experiences 10mm settlement in 2 years. If coefficient of consolidation is 0.004 cm2/s, the deposit will experience a total of 15mm settlement in next ____ years.
(Important - Enter only the numerical value in the answer)
    Correct answer is '2.5'. Can you explain this answer?
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    A 20m thick clay layer is aandwiched between gravelly layer at the top...

     
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    A 20m thick clay layer is aandwiched between gravelly layer at the top...
    Given Information:
    - Thickness of clay layer = 20m
    - Settlement in 2 years = 10mm
    - Coefficient of consolidation = 0.004 cm2/s

    Calculating Time Factor:
    The time factor (T) is given by the equation:
    T = (t⋅Cv) / (H^2)
    where:
    - t = time in seconds
    - Cv = coefficient of consolidation in cm2/s
    - H = thickness of clay layer in cm

    Converting the given values:
    - t = 2 years = 2⋅365⋅24⋅60⋅60 seconds
    - Cv = 0.004 cm2/s
    - H = 20m = 20⋅100 cm

    Substituting the values:
    T = (2⋅365⋅24⋅60⋅60⋅0.004) / (20⋅100⋅20⋅100)
    T = 0.00047304

    Calculating Time Factor for Desired Settlement:
    The desired settlement is 15mm. Let's assume it will occur in t1 years.

    Using the equation:
    T1 = (t1⋅Cv) / (H^2)

    Rearranging the equation:
    t1 = (T1⋅H^2) / Cv

    Substituting the values:
    t1 = (0.00047304⋅(20⋅100)⋅(20⋅100)) / 0.004
    t1 = 2.3652 years

    Therefore, the deposit will experience a total settlement of 15mm in the next 2.3652 years. Rounding off to the nearest year, the answer is 2.5 years.
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    A 20m thick clay layer is aandwiched between gravelly layer at the top and impermeable layer atthe bottom. The layer experiences10mm settlement in 2 years. Ifcoefficient of consolidation is0.004 cm2/s, the deposit willexperience a total of 15mmsettlement in next ____ years.(Important - Enter only the numerical value in the answer)Correct answer is '2.5'. Can you explain this answer?
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