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Construction of a new building founded on a clayey soil was completed in January 2010. In January 2014, the average consolidation settlement of the foundation in clay was recorded as 10 mm. The ultimate consolidation settlement was estimated in design as 40 mm. Considering double drainage to occur at the clayey soil site, the expected consolidation settlement in January 2019 (in mm, round off to the nearest integer) will be _____________
Correct answer is '15'. Can you explain this answer?
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Construction of a new building founded on a clayey soil was completed ...
Ultimate consolidation = 40 mm Recorded consolidation = 10 mm
∴ Total recorded consolidation
⇒ 40 × 0.375
Most Upvoted Answer
Construction of a new building founded on a clayey soil was completed ...
Given information:
- Construction of a new building founded on a clayey soil was completed in January 2010.
- In January 2014, the average consolidation settlement of the foundation in clay was recorded as 10 mm.
- The ultimate consolidation settlement was estimated in design as 40 mm.
- Double drainage is expected to occur at the clayey soil site.
Explanation:
Consolidation Settlement:
Consolidation settlement is a time-dependent settlement that occurs in saturated cohesive soils, such as clay, due to the expulsion of water from the soil layers.
Double Drainage:
Double drainage refers to the situation where both the top and bottom of the clay layer are free to drain water. In this case, the consolidation settlement is expected to be reduced compared to a single drainage condition.
Calculating Consolidation Settlement:
To calculate the expected consolidation settlement in January 2019, we need to consider the time factor and the settlement characteristics of the clayey soil.
Time Factor:
The consolidation settlement is a function of time, and it follows a logarithmic relationship. The settlement decreases with time until it reaches a certain value known as the ultimate consolidation settlement.
Settlement Characteristics:
The settlement characteristics can be determined using the formula:
𝑠 = 𝑠_𝑢 × 𝑟^𝑛
where:
- 𝑠 = settlement at a given time
- 𝑠_𝑢 = ultimate consolidation settlement
- 𝑟 = ratio of time passed to the time taken for 90% consolidation settlement (𝑡_𝑢)
- 𝑛 = slope of the settlement-time curve (can be determined based on the soil properties)
Calculating the settlement ratio (r):
To calculate the settlement ratio (r), we need to determine the time taken for 90% consolidation settlement (𝑡_𝑢) and the time passed between January 2014 and January 2019.
Given that the consolidation settlement in January 2014 is 10 mm and the ultimate consolidation settlement is 40 mm, we can determine the settlement ratio as follows:
𝑟 = 𝑠/𝑠_𝑢 = 10/40 = 0.25
Calculating the expected consolidation settlement in January 2019:
To calculate the expected consolidation settlement in January 2019, we need to determine the settlement at that time using the settlement ratio (r) and the time factor.
Since the consolidation settlement follows a logarithmic relationship, we can use the settlement-time curve to determine the slope (𝑛) and calculate the settlement at a given time.
Given that the expected consolidation settlement in January 2019 is required, we can assume 𝑡_𝑢 = 9 years (January 2010 to January 2019).
Using the settlement ratio (r = 0.25) and the time factor (𝑡/𝑡_𝑢 = 2019-2014/9 = 5/9), we can calculate the expected settlement as follows:
𝑠 = 𝑠_𝑢 × 𝑟^𝑛 = 40 × (0.25)^(5/9) ≈ 14.95 ≈
- Construction of a new building founded on a clayey soil was completed in January 2010.
- In January 2014, the average consolidation settlement of the foundation in clay was recorded as 10 mm.
- The ultimate consolidation settlement was estimated in design as 40 mm.
- Double drainage is expected to occur at the clayey soil site.
Explanation:
Consolidation Settlement:
Consolidation settlement is a time-dependent settlement that occurs in saturated cohesive soils, such as clay, due to the expulsion of water from the soil layers.
Double Drainage:
Double drainage refers to the situation where both the top and bottom of the clay layer are free to drain water. In this case, the consolidation settlement is expected to be reduced compared to a single drainage condition.
Calculating Consolidation Settlement:
To calculate the expected consolidation settlement in January 2019, we need to consider the time factor and the settlement characteristics of the clayey soil.
Time Factor:
The consolidation settlement is a function of time, and it follows a logarithmic relationship. The settlement decreases with time until it reaches a certain value known as the ultimate consolidation settlement.
Settlement Characteristics:
The settlement characteristics can be determined using the formula:
𝑠 = 𝑠_𝑢 × 𝑟^𝑛
where:
- 𝑠 = settlement at a given time
- 𝑠_𝑢 = ultimate consolidation settlement
- 𝑟 = ratio of time passed to the time taken for 90% consolidation settlement (𝑡_𝑢)
- 𝑛 = slope of the settlement-time curve (can be determined based on the soil properties)
Calculating the settlement ratio (r):
To calculate the settlement ratio (r), we need to determine the time taken for 90% consolidation settlement (𝑡_𝑢) and the time passed between January 2014 and January 2019.
Given that the consolidation settlement in January 2014 is 10 mm and the ultimate consolidation settlement is 40 mm, we can determine the settlement ratio as follows:
𝑟 = 𝑠/𝑠_𝑢 = 10/40 = 0.25
Calculating the expected consolidation settlement in January 2019:
To calculate the expected consolidation settlement in January 2019, we need to determine the settlement at that time using the settlement ratio (r) and the time factor.
Since the consolidation settlement follows a logarithmic relationship, we can use the settlement-time curve to determine the slope (𝑛) and calculate the settlement at a given time.
Given that the expected consolidation settlement in January 2019 is required, we can assume 𝑡_𝑢 = 9 years (January 2010 to January 2019).
Using the settlement ratio (r = 0.25) and the time factor (𝑡/𝑡_𝑢 = 2019-2014/9 = 5/9), we can calculate the expected settlement as follows:
𝑠 = 𝑠_𝑢 × 𝑟^𝑛 = 40 × (0.25)^(5/9) ≈ 14.95 ≈
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Construction of a new building founded on a clayey soil was completed in January2010. In January 2014, the average consolidation settlement of the foundation in clay was recorded as 10 mm. The ultimate consolidation settlement was estimated in design as 40 mm. Considering double drainage to occur at the clayey soil site, the expected consolidation settlement in January 2019 (in mm, round off to the nearest integer) will be _____________Correct answer is '15'. Can you explain this answer?
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