Experimental Evidence for Size Effect

The size effect law proposed by Bazant (Eq. (1.4.10)) has been verified by a large number of experimental data, for both notched fracture specimens and unnotched structures. We will postpone a full discussion of the implications of size effect for structural analysis until Chapter 10, but we will review the evidence now. ‘

Results from 23 test series, among those available, are briefly examined in the following, corresponding to various authors, materials, and specimens. The essentials of the specimen characteristics are summa­rized in Table 1.5.1 and Fig. 1.5.1. In particular, the coefficient c?,- corresponding to Eq. (1.4.1) to each series of experiments is included in Table 1.5.1. Some characteristics of the materials, together with the size range and the best fits for В f’t and Do, are summarized in Table 1.5.2, where the sources of the data arc also displayed. Further details of the tests are given in the following; however, detailed descriptions are not given; they can be obtained from the referenced sources.

Since various fitting procedures have been used in the literature to get the optimal fit of the size effect law to the experimental data, a unified procedure has been useebin this book. In this procedure the nonlinear regression is directly performed on the data presented as a bilogarithmic diagram (see Chapter 6 for a discussion of the fitting procedures). To do so, we call v — In o/v„, and take v to be the variable whose quadratic error is to be minimized with the following approximating equation —equivalent to (1.4.10):

v — ln(B/t’) — 0.5 In ^1 + (1.5.1)

The optimal fits for В f’t and Do were calculated using a standard Levenbcrg-Marquardt algorithm. The values of Bf[ and Do with their standard errors are given in Table 1.5.2.

Experimental Evidence for Size Effect

Experimental Evidence for Size Effect

DEN-S;p

ГГ-ійгГ

D – rD/6

 

DEN-T

 

In ®/6 IP і lu ,id/6

 

P/15* 4D/3

 

8D/3

 

LRB-UB D

P/2^ ^jjrP/2

 

thickness b

 

Experimental Evidence for Size Effect

Figure 1.5.1 Summary of specimens used for size effect verification.

 

Table 1.5.2 Essential data of size effect tests

Series

Material

daa

(mm)

Strength1′

(MPa)

Elastic Modulus (GPa)

Size Range (mm)

ВП

(MPa)

Do

(mm)

A1

concrete

12.7

23.1

n. a.

75-381

4.5 ±0.9

ЗЇГЗГІ T

A2

concrete

12.7

35.4

n. a.

76-381

2.8 ±0.5

157 ±99

A3

concrete

12.7

14.3

n. a.

76-381

3.2 ±2.1

34 ±52

A4

concrete

12.7

15.6

n. a.

76-381

1.7 ±0.3

126 ±78

A5

concrete

12.7

46.8

n. a.

76-381

2.9 ±0.4

212 ± 114

A6

concrete

12.7

32.7

n. a.

76-381

4.1 ±0.7

55 ± 23

131

concrete

12.7

34.1

n. a.

76-305

6.0 ±0.3

60 ± 10

В 2

concrete

12.7

37.4

n. a.

76-305

3.9 ± 0.2

54 ± 10

B3

concrete

12.7

29.1

n. a.

76-152

2.7 ±0.1

184 ±38

134

concrete

12.7

39.7

n. a.

76-305

4.6 ±0.1

719 ± 130

Cl

mortar

4.83

48.4

n. a.

76-305

14 ±4

7.7 ± 4.4

C2

mortar

4.83

48.1

n. a.

76-305

6.6 ± 1.3

10 ±5

C3

mortar

4.83

46.4

n. a.

76-152

3.3 ±0.1

95 ± 17

C4

mortar

4.83

49.0

n. a.

76-305

5.9 ±0.2

190 ±25

DI

HSC

9.5

96.0

n. a.

38-152

32 ±8

19 ± 11

111

marble

4

l. T-

36

12.5-100

3.7 ±0.2

47 ± 10

E2

granite

2

12.3е

39

12.5-100

5.1 ±0.2

35 ±5

1;1

limestone

1.5

3.45е

30.5

13-102

3.3 ±0.1

45 ±6

G1

Si02

0.02

58

5-32

17 ±3

2.6 ± 1.2

G2

SiC CN-137

2

130

7-37

36 ±4

101± 157

G3

SiC CN-163

2

140

7-37

35 ±3

7.3 ±2.2

HI

concrete

9.5

33.3

n. a.

76-610

2.7 ± 0.1

352 ± 63

112

concrete

9.5

23.6

n. a.

76-1219

1.95 ± 0.05

601 ± 83

11

microcon.

6.35

45.8

13-51

45.9

36 ± 14

6±6

J1

mortar

4.83

43.7

n. a.

38-152

5.4 ±0.3

37 ±6

12

mortar

4.83

43.6

n. a.

38-152

6.2 ±2.1

23 ± 20

K1

« mortar

4.83

46.8

n. a.

41-163

2.2 ±0.1

151 ±40

K2

mortar

4.83

46.2

n. a.

21-330

4.6 ± 1

11 ±6

LI

microcon.

6.35

па

48-53

25-102

10.3 + 1.3

178± 178

“Maximum aggregate or grain size. b Compressive unless otherwise stated. “Splitting tensile strength.

 

Experimental Evidence for Size EffectExperimental Evidence for Size Effect

Experimental Evidence for Size Effect

Experimental Evidence for Size Effect

Figure 1.5.2 Size effect results of Walsh (1972).

 

Подпись: 0.1 1 10 Figure 1.5.3 Size effect results of Bazant and Pfeiffer (1986, 1987).

D/Do