second generation eurocode 8 part 3: the european document
TRANSCRIPT
Second generation Eurocode 8 Part 3: the European document on
seismic assessment and retrofit of existing structures
Paolo Franchin([email protected])
Assessment of existing structures - JCSS workshop β January 28th/29th 2021
Summary 1st generation Eurocode 8 Part 3 (2005)
Specificity of assessmet wrt design Single knowledge level (KL) Confidence factor
Forces are not good predictors of performance Displacement-based
Assessment deals with non-conforming structures Nonlinear analsysis and ad hoc deformation criteria
2nd generation Eurocode 8 (2020)
Displacement-based approach for both assessment and design Multiple Knowledge Levels Knowledge-dependent partial factors on resistance(*)
A probabilistic method of assessment also introduced
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(*) Demand = Acvtion effect & Capacity = Resistance in the Eurocodes system
Seismic risk (consequences of damage) mostly associated with exisiting structures(e.g., Italy, 85% of πΈπΈ πΏπΏ )
Quantitative procedures!Qualitative assessment based on pastperformance not really useful for seismic
Eurocode 8 Part 3 2005 (1st generation)
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Primary role of knowledge acquisition (existingβ new) Information classified into:
Geometry (Construction) Details Materials
Quantified by Knowledge level (KL) Values: Limited, Normal, Full Controlled by the least amount of information in G, D and M & unique over the structure
KL β Confidence factor (CF) which divides material strength: 1,35/1,20/1,00 CF coexists with πΎπΎππ (e.g., πΎπΎππ , πΎπΎπ π ) used in traditional verification format
Inelastic and possibly defective response is the rule. Rules for nonlinear static analysis Novel models for:
inelastic deformation capacity (chord rotation) shear strength of members and joints in the inelastic range strength & deformation capacity of retrofitted members
0%2%4%6%8%
10%12%14%16%18%
0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%
Vb/W
RDR
Eurocode 8 Part 3 2005 (1st generation)
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Experimental nature of the document is apparent Most material (models for πππ¦π¦ and πππ’π’, or πππ π ) is in informative annexes KL depends on G, D, M information but it only affects M (through CF) CF values are judgemental Not really streamlinedβ¦ Four different set of material properties used:
Mean (πΈπΈππππ, ππππππ, πππ¦π¦ππ) in the model, which provides action effects on ductile modes of failure (ππ)
Mean divided by CF (ππππππ/πΆπΆπΆπΆ, πππ¦π¦ππ/πΆπΆπΆπΆ) for evaluating the resistance of ductile failuremodes (πππ¦π¦ , πππ’π’)
Mean divided by CF and πΎπΎππ ( πππππππΆπΆπΆπΆπΎπΎππ
, πππ¦π¦πππΆπΆπΆπΆπΎπΎπ π
) for the resistance of brittle modes (πππ π π π )
Mean times CF, for the demand on brittel modes (πππΈπΈπ π ) if analysis model is linear
Nonetheless, more than 15 years of practical application Increased confidence(*) in nonlinear analysis methods & displacement-based
verifications and associated deformation models Have shown that information should be sought where it is more relevant Thousands of buildings have been assessed and retrofitted
(*) Obviously the situation in the Engineering practice is spatially non homogeneous, as it is not the seismic hazard in Europe
Eurocode 8 Part 3 2020 (2nd generation)
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CEN/TC250 M515 (Revision of the entire Eurocodes system)
Extension of scope EN1998-3:2005 only dealt with buildings in RC and, marginally, steel prEN1998-3:2020 includes buldings and bridges + RC, steel, masonry, timber
Technical updating Displacement-based assessment now default, scope for force-based reduced
Displacement-based design introduced for new structures in Part 1-1
(Updated) deformation and strength models moved from annexes in Part 3 β mainbody of Part 1-1 (i.e., used for new & existing structures)
Only one set of properties used, the mean ones In the (nonlinear analysis) model to determine action effects
In the resistance formulas (πππ¦π¦ ,πππ’π’,πππ π π π , etc)
To evalutate demand on brittle failure modes (πππΈπΈπ π , curbed to plastic shear) with linear analysis model
Eurocode 8 Part 3 2020 (2nd generation)
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Technical updating (contβd) More refined treatment of acquired knowledge
Three distinct KLs introduced for G, D and M: KLG, KLD and KLM
Each KL need not be uniform over the structure if newly introduced preliminary analysisis carried out(*)
Safety On the demand side
Near Collape (NC) verification replaces Significant Damage (= Life safety) as default
On the capacity side a unified(**) partial factorsβ format to account for
Model (epistemic) uncertainty in the resistance formulas
Uncertainty (aleatoric and epistemic) in the input variables, classified in the Material properties, Geometric parameters, Construction details categories (***)
Reliability differentiation Consequence class (CC), like US risk category, determine return period of seismic action
for NC verification
Resistance of secondary & non-critical members taken equal to its median (i.e., πΎπΎRd = 1)
(***) Stronger link between information and verifications(*) More focussed field investigations, save money and time (**) Consistency across different materials and verifications
Resistance models: inelastic rotation capacity
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Resistance formulas Models are a variable blend of mechanical and empirical
ππy = ππyπΏπΏV + ππVπ§π§
3+ππyππbLππy
8 ππc+ 0,00ππππ 1 +
βππ,πππΏπΏV
ππu = ππy + ππupl
ππupl = ππu β ππy πΏπΏpl 1 β
2πΏπΏplπΏπΏV
+ Ξππu,slip
flexure slip shearRC beam/columnwith hollow-core section
ππy ππuππ
ππ
ππupl
ππ = πΆπΆ
πΆπΆ ππ
ππpππuππu
ππyππy
πΏπΏy πΏπΏuππy
πΏπΏ V=ππ
/ππππuππupl
ππy = ππyπΏπΏV + ππVπ§π§
3+ππyππbLππy
8 ππc+ 0,00ππππ 1 β min 1;
πΏπΏVπππ·π·
ππu = ππy + ππupl
ππupl = ππu β ππy πΏπΏpl 1 β
2πΏπΏplπΏπΏV
+ Ξππu,slip
RC beam/columnwith circular section
Resistance models: inelastic rotation capacity
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Resistance formulas Models are a variable blend of mechanical and empirical
ππ = πΆπΆ
πΆπΆ ππ
ππpππuππu
ππyππy
πΏπΏy πΏπΏuππy
πΏπΏ V=ππ
/ππππuππupl
ππupl = π π conformπ π axialΞΊreinfπ π concreteπ π shearspanπ π confinementππu0
pl
π π concrete = min 2;ππc ππππππ
25
0,1
π π axial = 0,2Ξ½
0,039 rad(ππc = 25MPa, ππ = 0,
πΏπΏVβ = 2,5)
ππy = ππyπΏπΏV + ππVπ§π§
3+ππyππbLππy
8 ππc+ 0,00ππππ 1 +
βππ,πππΏπΏV
ππu = ππy + ππupl
flexure slip shear
π π shearspan =1
2,5min 9;
πΏπΏVβ
0,35
ππy ππuππ
ππ
ππupl
RC beam/columnwith rectangular section
Resistance models: inelastic rotation capacity
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Resistance formulas Variable blend of mechanical and empirical Unbiased, CV of exp/pred ratio (model uncertainty) is available
βDesignβ models usually conservative, CV not documented
(*) Examples from Grammatikou et al 2018 and Lignos and Krawinkler 2011
ππu,pred[%]
ππ u,exp
[%]
ππu,exppl [β]
ππ u,pred
pl[β
]CV = 42%CV = 35%
ππu = ππy + ππupl
ππy =πΏπΏ 1 β ππ6 ππb πΈπΈπΌπΌx
ππy =πΏπΏV3ππy
πΈπΈπΌπΌx(1 β ππ)ππb
ππupl = 7.37
βπ‘π‘π€π€
β0.95 πΏπΏπππππ¦π¦
β0.5
1 β πππΊπΊ 2.4
Reinforced concrete Steel
ππy = ππyπΏπΏV + ππVπ§π§
3+ππyππbLππy
8 ππc+ 0,00ππππ 1 +
βππ,πππΏπΏV
Resistance models: shear strength in RC
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Resistance formulas Variable blend of mechanical and empirical Unbiased, CV of exp/pred ratio (model uncertainty) is available
(*) Examples from Biskinis et al 2004 and Biskinis and Fardis 2018
~205 rect. beams/columns~75 circ. Columns~40 rect. & ~55 non-rect. walls/box sectionsall with 4.1β₯Ls/h>1.0, Median ππππππππ/πππππππππ π =1.00
CV=17%
~121 rect. beams/columns~43 circ. Columns~24 rect. & ~70 non-rect. walls/box sectionsMedian ππππππππ/πππππππππ π =1.00
CV=23,3%
EN1998-3:2005 prEN1998-1-1:2020
EN1992 prEN1992:2020ππRc + ππRs β€ ππRmax
ππRcβ + ππRs ππ ππ β€ ππRmaxβ
ππRcβ + ππRs ππ ππ + ππRN β€ ππRmaxβ
ππRc(ππππ) + ππRs β€ ππRmax(ππππ)
ππππ =1
2 As1 πΈπΈsπππ§π§βππ2
+ππ2
cot ππ
ππRc ππππ + ππRs + πππ π π π β€ ππRmax(ππππ)
ππππ =1
2 As1 πΈπΈsπππππ§π§βππ2
+ππ2
cot ππ
ππy
ππy
ππ
Partial factors on resistance
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Evaluation of median of resistance with best estimate properties Lower fractile for verification through a single member-level partial
factor
ππu,pred[%]
ππ u,exp
[%]
ππu,exppl [β]
ππ u,pred
pl[β
]CV = 42% CV = 35%1
πΎπΎπ π π π ,ππ
~121 rect. beams/columns~43 circ. Columns~24 rect. & ~70 non-rect. walls/box sections
CV=23,3%
~171 rect. beams/columns~26 circ. Columns~36 rect. & ~70 non-rect. walls/box sections
CV=22,1%1
πΎπΎπ π π π ,ππππR ππRmax
Partial factors on resistance: formulation
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Fractile k can be obtained from median, if ππln R,tot is known
π π k = ππππln R+π π ππln R,tot = οΏ½π π πππ π ππln R,tot β πΎπΎRd =οΏ½π π π π k
= ππβπ π ππln R,tot
Digitare l'equazione qui. The total logarithmic standard deviation is a function of Model uncertainty (CV of exp/pred) ππln R Variability (aleatoric+statistical) of input variables (e.g., ππc, πΏπΏV,ππw)
All formulas in Eurocode 8 can be put in the form
π π ππ = οΏ½π π ππ ππR β lnπ π ππ = ln οΏ½π π ππ + ΜππR
-3 -2 -1 0 1 2 30
0.5
1
1.5
ΟlnRΟlnR,tot
Input variables Model error
Partial factors on resistance: formulation
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Linearization of ln οΏ½π π (ππ) around οΏ½ππ leads to an expression for ππln R,totDigitare l'equazione qui.lnπ π ππ = ln οΏ½π π οΏ½ππ + οΏ½ οΏ½
ππ ln οΏ½π π ππ ln π₯π₯i οΏ½ππ
ln π₯π₯i β ππln ππi + ΜππR =
Digitare l'equazione qui.Digitare l'equazione qui.lnπ π ππ = ln οΏ½π π οΏ½ππ + οΏ½
οΏ½π₯π₯iοΏ½π π οΏ½ππ
οΏ½ππ οΏ½π π πππ₯π₯i οΏ½ππ
ln π₯π₯i β ππln ππi + ΜππR =
Digitare l'equazione qui.Digitare l'equazione qui.Digitare l'equazione qui.lnπ π ππ = ln οΏ½π π οΏ½ππ + οΏ½ππi Μππi + ΜππR
Total logarithmic standard deviation is then
ππln R,tot = ππln R2 + β ππiππln ππππ2
The ππln ππππ is only imperfectly known (limited testing)
ππln R,tot πΎπΎπΏπΏ = ππln R2 + β ππiπ π ln ππππ2
ππiππln ππππ
ππ lnπ π
οΏ½ ππiπ π ln ππi2
Median @ medianCorrection for the log Sensitivity to π₯π₯i
Tangent/Secant
Partial factors on resistance: formulation
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Partial factors on resistance: calibration
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ππln R,tot ππ,π²π²π²π² β πΎπΎRd ππ,π²π²π²π² depends on the structural member, i.e. ππ
πΎπΎRd ππ,π²π²π²π² = ππβπ π ππln R2 +β ππi ππ π π ln π₯π₯ππ
2
Luckily πΎπΎRd ππ is reasonably stable with ππ
Further, KLG, KLD, KLM each has 3 values This leads to 33 = 27 values of πΎπΎRd ππ
One KL, however, normally dominates each formula
"ππππln R,tot
πππΎπΎπΏπΏ" =
βππβπΎπΎπΎπΎ ππjπ π ln ππj2
ππln R,tot
It is possible to evaluate on a large parametersβ space the factor for each formula and then tabulate an average value as a function of the dominant KL
Min., Average, High
Sum only over π₯π₯i belongingto KLj (e.g., ππc is KLM)
π²π²π²π² = πΎπΎπΏπΏπΏπΏ πΎπΎπΏπΏπ·π· πΎπΎπΏπΏππ
Partial factors on resistance: calibration
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For each formula a parameter space has been defined 27 values of πΎπΎRd,KL ππ have been computed, then simplified to 3 wrt to dominant KL For now, Β«calibrationΒ» = matching the resistance implied by the previous code (2005)
KLD 1 2 3
πΎπΎπ π π π 1,67 1,62 1,57
ππ u/πΎπΎ
Rd,KLππ
ππ u/πΎπΎ
Rd,KL
ππu in EN1998-3:2005 ππu in EN1998-3:2005
(*) Example: rectangular RC member with short lap-splice and ribbed bars
ππlnR,totCoefficients ππππAssumed ππln ππππ
Member-dependent πΎπΎRd β average one 33 = 27 πΎπΎRd values and dominant KL (Details in this case)
Simplified table with 3 πΎπΎRd values (dominant KL only)
Conclusions Seismic assessment and retrofit design in Eurocode 8 is
Quantitative Displacement-based Employs nonlinear analysis and inelastic deformation criteria
Safety on the resistance side is ensured by using πΎπΎRd, member-level partial factors on resistance that
Divide the median resistance evaluated with best-estimate properties The same properties that enter into the (nonlinear) model
Are consistently derived across all materials and failure modes Account for model uncertainty and uncertainty on input variables Are tabulated vs the dominant KL
Each formula is most sensitive to one between Geometry, Details and Materials Can be changed at national level with a single formula (*)
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(*) not shown! Note that this reduces the number of NDPs to just one