R.D.J.M. Steenbergen/A.H.J.M. Vervuurt · Determining the in situ concrete strength of existing structures for assessing their structural safety
from one batch or pour, whereas an entire structure mostly consists of several concrete pours. In assessing the strength of an existing structure, we are interested in the strength of the section that is decisive for the stress distribution. Firstly, this section is not exactly known beforehand. Secondly, concrete cores are never drilled from that section; they are drilled from a more or less unimportant edge of the structure. For this reason, a translation has to be made between the statistical distribution of the measured strength of cores somewhere in the structure and the statistical distribution of the strength of the section governing the structural analysis. An accidentally small standard deviation obtained from tests on cores often taken from an edge of a structure may therefore be not representative for the governing section, especially if that low standard deviation is much smaller than the average standard deviation obtained from many experiments on similar types of concrete structures. For this reason, in order to establish a safe method, a minimum standard deviation smin is introduced which is to be applied if the measured standard deviation turns out to be less than this smin. This minimum standard deviation is considered to be a fixed property of the population considered; it is a safe value established by expert judgment. No statistical uncertainty is involved because the value of smin is only used in case a real, measured standard deviation is judged to be too small for safety reasons. In the proposed new method, the characteristic value of the concrete compressive strength is determined by the minimum of two values: A) the strength based on the measured test results, including the statistical uncertainty, and B) the strength based on the mean values of the measured test results and a minimum, constant standard deviation smin. This may be considered as a safe approach because very small, measured standard deviations are fixed at a larger smin. Based on a log-normal strength distribution, the characteristic concrete compressive strength is then obtained from the lowest value of: method A: ¨« 1 ¬« fck = exp fcm (Y ) u exp ©<tn<1, p=0.05 u s(Y ) u 1 + n ®« ª« and
{
}
(4)
method B: ¨« 1 ¬« fck = exp fcm (Y ) u exp ©<1.64 u smin(Y ) u 1 + n «® ª«
{
}
(5)
Subsequently, the value for smin(Y) in the log-normal domain can be calculated from: 2¥ £ £ s ¥ smin(Y )= ln ²1 + ² min ´ ´ ² ¤ fcm ¦ ´ ¤ ¦
(6)
The test results of cores taken from existing structures may be adopted for determining the value of the minimum standard deviation smin. Similar types of structures or structures that are produced identically (e.g. prefabricated
Fig. 1. Cumulative distribution of the standard deviation of the concrete compressive strength for two types of existing structure (types I and II)
Table 2. Minimum value of standard deviation (smin) for two types of structure and different probabilities of being exceeded
smin in N/mm2 related to probability of being exceeded type
80 %
50 %
35 %
20 %
10 %
I
5
7
9
10
11
II
10
11
12
13
14
beams versus in situ cast concrete) may serve as a solid basis for determining smin. This is illustrated in Fig. 1. The figure shows the cumulative distribution function for the standard deviation obtained from a number of existing structures of different types (type I = slab structures, type II = slender T-beams). It should be noted that, for practical use, a more generalized and internationally accepted value for smin is recommended. The value smin can be obtained based on the cumulative distribution function (Fig. 1) and a safe value for the probability of exceedance. According to Fig. 1, for structure types I and II, values for smin at different probabilities of exceedance are given in Table 2. In the literature, the standard deviation of the concrete compressive strength at t = 28 days is generally assumed to be constant at s = 5 N/mm2 (e.g. fib Model Code [5]). This is confirmed by numerous test results in concrete plants. From Fig. 1 it is concluded that a higher value for s is found for 80 % of the type I structures. For the type II structures, this figure rises to 99 %. Therefore, it is concluded that for existing structures, the standard deviation may be expected to be greater than generally assumed for new structures and a larger value for smin is suggested. An smin value equal to or less than the mean value in Fig. 1 would be appropriate. Applying an excessively large value would – unreasonably – cancel lower measured standard deviations of concrete strength. The fixed value smin is only needed to correct for possibly excessively low measured standard deviations of core strengths that are not taken from the governing section in the structure; for that
Structural Concrete 13 (2012), No. 1
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