Lecture 01 - Introduction to Finite EM.pdf

Introduction to Finite Element Modelling

1. Introduction to Finite Element
Method (FEM)
Dr. K. H. S. M. Sampath
Department of Civil Engineering
University of Moratuwa
1

2. 2
Why study FEM ?
•FEM has become an integral part of the design and development of
numerous engineering systems
•Aerospace industry
•Automotive industry
•Electrical (Transformer, Relays, etc.)
•Electronics (Integrated circuits, Appliances, etc.)
•Power industry (Nuclear, Thermal)
•Construction
•Healthcare (implants, devices, etc.)

3. Introduction
•In engineering problems ,along with the differential equations, we also have additional
constraints called the boundary conditions (BCs)
•Differential equations + BCs→ Boundary value problem (defined for a specific domain or geometry)
33

4. •Analytical methods (Direct integration, Laplace transforms, etc.) are applicable only for
simple geometries
Solutions to boundary value problems
Numerical methods•How do we handle complex geometries ?
4

5. •FEM is a numerical method used to obtain an approximate solution
for a given boundary value problem
•Linear system of equations are solved using a computer
(Ex: Gauss elimination algorithm)
What is finite element method (FEM)?
Differential
Equation +
BCs
5
FEM
Linear system
of equations
(Ax=b)

6. Initial value and Boundary value Problems
OfteninEngineeringanalysis,thegoverningequationscorrespondingtoagivenproblemis
expressedasadifferentialequation.Thecompleteproblemcanbedefinedonlyif,inadditionto
thegoverningequation,theinitialconditionorboundaryconditionsofacombinationofbothare
expressed.
6

7. Initial value and Boundary value Problems
Some examples of civil engineering problems
1. A cantilever beam2
2
()d Mx
dx EI

=
Governing equation Initial condition0,()0
()
0, 0
xx
dx
x
dx


==
==
2. A body of mass “m” in motion
m
Force, F(t)
Displacement, u(t)
Initial condition2
2
() ()
()
dutdut
m c Ft
dt dt
+=
Governing equation Initial condition0
0,()0
()
0,
tut
dut
tu
dt
==
==
7

8. Initial value and Boundary value Problems
Some examples of civil engineering problems
3. Aloaded rectangular plate
Governing equation
Inthisequationwdenotesdeflection
inzdirectionduetotheloadp
zon
surfacex-y.ThetermDdenotes
thebendingorflexuralrigidityoftheplate
expressedas,
Boundary conditions(,0)0, (,)0
(,0) (,)
0, 0
wx wxb
wx wxb
dy dy
==

==
8
Fixed

9. Initial value and Boundary value Problems
Some examples of civil engineering problems
4. Steady state flow of a quantity (heat, mass, etc)312
1 2 3
()VVV Volume
Q
xxx t
 
++= =
 
Governing equation
Boundary conditions
Forflowofwaterthroughsoilswecan
furthersimplifytheaboveequation
usingDarcy’sequationasfollows.1 1 2 2 3 3
1 2 3
, ,
h h h
Vk Vk Vk
x x x
  
=− =− =−
   1 2 3
2 2 2
1 2 32 2 2
0
h h h
k k k Q
x x x
  
+ + +=
  
Thiskindofproblemsaredifficult
tosolveanalytically.
9
Impermeable
boundarywhere
flowrateiszero
flow
permeableboundarywhere
head,hcanbespecified
Flowdomain

10. Initial value and Boundary value Problems
Some examples of civil engineering problems
5. Concrete dam problem
Impermeable dam
(a flow boundary)
Different material properties and
material behaviour
Complex boundary
conditions
•Problemcombinesseveralgoverningequations.
•Thiskindofproblemsaredifficulttosolveanalytically.
10

11. Initial value and Boundary value Problems
Some examples of civil engineering problems
6. Deep excavation with multiple levels of supports
Bothverticalandlateraldisplacementsareassumedtobezero
lateral displacements are
assumed to be zero
11
Anchors
Sheetpile
Mechanically
stabilized wall
Excavatedarea
Existing
structures
•Thiskindofproblemsaredifficulttosolveanalytically.
•Analyticalmethodssuchasforcebalancemethodfailtosolvefordeformations.

12. Engineering design
Physical Problem
Mathematical model
Governed by differential
equations
..General scenario..
Numerical model
e.g., finite element model
(Approximate solutions)
Finiteelementanalysis(FEAorFEM)canbeeffectivelyusedtoobtainanapproximatesolutionfor
engineeringproblemsinvolvingcomplexgeometry,complexboundaryconditions,differentmaterial
properties,etc.
12
Analytical solutions
Exact solutions
(Closed-form solutions)

13. Mathematical Treatment
13

14. Finite Element Method –Discretization
Finiteelementanalysis(FEAorFEM)isbasedonideaofbuildingcomplicatedobjectwithsimpleblocksor
dividingacomplicatedobjectintosmallandmanageablepiecesknownasfiniteelements.
Elements
Nodes
Elements are connected to each other at nodes and
full continuityis usually maintained at the nodes.
The load vs displacement relationship (constitutive
relationship) of an element is given by the stiffness
matrix (element stiffness matrix).
Once the elements are assembled to form the idealized
physical problem, the load displacement relationship of
the entire system is called the global stiffness matrix.
14
During FEM, the global stiffness matrix is solved for
unknowns to find the displacement at each node.
Polynomial functions are
widely used to define nodal
displacements.

15. Finite Element Method Discrete structural systems and discretized continuum
Steeltowers,trusses,
portalframesaresome
examplesfordiscrete
structuralsystems.
Indiscretestructuralsystems,theelements
andnodesarereadilyidentifiable.
Elements
Nodes
Nodal displacements
Finite element model
Physical model
Indiscretizedcontinuums,weneedto
definetheelements(i.e.,Meshing).
Almostallthegeotechnicalproblems
arediscretizedcontinuums.
Element
Node
Indiscretestructuralsystemsthestiffness
matrixis“exact”
Indiscretizedcontinuums,thestiffness
matrixis“approximate”(i.e.,solution
issensitivetothediscretization(mesh) 15

16. Finite Element MethodDiscretized continuum
Meshing of a geotechnical problem
ElementsNodes Relativelylargeelements(coarsermesh)nearmodel
boundariessincewedon’tneedaccurateinformation
nearboundaries
Smaller elements(finer mesh)
in the areas where more
accurate information is needed.
16

17. 6
Discretization
Process of Finite Element Method
17

18. 18
1
34
Node
2
Process of Finite Element Method
Global Stiffness Matrix

19. •Start with the boundary value
problem
•Write the weighted residual
statement
•Obtain the weak form
•Use interpolation equation for
element quantities
•Assemble to obtain global
quantities
19
Process of Finite Element Method

20. General Procedure in Finite Element Method
•Preprocessing
–Definethegeometricdomainoftheproblem(identifyboundariesanddimensions).
–Definethephysicalconstraints(boundaryconditions).Definetheloadings.
–Definethematerialpropertiesoftheelements(someformofloaddisplacementrelationship).
–Definetheelementgeometriesandconnectivities(meshthemodel).
•Analysis
–computestheunknownvaluesoftheprimaryfieldvariable(s)(i.e.,displacement,etc.)atthenodes.Valuesat
locationsotherthannodesareinterpolated.
–computedvaluesarethenusedtocomputeadditional,derivedvariables,suchasreactionforces,elementstresses
andstrains,andetc.
•Postprocessing
–Postprocessorsoftwarecontainssophisticatedroutinesusedforsorting,printing,andplottingselectedresultsfrom
afiniteelementsolution.
20

21. Advantages of FEM
• Can readily handle complex geometry
• Can handle complex analysis types:
➢Vibration
➢Transients
➢Nonlinear
➢Heat transfer
➢Electricity transfer
➢Fluids
• Can handle complex loading:
➢Node-based loading (point loads).
➢Element-based loading (pressure, thermal, inertia forces).
➢Time or frequency dependent loading.
• Can handle complex restraints/boundary conditions
• Composite structures (i.e., soil + steel) can be analyzed 21

22. Advantages of FEM (contd..)
•Can handle bodies comprised of nonhomogeneous materials:
➢Every element in the model could be assigned a different
set of material properties.
• Can handle bodies comprised of non-isotropicmaterials:
➢Orthotropic (different in perpendicular directions)
➢Anisotropic
• Special material effects are handled:
• Temperature / stress dependent properties.
➢Plasticity
➢Creep
➢Swelling
• Special geometric effects can be modeled:
➢Large displacements (e.g., flow problems).
➢Large rotations.
➢Contact (gap) condition (e.g., cracks, fractures).
Direction dependent
material behaviour
22

23. Disadvantages of FEM
•Aspecificnumericalresultisobtainedforaspecificproblem.Ageneralclosed-
formsolution,whichwouldpermitonetoexaminesystemresponsetochangesin
variousparameters,isnotproduced.
•TheFEMisappliedtoanapproximationofthemathematicalmodelofasystem
(thesourceofso-calledinheritederrors.)
•Experienceandjudgmentareneededinordertoconstructagoodfiniteelement
model.
•ApowerfulcomputerandreliableFEMsoftwareareessential.
•Inputandoutputdatamaybelargeandtedioustoprepareandinterpret.
23
A Golden Rule in FEM:
You need to know the answers to the problem before going into the FE analysis.

24. Idealization of Geotechnical
Problems
24

25. Outline
➢The need for modelling of Geotechnical Engineering problems - Deep Excavation
➢Steps involved in FE modelling of geotechnical problems
➢Geometric idealization of the problem
➢Subsurface idealization and assigning external loads
➢Selection of material models and parameters
➢Assigning model boundaries and modelling of lateral supports
➢Define initial stresses
➢Simulation of construction sequence
➢Modelling of ground water and dewatering
➢Interpretation of the results of FE analysis
➢Other issues
➢Monitoring and interpretation of monitoring results
The following case studies will be explained at the relevant sections of the outline
Case study 1: Capitol twin peaks building deep excavation
Case study 2: LTL building deep excavation
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26. The Need for Modelling of Geotechnical Problems -Deep Excavations
Deepexcavationsforbasementetc.havebecomeanessentialpartinmodern
dayandtheseconstructionsaretobedoneinurbanenvironmentswithmany
otherdevelopmentsatverycloseproximity.Disturbancetoexistingfacilities
shouldbemademinimumbothduringtheconstructionandoperationstages.
Movements,deformationsintheneighboringstructuresshouldbemade
minimumbyappropriatedesignsandconstructiontechniquessupportedby
adequatemonitoring.
Responseofthesubsoiltotheproposedexcavationshouldbeassessedby
accuratemodelling.
Deformationcontrolisthemaintask,andtheexcavationsupportstructure
shouldbelaterallysupportedatnumberoflocations.
Thefoundationconditionofexistingbuildingsshouldbeaccuratelymodelled.
ForStaticallyindeterminateproblem,Limitequilibriumorempiricalmethodsarenotadequate.NumericalmethodssuchasFinite
Elementmethodshouldbeused.
Thebehaviourofthesoil;drained,undrained,consolidationtobemodelledusingappropriateconstitutivemodels.Insitu(SPT,CPT,
pressuremeter,etc)andlaboratorytests(triaxial,centrifugemodelling,etc)tobedonetoobtainparameters.
UserfriendlyCommercialsoftwareisavailable,butshouldbeusedwithaproperunderstanding.Needtomodelthecompleteprocess.
26

27. •Modelling of these excavations with the finite element technique commenced in late 1970’s.
•Considerable advances were made in 1980, 1990s to date.
•Advanced made in the process of numerical simulation were aided by comparisons done with monitored
ground response and acquiring data on necessary soil characteristics.
Comparison of
stress distribution
27
Evolution of the Modelling of Geotechnical Problems
Comparison of
deformationInstrumentation usedBell Common Tunnel (1984)

28. Steps Involved in FE Modelling of Geotechnical Problems
1.Create the geometry model (2D idealization, model dimensions, soil layers, external
loads, structures and other elements, drains, wells etc)
2.Input material parameters (including interfaces)
3.Define the geometric boundary conditions (displacement boundary)
4.Generating the mesh
5.Define initial p.w.p and initial effective stress conditions (whenever applicable water
flow boundary and consolidation boundary shall be defined here)
6.Simulation of construction sequence (structures, excavation, fill, dewatering, anchors
(including prestressing), props, geogrids, etc)
7.Interpretation of results
28

29. Geometric Idealization of the Problem
This involves 2D idealization of complex 3D problems. Idealization can be made using plain strain or
axisymmetric idealization.
Plain Strain Idealization
Examples of plain strain idealization
➢Highway embankments
➢Rectangular or strip footings
➢Deep excavations with rectangular plan view
➢Slopes
➢Retaining walls
➢Tunnels and pipe lines
Actual problem
2D idealized
problem
29
Examples of axisymmetric idealization
➢Circular and square footings
➢Deep excavations with circular plan view
➢Problems with rotational symmetry around an axis
Note: If axisymmetric idealization is used, the
subsurface layers must be modelled as horizontal layers
Axisymmetric idealization
2D idealized
problem
Actual problem

30. Geometric Idealization of the Problem
Plain Strain Idealization
Actual problem
2D idealized
problem
30
Axisymmetric idealization
2D idealized
problem
Actual problem
•Strains can only take place in the xyplane.
•Along the longitudinal axis (out of plane direction)
the strain is assumed to be zero, ε
z
= 0.
•Consequently, the length of the excavation must
be significantly larger than the width of the
excavation.
•The axisymmetric model means the lateralor the radial
strains of the model are equal in all direction, ε
x=ε
z.
•The model is symmetrical along the vertical Y axis and
the model is rotated at the Y axis, hence the model in
Figure results in a circular excavation.
•Note: in Plaxisthe rotating axis is always at the left
boundary.

31. Several cross sections may be selected for the analysis considering the subsurface variations, external loading conditions
and the geometry of the problem (i.e., excavation depths, fill heights, support conditions, ground water conditions, etc.)
* Plain strain idealization is used to idealize the problem in 2D
Cross-sections considered in the analysis
considering various excavation regions
Case 1: Capitol twin peaks project, Slave Island
This is a multi-level excavation that goes up to a maximum of 14.3 m depth.
31
Geometric Idealization of the Problem

32. Subsurface Idealization
Boreholes or any other geotechnical investigation data close to the sections shall be utilized in the idealization of
subsurface. Since the length of the sections is large compared to the excavation depth, LHS and RHS were modelled
separately.
32
Case 1: Capitol twin peaks project, Slave Island

33. Sections D-D is also selected for analysis since the subsurface
is relatively weak and the excavation depth is relatively high
Section D-D
33
Subsurface Idealization
Case 1: Capitol twin peaks project, Slave Island

34. 34
Subsurface Idealization
A Typical borehole log
A sub soil profile deduced with five boreholes

35. BH-01 and BH-02 were advanced close to
Section A-A Left. Considering the subsurface
characteristics at both boreholes, subsurface at
BH-02 was used in the modelling of Section A-A
Left
Maximum excavation depth
through Section A-A
Similar reasoning was used in the idealization of
subsurface through other sections
35
Subsurface Idealization
Case 1: Capitol twin peaks project, Slave Island

36. Case 2: LTL mix development, Kollupitiya
Geometric Idealization of the Problem
This requires an excavation of 16.25 m for the construction of five basement levels. With reference to the borehole and
structural details, Section X-X was considered as the critical section. The clear distance between the diaphragm walls
laterally supported by props without corner bracings is maximum at this section when the tapered shape is considered.
BH-01
BH-02
BH-03
BH-04
•Plain strain idealization is
used to idealize the problem
in 2D.
•Considering the symmetry of
the subsurface and loading
conditions through Section
X-X, only one half of the
geometry was modelled.
36

37. Subsurface Idealization
BH-01
BH-02
BH-03
BH-04
Case 2: LTL mix development, Kollupitiya
Since limited number of boreholes were advanced at the site and
all the boreholes revealed somewhat similar subsurface
characteristics with BH-01 and BH-02 showing a relatively weak
subsurface. Considering the above, subsurface revealed through
BH-01 and 02 have been conservatively employed in modelling the
subsurface of the section analysed.
37

38. Assigning External Loads
If the structures applying external loads are not present on the retained side of the wall, a minimum obligatory surcharge
of 10 kN/m
2
were applied as per the BS 8002 guidelines.
If the structures on shallow foundations are present on the retained side, a surcharge of 10 kN/m
2
– 20 kN/m
2
per floor
(depending on the importance of the structure) is applied on the retained side.

Point loads shall be converted to line loads by dividing from the effective length.
P
P
P
x
Line load = P/x
38

39. Selection of Material Models and Parameters for Structural Elements
Commonly used material models in Geotechnical Engineering Problems
•Linear elastic model
•Mohr-Coulomb (MC) model
•Soft Soil Model
•Hardening Soil Model
•Soft Soil Creep
•Hardening Soil with Small Strain
•Modified Cam-clay
39

40. Selection of Material Models and Parameters for Structural Elements
Some of the widely used material models are discussed here.
Linear Elastic Model
This model uses Hooke’s law of isotropic linear elasticity. The linear elastic model is too limited for the simulation of soil
behaviour. It is primarily used for still structural elements in soil (concrete, masonry, sound rock, steel, timber, geogrids, etc.)
40

41. Selection of Material Models and Parameters for Structural Elements
OedometricModulusofDeformation(E
oed)
•Theresultsfromoedometrictestarerepresentedintermsof
oedometriccurve(Δε=f(Δσ
ef)).
•Ifthestress-straincurveisreplacedforacertainintervaloftwo
neighboringstressesσ
1ef-σ
2efbyasecantline,itisacceptableto
assumealinearbehaviorofsoilwithinthisintervalandrepresent
thesoilcompressibilitybyasΔσ
ef/Δε-calledtheoedometric
modulusofdeformation.
•Theoedometricmodulusofdeformationis,therefore,asecant
moduluslinkedtoacertainstressintervalσ
1ef-σ
2efselectedon
thestress-straindiagramΔε=(Δσ
ef)
41

42. 2D Modeling of different types of Embedded Walls using Plate Elements
Soldier Pile Walls
A soldier pile wall can be modelled by two plate
elements. One plate for the timber lagged section and
another plate for the embedded section of the wall.EA= EI=
Plate properties for the timber lagged section
42

43. 2D Modeling of different types of Embedded Walls using Plate Elements
Contiguous bored piled or secant piled walls
s
D
s
??????=
????????????
2
4
�
??????=
????????????
4
64
�
43
Secant Piled Wall
Secant Piled Wall
Contiguous bored
Piled Wall

44. 2D Modeling of different types of Embedded Walls using Plate Elements
D = thickness of the plate
Unit width
Normal stiffness, EA
where A = D × 1
Bending stiffness, EI
where I = 1/12×1× D
3

44
Diaphragm walls

45. Selection of Material Models and Parameters for Soils
Different definitions of E during drained loading of soil
50% of
q
peak
Relationship between undrained and drained
Young’s modulus
Relationship between drained Young’s modulus
and shear modulus, G and Oedometer modulus,
E
oed
45
Stiffness parameter (E
i) of soil predicts the ground movement.
E
i – Soil stiffnes at i
th
stress level
Eg: E
50 – Stiffness at stress level of 50% of the ultimate strength
E
ur-soil unloading –reloading stiffness modulus

46. Mohr Coulomb Model
•Mohr-Coulomb is widely adopted by practicing engineers to
model the soil behaviour. In Mohr Coulomb model, non-
linear soil behaviour is modelled as a linear elastic –
perfectly plastic relationship.
•Thesoilstiffness,takenasE
50,isconstantthroughoutthe
elasticzone,untilthestressstatereachestheplastic(failure)
zone.
•Inreality,thesoilbehavesnon-linearlywhichmeansthesoil
stiffnessisneverconstant,insteaditchangeswiththestress
levelwithinthesoilmass.
•Therefore,
•Atstresslevellessthan50%oftheultimatestrength,
theMCmodelwillover-predictthegroundmovement,
•Atstresslevelhigherthan50%(meansfactorofsafety
lessthan2)itcandangerouslyunderpredictthe
groundmovement.
Mohr Coulomb model
50% of q
peak
Overpredicts
deformation
Largely underpredicts
deformation
46
Selection of Material Models and Parameters for Soils

47. 47
Mohr Coulomb Model
Selection of Material Models and Parameters for Soils
•MC model assumes the soil unloading –reloading stiffness modulus,
Eur, equal the soil loading stiffness, E50,
i.e., E
ur=E
50
•Under unloading-reloading condition, soils generally have much stiffer
modulus compared to under loading condition.
•The unloading-reloading stiffness can be easily higher by a factor of 2
to 5 as compared to the loading stiffness
i.e., E
ur≈ 2~5 E
50
•This means that when applied to evaluate excavation problems, the
MC model will generally over predict the soil heave in an unrealistic
manner.
•Due to this reason, in excavation problem, when MC model is adopted,
it is suggested to input the soil stiffness in E
urvalue rather than E
50.

48. Expected Material Behavior in Excavation Problems
Mohr Coulomb
model generally
overpredicts
ground heave due
to use of E
50 in
the model
48
Mohr Coulomb Model
Selection of Material Models and Parameters for Soils
Material Behaviourin Excavation Problem
•Consider a typical excavation problem with the stress paths
experienced by soil mass below the excavation level and behind the
retaining wall.
•Soils at point B (below the excavation level) undergo unloading
case at all construction stages.
•Soils atpoint A (behind the retaining wall) goes through
several changes,
•at stage 1 it undergoes unloading,
•at stage 2 (prestressing) it undergoes reloading,
•at stage 3 again it undergoes unloading.
•Soils below excavation behaves with Eur, even soils behind
wall behaves between Eurand E50.
•Use of E50 is too conservative.
The soil stiffness for isotropic loading, shearing and unloading-reloading can be
automatically catered for in the model Hardening Soil model. Therefore, it predicts
more realistic wall deformations, bottom heave, and settlement trough behind wall.

49. Mohr Coulomb model requires a total of five parameters, which can be obtained through basic testing
Instead of using Young’s modulus as a stiffness parameter, alternate stiffness parameters can also be used.
49
Mohr Coulomb Model
Selection of Material Models and Parameters for Soils

50. Modelling of Undrained Behaviour
•It is the common understanding that analyzing undrained behaviour of clay, has to be done with total strength
parameters, S
u or c
u, f
u = 0, and undrained/total stiffness parameters, E
u and undrained Poisson’s ratio, n
u=0.5.
•However, in many FEM codes, the undrained analysis is often calculated by effective stress approach.
50
Selection of Material Models and Parameters for Soils

51. Modelling of Undrained Behaviour in Mohr Coulomb model
There are three combination of input in modelling the undrained shear strength
51
Selection of Material Models and Parameters for Soils
Real
C
u
MC
model
C
u

52. Modelling of Undrained Behaviour in Mohr Coulomb model
52
Selection of Material Models and Parameters for Soils
Undrained (A) Analysis
The Drainage type Undrained (A) enables modelling undrained behaviourusing effective parameters for stiffness and strength.
The characteristic features of method Undrained (A) are:
• The undrained calculation is performed as an effective stress analysis. Effective stiffness and effective strength parameters
are used.
✓Undrained shear strength suis not an input parameter but an outcome of the constitutive model.
✓When material type is selected as “Undrained”, PLAXIS will automatically add bulk modulus of water to effective
stiffness parameters of soil, transforming E
50’ and ʋ’ into E
uand ʋ
u.
• Pore pressures are generated, but may be inaccurate, depending on the selected model and parameters.
•Since pore pressure are generated, it enables the determination of effective stresses during plastic calculations.
• Advantage of using effective strength parameters in undrained conditions is that the increase of shear strength with
consolidation is automatically obtained.

53. Modelling of Undrained Behaviour in Mohr Coulomb model
Since soil behaviour is always governed by effective stresses, undrained A is a preferable method in modelling undrained behaviour of
clay. It can predict the excess pore water pressure in a relatively accurate manner, and increases of shear strength during consolidation
can be calculated.
However, care must be taken if Mohr Coulomb soil model is adopted as undrained A may over predicts the undrained shear strength.
53
Selection of Material Models and Parameters for Soils

54. Modelling of Undrained Behaviour in Mohr Coulomb model
54
Selection of Material Models and Parameters for Soils
Undrained (B) Analysis
The Drainage type Undrained (B) enables modelling undrained behaviourusing effective parameters for stiffness
and undrained strength parameters.The characteristic features of method Undrained (B) are:
• The undrained calculation is performed as an effective stress analysis.
• Effective stiffness parameters and undrained strength parameters are used.
• Pore pressures are generated, butmay be highly inaccurate.
• Undrained shear strength s
uis an input parameter.
• Consolidation analysis should not be performed after the undrained calculation. If consolidation analysis is
performed anyway, s
umust be updated.

55. Modelling of Undrained Behaviour in Mohr Coulomb model
55
Selection of Material Models and Parameters for Soils
Note: Under undrained loading, the MC model will follow an
effective stress path where mean effective stress p’ remains
constant until failure. However, soft soils like NC clay and
peat will follow an effective stress path in undrained loading
where p’ reduces significantly.

56. Modelling of Undrained Behaviour in Mohr Coulomb model
56
Selection of Material Models and Parameters for Soils
Undrained (C) Analysis
The Drainage type Undrained (C) enables simulation of undrained behaviourusing a total stress analysis with undrained
parameters. In that case, stiffness is modelled using an undrained Young's modulus E
uand an undrained Poisson ratio ν
u, and
strength is modelled using an undrained shear strength c
u(s
u) and φ = φ
u= 0°. The characteristic features of method
Undrained (C) are:
• The undrained calculation is performed as a total stress analysis.
•Material type is used as non-porous or drained
• Undrained stiffness parameters and undrained strength parameters are used.
• Pore pressures are not generated.
• Undrained shear strength s
uis an input parameter.
• Consolidation analysis should not be performed after the undrained calculation. If consolidation analysis is performed anyway,
s
umust be updated.
•Disadvantage of this approach is that no distinction is made between effective stresses and pore pressures. Hence, all
output referring to effective stress should now be interpreted as total stresses and all pore water pressures are zero.

57. Modelling of Undrained Behaviour in Mohr Coulomb model
57
Selection of Material Models and Parameters for Soils
Compatible material models for different undrained types
For further reference:
PLAXIS Fundamental -Modelling of Undrained Behavior
https://youtu.be/-dxX3A7yJ5Y

58. The lesson learned is: while it is generally true that drained condition govern the safety of retaining wall, when facing excavation
in very soft clay, it is also very important to check the undrained behaviour in both undrained A and B as well.
58
Modelling of Undrained Behaviour in Mohr Coulomb model
Selection of Material Models and Parameters for Soils
Singapore Nicoll highway deep excavation failure on April 21, 2004 gives
very valuable lessons in modelling the undrained behavior of soft clays.
The investigation report revealed the importance of analyzing both Undrained A and Undrained B methods
(Magus et al, 2005). In this Nicoll highway case, the undrained B showed more critical results.

59. Hardening Soil Model
The real soil stress strain behaviour shows that when loaded, the soil behaves nonlinearly. As the load goes higher the
stiffness modulus of the soil becomes lower and lower.
•This non-linear stress strain behavior can be approximated by
hyperbolic model developed by Duncan & Chang, 1970.
•In Plaxis, this hyperbolic model is known as Hardening Soil
model (HS model), and often applied in evaluating soft soil or
hard ground condition.
59
Selection of Material Models and Parameters for Soils

60. 60
Hardening Soil Model
Selection of Material Models and Parameters for Soils

61. (Reference confining stress)
The strength parameters of Hardening soil
model coincide with those of the Mohr
Coulomb model (i.e. c
/
, f
/
)
Undrained behaviour can be modelled
using undrained Type A and Undrained
type B in hardening soil model
61
Required parameters for Hardening Soil Model
Selection of Material Models and Parameters for Soils

62. Soft soil and Soft soil creep model
Indeed, most soft soil problems can be analysed using Hardening soil model, but the Hardening Soil model is not suitable
when considering very soft soils with a high compressibility, i.e E
ref

oed = E
ref

50 < 0.5. For such soils, the Soft Soil model or soft
soil creep model may be used.
A feature of soft soils is the linear stress-dependency of soil stiffness.
In Soft soil creep model modified creep index, m* is required in addition to the
above parameters
C
c, C
s can be determined through a laboratory
consolidation test
C
a is the coefficient of secondary consolidation 62
Selection of Material Models and Parameters for Soils

63. Obtaining Geotechnical Parameters from Commonly used Tests in Sri Lanka
Undrained shear strength
T is the measured torque
D and H being the diameter, i.e., the width of two blades, and height. The
equation for K assumes a uniform distribution of shear strength across the
ends and perimeter of the cylinder.
For many vanes, H/D = 2 and so K = 3.66D
3
.
Vane shear test
NC
OC
63
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&#3627408482;=????????????
??????&#3627408483;

64. Standard Penetration Test
Stroud and Butler’s correlation
plasticity index
Cone Penetrometer Test
64
Obtaining Geotechnical Parameters from Commonly used Tests in Sri Lanka
Undrained shear strength

65. SPT test
Peak (φ) and constant-volume (φcv) angles of shearing resistance of siliceous sands
and gravels:
Clay’s constant-volume angle of shearing resistance (φcv) from its plasticity index (Ip)
65
Obtaining Geotechnical Parameters from Commonly used Tests in Sri Lanka
Drained shear strength
Constant volume →Critical state
In the critical state, a soil has undergone
sufficient shearing and deformation such
that it has reached a state of equilibrium
characterized by constant volume and
constant effective stress.

66. Drained shear strength parameters and
drained Young’s modulus
CPT test
for poorly graded sands
situated above the water table
66
Obtaining Geotechnical Parameters from Commonly used Tests in Sri Lanka

67. Drained Young’s modulus using SPT
and CPT
67
Obtaining Geotechnical
Parameters from Commonly used
Tests in Sri Lanka

68. Undrained Young’s modulus using s
u
68
Obtaining Geotechnical
Parameters from Commonly used
Tests in Sri Lanka

69. ArangeofvaluesforPoisson’sratiosobtainedfromliteratureforvarioussoiltypesaregiveninthetable
below.
➢Generally,avalueof
▪m=0.3-0.35forsandsand
▪m=0.4–0.5forclaysareused
Typical drained Poisson’s ratio values
69
Obtaining Geotechnical Parameters from Commonly used Tests in Sri Lanka

70. Interface Shear Strength Parameters
Numerical analysis shows that the lower the interface shear strength parameters (c
a and ), the larger the bending
moment.
Therefore, it is important to estimate a reasonably “right” value for this interface or friction reduction factors, R
inter.
where,
??????
????????????&#3627408481;??????&#3627408479; =
??????
??????
??????′
=
&#3627408481;??????????????????
&#3627408481;??????????????????′
Suggested Reduction Factors, R
inter (Brinkgreeve and Shen, 2011)
70

71. Modelling of Lateral Supports
Anchors and struts can be modelled using the fixed end anchors and node to node anchors in places where appropriate.
Anchored walls
Propped walls
Node to
node
anchor
Beam can be
modelled as
a plate
Node to node anchor
Grouted region can be
modelled as a geogrid
May be modelled as a fixed end anchor
Fixed end
If the width of excavation is small
compared to its depth, node to
node anchors may be used.
width
If the width of excavation is large
with intermediate king posts in
between, fixed end anchors may
be used.
If the rakers are propped to
existing piles, basement
foundation or a rigid
support, fixed end anchors
may be used. Otherwise, a
node to node anchor and a
plate element may be used.
71

72. Case 1: Capitol twin peaks project, Slave Island
Vertical supports are
modelled as a plate
72
Modelling of Lateral Supports

73. Case 2: LTL mix development, Kollupitiya
Horizontal spacing
of anchors
73
Modelling of Lateral Supports

74. Bottom boundary shall be the top of very stiff layer or the bed rock level. Lateral boundaries shall be selected
considering the geometry of the problem (i.e., length of the wall, depth of excavation, symmetry of the problem, etc).
Assigning Model Boundaries, Lateral Supports and External Loads
Case 1: Capitol twin peaks project, Slave Island
H
2
H
1
≈ 1.5 – 2.0H
2
≈ 1.5 – 2.0H
1
Inclined props were modelled
as node-to-node anchors
Steel I sections were modelled
as plate elements
Section A-A (LHS)
Rock level
74
Note:

75. Assigning Model Boundaries, Lateral Supports and External Loads
Case 1: Capitol twin peaks project, Slave Island
Section B-B (LHS)
≈ 1.5 – 2.0H
1
H
1
H
2
≈ 1.5 – 2.0H
2
Node to node
anchor is used
(fixed end anchor is used)
75

76. Assigning Model Boundaries, Lateral Supports and External Loads
Case 2: LTL mix development, Kollupitiya
Since the problem is symmetrical only RHS is modelled.
Line of symmetry
In this project, installation of lateral support with excavation and the removal of props with the construction of basement
slabs is modelled together.
76

77. Defining Initial Stress Conditions
Initially, when creating the finite element model, although the soil parameters has been assigned and the finite element
mesh has been created, the stresses due to soil body self-weight has not been counted for. A special procedure is
necessary to generate or to calculate the initial stresses within the soil body.
If the soil layers and the ground water table is horizontal, the horizontal stresses can be calculated using the K
0 procedure
77

78. Cases where K
o
Procedure is inaccurate
Where the ground surface, the subsoil layer, or the
ground water level is not horizontal, the ko procedure
will lead to the existence of unbalance forces within
the soil body, which are obviously not correct. In
such cases, to maintain equilibrium, there should be
shear stresses developed within the soil body.
Therefore, the ko procedure should not be used,
instead a gravity loading procedure, where the
shear stresses are calculated should be chosen.
78
Defining Initial Stress Conditions

79. Simulation of Construction Sequence
Case 1: Capitol twin peaks project, Slave Island Section A-A (LHS)
1. Installation of I sections for timber shoring and the application of 10 kN/m
2
on the retaining side.
2. Inclined excavation up to -8.5 m elevation along the first level props and dewatering.
3. Installation of the steel I section 8.0m away from the wall and installation of first level of inclined props.
4. Continue inclined excavation along the second level props and dewatering.
5. Installation of second level of inclined props.
6. Carry out the remaining excavation and dewatering.
79

80. Case 1: Capitol twin peaks project, Slave IslandSection B-B (LHS)
1.Application of 10 kN/m
2
on the retaining side and free
excavation up to -4.0 m elevation.
2.Installation of I sections for timber shoring at -4.0 m
elevation.
3.Excavation up to -5.5 m elevation and dewatering.
4.Installation of the first level of horizontal props at -5.5 m
elevation.
5.Continue excavation up to -8.0 m elevation and dewatering.
6.Installation of second level of horizontal props at -8.0 m
elevation.
7.Continue excavation up to -10.3 m elevation and dewatering.
8.Installation of I sections for timber shorings at -10.3 m
elevation and installation of horizontal prop at -10.3 m
elevation.
9.Continuetheremainingexcavationupto-14.3melevation
anddewatering.
80
Simulation of Construction Sequence

81. Case 2: LTL mix development, Kollupitiya
1.Applyingasurchargeof30kN/m
2
2.Installationofthediaphragmwall.
3.Excavatingupto-1.5mlevelandsupportthediaphragmwall(1
st
temporarysupport)at0.0mlevel.
4.Excavatingupto-4.5mlevelandsupportthediaphragmwall(2
nd
temporarysupport)at-4.0mlevel.
5.Excavatingupto-8.0mlevelthensupportthediaphragmwall(3
rd
temporarysupport)at-7.5mlevelanddewatering.
6.Excavatingupto-11.0mlevelthensupportthediaphragmwall(4
th
temporarysupport)at-10.5mleveland
dewatering.
7.Excavatingupto-14.0mlevelthensupportthediaphragmwall(5
th
temporarysupport)at-13.5mleveland
dewatering.
8.Excavatingupto-16.5mlevel(includinganaccidentaldepthof0.25m)whiledewateringandconstructingtheraft
foundationat-16.25mlevel.
9.Removingthesupport(5
th
temporarysupport)at-13.5mlevelandconstructingthefourthbasementat-12.0mlevel.
10.Removingthesupport(4
th
temporarysupport)at-10.5mlevelandconstructingthethirdbasementat-9.0mlevel.
11.Removingthesupport(3
rd
temporarysupport)at-7.5mlevelandconstructingthesecondbasementat-6.0mlevel.
12.Removingthesupport(2
nd
temporarysupport)at-4.0mlevelandconstructingthefirstbasementat-2.0mlevel.
13.Removingthesupport(1
st
temporarysupport)at0.0mlevel.
14.Activate UDL loading of 390 kN/m on diaphragm wall.
In this project, basement raft foundation and slabs construction while
removing props were also modelled (refer to Stage 8 – 14 below).
81
Simulation of Construction Sequence

82. Modelling of Ground Water and Dewatering
To properly model the ground water seepage on a deep excavation problems, one must first understand whether water
can pass through the retaining wall or not and whether the retaining wall is installed as a water cut-off system.
Groundwater flow through
a permeable wall
Permeable
wall
Permeable soil
Impermeable
wall
Permeable soil
Water flow should not be allowed from
the bottom of the model and through the
line of symmetry
Permeable soil
Groundwater flow underneath
an impermeable wall
No groundwater flow. P.w.p can
be calculated using phreatic
surface on both sides
Impermeable
wall
Static water
levels
Retaining wall acts as a water
cut-off system
82

83. Interpretation of Results of FE Analysis
The following results shall be obtained from FE modelling and interpreted in the right context
1.Lateral deformation profile of the wall during different construction stages. This should be compared with the
permissible lateral deflection.
2.Anticipated settlement profile on the retained side of the wall. This has to be checked with the allowable settlement
close to existing structures.
3.Bending moment and shear force envelopes. The wall shall be capable of sustaining the ultimate values of bending
moments and shear forces.
4.Maximum axial forces on lateral supports. Different props and anchors shall be capable of sustaining the ultimate
values of axial forces without causing any structural failure.
5.Mobilized earth pressure distribution and pore water pressure distribution on the active side and passive side of the
retaining wall. This can be used to carry out conventional stability checks.
During excavation, regular monitoring of deformation and ground water shall be carried out to validate and calibrate
the model.
83

84. Other Issues to be Addressed
1.It is required to estimate the anticipated flow rate into the excavation. Manual methods such as flow nets, method of
fragments or numerical methods such as FEM or finite difference method shall be adopted. The dewatering method
and the required details such as pump capacity, number of pumps, pump layout, etc shall be decided based on the
estimated flow rate.
2.If the anticipated drawdown is not acceptable, ground water recharge shall be done.
3.Stability against piping is a prime concern in deep excavations. This is particularity important if the subsurface consist
of sandy material.exit
critical
i
i
FOS =pipingagainst
Maximum exit
hydraulic gradient, i
exit
Equipotential lines obtained through a
simple spreadsheet analysis of seepage
using finite difference method.
Analysis of seepage using flow nets.
84

85. Ground Water Recharge
Ground water recharge shall be carried out if the estimated draw down particularly near existing structures is not
acceptable. Recharge wells are quite commonly used to recharge the ground water table during deep excavations.
Illustration on different methods
of ground water recharge
85

86. A typical recharge well used at LTL mix development
Proposed recharge wells
Observation wells (can be used
to recharge if necessary)
Case 2: LTL mix development, Kollupitiya
Recharging is mainly done to avoid significant draw down near
important structures
86
Ground Water Recharge

87. Monitoring Process
Monitoring is a very important aspect in geotechnical engineering problems. It will help to ensure the safety of the
construction as well as adjacent structures. In addition, monitoring records can be effectively used to validate and
calibrate the numerical models.
The following characteristics shall be monitored during deep excavations.
➢Lateral deformation of the wall (several points at around 5 m horizontal intervals should be established along the
wall and coordinates (x, y and z) should be established by surveying techniques to an accuracy of 1 mm or
better).
➢Lateral deformation profile along the depth of the wall (several inclinometers shall be installed through the
diaphragm wall or just outside the wall and monitor the lateral deformation profile of the wall regularly).
➢Ground settlement (several survey points or settlement plates shall be installed near important structures and
the ground settlement shall be monitored regularly).
➢Ground water level (several observation wells shall be installed to monitor the ground water table variation with
dewatering. The same can be used for ground water recharge if necessary).
➢Condition of adjacent structures (pre-excavation condition of the adjacent structures shall be established prior to
commence the excavation and propagation of existing cracks, any structural distress, etc. shall be monitored
during and after the excavation).
87

88. Proposed Locations for Inclinometers and Observation Wells
Case 1: Capitol twin peaks project, Slave Island
Inclinometers were proposed at the
locations where anticipated lateral
deformation is significant and critical.
Observation wells were proposed
near adjacent structures.
88

89. Proposed Locations
for Inclinometers
and Observation
Wells
Case 2: LTL mix development, Kollupitiya
89

90. PLAN VIEW
Monitoring of Lateral Deformation using Inclinometers
90

91. Monitoring of Lateral Deformation using Survey Techniques
91

92. Monitoring of Ground Settlement using Survey Techniques
92

93. Monitoring of Ground Water Table using Observation Wells
93

94. 94
Thank You.