Prediction of the compressive strength in high-strength concrete cores through the destructive metho

Abstract

Keywords: Cast Specimen; Compressive Strength; Core Drilling; Cure Environment; Destructive Test; High-Strength Concrete

Introduction

Various studies have suggested increasing the number of smaller-sized cores [9, 34]. According to the study conducted by Vasanelli et al. [35], the limited number of extracted cores does not provide a faithful representation of the concrete strength in the examined structure. The accurate conversion of core results relative to standard specimens is directly dependent on the number of cores extracted. Moreover, uncontrolled factors constitute sufficient reasons to increase the number of cores [36]. Following the research by Boussahoua et al. [37], the minimum number of cores that ensure a proper evaluation of concrete strength is seven to nine cores. According to the authors, statistical origin error is strongly influenced by the number of cores. However, Alwash et al. [38] note that precision adds little value beyond seven to eight cores, and other authors [39, 40] have concluded that compression strength stabilization occurs from nine cores onward. Contrary to specific standards such as EN 13791 [39], ACI 228 1R [41], and NA17004 [42], which recommend reducing the number of cores to avoid compromising the strength of structures. The mechanical properties of cores are influenced by several factors. For instance, researchers [10, 43] have highlighted various elements affecting core performance, including moisture, the length-to-diameter ratio (L/D), drilling direction, and the type of coring equipment used. However, there are still many factors in this domain that remain to be explored. The standards commonly applied for coring in existing structures include the American Concrete Institute (ACI) standards [41, 44, 45] and European standards [30, 46]. The mentioned studies predominantly focus on ordinary concrete containing coarse aggregates. Nevertheless, there is a scarcity of research focused on concrete designed for thin elements, such as slabs and walls [47-49]. However, literature reveals that several studies have been conducted using non-destructive tests to assess the quality of concrete. For instance, Ju et al. [50] estimated the compressive strength of high-strength concrete (HSC) from nuclear power plants using non-destructive tests on concrete specimens up to 100 MPa. The authors compared results from 30 mm, 50 mm, and 100 mm cores with those obtained from non-destructive tests. Similarly, Wankhade and Landage [51] conducted a study on a water reservoir and emphasized the importance of these non-destructive tests in identifying and detecting internal defects and cracks in concrete. However, the combined use of non-destructive tests to assess concrete strength in structures was examined by Jain et al. [52]. The validation of non-destructive tests is thus performed through destructive tests, granting them crucial importance. Ivanchev [53], along with Shrestha and Giri [54], introduced these two methods for the evaluation of compressive strength. This study aims to assess the ability to predict the compressive strength of high-strength concrete based on compression strength tests of cores and cast specimens. The correlation of compressive strength is examined across various core sizes and standard cylindrical specimens,

Concrete is widely used worldwide for the construction of structures of various sizes, whether they are large, medium, or small [1-4]. According to Monteiro et al. [5] 30 billion tons of concrete are produced globally each year. Generally, the nominal compressive strength is the most important property of concrete, and it is determined at 28 days of age [6-8]. This strength is tested on standard-shaped specimens, such as cylinders with a diameter of 150 mm and a length of 300 mm or cubes with sides of 150 mm [9, 10]. To this end, several studies have been conducted to convert the strength of cylinders to the strength of cubes, and a factor of 1.2 has been proposed for ordinary concrete [11, 12]. However, this factor decreases with the increase in concrete strength. The IS 516 (Part 4): 2018 standard recommends that the equivalent strength of a cylinder with a length-to-diameter ratio of 2 should be corrected by a correction factor of 1.25 compared to a cube [13]. However, when it comes to in-situ testing (destructive testing) to verify the quality of concrete, non-standard-sized specimens referred to as cores are commonly used. Cores are smaller in size compared to standard cylindrical specimens, which are referred to as the scale effect [14]. Compared to other non-destructive tests, these destructive tests provide more accurate compressive strengths [15, 16]. It would be prudent, therefore, to evaluate compressive strength using concrete cores. The compressive strength of cores obtained through coring (destructive testing) of both old and new structures can be influenced by the size of the specimens [17]. Numerous experimental studies in the literature examine the impact of specimen size and shape [18-21]. For instance, authors [22, 23] established a linear correlation between the compressive strengths of cubes and microcores. Chockalingam et al. [24] simultaneously investigated the effects of specimen shape, size, and aggregate size, noting that as aggregate size and specimen length increase, compressive strength, splitting tensile strength, and flexural strength decrease. A recent study examined the effects of sample size, aggregate size, and compressive strengths between 25 MPa and 30 MPa [13]. Zhu et al. [25] established the role of aggregate and sample size on the overall fragility of the structure. Other researchers have explored the influence of the maximum aggregate size on the strength of microcores [26, 27]. The smallest dimensions of microcores tested were 28 mm, as studied by Indelicato and Kilinc et al. [9, 28]. Regarding regulations, the American standard ASTM C42 for obtaining drilled cores requires a dimension of 95 mm [29]. In contrast, the new European standard EN 13791:2019 [30] requires a dimension of 100 mm and recommends that core size be at least three times the maximum aggregate size used in concrete production. It is worth noting that ISO/DIS 7032 [30,31], DIN 1048 Teil 2 [32], and the guidelines of ACI Committee 301 [33] permit the use of cores smaller than 50 mm in specific situations.

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Concrete Preparation A compressive strength of concrete exceeding 45 MPa has been developed, considered as high strength according to ACI 213R and DTR BC248 [55, 56]. This compressive strength was measured following ASTM C469 and ASTM

considering the effects of the curing environment. With the insights drawn from the results, it will become feasible to estimate the in-situ compressive strength of concrete and suggest the minimum number of cores needed for accurate predictions according to the established conversion model.

Experimental Design

Table 2. Physical characteristics of fine and coarse aggregates

Materials Used High-strength concrete was prepared using standard Portland cement of type CEM II/A 42.5. At the age of 28 days, this binder exhibits a compressive strength of 45.78 MPa and a flexural strength of 8.47 MPa. The chemical properties of the binder are detailed in Table 1. Table 2 presents the detailed properties of the 0/3.15 sand and 3/8 gravel used, while Figure 1 illustrates their respective particle size distribution.

Figure 1. Particle size distribution of the sand and aggregate.

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Figure 2. Tested concretes: (a) Cast specimen, (b) Concrete blocks for core drilling. C39 on cylinders with a diameter of 150 mm and a height of 300 mm [57, 58]. The materials used in the concrete mix include sand, aggregates, Portland cement, and tap water, as presented in Table 3. The Dreux-Gorisse method was employed as the concrete formulation method. Specimens Produced The experimental program is conducted in two series of tests, involving cast specimens as well as cores extracted from the same concrete. The first series, comprising 36 cast specimens with diameters of 50 mm, 100 mm, and 150 mm and a length-to-diameter ratio equal to 2 (L/D=2), was subjected to two environmental conditions: exposed to air (natural conditions) and submerged in water at 20 °C (Fig. 2a). The second series involves extracting 27 cores from blocks with diameters of 50 mm, 75 mm, and 100 mm, nine cores for each type (see Fig. 2b). It is noteworthy that these blocks were exposed to open air. Core drilling was performed following ASTM C42 [29], and compression tests

were conducted within 7 days of coring. Before testing, the cores were prepared following the guidelines of standard NA 5071 and DIN EN 12.504-1 [59, 60]. In this research, two length-to-diameter ratios equal to 1 and 2 were used for the cores, with their extraction performed in the direction of concrete casting. Table 4 summarizes the densities of the cast specimens as well as the cores extracted from the concrete blocks. These values represent the averages of nine specimens obtained at the age of 28 days, all made with the same concrete mix. The standard deviation and coefficient of variation values are provided for each studied specimen. To better present the experimental results, various forms of conversion models were tested, namely linear regression (1), power function (2), exponential function (3), logarithmic function (4), and polynomial function (5). These forms are commonly employed in the literature to assess

Table 4. Mean densities of cast specimens and cores Density of cast specimen Density (t/m3)

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the compressive strength of concrete in existing structures [15, 61, 62].

(1) (2) (3) (4) (5) With: or : Mean compressive strength of cores in MPa, : Mean compressive strength of standard cast specimens preserved in water or air, depending on the combination D: Core diameter in mm. The parameters a, b, and c were accurately determined from the experimental data using the least squares method. To assess the quality of the conversion model, statistical indices such as standard deviation, coefficient of variation, and coefficient of determination are utilized. Additionally, the standard deviation (SD) of the model concerning the mean compressive strength and the root mean square error (RMSE) of prediction have been used to assess the disparity between the compressive strength predicted by the model and the experimental strength. These indices have been calculated according to equations (6) and (7).

is the experimentally obtained compresWhere is the compressive strength calculated by sive strength, is the mean compressive the proposed model, and strength of the model.

Experimental Results

Case of Cores with L/D = 1 Individual simulation of the compressive strength of various cores compared to that of standard specimens, whether stored in water or air, was conducted. In total, 81 simulations were performed. To establish an appropriate relationship between the diameter (D) of the cores and the compressive strength ratios fc(d)/fc(150), correlations were conducted based on (D) and the curing method. Five different mathematical equations were tested, and equation selection was based on an analysis of four statistical indicators, including the coefficients of determination, correlation coefficient, coefficient of variation, and mean relative error. From the results obtained in Table 5, it is evident that the coefficient of variation (CV) and average relative error (ARE) are low for the exponential function in both curing conditions. As depicted in Figure 3, equations 8 and 9 were chosen as the ideal representations of the correlation between the diameter (D) of the cores and the ratios fp(d)/ fc(150), with the first equation applying to wet curing and the second to air curing. This equation format was also selected for non-destructive tests [63- 65]. (8)

Table 5. Regression formulas used and associated statistical indices (L/D=1) − f c(150) in water Function form

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Figure 3. Size effect for cores L/D=1. (a): Cure in water, (b): cure in air.

Figure 3 illustrates the ratios of 50 mm, 75 mm, and 100 mm cores to standard specimens fp(d)/fc(150), where the L/D ratio is 1. The presented results below are individual ratios from 81 simulations. The colors black, red, and blue correspond to 50 mm, 75 mm, and 100 mm cores, respectively. Conditional coring was performed, and the cores were meticulously prepared following the previously mentioned standards. The individual simulation results show that 60.49% of the fp(100)/fc(150) ratios are below 1, with an average of 0.972 (Fig 3a). In contrast, the fp(75)/fc(150) and fp(50)/fc(150) ratios are all below 1, with averages of 0.615 and 0.576, respectively. Thus, it can be observed that the compression results of the 100 mm cores are close to 1, while the other two cores require correction factors, despite their low slenderness (L/D=1). Equation (3) was selected as the most appropriate relationship, and model analysis provided us with a coefficient of determination R² equal to 0.663. The ratios fp(d)/fc(150) obtained from the experimentation show an increase when fc(150) is cured in the air. Indeed, the average of the fp(100)/fc(150) ratios is 1.05, demonstrating a slight superiority of the fp(100) cores in this specific context. However, the averages of fp(75)/fc(150) and fp(50)/fc(150) ratios are 0.665 and 0.624, respectively. An increase in these ratios is observed compared to curing in water. In the case of air curing, the suggested exponential model (Fig. 3b) has a coefficient of determination (R²) equal to 0.672. Below presents the variation of the Root Mean Square Error (RMSE) with the number of cores for the coring technique, as well as the standard deviation (SD) of the conversion model calculated according to equation 6 (Fig. 4). These two statistical parameters are related to the curing environment. A decrease in prediction error (RMSE) is observed with an increase in the number of cores in both curing environments, but the stability of the RMSE

error seems to manifest only from 8 to 9 cores for the 75 mm and 100 mm cores in the case of wet curing (Fig. 4a). On the other hand, no stability in the RMSE error was observed for the 75 mm and 100 mm cores in air curing. This is likely due to the influence of the L/D ratio of 1. However, stability in the 75 mm cores was observed in both curing conditions, from 5 cores, corresponding to strength of about 2 MPa. The standard deviation (SD) of our conversion model, measured during the determination of fc(150) in water, stabilizes from 6 cores onward (Fig. 4b). There is a slight variation in compression between 6 and 9 cores of different sizes. The 100 mm core exhibits the maximum standard deviation of the model, reaching 3 MPa. Stabilization in the case of air curing is observed between 5 and 7 cores, and then increases slightly for compressive strengths equivalent to those obtained with water curing (Fig. 4d). This is due to the curing conditions of high-strength concrete (in the open air), meaning the increase in uncontrolled parameters such as humidity and temperature, reducing the quality of the conversion model. However, increasing the number of cores will stabilize the standard deviation (SD) and the root mean square error (RMSE) of the exponential model. Table 6 presents the ratios between the cores and cast specimens of the same dimensions with the L/D ratio for cores equal to 1. The mean values, standard deviation (SD), and coefficient of variation of the compressive strengths of the cores were calculated based on 81 simulations. Overall, a prevalence of core strengths over cast specimens was observed. Analyzing the statistical indicators, it is noted that the fp(50)/fc(150) ratio of specimens cured in air exhibits a higher standard deviation and coefficient of variation.

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6. This visualization provides insight into the predictive

capability of the models as the number of cores increases. It is observed that increasing the number of cores decreases the prediction error, and consequently, the model is considered stable and reliable with at least 7 cores for the 100 mm and 50 mm cores (Fig. 6a). Several authors converge on the same conclusion, suggesting that the optimal number of cores is estimated between seven and nine [37, 38]. On the other hand, the 75 mm core stabilizes between 5 and 9 cores. In this curing case, the mean prediction error remains stable at 6.7 MPa, 2 MPa, and 5 MPa for the 100 mm, 75 mm, and 50 mm cores, respectively. The standard deviation (SD) of the model shows little variation beyond 6 cores for all three diameters (D) studied (Fig. 6b). As anticipated, there is a consistent pattern of stability in the average prediction errors (RMSE) and standard deviation (SD) during water curing. Conditional coring helps reduce uncertainties in the evaluation, along with the required number of cores, and consequently, the costs of in-situ tests.

Conclusion

In this study, a series of destructive tests (DT) was conducted on blocks cured in the open air, while another series was performed on cast high-strength concrete specimens cured in two different environments: open air and in water. The aim was to analyze the impact of specimen size, L/D ratio, and curing environment on compressive strength. The test results were compared to those of standard specimens to explore potential relationships for estimating average compressive strength. Various statistical indicators were employed to enhance this study. The obtained results lead to the following conclusions: - The individual simulation of compressive strength for various ratios of fp(d)/fc(150) led to the development of exponential equations, enabling an accurate estimation of the compressive strength of high-strength concrete.

Indeed, the statistical indicators (CV) and (ARE) are lower in the case of exponential equations. Modeling the ratios fp(d)/fc(150) as a function of the diameter (D) of the cores remains below 1. In this regard, the conversion models depend on the core size, the L/D ratio, and the curing environment. Indeed, reducing the size results in a significant decrease in the fp(d)/fc(150) ratio, observed under constant L/D ratio and curing conditions. The transition from an L/D ratio of 1 to an L/D ratio of 2 in the case of wet curing results in a reduction of 3.24% for fp(100)/fc(150), 6.34% for fp(75)/fc(150), and 9.52% for fp(50)/fc(150). There is a decrease of 4.55%, 7.13%, and 11.79% for cores of 50 mm, 75 mm, and 100 mm, respectively, in the case of air curing. The results highlight the significant impact of core size in the proposed models, underscoring its importance as a crucial parameter. Air curing leads to a decrease in the ratios fp(d)/fc(150), especially when L/D=1. The core of 100 mm shows a reduction of 10.13%, while decreases of 8.64% and 10.33% are recorded for the 75 mm and 50 mm cores, respectively. However, core size has demonstrated a more significant influence compared to the two previously emphasized parameters. The effectiveness of our exponential models relies on various statistical indicators, including prediction errors (RMSE) and standard deviation (SD) of the conversion models. Comparison with water-cured standard cylindrical specimens allowed us to reduce the number of cores. Indeed, both statistical parameters stabilize, in wet curing, from 7 to 8, depending on the L/D ratio. However, when compared to air-cured standard cylindrical specimens, it was shown that at least 9 cores are needed. In practice, when the quality control level of the concrete is high, 7 cores may suffice. Given that this experimental study was conducted for a specific formulation and a w/c ratio of 0.43, additional experimental work involving other formulations, the direction of concrete flow, and L/D ratios equal to 1 for molded specimens would be necessary to further improve the precision and applicability of the developed models. This would contribute to the generalization of

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prediction equations for high-strength concrete in engineering practice. Although the coring method of resistance evaluation is partially destructive, it remains the most reliable for evaluating compressive strength. The use of small-diameter cores is crucial for maintaining the structural stability of concrete structures.

Data Availability Statement

The authors confirm that the data that supports the findings of this study are available within the article. Raw data that support the finding of this study are available from the corresponding author, upon reasonable request.

Conflict Of Interest

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethics

There are no ethical issues with the publication of this manuscript.

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