Research on the Rebound Hammer Testing of High-Strength Concrete’s Compressive Strength in the Xinjiang Region

Abstract

Enhancing the assessment of compressive strength and the efficiency of rebound hammers in non-destructive testing for high-strength concrete is an urgent issue in construction engineering. This study involved C50 to C90 high-strength concrete specimens, utilizing rebound hammers with nominal energies of 4.5 J and 5.5 J, along with a compression machine. A regression analysis was performed on the compressive strength and rebound values, resulting in linear, polynomial, power, exponential, and logarithmic equations for two different types of rebound hammers. Additionally, the precision of rebound hammers with different nominal energies and the representativeness of various rebound representative values in the measurement area were investigated. The experimental results indicate that the precision of the regionally representative strength curve in Xinjiang meets national specifications. The 4.5 J nominal energy rebound hammer exhibited a higher testing accuracy. When reducing the high-strength concrete measurement area’s rebound representative values from 16 to 14, 12, and 10, the coefficients of variation for the different rebound representative values were mostly below 10%. Within high-strength concrete structures, the strength curve formula derived from rebound representative value 16 is equally applicable to 14, 12, and 10. In practical engineering applications, prioritizing 10 ensures testing accuracy while reducing on-site testing efforts. The outcomes of this experiment establish a foundation for the development and promotion of rebound method-testing technology for high-strength concrete in Xinjiang.

1. Introduction

With the continuing development of China’s infrastructure, the safety of existing structures such as buildings, bridges, tunnels, and other vital infrastructures has become a significant concern. It is now crucial to assess the structural capacity of these structures under various situations, whether for predicting seismic reactions, evaluating changes in usage, or inspecting after partial structural damages. For a thorough evaluation of the mechanical properties of concrete and an accurate estimation of load-bearing capacity [1], objective measurements are crucial. Environmental factors, including temperature, humidity, materials, and other conditions, greatly impact the mechanical properties of concrete. Moreover, unsatisfactory curing during construction and other oversights can lead to issues with strength [2,3,4]. In such instances, it may be suggested by researchers to conduct destructive testing on concrete core samples from structural components to evaluate the compressive strength of concrete. Nevertheless, this method provides a clear and precise indication of a component’s compressive strength, but restrictions exist with respect to the amount of core samples that can be extracted from a structure. Furthermore, this option may incur a high cost and result in structural instability as well as complications with future repair techniques, among other issues [5,6,7,8].

Therefore, non-destructive testing (NDT) is frequently employed in quality assessments for engineering projects. NDT refers to a technology that allows for the direct assessment of the strength and defects of concrete structural components in their original location without causing any damage to the concrete structure. Many NDT methods are utilized on construction sites to estimate the compressive strength of concrete [9,10,11,12]. Among all NDT methods, the Schmidt rebound hammer, invented by Swiss engineer Schmidt in the late 1940s, stands out due to its portability and ease of operation, making it widely used on construction sites. In this experiment, we primarily utilized the rebound hammer to perform compressive strength tests on concrete [13].

In the context of rebound hammer applications, Samia Hannachi et al. analyzed several factors influencing the on-site assessment of concrete compressive strength using the rebound hammer. They emphasized the importance of establishing calibration curves for different concrete specimens and the need for frequent recalibration to address potential errors [14]. B.F. Ogunbayo et al. conducted Schmidt rebound hammer tests on columns within Higher Educational Institutions. The results indicate that the concrete columns in the HEL buildings were safe and met the construction requirements [15]. Katalin Szilágyi et al. gained a better understanding of the statistical characteristics of concrete rebound hardness through an extensive database comprising thousands of test locations. They provided recommendations for re-evaluating specific statements related to rebound hammer tests in the standards [16,17]. Ashraf A.M. Fadiel et al. utilized industrial waste materials as partial substitutes for concrete raw materials and tested the compressive strength of the concrete at various ages after formation. The test results were found to be satisfactory [18,19]. Some researchers have employed alternative testing methods to assess concrete structures. Yi Han et al. found that ultrasonic pulse velocity was significantly correlated with compressive strength. Surface resistivity tests showed that quaternary admixtures significantly improved the durability of concrete [20]. Abed et al. demonstrated the potential of the rebound method and auxiliary cementitious materials for the development of eco-efficient, self-compacting high-performance concretes by means of hardness and ultrasonic pulse velocity tests over a period of 2 years and repeated tests after 150 freeze–thaw cycles [21]. Yi Han et al. found that the addition of calcium carbonate nanoparticles significantly increased the compressive strength, ultrasonic pulse velocity, and surface resistivity of ultra-high-performance concrete, improving the mechanical properties, durability, and sustainability of the concrete [22].

These research findings represent specialized studies conducted by foreign scholars in diagnosing concrete structures, which have significantly contributed to the advancement of the rebound method in non-destructive testing. Moreover, they have provided valuable reference points for the development of corresponding standards and regulations in the United States, Japan, and various European countries. In the current context, as the design strength of concrete continues to increase, there is a growing need for enhanced precision and accuracy in rebound testing.

In 2013, the Chinese Ministry of Housing and Urban-Rural Development issued the ‘Technical Specification for Strength Testing of High-Strength Concrete’ (JGJ/T 294—2013) [23]. This industry standard was established nationwide; however, it received limited validation for the national compressive strength curve, hindering its effective promotion and utilization. In recent years, the application of high-strength concrete in practical engineering projects has been expanding. JGJ/T 294—2013 [23] encourages the use of specialized compressive strength curves or regional compressive strength curves. As a result, many provinces and municipalities have developed their own local standards for rebound testing. These local standards vary significantly due to differences in concrete raw materials and construction processes across regions [24,25,26,27]. Researchers like Guan Pinwu et al. [28] proposed the use of the Q-value rebound hammer test to derive regression curves that are smoother than the nationally unified compressive strength curve, thereby enhancing the accuracy of concrete strength testing with rebound hammers. Jia Bao et al. [29] employed two different high-strength concrete rebound hammers to test concrete specimens and derived a regional compressive strength curve for high-strength concrete in the Nanjing area. They also analyzed the testing accuracy of the two rebound hammers. These diverse testing methods have improved precision in testing and have played a significant role in promoting and expanding the use of the rebound method.

This article is divided into three parts, building upon the previous research on non-destructive testing using the rebound method to assess concrete strength. Firstly, it analyzes the use of the rebound hammer and materials associated with high-strength concrete. The experiments involve specifying concrete strength levels, curing concrete specimens, collecting test data from high-strength concrete specimens, and establishing strength measurement curves. Secondly, it evaluates the accuracy and applicability of two different models of rebound hammers and compares them with national standards. Lastly, through data analysis, this article reduces the representative rebound values in high-strength concrete strength measurements from 16 to 10, aiming to significantly enhance the on-site efficiency of non-destructive testing. This method offers feasible testing standards and recommendations for assessing high-strength concrete in the Xinjiang region.

2. Overview of the Experiment

2.1. Experimental Equipment

The experimental equipment used in this test mainly includes a rebound hammer and a pressure testing machine. The types of rebound hammers include high-strength rebound hammers with a nominal kinetic energy of 4.5 J and 5.5 J. Both of these high-strength rebound hammers can be used for the rebound testing of concrete standard specimens with a strength grade of C50 or higher, as indicated in reference [30]. The high-strength rebound hammers with nominal energies of 4.5 J and 5.5 J follow the same procedure for testing concrete. First, the impact rod is pressed lightly against the concrete surface, and when releasing the pressure, the impact rod extends. The hammer is then attached to the hook. During testing, ensure that the axis of the instrument remains perpendicular to the testing surface of the concrete. Apply pressure slowly and uniformly, read the rebound value when the impact rod retracts into the housing, and record the rebound value. After use, the rebound hammer should be returned to its initial state by extending the impact rod out of the housing, cleaning the impact rod and the exterior, and, when not in use, pressing the impact rod into the housing and locking the core before storing it in the instrument box. The basic technical performance of the 4.5 J and 5.5 J high-strength rebound hammers is provided in

Table 1. The 4.5 J and 5.5 J high-strength rebound hammer’s basic technical performance.

Model	Nominal Energy/J	Spring Stiffness/(N/m)	Hammer Stroke/mm	Radius of the Striker Sphere/mm	Steel Drill Rate Constant Rebound Value	Strength Measurement Range/MPa
HT-450K	4.5	900 ± 40	100 ± 0.5	35 ± 1	88 ± 2	50~100
HT-550KC	5.5	1100 ± 50	130 ± 0.5	18 ± 1	83 ± 2	50~100

. The pressure testing machine has the model number (SYE-3000D). Before using the rebound hammer, it should be calibrated on a steel anvil. It can only be used after successful calibration.

2.2. Experimental Materials and Test Block Preparation

The cement, sand, aggregate, admixtures, and other materials used in this experiment were all sourced from representative raw materials in the Xinjiang region. The cement used was P.O 52.5 ordinary Portland cement produced by Xinjiang Tianchen Cement Co., Ltd. in Urumqi, China (basic physical properties are in

Table 2. Cement performance index.

Test Items			Standard	Measured Value
Physical properties	Fineness	Specific surface area (m2/kg)	≥300	371
	Setting time (min)	Initial	≥45	181
		Final	≤600	240
Strength	Compressive strength (MPa)	3 d	≥23	31.8
		28 d	≥52.5	56.0
	Flexural strength (MPa)	3 d	≥4.0	6.1
		28 d	≥7.0	8.9

The various performance indicators of cement comply with the requirements of GB175-2007 “General Portland Cement” [32].

). The sand is natural sand produced in Urumqi, Xinjiang, with a fineness modulus of 3.2. The coarse aggregate has a particle size ranging from 5 to 20 mm. The admixture was a high-performance polycarboxylate superplasticizer produced by Xinjiang Hengtai Jinsheng New Building Materials Co., Ltd., (Urumqi, China) with a water reduction rate of 26%. The mineral admixtures included fly ash and mineral powder. The fly ash was Class F Type I fly ash, produced by Fukan Lianzhong New Building Material Factory, and the mineral powder was S75-grade mineral powder, produced by Xinjiang Baoxin Shengyuan Building Materials Co., Ltd. (Urumqi, China). The performance indicators of the fly ash and mineral powder are provided in

Table 3. Performance indicators of fly ash.

Parameters	Fineness (%)	Water Demand (%)	Ignition Loss (%)	Moisture Content (%)	Density (g/cm3)	Stability (mm)	Strength Activity Index (%)
Standard	≤12.0	≤95	≤5.0	≤1.0	≤2.6	≤5.0	≥70.0
measured value	9%	90%	2.5%	0.1%	2.52	1.0	81

and

Table 4. Performance indicators of mineral powder.

Parameters	Specific Surface Area (m2/kg)	Moisture Content (%)	Flowability Ratio (%)	Density (g/cm3)	7-Day Activity Index (%)	28-Day Activity Index (%)
Standard	≥300	≤1.0	≥95	≥2.8	≥55	≥75
measured value	547	0.1	106	2.94	65	102

. Standard cubic concrete test blocks (150 × 150 × 150 mm) of nine different design strength grades (C50, C55, C60, C65, C70, C75, C80, C85, and C90) were prepared according to the actual engineering mix ratios in Xinjiang. For each strength grade, at least three test blocks were produced. The design curing period ranged from 7 days to 365 days. The materials and mix ratios met the relevant specifications. The test blocks were cured naturally in accordance with GB/T50081-2019 [31]. After demolding, the test blocks should be stacked in a “品” shape in a location protected from direct sunlight and rain, and they should be cured naturally for 14 days with twice-daily water sprinkling to meet the conditions of natural curing. In the case of the 4.5 J high-intensity rebound meter,

Table 5. Table of the number of test specimens and test ages.

Strength Rating	Number of High-Strength Concrete Specimens Produced and Test Ages for Each Strength Grade								Number of Specimens Produced
	7 d	14 d	28 d	60 d	110 d	220 d	365 d	520 d
C50	6	6	6	6	6	6	6	12	54
C55	6	6	6	6	6	6	6	12	54
C60	6	6	6	6	6	6	6	12	54
C65	6	6	6	6	6	6	6	12	54
C70	6	6	6	6	6	6	6	12	54
C75	6	6	6	6	6	6	6	12	54
C80	6	6	6	6	6	6	6	12	54
C85	6	6	6	6	6	6	6	12	54
C90	6	6	6	6	6	6	6	12	54
Statisticians	54	54	54	54	54	54	54	54	486

includes the production of the test blocks and the age of the test. The 5.5 J high-intensity rebound meter test blocks are the same as the 4.5 J high-intensity rebound meter test blocks.

2.3. Steps and Key Points of the Rebound Compressive Strength Test

The measurement of rebound values should be conducted in accordance with JGJ/T 294—2013 [23]. Clean the test block, place two opposite sides of the molded surface between the upper and lower pressure plates of the press, applying a pressure of 60 to 100 kN (determined by interpolation), and maintain this pressure. On each of the two opposite sides of the specimen, perform 8 rebound impacts, as shown in Figure 1. From a total of 16 rebound readings, discard the highest 3 and lowest 3 values and calculate the arithmetic average of the remaining 10 readings as the rebound index R of the specimen, calculated to the nearest 0.1. After measuring the rebound values, load the test block to failure. For the layout of the rebound measurement points and the placement of test blocks, refer to the diagram shown in Figure 1.

In the study of the strength curve of high-strength concrete, it was observed that high-strength concrete is primarily composed of high-quality cement, high-grade aggregates, fine-grained mineral admixtures, and it exhibits good density and durability. In comparison to conventional concrete, carbonation has a relatively minor impact on the strength curve of high-strength concrete [33,34,35]. Therefore, in this experiment, the influence of carbonation depth on high-strength concrete was not considered.

3. The Establishment of the Strength Curve

After organizing the rebound values and compressive strength data of concrete test blocks with design strength grades ranging from C50 to C90, it was found that the compressive strength values of concrete follow a normal distribution. A regression analysis was performed on the test block data using the least squares method to derive the regression curve. Following the guidelines of JGJ/T 294—2013 [23], the formulas for calculating the average relative error and relative standard deviation $e_r$ of the strength curve for high-strength concrete were as follows:

$$\mathsf{\delta }=\pm \frac{1}{\mathrm{n}}{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}\left|\frac{{\mathrm{f}}_{\mathrm{c}\mathrm{u},\mathrm{i}}^{\mathrm{c}}}{{\mathrm{f}}_{\mathrm{c}\mathrm{u},\mathrm{i}}}-1\right|\times }100\%,$$

(1)

$${\mathrm{e}}_{\mathrm{r}}=\sqrt{\frac{1}{\mathrm{n}-1}\times {\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\left(\frac{{\mathrm{f}}_{\mathrm{c}\mathrm{u},\mathrm{i}}^{\mathrm{c}}}{{\mathrm{f}}_{\mathrm{c}\mathrm{u},\mathrm{i}}}-1\right)}^2}}\times 100\%,$$

(2)

In the formulas, δ represents the average relative error of compressive strength, rounded to the nearest 0.1. $e_r$ represents the relative standard deviation of strength for the regression equation, denoted to the nearest 0.1. $f_{cu,i}$ stands for the concrete compressive strength value obtained from the i-th test specimen, accurate to 0.1 MPa. $f_{cu,i}^c$ stands for the strength conversion value of concrete, calculated from the average rebound value R of the same test block according to the regression equation, accurate to 0.1 MPa. n is the number of test specimens used in formulating the regression equation.

3.1. Strength Curve of the 4.5 J High-Strength Rebound Hammer

Building upon references [36,37], in order to accurately depict the relationship between the rebound values and compressive strength, five different regression equations with various functional forms were selected for fitting. These forms included a linear function, polynomial function, power function, exponential function, and logarithmic function. The regression equations for these five function forms and their associated parameters are provided in

Table 6. The 4.5 J high-strength rebound meter’s strength curve regression formula and related parameters.

Function Form	Correlation Coefficient	${\mathrm{e}}_{\mathrm{r}}/\%$	$\mathsf{\delta }/\%$	Regression Formula
linear function	0.6135	16.34	13.26	$f_{cu}^c=1.548R-25.9$
a polynomial function	0.6135	16.34	13.29	$f_{cu}^c=-0.001616R^2+1.761R-33.01$
power function	0.6134	16.32	13.24	$f_{cu}^c=0.3745R^{1.279}-3.4$
logarithmic function	0.6133	16.40	13.33	$f_{cu}^c=101.6\ln (R)-349$
exponential function	0.6124	16.28	13.25	$f_{cu}^c=22.22e^{0.01926R}-3.9$

. From Table 6, it can be observed that the relative standard deviation $e_r$ and the average relative error δ for the five function forms do not differ significantly and all meet the requirements of JGJ/T 294—2013 [23] for the relative standard deviation of the rebound method’s regional strength curves ($e_r$ ≤ 17%). Among these, the exponential function exhibits a smaller relative standard deviation, and, as a result, Equation (3) was chosen as the expression for the strength curve of the 4.5 J high-strength rebound hammer.

$$f_{cu}^c=22.22e^{0.01926R}-3.9,$$

(3)

In the formulas, $f_{cu}^c$ is the converted compressive strength of concrete test blocks. R is the arithmetic mean rebound value measured by the 4.5 J high-strength rebound hammer.

3.2. Strength Curve for the 5.5 J High-Strength Rebound Hammer

For the rebound hammer with a nominal kinetic energy of 5.5 J, we also used linear, polynomial, power, exponential, and logarithmic functions for data fitting. Please refer to

Table 7. The 5.5 J high-strength rebound meter’s strength curve regression formula and related parameters.

Function Form	Correlation Coefficient	${\mathrm{e}}_{\mathrm{r}}/\%$	$\mathsf{\delta }/\%$	Regression Formula
linear function	0.6135	16.34	13.26	$f_{\mathrm{cu}}^{\mathrm{c}}=2.448R-32.05$
a polynomial function	0.6135	16.34	13.29	$f_{\mathrm{cu}}^{\mathrm{c}}=0.02427R^2+0.279R+15.92$
power function	0.6134	16.32	13.24	$f_{\mathrm{cu}}^{\mathrm{c}}=0.4193R^{1.381}-2.5$
logarithmic function	0.6133	16.40	13.33	$f_{\mathrm{cu}}^{\mathrm{c}}=107\ln (R)-328.4$
exponential function	0.6124	16.28	13.25	$f_{\mathrm{cu}}^{\mathrm{c}}=20.24e^{0.03049R}-2.6$

for the specific results. From Table 7, it can be observed that for the regression equations of the five functions in the rebound method’s regional strength curve, the relative standard deviation $e_r$ must meet the requirements of JGJ/T 294—2013 [23], i.e., $e_r$ ≤ 17%. Among them, the exponential function has the smallest relative standard deviation. Therefore, Equation (4) was chosen as the expression for the strength curve of the 5.5 J high-strength rebound hammer.

$$f_{\mathrm{cu}}^{\mathrm{c}}=20.24e^{0.03049R}-2.6,$$

(4)

In the formulas, $f_{cu}^c$ is the converted compressive strength of the concrete test blocks. R is the arithmetic mean rebound value, measured by the 5.5 J high-strength rebound hammer.

4. Comparison of Regional Curves and National Curves

The best-fit regional curves obtained from the above experiments were compared with the national curves [38]. The comparison between the regression curves of the two rebound hammers, the estimated values from the national curve, and the measured compressive strength is shown in Figure 2. From Figure 2a, it can be observed that the national curve and the regional curve exhibit significant differences. Below 70 MPa, the conversion values of the national curve are slightly lower than those of the regional curve, and the regional strength curve of the 4.5 J high-strength rebound hammer better reflects the trend of the data. Similarly, in Figure 2b, it can be seen that the national curve is positioned below the experimental data, at around 70 MPa, and exhibits greater dispersion on both sides, especially when the strength exceeds 70 MPa. In contrast, the regional strength curve for the 5.5 J high-strength rebound hammer is generally situated in the middle portion of the data.

The comparison of the relative standard deviation $e_r$ and the average relative error δ between the regression curves of the two rebound hammers and the national curve are shown in

Table 8. Comparison between the regression curve of the 4.5 J rebound hammer and the national curve.

The Curve Equation	$\mathbf{Relative} \mathbf{Standard} \mathbf{Deviation} {\mathit{e}}_{\mathit{r}}$/%	Average Relative Error δ/%
National: $f_{cu}^c=0.0079R^2+0.75R-7.83$ [23]	16.51	13.43
4.5 J: $f_{cu}^c=22.22e^{0.01926R}-3.9$	16.28	13.25

and

Table 9. Comparison between the regression curve of the 5.5 J rebound hammer and the national curve.

The Curve Equation	$\mathbf{Relative} \mathbf{Standard} \mathbf{Deviation} {\mathit{e}}_{\mathit{r}}$/%	Average Relative Error δ/%
National: $f_{cu}^c=2.51246R^{0.889}$ [23]	15.28	12.61
4.5 J: $f_{cu}^c=20.24e^{0.03049R}-2.6$	13.94	10.95

. The results in Table 8 indicate that the relative standard deviation $e_r$ = 16.51% and the average relative error δ = 13.43%, both of which are higher than the errors of the regional strength curve for the 4.5 J high-strength rebound hammer. Similarly, Table 9 also shows that the errors of the national curve are higher than those of the regional curve. The relative standard deviations $e_r$ for the 4.5 J and 5.5 J high-strength rebound hammers are 16.28% and 13.94%, respectively, both of which meet the requirement of JGJ/T 294—2013 [23] for the relative standard deviation of the rebound method’s regional strength curves ($e_r$ ≤ 17%). Therefore, the analysis above reflects the superior applicability of the regional strength curve in Xinjiang compared to the national strength curve.

5. Comparative Analysis of the Test Results for the High-Strength Rebound Hammer

JGJ/T 294—2013 [23] provides strength curves for two high-strength rebound hammers with nominal kinetic energies of 4.5 J and 5.5 J, but it does not investigate the testing accuracy of these two rebound hammers. The data from this experiment used the aforementioned two rebound hammers with nominal kinetic energies, enabling a comparative analysis of their accuracy.

In Figure 3, all age test data for the two high-strength rebound hammers are plotted, allowing for a clear observation of the strength variation of high-strength concrete from C50 to C90. The rebound value range for the 4.5 J high-strength rebound hammer tests is 52.9 to 79.3, while the rebound value range for the 5.5 J high-strength rebound hammer is 30.8 to 56.9. This reveals that the measurements with the 4.5 J high-strength rebound hammer generally surpass those of the 5.5 J high-strength rebound hammer within this range.

Furthermore, $\Delta f_{cu}^c/\Delta R$ is an important parameter for determining the testing accuracy of the rebound hammers. It reflects the change in high-strength concrete’s compressive strength for a unit change in the rebound value. A smaller $\Delta f_{cu}^c/\Delta R$ can indicate a flatter slope of the curve, which implies a higher testing accuracy. Conversely, higher $\Delta f_{cu}^c/\Delta R$ values suggest a lower testing accuracy [39]. The calculated results are shown in

Table 10. Comparison of the $\Delta f_{cu}^c/\Delta R$ values for the 4.5 J and 5.5 J high-strength rebound hammers.

Different Types of Rebound Hammers	Measured Strength $\mathbf{Range} \Delta {\mathit{f}}_{\mathit{c}\mathit{u}}^{\mathit{c}}$/MPa	Measured Rebound $\mathbf{Value} \mathbf{Range} \Delta \mathit{R}$	$\Delta {\mathit{f}}_{\mathit{c}\mathit{u}}^{\mathit{c}}/\Delta \mathit{R}$ /MPa
4.5 J rebound hammer	50.0~118.4 $\Delta f_{cu}^c$ = 68.4	52.9~79.3 $\Delta R$ = 26.4	2.59
5.5 J rebound hammer	48.2~121.8 $\Delta f_{cu}^c$ = 73.6	10.95 $\Delta R$ = 26.1	2.92

. In this experiment, the $\Delta f_{cu}^c/\Delta R$ value for the 4.5 J high-strength rebound hammer is 2.59 MPa, and for the 5.5 J high-strength rebound hammer, the $\Delta f_{cu}^c/\Delta R$ value is 2.92 MPa. This further indicates that the 4.5 J high-strength rebound hammer has a higher accuracy and testing precision when assessing high-strength concrete.

By plugging the rebound values measured with the 4.5 J high-strength rebound hammer and the 5.5 J high-strength rebound hammer into the corresponding strength curve formulas as defined in JGJ/T294 [23], the converted compressive strength values for concrete were obtained, as shown in Figure 4. The results indicate that when testing the strength of high-strength concrete, the 4.5 J high-strength rebound hammer offers better accuracy and applicability compared to the 5.5 J high-strength rebound hammer.

6. Coefficient of Variation and Dispersion Analyses of Different Rebound Proxies and Line Scale Rebound Proxies in the Survey Area

As mentioned earlier in JGJ/T 294—2013 [23], the collection and calculation method of rebound representative values has been defined. With the advancement of high-strength concrete, its homogeneity has improved over time. If the number of measuring points within the rebound test area is reduced, it can significantly enhance the efficiency of on-site testing. Based on the existing 16 rebound test values in each test area, an analysis and calculation of different quantities of rebound values can be carried out. The data analysis method is as follows:

• Take 14 rebound test values out of the 16, remove the 2 highest values and 2 lowest values, and calculate the average of the remaining 10 values to obtain the rebound representative value for the test area, denoted as R₁₄.
• Take 12 rebound test values out of the 16, remove the highest value and the lowest value, and calculate the average of the remaining 10 values to obtain the rebound representative value for the test area, denoted as R₁₂.
• Take 10 rebound test values out of the 16 and calculate the average to obtain the rebound representative value for the test area, denoted as R₁₀.

Comparing the rebound representative values obtained as described above with the rebound representative values specified in JGJ/T 294—2013 [23], you can assess their dispersion by calculating the coefficient of variation for the different rebound representative values. Utilize the following formula to calculate the coefficient of variation and standard deviation for the rebound values in the test area:

$${\mathrm{S}}_{\mathrm{k}}=\sqrt{\frac{{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{({\mathrm{R}}_{\mathrm{i}}-{\mathrm{R}}_{\mathrm{k}})}^2}}{\mathrm{n}-1}},$$

(5)

$$\mathrm{C}{\mathrm{V}}_{\mathrm{k}}=\frac{{\mathrm{S}}_{\mathrm{k}}}{{\mathrm{R}}_{\mathrm{k}}}\times 100\%,$$

(6)

In the formulas, CV_k represents the coefficient of variation for each rebound mode; S_k is the standard deviation of each rebound representative value; and k is the mean of the different rebound values in the test area, with values taken at 10, 12, 14, and 16. By calculating using Formulas (5) and (6), the computed values for CV16, CV14, CV12, and CV10 are obtained.

The summary of coefficient of variation at various ages is illustrated in Figure 3. It provides an overview of the coefficient of variation at different ages. Notably, within the initial 28 days, the coefficient of variation for high-strength concrete is significantly higher than in other stages, exceeding 10%. This occurrence might be attributed to the early stage of compressive-strength development in high-strength concrete, leading to irregular development in surface hardness among different specimens, resulting in a coefficient of variation greater than 10%. As the concrete ages, the strength tends to stabilize, and the coefficient of variation typically reduces to below 10%. When testing high-strength concrete structures, components that have not attained the designed strength within the initial 28 days should be allowed to age until the strength stabilizes before conducting the tests.

A statistical analysis of the proportion of the coefficient of variation in Figure 5 is provided in Table 10. According to

Table 11. Coefficient of variation statistical table.

Coefficient of Variation	4.5 J Rebound Hammer
	≤10%	≥10%
CV16	95.04%	4.96%
CV14	95.04%	4.96%
CV12	95.04%	4.96%
CV10	95.04%	4.96%

A coefficient of variation less than 10% indicates low variability. A coefficient of variation between 10% and 100% indicates moderate variability. A coefficient of variation greater than 100% indicates high variability.

, the coefficient of variation for the 4.5 J rebound hammer is less than 10%, accounting for 95.04% of the total data. This indicates that the majority of the data has relatively small fluctuations, demonstrating higher reliability. The reduction in rebound test points does not significantly impact the stability of the rebound data.

In practical testing, it is possible to reduce the number of rebound test points, thereby reducing the workload, while ensuring that the rebound values are close to the true values. When the representative values R₁₄, R₁₂, and R₁₀ are plugged into Equation (3), as mentioned earlier, the relative standard deviation and average relative error can be calculated, and the results are shown in

Table 12. Table for the statistics of different rebound test points $e_r$ and δ in the test area.

Rebound Representative Values	4.5 J Rebound Hammer
	${\mathit{e}}_{\mathit{r}}$/%	δ/%
R16	16.28%	13.25%
R14	16.34%	13.30%
R12	16.32%	13.34%
R10	16.21%	13.02%

R₁₀, R₁₂, R₁₄, and R₁₆ represent the rebound representative values for various rebound methods in the test area.

. From the analysis in Table 12, it can be concluded that the rebound representative values R₁₀, R₁₂, and R₁₄ all meet the requirement of a relative standard deviation within 17%, as specified in JGJ/T 294—2013 [23]. However, R₁₀ exhibits a lower relative standard deviation and average relative error compared to the others.

The analysis results from Table 11 and Table 12 indicate that the rebound representative values obtained using the three data processing methods are close to the values obtained from the JGJ/T 294—2013 [23] standard. In other words, the data distribution curves obtained from the three data processing methods, which include the 16 original rebound values, are generally consistent. We will now focus on the normal distribution histogram for the C50 standard rebound data and the average of the 10 rebound data points, according to the standard procedure. The frequency histogram of the rebound values and the normal distribution curve can be seen in Figure 6 and Figure 7.

The histograms in Figure 6 and Figure 7 visually demonstrate that the dispersion of the 10 rebound points is lower than that of the representative values obtained by the standard method. The mean of the normal distribution curves for both methods is similar, indicating that directly taking 10 rebound points did not alter the data distribution significantly. In the Gauss fitting, the standard deviation for Figure 6 is 9.68, with an R² of 0.8, while the standard deviation for Figure 7 is 9.0, with an R² of 0.84. A smaller standard deviation indicates more concentrated data and less dispersion. Although both have correlation coefficients above 0.8, showing good correlations, it is evident that the correlation in Figure 7 is more significant. In well-constructed high-strength concrete buildings, adopting the method of directly using 10 rebound values can be effective.

7. Conclusions

This paper presents a dedicated experimental study on the rebound method for testing the compressive strength curves of high-strength concrete in the Xinjiang region. The following conclusions can be drawn from this research:

• Based on the experimental results, strength measurement curves for the high-strength concrete were established separately in the Xinjiang region using 4.5 J and 5.5 J rebound hammers. The relative standard deviation of the regional strength measurement curve outperformed the national strength measurement curve, indicating a higher accuracy in strength measurement and excellent regional applicability.
• In the comparative analysis of the accuracy between the 4.5 J and 5.5 J high-strength rebound hammers, it was observed that the rebound values tested by the 4.5 J high-strength rebound hammer had a range of 52.9 to 79.3, which is much larger than the range of 30.8 to 56.9 observed in the tests with the 5.5 J high-strength rebound hammer. Additionally, the $\Delta f_{cu}^c/\Delta R$ value for the 4.5 J high-strength rebound hammer was 2.59, while the $\Delta f_{cu}^c/\Delta R$ value for the 5.5 J high-strength rebound hammer was 2.92. This indicates that the testing accuracy of the 4.5 J high-strength rebound hammer is higher than that of the 5.5 J high-strength rebound hammer.
• Taking the average of 10 valid rebound values directly yields the smallest relative standard deviation with the least variation. This method not only ensures the accuracy of the tests but also reduces the workload at the site.