Logiciel K Rea v3 - Terrasol - Geodeltia file•1 Logiciel K‐Rea v3 Analysis of retaining walls...

•1

Logiciel K‐Rea v3 Analysis of retaining walls (simple or double)

using the subgrade reaction coefficient methodand including partial safety factors and ULS checksand including partial safety factors and ULS checks

•V. BernhardtV. Bernhardt / F. Cuira

•Overview of K‐Rea v3 features and capabilities

• Double‐walls and rear‐walls calculations

• Introduction to the NF P 94‐282 standard and the ULS calculations and checks implementation in K‐Rea v3

Page 2February 2012

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The subgrade reaction method allows for the analysis of flexible retaining walls such as diaphragm walls, soldier-pile walls, or h t il ll

Introduction

sheet-pile walls.

It enables to calculate the horizontal displacements and bendingmoments of the retaining wall through its various construction stages:

• The initial stage consists in building the retaining wall itself.

• The following stages correspond to various actions such as earthworks (excavations, fills, …), installation of anchors or

Page 3February 2012

earthworks (excavations, fills, …), installation of anchors or struts, change of the water level, or load application.

• The wall is assumed to extend to infinity in the out-of-plane direction=> the problem is plane strain (except in the case of circular retaning walls).

• The wall inertia can vary with depth. The wall can be subjected to:

Earth and water pressures

The calculation method

Earth and water pressures

Horizontal loads

Forces applied by struts or anchors

Imposed external moments

Rotation springs (embedment of external structures).

• The earth and water pressures are modeled by horizontal pressures

Page 4February 2012

applied on both sides of the wall. Earth pressures are related to the walldisplacements by an elasto-plastic soil behaviour law. The parametersfor this law are calculated at each depth: they depend on the soilproperties of the corresponding layer, and on the vertical stress in the soil(depending on the excavation level, the water level and the possible loads).

•3

• Soil layers are modeled as springs reacting linearlyuntil they reach a

Reactions applied by the soilonto the beam = springsReactions applied by the soilonto the beam = springs

• The retaining wall is assumed to be a flexible beam, laying on elasto-plastic supports.

The calculation method

yplastification stress (eitheron active or passive pressure side).

• In construction stages, various actions can bedefined, resulting in forces acting on the beam.

• The calculation consists in

Reaction applied by the soil onto thebeam in a given pointReaction applied by the soil onto thebeam in a given point

Page 5February 2012

• The calculation consists in finding the equilibrium state between the beamdisplacements and the stresses in the soil layers: iterative calculation.

Pa: pressure applied by the soil at limit equilibrium(active pressure)Pp: pressure applied by the soil at limit equilibrium(passive pressure)Kh: soil reaction modulus

Pa: pressure applied by the soil at limit equilibrium(active pressure)Pp: pressure applied by the soil at limit equilibrium(passive pressure)Kh: soil reaction modulus

• At-rest pressurepi = p0 = k0 σ’v0

for the first calculationstage with σ’v0: vertical

Elasto-plastic soil behaviour

stage with σ v0: vertical effective stress at rest

• Active pressurepa = ka σ’v – ca c

• Passive pressurepp = kp σ’v + cp c

• Modulus of subgrade reaction

Page 6February 2012

UphillDisplacements towards uphillUphill

Displacements towards uphillUphill


Displacements towards uphill

reactiongradient = kh + dkh . z with kh: modulus (i.e. coefficient) of subgrade reaction

•4

Soil behaviour changes after soil plastification

Elasto-plastic soil behaviour

Soil behaviour changes

UphillDisplacements towards uphill






Page 7February 2012

when the wall is « separated » from the soil(no traction allowed)


UphillUphillDisplacements towards uphill


UphillUphillDisplacements towards uphill

Soil behaviour varies depending on loading conditions: consolidation phenomenon is taken into account with unloading and reloading coefficients (for soft clays for example).

Unloading/reloading coefficients

Reloadingconditions

UphillDisplacements towards uphillUphill



Displacements towards uphill

Page 8February 2012

• Δpi = kr Δσ’v if Δσ’v > 0 with kr: reloading coefficient

• Δpi = kd Δσ’v if Δσ’v < 0 avec kd: unloading coefficient

As the initial state is modified, the displacement required to reach plastification as changes, especially in soft soils.

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Required data include:

The project data

Required data include:

Project general settings

Soil properties

Retaining wall properties

Page 9February 2012

General settings

Page 10February 2012

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Soil properties

Soil database

Soil properties

database


Coefficients specific to the calculation

method

Various wizards(automatic and

advanced modes)

Earth pressure obliquities will be taken into account

automatically by the coefficients wizards.

3 wizards:

Active and passive earth pressure coefficients

Kérisel and Absi (tables)

Coulomb method (formulae)

2

2cos

aK


2

coscossinsin

1cos

a

aa

a

2

2

coscos

sinsin1cos

cos

p

pp

pK

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Rankine formulae

22

22

coscoscos

coscoscoscosaK

22

22

coscoscos

coscoscoscospK

Active and passive earth pressure coefficients

Caquot formulae for ca and cp:

24tan2

aK

24tan2

pK

Note:

• If no slope ( = 0):

• The Rankine formulae do not take into accountfriction between soil and wall


1cosexpsin1

cossincos

tan

1 tan

ac

1cosexpsin1

cossincos

tan

1 tan

pc

Balay method

3 wizards:

*91330*

aE

k mh

Subgrade reaction modulus

Schmitt method

9133,02

31

3

4

*1,2

EI

E

k

m

h


Chadeisson curves

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Possibility to define a cylindric rigidity for circular walls

Wall properties

+ wizards for continuous walls, combined walls and sheet-pile walls


Definition of construction stages

In K-Rea, the construction stages are completely defined through the user interface. The typical process is the following:

• Creation of new calculation stages

• Definition of the actions to be performed in each stage

• Automatic graphical display of the current state of the project

• Calculation

• Output


• Output

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Creation of a new calculation stage


Various action types are used to define the construction stages. They are divided into 6 categories:

Definition of construction stages

Initial conditions

Loading / Forces / Couples

Earthworks

Anchors / Wall

Soil properties


Soil properties

Hydraulic conditions

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• « Caquot » load (uniform and distributed. It is removed when

th k li d th

These actions can be applied only once, in the initial conditions.

UphillUphillDownhill UphillUphillDownhill UphillUphillDownhill UphillUphillDownhill

Initial conditions

earthworks are applied on the same side)

• Reduced pressures for soldier-pile walls. Pressures are applied again at 100 % (i.e. without reduction) after sheeting installation

Between z1 and z2:

Active pressure multiplied by R

Passive pressure multiplied by R*C

Water pr. of both sides multiplied by R

Kh multiplied by R


after sheeting installation

• Maximum pressure (in the case of precast walls)

UphillDownhill UphillDownhill UphillDownhill UphillDownhill

• Boussinesq load(localised, limited extent)

Loads - forces - couples

• Graux load


(localised, limited extentand diffused)

Layer 1

Layer 2 Diffusion

Layer 1

Layer 2 Diffusion

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• External moments (additional moment,due to an embeddedfl f l )

Loads - forces - couples

floor for example)

• Horizontal loads(trapezoidal) UphillDownhill UphillDownhill UphillDownhill UphillDownhill


• Linear loads

• Simple (possibility to excavate, change water level and apply a Caquot load on excavation side at the same time)

• With berm

3 different excavation types:

Earthworks

• With sheeting installation (if the « reduced pressures » option was activated in the initial stage)

Uphill

Downhill

Uphill

Downhill

Uphill

Downhill

Uphill

Downhill


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• Fill (with the option to define a separation at formation level, and/or to apply a Caquot load on top of the fill)

Earthworks

UphillDownhill UphillDownhill UphillDownhill UphillDownhill


• Struts(unilateral or bilateral mode)

3 types of anchors can be applied and superposed:

Anchors – Retaining wall

bilateral mode)

• Anchors (unilateralor bilateral mode)


• Rotation springs (allow for definition of a rotation stiffness)

These elements can be deactivated in later stages.

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• Modification of the wall stiffness

Anchors – Retaining wall


• Wall upraising (additional wall element on top)

• Modification of the soil properties (separate modification of eachsoil parameter, either on one side only, or for both sides at the same time)

Soil properties


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• Hydraulic gradient

Hydraulic conditions


On the main screen: horizontal displacements of the retaining wall, bending moments, shear forces

Output


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In the dedicated output window, additional curves are displayed:

• earth and water pressures on both sides of the wall

• axial forces in anchors

Graphical output


For both sides of the wall:

All values displayed as curves, plus:

• Soil state for each cell• Vertical effective

pressures

Tabular output

pressures• Limit pressures

on active and passive sides

• Annular pressure for a circularretaining wall


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Additional output

Additional results formats are available in K-Rea, such as envelope curves(final or intermediate), or the results synthesis.


Printings

A printing wizard enables to:

• Select which contents shouldbe printed

• Setup the printing options

• Send the printings either to a printer or to the Windows©

clipboard.


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Printings

• K-Rea printings (physical printer or pdf generator): example of data summary and phases synthesis.






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General principles: • K-Rea v3 deals with

double sheetpile walls made either of a main wall anchored on a smaller rear

Calculation of double walls

wall, or of 2 parallel walls (cofferdams or open excavations for instance)

• 2 levels of linking anchorsmaximum

• The input data (soil and walls) should be definedf b th ll (it’ ibl


for both walls (it’s possible to copy data from Wall 1 to Wall 2 if relevant)

General principles:

• The aim of the calculation is to find a situation for which forces at anchoring points are balanced between both walls


between both walls=> iterative process with a convergence criterion on the forces in each anchor.

• The only interaction considered between both walls is the linking anchor(s) (no interaction throughthe soil volume)


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General principles: • ULS checks are NOT available automatically for double walls.

• But it is possible to convert a double-wall project into 2 simple wall projects, and to perform ULS checks for each wall individually.



Input data



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Output



Output



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Output







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• NF P 94-282 : national (french) application standard of EC7 for retaining walls

• Applies to vertical retaining walls: diaphragm walls, sheetpile walls,

Standard NF P 94-282

pp g p g , p ,combined walls…

• Defines the failure mechanisms that should be checked and the global calculation approach

• This presentation is focused on the application of this standard withinK-Rea v3, but the values of partial safety factors may be changedfor each K-Rea project and thus K-Rea may be used for ULS calculations according to other local application standards of EC7


calculations according to other local application standards of EC7 applying approach n 2.

• « Design value »:

Ed = m x Ek

Vocabulary

Design value Characteristic value

Partial factor

• m ≥ 1 for actions, ≤ 1 for strengths


• Design approach 2

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• « Well-known » calculation models LEM: Limit Equilibrium Model

o Limit equilibrium = work with limit active/passive earth pressures (« available »)

o Suitable for pre-design (for projects with no or one level anchor)

Vocabulary

o Suitable for pre-design (for projects with no or one level anchor)

o Does not account for wall stiffness => no displacements

Fa

Active earthpressure

Passive earth


Counter active earth pressure

Counter passive earth pressure

requested

available

Fbpressure

Fca α.Fcb

zn zn : transition level

z

ΔU

• « Well-known » calculation models SSIM: Soil Structure Interaction Model

o SSIM – K: subgrade reaction coefficients

o SSIM – F: finite elements or finite differences

Vocabulary

ContinuumE, , c’,φ’…

pb

pa

p0

ph

dh

Elastoplastic

springs


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• ULS checks1. Global stability

2. Failure on the passive side of the wall

3 Structural strength of the wall

Required checks

3. Structural strength of the wall

4. Stability of the bottom of the excavation

5. Balance of vertical forces

6. Stability of the anchoring block (Kranz)

7. Strength of the anchors

8. Hydraulic stability

S S


• SLS checks1. Displacements

2. Durability

3. Creeping of anchors

Calculation with ULS checksCalculationwihout ULS

checks

ULS calculationSLS calculationBasic

calculation

Application in K-Rea v3

SLS ResultsM bili d

« SSIM » model(without weighting

factors)

Limit equilibriummodel «LEM» (withweighting factors)

Cantilver phases

« SSIM » model (with 1,11 applied to

variable loads)

Phases with anchor(s)

ULS resultsMobilised pressure

ULS resultsMobilised pressure

« SSIM" model(without weighting

factors)

Basic resultsMobilised pressures


‐Mobilised pressures‐ Displacements‐ Forces (V, M)

Kranzmodel

‐Mobilised pressure ‐ Displacements‐ Charac. forces (Vk, Mk)‐ Design forces(Vd, Md)

ULS checks‐ Faillure on the passive side‐ Vertical equilibrium‐ Anchoring block stablity

‐Mobilised pressure ‐ Design forces (Vd, Md)

ULS checks‐ Faillure on the passive side‐ Vertical equilibirum

‐Mobilised pressures‐ Displacements‐ Forces (V, M)

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• Data: definition of partial safety factors

SSIM

Additional data required in K-Rea v3

SSIM general

model

LEM model

Vertical


Vertical forces

Kranz

Construction phases: phase type

Ph t


Phase nature (temporary / permanent)

Cantilever or anchored


Cantilever or anchored phase – Automatic identification

•26

Construction phases: example of actions definition


Distributed surcharge on


gthe soil: permanent or variable

Linear force applied to the wall

• Principle of the check Make sure that the available passive earth pressure is superior,

with enough safety, to the passive earth pressure required for moments equilibrium

Failure on the passive side of the wall

moments equilibrium

For an « isostatic » system (wall with no or 1 anchor level), failureon the passive side is equivalent to a insufficient embedment of the wall

• Calculation models Cantilever wall: LEM is compulsory - chapter 8.4.2 – (2)

Anchored wall: LEM or SSIM Use of LEM method is limited to


Anchored wall: LEM or SSIM. Use of LEM method is limited to phases with one single anchor level

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• Phase with anchors (one or several levels of anchors)

km,kt,

B.B

a


b

SSIM model



Passive earthpressure

Limiting earthpressure kt,B

km,B

kmBB

γa γb

T h 1 35 1 10

• Phase with anchors (one or several levels of anchors)


b

km,kt,.B

a

Temporary phase 1,35 1,10

Permanent phase 1,35 1,40

French method (approach 2): Bt,k and Bm,k obtained using a calculation of “SSIM” type led with coefficient 1,11 applied to characteristic values of unfavourable variable surcharges

x = 1 50 for a temporary phase (global safety)


a x b = 1,50 for a temporary phase (global safety)

a x b = 1,90 for a permanent phase (global safety)

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• Phase with no anchor (cantilever phase)

Limit equilibriumth d (LEM)


Fa

Fb


Passive earthpressure

F

zn zn : transition levelΔU

method (LEM)


Counter active earth pressure

Counter passive earth pressure

requested

available

Fca α.Fcb

z


LEM model = calculation with design values !

Active earth pressures (Fa, Fca): design values = 1 35 x characteristic values


design values = 1,35 x characteristic values

Passive earth pressures (Fb, Fcb): design values = 1/b x characteristic values

b = 1,40 for permanent phases

b = 1,10 for temporary phases

Surcharges: design values = q x characteristic values


Nature of the surcharge Favourable UnfavourablePermanent 1.00 1.35

Variable 0.00 1.50

•29

Checking the embedment



0b f 20,1f

• fb : embedment « available » below the zero differential pressure point (O)

• f0 : minimum embedment

O

C

f0fbRC

Differentialpressure


below the zero differential pressure point (O), required to achieve moments equilibrium (point C, also called critical level)

C

z

P

• Output: ULS checks / failure on the passive side



Cantilever phase => LEM model

•30

• Calculation of ULS forces

SSIM model (anchored wall)

o Moment: Md = 1,35 x Mk

o Shear force: Vd = 1,35 x Vk

Structural strength of the wall

o Shear force: Vd 1,35 x Vk

LEM model (cantilever wall)

o Calculation by integration of pressures implied in the limitequilibrium of the wall

o Leads directly to design values of forces

o Only method « D » enables integration on the whole heightof the wall


o For method « F », integration downto critical level only

• Check of the wall structural strength=> EC 3 or 2 depending on the material

ULS forces (SSIM-K calculation)



•60

•31

ULS forces (LEM calculation)



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Output: detailed tables, envelope curves, summary tables, etc



•32

• Goals Evaluate the vertical resultant force => check of the heave, bearing

capacity at the bottom of the wall

Check whether assumed inclinations of active/passive earthpressures are relevant

Balance of vertical forces

pressures are relevant

If heave is not structural => adjust these inclinations (active pressure, passive pressure and counter passive pressure)

Bearing capacity to be checked according to the relevant standard for foundations design

• General principle: ddd0d TvFvPvPRv • Rv : vertical resultant (design value)


• Rvd : vertical resultant (design value)

• P0 : wall weight

• Pvd : vertical resultant of earth pressures (design value)

• Fvd : vertical resultant of loads applied onto the wall (design value)

• Tvd : vertical resultant of anchor forces (design value)

Output: ULS checks / balance of vertical forces

Balance of vertical forces


•33

General principle

• Make sure the free length is long enough to prevent any transferof the anchor load to the wall.

Stability of the anchoring block (Kranz)

A B

E A hoof the anchor load to the wall.

• Equivalent to checking the stability of the anchoring block « ABCDA » = Kranz model

• Simplified Kranz model = plane failure surface (CD):

C

E

écran

tirantα

β

Anchor

Wall


D: zero shear force point

C: effective anchoring point (middle of grouted part or bottom of the rear wall)

Dβ

A B

P2EFe

• Limit equilibrium of the anchoring block

• P1 : wall reaction


C

α

P1

T

θ2E

F

W

R

1

• P2 : uphill active pressure

• Fe : external loads

• W : « net » weight

• T : anchor force

• Rf : friction strength

• Rc : cohesion strength

• φ : friction angle


Dβ

θ1

Rf

Rc

φ 0TPPFWRR 21efc

•34

• Several soil layers => discretisation of the volume in blocks


AB

X

Layer 1

Block1 Block 2 Block n. . .

C

Layer 2. . .

Layer i0

Layer i0 +1

. .


D

Z

Layer i0+n

. .

• Equilibrium of an « isolated block »

Bloc « k »


Bishop assumption

V1(k) = 0 et V2

(k) = 0

V1(k)

V2(k)

H1(k)

H2(k)W(k)

Fe(k)

Ck


Rf(k)

Rc(k)

φk

k

Dk

•35

• Resolving the general equilibriumResolution with « successive equilibriums »: 3n-1 equations, 3n-1 unknowns

P2


Tdst

Fe3+W3

Fe2+W2

Rc3+Rf3

Rc2+Rf2

H2/2=H1/3

H1(k) = H2

(k-1)

Action/Reaction


P1

Rc1+Rf1Fe1+W1

H2/1=H1/2

• Check:

1 10

TT kdsb,

ddsb,


1,10ddsb,

refdref, T 35,1T ddsb,dref, TT

• Tdsb,k : characteristic value of the destabilising force

• Tref k : characteristic value of the anchor force


Tref,k : characteristic value of the anchor force

•36

A B1B2 B3

• Case with several anchors (example)


C1

Wall

α1

C2

α2

α3


D

C3

A B1

Situation 1



C1

α1

C2

α2

α3

T1

T2

T3

Situation 1

All 3 anchors are taken into account


D

C3

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A B2

Situation 2



C1

α1

C2

α2

α3

T2

Situation 2

Only anchor 2 is taken into account


D

C3

A B3

Situation 3α



C2

α2

α3

T2

T3 C1

α1

Anchors 2 and 3 are taken into account


D

C3

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Output: ULS checks / Kranz



Thank you for your attention

Contact us

TERRASOL – Software departmentImmeuble Central Seine42/52, quai de la Râpée75583 PARIS CEDEX 12

FRANCEPhone: +33 1 82 51 52 00

Fax: +33 1 82 51 52 99


Fax: +33 1 82 51 52 99

Email: [email protected]

Website: www.terrasol.com

Logiciel K Rea v3 - Terrasol - Geodeltia file•1 Logiciel K‐Rea v3 Analysis of retaining walls...

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Transcript of Logiciel K Rea v3 - Terrasol - Geodeltia file•1 Logiciel K‐Rea v3 Analysis of retaining walls...