Issue 60

A. Elakhras et alii, Frattura ed Integrità Strutturale, 60 (2022) 73-88; DOI: 10.3221/IGF-ESIS.60.06

MC-FD FRC

MC-FD FRC

MC-FGC

Beam Code L/d

at first cracking

at max stress

at max stress

K IC S , MPa.m 0.5

CTOD C S , mm

C f S , mm

K IC S , MPa.m 0.5

CTOD C S , mm

C f S , mm 7.70

K IC S , MPa.m 0.5

CTOD C S , mm

C f S , mm 43.3

B4-1

0.888

B4-2

4

1.49

0.0048

0.892

2.09

0.20

7.695

2.10

0.038

43.1

B4-3

0.897

7.69

43.0

B5-1

0.972

9.373

46.10

B5-2

5

1.36

0.0046

0.975

1.86

0.196

9.361

2.05

0.039

45.90

B6

6

1.28

0.00464

1.108

1.50

0.0143

7.668

2.00

0.040

52.7

Table 3: The proposed parameters of ETPFM for MC-FD FRC and MC-FGC.

Reliability of the present predicted fracture toughness Reliability of the predicted K IC from ETPFM for MC-FD FRCwas examined, at first cracking and maximum stress, with L/d ratios equal to 4, 5, and 6. The concept of the maximum size of the non-damaged defect ( max d ) was used in this study [30,31,44–47]. It is based on the concept of critical distance theory and has an obvious indication of the maximum imperfection size present in a material. Pook[48,49] used this theory to calculate the maximum size of imperfection in metals subjected to repeated loads. Alternatively, max d it is analogous to the characteristic length (  2 F ch t l EG f ) [49–51]. fl f is the flexural strength for smooth specimens. The values of fl f of smooth specimens were obtained from previous research by Sallam and co-workers [5]for the same dimensions of MC specimens. The consistency of K IC has been examined by comparing the value of max d with nominal maximum aggregate size (NMAZ). Logically, the values of max d /NMAZ should be around unity. Sallam and co-workers found that for rigid pavement, the ratio max d /NMAZ  2 [31] and for flexible pavement, this ratio is less than 0.75 [46]. Fig. 9-a shows the max d /NMAZ for MC-FDFRC at the first cracking range between 1.01 and 1.54. The values were considered close to unity. Also, the maximum damage of ETPFM was considered close to the NMAZ. Also, Fig. 9-b shows that max d /NMAZ for MC-FD FRC at maximum stress range between 1.38and 2.89. The increase in max d /NMAZ ratios is considered appropriate at maximum stress, as the damage is larger than at first cracking. In the case of through-thickness crack, max d /NMAZ was found to be less than unity [30,31]. A similar finding was found in the present work for MC-FD FRC at first cracking with a small increase due to fibers' closing effect in MC. The discrepancy and the higher values of MC-FD FRC at maximumstresscompared to [30,31]can be attributed to the bridging and closing effect of short steel fibers, which subsequently increases the ratio between the fracture toughness and the smooth specimen flexural strength. These findings indicate that K IC value for MC-specimens predicted from ETPFM is considered appropriate according to max d concept. Comparison between experimental and predicted results from ETPFM Another effective method to examine the reliability of ETPFM methods is by comparing the expected results of CMOD C predicted from this method by the present experimental results at first crack initiation. Due to the direct proportionality between K IC and the characteristic crack length according to each method, the predicted CMOD C can be calculated based on the predicted effective crack growth extension (C f S or ∆ a e ) and critical flexural strength. Thus, the proposed equation to predict CMOD C by C f values calculated from ETPFM is Eqn. (4), see Tab. 3. Fig. 10 shows the predicted CMOD C S values from ETPFM and the experimental values of stress-CMOD C , Fig. 5, for all specimens with different L/d ratios equal to 4, 5, and 6 at first cracking for MC-FD FRC and MC-FGC. All values of the experimental and predicted results of Thus, max d is equal to           f 2 1 1.12 IC fl K , where

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