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# Improved formulation for compressive fatigue strength of concrete

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Presentation from ICCRRR 2015

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### Improved formulation for compressive fatigue strength of concrete

1. 1. 07-10-2015 Challenge the future Delft University of Technology Improved Formulation for Compressive Fatigue Strength of Concrete Dr. Eva Lantsoght, Dr. Cor van der Veen, Dr. Ane de Boer
2. 2. 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)
3. 3. 3Improved formulation for compressive fatigue strength of concrete Literature survey Introduction • 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
4. 4. 4Improved formulation for compressive fatigue strength of concrete Literature survey Important 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 1,2 1,0 0,8 0,6 0,4 0,2 0 0 1 2 3 4
5. 5. 5Improved formulation for compressive fatigue strength of concrete Literature survey Fatigue high strength concrete Reference fc,mean,max (MPa) Influence fc? Petkovic et al., 1990 95 No Kim & Kim, 1996 103 Yes Hordijk et al., 1995 78,2 No Lohaus et al., 2011 170* No Lohaus & Anders, 2006 145* Yes Tue & Mucha, 2006 65 Yes *: specimens with fibre reinforcement
6. 6. 6Improved formulation for compressive fatigue strength of concrete Literature survey Fatigue 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”
7. 7. 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 = 1,5 EC 2-2+NA: mismatch at Ni = 106, γc = 1,35 Kim & Kim: influence of fc’ , γc = 1,5
8. 8. 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
9. 9. 9Improved formulation for compressive fatigue strength of concrete Database of test results (2) Region of low-cycle fatigue? Distribution concrete classes in database
10. 10. 10Improved formulation for compressive fatigue strength of concrete Proposed methods for 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 , ,1 14 1 10 cd max i i E R iN         , cd,min,i i cd,max i E R E  , , cd min,i cd,min,i cd fat E f   , , , cd,max,i cd max i cd fat E f   , 1 0( ) 1 400 ck cd fat cc cd f f k t f       
11. 11. 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
12. 12. 12Improved formulation for compressive fatigue strength of concrete Proposed methods for 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 1 log for 10 1 max i i max,EC S N N S     3 1 1 1 * 400 7 ck max,EC i f S R             * min i max,EC S R S  61 log 14 for 10 1 cd,max,i i i i E N N R    
13. 13. 13Improved formulation for compressive fatigue strength of concrete Proposed methods for assessment (2) • Comparison proposal – experiments with Smin = 0,05
14. 14. 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
15. 15. 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
16. 16. 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 Char Design 1,5 1,212 0,063 5,2% 1,109 Assessment 1,5 1,135 0,081 7,1% 1,002
17. 17. 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
18. 18. 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 1 log for 10 1 max i i max,EC S N N S     3 1 1 1 * 400 7 ck max,EC i f S R             * min i max,EC S R S 
19. 19. 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( ) 1 400 ck cd fat cc cd f f k t f        , ,1 14 1 10 cd max i i E R iN         , cd,min,i i cd,max i E R E  , , cd min,i cd,min,i cd fat E f   , , , cd,max,i cd max i cd fat E f  
20. 20. 20Improved formulation for compressive fatigue strength of concrete Contact: Eva Lantsoght E.O.L.Lantsoght@tudelft.nl elantsoght@usfq.edu.ec