SOME CONSIDERATIONS ON THE USE OF

1
SOME CONSIDERATIONS ON THE USE OF FINITE ELEMENT
METHODS IN ULTIMATE LIMIT STATE DESIGN C.
Bauduin Besix, Brussels Brussels University
2

• WAYS TO INTRODUCE SAFETY WHEN USING FEM
• Eurocode format
• Specific aspects of FEM in ULS design
• Design procedure
• Considerations on j c reduction
• FACTORS AFFECTING THE RESULTS OF FEM IN ULS
  DESIGN
• Initial stress state
• Soil model
• Stiffness parameters
• Yielding of structural members supports

3
WAYS TO INTRODUCE SAFETY IN GEOTECHNICAL DESIGN
EdltRd 1. Ed Rd obtained by applying partial
factors applied right at the source, i.e. on the
basic variables MFA 2. Ed Rd obtained by
applying partial factors partial factors applied
on the effects of loads and on the resistances
LRFA
4
EUROCODE FORMAT for GEOTECHNICAL and STRUCTURAL
FAILURE (except for piles)
OFTEN DA 1/1 DA 2 apply factors to action
effects LRFA
5
REQUIREMENTS TO FEM CALCULATIONS IN ULS DESIGN
GEO STR 1 CHECK FOR FAILURE OF SOIL
BODY2 DELIVER DESIGN VALUES OF SUPPORT
REACTIONS (ANCHOR, SOIL REINFORCEMENT, PILE)
FORCES AT DESIGN VALUE OF SOIL
PARAMETERS3 DELIVER DESIGN VALUES OF INTERNAL
FORCES AT DESIGN VALUE OF SOIL PARAMETERS
6
SPECIFIC ASPECT OF FEM
7
SAFETY IN ULS GEOTECHNICAL DESIGN USING FEM

• 1. MFA ?
• LRFA ?
• DESIGN APPROACH PARTIAL FACTORS NATIONAL
  DECISION!

1 MFA can be applied using FEM to almost all
types of geotechnical problems. 2 RFA for
FEM is much more restricted Probably only to
problems where the ultimate states are reached by
an increase of the external load, and where no
action originates from the weight of the soil.
E.g bearing capacity problems. APPLY MFA FOR
FEM i.e. DA 1 or DA 3
8
APPLICATION OF MFA IN FEM Conceptually MFA can
be introduced through

• calculations using right from the start design
  values of all relevant variables
• calculations during which the variables are
  increased or decreased until their values reach
  the design value
• ? c or cu reduction at each relevant stage

9
DESIGN VALUES FROM START OR ? - c REDUCTION

• Non linear calculation displacement stress
  field influenced by stress history
• Consolidation
• Staged loading
• ? Check safety as distance between stress field
   as realistic as possible  and  failure 
• MFA ? - c or CU REDUCTION FROM
  CHARACTERISTIC STRESS FIELD IS PREFERABLE
• especially when the stress history plays
  important role.

10
?M
?d , cd
?K , cK
initial
?, c (cu)
?F
MK, AK.
Md, Ad.
Md2, Ad2.
Md1, Ad1.
DESIGN FROM START
CHARACTERISTIC
STAGE
?- C REDUCTION
Mchar, Achar 1,35
11
?- C REDUCTION AT EACH STAGE

• AT EACH STAGE, DESIGN IS CHECKED  AS  DISTANCE 
  BETWEEN MOST PROBABLE STRESS STATE AND ULS
  SITUATION
• check against GEO failure
• delivers Md corresponding to design values soil
  properties
• for compatible STR design
• IS DIFFERENT FROM  WHAT IF SOIL IS 1.25 LESS
  STRONG THAN EXPECTED 
• Difference is expected to be larger in case of
  complicated construction sequences or
  consolidation periods than in straightforward
  situations

12
LRFA MULTIPLYING CHARACTERISTIC M AT EACH STAGE
BY LOAD FACTOR

• MD Mk 1.35 OR 1.5
• AD Ak 1.35 OR 1.5
• DESIGN VALUE OF ACTION EFFECTS COMPATIBLE WITH
  STRUCTURAL DESIGN CODES
• CHECKING FOR GEOTECHNICAL FAILURE IS NOT
  STRAIGHTFORWARD

13
LRFA MULTIPLYING CHARACTERISTIC M AT EACH STAGE
BY LOAD FACTOR

• FOR SOIL-STRUCTURE INTERACTION PROBLEMS
• STRESS AT CHARACTERISTIC LEVEL MAY BE
  SIGNIFICANTLY HIGHER THAN AT ULS DISPLACEMENTS
  TOO SMALL TO ALLOW STRESSES TO RELEASE TO YIELD
  VALUE

14

• DISPLACEMENTS TOO LOW TO ALLOW RELEASE OF
  STRESSES TO YIELD STRESS
• Example STIFF WALL, HIGHLY OC SOIL

Pressure on wall, bending moment
Wall displacement
ULS
CHAR
15

• WHEN SOIL STRENGTH PLAYS NO or MINOR ROLE
• Example tunnel

E, ?
16
ILLUSTRATION SIMPLE EXCAVATION PROBLEM
? 17 - 19 ?K 28 , C 1
NO STRESS HISTORY DUE TO STAGED CONSTRUCTION
17
SIMPLE AND STRAIGHTFORWARD EXCAVATION

• Geotechnical strucural design governed by ?/
  1,25
• Ad Md not dependent of  path 

18
STAGED EXCAVATION1 2
3 4
5
sand mohr coulomb EFFECT OF STRESS HISTORY
19
COMPARISON OF CALCULATION RESULTS

• CHARACTERISTIC ?-C REDUCTION
• SOIL PARAMETRS DESIGN VALUE FROM START
• CHARACTERISTIC 1,35

Different results
Structural dsg strut
20
CORRESPONDANCE WITH EC 7 FORMAT
21
CORRESPONDANCE WITH EC 7 FORMAT

• DA 1 CHECKS FOR BOTH  PATHES 
• design to be based on most severe of both
• DA 2 ALLOWS LRFA ONLY
• check against failure in the ground ? ?
• DA 3 REQUIRES STR ACTIONS 1.35 or 1.5 FOLLOWED
  BY j C REDUCTION
• NO CHECK  CHARACTERISTIC 1.35 
• not always at the side of safety for structural
  design of stiff structures

22
PROPOSED PROCEDURE TO PERFORM ULS DESIGN WITH FEM
in DA1

• PERFORM ALL STAGED CONSTRUCTION USING
  CHARACTERISTIC VALUES OF SOIL PARAMETERS
• FOR EACH RELEVANT STAGE, PERFORM ?? - c REDUCTION
• checks against geotechnical failure
• delivers compatible design values of M, A

• MULTIPLY CHARACTERISTIC VALUE OF M BY 1.35 1.50
• Compatible Md Ad with structural codes
• STRUCTURAL DESIGN FOR MAX OF BOTH M, A

23
PROPOSED PROCEDURE TO PERFORM ULS DESIGN WITH FEM
in DA3

• PERFORM ALL STAGED CONSTRUCTION USING
  CHARACTERISTIC VALUES OF SOIL PARAMETERS
• FOR EACH RELEVANT STAGE
• a) INCREASE STRUCTRAOL LOADS BY FACTOR 1.35
  1.5
• b) PERFORM ?? - c REDUCTION
• checks against geotechnical failure
• delivers compatible design values of M, A

24
CONSIDERATIONS ON THE j c REDUCTION

• PERFORMED WITH
• MOHR-COULOMB MODEL
• DILATANCY 0
• 1 FULLY DRAINED SITUATION (effective stress
  analysis, j c)
• reduction of j c no problem
• 2 FULLY UNDRAINED SITUATION ( total stress
  analysis, cu)
• reduction of cu no problem
• 3 STAGED LOADING INCLUDING CONSOLIDATION

25
CONSIDERATIONS ON THE j c REDUCTION

• 3 STAGED LOADING INCLUDING CONSOLIDATION
• undrained analysis using effective stress
  parameters

t
Cu MC
cu cap
ESP MC
TSP MC
REAL ESP
REAL TSP
Plastic yield cap
MC Failure envelope
s
26
CONSIDERATIONS ON THE j c REDUCTION

• 3 STAGED LOADING INCLUDING CONSOLIDATION
• What does MC j c reduction mean?
• Cap model with j c reduction probably not
  realistic and very strongly influenced by shape
  of yielding cap
• Evaluate cu field using effective stress
  parameters and cap model
• and perform cu reduction
• further development is needed

27
CONSIDERATIONS ON THE j c REDUCTION

• DILATANCY 0
• AT THE SIDE OF SAFETY FOR FAILURE IN THE GROUND
• NOT ALWAYS AT THE SIDE OF SAFETY FOR STRUCTURAL
  MEMBERS (CONSTRAINED DILATANCY)

28
CONSIDERATIONS ON THE j c REDUCTION

• PARTIAL FACTOR HAS SOME TO SOME EXTENT A
   CONVENTIONAL  CHARACTER, NOT NECESSARELY A
   PHYSICAL EXPLANATION 
• NEED OF BUILDING UP EXPERIENCE BY COMPARATIVE FEM
  RE-DESIGN OF SUCCESSFUL STRUCTURES
• PROBABILISTIC BACKING?

29
FACTORS AFFECTING THE RESULTS OF ULS CALCULATIONS

• INITIAL STRESS K0
• SOIL MODEL
• STIFFNESS PARAMETERS
• YIELDING OF STRUCTURAL MEMBERS
• ? COLLAPSE OF SOIL BODY
• ? DESIGN VALUE OF MEMBER FORCE

30
INITIAL STRESS

• FAILURE OF THE SOIL BODY K0 MINOR ROLE
• ?-c reduction stresses release to yielding
  values, not very sensitive to K0
• MEMBER FORCE K0 IMPORTANT
• stresses may not drop to limiting values
• ! Importance of stiffness of structure gtlt K0
• ? CHARACTERISTIC VALUE
• (CAUTIOUS ESTIMATE) OF K0

31
INITIAL STRESS
?h M
K0 (OCR)
Wall displacement
32
SOIL MODEL FOR  CHARACTERISTIC CALCULATIONS 

• Present stage of knowledge
• SIMPLE ULS PROBLEMS MC SUFFICIENT
• 2. IF STRESS HISTORY PLAYS IMPORTANT ROLE
• IF SOIL STRUCTURE INTERACTION IS IMPORTANT
• ? USE ACCURATE (ADVANCED) MODEL
• FOR CHARACTERITIC PATH

33
PARTIAL FACTORS APPLIED - ONLY TO
STRENGTH PARAMETERS ? - OR ALSO TO
DEFORMATION PARAMETERS?

• Probably not much effect on full plastic
  mechanism.
• Importance of parametric study instead of
  design value of deformation parameters

?
?M
Gd GK
?
34
BEHAVIOUR OF STRUCTURAL MEMBERS AND SUPPORTS

• USUALLY TAKEN ELASTIC
• check MdltMRd at each section
• safe, somewhat conservative
• FULL ADVANTAGE OF ULS DESIGN USES PLASTICTY IN
  STRUCTURAL MEMBERS
• eg plastic hinges, yielding piles
• allows for more economic design

35
NON LINEAR BEHAVIOUR OF STRUCTURAL MEMBERS and
SUPPORTS

• CHECK FOR DUCTILE BEHAVIOUR
• rotational capacity concrete, steel members
• brittle failure piles, anchors,
  reinforcements
• 2. Non linear structural member Md ?1,35 Mk
  Rd ?1,35 Rk
• path  characteristic 1,35  to be adapted
• 3. ALWAYS CHECK GEOTECHNICAL STRUCTURE AGAINST
  SERVICEABILTY CRITERIA
• as large movements, cracking may develop

36
CONCLUSIONS AND RECOMMENDATIONS 1 DESIGN
PROCEDURE

• USE MATERIAL FACTORING APPROACH
• 2. ULS CHECK AS  DISTANCE  FROM CHARACTERISTIC
  STRESS FIELD BY ?-C REDUCTION
• DA 1 comb 2 DA 3
• 3. CHECK ALSO SOIL STRUCTURE INTERACTION BY
  MUTIPLYING  CHARACTERSTIC  MEMBER FORCES BY
  LOAD FACTOR
• DA 1 comb 1, DA 2

37
CONCLUSIONS AND RECOMMENDATIONS 2 SOIL
MODEL INTERACTION PARAMETERS

• 1. SOIL MODEL
• Secondary importance when soil collapse is
  analyzed
• Important for soil-structure interaction
• 2. K0, DEFORMATION PARAMETERS
• Secondary importance when soil collapse is
  analazed
• Important for soil-structure interaction
• Use sensitivity analysis instead of design
  values
• 3. STRUCTURAL MATERIAL AND SUPPORTS
• Non-linear behaviour may be used
• Check for ductility

38
CONCLUSIONS AND RECOMMENDATIONS3 DEVELOPMENTS

• VALUES OF PARTIAL FACTORS
• - same as for classical design or specific
  for FEM?
• NON-LINEAR STRUCTURAL BEHAVIOUR
• - calculation procedures
• GATHERING EXPERIENCE
• - comparative calculations
• - back-calculations of existing projects
• - exchange of calculation results