2.1 Considerations on compressive strength gain over time

One possible approach to the assessment of structural safety consists in the analysis of long time behavior of concrete during time considering effects of strength evolution and long lasting load. In determining admissible compressive stress, σ_cd, coefficients γ_c and β are used - design values based on characteristic values defined from probabilistic considerations for each limit state. γ_c coefficient represents differences between concrete from standard specimen and concrete from structural element as well uncertainties related to actions (^{Couto et al, 2015}), while β is derived from the product of partial coefficients, i.e., by the multiplication of benefic effects of compressive strength evolution over time (β₁) by harmful effects of long lasting load (β₂) (^{Silva Filho; Helene, 2011}).

Compressive strength evolution over time can be calculated by using mathematic models related to the compressive strength at 28 days. (^{Klemczak et al, 2015}). It is well knowed that this evolution varies depending on the cement type, ambient temperature and curing conditions (^{CEB, 1990}). Maintaining the ideal curing conditions and temperature at 20ºC, it is possible to estimate strength gain over time, using equations (1) and (2), proposed by fib Model Code 2010 (^{CEB, 2012}). This formulation is accepted by Brazilian Standard ABNT NBR 6118:2014 to ages under 28 days.

The loss of load capacity by long lasting loads was studied by Rüsch (1960). This decrease is constant and independent of studied concrete f_ck, besides that, is maximum of 25% (^{Silva Filho; Helene, 2011}). The fib Model Code 2010 (^{CEB FIP, 2012}) proposes an equation (3) to determine coefficient 𝛽₂, wherein the reduction coefficient varies according to the loading age.

It is estimated that the Brazilian Standard NBR 6118:2014 sets value of 1.16 to β₁ and 0.73 to β₂, considering load values at 28 days until 50 years, resulting in a β of 0.85 (^{Silva Filho; Helene, 2011}). It is observed that this values are conservative, since it admits a strength gain of only 16% in a period of 50 years and a greater decrease than the maximum established by Rüsch (1960) (^{Helene, 2011}). Thus, it is appropriate check the values of β₁ e β₂ considering formulation proposed by fib Model Code 2010 (^{CEB, 2012}) and considerations made by Rüsch (1960).

2.2 Considerations on variability of compressive strength test results

Another factor to be verified is the variability of compressive strength test results. ^{Magalhães (2014)} points out that all steps of concrete production leads to a dispersion of test results, which can be grouped in 3 different aspects: influence of materials, production methods and test procedures. Table 1 shows main factors that can affect compressive strength test results, as well the maximum variability of each factor.

Table 1 Factors that can affect compressive strength test results 

Source: Adapted from ^{Helene and Terzian (1992)}.

It can be seen that several procedures involved in preparation, acquisition and test can directly affect test results and may reduce by up to 50% of concrete compressive strength. Indeed, this variability is true, as we can see in data from research and laboratorial tests. ^{Santiago (2011)} compiled technological control data of more than six thousand test specimens, coming from nine Brazilian states. The author identified non-conformity percentages of up to 28% for C40 concrete class. This values reaches 84% for C50 concrete class.

2.3 Considerations on concrete acceptance

Another aspect to be considered is concrete receiving and acceptance. Observing the main Brazilian national and international concrete standards, it appears diverging aspects regarding method and acceptance criteria. (^{Pacheco; Helene, 2013}; ^{Magalhães, 2014}). The Brazilian standard, NBR 12655 (^{ABNT, 2015}), presents two kinds of concrete sampling: total and partial. In partial concrete sampling, only some of the total batches is sampled. In total concrete sampling, all batches are sampled and the acceptance criterion is that none of the individual sample presents compressive strength below than the characteristic strength. Despite the high cost, this sampling method is widely used in Brazil (^{Pacheco; Helene, 2013}).

The American standard, ACI 318-11: Building Code Requirements for Structural Concrete, establish three different criteria: the average of 3 consecutive test results must be equal or exceeds characteristic strength defined in design; no individual strength test is below than f_ck-3,5MPa (to concrete with f_ck below 35 MPa) and no individual strength test is below than 0,9* f_ck (to concrete with f_ck below 35 MPa) (^{Magalhães, 2014})_. Additionally, the standard does not provide total concrete sampling, establishing minimum criterion of only one sample per day to each 115 m³ of concrete or each 465 m² of builded area. (^{Pacheco; Helene, 2013}).

Another widely used standard, the British standard BS EN 206:2013 - Concrete. Specification, performance, production and conformity, presents different criterion according to the period of production: initial production or continuous production, when more than 15 results are avaible (^{Magalhães, 2014}). The first criterion is related to the average of test results, that must be above or equal to f_ck+4,0MPa, to initial production, and above or equal to f_ck+1.48*s (standard deviation of results), to continuous production. The second criterion is related to individual test results, that, for both types of production, must be above than f_ck-4,0MPa (^{Pacheco; Helene, 2013}; ^{Magalhães, 2014}).

^{Larrossa et al (2014)} conducted a comparison of the above mentioned sampling criteria to 32 concrete batches. The authors pointed out that NBR 12655 (^{ABNT, 2015}) presents most rigid criteria, followed by EN 206 and ACI 318-11. Indeed, comparing acceptance criteria adopted by international standards with the established by Brazilian standard, it can be seen that the acceptance criteria is more restrictive (^{Pacheco; Helene, 2013}; ^{Magalhães, 2014}).

3.1 Methodological procedures

In conformity control realized in a building construction, by following procedures of NBR 12655 (^{ABNT, 2015}), concrete compressive strength (f_c) of three batches of 8m³ presented test results below than the f_ck of 40 MPa, specified by designer. As the building presents obstacles to extraction of concrete cores, since the structure is made of concrete-filled steel columns, a study of concrete compressive strength evolution was made, in order to helps in the safety assessment of structure. It is noteworthy that this analysis is complementary and must be performed together with other verifications, as the design review with the obtained concrete compressive strength and realization of non-destructive tests. Concrete mix proportions are presented in table Table 2.

Table 2 Concrete mix proportions 

Source: Concrete supplier

On specified dates, compressive tests were made at certified laboratory, following standards procedures. All specimens were grinded and tests were performed in a universal machine EMIC - PC 200 CS. Results are presented in Table 3.

Table 3 Compressive strength test results of non-conforming samples 

Source: Adapted from tests reports

Regarding to conformity control used in building construction, it is important to mention that total concrete sampling was used (100%), where all of the batches are sampled. In this case, NBR 12655 (2015) states that the acceptance criterion is when all of the individual samples meet the f_ck specified by designer. As can be seen in Table 3, the potential strength, at 28 days, does not show strength above or equal than the 40 MPa specified.

Another pointed aspect is strength evolution after 28 days. In a study conducted by concrete supplier, in a year, the concrete presented a strength gain of 32.6% (cement CPV-ARI sulphate resistant with 22% of pozzolan addition), higher than the 16% considered by the ABNT NBR 6118:2014.

3.2 Results and analysis

From test results, it was performed an analysis of concrete compressive strength gain. Initially, β₁ values were calculated using s value of 0.20, since cement type is CPV-ARI. However, an addition of 33% of pozzolan was made (value relative to cement content), so it is appropriate calculate a β₁ value to a CPIV cement type, which contains 15% to 50% of pozzolan. Finally, a third β₁ value was calculated, for an intermediate s value. β₁ values for a 50 years, used in β calculation, are presented in Table 4.

Table 4 β₁ coefficient for different cement types 

Compressive strength evolution over time for the three assumptions (CPV-ARI, CPIV e CP “intermediate”), considering lowest value of f_ck,est (37,1 MPa) and a period of 365 days, can be verified in Figure 1.

Figure 1 Strength evolution according to fib Model Code 2010 

As can be seen in Figure 1, to achieve specified 40 MPa, it will take 45 days for β₁ to CPIV concrete, 51 days for β1 to CP “intermediate” and 72 days for β1 to CPV ARI. After defining β1, it was calculated β coefficient, considering two different β₂ - 0.73, as defined by ABNT NBR 6118:2014, and 0.75, maximum value as defined by Rüsch (1960). Values are presented in Table 5.

Table 5 β coefficients for different types of cement and load 

For verification of safety in this study case, it was calculated the design compressive strength of concrete f_cd, according to Equation 4, using coefficients defined in Table 5. Results are presented in Table 6.

Table 6 Concrete compressive stress 

The values obtained showed that only when considering exclusively cement CPV ARI the final stress obtained is below than the expected. For concrete with cement with pozzolan addition, as is the case of this study, design compressive concrete strength is above that required. It can be seen a conservative nature of ABNT NBR 6118:2014 - expected characteristic of a technical standard. However, there is a possibility of using consolidated knowledge and move forward in the study of compressive concrete strength gain after 28 days.

It is noteworthy that, according to ABNT NBR 6118:2014, if the compressive strength kept lower than design f_ck, a new structural design with the obtained value should be realized. Still remaining the unsafety, the use of structure should be limited, a reinforcement should be designed or even the total or partial demolition of non-conformity elements should be done.