RATE EFFECTS

Dr. Volker Slowik
Objectives

Within the context of a linear elastic dynamic analysis

1. How many times can the tensile strength of concrete be exceeded by cyclic loads before cracking?
2. How is concrete fracture resistance affected by low cycle variable amplitude loading fatigue?
3. How can we determine the extent of crack growth during a seismically excited crack in a dam?

Current assupmtions

1. Empirical rules

Never validated!

Experiments

Set-Up

  

Loading:

  

1. Harmonic loading, with increased frequencies (up to 10Hz), and constant amplitude;
2. Variable amplitude loading to simulate the presence of spikes.

   
   

Test Matrix

Specimen Experiment Frequency Loading rate [Hz]

G01 CMOD controlled - 1 m/s

G02 load controlled - 100 N/s

G03 CMOD controlled - 1 m/s

G04 fat. loading CMOD contr. 3

G05 fatigue loading 3 -

G06 fatigue loading 3 -

G07 fatigue loading 3 -

G08 fatigue loading 3 -

G09 cyclic loading - 1 m/s

G10 fatigue loading 3 -

G11 fatigue loading 3 -

G12 fatigue loading 3 -

G13 fatigue loading 10 -

G14 CMOD controlled - 1 m/s

G15 fatigue loading 10 -

G16 fatigue loading 3 -

G17 fatigue loading 3 -

G18 fatigue loading 3 -

G19 fatigue loading 3 -

G20 fatigue loading 3 -

G21 fatigue loading 3 -

K01 CMOD controlled - 1 m/s

K02 cyclic loading - 1 m/s

K03 cyclic loading - 1 m/s

K04 CMOD controlled fast" - 1mm/s

K05 "CMOD controlled fast" - 1mm/s

K06 fatigue loading 3 -

K07 CMOD controlled - 1 m/s

K08 fatigue loading 3 -

K09 CMOD controlled - 1 m/s

K10 fatigue loading 3 -

K11 CMOD controlled - 1 m/s

K12 fatigue loading 3 -

K13 fatigue loading 3 -

K14 fatigue loading 3 -

K15 fatigue loading 3 -

K16 CMOD controlled - 1 m/s

K17 fatigue loading 3 -

K18 fatigue loading 3 -

Results

1. Confirmed that for a seismic load the static one, the strength is increased by .

   

2. No physical justification to allow for tensile excursion from a purely ``material'' point of view (as this is simply a tool to address the inherent limitations of a linear elastic analysis).
3. Spikes accelerate the rate of crack growth (contrary to metals)
4. No substantial difference in strength and fatigue life between specimens tested at 3 Hz from those tested at 10 Hz.
5. During repeated loading, crack propagation is primarily driven by the reduction in the fracture process zone.

   

Computational Model

• A simplified computational model is proposed. This model should
  1. Determine rate of crack growth in terms of load history
  2. Account for size effects and load histories
• No such model was previously proposed.
• Model was calibrated with our experimental results and assessed with others.
• Model could be used in conjunction with a linear elastic dynamic analysis to determine crack growth through cycle by cycle integration.
• Current fatigue models (Paris, Forman, etc...) were found to be not applicable for concrete

  

  where a is the crack length, N, the number of load cycles, K the stress intensity factor, and are material properties.

• Walker Law could provide an adequate fit, however it can not account for size effect, and load history.

  

• Proposed model

  

  Where is the maximum stress intensity factor in the past load history; the individual cycle maximum stress intensity factor; n,m, p material properties; the fracture toughness; is a function which takes into account the sudden increase of the equivalent crack length due to the peak load;

• Crack propagation for each load cycle can then be determined from

  

  and this could be implemented within a linear elastic dynamic analyis propgram of concrete dams.

• The following results are obtained for the large and small specimens.