geotech and foundation -x

By

Engr. Saeedullah jan Mandokhail Assistant Professor

GEOTECHNICAL AND FOUNDATION ENGINEERING

Balochistan University Of Information Technology Engineering & Management Sciences

(BUITEMS), Quetta

1

BEARING CAPACITY OF SOILS

2

BEARING CAPACITY OF SOILS

4

•Terzaghi’s Ultimate Bearing Capacity

•Meyerhof’s Method

•Brinch Hansen’s Method

•Vesic’s Method

THE BEARING CAPACITY OF SHALLOW FOUNDATION

5

A shallow foundation must:

1. be safe against an overall shear failure in the soil

that supports it.

2. cannot experience excessive displacement (in

other words, settlement).


6

Bearing capacity is the power of foundation soil to

hold the forces from the superstructure without

undergoing shear failure or excessive settlement.

Foundation soil is that portion of ground which is

subjected to additional stresses when foundation and

superstructure are constructed on the ground.

Ultimate Bearing Capacity (qf) is the maximum

pressure that a foundation soil can withstand without

undergoing shear failure or which will produce shear

failure in the soil.


7

Net ultimate Bearing Capacity (qn) :

It is the maximum extra pressure (in addition to initial overburden pressure) that a foundation soil can withstand without undergoing shear failure.

qn = qf - qo

Here, qo represents the overburden pressure at foundation level and is equal to γ.D for level ground without surcharge where ү is the unit weight of soil and D is the depth to foundation bottom from Ground Level.


8

Safe Bearing Capacity (qs): it is the maximum value of

contact pressure to which the soil can be subjected

without risk of shear failure. This is based solely on

the strength of the soil and is simply the ultimate

bearing capacity divided by a suitable factor of safety.

Allowable Bearing Pressure (qa): It is the maximum

pressure the foundation soil is subjected to

considering both shear failure and settlement.

BEARING CAPACITY FAILURE

9

General shear failure

Local shear failure

Punching shear

failure

Failures

Local shear

Intermediate case

+/- gradual failure

Punching

Loose sands,

weak clays (dr.)

F. surf. not defined

Gradual failure

General shear

Dense soils,

Rock, NC clays

Defined failure

surf.

Fast failure

10

COMMENTS ON SHEAR FAILURE

Usually only necessary to analyze general shear failure.

Local and punching shear failure can usually be anticipated by settlement analysis.

Failure in shallow foundations is generally settlement failure; bearing capacity failure must be analyzed, but in practical terms is usually secondary to settlement analysis.

11

Terzaghi’s Bearing Capacity Theory

Terzaghi developed the theory for continuous foundations

(simplest, 2D problem).

BNqNNcq qcult '5.0'

BNNNcq qzDcult '4.0''3.1

BNNNcq qzDcult '3.0''3.1

From model tests, he expanded the theory to:

12

Nc = cohesion factor

Nq = surcharge factor

Nγ = self wt factor

TERZAGHI’S BEARING CAPACITY THEORY

13

THE BEARING CAPACITY OF SOILS

14


15


16

GROUNDWATER LEVEL EFFECTS

D

19

Case I

w '


20

B

DDw

11'

Case II


21

Case III

'


22

For total stress analysis:

'

regardless of the case

(gw effects are implicit in cT and fT)


23


24

In case the water table lies at any intermediate depth less than

the depth (Df+ B), the bearing capacity equations are affected

due to the presence of the water table.

Case 1. When the water table lies above the base of the foundation.

25


26


SOLVED EXAMPLE:

A strip footing of width 3 m is founded at a depth of 2 m below the ground

surface in a (c - ɸ) soil having a cohesion c = 30 kN/m2 and angle of

shearing resistance ɸ = 35°. The water table is at a depth of 5 m below

ground level. The moist weight of soil above the water table is 17.25 kN/m3.

Determine (a) the ultimate bearing capacity of the soil, (b) the net bearing

capacity, and (c) the net allowable bearing pressure and the load/m for a

factor of safety of 3. Use the general shear failure theory of Terzaghi.

27

If the water table in Ex. 12.1 rises to the ground level, determine the net

safe bearing pressure of the footing. All the other data given in Ex. 12.1

remain the same. Assume the saturated unit weight of the soil ɣsat= 18.5

kN/m3.

29

THE GENERAL BEARING CAPACITY

EQUATION

Meyerhof (1963) presented a general bearing capacity equation which

takes into account the shape and the inclination of load. The general form

of equation suggested by Meyerhof for bearing capacity is

31

STANDARD PENETRATION TEST

The method has been standardized as ASTM D-1586 (1997) with periodic

revision since 1958. The method of carrying out this test is as follows:

1. The split spoon sampler is connected to a string of drill rods and is lowered

into the bottom of the bore hole which was drilled and cleaned in advance.

2. The sampler is driven into the soil strata to a maximum depth of 18 in by

making use of a 140 Ib weight falling freely from a height of 30 in on to an

anvil fixed on the top of drill rod. The weight is guided to fall along a guide rod.

The weight is raised and allowed to fall by means of a manila rope, one end

tied to the weight and the other end passing over a pulley on to a hand

operated winch or a motor driven cathead.

3. The number of blows required to penetrate each of the successive 6 in

depths is counted to produce a total penetration of 18 in.

4. To avoid seating errors, the blows required for the first 6 in of penetration

are not taken into account; those required to increase the penetration from 6

in to 18 in constitute the N-value.

The SPT is conducted normally at 2.5 to 5 ft intervals. The intervals may be

increased at greater depths if necessary.

33

ULTIMATE BEARING CAPACITY OF FOOTINGS

BASED ON SPT VALUES (N]

Standard Energy Ratio Res Applicable to N Value

The empirical correlations established in the USA between N and soil

properties indicate the value of N conforms to certain standard energy ratios.

Some suggest 70% (Bowles, 1996) and others 60% (Terzaghi et al., 1996).

The relation between Ncor and ɸ established by Peck et al., (1974) is given in a

graphical form in Fig. The value of Ncor to be used for getting ɸ is the corrected

value for standard energy. The angle ɸ obtained by this method can be used

for obtaining the bearing capacity factors, and hence the ultimate bearing

capacity of soil.

Cohesive Soils

Relationship Between Ncor and qu (Unconfined Compressive Strength)

Relationships have been developed between Ncor and qu (the undrained

compressive strength) for the ɸ = 0 condition. This relationship gives the value

of cu for any known value of Ncor. The relationship may be expressed as Eq.

where the value of the coefficient & may vary from a minimum of 12 to a

maximum of 25

35

SETTLEMENT ANALYSIS/CONSOLIDATION


INTRODUCTION

Structures are built on soils. They transfer loads to the subsoil

through the foundations. The effect of the loads is felt by the soil

normally up to a depth of about two to three times the width of the

foundation. The soil within this depth gets compressed due to the

imposed stresses. The compression of the soil mass leads to the

decrease in the volume of the mass which results in the settlement

of the structure.

This compression of the soil mass due to the imposed stresses may

be almost immediate or time dependent according to the

permeability characteristics of the soil.

The compressibility characteristics of a soil mass might be due to any

or a combination of the following factors:

1. Compression of the solid matter.

2. Compression of water and air within the voids.

3. Escape of water and air from the voids.

It is quite reasonable and rational to assume that the solid matter and

the pore water are relatively incompressible under the loads usually

encountered in soil masses. The change in volume of a mass under

imposed stresses must be due to the escape of water if the soil is

saturated.


CONSOLIDATION

When a saturated clay-water system is subjected to an external

pressure, the pressure applied is initially taken by the water in the

pores resulting thereby in an excess pore water pressure. If drainage

is permitted, the resulting hydraulic gradients initiate a flow of water

out of the clay mass and the mass begins to compress. A portion of

the applied stress is transferred to the soil skeleton, which in turn

causes a reduction in the excess pore pressure. This process,

involving a gradual compression occurring simultaneously with a

flow of water out of the mass and with a gradual transfer of the

applied pressure from the pore water to the mineral skeleton is

called consolidation


SPRING ANALOGY

Valve

Springs


The process of consolidation of a clay-soil-water system may be

explained with the help of a mechanical model as described by

Terzaghi and Frohlich (1936).

Consolidation may be due to one or more of the following factors:

1. External static loads from structures.

2. Self-weight of the soil such as recently placed fills.

3. Lowering of the ground water table.

4. Desiccation/Dryness


DURING CONSOLIDATION

42

remains the same (=q) during consolidation. u decreases (due to

drainage) while ’ increases transferring the load from water to the

soil.

GL

saturated clay

q kPa

A

u

’

u

’

q

CONSOLIDATION THEORY

43

44

SETTLEMENT

Immediate Settlement: The portion of the settlement of a structure

which occurs more or less simultaneously with the applied loads.

This is computed using elasticity theory (Important for Granular

soil)

Primary Consolidation: Due to gradual dissipation of pore pressure

induced by external loading and consequently expulsion of water

from the soil mass, hence volume change. At the present time the

only theory of practical value for estimating time-dependent

settlement due to volume changes, that is under primary

consolidation is the one-dimensional theory. (Important for

Inorganic clays)

Secondary Consolidation: Occurs at constant effective stress with

volume change due to rearrangement of particles. (Important for

Organic soils)

45

SETTLEMENT The total Settlement/compression of a saturated clay strata under

excess effective pressure may be considered as the sum of

1. Immediate compression,

2. Primary consolidation, and

3. Secondary compression.

STRESS HISTORY

Normally Consolidated Clay

If the present effective stress is the maximum to which

the clay has ever been subjected

CLAY 100,000 years ago

80,000 years ago

30,000 years ago

10,000 years ago

5,000 years ago

1,000 years ago

Today

STRESS HISTORY

Overconsolidated Clay

If the effective stress at some time in the past has been

greater than the present value

20,000 years ago

100,000 years ago

80,000 years ago

30,000 years ago

CLAY

ICE AGE 18,000 years ago

5,000 years ago

Today

OVERCONSOLIDATION RATIO, OCR

present

c

σ'

σ'OCR

OVERCONSOLIDATION RATIO, OCR

Normally Consolidated: OCR =1

Overconsolidated: OCR > 1

How can OCR > 1?

Erosion of overburden

Recession of glacial ice sheets

Permanent rise of water table

TERZAGHI’S THEORY OF 1.D CONSOLIDATION

Terzaghi (1925) advanced his theory of one-dimensional consolidation

based upon the following assumptions.

1. The clay layer is homogeneous.

2. The clay layer is saturated.

3. The compression of the soil layer is due to the change in volume

only, which in turn, is due to the squeezing out of water from the void

spaces.

4. Darcy’s law is valid.

5. Deformation of soil occurs only in the direction of the load

application.

6. The coefficient of consolidation C v is constant during the

consolidation.

TERZAGHI 1-D CONSOLIDATION EQUATION

51

x

z

y dx dy

dz

Qin

Qout

TERZAGHI ONE-DIMENSIONAL EQUATION

To derive the equation for time rate of settlement using an element of the soil sample of thickness dz and cross-sectional area of dA = dxdy, we will assume the following:

The soil is saturated, isotropic and homogeneous

Darcy’s law is valid

Flow only occurs vertically

The strains are very small

52


53

dxdydtvdtAvdtqQ zzvin

dxdydtdzz

vvdtqqQ z

zzzout

dzdxdydtz

vdtvAdtqdt

t

V

QQdtt

VV

zzz

inout


Since the change in volume of the soil (V) is

equal to the change in volume of pore water

expelled (Vw), which is equal to the change in

volume of the voids (Vv) therefore,

54


55

dtt

Vedt

t

eVdt

t

V

dtt

eVdt

t

V

dtt

Vdt

t

V

ss

s

v

)(

ONE-DIMENSIONAL EQUATION

56

As there is no change in the volume of solid

therefore,

dtt

eVdt

t

Vs

e

dxdydz

e

VVs

eV

Vs

111

1

As we know that


57

dxdydzdtt

e

edt

t

e

e

dxdydzdt

t

V

1

1

1

t

e

ez

v

dxdydzdtt

e

edzdxdydt

z

v

z

z

1

1

1

1


58

From Darcy’s law

w

w

w

zz

zz

zz

uhhu

z

ukv

z

hi

z

hkv

ikv


59

By Partial Differentiation with respect to depth z gives

2

2

z

uk

z

v

z

uk

zv

z

w

zz

w

zz


60

As we know that the change in total vertical pressure

is equal to the change in pore water pressure. i.e., u

=v we can write

v

vv

v

ea

t

ua

t

e

t

ue

t

e


61

t

u

e

a

z

v vz

1v

v me

a

1where

t

um

z

vv

z

Therefore,

62


2

2

z

uC

t

uv

2

2

2

2

z

u

m

k

t

u

z

uk

t

um

wv

z

w

zv

v

wv

z Cm

k

63


2

2

z

uC

t

uv

64

COEFFICIENT OF CONSOLIDATION

For a given load increment, the coefficient of consolidation Cv can

be determined from the laboratory observations of time versus dial

reading.

There are several procedures presently available to estimate the

coefficient of consolidation, some of which are described below.

Logarithm-of-time method

The logarithm-of-time method was originally proposed by

Casagrande and Fadum (1940) and can be explained by referring to

Figure

65


66


1.Plot the dial readings for specimen deformation for a given load

increment against time on semi log graph paper as shown in Figure.

2. Plot two points, P and Q, on the upper portion of the

consolidation curve, which correspond to time t1 and t2,

respectively. Note that t2=4t1.

3. The difference of dial readings between P and Q is equal to x.

Locate point R, which is at a distance x above point P.

4. Draw the horizontal line RS. The dial reading corresponding to

this line is d0, which corresponds to 0% consolidation.

5. Project the straight-line portions of the primary consolidation and

the secondary consolidation to intersect at T . The dial reading

corresponding to T is d100, i.e., 100% primary consolidation.

67


6. Determine the point V on the consolidation curve that corresponds

to a dial reading of d0 +d100/2 = d50. The time corresponding to

point V is t50, i.e., time for 50% consolidation.

68


69


SOLUTION TO TERZAGHI EQUATION

70

v

m

m

av TMM

U 2

02

exp2

1

2/)12( mMWhere

2

2

z

uC

t

uv


71

%)100log(933.0781.1T

:%10053

100

%

4T

:%530

v

av

2

v

av

av

av

U

UFor

U

UFor

DEGREE OF CONSOLIDATION

The ratio, expressed as a percentage, of the

amount of consolidation at a given time within a

soil mass, to the total amount of Consolidation

obtainable under a given stress condition.

It is the ratio of the settlement occurred at a

particular time and depth to the total expected

settlement. This parameter can be expressed as

72


73

t

v

t

tv

s

sU

s

ssU

1


74

0

0

0

1u

uU

u

uuU

v

v

0

0

0

1e

eU

e

eeU

v

v


75


76

Tv Tv U

0.00 0.00 0

0.00 0.04 5

0.01 0.09 10

0.02 0.13 15

0.03 0.18 20

0.05 0.22 25

0.07 0.27 30

0.10 0.31 35

0.13 0.35 40

0.16 0.40 45

0.20 0.44 50

0.24 0.49 55

0.28 0.53 60

0.34 0.58 65

0.40 0.63 70

0.48 0.69 75

0.57 0.75 80

0.68 0.83 85

0.85 0.92 90

1.13 1.06 95

100

U-Tv RELATION

77

0

20

40

60

80

100

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

U (

%)

Tv

U-Tv RELATION

78

0

20

40

60

80

100

0 0.25 0.5 0.75 1 1.25 1.5

U (

%)

Tv

U-Tv RELATION

79

0

20

40

60

80

100

0 0.25 0.5 0.75 1 1.25 1.5

U (

%)

Tv

U-Tv RELATION

80

0

20

40

60

80

100

0 0.25 0.5 0.75 1 1.25 1.5

U (

%)

Tv

U-Tv RELATION

81

0

20

40

60

80

100

0 0.25 0.5 0.75 1 1.25 1.5

U (

%)

Tv

U-Tv RELATION

82

0

20

40

60

80

100

0 0.25 0.5 0.75 1 1.25 1.5

U (

%)

Tv

U-Tv RELATION

83

0

20

40

60

80

100

0 0.25 0.5 0.75 1 1.25 1.5

U (

%)

Tv

a b

U-Tv RELATION

84

0

20

40

60

80

100

0 0.25 0.5 0.75 1 1.25 1.5

U (

%)

Tv

a b = 0.15 a

b/a =0.15

U-Tv RELATION

85

0

20

40

60

80

100

0 0.25 0.5 0.75 1 1.25 1.5

U (

%)

Tv

50

90

100

CONSOLIDOMETER

OBTAINING T90 FROM THE EXPERIMENTAL RESULTS

CONSOLIDATION PARAMETERS

rS

wGe 0

90

2

90

2

90 848.0

tt

TC HH dd

v

)1( 0

0

eH

He

k = cvmvw

)1(

)1`(

0

0

e

am

e

em

vv

v

v

`

v

v

ea

modulus Constraint1

vmE

EXAMPLE

For the following given information of an Oedometer test calculate

the consolidation parameters of the soil.

Moisture content, % w= 32

Specific gravity, G = 2.7

Diameter, mm D = 74.94

Height, mm H =19.22

EXAMPLE

t[min] t After stress-1: 50 kPa After stress-2: 100 kPa After stress-3: 200 kPa

0 0.00 0.0 0.0 0.0

0.25 0.50 0.5 0.177 0.213

1 1.00 0.58 0.254 0.314

2 1.41 0.689 0.316 0.383

4 2.00 0.81 0.399 0.468

6 2.45 0.887 0.454 0.51

9 3.00 0.977 0.506 0.543

16 4.00 1.095 0.553 0.569

25 5.00

36 6.00

1.095 0.553 0.569

Elasped time Vertical displacment /Dial Gauge reading (mm)

Total Displacement

EXAMPLE

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 1 2 3 4 5

Ver

tica

l dis

pla

cem

ent

Square root of time

3.4

TIME FOR 90% CONSOLIDATION T90

From the graph

90

90

3.4

11.56 minutes

t

t

0 0

0 0.32 2.7 0.864

se w G

e

0.41mm

0

0

`

19.22 0.41 18.81

H H

H mm

From the graph

Total vertical displacement after each stage

1

2

3

1.095 0 1.095 (for 50 kPa)

0.553 0 0.553 (for 100 kPa)

0.569 0 0.569 (for 200 kPa)

H mm

H mm

H mm

0

01

18.8110.09

1 0.864

s

s

HH

e

H mm

11

22

33

1.0950.108 (for 50 kPa)

10.09

0.5530.055 (for 100 kPa)

10.09

0.5690.056 (for 200 kPa)

10.09

s

s

s

He

H

He

H

He

H

0

1 0 1

2 0 2

3 0 3

0.864 0.108 0.756

0.756 0.055 0.701

0.701 0.056 0.645

f

f

f

f

e e e

e e e

e e e

e e e

Final void ratio

COEFFICIENT OF CONSOLIDATION CV

Coefficient of consolidation Cv

2 2 3 2

90 90

6 2

0.848 0.848(18.81 10 / 2)

11.56

6.49 10 / min

vv

v

T d dC

t t

C m

Coefficient of volume compressibility mv

6 2

3

0

0.10810 1.158 m /MN

(1 ) 50 10 (1 0.864)v

em

e

COEFFICIENT OF PERMEABILITY, K

6 6 3

10

3

(6.49 10 / 60) (1.158 10 ) 9.8 10

12.275 10 /

4.4 10 /

v v wk c m

k

k m s

k mm hour

COMPRESSION CURVE

0.6

0.64

0.68

0.72

0.76

0.8

10 100 1000

Void

rat

io ,e

Effective pressure, kPa

ANALYSIS OF THE LABORATORY MEASUREMENTS FOR EACH

STAGE

Loading stage 1 2 3

Pressure `z[kPa] 50 100 200

Initial void ratio, e0 0.864 0.756 0.701

Initial height, H0 [mm] 18.81 17.715 17.162

Height change, H 1.095 0.553 0.569

Void ratio change, e 0.108 0.055 0.056

Final void ratio, ef 0.756 0.701 0.645

t90 [min] 11.56

Cv [m2/in] 6.4910-6

mv [m2/MN] 1.158

K [m/s] 12.27510-10

An 8 ft clay layer beneath a building is overlain by

stratum of permeable sand and gravel and is underlain

by impermeable bedrock. The total expected total

settlement for the clay layer due to the footing load is

2.5 in. the coefficient of consolidation (cv) is 2.68 10-3

in2/min. How many years it will take for 90 % of total

expected consolidation settlement to take place.

Compute the amount of consolidation settlement that

will occur in one year? How many years will it take for

consolidation settlement of one inch to take place?

EXAMPLE

EXAMPLE

Sand and gravel

Impermeable bedrock

Clay 8.0 ft

St = 2.5 in

cv = 2.68 10-3 in2/min

tyears = ? for U = 90%

S 1 year = ? for t = 1 year

t = ? for S = 1 in

v

drv

dr

vv

C

Tt

tCT

H

H2

2

years 55.5

min 109168.2

1068.2

)96)(848.0(

6

3

2

t

t

t

15.0

)96(

)60243651(1068.22

3

2

v

v

dr

vv

T

T

tCT

H

For TV = 0.15, U = 43 %

in 075.1

)5.2(43.0

)(

s

s

sUs

s

sU

in 075.1

)5.2(43.0

)(

s

s

sUs

s

sU

EXAMPLE

EXAMPLE

%40

4.05.2

1

U

U

s

sU

For U = 40 %, TV = 0.126 years 82.0

min 1033.2

1068.2

)96(126.0

5

3

2

2

t

t

t

C

Tt

v

drv H

EXAMPLE

A foundation is to be constructed on a site

where the soil profile is as shown in the figure,

the coefficient of consolidation CV = 4.9610-6

m2/min. How long it will take for half the

expected consolidation settlement to take place

if the clay layer is underlain by (a) permeable

sand and gravel? (b) Impermeable bedrock?

EXAMPLE

Elev. 185.6 m

Elev. 192 m

Elev. 198 m

Elev. 200 m

Water table

Sand and gravel

Unit weight = 19.83.0 kN/m3

Clay

Unit weight = 17.10 kN/m3

Water table

Elev. 195.5 m

EXAMPLE

Elev. 185 m

Elev. 190 m

Elev. 198 m

Elev. 200 m

Water table

Sand and gravel

Unit weight = 20 kN/m3

Clay

Unit weight = 17 kN/m3

Water table

Elev. 195 m

EXAMPLE

CV = 4.9610-6 m2/min

Hdr = H/2 = 6.4/2 = 3.2 m (two way drainage)

t =?

U = 50 %

For U = 50 %, Tv = 0.196

years 77.0

min 10046.4

1096.4

)2.3(196.0

5

6

2

2

t

t

t

C

Tt

v

drv H

FIELD CONSOLIDATION LINE

The modified curve of the logarithm of vertical effective stress

versus void ratio (e- log`) is called the field consolidation line.

There are two methods for determining the field consolidation

line, one for normally consolidated clay, and the other for over

consolidated clay.

In the case of normally consolidated clay, determination of the

field consolidation line is fairly simple. However for over

consolidated clay, finding the field consolidation line is

somewhat difficult.


In the case of normally consolidated clay, with the

given (e- log`) curve develop from the laboratory

test, the point on the (e- log`) curve

corresponding to 0.4 eo is determined let point f. a

straight line connecting points a (point a is the

point designated by a pressure of `0 and void

ratio of eo) and f gives the field consolidation line

for normally consolidated clay.

NORMALLY CONSOLIDATED CLAY


Normally consolidated clay

e

log `



a


e

eo

`o

log `


point a is the point designated by a pressure of `0 and void ratio of eo


a


e

eo

`o

0.4 eo

log `

f


Point f on the (e- log`) curve corresponding to 0.4𝑒𝑜 is determined


a


e

eo

`o

0.4 eo

log `

f

NORMALLY CONSOLIDATED CLAY a straight line connecting points a and f gives the field consolidation

line for normally consolidated clay.


a


e

eo

`o

0.4 eo

log `

f

af is called field

consolidation line


COMPRESSION INDEX

a

e

e1

log `1

e2

log `

f

log `2

The slope of the field consolidation line is called compression index

12

12

`log`log

eeCc

COMPRESSION INDEX

0

0

0

0

1

212

12

)(log

)(loglog

loglog

c

c

Ce

eeeeC

MAXIMUM PAST PRESSURE The earliest and the most widely used method was

the one proposed by Casagrande (1936).

The method involves locating the point of maximum

curvature on the laboratory e-log p curve of an

undisturbed sample,

a tangent is drawn to the curve and a horizontal line

is also constructed.

The angle between these two lines is then bisected.

The abscissa of the point of intersection of this

bisector with the upward extension of the inclined

straight part corresponds to the preconsolidation

pressure `m

MAXIMUM PAST PRESSURE

e

` (log scale)

locating the point of maximum curvature

g

MAXIMUM PAST PRESSURE

h

i

e

` (log scale)

Horizontal line

tangent is drawn to the curve and a horizontal line is

also constructed

MAXIMUM OVERBURDEN PRESSURE

g

h

j

e

` (log scale)

i

angle between these two lines is then bisected

MAXIMUM OVERBURDEN PRESSURE

k

g

h

j

e

` (log scale)

i

Draw upward extension of the inclined straight part of

the curve

MAXIMUM PAST OVERBURDEN PRESSURE

g

h

j

e

` (log scale)

`m

k

i

The abscissa of the point of intersection of this bisector with the

upward extension of the inclined straight part corresponds to the

preconsolidation pressure `m

DEEP FOUNDATIONS PILE FOUNDATIONS

INTRODUCTION

Pile foundation used to support structure

poor quality soil

bearing capacity failure

excessive settlement

End-bearing pile

Pile driven until it comes to rest on a hard

impenetrable layer of soil or rock

Friction pile

load of the structure must come from the skin

friction or adhesion between surface of the pile

and the soil

PILE TYPES

Timber pile

Concrete pile

Cast-in-Place

Precast

Steel

H-pile

Pipe

PILE CAPACITY

Structural strength of the pile

Material, size and shape

Supporting strength of the soil

Load transmitted by friction between soil and sides

of pile

Load transmitted to the soil directly to the soil

below the pile tip

THEORETICAL PILE FOUNDATION ANALYSIS

Friction piles in Cohesionless and Cohesive

soils.

Ultimate Load determined by Geotechnical

Engineer

Allowable Load determined by building code

Factor of Safety determined by Engineer

PILE-DRIVING FORMULAS

In theory one can calculate the load-bearing capacity of a pile based on the amount of energy required to drive the pile by the hammer and resulting penetration of the pile.

Engineering news formula – Not accurate

Danish formula

Use factor of safety of 3 for determination of the design load, Q(a).

Q(d) = eh(Eh)/(S + 1/2(So)))

eh = efficiency of pile hammer

Eh = hammer energy rating (Table 10-7)

S = avg. penetration of the pile from the last

few driving blows

So = elastic compression of the pile

[(2ehEhL)/(AE)]1/2

L = length of the pile

A = cross sectional area of the pile

E = modulus of elasticity of the pile material

EXAMPLE PROBLEM

Pile Driving Formula

To determine the number of impacts required for

the last foot of penetration based on the given

design capacity.

Note it can be the last foot or more and the

ultimate capacity may be given rather than the

design capacity.

PILE LOAD TESTS

Design based on estimated loads and soil

characteristics

Load test piles

Hydraulic jack

static weight

bearing failure

excessive settlement

PILE GROUPS AND SPACING

Piles placed in groups of three or more

Pile groups tied together by a pile cap

attached to the head of the individual piles and

causes several piles to work together.

Pile spacing

minimum spacing

CONSTRUCTION OF PILE FOUNDATIONS

Piling types

Timber, concrete and steel

Pile hammers

Top of the Pile

Cap, cap-block and cushion

Hammer-Pile systems

Base of the Pile

Driving shoes

BS8004 defines deep foundation with D>B or D>3m.

Pile foundation always more expensive than shallow foundation but will overcome problems of soft surface soils by transferring load to stronger, deeper stratum, thereby reducing settlements.

Pile resistance is comprised of

end bearing

shaft friction

For many piles only one of these components is important. This is the basis of a simple classification

PILE FOUNDATIONS

ROCK

SOFT SOIL PILES

End bearing pile rests on a

relative firm soil . The load of the

structure is transmitted through

the pile into this firm soil or rock

because the base of the pile bears

the load of the structure, this type

of pile is called end bearing pile

Most of the piles used in Hong

Kong are end bearing piles.

This is because the majority of

new developments are on

reclaimed land

END BEARING PILES

SOFT SOIL PILES

FRICTION PILES If the firm soil is at a considerable

depth, it may be very expensive to

use end bearing piles. In such

situations, the piles are driven

through the penetrable soil for some

distance. The piles transmit the load

of structure to the penetrable soil by

means of skin friction between the

soil.

TYPES OF PILE

The pile installation procedure varies considerably, and

has an important influence on the subsequent response

Three categories of piles are classified by method of

installation as below:

Large displacement piles

They encompass all solid driven piles including precast concrete

piles, steel or concrete tubes closed at the lower end

Small displacement piles

They include rolled steel sections such as H-pile and open-end

tubular piles

Replacement piles

They are formed by machine boring, grabbing or hand-digging.

Combinations of vertical, horizontal and moment

loading may be applied at the soil surface from the

overlying structure

For the majority of foundations the loads applied to

the piles are primarily vertical

For piles in jetties, foundations for bridge piers, tall

chimneys, and offshore piled foundations the lateral

resistance is an important consideration

The analysis of piles subjected to lateral and moment

loading is more complex than simple vertical loading

because of the soil-structure interaction.

Pile installation will always cause change of adjacent

soil properties, sometimes good, sometimes bad.

LOADS APPLIED TO PILES V

M H

MODES OF FAILURE

The soil is always failure by punching shear.

The failure mode of pile is always in buckling

failure mode.

TOTAL AND EFFECTIVE STRESS ANALYSIS

To determine drained or undrained condition, we may need to consider the following factors:

• Drainage condition in the various soil strata

• Permeability of soils

• Rate of application of loads

• Duration after the application of load

A rough indicator will be the Time Factor (Tv=cvt/d2)

DISPLACEMENT PILE (A/D)

Advantage Disadvantages

Pile material can be inspected for

quality before driving

May break during driving

Construction operation affect by

ground water

Noise and vibration problems

Can driven in very long lengths Cannot be driven in condition of

low headroom

Construction operation not affected

by ground water

Noise may prove unacceptable.

Noise permit may be required

Soil disposal is not necessary Vibration may prove unacceptable

due to presence of sensitive

structures, utility installation or

machinery

REPLACEMENT PILE (A/D)

Advantage Disadvantages

Less noise or vibration problem Concrete cannot be inspected after

installation

Equipment can break up practically all

kinds of obstructions

Liable to squeezing or necking

Can be installed in conditions of low

headroom

Raking bored pile are difficult to

construct

No ground heave Drilling a number of pile groups may

cause ground loss and settlement of

adjacent structures

Depth and diameter can varied easily Cannot be extended above ground

level without special adaptation

ULTIMATE CAPACITY OF AXIALLY LOAD SINGLE PILE IN SOIL

Estimated by designer based on soil data and

somewhat empirical procedures. It is common

practice that the pile capacity be verified by pile load

test at an early stage such that design amendment

can be made prior to installation of the project piles.

The satisfactory performance of a pile is, in most

cases, governed by the limiting acceptable

deformation under various loading conditions.

Therefore the settlement should also be checked.

W

Q u

Q b

Q s

Basic Concept

The ultimate bearing capacity (Qu )of a pile

may be assessed using soil mechanics

principles. The capacity is assumed to be the

sum of skin friction and end-bearing

resistance, i.e

Qu =Qb+Qs-W ……………………….(1)

where

Qu total pile resistance,

Qb is the end bearing resistance and

Qs is side friction resistance

behavior

Shaft resistance fully mobilized at small pile

movement (<0.01D)

Base resistance mobilized at large movement

(0.1D)

W

Qs

QB

QT

ho

D

QDES = QB/FB + Qs /Fs –W……(2)

d

ULTIMATE LIMIT STATE DESIGN

Where FB and FS is the factor of safety

of components of end bearing strength

and shaft friction strength

Qb=Ab [ cb Nc + Po(Nq-1) + d/2N+Po] - Wp

Where Ab is the area of the base , cb is the

cohesion at the base of the pile, Po is the

overburden stress at the base of the pile and d

is the width of the pile.

QU = QB + Qs–W……(3)

DRIVEN PILE IN GRANULAR SOILS

The concepts of the calculation of end-bearing

capacity and skin friction for bored piles in granular

soils also apply to driven piles in granular soils. The

pile soil system involving effects of densification

and in horizontal stresses in the ground due to pile

driving.

BORED PILE IN CLAYS

The ultimate end bearing resistance for piles in clays is

often related to the undrained shear strength, cu, as

qB=Nccu

QB=ABNccu

where

Nc= 9 when the location of the pile base below

ground surface exceeds fours times the pile diameter

BORED PILE IN CLAYS

The ultimate shaft friction (qs) for soils in stiff over-

consolidated clays may be estimated on the semi-

empirical method as:

qs=aCu

a is the adhesion factor (range from 0.4 to 0.9)

DRIVEN PILE IN CLAYS

The design concepts are similar to those

presented for bored piles in granular soils.

However, based on the available instrumented

pile test results, a design curve is put forward

by Nowacki et al (1992)

PREDICTION OF ULTIMATE CAPACITY OF PILE

Pile Driving Formula

Pile driving formula relate the ultimate bearing capacity of driven

piles to final set (i.e. penetration per blow). In Hong Kong, the Hiley

formula has been widely used for the design of driven piles as:

Rd=(hhWhdh)/(s+c/2)

Where

Rd is driving resistance, hh is efficiency of hammer, Wh is the weight

of hammer, dh is the height of fall of hammer, s is permanent set of

pile and c is elastic movement of pile

Note: Test driving may be considered at the start of a driven piling

contract to assess the expected driving characteristics.

PREDICTION OF ULTIMATE CAPACITY OF PILE

Pile Load Test

Static pile load test is the most reliable means of

determining the load capacity of a pile. The test

procedure consists of applying static load to the pile in

increments up to a designated level of load and

recording the vertical deflection of the pile. The load is

usually transmitted by means of a hydraulic jack placed

between the top of the pile and a beam supported by

tow or more reaction piles. The vertical deflection of the

top of the pile is usually measured by mechanical

gauges attached to a beam, which span over the test

pile.

SOIL IMPROVEMENT

SOIL IMPROVEMENT

Soil improvement in its broadest sense is the

alteration of any property of a soil to improve its

engineering performance.

This may be either a temporary process to permit the

construction of a facility or may be a permanent

measure to improve the performance of the

completed facility.

The result of an application of a technique may be

increased strength, reduced compressibility, reduced

permeability, or improved ground water condition.

METHODS OF SOIL IMPROVEMENT

Removal and replacement

Precompression

Vertical drains

In-situ densification

Grouting

Stabilization using admixtures

Reinforcement

REMOVAL AND REPLACEMENT

One of oldest and simplest methods is simply

to remove and replace the soil

Soils that will have to be replaced include

contaminated soils or organic soils

Method is usually practical only above the

groundwater table

PRECOMPRESSION

Simply place a surcharge fill on top of the soil that

requires consolidation

Once sufficient consolidation has taken place, the fill

can be removed and construction takes place

Surcharge fills are typically 10-25 feet thick and

generally produces settlement of 1 to 3 feet.

Most effective in clay soil

ADVANTAGES OF PRECOMPRESSION

Requires only conventional earthmoving

equipment

Any grading contractor can perform the work

Long track record of success

DISADVANTAGES OF PRECOMPRESSION

Surcharge fill must extend horizontally at least

10 m beyond the perimeter of the planned

construction, which may not be possible at

confined sites

Transport of large quantities of soil required

Surcharge must remain in place for months or

years, thus delaying construction

VERTICAL DRAINS

Vertical drains are installed under a surcharge load to

accelerate the drainage of impervious soils and thus

speed up consolidation

These drains provide a shorter path for the water to

flow through to get away from the soil

Time to drain clay layers can be reduced from years to

a couple of months

VERTICAL DRAINS

WICK DRAINS

Geosynthetics used as

a substitute to sand

columns

Installed by being

pushed or vibrated into

the ground

Most are about 100

mm wide and 5 mm

thick

IN-SITU DENSIFICATION

Most effective in sands

Methods used in conventional earthwork are

only effective to about 2 m below the surface

In-situ methods like dynamic deep compaction

are for soils deeper than can be compacted

from the surface

DYNAMIC VS. VIBRATORY

178

VIBROFLOTATION

From Das, 1998

Vibroflotation is a technique for

in situ densification of thick

layers of loose granular soil

deposits. It was developed in

Germany in the 1930s.

179

VIBROFLOTATION-PROCEDURES

Stage1: The jet at the bottom of the Vibroflot is turned on and lowered into the ground

Stage2: The water jet creates a quick condition in the soil. It allows the vibrating unit to

sink into the ground

Stage 3: Granular material is poured from the top of the hole. The water from the lower jet

is transferred to he jet at the top of the vibrating unit. This water carries the granular

material down the hole

Stage 4: The vibrating unit is gradually raised in about 0.3-m lifts and held vibrating for

about 30 seconds at each lift. This process compacts the soil to the desired unit weight.

From Das, 1998

VIBRATORY PROBE COMPACTION

Long probe mounted onto a vibratory pile driver

compacts the soil around the probe;

penetrations spaced in a grid pattern similar to

vertical drains

VIBRATORY PROBE COMPACTION

BEWARE OF TRANSMISSION OF GROUND

VIBRATIONS

VIBROFLOTATION

Probe includes the vibrator mechanism and water jets

Probe is lowered into the ground using a crane

Vibratory eccentric force induces densification and water jets assist in insertion and extraction

Vibratory probe compaction is effective if silt content is less than 12-15% and clay is less than 3%

Probes inserted in grid pattern at a spacing of 1.5 to 3 m

VIBROFLOTATION

Ground Type Relative

Effectiveness

Sands Excellent

Silty Sands Marginal to Good

Silts Poor

Clays Not applicable

Mine Spoils Good (if granular)

Dumped Fill Depends upon nature

of fill

Garbage Not Applicable

VIBRO-REPLACEMENT STONE COLUMNS

Vibro-Replacement extends the range of soils

that can be improved by vibratory techniques to

include cohesive soils. Reinforcement of the

soil with compacted granular columns or "stone

columns" is accomplished by the top-feed

method.

Top-feed vibroflot rig

Adding stone in top-feed installation Bottom-feed vibroflot rig

VIBRO-REPLACEMENT STONE COLUMNS

187

DYNAMIC COMPACTION

Dynamic compaction was first used in

Germany in the mid-1930’s.

The depth of influence D, in meters, of soil

undergoing compaction is conservatively

given by

D ½ (Wh)1/2

W = mass of falling weight in metric tons.

h = drop height in meters

From Holtz and Kovacs, 1981

Uses a special crane to lift 5-30 tons to heights of 40 to 100 feet then drop these weights onto the ground

Cost effective method of densifying loose sands and silty soils up to 15 to 30 feet deep

DYNAMIC COMPACTION

GROUTING

Defined as the injection of a special liquid or

slurry material called grout into the ground for

the purpose of improving the soil or rock

Types of grouts

Cementitious grouts

Chemical grouts

GROUTING METHODS

Intrusion grouting

Consists of filling joints or fractures with grout

Primary benefit is reduction in hydraulic conductivity

Used to prepare foundation and abutments for dams

Usually done using cementitious grouts

Permeation grouting

Injection of thin grouts into the soil

Once the soil cures, becomes a solid mass

Done using chemical grouts

Used for creating groundwater barriers or preparign ground before tunneling

GROUTING METHODS

Compaction grouting

When low-slump

compaction grout is

injected into granular soils,

grout bulbs are formed that

displace and densify the

surrounding loose soils.

Used to repair structures

that have excessive

settlement

GROUTING METHODS

Jet grouting

Developed in Japan

Uses a special pipe with horizontal jets that inject grout into the ground at high pressures

Jet grouting is an erosion/replacement system that creates an engineered, in situ soil/cement product known as Soilcretesm. Effective across the widest range of soil types, and capable of being performed around subsurface obstructions and in confined spaces, jet grouting is a versatile and valuable tool for soft soil stabilization, underpinning, excavation support and groundwater control.

STABILIZATION USING ADMIXTURES

Most common admixture is Portland Cement

When mixed with soil, forms soil-cement which is comparable to a weak concrete

Other admixtures include lime and asphalt

Objective is to provide artificial cementation, thus increasing strength and reducing both compressibility and hydraulic conductivity

Used to reduce expansion potential of clays

Used in surface mixing applications

REINFORCEMENT

Soil is stronger in compression than in

tension

To improve strength in tension,

geosynthetics placed in soil for soil

reinforcement

REINFORCED EARTHWALL CONSTRUCTION

SOIL NAILING

The fundamental concept

of soil nailing consists of

reinforcing the ground by

passive inclusions, closely

spaced, to create in-situ a

coherent gravity structure

and thereby to increase

the overall shear strength

of the in-situ soil and

restrain its displacements.

SLOPE STABILITY ANALYSIS

197


198


199


The field of slope stability encompasses the

analysis of static and dynamic stability of

slopes of earth and rock-fill dams.

200


201

TYPES OF LANDSLIDE

Rock failure

failure plane pre-

determined

Soil failure

failure plane along line

of max stress

TYPES OF LANDSLIDE

Rock failure

failure along pre-determined planes of weakness

Soil failure

failure along lines of max. stress

frictional, cohesive = rotational

frictional, incohesive = planar

MASS MOVEMENTS CLASSIFICATION

FALLS, FLOWS, SLIDES AND SUBSIDES.

Falls and subsides involve vertical drops. Slides and flows involve downward and outward motion.

Sliding involves a coherent mass.

Flowing involves the moving mass behaving like a viscous fluid.

MASS MOVEMENTS FALL

MASS MOVEMENTS SLIDES

ROTATIONAL

Downward and outward

movement on a curved

surface.

Note the rotation of head

and the up movement of

the toe.

MASS MOVEMENTS TRANSLATIONAL SLIDES

THREE TYPES

1. Move as coherent blocks.

2. May deform and break-up as a debris slide.

3. Involve lateral spreading where the underlying

material fails and flows,

MASS MOVEMENTS FLOWS

Movements that behave like fluids with internal reorganization

Loess flows - the flow of loose silt,

Earth flows - wet flows moving slowly on slick surface,

Debris flows - massive rock falls that convert into highly

fluidized rapidly moving Debris flows.

MASS MOVEMENTS FLOWS

EARTH FLOW: PORTUGUESE BEND

View of the toe of the bulged up earth flow in 1959. Note the remains of the houses and the roads and the damaged pier.

TYPES OF SLOPE FAILURE

The common modes of slope failure in soils are

by:

Translational failure

Rotation failure

Flow failure and

Block movement failure

210

SLOPE FAILURE

211 TRANSLATIONAL SLOPE FAILURE

SLOPE FAILURE

212 ROTATIONAL SLOPE FAILURE

SLOPE FAILURE

213

FLOW SLOPE FAILURE

SLOPE FAILURE

214

BLOCK MOVEMENT SLOPE FAILURE

SLOPE FAILURE

EXTERNAL PROCESSES CAUSING FAILURE

Processes include: 1) steepen slope, 2) remove support from bottom of slope, and 3) add mass high up on slope.

ROTATIONAL LANDSLIP ANALYSIS

For undrained frictionless failure

total stress analysis

For cohesive and frictional failure

method of slices

Bishop’s conventional method (can take into

account pore water pressure)

METHODS OF SLOPE STABILITY ANALYSIS

Limit equilibrium method

Total stress analysis

Effective tress analysis

217

LIMIT EQUILIBRIUM METHOD

It is not a rigorous theoretical method but is used

because it gives simple and reasonable estimates of

collapse. The method has advantages over Rankin’s

method.

It can cope/handle with any geometry, It can cope with

applied loads and Friction between soil and retaining

walls (and other structural elements) can be accounted.

For any point on the failure plane we have:

218

f tannc

TOTAL STRESS ANALYSIS

If analysis is of undrained stability then the failure

criterion must be expressed in terms of total stress using

undrained parameters cu and fu.

A total stress analysis is only valid if the soil is

saturated and does not drain.

In practice this generally means total stress analysis is

limited to assessment of the short term stability of

clayey soils.

Must use total stresses and undrained parameters cu

and fu

219

unuc f tan

EFFECTIVE TRESS ANALYSIS

An effective stress analysis can be performed

whenever the pore pressures are known.

In practice this usually means that effective

stress analysis can only be used to assess the

long term stability. When performing effective

stress stability calculations the critical state

parameters c = 0, f = fult should be used.

220

``tan` f c

LIMIT EQUILIBRIUM METHODS OF SLOPE STABILITY

All limit equilibrium methods of slope stability

analysis have four characteristics in common

(Duncan and Wright, 1980):

1) All use the following definition of the factor of

safety (F):

221

mequilibriufor required stressShear

soil ofstrength Shear

F

sF

LIMIT EQUILIBRIUM METHODS OF SLOPE STABILITY

2) Placing a factor of safety is appropriate

3) All assume that the strength parameters are

independent of stress-strain behavior.

4) All use some or all of the equations of

equilibrium to calculate the average values of

and n on each slice, where n is the normal

stress on the base of the slice.

222

UNDRAINED INFINITE SLOPES

Consider an infinite slope in a cohesionless soil

without seepage. The thickness is supposed to

be unity. The soil is often assumed to be

homogeneous; however, in real situations. The

soil may be highly stratified with widely varying

shear strengths. If we isolate an element and

examine the forces for stability that is:

223

224

z

z

W

FD

N

FR

b

l

cos

sin

WN

WFD

From the geometry of figure

And the resisting force

against the failure FR can be

expressed as:

f

f

tancos

tan

WF

NF

R

R

cos

)1(

lzW

zbVW


Applying limit equilibrium conditions

225

f

f

f

f

tantan

cos/sintan

sintancos WW

FF DR

It shows that for stability conditions slope angle

should be less or equal to angle of internal friction-f.


Factor of safety (in terms of resisting to driving

force)

226

f

f

tan

tan

sin

tancos

F

W

WF

F

FF

D

R


227

Factor of safety (in terms of undrained shear

strength )

2sin

2

)sincos2(

2

sincos

sin

z

SF

z

SF

z

SF

W

SF

F

FF

u

u

u

u

D

R


Critical depth against slope failure

It is the depth at which the slip surface may be

expected to develop. If the FS is taken as unity

the depth z is supposed to be the critical depth

zc. It can be expressed as:

228

2sin

2

2sin

2

uc

u

Sz

z

SF

EXAMPLE

Calculate the factor of safety relating to the

undrained stability of a long slope of 1 V:1.5 H if

at a depth of 1.8 m a weak layer of cohesive soil

occurs for which Su = 24 kPa and for the

overburden = 18.5 kPa.

229

u2SF

zsin 2

2 24F

18.5 1.8sin(2 33.69)

F 1.56

EXAMPLE

The soil in a long slope has undrained shear

strength of 50 kPa and a unit weight of 18 kPa.

Using the infinite slope method, estimate the

depth at which a shear may develop when the

slope angle is 220.

230

uc

c

c

2Sz

sin 2

2 50z

18sin(2 22)

z 8.0 m

ROTATIONAL SLIP

total stress analysis or

fu = 0

strength parameters

are those of undrained

soil

We

CrF

2

where

F = restraining moment

disturbing moment

C = cohesive strength (Pa)

r = slip circle radius (m)

= slip sector in radians

W = weight of sliding sector (N)

e = eccentricity of sliding sector (m)

LOCATION OF SLIP CIRCLE CENTRE

No simple way – trial and error

THE METHOD OF SLICES

When the soil forming the slope has to be analyzed

under a condition where full or partial drainage

takes place the analysis must take into account both

cohesive and frictional soil properties based on

effective stresses. Since the effective stress acting

across each elemental length of the assumed

circular arc failure surface must be computed in this

case, the method of slices is one of the convenient

methods for this case. The method of analysis is as

follows:

233


234


235


236


237

O

A

B R


238

O

A

B R


239


240


241

Xn+1

l

W N

FR

FU

Xn

En

En+1

FD

THE METHOD OF SLICES 1) The soil mass above the assumed

slip circle is divided into a number

of vertical slices of equal width.

2) The number of slices may be

limited to a maximum of eight to

ten to facilitate computation.

3) In this method it is assumed that

the interslice forces are equal and

opposite and cancel each other,

i.e., Xn = Xn+1, En = En+1

4) The forces used in the analysis

acting on the slices are shown in

the figure

242

Xn+1

l

W N

FR

FU

Xn

En

En+1

FD

O

A

B R


243

Xn+1

l

W N

FR

FU

Xn

En

En+1

FD

The forces are:

W = the weight of the slice.

N = the normal component of the weight

FD = Driving force

FR = Resisting force

FU = Pore water force

Xn = Xn+1 = Interslice forces

Pore pressure ratio ru

h

uur

v

u


244

Xn+1

l

W N

FR

FU

Xn

En

En+1

FD

It is now only necessary to resolve the

forces acting on the base of slices

``tan` fNcFR

uWN

FWN U

cos`

cos`

sinWFD

`tan)cos(` f ulWcFR


245

Xn+1

l

W N

FR

FU

Xn

En

En+1

FD

The factor of safety is then given as:

f

sin

`tancos`

W

uWcFS

F

FFS

D

R


246

This can also be expressed as:

Xn+1

l

W N

FR

FU

Xn

En

En+1

FD

b

pn

n

n

pn

n

nn

pn

n

n

pn

n

nn

pn

n

D

pn

n

R

W

ulWc

FS

W

ulWc

FS

F

F

FS

1

1

1

1

1

1

sin

`}tan)cos(`{

sin

`tancos`

f

f

OTHER METHODS OF ANALYSIS

Taylor’s stability analysis

used for frictional and cohesive soils

uses a dimensionless number to iterate towards a

solution

Bishop’s method

effect of forces on each side of slice considered

iterative method

SLOPE STABILIZATION METHODS

Slopes Flattened or Benched

Berm Provided at Toe

Protection Against Erosion Provided at Toe

Lowering of GWT to Reduce the Pore Pressures

Drainage of Slopes

Use of Driven or Cast-in-Place Piles

Retaining Wall OR Sheet piling OR Cylinder

Piles Provided to Increase Resistance to Sliding

SLOPES FLATTENED OR BENCHED

BERM PROVIDED AT TOE

Weight Increases the Resistance to Sliding

PROTECTION AGAINST EROSION PROVIDED AT TOE

LOWERING OF GWT TO REDUCE THE PORE PRESSURES

DRAINAGE OF SLOPES

Drains are added to stabilize slopes

USE OF DRIVEN OR CAST-IN-PLACE PILES

RETAINING WALL OR SHEET PILING OR CYLINDER PILES

PROVIDED TO INCREASE RESISTANCE TO SLIDING

PLAN FOR BUILDING DESIGN TO AID SLOPE STABILITY

EARTH AND ROCK FILL

DAMS

DAM

Dam is a solid barrier constructed at a suitable

location across a river valley to store flowing

water.

Storage of water is utilized for following

objectives:

Hydropower

Irrigation

Water for domestic consumption

Drought and flood control

Other additional utilization is to develop fisheries

COMPONENTS OF DAM

Body of Dam

Foundation

Top road

Gates and lifting devices

Spill way or Sluice

Canal

Reservoir

Main river course

Stilling Basin

Drainage gallery

COMPONENTS OF DAM

Reservoir

Water

Foundation Soil

Dam Body

Foundation

Upstream Down Stream

Drainage Gallery

Spill Way

Gate

Sluice gate

Heel: contact with the ground on the upstream side

Toe: contact on the downstream side

Abutment: Sides of the valley on which the structure of the dam rest

Galleries: small rooms like structure left within the dam for checking operations.

Diversion tunnel: Tunnels are constructed for diverting water before the construction of dam. This helps in keeping the river bed dry.

Spillways: It is the arrangement near the top to release the excess water of the reservoir to downstream side

Sluice way: An opening in the dam near the ground level, which is used to clear the silt accumulation in the reservoir side.

COMPONENTS OF DAM

Abutment

Abutment

Main River Course

Right bank Canal

Reservoir

Left Bank Canal

Upstream

Downstream

Plan of Dam

Function Example

Power

generation

Hydroelectric power is a major source of electricity in the

world. many countries have rivers with adequate water flow, that

can be dammed for power generation purposes.

Stabilize

water flow /

irrigation

Dams are often used to control and stabilize water flow, for

agricultural purposes and irrigation. They can help to stabilize or

restore the water levels of inland lakes and seas. They store water

for drinking and other direct human needs,

Flood

prevention Dams are created for flood control.

Land

reclamation

Dams (often called dykes or levees) are used to prevent ingress of

water to an area that would otherwise be submerged, allowing its

reclamation for human use.

Water

diversion Dams are used for the purpose of diversion.

FUNCTIONS OF DAMS

http://en.wikipedia.org/wiki/Hydroelectric_power

http://en.wikipedia.org/wiki/Agriculture

http://en.wikipedia.org/wiki/Irrigation

http://en.wikipedia.org/wiki/Dike_(construction)

http://en.wikipedia.org/wiki/Levee

http://en.wikipedia.org/wiki/Land_reclamation

CLASSIFICATION OF DAMS

Based on Size

Based on function

Based on material used

CLASSIFICATION BASED ON SIZE

Small Dam (<10 m high)

Medium size Dam (10 – 25 m high)

Large Dam (>25 m high)

Major Dam (>150 m high)

CLASSIFICATION BASED ON PURPOSE

Hydro-electric dam

Irrigation dam

Water supply dam for city for the purposes of drinking water, recreation, navigation thro canals, industrial use.

Flood Control

Habitat dam for fishes & wild life

Effluent containing dams from industry, mine, factory etc.

Multi-purpose dam

CLASSIFICATION BASED ON MATERIAL OF CONSTRUCTION

Masonry Dam

Concrete Dam

Timber Dam

Steel Dam

Earth Dam

Rockfill Dam

Composite Dam

Combined Earth & Rockfill Dam

Earth Dam

EARTH DAMS They are trapezoidal in

shape

Earth dams are constructed where the foundation or the underlying material or rocks are weak to support the masonry dam or where the suitable competent rocks are at greater depth.

Earthen dams are relatively smaller in height and broad at the base

They are mainly built with clay, sand and gravel, hence they are also known as Earth fill dam or Rock fill dam

Earth-Fill Embankment Dam

A earth-fill dam in Australia.

Earth-Fill Embankment Dam

Homogeneous Embankment Dam

Diaphragm Earth Dam

Embankment Dam

Rock fill Dam with RC facing

MATERIALS FOR CONSTRUCTION

Earthfill dam – Locally materials

Rockfill dam – Rocks of all sizes are used for

stability and impervious membrane for water

seal.

METHODS OF CONSTRUCTIONS

Rockfill Dam

Rock placed in layers – Materials are dumped

on the embankment surface and pushed over

the advancing construction face with a

buldozer

Dumped in high sluiced lift – The material is dumped down the sloping face of the construction lift and sluiced with high pressure water jets from monitors. The fines and smaller rocks are deposited at the top of the lift and the larger rocks slide and rolled down the face of the slope to the lower part of the lift.

Earthfill Dam

Excavate the materials

Hauling to the dam,


Mixe to predetermine water content and

unformity of properties

Sread it in layers and

Compact to desire density


ADVANTAGES OF CONSTRUCTION IN LAYERS

Rock with a higher percentage of fines can be placed, there is less danger segregation of fines accumulations

Embankment obtained is more denser, uniform and less compressible

It can be built with any slide slope inclination but rockfill dumped in high lift is placed on the angle of repose of the materials

etc

STABILITY

The stability of an embankment lies in its ability

to resist shearing stresses created by external

applied loads such as reservoiur water

pressure and internal forces caused by the soil

mass and embankment slope

STABILITY OF DOWNSTREAM SLOPE DURING

STEADY SEEPAGE

Examine the most critical condition i.e when the reservouir is full and the seepage is taking place at full rate

Draw the flow net and determine the points of intersections of equipotentiallineswith failure arc

Get the critical arc

Calculate the shear strength developed on the slices and find the net shear strength

About 1,600 cubic meter per second of water is

diverted from the Indus River near the town of

Ghazi about 7 km downstream of Tarbela

Dam (3,478 MW).

It then runs through 52 km long , 100 metre wide

and 9 meter deep open concrete-lined channel

down to the village of Barotha where the power

complex is located.

After passing through the powerhouse, the water

is returned to the Indus.

The project took about 10 years and $2.2 billion

to complete, 1,450MW powerhouse at Barotha.

http://en.wikipedia.org/wiki/Tarbela_Dam



FOUNDATION DYNAMICS

Initially intended for the calculation of the vibrations of the

massive foundations of heavy machines, the analyses of

dynamic soil-structure interaction have also been long used for

seismic calculations.

in the first case the machine (or the rail or road traffic) is in

general the source of the vibrations

in the second case the soil directly provides the loads.

In both cases however, the objectives are identical, i.e. to

evaluate the movements of the foundation under the action of

external loads, and consequently anticipate the displacements

of the machine or of the structure keeping in mind both the

characteristics of the foundation and the properties of the soil.

FOUNDATION DYNAMICS

SIMPLEST FORM OF VIBRATING SYSTEM

D

d = D sinnt

m

k

T

Time

Displacement

Frequency 1

T

Period, Tn in [sec]

Frequency, fn= in [Hz = 1/sec] 1

Tn

Displacement

k

m n= 2 fn =

MASS AND SPRING

time

m1

m

Increasing mass

reduces frequency

1

nmm

k2

nf

MASS, SPRING AND DAMPER

Increasing damping

reduces the amplitude

time

m

k c1 + c2

)()()()( tftKxtxCtxM

M = mass (force/acc.)

C = damping (force/vel.)

K = stiffness (force/disp.)

)t(x)t(x)t(x

Acceleration Vector

Velocity Vector

Displacement Vector

)t(f Applied force Vector

BASIC SDOF MODEL f(t)

x(t)

k c

m

INTRODUCTION TO

LIQUEFACTION

WHAT IS LIQUEFACTION?

Liquefaction-when the strength and

stiffness of a soil is reduced due to

earthquake shaking

Liquefaction occurs in saturated soils

NIIGATA 1964 AND KOBE, JAPAN 1995

HISTORY

Serious attention because of Japan, Alaska and Nigata

earthquake in 1964.

CYCLIC MOBILITY

OVERTURNING

SAND BOILING

1. WHY IS LIQUEFACTION DANGEROUS?

2. WHAT DO YOU NEED FOR LIQUEFACTION TO

OCCUR?

A. DRY SOIL AND AN EARTHQUAKE

B. SATURATED SOIL AND AN EARTHQUAKE

C. SATURATED SOIL

1. WHY IS LIQUEFACTION DANGEROUS?

LIQUEFACTION CAN CAUSE BUILDINGS AND

INFRASTRUCTURE TO COLLAPSE.

2. WHAT DO YOU NEED FOR LIQUEFACTION TO

OCCUR?

A. DRY SOIL AND AN EARTHQUAKE

B. SATURATED SOIL AND AN EARTHQUAKE

C. SATURATED SOIL

geotech and foundation -x

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