The University of New South Wales Soil Mechanics - CVEN2201 School of Civil & Environmental Engineering By Arman Khoshghalb

1

TUTORIAL 7 – Consolidation 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 13 are correct (Holtz et al.).

The University of New South Wales Soil Mechanics - CVEN2201 School of Civil & Environmental Engineering By Arman Khoshghalb

2

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.

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 obtained from a soil sample. For this clay, LL=85,

PL=38, ρs = 2.70 Mg/m3 and w = 102.4%. Initially, the specimen height was 2.54 cm and its

volume was 75.14 cm3. (a) Plot the data as void ratio versus log pressure.

Evaluate the preconsolidation pressure and the virgin compression index.

(b) Construct the field virgin compression curve using the Schmertmann procedure for an OCR of

unity and evaluate the field virgin compression 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.)

Pressure (kPa) Void ratio 20 0.864 40 0.853 80 0.843 160 0.830 320 0.785 640 0.696

1280 0.602 320 0.628 80 0.663 20 0.704 0 0.801

Pressure (kPa) Void ratio 0 2.743 5 2.712

10 2.703 20 2.679 40 2.541 80 2.211

160 1.849 320 1.486 640 1.224 160 1.285 40 1.374 5 1.499

The University of New South Wales Soil Mechanics - CVEN2201 School of Civil & Environmental Engineering By Arman Khoshghalb

3

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 clay 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.).

The University of New South Wales Soil Mechanics - CVEN2201 School of Civil & Environmental Engineering By Arman Khoshghalb

4

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:

Sample Cc Cr �� ���� (���)

A 0.37 0.14 1.2 83 B 0.59 0.19 1.9 100

If the unit weight of the fill is 20 kN/m3, 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.

8- Figure opposite shows a proposed site where an

excavation will be made. The 3m layer of sand will

be removed, so that the top of the 8m normally

consolidated clay layer will be exposed. Assume full

capillarity in the clay only. (a) Assume that the water-

table 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,

�� ≅ 0.03��0.07, 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

Soft Clay

Medium Clay

Bed rock

WT

6m

Silty sand

= 15 kN/m3

= 17.5 kN/m3

= 17 kN/m3

= 16 kN/m3

4m

2.1m

3.5m

A

B

1.7m

3.3m

3m

8m

1m 1m

18.85 kN/m3

Cc = 0.4 Cr = 0.08

17.28 kN/m3