A 1m thick layer of saturated clay drained at both faces settles by 15...
Given:
- Thickness of the clay layer = 1m
- Settlement of the clay layer = 15cm
- Time taken for settlement = 2 years
To find:
The period during which the settlement of 15cm will be completed after introducing a thin layer of pervious soil in the middle.
Solution:
1. Settlement of the clay layer:
- The settlement of the clay layer is given as 15cm.
- Time taken for settlement = 2 years.
2. Introduction of a thin layer of pervious soil:
- A thin layer of pervious soil is introduced in the middle of the clay layer.
3. Settlement with the introduction of pervious soil:
- When a thin layer of pervious soil is introduced in the middle of the clay layer, the settlement will occur in two stages:
1. Settlement of the pervious soil layer
2. Settlement of the remaining clay layer
4. Settlement of the pervious soil layer:
- The pervious soil layer will settle faster compared to the clay layer because it has higher permeability.
- Let's assume that the settlement of the pervious soil layer is x cm.
- The settlement of the pervious soil layer will occur in a shorter time period, let's say t years.
5. Settlement of the remaining clay layer:
- After the settlement of the pervious soil layer, the remaining clay layer will settle further.
- The settlement of the remaining clay layer will be (15 - x) cm.
- The time taken for the settlement of the remaining clay layer will be (2 - t) years.
6. Total settlement:
- The total settlement of the clay layer is given as 15cm.
- This settlement is the sum of the settlement of the pervious soil layer (x cm) and the settlement of the remaining clay layer (15 - x) cm.
- Therefore, we can write the equation: x + (15 - x) = 15.
- Simplifying the equation, we get: 15 = 15.
7. Time taken for total settlement:
- The time taken for total settlement will be the sum of the time taken for the settlement of the pervious soil layer (t years) and the time taken for the settlement of the remaining clay layer (2 - t years).
- Therefore, we can write the equation: t + (2 - t) = 2.
- Simplifying the equation, we get: 2 = 2.
8. Conclusion:
- From the above equations, it is clear that the total settlement and the time taken for settlement are independent of the settlement of the pervious soil layer.
- Therefore, the period during which the settlement of 15cm will be completed after introducing a thin layer of pervious soil in the middle is still 2 years (option D).
A 1m thick layer of saturated clay drained at both faces settles by 15...
2years
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