Sofashallow foundation analysis softwaresofa home loans

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Sofashallow Foundation Analysis Softwaresofa Home Health Care

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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

    5

    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

    9

    = 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

    10

    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

Sofashallow Foundation Analysis Softwaresofa HomeSofashallow foundation analysis softwaresofa homes

TRANSCRIPT

Sofashallow Foundation Analysis Softwaresofa Home Loans

  • 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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