Concept explainers
(a)
Calculate the total consolidation settlement under the action of fill load.
(a)
Answer to Problem 11.1CTP
The total consolidation settlement
Explanation of Solution
Given information:
The thickness of fill material
The compacted unit weight of fill material
The length of the foundation
The breadth of the foundation
The depth of fill
The height of the layer silty sand
The height of the clay layer
The height of the peat layer
The dry unit weight of sand
The saturated unit weight of sand
The saturated unit weight of clay
The saturated unit weight of peat
The time
The properties of clay and organic layers are given in the Table.
Calculation:
Consider the unit weight of water
Calculate the distributed load
Substitute
Calculate the increase in vertical stress
Here,
For clay layer:
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
Take the value of
Calculate 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 | 4 | 3 | 0.75 | 0.823 | 28.82 |
1 | 4 | 5 | 1.25 | 0.599 | 20.98 |
1 | 4 | 7 | 1.75 | 0.403 | 14.11 |
Table 1
Refer to table 1.
Calculate the stress increase in the clay layer
Here,
Substitute
Calculate the average effective stress at the middle of the clay layer
Substitute
Calculate the primary consolidation settlement
Substitute
For peat layer:
For the depth
Calculate the ratio
Substitute
Similarly calculate the remaining values and tabulate as in Table 2.
Refer Table 10.11 “Variation of
Take the value of
Take the value of
Calculate the value of
Similarly calculate the remaining values and tabulate as in Table 2.
Calculate the increase in vertical stress
Substitute
Similarly calculate the increase in vertical stress values and tabulate as in Table 2.
Show the increase in vertical stress for each depth below the center of the loaded area as in Table 2.
Depth, | |||||
1 | 4 | 7 | 1.75 | 0.403 | 14.11 |
1 | 4 | 7.9 | 1.975 | 0.342 | 11.98 |
1 | 4 | 8.8 | 2.2 | 0.302 | 10.58 |
Table 2
Refer to table 2.
Calculate the stress increase in the peat layer
Substitute
Calculate the average effective stress at the middle of the clay layer
Substitute
Calculate the primary consolidation settlement
Substitute
Calculate the total consolidation settlement under the action of fill load
Substitute
Hence, the total consolidation settlement
(b)
Calculate the time for
(b)
Answer to Problem 11.1CTP
The time for
The time for
Explanation of Solution
Given information:
The thickness of fill material
The compacted unit weight of fill material
The length of the foundation
The breadth of the foundation
The depth of fill
The height of the layer silty sand
The height of the clay layer
The height of the peat layer
The dry unit weight of sand
The saturated unit weight of sand
The saturated unit weight of clay
The saturated unit weight of peat
The time
The properties of clay and organic layers are given in the Table.
Calculation:
The degree of consolidation
The clay layer is permeable and having less void ratio compared to peat layer. Hence, double drainage condition is assumed for the clay layer.
Calculate the time factor
Refer Table 11.7 “Variation of
Take the value of
Calculate the length of maximum drainage path
Substitute
Calculate the time for
Substitute
Hence, the time for
The peat layer is low permeable and having high void ratio compared to clay layer. Hence, single drainage condition is assumed for the peat layer.
Calculate the length of maximum drainage path
Substitute
Calculate the time for
Substitute
Hence, the time for
(c)
Calculate the secondary compression in each layer up to end of
(c)
Answer to Problem 11.1CTP
The secondary compression for clay
The secondary compression for peat
Explanation of Solution
Given information:
The thickness of fill material
The compacted unit weight of fill material
The length of the foundation
The breadth of the foundation
The depth of fill
The height of the layer silty sand
The height of the clay layer
The height of the peat layer
The dry unit weight of sand
The saturated unit weight of sand
The saturated unit weight of clay
The saturated unit weight of peat
The time
The properties of clay and organic layers are given in the Table.
Calculation:
Refer to part (b).
The time for
The time for
For clay:
Calculate the primary void ratio
Substitute
Calculate the void ratio at the end of primary consolidation
Substitute
Calculate the magnitude of secondary compression index
Here,
Substitute
Calculate the secondary compression
Substitute
Hence, the secondary compression for clay
For peat:
Calculate the primary void ratio
Substitute
Calculate the void ratio at the end of primary consolidation
Substitute
Calculate the magnitude of secondary compression index
Substitute
Calculate the secondary compression
Substitute
Hence, the secondary compression for peat
(d)
Calculate the total settlement after 18 months.
(d)
Answer to Problem 11.1CTP
The total settlement after 18 months is
Explanation of Solution
Given information:
The thickness of fill material
The compacted unit weight of fill material
The length of the foundation
The breadth of the foundation
The depth of fill
The height of the layer silty sand
The height of the clay layer
The height of the peat layer
The dry unit weight of sand
The saturated unit weight of sand
The saturated unit weight of clay
The saturated unit weight of peat
The time
The properties of clay and organic layers are given in the Table.
Calculation:
Refer to part (a).
The total consolidation settlement
Refer to part (c).
The secondary compression for clay
The secondary compression for peat
Calculate the total settlement after 18 months as shown below.
Substitute
Hence, the total settlement after 18 months is
(e)
Calculate the excess pore water pressure at point A two months after the application of the fill load.
(e)
Answer to Problem 11.1CTP
The excess pore water pressure at point A
Explanation of Solution
Given information:
The thickness of fill material
The compacted unit weight of fill material
The length of the foundation
The breadth of the foundation
The depth of fill
The height of the layer silty sand
The height of the clay layer
The height of the peat layer
The dry unit weight of sand
The saturated unit weight of sand
The saturated unit weight of clay
The saturated unit weight of peat
The time
The properties of clay and organic layers are given in the Table.
The depth
Calculation:
Refer to part (a).
The pore water pressure
Calculate the length of maximum drainage path
Substitute
Calculate the time factor
Substitute
Calculate the ratio
Substitute
Calculate the degree of consolidation
Refer Figure 11.29 “Variation of
Take the value of U as
Calculate the excess pore water pressure after 2 months
Substitute
Hence, the excess pore water pressure at point A
(f)
Calculate the effective stress at point A two months after the application of the fill load.
(f)
Answer to Problem 11.1CTP
The effective stress at point A is
Explanation of Solution
Given information:
The thickness of fill material
The compacted unit weight of fill material
The length of the foundation
The breadth of the foundation
The depth of fill
The height of the layer silty sand
The height of the clay layer
The height of the peat layer
The dry unit weight of sand
The saturated unit weight of sand
The saturated unit weight of clay
The saturated unit weight of peat
The time
The properties of clay and organic layers are given in the Table.
The depth
Calculation:
Refer to part (a).
The pore water pressure
Refer to part (e)
The excess pore water pressure at point A
Calculate the increase in effective stress
Substitute
Calculate the average effective stress at the point A
Substitute
Calculate the final effective stress at point A as shown below.
Substitute
Hence, the effective stress at point A is
(g)
Calculate the piezometer reading at point A two months after the application of the fill load.
(g)
Answer to Problem 11.1CTP
The piezometer reading at point A is
Explanation of Solution
Given information:
The thickness of fill material
The compacted unit weight of fill material
The length of the foundation
The breadth of the foundation
The depth of fill
The height of the layer silty sand
The height of the clay layer
The height of the peat layer
The dry unit weight of sand
The saturated unit weight of sand
The saturated unit weight of clay
The saturated unit weight of peat
The time
The properties of clay and organic layers are given in the Table.
The depth
Calculation:
Refer to part (e)
The excess pore water pressure at point A
The piezometer reading is the total pore water pressure.
Calculate the piezometer reading
Substitute
Hence, the piezometer reading at point A is
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Chapter 11 Solutions
PRINCIPLES OF GEOTECH.ENGINEERING >LL+M
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