Procedia Engineering 193 ( 2017 ) 35 41

3. Analysis of test results 

Table 2 summarizes the results for the hardened concretes. Mass changes in the specimens tested against freeze-

thaw cycles are shown in Fig. 1 and 2. The number of free-thaw cycles was 150, while the 

ǻm values for one 

specimen of concrete B were extrapolated to 165 cycles. The graphs indicate the varied nature of the changes. For 

concrete A, the specimens show mass increase from the very beginning of cyclic freezing. For concrete B, the mass 

increase is minor (1-6 g) for about 100 cycles. At 100-125 cycles, a substantial increase in mass gain is observed, 

which indicates a rapid deterioration process, crack formation and absorption of additional water amount. 

Microcracks were observed at the surface of the specimens.  

      Table 2. Properties of the hardened concrete specimens. 

Properties 

Concrete A 

Concrete B 

f’

cm

, MPa 

65.0 

94.9 

n

w,

 % 

5.2 

3.8 

ǻm 150, g 

12.6 

22.5 

ǻR 150, % 

30.5 

19.8 

ǻg 150, % 

0.52 

0.90 

 

 

Fig. 1. Changes in mass in concrete A during freeze-thaw cycles. 

0

2

4

6

8

10

12

14

16

0

25

50

75

100

125

150

Number of cycles N

M

as

s

 c

hange 

ǻ

m,

 g

#1

#2

#3

#4

#5

---

39

 Jerzy  Wawrzeńczyk and Agnieszka Molendowska  /  Procedia Engineering   193  ( 2017 )  35 – 41 

 

Fig. 2. Changes in mass in concrete B during freeze-thaw cycles. 

Knowing the history of variations in mass of the specimens against the number of freeze-thaw cycles for each 

specimen, the critical number of cycles needed to damage it was determined. The mass increase 

¨m, used as the 

indication of frost damage, allowed the analysis of the frost deterioration process by the probabilistic approach.  

When 

ǻm

gr

 was assumed to be 10 g for concrete A and 12 g for concrete B, the number of cycles needed to reach 

the limiting mass increase was determined from the graphs for each specimen in the series (Table 3).  

              Table 3. Number of freeze-thaw cycles at which concrete fails. 

Properties 

Number of cycles 

sample #1 

sample #2 

sample #3 

sample #4 

sample #5 

sample #6 

Concrete A 

N for 

ǻm = 10g 

133 108 116 124 133  - 

Concrete B 

N for 

ǻm = 12g 

132 133 138 140 143 158 

      

The statistical analysis of the results was performed with the use of the STATISTICA package [13]. The data in 

Table 3 were used to plot the graphs of the distribution of points on the Weibull grid as shown in Fig. 3. The 

characteristic life parameter, shape parameter and least life parameter of the three-parameter Weibull distribution 

were determined for the given concrete. Values of the parameters are summarized in Table 4. These values were the 

basis for preparing the reliability plots against uptime (number of freeze-thaw cycles), on which confidence curves 

were added for the mean values, with the probability assumed to be 90% (Fig. 4). 

      Table 4. Weibull parameters. 

Parameters 

Concrete A 

Concrete B 

Characteristic life parameter, 

Į 39.104 

11.844 

Shape parameter, 

ȕ 3.7365 

0.67003 

Least life parameter, 

Ȗ 90.303 

131.92 

 

 

0

4

8

12

16

20

24

28

0

25

50

75

100

125

150

175

Number of cycles N

M

as

s

 c

hange 

ǻ

m,

 g

#1

#2

#3

#4

#5

#6

---

40  

 Jerzy Wawrzeńczyk and Agnieszka Molendowska  /  Procedia Engineering   193  ( 2017 )  35 – 41 

a)

2.8

2.9

3.0

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

X= log(N-

Ȗ)

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

Y

=

 l

og(l

og(1/(1-F

(N

))))

b)

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

X= log(N-

Ȗ)

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

Y= log(log(1/(1-F(N

))))

 

Fig. 3. Weibull regression results a) concrete A, b) concrete B. 

a) 

50

75

100

125

150

F-T cycles N

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Reliabilit

y R(

N)

b)

50

75

100

125

150

F-T cycles N

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Reliability R(N)

 

Fig. 4. Reliability functions with confidence intervals a) concrete A, b) concrete B. 

This analysis allows taking into account not only the mean values but also the scatter of the results from mass of 

the specimens exposed to freezing and freeze-thaw resistance tests. Also the curves of reliability and probability of 

the time of correct work can be plotted. The plots help determine the probability (“risk”) of the limiting defects in 

the frozen concrete against the number of freeze-thaw cycles. For concrete A, for probability R(N)=80% the number 

of cycles ranges from 101 to 123, with the average number of 116. For concrete B, the number of cycles is in the 

range 130-135, with the average cycle number of 132. Concrete A will not survive 150 cycles (F150). Probability 

that concrete B will survive 150 cycles is R(N)=27%, although when the freeze-thaw resistance is evaluated 

according to the procedure set out in the standard, the decrease in strength 

ǻR does not exceed 20%.