Presentation from ICCRRR 2015

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. 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. 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. 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. 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. 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. 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. 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. 9Improved formulation for compressive fatigue strength of concrete
Database of test results (2)
Region of low-cycle fatigue? Distribution concrete classes in database

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. 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. 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. 13Improved formulation for compressive fatigue strength of concrete
Proposed methods for assessment (2)
• Comparison proposal – experiments with Smin = 0,05

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. 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. 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. 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. 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. 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. 20Improved formulation for compressive fatigue strength of concrete
Contact:
Eva Lantsoght
E.O.L.Lantsoght@tudelft.nl
elantsoght@usfq.edu.ec