The University of New South Wales School of Civil & Environmental Engineering
Soil Mechanics Mechani cs - CVEN2201 By Arman Khoshghalb
TUTORIAL 7 – Consolidation theory, theory, One-dimensional settlement of soil deposits
1- For e versus log curves given opposite, verify that the values given for the preconsolidation pressure and the compression index of tests 9, 11 and and 13 are correct (Holtz et al.).
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The University of New South Wales School of Civil & Environmental Engineering
Soil Mechanics - CVEN2201 By Arman Khoshghalb
2- The pressure versus void ratio data determined from a consolidation test on an undisturbed clay specimen is as opposite (Holtz et al.). (a) Plot the pressure versus void ratio curve on both arithmetic and semi-logarithmic graphs. (b) What are the compression, recompression, modified compression and modified recompression indices for this soil? (c) Estimate the stress to which this clay has been preconsolidated.
Pressure (kPa) 20 40 80 160 320 640 1280 320 80 20 0
Void ratio 0.864 0.853 0.843 0.830 0.785 0.696 0.602 0.628 0.663 0.704 0.801
3- As part of a construction project, a 7.5 m thick layer of clay is to be loaded with a temporary 3 m thick sand layer, as shown in the figure. The figure shows the water-table location, soil unit weights, and the compression curve properties for the clay. Assume the sand layer remains dry. (a) Calculate the value of in the middle of the clay layer (at 3.75 m below the water table) before the sand layer is applied, and after consolidation is complete. (b) Based on your answer in part (a), and the compression curve characteristics, calculate the settlement that will occur under these conditions. (c) How much will the clay layer heave when the 3 m sand layer is removed? (Holtz et al.)
4- The following consolidation test data were Pressure (kPa) Void ratio obtained from a soil sample. For this clay, LL=85, 3 0 2.743 PL=38, ρ s = 2.70 Mg/m and w = 102.4%. 5 2.712 Initially, the specimen height was 2.54 cm and its 10 2.703 volume was 75.14 cm3. 20 2.679 40 2.541 (a) Plot the data as void ratio versus log pressure. 80 2.211 Evaluate the preconsolidation pressure and the 160 1.849 virgin compression index. 320 1.486 (b) Construct the field virgin compression curve 640 1.224 160 1.285 using the Schmertmann procedure for an OCR of 40 1.374 unity and evaluate the field virgin compression 5 1.499 index. (c) Construct the field virgin compression curve using the Schmertmann procedure for an OCR=2.5 and evaluate the field virgin compression index. (d) At the midpoint of a 7.5 m thick soil layer, the void ratio is 1.9. Find this point on the field virgin compression curve determined in part (b). What is the corresponding pressure? If this pressure is doubled over the entire site, compute the consolidation settlement of the layer. (e) Using the appropriate empirical relationships, estimate the compression and recompression indices for this clay. How well the empirical relationships agree with the laboratory data? (Holtz et al.) 2
The University of New South Wales School of Civil & Environmental Engineering
Soil Mechanics - CVEN2201 By Arman Khoshghalb
5- A large oil storage tank 90 m in diameter is to be constructed on the soil profile shown opposite. Average depth of the oil in the tank is 18 m, and the specific gravity of the oil is 0.92. Consolidation tests on a sample taken from the middle of the clay layer yield = 0.154, = 0.0112 and = 260. Estimate the maximum total consolidation settlement of the tank. Neglect any settlements in the sand. Work this problem: (a) Assuming conditions at the mid-depth of the c lay are typical of the entire clay layer (b) Dividing the clay layer into four thinner layers. Use Boussinesq method to find the stress increase due to the oil tank and assume that the initial void ratio is constant throughout the clay layer (Holtz et al.).
6- Three uniformly distributed loads of 100 kPa each are applied to 10 × 10 square areas on the soil profile shown in the figure below. Undisturbed samples of the clay were taken prior to construction, and consolidation tests indicated that the average preconsolidation stress is about 110 kPa, the average compression index is 0.50, and the average recompression index is 0.02. Estimate the total consolidation settlement for the clay layer only under the centre of the middle loaded area (Holtz et al.).
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The University of New South Wales School of Civil & Environmental Engineering
Soil Mechanics - CVEN2201 By Arman Khoshghalb
7- A 4m thick fill is to be placed (over a large area) on the soil profile shown opposite. The consolidation tests performed at points A and B yielded the following results:
2.1m
= 15 kN/m3 Silty sand
3.5m
Sample
A B
Cc 0.37 0.59
Cr 0.14 0.19
1.2 1.9
() 83 100
4m
WT
3.3m
3
= 17.5 kN/m
Medium Clay
A
3
= 17 kN/m
3
If the unit weight of the fill is 20 kN/m , determine the ultimate consolidation settlement of the fill at the ground surface. One-point settlement calculation using conditions at the middle of each layer would be adequate; however the void ratio should not be assumed constant (with depth) in the clay layers.
1.7m 6m
Soft Clay
B
3
= 16 kN/m
Bed rock
8- Figure opposite shows a proposed site where an excavation will be made. 17.28 kN/m3 3m The 3m layer of sand will be removed, so that the top 1m 1m of the 8m normally 3 consolidated clay layer will 18.85 kN/m 8m be exposed. Assume full Cc = 0.4 capillarity in the clay only. Cr = 0.08 (a) Assume that the watertable location remains the same during excavation. Compute the , and values at the middle of the clay layer before and after the excavation. (b) Assuming 1-D conditions, compute how much the clay layer will deform due to this excavation. Specify whether this is settlement or heave.
,
Answers: Q2: b) = 0.3, = 0.06, = 0.16, = 0.03 c) = 330 Q3: a) Before applying the sand layer: 40.1; After completing the consolidation: 88.1 b) 16.2 c) 7.7 , Q4: a) = 1.2, = 39 b) = 1.35 c) = 1.32 d) 164, 105 e) ≅ 0.67, ≅ 0.030.07, Not good Q5: a) 55 b) 57 Q6: 7.5 Q7: 51.5 Q8: a) Before excavation: = 127.2, = 29.4, = 97.8; After excavation: = 75.4, = 29.4, = 46.0 b) 11.7 - heave
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