PSI - Issue 10

A. Marinelli et al. / Procedia Structural Integrity 10 (2018) 104–111 A. Marinelli and M.R. Stewart / Structural Integrity Procedia 00 (2018) 000 – 000

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7

Span/Depth ra tio= Span/Depth ra tio= Span/Depth ra tio=

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.8 0.6 0.4 0.2 0.0 Deflection at mid-span [mm] 0 1600 100 200 300 Deflection at Mid-Span (mm) 160 1800 1800 1800 1400 1600 1800 Span/Depth ratio 200

Span/Depth Ratio = 5/2 Span/Depth ratio = 4 Span/Depth ratio = 6 Span/Depth r tio=

Span/Depth ratio

Span/Depth Ratio = 5/2 Span/Depth Ratio = 4 Span/Depth Ratio = 6

Span/Depth ra tio= Span/Depth ra tio=

0.12 0.12

0.1 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6 5/2 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6 5/2 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6 5/2 Span/Depth ratio

0.06 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6 4.0 1800 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6 4.0 0.08 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6 4.0 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Spa 5/2 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Spa 5/2 0.08 1800 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Spa 5/2 Span/Depth ratio

1800 pan/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6 4.0 pan/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6 4.0 1800 pan/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6 4.0 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6

1000 1000 1200 1200 1400 0 1400 1400 1600 1600 1600 1800

0.04 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6 6.0 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6 6.0 1600 6.0 1600 6.0 0.04 1800 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6 6.0 6.0

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CMOD (mm)

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Specimen span [mm]

(a)

1200 1400 (b) Fig. 6. (a) Deflection at mid-span vs. span length for all span/depth ratios; (b) CMOD vs. span length for all span/depth ratios. 1200 1400

1000 1000 1200

1000 1000 1200 1000

Span/Depth ra tio= Span/Depth ra tio= Span/ epth ra tio=

Span/Depth ratio

800 Span/Depth ratio Span/Depth ratio 300 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6 5/2 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6 300 Span/Depth Ratio = 5/2 Span/Depth Ratio = 4 Span/Depth Ratio = 6 Span/Depth ra tio= Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 S 5/2 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 S Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 S / t ti 6 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 1800 Span/Depth ra tio= Span/Depth ra tio= 1800 150 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6.0

Span/Depth Ratio = 5/2 Span/Depth Ratio = 4 Span/Depth Ratio = 6

200 200 400 200 400 100 1400 1600 1800 1400 1600 1800 16 0 1800 400 600 600 600 800 800 800

0 0 0 200 200 400 200 400 14 0 1600 1400 1600 1800 1200 1400 1600 1800 600 800 800

3.5

400 600 600 Fracture Energy (Nm/m 2 ) 1800 4.0 6.0 4.0 6.0 4.0 6.0 200 100 0 Fracture energy [Nm/m 2 ] Load (N) Load (N) Load ( 200 5/2 5/2 0 50 0 100

800 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6 4.0 1800 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 S an/ Depth Ratio = 6 4.0 : 250 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 S an/ Depth Ratio = 6 4.0 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 5/2 5/2 Span/Depth ratio Load (N) Load (N) Load 100 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6 1600 Span/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6 1600 Load (N) Load (N) Load (N) 180 1800

3 3

200 200 400 200 400 0 400 600 600 800 800 800

200 200 200 400 400 600 400 600 600 800 800

600 Load (N) Load (N) Load (N) 2 2.5 2

1.5 pan/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6 6.0 pan/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6 6.0 1600 pan/Depth Ratio = 5/2 Span/ Depth Ratio = 4 Span/ Depth Ratio = 6

1 1

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Flexural Strength (MPa)

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uth Opening Displacement (mm) uth Opening Displacement (mm) uth Opening Displacement (mm) 1200 1200 1200 (a)

0 0 0 Crack Mouth Opening Displacement (mm) Crack Mouth Opening Displacement (mm) Crack Mouth Opening Displacement (mm) 0.4 0.6 0.8 1 1.2 Crack Mouth Opening Displacement (mm) 0.4 0.6 0.8 1 1.2 Crack Mouth Opening Displacement (mm) 1.4 0.4 0.6 0.8 1 1.2 rack Mouth Opening Displacement (mm) 0.8 1 1.2 1.4 1000 1200 1200 1200 1200 1000 800 1000 1 00 800 (b) Fig. 7. (a) Flexural strength vs. span length for all span/depth ratios; (b) Fracture Energy vs. span length for all span/depth ratios. 0 0 0 0.2 0.2 0.2 1.4 1.4 1.4 1.4 1200 1000 1000 0.2 0.2 0.2 0.4 0.4 0.4 0.6 0.6 0.6 1 0 0 0 Crack Mouth Opening Displacement (mm) Crack Mouth Opening Displacement (mm) Crack Mouth Opening Displacement (mm) 1.4 800 1000 800 Most of the specimens failed in a similar manner for all shapes, with cracks appearing to propagate from the tip of the notch and then veering slightly off-center (Fig.4). With the span/depth ratio of 6, there were occasions when the specimens failed off-center, with the crack starting at a random location between the notch and roller supports. Most irregular failure modes observed were attributed post-failure to the presence of relatively large mineral build ups within the specimen that promoted failure planes around them. Crack Mouth Opening Displacement (mm) Crack Mouth Opening Displacement (mm) Crack Mouth Opening Displacement (mm) 1000 1000 1000 1000 1000 800 Load (N) 800 800 Load (N) 1000 600 Load ) 800 0 0 0 The main objective of this research was to examine the effect that test specimen size and shape have on several key properties of P rtland limestone, ncluding deflection at mid-span at peak load, CMOD t peak load, flexural strength and, in particular, fracture energy. This was achieved by subjecti g a batch of specimens, containing three different shapes (span over depth ratio) that came in t ree different sizes (spans), to a series of three-point bending tests at Edinburgh Napier University’s Heavy Struct res l aboratory. For the specimens tested, a bilinear relationship between the studied deflection and specimen span length was identified for span/depth ratios of 5/2 and 4, with a gentle positive gradient existing between span lengths of 200 mm and 400 mm, before a dramatic increase between span lengths of 400 mm and 800 mm. For test specimens with a span/depth ratio of 6, this deflection appeared to increase linearly with span length. It was also observed that this deflection appeared to be independent from the span/depth ratio of the specimens, for span lengths 200 mm and 400 mm but for span lengths at 800 mm, it increased as the span/depth ratio decreased. A similar pattern of observations was made for the CMOD at peak load, leading to the conclusion that it appears likely for a critical specimen size to exist for Portland limestone, where the effect of specimen size and shape becomes more apparent. A negative correlation between the flexural strength of Portland limestone specimens and their span lengths for all three shapes was observed, supporting the findings by Rokugo et al. (1995). This was most evident for span/depth ratio of 6, with a significant decrease in flexural strength recorded between the span lengths of 200 mm and 400 mm. 200 200 400 200 400 400 600 600 600 800 0 0 0 0.2 0.2 0.2 0.4 0.4 0.4 0.6 0.6 0.6 1 Load (N) Load (N) Load (N) 0 0 0 200 200 200 400 400 600 400 600 600 800 800 800 0 0 0 0.2 0.2 0.2 0.4 0.4 0.4 0.6 0.6 0.6 0.8 0.8 1 1 Load (N) Load (N) Load (N) Crack Mouth Opening Displacement (mm) Crack Mouth Opening Displacement (mm) Crack Mouth Opening Displacement (mm) 0 0 0 200 200 400 200 400 400 600 600 600 Load (N) Load (N) Load (N) 800 800 0 0 0 0.2 0.2 0.2 0.4 0.4 0.4 0.6 0.6 0.6 0 0 0.8 0.8 0.8 1 1 1 1.2 1.2 1.2 1.4 1.4 1.4 1 1 Crack Mouth Opening Displacement (mm) Crack Mouth Opening Displacement (mm) Crack Mouth Opening Displacement (mm) 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 0 0 0 200 200 400 200 400 400 600 600 0.2 0.2 0.2 0.4 0.4 0.4 0.6 0.6 0.6 1 0.8 0.8 0.8 1.2 1.2 1.2 Crack Mouth Opening Displacement (mm) Crack Mouth Opening Displacement (mm) Crack Mouth Opening Displacement (mm) 0.8 1.2 0 0 0 200 200 200 400 400 600 400 600 600 800 0 0 0 1.2 1.4 1.4 Load (N) Load (N) Load (N Crack Mouth Opening Displacement (mm) Crack Mouth Opening Displacement (mm) Crack Mouth Opening Displacement (mm) 0.2 0.2 0.2 0.4 0.4 0.4 0.6 0.6 0.6 0.8 0.8 0.8 1 1 1 1.2 1.2 1.2 1.4 1.4 1.4 Crack Mouth Opening Displacement (mm) Crack Mouth Opening Displacement (mm) Crack Mouth Opening Displacement (mm) 0 1 0.2 0.4 0.6 4. Conclusions 0.2 0.2 0.2 0.4 0.4 0.4 0.6 0.6 0.6 0.8 0.8 1 1 1.2 1.2 0.8 0.8 0.8 0 0 0 0.2 0.2 0.2 0.4 0.4 0.4 0.6 0.6 0.6 0.8 0.8 1 1

1 1 1

Crack Mouth Opening Displacement (m Crack Mouth Opening Displacement (m Crack Mouth Opening Displacement (m 0.8 1.2

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1.2 1.2

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Crack Mouth Opening Displacement Crack Mouth Opening Displacement Crack Mouth Opening Displacement 0.8 1.2 1.2 1.4

1.2 1.2