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SoFA version 1.0

Konstantinos Nikolaou Dimitris Pitilakis

Ivan Kraus

ShallOw Foundation Analysis Software

Aristotle University of ThessalonikiThessaloniki 2012

Solved Examples

SoFA version.1.1

Solved Examples Konstantinos Nikolaou

Dimitris Pitilakis

Ivan Kraus

ShallOw Foundation Analysis Software

Aristotle University of Thessaloniki

Thessaloniki 2013

http://www.sofasoftware.weebly.com

SoFA Solved Examples Shallow Foundation Analysis Software

2

Contents

Contents .................................................................................................................................................... 2

Acknowledgements ................................................................................................................................... 3

Introduction ............................................................................................................................................... 3

Example # 1 Rectangular foundation - Cohesive soil ............................................................................ 4

Example # 2 Rectangular Foundation Cohesionless soil ....................................................................... 8

Example # 3 Strip Foundation Cohesionless soil ................................................................................. 13

Example # 4 Earthquake Bearing Capacity ......................................................................................... 18

Example # 5 Settlement Calculation .................................................................................................... 24

Further Reading ...................................................................................................................................... 28

Appendix - List of symbols ..................................................................................................................... 29

SoFA Solved Examples Shallow Foundation Analysis Software

3

Acknowledgements We gratefully acknowledge the contribution of Ivan Kraus (University of Osijek) to this manual.

Introduction This manual contains solved examples that were used to validate SoFA v.1.1.

For an advanced description of the algorithms and formulas used, consult the analytical users manual.

If you discover what you think is a bug, report it here. Please try to include all SoFA reports.

!

All loads considered act at the base of the footing and NOT at the theoretical

point of column fixity (for more information check out the analytical users'

manual).

SoFA does NOT calculate the footing self weight .

http://sofasoftware.weebly.com/documentation.htmlhttp://sofasoftware.weebly.com/bug-report.html

SoFA Solved Examples Shallow Foundation Analysis Software

4

Example # 1 Rectangular foundation - Cohesive soil Calculate the ultimate static bearing capacity of the shallow foundation depicted in fig. 1.

Figure 1

x =y

=

154.5

1545= 0.1 m & y =

x

=1931.25

1545= 1.25 m

x = 2 x = 2 2 0.1 = 1.8 m

y = y 2 y = 4 2 1.25 = 1.5 m

= min Bx , By

= 1.5 m & = Lx , Ly

= 1.8 m

<

= + + = 19 1 + 18 2 1 + 0 = 37 kPa

For cohesive soils under undrained loading conditions according to Eurocode 7:

= . +

c = 1 + 0.2

= 1 + 0.2

1.5

1.8= 1.17

= x2 + y

2 = 202 + 1002 = 102 kN

c =1

2+

1

2 1

u=

1

2+

1

2 1

102

1.5 1.8 100= 0.89

= 5.14 100 1.17 0.89 1 + 37 = 572.2 kPa

= = 572.2 1.5 1.8 = 1545 kN

SoFA Solved Examples Shallow Foundation Analysis Software

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Calculation performed using SoFA:

Click the Bearing Capacity button to access window showing the Safety Factory for Static Load Case:

SoFA Solved Examples Shallow Foundation Analysis Software

6

Shallow Foundation Bearing Capacity

-------------------------------------------------------------

Kostis Nikolaou ([email protected])

Dimitris Pitilakis

Aristotle University of Thessaloniki - 2012

-------------------------------------------------------------

Geometry of the problem

* Dimentions(dx/dy) = 2.000 x 4.000 [m]

* Depth of foundation (df) = 2.000 [m]

* Depth of water level(dw) = 1.000 [m]

* Foundation base inclination(omega) = 0.000 [rad.]

* Soil inclination(beta) = 0.000 [rad.]

Design Loads - Static Load Case

* Vd = 1545.000 [kN]

* Hdx = 20.000 [kN]

* Hdy = 100.000 [kN]

* Mdx = 1931.250 [kNm]

* Mdy = 154.500 [kNm]

Soil Properties

* Type = C [C: cohessive CL: cohesionless]

* Loading= UN [D: drained UN: undrained]

* phik = 0.0 [deg.]

* ck = 0.0 [kPa] - drained shear strength

* cuk = 100.0 [kPa] - undrained shear strength

* soil Weight = 19.00 [kN/m^3]

Eccentricities (Static Load Case): ex = 0.10 ey = 1.25 [m]

Effective Dimentions: 1.500 x 1.800 [m]

Effective Area: 2.700 [m^2]

-------------------------------------------------------------

Bearing Capacity Check -- Undrained Conditions -- Static Load Case

-------------------------------------------------------------

* Eurocode 7 (2004)

sc=1.167 ic=0.894 bc=1.000

- qu_un = 573.359 [kPa]

- Vu = qu*B*L = 1548.069[kN]

- Vu/1.40 = qu*B*L/1.40 = 1105.764[kN] < 1545.000 [kN] - NOT ok -

- FS = qu/N*Aeff = 1.002

* EAK (2000)

sc=1.167 ic=0.971

- qu_un = 618.989 [kPa]

- Vu = qu*B*L = 1671.272[kN]

- Vu/1.40= qu*B*L/1.40 = 1193.765[kN] < 1545.000 [kN] - NOT ok -

- FS = qu/N*Aeff = 1.082

SoFA Solved Examples Shallow Foundation Analysis Software

7

* DIN4017 (2006)

sc=1.167 ic=0.894 bc=1.000 gc=1.000

- qu_un = 573.359 [kPa]

- Vu = qu*B*L = 1548.069[kN]

- Vu/1.40= qu*B*L/1.40 = 1105.764[kN] < 1545.000 [kN] - NOT ok -

- FS = qu/N*Aeff = 1.002

* Meyerhof (1953,1963)

sc=1.167 ic=0.918 dc=1.267

sq=1.000 iq=0.918 dq=1.000

- qu_un = 631.535 [kPa]

- Vu = qu*B*L = 1705.145[kN]

- Vu/1.40= qu*B*L/1.40 = 1217.961[kN] < 1545.000 [kN] - NOT ok -

- FS = qu/N*Aeff = 1.104

* Hansen (1970)

sc=0.003 ic=0.019 bc=0.000 gc=0.000 dc=0.444

- qu_un = 734.360 [kPa]

- Vu = qu*B*L = 1982.771[kN]

- Vu/1.40= qu*B*L/1.40 = 1416.265[kN] < 1545.000 [kN] - NOT ok -

- FS = qu/N*Aeff = 1.283

SoFA Solved Examples Shallow Foundation Analysis Software

8

Example # 2 Rectangular Foundation Cohesionless soil Calculate the ultimate static bearing capacity of the shallow foundation depicted in fig. 2.

x =y

=

900.8

4504= 0.2 m & y =

x

=900.8

4504= 0.2 m

x = x 2 x = 2 2 0.2 = 1.6 m

y = y 2 y = 2 2 0.2 = 1.6 m

= min Bx , By

= 1.6m & = Lx , Ly

= 1.6 m

< < + =

= + .

= f + = 18 1 + 19 1 + 0 = 37 kPa

= w f + sat w f + w

=19 2.5 2 + 20 10 (2 + 1.6 2.5)

1.6= 12.81 kN/m3

For cohesionless soils under drained loading conditions, according to Eurocode 7:

u = c c c c +

q q q q +1

2

= tan2

4+

2 = 2

4+

35

2 35 = 33.3

= 2 q 1 = 2 33.3 1 35 = 45.2

SoFA Solved Examples Shallow Foundation Analysis Software

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= 1 +

= 1 +

1.6

1.6 35 = 1.57

= 1 0.3

= 1 0.3

1.6

1.6= 0.7

= x2 + y

2 = 450.42 + 450.42 = 636.96

= cos2 + sin

2 = 1.5

=2+/

1+/= 1.5 & =

2+/

1+/= 1.5

q = 1

+

= 1 636.96

4504 + 0

1.5

= 0.795

= 1

+

+1

= 1 636.96

4504 + 0

2.5

= 0.683

bq = b = 1

2= 1.0

u = 0 + 1 18 + 1 19 33.3 1.57 0.795 +1

2 1.6 12.81 45.2 0.7 0683 = 1759.3 kPa

u = u = 1759.3 1.6 1.6 = 4504 kN

Calculation performed using SoFA:

SoFA Solved Examples Shallow Foundation Analysis Software

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Click the Bearing Capacity button to access the windows showing the Safety Factory for Static Load Case

and the Ultimate Bearing Capacity:

SoFA Solved Examples Shallow Foundation Analysis Software

11

Shallow Foundation Bearing Capacity

-------------------------------------------------------------

Kostis Nikolaou ([email protected])

Dimitris Pitilakis

Aristotle University of Thessaloniki - 2012

-------------------------------------------------------------

Geometry of the problem

* Dimentions(dx/dy) = 2.000 x 2.000 [m]

* Depth of foundation (df) = 2.000 [m]

* Depth of water level(dw) = 2.500 [m]

* Foundation base inclination(omega) = 0.000 [rad.]

* Soil inclination(beta) = 0.000 [rad.]

Design Loads - St

TRANSCRIPT

Shallow Foundations

Shallow Foundations Bearing Capacity

The problems of soil mechanics can be divided into two principal groups -stability problems and elasticity problems

- Karl Terzaghi, 1943

Karl Terzaghi (1883-1963)

Father of modern soil mechanics

Born in Prague, Czechoslovakia

Wrote Erdbaumechanick in 1925

Taught at MIT (1925-1929)

Taught at Harvard (1938 and after)

Karl Terzaghi at Harvard, 1940

Foundation: The lowest part of a structure is generally referred to as

foundation. Its function is to transfer load of the superstructure to the soil

on which it is resting.

Foundation Soil or Bed: The soil or bed to which loads are transmitted

from the base of the structure.

Footing: The portion of the foundation of the structure, which transmits

loads directly to the foundation soil.

Bearing Capacity: The load carrying capacity of foundation soil or rock

which enables it to bear and transmit loads from a structure.

Definitions

Ultimate Bearing Capacity : Maximum pressure which a foundation canwithstand without the occurrence of shear failure of the foundation.

Gross Bearing Capacity: The bearing capacity inclusive of the pressureexerted by the weight of the soil standing on the foundation, or thesurcharge pressure as it is sometimes called.

Net Bearing Capacity: Gross bearing capacity minus the originaloverburden pressure or surcharge pressure at the foundation level.

Safe Bearing Capacity: Ultimate bearing capacity divided by the factor ofsafety which may range from 2 to 5 depending upon the importance ofthe structure and soil profile at the site.

Allowable Bearing Pressure: The maximum allowable net loadingintensity on the soil at which the soil neither fails in shear nor undergoesexcessive settlement detrimental to the structure.

Factors Affecting Bearing Capacity

1. Nature of soil and its physical and engineering properties.

2. Nature of the foundation and other details such as the size, shape, depth below the ground surface and rigidity of the structure.

3. Total and differential settlements that the structure can withstand without functional failure.

4. Location of the ground water table relative to the level of the foundation

5. Initial stresses if any

Bearing Capacity Failure

Transcosna Grain ElevatorCanada (Oct. 18, 1913)

West side of foundation sank 24-ft

Stability ProblemBearing Capacity Failure

Bearing Capacity Analysis

How do we estimate the maximum bearing pressure that the soil can withstand before failure occurs?

Bearing Capacity Failures

Types/Modes of Failure

general shear failure

local shear failure

punching shear failure

General Shear Failure

1. Sudden or catastrophic failure

2. Well defined failure surface

3. Bulging on the ground surface

adjacent to foundation

4. Common failure mode in dense

sand

Local Shear Failure

1. Common in sand or clay with medium compaction

2. Significant settlement upon loading

3. Failure surface first develops right below the foundation and then slowly extends outwards with load increments

4. Foundation movement shows sudden jerks first (at qu1) and then after a considerable amount of movement the slip surface may reach the ground.

5. A small amount of bulging may occur next to the foundation.

Punching Shear Failure

1. Common in fairly loose sand or soft clay

2. Failure surface does not extends beyond the zone

right beneath the foundation

3. Extensive settlement with a wedge shaped soil

zone in elastic equilibrium beneath the

foundation. Vertical shear occurs around the

edges of foundation.

4. After reaching failure load-settlement curve

continues at some slope and mostly linearly.

Model Tests by Vesic (1973)

General Guidelines

Footings in clays - general shear

Footings in Dense sands ( > 67%)

-general shear

Footings in Loose to Medium dense

sands (30%< < 67%) - Local Shear

Footings in Very Loose Sand ( < 30%)-punching shear

rD

rD

rD

Methods of Determining Bearing Capacity

1. Bearing capacity tables in various building codes.

2. Analytical methods

3. Model tests

4. Plate bearing tests

5. Penetration tests

6. Laboratory tests

Bearing Capacity from Building Codes

Analytical Methods

1. Theory of Elasticity (Schleichers method)

2. Classical earth pressure thery Rankinesmethod, Paukers method and Bellsmethod.

3. Theory of Plasticity- Fellenius method,Prandtls method, Terzaghis method,Meyerhofs method, Skemptons method,Hasens method and Ballas method.

Terzaghi Bearing Capacity Formulas

Assumptions in Terzaghi Bearing Capacity Formulas

L/B ratio is large --------> plain strain problem

D B

Shear resistance of soil for D dpeth is neglected

No sliding between footing and soil

soil: a homogeneous semi-infinite mass

footing is very rigid compared to soil

General shear failure

Shear strength is governed by Mohr-Coulomb Criterion

Terzaghi Bearing Capacity Formulas

BNNqcNq qcu '5.0.

For Square foundations:

For Continuous foundations:

BNNqcNq qcu '4.0.3.1

For Circular foundations:

BNNqcNq qcu '3.0.3.1

Bearing Capacity Factors

Angle of shearing resistance (f) (Deg.)

Terzaghis bearing capacity factors

Nc Nq N

0 5.7 1 0

5 7.3 1.6 1.5

10 9.6 2.7 1.2

15 12.9 4.4 2.5

20 17.7 7.4 5

25 25.1 12.7 9.7

30 37.2 22.5 19.7

35 57.8 41.4 42.4

40 95.7 81.3 100.4

45 172.3 173.3 297.5

50 347.5 415.1 1153

For local shear failure, Terzaghi suggests the following values for c and f.

cc3

2'

)(3

2)'( ff TanTan

The corresponding values of bearing capacity factors are Nc, Nq and N which are less than the correspondingvalues for general shear failure. Also c f must be usedwherever c and f occur in the computation for bearingcapacity.

Further Developments

Skempton (1951)

Meyerhof (1953)

Brinch Hanson (1961)

De Beer and Ladanyi (1961)

Meyerhof (1963)

Brinch Hanson (1970)

Vesic (1973, 1975)

General Bearing Capacity Equation(IS 6403-1981)

idsBNidsNidscNq qqqqzDccccult 5.0

factorsn inclinatio arei andi,i

factorsdepth ared andd,d

factors shape ares ands,s

factorscapacity bearing are N andN,N

foundation below soil oft unit weigh effective

level foundationat pressure overburden effective

soil ofcohesion undrainedc

foundation ofwidth B

qc

qc

qc

qc

zD

square)for 0.8 andcircular for 0.6 to(Equal 4.01

square)or circular for 1.2 to(Equal 2.01

square)or circular for 1.3 to(Equal 2.01

L

Bs

L

Bs

L

Bs

q

c

0

0

10 for 1

10 for )2/45tan(1.01

)2/45tan(2.01

f

ff

f

dd

B

Ddd

B

Dd

q

q

c

degreesin are anf where)/1(

)90/1(

2

2

ff

i

ii qc

As Per IS 6403

)( tan).1(2

)2/45(tan)tan(exp(

)( ).1(

2

f

ff

f

q

q

qc

NN

N

CotNN

Groundwater Table Effect

Groundwater Table Effect; Case I

1. Modify zD

2. Calculate as follows:

wb

Groundwater Table Effect; Case II

1. No change in zD

2. Calculate as follows:

B

DDww 1

Groundwater Table Effect; Case III

1. No change in zD

2. No change in

Allowable Bearing Capacity

F

qq ulta

.. Allowable Bearing Capacity

F . Factor of safety

aq

Factor of Safety

Depends on:

Type of soil

Level of Uncertainty in Soil Strength

Importance of structure and consequences of failure

Likelihood of design load occurrence

Minimum Factor of Safety

Selection of Soil Strength Parameters

Use Saturated Strength Parameters

Use Undrained Strength in clays (cu)

Use Drained Strength in sands,

Intermediate soils that where partially drained conditions exist, engineers have varying opinions; Undrained Strength can be used but it will be conservative!

f and c

Accuracy of Bearing Capacity Analysis

In Clays ..Within 10% of true value (Bishop and Bjerrum, 1960)

Smaller footings in Sands. Bearing capacity calculated were too conservative but conservatism did not affect construction cost much

Large footings in Sands Bearing capacity estimates were reasonable but design was controlled by settlement

Accuracy; Bearing Capacity Analysis

Bearing Capacity from Model Tests Housels Approach

Housel(1929) based on experimental investigationgave a practical method of determining bearingcapacity of a foundation. He made oneassumption that the bearing capacity of afoundation consists of two components.

1. One which is carried by the soil column directlybeneath the foundation

2. The second part which is carried by the soilaround the perimeter of the founda

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