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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
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)
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
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
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
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”
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
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
9Improved formulation for compressive fatigue strength of concrete
Database of test results (2)
Region of low-cycle fatigue? Distribution concrete classes in database
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
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
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
13Improved formulation for compressive fatigue strength of concrete
Proposed methods for assessment (2)
• Comparison proposal – experiments with Smin = 0,05
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
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
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
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
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
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
20Improved formulation for compressive fatigue strength of concrete
Contact:Eva [email protected]@usfq.edu.ec
