Pad Foundation Theory Enu

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Theory

Subtitle

Pad Foundations according to EN 1997-1


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Pad Foundations according to EN 1997-1: Theoretical Background


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All information in this document is subject to modification without prior notice. No part or this manualmay be reproduced, stored in a database or retrieval system or published, in any form or in any way,electronically, mechanically, by print, photo print, microfilm or any other means without prior writtenpermission from the publisher. SCIA is not responsible for any direct or indirect damage because ofimperfections in the documentation and/or the software.

Copyright 2009 SCIA. All rights reserved.


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Table of contents

Version Information...................................................................................................................... 1Introduction ................................................................................................................................... 1Pad Foundation Check ................................................................................................................ 2

Determination of Design Values ...................................................................................................... 3Determination of Effective Geometry .............................................................................................. 5

Weight G ........................................................................................................................................ 7Distances gx & gy .......................................................................................................................... 8Effective Geometry ......................................................................................................................... 8

Bearing Check ................................................................................................................................... 9Undrained Bearing Resistance ...................................................................................................... 9Drained Bearing Resistance ........................................................................................................ 10Known Soil Capacity Bearing Resistance .................................................................................... 12

Sliding Check ................................................................................................................................... 13Eccentricity check ........................................................................................................................... 14Uplift Check ..................................................................................................................................... 15

Annex: Pad Foundation Stiffness ............................................................................................. 16References .................................................................................................................................. 17


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Version Information

Welcome to the Theoretical Background for Pad Foundations according to EN 1997-1.

This document provides background information regarding the Pad Foundation checks.

Version info

Document Title Theoretical BackgroundPad Foundationsaccording to EN 1997-1

Release 2010.0

Revision 11/2009


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IntroductionIn this Theoretical Background, in depth information is given regarding the Pad Foundation checksaccording to EN 1997-1.

The checks are executed according to the following codes:

EN 1997-1:2004

Eurocode 7: Geotechnical designPart 1: General rules

CEN, 2004.

EN 1997-1:2004/AC:2009 Correction Sheet


CEN, 2009.

The annex to this Theoretical Background specifies the calculation of the stiffness factors of a PadFoundation.


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2

Pad Foundation Check

In this chapter the different steps of the Pad Foundation Checks are specified.

First of all, the required safety and resistance factors need to be determined depending onthe chosen Design Approach.

Using these safety factors, the vertical design loading Vd, horizontal design loading Hdandeffective geometry of the pad are determined.

Based on this effective geometry the different checks are executed.

The above steps are detailed in the following paragraphs.


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3

Determination of Design Values

The Pad Foundation check is executed for a Result Class.

Depending on the Design Approachset in the National Annex Setup, the sets of safetyfactors are read from the setup as follows:

- For Design Approach 1the safety sets depend on the combination type.For combinations of type EN-ULS (STR/GEO) Set B sets M1& R1are used.

For combinations of type EN-ULS (STR/GEO) Set C sets M2& R1are used.For any other combination sets M1& R1are used.

- For Design Approach 2, in all cases sets M1& R2are used.

- For Design Approach 3, in all cases sets M2& R3are used.

For detai led inform ation regarding the different com bination typ es, reference ismad e to EN 1990 [Ref.4]

In case the functionality Subsoil is activated in the Project Dataa new class GEOis generated autom atical ly for use in the Pad Foun dationcheck.

This class conta ins al l combinat ions of the fo l lowing ty pes:

EN-ULS (STR/GEO) Set B

EN-ULS (STR/GEO) Set C


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A Resul t Class m ay also con ta in load c ases o r non - linear com binat ions. Theseare seen as Any combination for the check.

For Design A pproach 1 the class for which the check is executed needs toconta in at least one comb inat ion of each of the fo l lowing types:EN-ULS (STR/GEO) Set B

EN-ULS (STR/GEO) Set C

In case the class for which the user wishes to execute the check does not

comp ly wi th th is requi rement, the check is not executed and a warn ing is

shown instead.

For Design Approaches 2 & 3 there is no requi rement for the content of the

class.

Using the above information, the design values for the soil properties are determined:

Design Value Formula

With: read from Subsoil Library

read from National Annex Setup

With: c read from Subsoil Library

cread from National Annex Setup

With: curead from Subsoil Library

curead from National Annex Setup

With: specific weight read from Library

read from National Annex Setup

With: Backfillweight read from Pad foundation input Dataread from National Annex Setup

A final safety factor which needs to be determined concerns the safety factor for the weightof the pad foundation and the backfill material. This safety factor is taken as the safety

factor for the first permanent load case for the combination under consideration i.e. G.

In case a com bination do es not have a permanent load case, Gis taken as1,00.


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5

Determination of Effective Geometry

The next step in the check concerns the determination of the effective geometry of the padfoundation.

The following picture illustrates the different actions working on the foundation.

In this picture the following notations are used:

Action Info

G Weight of the foundation and of any backfill material inside the area of abcd.

g Load application point for load Greferenced to the center point of thefoundation base

P Vertical Rzreaction of the support

p Load application point for load P referenced to the center point of the

foundation base.This is read as the load eccentricities ex and ey from the Pad Foundationlibrary.

H Horizontal Rxor Ryreaction of the support

h =(h1 + h2)

Load application point of the horizontal load H referenced to the foundationbase.

With h1 and h2 read from the Pad Foundation Library.


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M Moment Mxor Myreaction of the support

Vd = G + P

Ultimate load vertical to the foundation base including the weight of thefoundation and any backfill material.

e Load application point for load Vdreferenced to the center point of the

foundation base

Using the Support React ion El iminat ion factors def ined in the GeotechnicsSetup the reaction forc es Rx, Ry, Rz, Mx, My can be mo dif ied.

These factors c an be used in c ase the user for example models only a p ad

foundat ion and om i ts other found at ion elements l ike a r ing beam. The user can

then speci fy that for example only 50% of a react ion should be used to d esign

the pad foundat ion since the oth er 50% goes into the r ing beam.

The eccentricity eis calculated as follows:

For a general 3D case this formula is written as:


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Weight G

The weight G consists of three parts:

1) The weight of the foundation block, GBlock

This depends on the shape of the block (prismatic or pyramidal), dimensions and also the

density Blockof the block material.

The density of the block depends on the Water table level.

Water level Block Density

No influence Block

at foundation base Block

at ground level ( Block W)

The Water Density Wis taken as 9,81 kN/m

2) The weight of the backfill around h2, GBackfill,Around

This depends on the shape of the block (prismatic or pyramidal), dimensions and also thedensity of the backfill material.

The backfill density Backfill,dis specified inDetermination of Design Values

The density of the backfill depends on the Water table level.

Water level Backfill Density

No influence Backfill,d

at foundation base Backfill,d

at ground level ( Backfill,d W)

The Water Density Wis taken as 9,81 kN/m

3) The weight of the backfill above the foundation block, GBackfill,Above

This depends on the height and density of the backfill as specified in the input of the PadFoundation.

Note that the height of th e backfi l l material can also be negative. A negativevalue is used to ind icate that the soi l is lower than the top of the foun dat ion

block.


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The three parts are illustrated on the following picture:

The design value of the total weight G can then be calculated as follows:

Gd= G* [GBlock+ GBackfill,Around+ GBackfill,Above]

With Gthe safety factor of the permanent loading for the combination under consideration, asdefined inDetermination of Design Values.

Distances gx & gy

Using the weight and the volume, the center of gravity of the block and backfill are determined.The distances gx and gy are then calculated from this centroid to the center point of thefoundation base.

Effective Geometry

As a final step, using the eccentricities ex and ey the effective geometry of the foundation base iscalculated as follows:

L1 = A2 * |ex|

L2 = B2 * |ey|

With A & B read from the Pad Foundation library.

B = min (L1 ; L2)

L = max (L1 ; L2)

A = B * L

In case B < 0 m or L < 0 m the geometry is incorrect.

In th is case, the check is not executed and a warn ing is given on the ou tput


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Bearing CheckThe Bearing check is executed according to EN 1997-1art. 6.5.2and Annex D [Ref.1]

The Bearing resistance Rddepends on the fact if the soil condition is drained or undrained.

In case the user knows the soil capacity, for example from a geotechnical report, Rdcanbe read directly from the input data instead of calculated.

Undrained Bearing Resistance

The formulas in this paragraph are used in case the Typefield in the Subsoil Library is setto Undrained.

The design value of the undrained bearing resistance is calculated as follows:

Value Formula

cud As specified inDetermination of Design Values

bc Inclination of the foundation base (always horizontal base)

= 1,00sc Shape of the foundation (rectangular shape)

ic Inclination of the load, caused by horizontal load Hd

and Hd A * cud

in case Hd> A * cudthe value of icis set to 0,5

Hd Resulting horizontal load

Hx Horizontal support reaction Rx as defined inDetermination of Effective Geometry

Hy Horizontal support reaction Ry as defined inDetermination of Effective Geometry

B Effective width as defined inDetermination of Effective Geometry

L Effective length as defined inDetermination of Effective Geometry

A Effective area as defined inDetermination of Effective Geometry


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q Overburden at the foundation base [Ref.5]

=(h1 + h2 + hbackfill)* Backfill,d

With:

h1 & h2 read from the Pad Foundation Library

hbackfillread from the Pad Foundation input

Backfill,das defined inDetermination of Design Values

R,v Resistance factor read from the National Annex Setup

Drained Bearing Resistance

The formulas in this paragraph are used in case the Typefield in the Subsoil Library is setto Drained.

The design value of the drained bearing resistance is calculated as follows:

Value Formula

cd As specified inDetermination of Design Values

Nc Bearing resistance factor

Nq Bearing resistance factor

N Bearing resistance factor

bc Inclination of the foundation base (always horizontal base)

= 1,00

bq Inclination of the foundation base (always horizontal base)

= 1,00

b Inclination of the foundation base (always horizontal base)

= 1,00

sc Shape of the foundation (rectangular shape)

sq Shape of the foundation (rectangular shape)


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s Shape of the foundation (rectangular shape)

ic Inclination of the load, caused by horizontal load Hd

iq Inclination of the load, caused by horizontal load Hd

i Inclination of the load, caused by horizontal load H d

m

mL

mB

Angle of the horizontal load Hdwith the direction L

As specified inDetermination of Design Values

B Effective width as defined inDetermination of Effective Geometry

L Effective length as defined inDetermination of Effective GeometryA Effective area as defined inDetermination of Effective Geometry

Hd Resulting horizontal load

Hx Horizontal support reaction Rx as defined inDetermination of EffectiveGeometry

Hy Horizontal support reaction Ry as defined inDetermination of EffectiveGeometry

Vd As specified inDetermination of Effective Geometry

qd Effective overburden at the foundation base [Ref.5]

=(h1 + h2 + hbackfill)* t

With:

h1 & h2 read from the Pad Foundation Library

hbackfillread from the Pad Foundation input


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tis depending on the water level as follows:

Water level t

No influence Backfill,d

at foundation base Backfill,d

at ground level ( Backfill,d W)

Backfill,das defined inDetermination of Design Values

Wis taken as 9,81 kN/m

Effective weight density of the soil below the foundation level

depending on the water level as follows:

Water level d

No influence d

at foundation base ( d W)

at ground level ( d W)

das defined inDetermination of Design Values

Wis taken as 9,81 kN/m

R,v Resistance factor read from the National Annex Setup

Known Soil Capacity Bearing Resistance

In case the Soil capacity is known, this value can be used directly instead of using the EN1997-1 bearing resistance calculation outlined above.

This procedure is applied in case the checkbox Known soil capacity, use Sigma oc isactivated in the Geotechnical Design Setup.

The design value of the bearing resistance is calculated as follows:

Value FormulaA Effective area as defined inDetermination of Effective Geometry

od Design value of the admissible soil capacity, taken as oc

oc Read from the Subsoil Library


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Sliding CheckThe Sliding check is executed according to EN 1997-1art. 6.5.3[Ref.1]

The Sliding resistance Rddepends on the fact if the soil condition is drained or undrained.

The value Rp,dspecifies the positive effect of the earth pressure at the side of thefoundation. Since this effect cannot be relied upon, this value is taken as zero [Ref.2].

The sliding resistance is dependent on the condition of the subsoil.

a) In case the Typefield in the Subsoil Library is set to Undrained.

Value Formula

cud As specified inDetermination of Design Values

A Effective area as defined inDetermination of EffectiveGeometry

R,h Resistance factor read from the National Annex Setup

In case the checkbox Water/air in clay subgradein the Subsoil Library is activated,

the value of Rdis limited as follows:

Value Formula


b) In case the Typefield in the Subsoil Library is set to Drained.

Value Formula


d Design friction angle at the foundation base


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Dependent on the Cast conditionspecified in the PadFoundation Library:

Cast Condition d

Prefabricated

In situ

As specified inDetermination of Design Values

R,h Resistance factor read from the National Annex Setup

Eccentricity check

EN 1997-1art. 6.5.4specifies that special precautions are required for loads with largeeccentricities.

According to [Ref.3] this is done by checking if the design load is within a critical ellipse orcritical diamond.

More specifically the eccentricity of the load should not exceed 1/3or 1/6of the width.

The maximal value of the eccentricity is defined in the Geotechnical Design Setup.

Based on the maximal value an eccentricity check is executed as follows according to

[Ref.3].

a) In case the maximal eccentricity is set to 1/3

b) In case the maximal eccentricity is set to 1/6

Value Formula

ex As specified inDetermination of Effective Geometry

ey As specified inDetermination of Effective Geometry

A Read from Pad Foundation Library

B Read from Pad Foundation Library


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c) In case the maximal eccentricity is set to No limit

In this case there is no limit i.e. any eccentricity is allowed. The unity check is then set to0,00.

Uplift CheckIn case the vertical design loading Vdis negative, it implies that the pad foundation is intension and may thus be uplifted from the ground.

The uplift check is written out as follows:

Value Formula

P The vertical Rzreaction as specified inDetermination of Effective Geometry

Gd The weight of the foundation and any backfill as specified inDetermination ofEffective Geometry

This check is executed ins tead of the Bear ing, Sl id ing and Eccentr ic i ty checks.


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Annex: Pad Foundation StiffnessThis annex specifies the calculation of the stiffness coefficients of a pad foundation.

Stiffness Formula

Stiffness X

Stiffness Y

Stiffness Z

Stiffness Rx

Stiffness Ry

Stiffness Rz

With:

Parameter

A Dimension read from Pad Foundation library

B Dimension read from Pad Foundation library

C1x Soil stiffness read from Subsoil Library

C1y Soil stiffness read from Subsoil Library

C1z Soil stiffness read from Subsoil Library

C2x Soil stiffness read from Subsoil Library

Ix

Iy


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References

[1] EN 1997-1


CEN, 2004.

[2] Frank R., Baudoin C., Driscoll R., Kavvadas M., Krebs Ovesen N., Orr T.,Schuppener B., Designers Guide to EN 1997-1 Eurocode 7: GeotechnicaldesignPart 1: General rules, Thomas Telford, 2004.

[3] Schneider K.-J., Bautabellen fr Ingenieure, 13. Auflage, Werner Verlag,1998.

[4] EN 1990, EurocodeBasis of Structural Design, CEN, 2002.

[5] Lambe T., Whitman R., Soil Mechanics, MIT, John Wiley & Sons, Inc,1969.

[6] EN 1997-1:2004/AC:2009 Correction Sheet


CEN, 2009.

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Pad Foundation Theory Enu