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07-10-2015
Challenge the future
DelftUniversity ofTechnology
Improved Formulation for Compressive Fatigue Strength of
ConcreteDr. Eva Lantsoght, Dr. Cor van der Veen, Dr. Ane de Boer
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2Improved formulation for compressive fatigue strength of concrete
Overview
• Literature survey• Parameters • HSC
• Code provisions• Database• Proposal
• For design• For existing structures
• Comparison methods & experiments
• Summary
Failed specimens: a,b: gravel concrete: c,d: limestone concrete (Hordijk et al., 1995)
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3Improved formulation for compressive fatigue strength of concrete
Literature surveyIntroduction
• Cycles of loading • => fc decreases
• With S-N curve • +- linear from 100
cycles (Kim & Kim, 1996)
• Proposal necessary• inconsistency in Dutch
NA Typical S-N line for concrete in compression (CEB Com GTG 15, 1998)
σmax/fcm
Log(s)72 3 4 5 61 8
0,9
0,8
0,7
0,6
C.L.=confidence limit
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4Improved formulation for compressive fatigue strength of concrete
Literature surveyImportant parameters
• Smin: increased, then Smax increased
• Rest periods: increased N
• Frequency f: • above Smax = 0,75 : N
decreases as f decreases
• Accelerated fatigue tests: overestimate N
σ-ε of the envelopes for concrete under cycles of compression (Fehling et al., 2013)
σ/fc
ε/εcu
1,21,00,80,60,40,2
0 0 1 2 3 4
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5Improved formulation for compressive fatigue strength of concrete
Literature surveyFatigue high strength concrete
Reference fc,mean,max (MPa) Influence fc?Petkovic et al., 1990 95 NoKim & Kim, 1996 103 YesHordijk et al., 1995 78,2 NoLohaus et al., 2011 170* NoLohaus & Anders, 2006
145* Yes
Tue & Mucha, 2006 65 Yes*: specimens with fibre reinforcement
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6Improved formulation for compressive fatigue strength of concrete
Literature surveyFatigue high strength concrete
• Conclusion fib task group 8.2, 2008:• HPC: lower fatigue limit compared to NSC
• Because of lower w/c ratio
• “one has not yet succeeded in finding adequate design rules for the fatigue behavior taking into consideration the special properties of HPC”
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7Improved formulation for compressive fatigue strength of concrete
Current code provisions
Model Code 2010, fck in formulas, γc = 1,5
EC 2-2: very conservative, γc = 1,5EC 2-2+NA: mismatch at Ni = 106, γc = 1,35
Kim & Kim: influence of fc’ , γc = 1,5
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8Improved formulation for compressive fatigue strength of concrete
Database of test results (1)
• 429 experiments• 234 without
fibers• Up to 145 MPa
• 195 with fibers• Up to 226 MPa
• Run-out specimens
• Remarks column
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9Improved formulation for compressive fatigue strength of concrete
Database of test results (2)
Region of low-cycle fatigue? Distribution concrete classes in database
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10Improved formulation for compressive fatigue strength of concrete
Proposed methodsfor design (1)
• fck/400 instead of fck/250• Model Code 2010• k1 = 1 instead of k1 = 0,85
• Similar to NEN-EN 1992-2+C1:2011
• γc = γc,fat = 1,5
, ,114
110cd max i
i
E
RiN
,
cd,min,ii
cd,max i
ER
E
,
,
cd min,icd,min,i
cd fat
Ef
, ,,
cd,max,icd max i
cd fat
Ef
, 1 0( ) 1400ck
cd fat cc cdf
f k t f
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11Improved formulation for compressive fatigue strength of concrete
Proposed methods for design (2)
• Comparison proposal – experiments with Smin = 0,05• Simple method, no iterations, suitable for HSC
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12Improved formulation for compressive fatigue strength of concrete
Proposed methodsfor assessment (1)
• Correct connection for 106 cycles
• k1 = 1• γc,fat = γc = 1,5
• For N = 1: Smax = 1• fck/400 for HSC
• Iterations, but stable• 1st iteration, try Smax,EC = 1• Convergence at 3rd
iteration
66 1log for 10
1max
i imax,EC
SN N
S
31 1 1 *400 7ck
max,EC ifS R
* mini
max,EC
SR
S
61log 14 for 10
1cd,max,i
i ii
EN N
R
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13Improved formulation for compressive fatigue strength of concrete
Proposed methods for assessment (2)
• Comparison proposal – experiments with Smin = 0,05
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14Improved formulation for compressive fatigue strength of concrete
Comparison proposals
Method γc,fat AVG STD COV Char 5%
Design 1.5 1.27 0.139 10.9% 1.044 1.089
Assessment 1.5 1.15 0.112 9.7% 0.965 1.004
• Best results: method for assessment, but requires iterations• 5% lower bound > 1 => suitable for Codes
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15Improved formulation for compressive fatigue strength of concrete
Effect of concrete class• Method becomes
slightly more conservative as concrete class increases
• Based on tested/predicted Smax
Comparison between unity checks (average value) for different concrete classes
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16Improved formulation for compressive fatigue strength of concrete
Check with NSC results
• Comparison for experiments from Hsu (1981) and Tepfers and Kutti (1979)
• Results of concrete tested under water: shorter fatigue life
• Use k1 = 0,85 only for concrete under water (e.g. offshore structures)
• Additional database of 165 experiments on NSC
Method γc,fat AVG STD COV CharDesign 1,5 1,212 0,063 5,2% 1,109
Assessment 1,5 1,135 0,081 7,1% 1,002
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17Improved formulation for compressive fatigue strength of concrete
Conclusions
• Dutch NA: mismatch at 106 cycles => need for new proposal
• Include recent test results of HSC• Database
• 429 experiments of HSC • 165 experiments of NSC
• Two methods: • for design • for assessment
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18Improved formulation for compressive fatigue strength of concrete
Summary - Assessment
• Connects at 106 to EC2-2• Static strength at 1 cycle• Suitable for HSC• 5% lower bound ≈ 1:
conservative• γc = γc,fat = 1,5
66 1log for 10
1max
i imax,EC
SN N
S
31 1 1 *400 7ck
max,EC if
S R
* mini
max,EC
SR
S
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19Improved formulation for compressive fatigue strength of concrete
Summary - Design
• No change at 106 cycles• Suitable for HSC• 5% lower bound > 1:
conservative• γc = γc,fat = 1,5• k1 = 1
• No iterations needed
, 1 0( ) 1400ck
cd fat cc cdff k t f
, ,1
14110cd max i
i
E
RiN
,
cd,min,ii
cd,max i
ER
E
,
,
cd min,icd,min,i
cd fat
Ef
, ,,
cd,max,icd max i
cd fat
Ef
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20Improved formulation for compressive fatigue strength of concrete
Contact:Eva [email protected]@usfq.edu.ec