Assignments and Project 2014a

Geotechnical Engineering

Tutorial Questions

Assignments

Group Project

Subject Timetable

Autumn Semester 2014

University of Technology, Sydney 48360 Geotechnical Engineering

Faculty of Engineering and IT 1 Autumn 2014

TUTORIAL 1 BASIC DESIGN

1. Consider the semi-circular mechanism shown in the figure below for the failure of a long

strip footing on a soil deforming under undrained conditions. Based on this mechanism failure

causes a rotation about point O.

The following soil properties are known:

t = 20 kN/m3

cu = 100 kPa

u = 0

a) Calculate the ultimate bearing pressure

for the footing when the soil deforms

under undrained conditions.

b) Evaluate the effects of any surcharge,

qo, which may be applied on the surface of

the soil, on the ultimate bearing capacity

of the footing.

2. A long vertical drain is going to be made in a soil. Assume the failure plane shown in the

figure opposite and evaluate the safety of the

cut under the following conditions:

Undrained conditions

Drained conditions

Consider all possible cases for water table in

the drain and pore water pressures.

The following clay properties are known:

t = 22 kN/m3

cu = 30 kPa u = 0

c = 0 = 27

You should assume that the lining of the drain does not provide any resistance to failure.

3. Write an expression for the undrained

bearing capacity of a strip footing shown in

the figure opposite. Assume the slip

mechanism shown, which is an arc centred

above one edge of the footing (point O).

You may assume the following parameters are

given: t , cu , u = 0.

Determine the minimum bearing pressure that

causes failure of the soil.

5m

45o

B B

O

q

B

R

O

q



TUTORIAL 2 TERZAGHIS THEORY OF BEARING CAPACITY

1. A long highway embankment is, for the

purpose of analysis, treated as a

rectangular block as shown in the figure.

The block has a surcharge of 10 kPa

applied to its upper surface to account for

traffic loading.

The total unit weight of the embankment fill is 22 kN/m3. The embankment is founded on a

deep layer of clay having the following properties: cu = 50 kPa, u = 0.

The water table is 1 m below the surface of the clay.

a) Use Terzaghis theory of bearing capacity to determine the factor of safety against bearing

failure of the clay under the embankment given that the height of the embankment, H, is 3m.

b) Determine the maximum height to which the embankment could be constructed so that the

factor of safety against bearing failure is 2.

2. An eccentrically loaded strip footing 4m wide carries a line load of P (kN pmr). The load is

applied 1.5m from the side of the footing. The footing is 1.5m below the surface and the water

table is located at the level of the footing base. The soil is a sand having a t = 20 kN/m3 and a

friction angle of = 40o.

One way of dealing with eccentric loading is

to determine the maximum and minimum

stresses exerted on the soil beneath the footing

and compare these to the ultimate bearing

capacity of the soil as found by Terzaghis theory. Use this approach to find the value of P that ensures a minimum factor of safety of 1.5

for the footing.

3. A section through a long strip footing in an

excavation is shown in the figure opposite. On

one side of the footing a slab exerts a pressure

of 20 kPa on the foundation soil while on the

other side the soil is unexcavated. The

foundation soil consists of a layer of clay

having the following properties:

t = 18 kN/m3, cu = 30 kPa, u = 0, c = 5 kPa, = 25

o.

The ground water level is 0.4m above at the base of the footing. Use Terzaghis theory of

bearing capacity with a factor of safety of 3 to determine the maximum allowable force, in

kN pmr, which could be placed on the footing.

4. A 3m diameter circular footing is going to be constructed on the surface of a loose sand

with a friction angle of = 35o and a unit weight of = 16 kN/m3.

a) Use Terzaghis bearing capacity equations and calculate the ultimate bearing capacity of

the foundation.

b) One method for increasing the capacity is to increase the depth of embedment of the

footing, by constructing the footing below the surface level. What would be the required

depth of embedment in order to increase the capacity by a factor of 2?

10m

1m

Surcharge 10 kPa

H Ebmankment

1.5m

1m

0.4m

Surcharge 20 kPa

P

4m

P

1.5m

1.5m



TUTORIAL 3 SHALLOW FOUNDATIONS

1. A 3m3m footing supports an inclined column of

a whare house. The column makes an angle of 15o

with the vertical and carries an axial load of P (kN).

The footing is founded 1m below the surface of a

level site. The foundation consists of a deep layer of

sand having a t of 19 kN/m3 and a friction angle of

30o. The water table is 0.5m below the surface of

the soil.

a) Determine the allowable axial load, P, which the

column could transmit to the footing with a factor of safety of 4 against bearing failure, based

on Hansens theory.

b) Assuming a friction angle = 0.6 between the soil and the footing, is there a possibility

that the footing could slide laterally under the inclined load? Is there any resistance against

sliding failure from the soil adjacent to the footing?

c) Suggest one method which could be used to determine the friction angle of the sand at the

site.

2. A 2 2 m square footing for a grandstand is to be

constructed on a sloping site as shown in the figure

below. The soil at the site is clay having the following

properties:

t = 20 kN/m3 cu = 150 kPa

Use Hansens theory of bearing capacity to

determine the ultimate bearing pressure which

could be placed on this footing.

3. An eccentrically loaded strip footing carries a line

load of P (kN per meter run). The footing is 4m wide

and the load is applied 1.5m from one side of the

foundation. The footing is founded 1.5m below the

soil surface and the water table is located at the base

of the footing. The properties of the sandy soil

obtained from SPT results are as follow:

t = 20 kN/m3, = 40o.

Determine the maximum allowable force, in kN per meter run of the footing using Hansens

theory of bearing capacity and a factor of safety of 2.5.

3m3m

1m

15o P

0.5m

4.0m

1.5m

1.5m

P

2 2 m s q u a re

2 0o

2 m

2 0o



TUTORIAL 4 SETTLEMENT OF SHALLOW FOUNDATIONS

1. It is proposed to construct a 1m wide strip footing adjacent to an existing raft footing. The

raft footing has plan dimensions of 10m x 10m. A uniform pressure of 54 kPa is applied to the

surface of the underlying soil by the raft. The raft has been in existence for a very long time.

The proposed strip footing is to exert a uniform pressure of 150 kPa on the soil. The Plan and

Section below illustrate the situation.

Clay

Existing raft

Proposed

strip footing PLAN

0.5m

Point X

2.5m

Proposed

strip footing Existing raft

0.5m

SECTION

Rock

Point X

10m

10m

1m

The soil profile at the site consists of a 2.5m deep layer of clay overlying rock. The water

table is at the surface of the soil. A sample of clay is taken from a depth of 1.25m directly

below Point X. The following soil properties are obtained by testing the sample:

Initial moisture content: 31% t = 20 kN/m3

Cc = 0.4 Cr = 0.1 pc = 50 kPa

In the design of the project concern has been expressed that the new strip footing may cause

excessive settlements of the soil beneath the existing raft. Determine the total final settlement

of the clay layer under Point X due to the strip footing. Point X is located mid-way along the

side of the raft nearest to the footing. Use the 1-D consolidation method employing a one-

point settlement computation based on conditions at the sampling point.

2. The soil conditions at a site consist of a 2m thick layer of clay over a 3m thick layer of sand

over rock. SPT testing is conducted on the sand giving the results shown the table opposite.

The depth quoted is below the ground surface and is defined as the depth to the completion

the second blow count.

SPT results Depth below

footing base (m)

Stress increase in

sand (kPa) Depth of test (m) Blow count

3.0 4,6,6 2.0 55

4.0 10,10,12 3.0 40



A 2m wide strip footing is to be constructed at the site. The footing will carry a uniform

pressure of 250 kPa and the base of the footing will found 1m below the surface. The stress

increases in the sand due to the footing have been determined under the middle of the footing

and shown in the table opposite.

Use the elastic settlement theory to determine the mean settlement of the footing due to the

settlement of the sand layer alone. In other words the settlement of the clay and rock are to be

ignored. The Youngs modulus of the sand may be determined as suggested by Parry. You should assume a Poissons ratio of 0.3 for the sand. Note that a good approximation to the weighting factors to be used in the calculation of the weighted average of N may be taken

based on the intensity of the stress increase at each point.

3. A 3m wide strip footing is to be constructed at

the surface of a 3 m clay layer underlain by

incompressible impermeable rock with water table

at the surface of the soil. The footing is to carry a

pressure of 100 kPa. Three samples of the clay are

taken from depths of 0.5, 1.5 and 2.5m. They each

indicated a total unit weight of 20 kN/m3, however

there was a significant difference in the value of the

coefficient of volume change, mv, for each sample.

To determine the settlement under the centre of the footing, analyses of the stress increase,

, caused by the footing at each of the sampling points have been carried out. The results of

soil testing and the analysis of stress increases are given in the table opposite.

a) Divide the clay under the footing into three sub-layers and calculate the settlement under

the centre of the footing using the 1-D consolidation approach.

b) Use an appropriate weighting approach to determine a single weighted value of mv for the

entire layer.

c) By assuming a value of ' = 0.25 determine the mean settlement of the footing using an

approach based on elasticity.

d) Examine the effect of Poissons ratio on the settlement. You may assume a Poissons ratio

of, for example, 0.4 and calculate the settlement again and compare it with the one obtained

before.

e) How long would it take for 50% of the consolidation settlement to occur? Assume a

coefficient of consolidation of cv = 110-7

m2/s. Assume the foundation base is permeable.

4. A 3 m wide flexible strip footing is founded on the surface of a deep soil deposit. The

footing carries a uniform pressure of 100 kPa. Determine the change in the vertical stress

under the edge and under the centre of the footing at a level 1.5m below the base of the

footing. .

Sample

point

Sample

depth

(m)

Mv

(m2/kN)

(kPa)

1 0.5 3.310-4

99

2 1.5 1.910-4

81

3 2.5 8.210-5

61



TUTORIAL 5 PILE FOUNDATIONS

1. A 6m long concrete pile is driven through a deep layer of loose

sand. The pile has a diameter of 500 mm. The unit weight of the sand

may be taken as 18 kN/m3.

a) Determine the allowable vertical capacity of the pile using a factor

of safety of 3.

b) Determine the settlement of the pile if a load of 400 kN is applied

to the pile. The Youngs modulus of the sand and the concrete pile may be taken as 40 MPa and 20 GPa, respectively.

2. A concrete pile is driven through 5m layer of loose sand and

penetrates 5m into medium dense gravel. The pile has a square

section of 600 mm by 600 mm. There is no sign of water in the sand

or gravel layer. The unit weight of sand and gravel may be taken as

15 kN/m3 and 20 kN/m

3, respectively.

Determine the allowable vertical capacity of the pile using a factor

of safety of 3.

3. What load would cause failure immediately after construction of

the cast-in-situ reinforced concrete pile shown in the figure

opposite? The pile has a diameter of 600 mm and a length of 8m

and the following soil properties are given:

Brown clay: t = 16 kN/m3, cu = 30 kPa, u = 0

Dense sand: t = 21 kN/m3, = 40o

Grey clay: t = 19 kN/m3, cu = 120 kPa, u = 0

4. A square group of 9 piles is arranged with 3 rows and 3 columns

spaced 3m c/c apart. The cast-in-situ piles have a diameter of 600

mm embedded 6m in a deep layer of stiff to very stiff clay having an

undrained cohesion of 100 kPa, a unit weight of t = 20 kN/m3, and a

Youngs modulus of 20 MPa. The group of piles has a rigid cap and Youngs modulus of the pile material can be taken as 2000 MPa.

a) Determine the ultimate capacity of the pile group assuming that

there is no interaction between the piles, i.e, the capacity of the

group is the sum of capacity of all piles.

b) Calculate the load required to cause block failure of the entire

group.

c) Calculate the allowable bearing capacity of the group piles based

on the results of parts (a) and (b), using a factor of safety of 2.

d) Determine the settlement of the pile cap assuming that a total load

of 3600 kN is applied to the pile cap.

Sand

Gravel

t=15kN/m3

t=20kN/m3

0.6m0.6m

5m

5m

6m

Clay

t=20kN/m3

3m 3m

3m

3m

Sand

t=18kN/m3

6m

0.5m

Brown clay 4m

Dense sand 2m

Grey clay 2m

2m



TUTORIAL 6 EARTH PRESSURE

1. Consider the wall in the opposite figure which

has been built in front of a stable rock. Gravel

backfill has been placed in the space between the

wall and the rock face with a drainage pipe. The

gravel has the following properties:

t = 19 kN/m3, c = 0, = 35o.

a) The worst case design scenario is when the

drainage pipe is blocked and the water table rises

to the top surface of the backfill. Determine the

resultant lateral force on the wall for this case

using Rankines theory of active earth pressure.

b) Determine the resultant force when the drainage pipe is working properly.

c) Determine the resultant force as in part (a) using Coulombs earth pressure theory. Consider only one possible mode of failure as shown in the figure as dotted line. The

friction angle between the wall and the gravel may be taken as 25o.

2. A section through a long retaining wall embedded

into rock is shown in the opposite figure. The wall

retains 4m of clay and 3m of sand and supports a

surcharge of 10 kPa as shown. The following

properties of the soils are given:

Clay: t = 18 kN/m3, c = 5 kPa, = 20o.

Sand: t = 20 kN/m3, c = 0, = 30o.

Use Rankines theory of lateral earth pressure to determine the bending moment (per meter run) in the

wall section at point A, a long time after construction

of the wall.

3. A vertical cut is proposed through a very

weak rock mass which has an inclined seam

carries groundwater as shown in the

opposite figure. Testing of the material in

the seam has revealed that it has the

following properties:

c = 8 kPa, = 15o.

In addition, piezometric measurements show

that the average pore pressure along the

entire length of the inclined seam may be

taken as 15 kPa. The total unit weight of the rock is t = 18 kN/m3.

To maintain the stability of the rock face, horizontal anchors may be used at an interval of 3m

(into the page). Determine the minimum tensile force required to be developed in each anchor

in order to maintain the stability of the rock face.

Clay

3m

2m

2m

Sand

WT

Rock Point A

10kPa

Pipe

0.6m

3m

0.5m

Pipe Pipe

Stable

rock

8m

Inclined seam 4m

Anchor



TUTORIAL 7 RETAINING WALLS

1. The retaining wall shown in the figure

opposite retains sand. A borehole has been

sunk behind the wall and SPT testing

carried out. The results are indicated in the

figure opposite. Use the SPT results to

determine values of the unit weight and

friction angle of the sand. Find the total

lateral force acting on side AB of the wall.

Use Rankines theory of earth pressure. Do not apply any code factors to the soil

properties.

2. Gabions consist of wire baskets filled with rocks. They

are often used as retaining walls. Consider the gabion wall

shown in the figure opposite. The design of this wall is to

be checked according to AS4678-2002. The wall retains a

natural soil near a minor road. There are no buildings in

the vicinity. A live load surcharge of 5 kPa should be

applied to the soil behind the wall. The following soil

properties have been determined from testing:

Soil: = 18 kN/m3 = 35o c = 0 kPa

Gabion: = 22 kN/m3 = 25o

You are to apply code factors as appropriate and use the Rankines theory for calculation of Ka. Evaluate the stability of the wall against sliding and overturning.

3. A concrete retaining wall supports a clay soil as shown in

the figure opposite. Behind the wall the clay is sealed with

asphalt pavement so that no water can enter the backfill. A

surcharge of 10 kPa is applied to the surface of the backfill

due to traffic loading. The following properties of clay are

known:

t = 18 kN/m3, c = 5 kPa, =

30o.

a) Use Rankines theory of earth pressure to determine the factor of safety against overturning for the wall. You

should ignore any passive soil resistance in front of the

wall. Use concrete = 25 kN/m3.

b) Assuming class I for clay backfill, use AS4678-2002 recommendations and check the

stability of the wall against overturning.

4m

0.4m

Asphalt seal

Clay 0.4m

10kPa

1.4m

3 m

S P T T e s t r e s u lts

D e p th S P T v a lu e s

0 .5 m 3 , 3 , 2

1 .5 m 1 , 5 , 3

2 .5 m 6 , 6 , 8

3 .5 m 6 , 1 0 , 1 0

1 m

1 m

A

B

S a n d

W a te r

2 m

U n c o n tro lle d

b a c k f i ll s a n d

N o g ro u n d w a te r

1 m



TUTORIAL 8 SLOPE STABILITY

1. A long clay canal bank is to be rapidly constructed to give the section shown in the figure

below. The level area adjacent to the canal is subjected to a surcharge of 50 kPa and water

fills the canal to a depth of 3m. The soil consists of clay having the following properties:

t = 17 kN/m3

cu = 40 kPa

u = 0o

A trial failure plane is shown in

the figure opposite. The centre

of the trial circle lies exactly

over the toe of the slope.

Determine the factor of safety

of the slope against undrained

failure of the clay occurring

along the failure plane. Tension

crack should not be considered.

2. A slope stability analysis by the simple method of slices is being carried out for a slope in

clayey sand. The following properties of the clayey sand are known:

t = 20 kN/m3 c = 5 kPa = 30o

A computer program has been used to determine the

factor of safety of the slope. It is decided to check the

program output for a particular slice, slice 5. This slice

is drawn in the figure opposite.

Draw up the following table in your solution book. In

the table certain values are given but many are left

blank (these are indicated by .. in the table). Note the

table uses usual nomenclature for slope stability

analyses and all dimensions are in metres and angles in

degrees.

Slice L b h zW N T u cL (N-ul) tan

5 2.1 2.0 4.6 26 1.4 .. .. .. .. .. ..

(i) Fill in the blanks in the table for slice 5. (ii) The factor of safety of soil slopes is usually required to lie between 1.3 and 1.5. What

factors would you consider in deciding whether to accept a value at the low end of the

range or at the high end of the range?

(iii) An engineer has determined the factor of safety of the slope (of which slice 5 is a part) using Taylors Charts. Comment on whether this is an appropriate method.

5 0 k P a 3 m

3 m

3 m

4 .5 m

C e n tro id o f

s h a d e d a re a

1

1

S li c e

5

C e n tr e o f c ir c l e

z

W a te r ta b l e ,

h y d r o sta ti c

co n d it io n s



3. A circular base slide is considered in clayey soil consisting of three layers (the top, the

middle and the bottom clay layers). Assume the values of variables shown on the figure are

given to you. The total weight of the sliding section per metre run is W and the distance between the centre of mass to the point of rotation is X.

Accordingly, provide a proper formula for the factor of safety of this slope against sliding in

the undrained condition (u = 0).

.

Cross Section of a Circular Base Slide

Not to Scale

R

O

W

Point of rotation

(Centre of circle) Xq

Top clay: cu1

Bottom clay: cu3

Middle clay: cu2

d1

d2

Cross Section of a Circular Base Slide

Not to Scale

R

O

W

Point of rotation

(Centre of circle) Xq

Top clay: cu1

Bottom clay: cu3

Middle clay: cu2

d1

d2



Assignment 1: Soil Mechanics Revision

Q1. The results of the particle size analysis of three soils are given in the following table.

Classify the soils according to the Unified Soil Classification System (USCS)?

Soil properties Soil 1 Soil 2 Soil 3

D100 (mm) 35 9 2

D60 (mm) 20 2 0.5

D50 (mm) 15 1.2 0.4

D30 (mm) 5 0.35 0.05

D10 (mm) 0.5 0.1 0.01

% finer than 60 m 8% 4% 40%

Liquid limit* (%) 34 NP 52

Plastic limit* (%) 25 NP 27

* Atterberg limit tests were conducted on the soil fractions passing 0.425 mm sieve. NP = non plastic

Q2. The soil conditions at a site consist of 6m of clay over shale bedrock. The water table is

1m below the surface. A sample of the clay was taken from a depth of 4 m. Laboratory

testing of the sample revealed the following properties:

Water content, w% = 14% Compression index, Cc = 0.4

Recompression index, Cr = 0.1 Pre-consolidation pressure, pc = 100 kPa

Total unit weight = 18 kN/m3

(a) Determine the total final settlement of the clay layer when it is subjected to a surface surcharge of 150 kPa. Use one-point estimation based on conditions at a representative

point located 4 m below the surface of the clay.

(b) The surcharge is left in place until all settlement stops. The surcharge is then removed. Determine the thickness of the clay layer a long time after removing the surcharge.

Q3. A canal is dug parallel to a river as shown in the following figure. A sandy silt seam of

average thickness 0.5 m cuts across the otherwise impermeable clay. The average vertical and

horizontal permeabilities are 210-7 m/s and 510-6 m/s, respectively. Assume a 1 m length of canal; determine the flow rate of water from the canal to the river.

(Answer: 9.210-8 m3/s)

10 m

RL 6 m

RL 8 m

RL 10 m

RL 9 m

Canal

Sandy silt seam

0.5 m (average)

Clay

ClayRiver

10 m

RL 6 m

RL 8 m

RL 10 m

RL 9 m

Canal

Sandy silt seam

0.5 m (average)

Clay

ClayRiver



Assignment 2: Bearing Capacity

Q1. A 4m wide strip footing is founded 1m below the surface of a level site. The water table

is at a depth of 2m below the surface. The soil at the site consists of clay having the following

properties:

t = 20 kN/m3 cu = 50 kPa u = 0

o

= 25o c = 8 kPa

Use Terzaghis theory of bearing capacity to determine the allowable bearing pressure which could be placed on the footing assuming a factor of safety of 3 for the following cases:

a) Immediately after loading the footing

b) Long time after loading the footing

Q2.A strip footing is shown in the following figure. The wall is fixed into the foundation.

Determine:

(a) the effective width (B) incorporating the weights of the foundation and fill material; (b) the factor of safety of the footing against the bearing capacity failure based on the

following data: (Use Hansens equations and the concept of effective area).

P = 250 kN pmr (excluding the weights of the foundation and fill material)

M = 60 kN.m pmr,

= 14

= 9

concrete = 25 kN/m3,

t (unsaturated soil) = 18 kN/m3

t(saturated soil) = 19 kN/m3

Shear strength parameters of the base soil:= 30, c = 0 kPa

Not to Scale

1.2m

1.7m

0.5m

0.3m

M

Water table

1.3m

Saturated Soil

P

Unsaturated Soil

Not to Scale

1.2m

1.7m

0.5m

0.3m

M

Water table

1.3m

Saturated Soil

P

Unsaturated Soil



Q3. It is proposed to construct a 6m by 6m flexible pad footing on the surface of a site. The

pad is to be loaded at a uniform pressure of 100 kPa. The soil conditions under the pad consist

of:

0 - 3m Sand total unit weight of sand = 20 kN/m3

3 - 6m Clay total unit weight of clay = 17 kN/m3

6m+ Sandstone

The water table is at a depth of 2 m below the ground surface. A road runs parallel to one side

of the pad footing 2 m away, as shown in the figure. The settlement of the clay layer along the

edge line of this road due to the pad is to be investigated. The clay is normally consolidated

with a compression index of 0.4 and an in situ moisture content of 26%. (Assume the specific

gravity of soil is equal to 2.65 and the soil above the water table is saturated.)

Determine the extra settlement of the clay at Points A and B shown in the figure due to the

construction of the pad footing. These points are on the edge of the road. Use the modified

one-dimensional approach with a one-point settlement estimation based on the conditions at

the mid-point of the clay layer.

Edge of

the road

A

2m

B

3m

6m

The pad footing is

uniformly loaded at

a pressure of

100 kPa and

founded on the

surface

6m

Edge of

the road

A

2m

B

3m

6m

The pad footing is

uniformly loaded at

a pressure of

100 kPa and

founded on the

surface

6m



Assignment 3: Settlement of Shallow Foundations

Q1. The soil conditions at a site consist of the following strata:

0 - 7m Clayey sand t = 19 kN/m3

7 - 10m Clay t = 17 kN/m3

Below 10m Shale bedrock

The water table is located 6m below the surface. A sample of the clay is taken from a depth of

8.5m and subjected to consolidation testing giving the following results:

Compression index, Cc = 0.3,

Recompression index, Cr = 0.1,

Pre-consolidation pressure, pc = 130 kPa,

Water content, w = 38%

A partly buried circular steel water tank of diameter 10m is to be constructed at the site.

Construction is to involve a two-stage process:

Stage 1: A circular excavation of diameter 10m is to be made to a depth of 5m. The sides of

this excavation will be vertical and will be retained by a circular steel caisson (tube) that is

lowered as the excavation proceeds.

Stage 2: The tank is to be completed by connecting a steel floor at the base of the caisson and

adding an additional steel section at the top of the caisson such that the completed tank will

hold a depth of water of 9m.

(a) Determine the thickness of the clay layer under the centre of the base of the excavation a

long time after completing Stage 1.

(b) When all ground movement associated with Stage 1 has ceased Stage 2 is undertaken and

the tank filled with 9m of water. Determine the thickness of the clay layer under the centre

of the tank a long time after filling the tank.



Q2. A rigid strip footing is constructed on top of a sand layer overlying a clay deposit, as

show in the figure.

The total unit weight of sand is 18 kN/m3, the Youngs modulus, Es = 50 MPa and the

Poissons ratio, = 0.3.

Before construction of the footing, laboratory tests on a saturated clay sample, taken at a

depth of 6m below the ground surface, gave the following results:

Cc =0.4, Cr =0.1, Consolidation coefficient, cv = 2x10-8

m2/s

Over consolidation ratio, OCR = 2, Water content, w = 25%, Specific gravity, Gs = 2.65.

[Hint: sat = w (Gs+e) / (1+e)]

(a) Calculate the immediate settlement of the footing based on the vertical deformation of the sand layer.

(b) Based on Boussinesqs equation, calculate the excess pore water pressures at points A and B immediately after applying the surcharge load. Assume the vertical stress is

applied instantaneously.

(c) Find the total settlement of this rigid footing due to consolidation of the clay layer long time after construction.

(d) Determine the average settlement of the footing after 90 days of applying the total load due to consolidation of clay only

(c) Calculate the settlement of the footing after 100 days of applying the total load.

NOTE: the over consolidation ratio or OCR (pc/vo) is defined as the highest stress experienced divided by the current vertical stress.

5m

3m

Impermeable bedrock

200 kPa

3m

Clay

Sand

Section (Strip Footing)

Not to Scale

3m

2.5m

BA

5m

3m

Impermeable bedrock

200 kPa

3m

Clay

Sand

Section (Strip Footing)

Not to Scale

3m

2.5m

BA



Assignment 4: Pile Foundations

Q1. A 500-mm square solid concrete pile is to be bored in cohesionless soil with two layers,

as shown in the following figure. The design capacity of the pile is 700 kN.

1. Determine the required length of the pile if the factor of safety is 3. 2. Find the settlement of this floating pile due to the design load (i.e. 700 kN).

Assume: Assume the average Youngs modulus of concrete and soil to be 20 GPa and 80 MPa, respectively.

Q2. The section of a 44 pile group in a layered saturated clay soil is shown in the following

figure. The bored concrete piles are square in cross section (0.4 m 0.4 m). The centre-to

centre spacing of the piles is 1 m. Determine the allowable load bearing capacity of the pile

group in an undrained condition based on the following approaches:

(a) Find the allowable group capacity based on individual pile failure. Use a factor of safety

of 2.5, along with the following equation for the pile group efficiency.

( ) ( )

(

)

where = pile group efficiency, n = number of piles in a row, m = number of rows of piles, d = pile diameter or side, and s = piles spacing.

(b) Based on Hansens equations, find the allowable block capacity of the pile group. Use a factor of safety of 3.5.

Assume the average unit weight of soil and concrete piles are 19 kN/m3 and 25 kN/m

3,

respectively.

Section

Not to Scale

x

3mAve. SPT: N = 20

L

Q

Ave. SPT: N = 40

Section

Not to Scale

x

3mAve. SPT: N = 20

L

Q

Ave. SPT: N = 40



Assignment 5: Earth Pressure

Q1. Use Rankines theory to determine the resultant forces acting on either side of the continuous piling wall shown in the figure. The wall is part of a harbour-side structure. Water,

1m deep, exists above the clay on one side of the wall and the water table is at the same level

in the soil on the other side of the wall. You should assume that active conditions develop on

the side marked by the letters A and B, and that passive conditions will exist on side CD. The

properties of the soils are as follows:

Gravely sand: t = 20 kN/m3 = 35

o

Clay: t = 18 kN/m3 cu= 25 kPa u = 0

o

c = 0 kPa = 25o

Consider two cases:

(a) Immediately after construction of the wall

(b) Long time after construction of the wall

C

B D

A

Gravely sand

Clay

Piling wall

2m

4m

1m

1m

Section

Not to Scale

2.5m

1m 1m

2.5mClay1: cu= 40 kPa

0.4m x 0.4m

2m

Clay2: cu= 60 kPa

Clay3: cu= 80 kPa



Q2. The figure opposite shows a section of a 4 m high gravity wall. The wall is inclined

toward the backfill at an angle equal to 80o measured with respect to the horizontal.

The backfill soil is cohesionless and has a unit weight of t = 19 kN/m3 and a friction

angle of = 30o. The wall friction angle is = 20o. There is no sign of water in the soil.

a) Calculate the lateral force on the wall due to active earth pressure using the Coulombs

method and the trial failure line shown in the figure.

b) Sketch the direction of the lateral force applied to the wall, clearly mark the inclination of

the force with respect to the horizontal and calculate the horizontal and vertical

components of the lateral force.

80o

4m

52o

Failure line

1m

3m

Q3. A section of an anchored retaining wall embedded 1.5 m into a saturated stiff clay layer is

shown in the figure opposite. The soil behind the wall is a sandy soil. The following

properties of the soils are known:

Sand: t = 17 kN/m3, c = 0 kPa, = 30o

Clay: t = 20 kN/m3, cu = 25 kPa, u = 0

o

The water table is 0.65m below the surface of the clay layer as shown. The short term stability

of the wall is going to be considered in an undrained analysis.

Use Rankins theory of lateral earth pressure and determine the active and passive total

horizontal pressure at points 1 to 6 on the wall.

Td

4m

1.5m

0.65m

Sand

Clay

1m 1

2

3

4

5

6



Assignment 6: Retaining Walls

Q1. A concrete cantilever wall is shown in the following figure. Determine the value of B to

reach a minimum global factor of safety of 2 for overturning stability of the wall.

Groundwater table is 5m below the base of the wall. The effect of passive force due to soil

should be included in your calculations.

(NOTE: no need to determine the factor of safety for sliding stability or bearing capacity

strength.)

1

Section

Not to Scale

1.3 m

0.5 m

6.5 m

c = 25 kN/m3

20

B

Compacted

backfill: sand

t = 19 kN/m3

= 35

Base soil: clayey sand

t = 18 kN/m3 c = 0 kPa, = = 32;

Compacted

backfill: sand

q = 30 kPa

1m

1

Section

Not to Scale

1.3 m

0.5 m

6.5 m

c = 25 kN/m3

20

B

Compacted

backfill: sand

t = 19 kN/m3

= 35

Base soil: clayey sand

t = 18 kN/m3 c = 0 kPa, = = 32;

Compacted

backfill: sand

q = 30 kPa

1m



Q2. The following figure shows a section of an anchored retaining wall embedded into a

saturated stiff clay layer. The sand has a unit weight of t = 18 kN/m3, c = 0 kPa and = 34o.

The clay has a unit weight of t = 20 kN/m3, cu = 80 kPa and u = 0

o. A uniform pressure of

40 kPa is applied on the soil surface. The short term stability of the wall is considered in an

undrained analysis.

Use the Rankins theory of lateral earth pressure to determine the active and passive

horizontal stresses. You should apply the requirements of AS 4678 and the partial factors of

safety method in estimation of soil pressures. Assume the soil is in-situ and use a structural

classification factor of n = 1.

(a) Determine the ultimate tension force for the anchor, Td, per meter run of the wall.

(b) Determin the the minimum unbonded length of the anchor.

Td

3m

1.5m

Sand

1m

40 kPa

Clay

Water table

Not to Scale



Q3. A section of a cantilever retaining wall is shown in the following figure. The soil

properties are:

Soil (kN/m3) c (kPa)

Fill Class I 20 35 0

Fill Class II 19 32 0

In Situ Base Soil 18 30 10

According to Rankins theory of lateral earth pressure and the requirements of AS 4678 in the estimation of soil pressure, examine the sliding and overturning stability of the wall.

Draw a few sketches, in your answering booklet, to show proper drainage systems providing

good surface and subsurface drainage around the wall. Groundwater table is 1m below the

base of the wall. (Assume for the base soil:

Structure

type: 2

Section

Not to Scale

0.5m

1m

6m

c = 24 kN/m3

4.5m

Base soil: sandy clay

Fill class I: sand

Fill class I: sand

Fill class II: sand

1.4m1.6m

Structure

type: 2

Section

Not to Scale

0.5m

1m

6m

c = 24 kN/m3

4.5m


Fill class I: sand

Fill class I: sand

Fill class II: sand

1.4m1.6m

Section

Not to Scale

0.5m

1m

6m

c = 24 kN/m3

4.5m


Fill class I: sand

Fill class I: sand

Fill class II: sand

1.4m1.6m



Assignment 7: Slope Stability

Q1. It is proposed to stabilise a highway cutting using a series of piles which are closely

spaced and designed strong enough so as to prevent any failure surface to intersect them. The

clay has a cohesion cu = 20 kPa and unit weight of 18 kN/m3. Assume no frictional shear

resistance can be developed in the clay. Based on Taylors charts:

a. Determine the factor of safety with respect to cohesion for the slope shown in the

figure without the piles being present, and indicate where approximately the failure

surface intersects the ground at the base of the excavation.

b. Determine the safety factor of the slope with the piles only at location A as shown in

the figure.

c. The piles would be more effective if located further up the slope e.g. at location B, as

shown in the figure. Determine the height hB necessary to produce a factor of safety of

1.5.

30o

Bedrock

Clay

Highway cutting

6m

6m Clay

30o

Bedrock

A

Clay

Highway cutting

Piles

6m

6m Clay

30o

Bedrock

B

Clay

Highway cutting

Piles

hB6m

6m Clay



Q2. A 6m deep excavation is to be made with side slope at an angle of 27o. The soil consists

of clay with a total unit weight of t = 17 kN/m3 and zero friction angle.

Using Taylors charts determine the undrained cohesion required to obtain a safety factor of 1.5 for the following conditions:

(a) The clay extends to a great depth.

(b) Bedrock is found at the bottom of the excavation.

Q3. A section of a long canal embankment is shown in the following figure. In this figure

point O is a trial point of rotation. The water table is 3 m above the bottom of the canal, as

shown in the figure. For the given failure surface:

(a) Calculate the radius of this circular failure.

(b) Calculate the depth of tension crack.

(c) Determine the factor of safety against undrained failure of the embankment. Allow for the possibility that heavy rainfall may occur and assume the crack is full of water

during wet periods.

The soil is layered clay and its properties are given in the following table:

Clay layer Area (m2) Unit weight (kN/m

3) cu (kPa) u

Clay above water level 78 18 36 0

Clay below water level 89 20 50 0



DESIGN PROJECT

Introduction

A company is planning to carry out a construction project. This land was used to be a storage

area for a petrochemical factory. Your firm (group) has been engaged to consider certain

geotechnical aspects of this project.

This is a group project. You are to form yourselves into a group of 4 and elect 1 member

as the group leader. You should submit the name of your group members and the group leader

to the subject coordinator by Week 4.

Project Description

The project consists of the construction of:

A concrete block walled industrial building with plan dimensions of 16 m 40 m. The building is to have an on-ground concrete floor slab 120 mm thick, with a finished RL

of 14.0 m. The walls are load bearing and there are some internal columns carrying the

weight of the roof and other elements.

A steel water tank having a diameter of 12 m and an effective height of 3.8 m, with its base at RL 17.5 m.

There is an existing one-storey double brick building on the site. The RL of the slab on the ground is 17.2 m.

A Site Plan is attached, showing the location of the tank, the car park (RL 17.0m) the

proposed and existing buildings. The Structural Engineer for the project has determined the

proposed building loads and they are as follows:

Wall vertical loading: 125 kN per meter run (NOTE: the weight of foundation is not included.)

Wall moment: 50 kN.m per meter run

Each column total load: 140 kN

Note: There would be 12 internal columns in the proposed building. They are located 6 m

centre-to-centre. The distance between the centre of each column and the back of the wall is 5

m.

In addition, 3 boreholes have been sunk at the locations shown on the Site Plan and the logs

of these boreholes are included in this brief.

REQUIRED TASKS FORM YOUR GROUP

The Group is required to prepare a brief report to address the following aspects:

1. Introduction to the project including client name, location of the project, the scope of the work and a cross section of the ground layers of the site based on the information given in the borehole logs

2. The sequence of construction that should be adopted.

3. A general layout of the retaining walls around the proposed building and the pedestrian access from car park to this building

4. The type of retaining structure that should be employed between the proposed building and the water tank.

5. The type of retaining structures that should be employed between the proposed and existing building as well as the proposed building and the planned car park.

6. Preliminary design aspects of these retaining structures. This should include sufficient results to enable the Structural Engineer to design the wall section.



7. The type and size of footings are required for the load bearing elements, i.e. walls, columns and the water tank. (NOTE: Use a proper eccentricity for load application to eliminate the effect of the

moment on the wall footings).

8. An estimate of the likely order of settlements of the tank, wall and column footings. (Assume the average Poissons ratio of the soil is 0.28 and use the following formula to calculate the soils Youngs modulus: Es = 500 (N+15)

9. Recommendations defining any future soil exploration/testing that would be required in order to be able to finalise the design. Be specific; if more boreholes are needed state where they should be

placed and suggest their depths; and if any testing is required explain what kind of tests would be

required.

The report (one per group) should address the above aspects. It can be noted that your report should

also have an Executive Summary, Table of contents, Conclusions and List of References. All figures

and tables in the report should have proper numbers and titles. If figures or tables are taken from a

source, the source or the reference should be provided or acknowledged. Every member in the group

must write some sections of the report. The name of the author(s) of each section of the report must be

clearly stated at the beginning of each section.

The report should include 2 Appendices. Appendix 1 should be allocated to the Group

Assessment table including some discussion on the effectiveness of the group. Appendix 2 should

simply be a collection of the paperwork and calculations generated by the group members. Once again

the name(s) of the members of the group responsible for the work presented in the Appendix 1 must be

stated. Comments should be included on any relevant matters pertaining to the functioning of the

group, for example:

Did all members pull their weights and what measures were taken to ensure that each member did do their share?

Did the group function successfully and what could have been done to make the group more effective?

Submission Day

Submission day will be on Friday Week 13 by 5 PM.

No hard copy is required. Please submit a CD including:

Project report in MS-Word [please write your name on the header of those pages that you

produce.]

Project slides in MS-PowerPoint with a minimum of 42 slides (including 2 slides for the title

and outline of the project, plus a minimum of 10 slides for each group member) [please write

your name on the footer of those slides that you produce.]

Oral presentation is not required however you might be interviewed to ensure the report and

slides are your own work.

Marks

Marks will be awarded for the following components of the project: The project slides (5%),

the written report (5%) and the adequacy of the design work and correctness of calculations

(5%). Individual marks will be adjusted at the discretion of the subject coordinator. The total

mark for the project is 15% of the overall mark of the subject.

Group Assessment Table

Each group must submit a group assessment table (i.e. Appendix 1), similar to that given in

the next page, with the written report. In this table, individual student should be given a mark

out of 20 for each of the five categories. The purpose of this table is to divide the group mark

proportionally among group members based on their individual contributions to the project.



The final individual mark will be determined by adjusting the group mark in proportion to

each student total contribution obtained in the group assessment table.

Group Assessment Table

Student Name:

1. 2. 3. 4.

Regular attendance at group meetings (out of 20)

Researching & contribution of ideas (out of 20)

Calculation and checking (out of 20)

Contribution in writing the report (out of 20)

Contribution in preparing presentation/poster

(out of 20)

Total (out of 100)

Signatures of group members

SITE PLAN

Steel water tank, = 12m

Gap between the building and tank: 1.5m

Proposed concrete block walled building

BH3

BH2

BH1

5m

30m

27m

N

Slope of the land:

There is a negligible fall from east to west through the area.

Existing Building (Double Brick):

Area: 16m25m

Height: 5 m; Gap: 6m

5m

20m 16m

Proposed car park area on flexible pavement (open

area no roof)

Q = 20 kPa

3m

Proposed retaining structures

max 3m

16m

Q = 2.5 kPa

G = 8 kPa

Driveway Entrance Garden Garden



BOREHOLE LOG 1

Other information: Sample D1 not tested, bore log description

verified from observation of sample

M

E

T

H

O

D

S

A

M

P

L

E

T

E

S

T

S

W

A

T

E

R

D

E

P

T

H

L

O

G

U

S

C

S

DESCRIPTION OF MATERIAL

Soil type and colour, structure, plasticity

and other characteristics

M

O

I

S

T.

Con.

CON

S

I S

T

E

NCY

REMARKS

Observed and other

relevant data

A

u

g

e

r

V

bit

D1

SPT

2,6,6

0

1

2

3

4

5

6

7

8

9

Sandy loam, brown with occasional roots

and organics. SP D VL

Hole stood without

supporting after

drilling

Client: DBI Development

JOB: Factory complex

Location: Industrial park

Port Kembla

Logged by: HT

Date: Autumn 2014

Hole No: BH1

Sheet 1 of 1

Surface RL 17.0

Rig: Edson 3000

Details Vertical hole,

Flight auger

SPT

5,7,7

SPT

8,9,10

SPT

3,7,8

SPT

5,8,9

SP

SC

SM

SP Sand, light brown becoming yellow with

depth. A fine grained, uniform silica

sand. Dune sand.

Clayey sand, appearance of sandstone.

Grey/brown, medium grained sand

grains.

Sandstone, grey medium grained

sandstone.

Sand, dark brown indurated sand,

slightly cemented, coffee rock.

Sand, grey at first becoming dark grey at

depth. Fine grained, uniform, silica sand.

A dune sand.

SM

SM

D

D

M

L

L

MD

MD

F

Becoming harder to

cut below 6.8m.

V bit refusal at 7.1m.

Water slowly seeped

into hole below

6mWater level noted

30 minutes after

drilling.



BOREHOLE LOG 2



M

E

T

H

O

D

S

A

M

P

L

E

T

E

S

T

S

W

A

T

E

R

D

E

P

T

H

L

O

G

U

S

C

S




M

O

I

S

T.

Con.

CON

S

I S

T

E

NCY

REMARKS

Observed and other

relevant data

A

u

g

e

r

V

bit D2

SPT

2,5,5

0

1

2

3

4

5

6

7

8

9

Sandy loam, brown with occasional roots

and organics. SP D VL

Hole stood without

supporting after

drilling




Port Kembla

Logged by: HT

Date: Autumn 2014

Hole No: BH2

Sheet 1 of 1

Surface RL 17.1

Rig: Edson 3000


Flight auger

SPT

4,6,6

SPT

6,7,8

SPT

3,6,7

SPT

6,7,7

SP

SC

SM

SP

Sand, light brown becoming yellow with

depth. Occasional light brown mottles

below 5m contained a trace of silt. A fine

grained, uniform silica sand. Dune sand.

Clayey sand, appearance of sandstone.

Red, medium grained sand grains.

Sandstone, Red medium grained

sandstone.


slightly cemented, coffee rock.

Sand, dark grey. Fine grained, uniform,

silica sand. A dune sand. SM

SM

D

D

M

L

L

L

MD

F

V bit cut slowly into

rock until sudden

refusal at 7.7m.

Water slowly seeped

into hole below

6.1m. Water level

noted 30 minutes

after drilling. VM



BOREHOLE LOG 3



M

E

T

H

O

D

S

A

M

P

L

E

T

E

S

T

S

W

A

T

E

R

D

E

P

T

H

L

O

G

U

S

C

S




M

O

I

S

T.

Con.

CON

S

I S

T

E

NCY

REMARKS

Observed and other

relevant data

A

u

g

e

r

V

bit D3

SPT

2,5,5

0

1

2

3

4

5

6

7

8

9

Sandy loam, brown SP D VL Hole stood without

supporting after

drilling




Port Kembla

Logged by: HT

Date: Autumn 2014

Hole No: BH3

Sheet 1 of 1

Surface RL 17.2

Rig: Edson 3000


Flight auger

SPT

2,5,5

SPT

6,8,9

SPT

6,7,7

SPT

6,7,8

SP

SC

SM

SP

Sand, light brown becoming yellow with

depth. A fine grained, uniform silica

sand. Dune sand.

Clayey Sandy, grey, appearance of

sandstone.

Sandstone, Red medium grained

sandstone.


negligible cementation.

Sand, grey. Fine grained, uniform, silica

sand. A dune sand. SM

SM

D

D

M

L

L

MD

MD

F

V bit cut slowly into

rock until sudden

refusal at 7.5m.

Water slowly seeped

into hole below

6.2m. Water level

noted 30 minutes

after drilling. VM



Subject Timetable

Week / Date

Lecture Tutorial Deliverables

1

24/2/14

Revision of Soil Mechanics including soil shear strength.

Tutorial 1: basic design

2 3/3/14

Site investigation: planning, investigation methods, evaluation, reporting.

Site investigation equipment and quiz samples

3 10/3/14

Introduction to Geotechnical Engineering. Shallow foundations: load deformation behaviour, ultimate load and working load, Terzaghis theory of bearing capacity, total and effective stress analyses.

QUIZ 1 (on soil mechanics and site investigation) Tutorial 2: shallow foundations.

4 17/3/14

Shallow foundations: Hansens bearing capacity analysis, eccentric loading and moments.

Tutorial 3: shallow foundations. Major project organisation

Major Project Group

Selection and Report

5 24/3/14

Settlement of shallow footings: Distribution of stresses under loaded areas. Immediate and total final settlements, settlement based on 1D and elastic theory, rate of settlement.

Tutorial 4: stress and settlement.

6 31/3/14

Deep foundations: pile types and methods of installation, load carrying capacity of single piles and pile groups.

QUIZ 2 (on shallow foundations and settlement)

7 7/4/14

Lateral earth pressures: at rest, active and passive states, Rankine and Coulomb theories, total and effective stress analyses.

Tutorial 5: deep foundations

8 14/4/14

Tutorial Week - No class No class Assignments 1-4 due on

18/4/14 -

21/4/14 Non Teaching Week - No class No class

9 28/4/14

Retaining walls: AS 4678, gravity walls, factors of safety against sliding, overturning and bearing capacity.

QUIZ 3 (on plies and lateral earth pressures)

10 5/5/14

Retaining walls: cantilever walls, anchored walls, braced walls.

Tutorial 6: earth pressure

Major project work.

11 12/5/14

Slope stability: failure mechanisms, infinite slopes, method of slice, Swedish and Bishop methods, total and effective stress analyses, Taylors charts, practical considerations.

Tutorial 7: retaining walls. Major project work.

12 19/5/14

Practical examples on retaining walls and slope stability analysis Tutorial 8: slope stability.

QUIZ 4 (on retaining walls and slope stability)

Assignments 5-7 due on

23/5/14

13 26/5/14

Site classification, reactive soils behaviour and ground improvement methods.

Major project work. Major Project report due on

30/5/14

14 2/6/14

Revision of main topics. No tutorial class

Assignments and Project 2014a

Documents

Transcript of Assignments and Project 2014a