Concept explainers
(a)
Calculate the average stress increase in the clay layer due to the applied load.
(a)
Answer to Problem 11.21P
The average stress increase in the clay layer
Explanation of Solution
Given information:
The foundation load
The length of the foundation
The breadth of the foundation
The depth of foundation
The height of the clay layer 1
The height of the clay layer 2
The dry unit weight of sand
The saturated unit weight
The liquid limit
Calculation:
Consider the unit weight of water
Calculate the distributed load
Substitute
Calculate the increase in vertical stress
Here,
For the depth
Calculate the width
Substitute
Calculate the ratio
Substitute
Calculate the ratio
Substitute
Similarly calculate the remaining values and tabulate as in Table 1.
Refer Table 10.11 “Variation of
Take the value of
Similarly calculate the remaining values and tabulate as in Table 1.
Calculate the increase in vertical stress
Substitute
Similarly calculate the increase in vertical stress values and tabulate as in Table 1.
Show the increase in vertical stress for each depth below the center of the loaded area as in Table 1.
Depth, | |||||
1 | 1.25 | 1.75 | 1.4 | 0.522 | 39.92 |
1 | 1.25 | 3.5 | 2.8 | 0.210 | 16.06 |
1 | 1.25 | 5.25 | 4.2 | 0.10 | 7.65 |
Table 1
Refer to table 1.
Calculate the stress increase in the clay layer
Here,
Substitute
Hence, the average stress increase in the clay layer
(b)
Calculate the primary consolidation settlement.
(b)
Answer to Problem 11.21P
The primary consolidation settlement
Explanation of Solution
Given information:
The foundation load
The length of the foundation
The breadth of the foundation
The depth of foundation
The height of the clay layer 1
The height of the clay layer 2
The dry unit weight of sand
The saturated unit weight of sand
The liquid limit
The moisture content
The specific gravity of soil solids
The preconsolidation pressure
The swell index
Calculation:
Consider the unit weight of water
The stress at the middle of the clay layer
Calculate the compression index
Substitute
Calculate the swell index
Substitute
Calculate the saturated unit weight of clay layer
Substitute
Calculate the void ratio
Substitute
Calculate the average effective stress at the middle of the clay layer
Substitute
The effective stress
Check for the condition
Substitute
Calculate the primary consolidation settlement
Substitute
Therefore, the primary consolidation settlement
(c)
Calculate the degree of consolidation after 2 years.
(c)
Answer to Problem 11.21P
The degree of consolidation after 2 years
Explanation of Solution
Given information:
The settlement after 2 years
The foundation load
The length of the foundation
The breadth of the foundation
The depth of foundation
The height of the clay layer 1
The height of the clay layer 2
Calculation:
Refer to part (b).
The primary consolidation settlement
Calculate the degree of consolidation after 2 years
Substitute
Hence, the degree of consolidation
(d)
Calculate the coefficient of consolidation for the pressure range.
(d)
Answer to Problem 11.21P
The coefficient of consolidation of the clay
Explanation of Solution
Given information:
The settlement after 2 years
The foundation load
The length of the foundation
The breadth of the foundation
The depth of foundation
The height of the clay layer 1
The height of the clay layer 2
Calculation:
Refer to part (c).
The degree of consolidation
Calculate the time factor
Refer Table 11.7 “Variation of
Take the value of
Calculate the length of maximum drainage path
Substitute
Calculate the coefficient of consolidation
Substitute
Hence, the coefficient of consolidation of the clay
(e)
Calculate the settlement in 3 years.
(e)
Answer to Problem 11.21P
The time settlement in 3 years
Explanation of Solution
Given information:
The foundation load
The length of the foundation
The breadth of the foundation
The depth of foundation
The height of the clay layer 1
The height of the clay layer 2
The time
Calculation:
Refer to part (b).
The primary consolidation settlement
Refer to part (d).
The coefficient of consolidation of the clay
Calculate the time factor
Substitute
Calculate the degree of consolidation
Refer Table 11.7 “Variation of
Take the value of
Calculate the settlement in 3 years
Substitute
Therefore, the time settlement in 3 years
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Chapter 11 Solutions
Principles of Geotechnical Engineering (MindTap Course List)
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