Chapter 8 Show your work and assumptions on the e versus

Compressibility of Soil and Rock Chapter 8

8-22. What would be the settlement of the same structure in Problem 8.21 if the

overconsolidation ratio of the clay were 1.0 and

σ

’vo +

Δσ

v = 305 kPa at the middepth of the clay

layer? Show your work and assumptions on the e versus log s curve of Problem 8.20.

SOLUTION:

vvov pvo

175 kPa; ‘ 305 kPa; OCR 1.0 ‘ ‘ 220 kPa

Δσ = σ + Δσ = = → σ = σ =

8-23. The consolidation curve of Fig. Ex. 8.9 is typical of a compressible layer 5 m thick. If the

existing overburden pressure is 50 kPa, compute the settlement due to an additional stress of

150 kPa added by a structure.

SOLUTION:

vvop o

120

150 kPa; ‘ 50 kPa; ‘ 120 kPa; OCR 1.7; H 5 m

Δσ = σ = σ = = = =

Compressibility of Soil and Rock Chapter 8

8-24. For the test data of Problem 8.12, construct the field virgin compression curve using the

Schmertmann procedure for an OCR of unity.

SOLUTION:

39.000, 2.765

2.5

3

3.5

Compressibility of Soil and Rock Chapter 8

8-25. Do Problem 8.24 for an OCR = 2.5.

SOLUTION:

39, 2.71

3

3.5

Compressibility of Soil and Rock Chapter 8

8-26. 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 Problem 8.24. What is the corresponding pressure? If this

pressure is doubled over the entire site, compute the consolidation settlement of the layer.

SOLUTION:

2.5

3

3.5

Compressibility of Soil and Rock Chapter 8

8-31. Figure P8.31 shows a proposed foundation site, with 10 ft of sand overlying 15 ft of clay

with consolidation properties shown. The clay is normally consolidated. Assume 1-D conditions.

(a) Compute the initial

σ

’v at the middle of the clay layer prior to excavation and construction. (b)

After excavation and during construction, the foundation area will be heavily loaded with the

structure and equipment so that

σ

’v at the middle of the clay layer will be increased to 3900 psf.

Determine the settlement that will occur under these conditions. (c) After construction is

completed, the equipment will be removed and the final

σ

’v at the middle of the clay layer will be

3200 psf.

SOLUTION:

vo

v

(a) ‘ (10 ft)(110 pcf) (7.5 ft)(120 62.4 pcf) 1532 psf

(b) 3900 1532 2368 psf

σ= + − =

Δσ = − =

Compressibility of Soil and Rock Chapter 8

8-32. 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 (refer to Fig. P8.32).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

σ

’v 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?

SOLUTION:

32

vo

(a) ‘ (3.75 m)(20.5 9.81kN m ) 40.09 kN m

σ= − =

Compressibility of Soil and Rock Chapter 8

8-33. Refer to Fig. 8.5a. Determine: (a) Using log interpolation between 100 and 1000,

determine the

σ

v value at a vertical strain,

ε

v = 20%. (b) If the initial void ratio, eo = 2.6, determine

Cr and Cc for this soil. For Cc use the portion of the curve between

σ

’v = 100 and 500 kPa. (c) If

the original clay layer thickness is 9.5 m, determine the settlement that occurs in the layer when it

is loaded from 200 to 400 kPa. [Note: You don’t need the results from part (b) to do this.]

SOLUTION:

v

(a) There are various approaches for interpolating logarithmic scales.

One approach for interpolating the desired x (or ‘ ) value is as follows:

σ

Compressibility of Soil and Rock Chapter 8

8-34. A large embankment is to be built on the surface of a 15-ft clay layer. Before the

embankment is built, the initial

σ

’v at the middle of the clay layer is 480 psf. The results from a 1-D

consolidation test on the clay from the middle of the layer are as follows:

σ

’p = 1800 psf Cr

ε

= 0.0352 Cc

ε

= 0.180

If the final

σ

’v at the middle of the layer after the embankment loading is 2100 psf, what is the

settlement, in inches, of the clay layer resulting from this loading?

SOLUTION:

p

vo vf

vo

‘1800 psf

(a) ‘ 480 psf, ‘ 2100 psf, OCR 3.75

‘ 480 psf

σ

σ= σ= = = =

σ

Compressibility of Soil and Rock Chapter 8

8-35. Figure P8.35 shows a proposed site where an excavation will be made. The 10 ft layer of

sand will be removed, so that the top of the 24 ft 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

σ

v.

σ

’v, and u 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, in inches. Specify whether this is settlement or heave.

SOLUTION:

v

(a) Before excavation

(10 ft)(110 pcf) (12 ft)(120 pcf) 2540 psf

σ=+=

Compressibility of Soil and Rock Chapter 8

8-36. Figure P8.36 shows the soil profile at a site where you plan to lower the water table. You

have results from two consolidation tests, one from the upper 12 ft thick overconsolidated crust,

and another from the lower 32 ft thick normally consolidated zone. You plan to lower the water

table from its current 12 ft depth to 20 ft below ground surface. The consolidation properties for

each layer are shown. Assume full capillarity. a) Compute the

σ

’v in the middle of each layer

before and after the water table is lowered. (b) Determine the total settlement that will result from

lowering the water table.

SOLUTION:

vvo

(a) Center of layer 1: original water table at 12 ft

(6 ft)(120 pcf) 720 psf; u 0; ‘ 720 psf

Center of layer 2: original water table at 12 ft

σ= = = σ =

Compressibility of Soil and Rock Chapter 8

8-37. When a consolidation test is performed on some soils, the virgin compression region is not

linear, but bilinear. Figure P8.37 shows such a compression curve from a 15 ft thick layer.

Required: (a) What vertical strain, occurs when the soil is loaded from an initial

σ

’v1 = 560 psf to

σ

’v2 = 3000 psf? (b) If you load the soil further, to

σ

’v3 = 4000 psf, how much additional settlement

occurs? (c) Finally, if you unload from 4000 psf back to

σ

’v4 = 3000 psf, what additional

deformation (in ft) occurs?

SOLUTION:

v

980 3000

(a) (0.032)log (0.14)log 0.00778 0.068 0.0758 7.58%

560 980

⎛⎞ ⎛ ⎞

ε= + = + = =

⎜⎟ ⎜ ⎟

⎝⎠ ⎝ ⎠

Compressibility of Soil and Rock Chapter 8

8-38. Refer to the compression curve marked Soil 13 in Fig. 8.9a. Disregard the small unloading

cycle in the middle of the curve. The initial void ratio for this soil is 1.17, and the preconsolidation

pressure is 290 kPa. Note: the right-hand vertical boundary of this graph is at

σ

’vc = 2000 kPa.

Required: (a) Determine the Cr and Cc for this soil based on the compression curve. (b) If a layer

of this soil 12 m thick is loaded from 50 to 800 kPa (two of the data points shown on the curve),

what settlement will result, in m?

SOLUTION:

rc

1.17 1.135 1.35 0.67

(a) C 0.0106; C 0.523

2000 2000

log log

1100

−−

== ==

⎛⎞ ⎛⎞

⎜⎟ ⎜⎟

⎝⎠ ⎝⎠