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The water level in a lake is 5m above the bed, and the saturated unit weight of lake bed soil is 20kN/m3. The unit weight of water is 10 kN/m3. What is the effective vertical stress at 5m depth below the lake bed?
  • a)
    150 kN/m2
  • b)
    50 kN/m2
  • c)
    75 kN/m2
  • d)
    100 kN/m2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The water level in a lake is 5m above the bed, and the saturated unit ...
Calculation: 
Given: γsat = 20kN/m3, γw = 10 kN/m3
The total stresses, σ = γw h+ γsat h2
pore water pressure u = γw (h1+h2)
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Most Upvoted Answer
The water level in a lake is 5m above the bed, and the saturated unit ...
Given:
- Water level above the lake bed = 5m
- Saturated unit weight of lake bed soil = 20 kN/m3
- Unit weight of water = 10 kN/m3

To find:
Effective vertical stress at 5m depth below the lake bed

Solution:
The effective vertical stress at a given depth below the lake bed is the sum of the weight of the overlying soil and the weight of the water column above it.

Step 1: Calculate the weight of the soil column above the given depth.

The weight of the soil column can be calculated using the formula:
Weight of soil column = Saturated unit weight of soil × Depth

Weight of soil column = 20 kN/m3 × 5m = 100 kN/m2

Step 2: Calculate the weight of the water column above the given depth.

The weight of the water column can be calculated using the formula:
Weight of water column = Unit weight of water × Depth

Weight of water column = 10 kN/m3 × 5m = 50 kN/m2

Step 3: Calculate the effective vertical stress.

The effective vertical stress at the given depth is the sum of the weight of the soil column and the weight of the water column.

Effective vertical stress = Weight of soil column + Weight of water column
Effective vertical stress = 100 kN/m2 + 50 kN/m2
Effective vertical stress = 150 kN/m2

Therefore, the effective vertical stress at 5m depth below the lake bed is 150 kN/m2.

Hence, the correct answer is option B) 50 kN/m2.
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