Rak-50 3149 e. l5- Structural Elements and Interfaces

7/27/2019 Rak-50 3149 e. l5- Structural Elements and Interfaces

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Structural Elements andInterfaces

PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES


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Structural elements Numerical analysis in geotechnical engineering generally require the

modelling of structural elements to simulate the behaviour of a structure

being involved in the design.

Structural elements could be modelled as continuum elements and this

would make the analysis very accurate but not convenient from the practical

point of view because the difficulty in generating the FE model.


elements becomes relevant because of the extremely high number of

elements needed and degrees of freedom introduced, thus making the

analysis extremely heavy from the computational point of view.

Furthermore, the output of structural forces, such as shear and normal

force and bending moment, can be obtained from volume elements but only

after integration of stresses which make the design process laborious.


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Structural elements in Plaxis

In order to overtake those difficulties, special finite elements have been

developed, in which the input is simplified and structural forces can be

obtained straightforwardly as output.

Another kind of special element which is very important in geotechnicalanalysis is the interface.

As it is often assumed in practice, the mechanical behaviour at the


,

hypothesis of perfect adhesion.

Hence, it is often assumed that the contact behaviour is linear elastic until

a failure stress is reached, and the behaviour is perfectly plastic henceforth.

Although in this Lecture special focus is given to those elements which are

implemented in PLAXIS finite element code, the formulation of structural

elements is general and similar elements can be found in other commercial

FE codes


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Structural elements in Plaxis

Plates and shells

(walls, floors, beams, tunnels)

Anchors


Geogrids (geotextiles)

Interfaces


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Plates and shells

3 or 5 noded line elements

3-noded beam elements are used in combination with 6-noded triangular

elements for the continuum, whereas 5-noded beams are used with 15-noded elements

3 degrees of freedom per node (horizontal and vertical displacement and rotation)


-

The out-of-plane dimensions depend on the type of analysis: it is a unit

thickness in plane strain, 1 rad in axisymmetry

To model walls, floors, tunnels


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Input parameters for plates

Flexural rigidity (b=1 m)

Normal stiffness (b=1 m)

Element thickness where d is the real (physical)structure of the sheet.

12

3bh

EEI

=

bhEEA=

12EI

d hEA

=

The flexural and axial rigidity of the structural element are input parameters:


b

hh

b

b = 1 m in plane strain

b = 1 meter in axisymmetry

completed by Poissons ratio .


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Plate weights

Compensate for overlap:( )

concrete soil realw d =

For soil weight use: unsat above phreatic level

sat below phreatic level



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Plate weights for tunnels

rinside

routsider

dreal

Special curved elements are specifically designed for tunnels.


Overlap is only for half the lining thickness

lining soil

( )outsideinside

rrr +=2

1

( )realsoilrealconcrete

ddw2

1=


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Boundary conditions

PLAXIS offers several alternatives depending on the particular kind of fixitythat has to be modelled.

By default, a structural element is free to rotate even if intersecting theexternal boundary of a mesh, unless a boundary condition is explicitlyspecified.

In order to prevent horizontal displacements on the left and right side of themesh and horizontal and vertical displacements at the bottom, PLAXIS offersthe standard fixities option.


Fixed rotation

X

Y

0

1 2

3

4 5

6

Free rotation

plate Rotation fixed at (partly) fixedboundaries

Rotation free at freeboundaries

ur ermore, s requ re o prescr e some ex ra con on, e.g. prevenrotations at the one end of the beam, the Moment fixity option has to beselected and applied to the desired end.


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Hinges

5

6

7

8

Rotation

Spring data:

Stiffness

Min/Max moment


Hinged connection

Rigid connection


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Determination of eff. plate weights

Material parameters:E= 20106 kPa

= 0.2

= 24 kN/m3

Plate:

d= 0.4 m

12

3bh

EEI

=

bhEEA =

EA

EIhd 12==


I= bd3

/ 12 = 1(0.4)3

/ 12 = 5.3310-3

m4

A = bd = 10.4 = 0.4 m2

wnet = wgross - soil d

EI 1105 kNm2/m

EA 8106 kN/m

wnet= 0.4 24 - 18 0.4 = 6.0 kN/m2


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Wall:

d= 0.2 m

I = 1(0.2)3 / 12 = 6.6710-4 m4

= = 2

Determination of eff. plate weights


. .

wnet = wgross - soil d

EI 0.13105 kNm2/m

EA 4.0106 kN/m

wnet = 0.2 24 - 18 0.2 = 3.0 kN/m2


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Determination of soil stiffness

Stresses at reference point

Initial stress:

' = 5 18 = 90 kPa (initial stress)


Initial pre-consolidation stress:c = 5 18 + 20 = 110 kPa ( pre-consolidation)

c = max. stress that ref. point has ever experienced in the past

5 m = depth of reference point (before excavation)

18 kN/m3 =unit weight of the soil

20 kPa = this is an assumed pre-overburden pressure (POP)

at soil surface, characteristic for the region considered


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Determination of soil stiffness

After excavation:

(0)

= 2.5 18 = 45 kPa

(0) = real vertical stress after excavation in reference point

2.5 m = depth of reference point after excavation

Stresses at reference point


18 kN/m3 =unit weight of the soil

After loading:

(2) = 45 + 6 + 125 = 176 kPa

(2) = real vertical stress after loading

45 kPa = ((0) see above)

6 kPa = weight of the floor

125 kPa = 2 200 kN + 2 300 kN (point loads) / 8 m (width of floor)


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Parameters for Mohr-Coulomb model

0

0.5

1

1.5

0 50 100 150 200 250 300 350 40

(kPa)

Assume the sample originatesfrom the reference point.Unloading from ' to 0 andreloading from 0 to ' does not


2

2.5

3

3.5

(

%)

behaviour)

From unloading/reloadingcurve, from ' to c (from 90 kPa to 110 kPa):

From primary loading curve from c to 2(from 110 kPa to 176 kPa):


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Parameters for Mohr-Coulomb model

0

0.5

1

1.5

0 50 100 150 200 250 300 350 400

(kPa)

(%)Combined:


2

2.5

3

3.5

%1.121 =+=

8690176 ==

7800

%1.1

86==

=

oed

E

4.0'=

kPa

( ) 364078002.06.0

4.1'21

'1

'1' =

+=

oedEE

kPa


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Fixed-end anchors

Elastic-perfectly plastic spring elements are provided: one end is fixed (nodisplacements allowed), the other end is connected to one node of the mesh.

These elements can be useful when modelling a symmetric problem, like anexcavation supported by props, in which, for symmetry reasons, one end of theanchor is prevented to move.

Input parameters are the axial rigidity EA, the spacing Lspacingand themaximum axial forcewhich can be applied to the anchor.



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Fixed-end anchors For the cases in which there is no logical reason to assume that the end will stay

fixed, PLAXIS provides node-to-node anchors, in which two nodes of the mesh areconnected by means of elastic-perfectly plastic spring elements.

Plate anchor is a typical examples of application of node-to-node anchors. An anchordesigned to support a diaphragm wall is connected to a vertical plate which mobilizes

passive thrust to increase the stabilizing forces.

A cofferdam consists in a dam obtained by enclosing a portion of the groundbetween two walls. This is yet another typical application of node-to-node anchors.


,

axial forcewhich can be applied to the anchor. A pre-stress can be assigned to theanchor by a double-click on the structural element.


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Geogrids

Geogrids are purely elastic elements with normal stiffness but no flexural rigidity.They cannot sustain compressive forces and they are connected to the finiteelement mesh by 3 or 5 nodes, depending on the type of finite element used in themesh (6 or 15-noded elements).

Geogrids are often used to model reinforced earth structures, geotextiles andanchors



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Geogrids

Structural elements are often

combined together to simulate the

mechanical behaviour of real

engineering structures, such as

grouted anchors, which are

modelled through a combination of

node-to-node anchors and


geogrids.


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Interfaces

Interfaces are special elements particularly thought for the soil-foundationinteraction.

Their effect is a reduction of contact friction, thus enabling a more realisticmodelling of the mechanical behaviour than a perfectly glued contact type, whichwould be what one obtains without introducing any interface.

Therefore, interface elements allow relative displacements between structureand subsoil.

As usual with special elements, the number of nodes used depends on the


element type used for the soil: 6-nodes 3-integration points interface elementsare used in combination with 6-noded finite elements, 10-noded 5-integrationpoints interface elements are used with 15-noded elements.


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Interfaces

The mechanical behaviour of interface elements is described as function ofsurrounding elements.

An elastic-perfectly plastic constitutive law is assumed, where the strength isobtained from the surrounding soil according to:

inter inter soilc R c= inter inter soil

tan R tan =

The user is requested to input the reduction factor Rinter and the strength


parameters of the interface elements are determined from the strength of soil fromequations above

Typical values which can be given to the reduction factor are given as follows:

Materials interaction: Rinter:

Clay/Steel 0.5

Sand/Concrete 1.0 - 0.8

Sand/Steel 2/3

Clay/Concrete 1.0 - 0.7

Soil/Geotextile 1.0Soil/Geotextile 0.9 - 0.5


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Interfaces Interface elements are used to reduce the high gradients of stress which areobserved in proximity of sharp edges of structural elements.

As shown in Figure, the stress distribution can be smoothened by extending theinterfaces well beyond the edges.



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Interfaces Another common use of interfaces is to make retaining walls (modelled byplates) impermeable (consolidation or flow problems)


Rak-50 3149 e. l5- Structural Elements and Interfaces

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