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
EBK PRINCIPLES OF GEOTECHNICAL ENGINEER
- A square foundation, 2.5x2.5m in size, supports a column load of 478 kN. The soil characteristics are given in the following figure. Field monitoring indicated that the foundation settlement was 46mm at the end of 2 years. (a) Estimate the average stress increase in the clay layer due to the applied load. (b) Estimate the primary consolidation settlement. (c) What is the degree of consolidation after 2 years? (d) Estimate the coefficient of consolidation for the pressure range. (e) Estimate the settlement in 3 years.arrow_forwardRefer to Figure 11.41. Given that B =1 m, L = 3 m, and Q = 110 kN, the soil characteristics given in the figure are Cs = 1/5 Cc, Ꝺ’c= 40 kN/m2. Field monitoring indicated that the foundation settlement was 19 mm during the first 12 months. a. Estimate the average stress increase in the clay layer due to the applied load. b. Estimate the primary consolidation settlement. c. What is the degree of consolidation after 12 months? d. Estimate the coefficient of consolidation for the pressure range. e. Estimate the settlement in 24 months. Answer must be: A. 6.33 B. 32.82 C. 57.89 D. 0.0013 E. 25.66arrow_forwardA foundation with dimensions BxL supporting a column load, P. The foundation rests on a sandy soil underlain by a clay layer (consolidation test result in Problem 2). • Estimate the primary consolidation settlement of the clay due to the foundation load. • What is the void ratio at the end of primary consolidation? • Calculate the secondary Consolidation settlement after 6 years knowing that the primary consolidation settlement took 2.5 years. Given: P = 350 kN, B =L=2.5 m, Df= 2 m, H1= 3 m, and H2=4.5 m. The soil properties are as follows: Sand: ya = 16.4 kN/m³; ysat = 18.8 kN/m³ Clay: Ysat = 17.6 kN/m²; eo = 0.82, Ca=0.02 Sand D Yd H GWT BxL Ysat Clay Ysat Sandy gravelarrow_forward
- KINDLY OBTAIN THE RIGHT ANSWER AND EXPLAIN Refer to Figure. Given that B =1 m, L = 3 m, and Q = 110 kN, the soil characteristics given in the figure are Cs = 1/5 Cc, Ꝺ’c= 40 kN/m2. Field monitoring indicated that the foundation settlement was 19 mm during the first 12 months. Estimate the average stress increase in the clay layer due to the applied load. Estimate the primary consolidation settlement. What is the degree of consolidation after 12 months? Estimate the coefficient of consolidation for the pressure range. Estimate the settlement in 24 months.arrow_forwardA CD triaxial compression test conducted on a clay specimen revealed that c'=5 kPa and o'=22°. What is the major principal stress at failure if the confining pressure is 35 kPa? Solve the problem graphically and then analytically.arrow_forwardGiven that B =1 m, L = 3 m, and Q = 110 kN, the soil characteristics given in the figure are Cs = 1/5 Cc, Ꝺ’c= 40 kN/m2. Field monitoring indicated that the foundation settlement was 19 mm during the first 12 months. Estimate the average stress increase in the clay layer due to the applied load. Estimate the primary consolidation settlement. What is the degree of consolidation after 12 months? Estimate the coefficient of consolidation for the pressure range. Estimate the settlement in 24 months.arrow_forward
- Estimate the ultimate consolidation settlement under the centerline of a 15 X 15 m mat foundation. The mat is 1 m thick reinforced concrete and the average stress on the surface of the slab is 75 kPa. The soil profile is shown below. Oedometer tests on samples of the clay provide these average values. ’p = 130 kPa, Cc = 0.40, Cr = Cs = 0.03 Neglect any settlements due to the sand layer. Please and thank you!! :)arrow_forwardA plate loading test was carried out on a medium dense sand, using a 1 ft wide square plate, and k1 was determined as 350 lb/in3. Determine the coefficient of subgrade reaction for a 7.5 ft wide square foundation and a 7.5 ft × 10.5 ft rectangular foundation.arrow_forward11.19 Refer to Figure 11.45. A square footing, 2 x 2 m in size, supports a column load of 300 kN. The soil characteristics are given in the figure. Field monitoring indi- cated that the foundation settlement was 19 mm during the first 12 months. a. Estimate the average stress increase in the clay layer due to the applied load. b. Estimate the primary consolidation settlement. c. What is the degree of consolidation after 12 months? d. Estimate the coefficient of consolidation for the pressure range. e. Estimate the settlement in 24 months. 300 kN 1m 2m x 2 m Ya = 14 kN/m3 I m Yu = 17 kN/m 24% G, = 2.74 LL = 46 2 m o'= 40 kN/m² C, = 1/5C. Sand Clay Figure 11.45 O Cengrge learring 2014arrow_forward
- In a geotechnical laboratory an oedometer test on a saturated clay soil was conducted. The results in the laboratory report stated that the Cc = 0.2, Cr = 0.04 and OCR = 4.5. The existing vertical effective stress in the field was 130 kPa. A building foundation was designed to construct above the soil condition. This will increase the vertical stress at the center of the clay by 150 kPa. The thickness of the clay layer is 2 m and its water content is 28%. Solve the primary consolidation settlement and determine the difference in the settlement if OCR value were 1.5 instead 4.5.arrow_forwardSITUATION 2: A normally consolidated clay layer 3m thíck has a void ratio of 1.10. Liquid Limit is equal to 40 and the average effective stress on the clay layer was 80 kPa. The average stress on it is increased to 120 kPa as a result of construction of a foundation. 13. Compute for the consolidation settlement that will occur on the clay layer. a. 17 mm b. 45 mm C. 68 mm d. 57 mm 14. Compute for the consolidation settlement that will occur on the clay layer if pre- consolidation pressure is 96 kPa. a. 68 mm b. 57 mm C. 17 mm d. 45 mm 15. Compute for the consolidation settlement that will occur on the clay layer if pre- consolidation pressure is 130 kPa. a. 45 mm c. 57 mm b. 68 mm d. 17 mmarrow_forwardA normally consolidated clay layer 3 m thick has a void ratio of 1.10. Liquid limit is equal to 40 and the average effective stress on the Clay layer was 80 Kpa The average stress on it is increased to 120 Kpa as a result of construction of a foundation. a. Compute for the consolidation settlement that will occur on the clay layer b. Compute for the consolidation settlement that will occur on the clay layer if preconsolidation pressure is 96Kpa. c. Compute for the consolidation settlement that will occur on the clay layer if preconsolidation pressure is 130 KPa.arrow_forward
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