rak-50 3149 e. l5- structural elements and interfaces
TRANSCRIPT
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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.
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
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
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
,
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
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
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)
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
-
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:
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
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
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
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Plate weights for tunnels
rinside
routsider
dreal
Special curved elements are specifically designed for tunnels.
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
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.
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
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
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
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==
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
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
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
. .
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)
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
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
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
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
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
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:
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
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.
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
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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.
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
,
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
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
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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
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
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
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
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
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
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.
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
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Interfaces Another common use of interfaces is to make retaining walls (modelled byplates) impermeable (consolidation or flow problems)
PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES