Bearing n Settlement 3

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Bearing Capacity & Settlement of Soil 8/19/1906

Bearing Capacity and Settlement of Soil

Bearing Capacity

DefinitionsTheAllowable Bearing Capacityis defined as the maximum pressure which

may be applied to the soil such that the two fundamental requirements are satisfied.

1) The factor of safety against shear failure of the supporting soil

must be adequate, a value between 2 or 3 normally being specified.

2) The settlement of the foundation should be tolerable and

particular, differential settlement should not cause any unacceptible damage nor

interfere with the function of the structure.

Ultimate Bearing Capacityis defined as the least pressure that will cause

complete shear failure of the soil in the vicinity of the foundation. Only aproximate

solution is available for Ultimate Bearing Capacity.

Three Type of Failure (Vesic, 1963, 1675)

for Dense or Stiff General Shear Failure

for Medium Density Local Shear Failure

for Loose or Soft Punching Shear

Requred Depth for Subsurface Exploration

It is essential that the soil conditions are known within the significant depth of any

foundation.

for square footing of width B 1.5 B

for strip footing of width B 3 B

Lowe and Zaccheo, 1975 presents guidelnes :

For Large structure wth seperate closely spced footng: All borng should extend

to no less then 9 M (30 ft) belowest part of foundaton unless rock is encountered at

shallower depth.

For Isolated rigid foundatons: Extend to depth where vertical stress decreasesto 10 % of bearng pressure. All borng should extend to no less then 9 M (30 ft)

belowest part of foundaton unless rock is encountered at shallower depth.

AASHTO 1996 states:

When substructure units will be supported on deep foundation the depth of

subsurface exploration shall extend to a minimum of 6 M (20 ft) below the anticipated

pile or shaft tip elevation. Where pile or shaft groups will be used, the subsurface

exploration shall extend at least two times the maximum pile group dimension below

the anticipated tip elevation unless the foundation will be end bearing on or in rock.

For pile bearing on rock, a minimum of 3 M (10 ft) of rock core shall be obtainedat each exploration location to ensure the exploration has not been terminated on a

boulder.

by U Win Aung Cho19-8-06

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Terzaghi's Theory of Bearing Capacity

Assumptions

1) Shear Strength between surface and footing depth D is neglected.2) Soil above depth D is considered only as a surcharge imposing a

uniform pressure qo=D on plane of footing3) General Shear failure takes place and volume of soil remains

unchanged prior to failure

4) Footing base is rough that is no Active Rankine State can not be

developed under the footing. There exist only elastic wedge under footing having an

angle of 5) Strip footing of width B and semi infinite length L (i.e. B/L=0)

qf1

2. B.

1

2tan ( ).

Kp

cos ( )2

1.. cKpc

cos ( )2

tan ( ). qoKpq

cos ( )2

.

qf1

2. B. N( ). c Nc( ). qo Nq( )

. for B/L=0

Kp Passive Pressure Coefficients derived by Circle method

Nqe

3 .

2 tan ( ).

2 cos 45 deg.

2

2.

=Nq

Nc cot ( ) Nq 1( ).

Local Shear Failure Terzaghi proposed modified parameters to be used

cl2

3c. l atan

2

3tan ( ).

for Square footing B/L=1

qf 0.4 . B. N. 1.3 c. Nc. D. Nq. (B/L=1)

for Rectangular Footing (0 < B/L < 1)Interpolate between above 2 equations or as follow

. . . B. . . . .


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. . .L

Modifications

MeyerhofMeyerhof varied wedge angle between and 45*deg+/2 to get minimum valueof N.

N Nq 1( ) tan 1.4 .( ). Nc cot ( ) Nq 1( ).

N q e tan ( ).

tan 45 deg.

2

2

.

Meyerhof provide shape and depth factors

sc dc for Nc

sq dq for Nq

sdfor N

Hansen

Hansen include shape, depth and other factors

q c N c. s c

. dc. i c

. g c. b c

. q N q. s q

. dq. i q

. g q. b q

. 0.5 e. B'. N

. s . d

. i . g

. b .

s stand for shape factor,

d for depth, i for inclination, g for ground (Base on slope) and b for Base

(tilted base) factor.

Bearing Capacity for Sand

Due to the extreme difficulty of obtaining undisturbed sand samples, the

allowable bearing capacity is normally estimated by means of correlations based

on the results of in-stu tests.

1) Plate Bearing Test

2) The Standard Penetration Test (ASTM D 1586-92 (1998))

3) The Dutch Cone Test (ASTM D 3441-94 (1998))

Standard Penetration Test (ASTM D 1586-92 (1998))

Di = 3.81 cm (1.5 in)

Do = 5.08 cm (2 in)

Free fall height 0.76 M (30 in)

Free fall weght 63.5 kg (140 lb)

Sampler is driven a total of 45 cm and numbers of below counts are recorded for

each 15 cm (6 in) intervals

Correction for SPT Values

There are many dfferent testng factors that can influence the accuracy of the SPTreadings.

Em = Hammer efficiency (for U.S. equipment 0.6 for safety hammer 0.45 for a

dou hnut hammer


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Cb = borehole diameter correction (1.0 for 65-115 mm, 1.05 for 150 mm,1.15 for

200 mm)

Cr = rod length correction (0.75 for upto 4 M of drll rod, 0.85 for 4 to 6 M, 0.95

for 6 to 10 M, 1.0 for drll rod n excess of 10 M)

N = measured SPT values

N60 = SPT N- value corrected for feld

N60 = 1.67 Em Cb Cr N

For the very fine sand and below the water table, if the measured N value greater

than 15, should be corrected as follow.

N'=15+1/2(N-15)

The Dutch Cone Test (ASTM D 3441-94 (1998))

Cone Penetration Test (CPT) gives cone resistance qc, force required to push conedivided by horizontal-projection-area of cone (1000 mm^2).

The cone is pushed 80 mm into the sand at a uniform rate of 15-20 mm/s. The cone

penetration resistance usually being determined at depth intervals of 200 mm

suqc qo

N k

su = undrained shear stress

Nk = cone factor (a constant for that soil). Nk has been found to range from 5 to75; however, most value are in the 10 to 30 range.

Relation between SPT and CPT

qc k N 60.

k = 0.1 to 1.0

0.1 to 0.2 for Silt, sandy silt

0.3-0.4 for Clean fine to medium sand

0.5 - 0.7 for Coarse sand and sand with little gravel

0.8 - 1.0 for Sandy gravels and gravel

The Buisman-DeBeer Method

This method in which the settlement under a given pressure is estimated using

qc and C a constant of compressibility of the sand

C 1.5qc

' o

.

sH

Cln

' o

' o

.

s

0

H

z1

Cln

' o

' o

. d

H = Thickness of Layer


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o= e ect ve over ur en pressure

= increment of vertical stress at the centre of the layers = settlement

Plate Bearing Test

In this test the sand is loaded through a steel plate at least 300 mm square,

readings of load and settlement being observed up to failure or at least 1.5 times of

estimated allowable bearing pressure. The load increments should be one-fifth of

estimated allowable bearing pressure. The test plate is located at foundation level in a

pit at least 1.5 M square.

Be sure that sand layer is homogeneous and no weak layer within significant

depth.

Bearing Capacity for Deep Foundation

Piles or Shaft on Sand

q ' oN q.

q 40 N.D

bB

. 400 N. kN/M^2

N = SPT value

Db = embeded length of pile

B = width of pile

Piles in Clay

q c uN c.

cu = undrained shear strength

Nc = 9 for D/B > 4

Ground Water Table

An adjustment to the ultimate bearing capacity is performed by adjusting the unit

weight of first term by using following equation (Myslivec and Kysela, 1978)

a b

h' D f

B t b

.

a =adjusted unit weight to be used in first term

b = buoyant unit weight of the soil (kN/M^3 or pcf)

t = total unit weighth' = depth of the ground water table below ground surface (M or ft)

Df = foundation depth from Ground surface

B = width of the footing

Moment and Eccentric Load

It is always desirable to design and construct shallow footing so that the vertical

load is applied at the centre of gravity of footing. There may be design situation

where the footing is subject to moment. This moment can be represented by a load P

that is offset a certain distance (eccentricity) from the center of gravity of the footing.

A usal requirement is that the load P must be located within the middle one-third of

footing.

Q B 6 e.( ).


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maxB

2

qminQ B 6 e.( ).

B2

Q = load applied to the footing (kN/M or kip/ft)

B = footing width

e = eccentricity

qmax, qmin = maximum and minimum bearing pressure

Earthquake Loading

It is common to use a larger allowable bearing capicity in the analysis. A common

recommendation is that the allowable bearing pressure can be increased by a factor of

1/3 for the earthquake analysis.


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Example Calculation Bearing Capacity

Soil Parameters

D

5

10

15

20

25

ft. tan

0.1139

0.1139

0.1584

0.1584

0.1584

c

780

780

700

700

700

psf.

113.28

112.3

108.8

101.69

100.1

pcf. SPT

12

15

14

15

16

wet

131.4

131.27

129.21

125.5

123.38

pcf.

i 0 4..i

atan tani

180

. in degree

Vsi

i

2.68 1000.N

m3

. 9.807.Vs

0.6770.671

0.65

0.608

0.598

= Vui

1 Vsi

Vu

0.3230.329

0.35

0.392

0.402

=

sati

i

Vui

9.807. 1000.N

m3

. sat

133.442

132.827

130.633

126.176

125.179

pcf=

Foundation Parameters

Foundation Type = Iso

L' 12 ft. B' 12 ft. B B'

ki

Di

Bin radian

SF 2.5

Water Tabel at Foundation Base

dw 4 ft. depth to water table under footing base

Hi

0.5 B. tan 45i

2deg..

Average

effective unit

weight of soil

in wedge zone

e 2 H. dw( )

dw

H2. wet.

sat wet

H2 H dw( )

2

.

by Hansen


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N qi

e tan i deg

..

tan 45i

2deg.

2

. s qi

1.0B'

L'sin

ideg..

N ci

N qi

1 cot i

deg.. s ci

1.0

N qi

N ci

B'

L'.

N i

N qi

1 tan 1.4 i

. deg.. s i

Max 1.0 0.4B'

L'. 0.6,

dqi

1 2 tan i

deg.. ki

. 1 sin i

deg.2. i q 1 g q 1 b q 1

dci

1 0.4 k i

. i c 1 g c 1 b c 1

g 1 b 1d 1.0 i 1

qi

weti

Di

.

qulti

ciN c

i

. s ci

. dci

. i c. g c

. b c. q

iN q

i

. s qi

. dqi

. i q. g q

. b q. 0.5 e

i

. B'. N i

. s i

. d. i

. g . b

.

qalli

qulti

SF

qult

4.218

5.444

7.71

9.367

11.154

Ton

ft2

= qall

1.687

2.177

3.084

3.747

4.461

Ton

ft2

= D

5

10

15

20

25

ft=


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Settlement of Soil

Settlement of cohesive and organic soils

Cohesive and organic soil can be susceptible to a large amount of settlement from

structure loads. The settlement of saturated clay or organic soil can have three differentcomponents:

1) Immediate (initial)

2) Consolidation

3) Secondary compression

Immediate or Initial

Surface loading causes both vertical and horizontal strains which means that two-or

three-dimensional Loading.

Immediate settlement is a result of undrained shear deformation, or in other cases

contained plastic flow.

Method Based on the Theory of ElasticityOne approach is to use the undrained modulus Eu from triaxial compression tests in

order to obtained the immediate settlement.

s i q B. Ip

. 1 2

E u

.

si = immediate settlement (M or ft)

q = applied uniform pressure (kPa or psf)

B = width of the foundation (M or ft)

Ip = dimensionless parameter derived from the theory of elasticity to account for the

thickness of the compressible layer, shape of the foundation, and flexibility of the

foundation

= poisson's ratio, normally assumed as 0.5 satuated plastic soil subjected toundrained loading

Eu = undrained modulus of the clay (kPa or pcf)

Plate Load Test

The plate load test could significantly under estimate the immediate settlement if

the test is performed near surface of sandy layer or surface crust of clay that is

overconsolidated.

When large building is built, pressure bulb is larger and could result in significant

plastic flow if there is a normally consolidated clay layer under-lying the stiff surface

layer.

Stress Path Method

Immediate settlement is measured in laboratory using model of the field loading

conditions. An undistrubed soil specimen could be set up in the tri-axial appratus and

then the specimen could be subjected to vertical and horizontal stresses that are

equivalent to the anticipated loading condition.Primary Consolidation

The increase in vertical will initially be carried by the pore water in the soil. This

increase in pore water pressure is known as excess pore water pressure ue. The excess

pore water pressure decrease with time, as water slowly flow out of the cohesive soil.

Slowly dissipation of the pore water pressure is known as primary consolidation.

On the basic of stress history, saturated cohesive soil may be underconsolidated,

normally consolidated or overconsolidated.


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OCR 'p

'vo

OCR = Over Consolidation Ratio

'p = preconsolidation pressure

'vo = existing vertical effective stress

underconsolidated if (OCR < 1) pore water pressure ue exist in the soil

normally consolidated (OCR = 1) completely consolidated under the existing

overburden pressure

overconsolidated (OCR > 1) Vertical effective stress in the past is greater then that

of existing condition

Required Test for Estimation of Primary Consolidation

The Oedometer Test (ASTM D 2435-96, 1998)

Soil sample of with diameter 2.5 inch and thickness of 1 inch is laid within the

appratus, aplying vertical pressure to the laterally confined specimen, and thensubmerging the specimen in distilled water. Vertical pressure is incrementally

increased with each pressure remaining on the specimen for a period of 24 hours. Dial

reading of the vertical deformation versus time are recorded for each vertical pressure.

Present a data on a semi-log graph which horizontal axis is effective vertical

pressure 'vc and vertical axis is vertical strain v. Vertical axis could also be in thevoid ratio e.

From this one can estimate 'p using Casagrande construction technique (1936). asdescribed bellow.

1) Locate the point of minimum radius on curve

2) Draw a line tangent to point A

3) Draw a horizontal line through point A4) Biset the angle of step 2 and 3

5) Extend the straight line portion to meet biseting line.

The point of interseting line is (point B) the maximum past pressure

(preconsolidation pressure)

Curved can be approximated as two straight lines, Recompression curved (flat) and

Virgin Consolidation Curve (steep).

Slope of Recompression curve is recompresion index Cr and Slope of Consolidation

curve is compression index Cc. Using Cr and Cc, e can be calculated.

Amount of Primary Consolidation Settlement

Cc e

log ' vc2 log ' vc1

for precompression curve

Cr e

log ' vc2 log ' vc1

for consolidation curve

for OCR < 1

s c CcHo

1 eo. log

' vo ' v v

' vo

.

for OCR = 1s c Cc

Ho

1 eo. log

' vo v

' vo

.


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for OCR > 1

case I : ' vo v 'vm

s c CrHo

1 eo. log

' vo v

' vo

.

case II : ' vo v 'vm>

s c CrHo

1 eo. log

' vm

' vo

. CcHo

1 eolog

' vo v

' vm

..

sc = settlement due to primary consolidation

Ho = initial thickness of the clay layer

eo = initial void ratio of saturated clay

'vo = initial effective vertical stress of clay

'v = for an underconsolidated soil, this represent the increse in vertical effectivestress that will occurs as the cohesive soil consolidates under its own weigh

v = increase in load, typically due to construction

'vm = maximum pass pressure

Secondary Compression

After primary consolidation (pore water pressure has dissipated), secondary

compression settlement is atarted.

s s C a Ho. . log t( ).

ss = Secondary Compression settlement

Ca = secondary compression ratio

Ho = initial thickness of the layer

*log(t) = change in log of time from the end of primary cnsolidation to theend of the design life of the structure


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Fopundation Settlement (IMMEDIATE) of Mat Foundation

Steinbrenner Influence Factors

I 1 M N,( )1

M ln

1 M2

1 M2

N2.

M 1 M2

N2

1.

. lnM M

21 1 N

2.

M M2

N2

1

.

I 2 M N,( )N

2 .atan

M

N M2

N2

1.

.

Foundation Properties

L 129.6 ft. B 129 ft. Foundation Size

L' L B'B

2

D 7 ft. Foundation Depth

D

B0.054=

L

B1.005= I F 0.85 Figure 5-7

H 3 B.

M

L'

B' N

H

B'

Ry 38461.802 103. lbf. qo

Ry

B L.Average Foundation Contact

Pressure under Foundation (From

Base Reaction under service

condition)Soil Properties

0.5 Satuated Clay Table 2-7

Es 40 10

6.Pa

.Es 5.802 10

3

psi= Medium Dense Clay Table 2-8

SPT 15 Penetration Blow Count/ft

Immediate Settlement

H qo B'.1

2

Es. I 1 M N,( )

1 2 .

1 I 2 M N,( )

.. I F.

H 0.765 in=


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References

1. SEISMIC DESIGN OF BUILDING STRUCTURESbyMichael R. Lindeburg,

PE. and Majid Baradar , PE.2001

2. STRUCTURAL CONCRETE, Theory and Design. by M. Nadim Hassoun1998

3. GEOTECHNICAL AND FOUNDATION ENGINEERINGby Robert W. Day 1999

4. FOUNDATION ANALYSIS AND DESIGN, BYJoseph E. Bowels, P.E.,

S.E., Fifth Edition. 1996

5. SOIL MECHANICSby Robert F. Craig 1977

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