IMPROVING THE PREDICTIONS ON CONCRETE STRENGTH VIA ULTRASONIC PULSE VELOCITY

Bogdan Bolborea1,2[0000-0003-2078-4853], Cornelia Baeră1,3[0000-0002-2914-7378], Aurelian Gruin1,2[0000-0003-2407-2626], Ana Cristina Vasile1,2[0009-0005-9837-2834], Alexandra Marina Barbu4[0009-0000-4860-1970]

1 N.I.R.D. URBAN-INCERC, Timişoara Branch, Traian Lalescu Street, no. 2, Timişoara, România

2 “Politehnica” University of Timişoara, Civil Engineering Faculty, Traian Lalescu Street, no. 2, Timișoara, România

3 “Politehnica” University of Timișoara, Faculty of Management in Construction and Transportation, Remus Street, no. 14, Timișoara România

4 N.I.R.D. URBAN-INCERC, Bucharest Branch, Sos. Pantelimon, no. 266, Bucharest, România
bogdan.bolborea@incd.com

Abstract. Numerous studies are dedicated to the advancement of non-destructive testing (NDT) techniques, aiming to improve both their efficiency and their capacity to accurately estimate the mechanical properties of concrete, with a focus on compressive strength. NDT methods are increasingly favored due to their non-invasive character, even though destructive testing (DT) generally yields more accurate measurements. Nevertheless, DT presents significant limitations, primarily due to the need for extracting core samples, which is often impractical in large-scale or heritage structures. The invasive nature of DT restricts the number of specimens that can be obtained, thereby limiting the statistical relevance of the results. Furthermore, variability in compressive strength may occur within the same structural element, which makes it difficult to acquire truly representative samples. Another limitation is that coring tends to avoid visibly defective zones, thereby underrepresenting internal flaws such as cracks, voids, or delaminated areas. This research aims to assess the validity of a previously proposed method by applying it to a new batch of core samples collected from a multi-storey reinforced concrete building. The evaluation relies exclusively on Ultrasonic Pulse Velocity (UPV) testing, which is used to estimate key physical and mechanical parameters, including air-dry density, dynamic modulus of elasticity, and static modulus of elasticity. These parameters form the basis for calculating the compressive strength of the concrete. For the purpose of estimating the dynamic modulus, the dynamic Poisson’s ratio was not measured experimentally, but was instead selected based on values commonly cited in the technical literature. This decision reflects a practical approach often employed in early-stage investigations and enables further focus on validating the broader applicability of the method across diverse structural conditions.

Keywords: NDT, UPV, modulus of elasticity, structural integrity.

Introduction

Reinforced concrete (RC) structures are widely used in construction, and maintaining their performance and serviceability over time requires effective quality control. One of the key aspects of such control involves determining mechanical parameters of concrete, including its density, compressive strength, and modulus of elasticity. While these characteristics can be evaluated with precision in laboratory conditions using molded specimens, such results may not accurately represent the in situ condition of existing structures. As a result, non-destructive testing (NDT) methods have gained traction as viable alternatives for structural assessment without causing material damage [1].

NDT techniques typically offer quicker execution and lower resource consumption than destructive testing (DT), which makes them well-suited for field applications. Among these, the Ultrasonic Pulse Velocity (UPV) method is commonly employed to detect internal discontinuities, including microcracking, material separation, or degradation induced by environmental exposure such as chemical attack or freeze–thaw cycling [2].

In addition to detecting internal defects, UPV testing is frequently used to estimate the compressive strength of concrete. Numerous studies have investigated the potential to correlate UPV values with compressive strength, either through single-parameter models or by combining UPV results with those from rebound hammer (RH) tests, such as the Schmidt hammer method [3, 4]. However, a universally applicable model remains difficult to establish, due to the influence of factors such as mixture composition, curing regime, and aggregate characteristics [5].

To improve estimation reliability, Facaoaru [6] proposed the SONREB method, which integrates data from both UPV and RH tests. This combined approach improves accuracy but requires prior knowledge about the concrete’s composition, specifically, cement type, dosage, and aggregate properties. In cases where such information is lacking, especially in older structures, applying inappropriate assumptions may lead to estimation errors of 25–30% [7]. To address this, Samarin and Smorchevsky [8] introduced a modified version of the SONREB method that limits the required input to aggregate type and concrete age, improving usability under conditions of incomplete data [9].

The SonReb method is a non-destructive testing (NDT) technique widely utilised for estimating the compressive strength of concrete. It is based on the integration of two established testing methodologies: the Ultrasonic Pulse Velocity (UPV) test and the Rebound Hammer (RH) test. The primary principle behind the SonReb method is that these two techniques respond differently to variations in concrete properties. Specifically, an increase in the moisture content of concrete enhances the pulse velocity readings while simultaneously reducing the rebound number captured by the hammer [10, 11].

To implement the SonReb method, practitioners perform the UPV and RH tests on the concrete structure in question, subsequently correlating the results from both tests using empirical models. These models, which have been refined through numerous studies, involve calibration curves that relate the rebound number and ultrasonic pulse velocity to actual compressive strength values [12, 13]. The effectiveness of this combined approach has been evidenced in various research efforts, demonstrating that it significantly improves the accuracy of strength estimations, especially in existing structures where conventional core sampling may not be feasible [14].

Furthermore, advancements in analytical methodologies, including regression models and artificial neural networks (ANN), have increased the predictive capability of the SonReb method [12, 14]. These developments allow for better calibration and adaptation of the SonReb equations to account for various factors affecting concrete strength, such as aggregate type, curing conditions, and concrete age [15]. The SonReb method is widely regarded as a highly efficient approach for assessing the strength and integrity of concrete in both new and existing structures. Its significance in civil engineering and structural health monitoring is well-established, making it an indispensable tool. [16, 17].

Further advancements in NDT methodologies have emerged through the RILEM NDT4 approach, which employs ISO-based resistance curves for estimating compressive strength through interpolation between UPV and RH values. Over time, diverse empirical formulations have emerged, based on experimental data gathered from concrete samples extracted from existing structures [18]. These innovations highlight the evolving landscape of NDT techniques, showcasing their potential for effective structural monitoring and performance assessment in the construction industry.

This research builds upon previous studies [19-21] and aims to further validate a proposed method for estimating the compressive strength of concrete using ultrasonic pulse velocity (UPV). The approach relies on a series of mathematical relationships that link UPV values to ultrasonic-based density, which helps calculate the dynamic modulus of elasticity, from which the static modulus of elasticity is derived, ultimately allowing for the estimation of concrete compressive strength. The proposed methodology aims to improve the accuracy and reliability of NDT techniques in assessing concrete properties, contributing to the development of more effective evaluation methods for structural integrity. Figure 1 illustrates the step-by-step process underlying the proposed method.

Fig. 1. Step-by-step process of the proposed method.

Materials and methods

Concrete mix design and casting

In this study, three concrete mixtures were prepared, differing only in the sand-to-gravel ratio, as presented in Table 1. All mixtures included CEM II/A 42.5R cement at a fixed dosage of 300 kg/m³ and a water-to-cement (W/C) ratio of 0.3. A chemical admixture, Master Rheobuild, was added at 1% of the cement mass to improve the workability of the concrete. The cement content remained unchanged across the mixtures, and the admixture dosage was also constant. The variable parameter was the sand-to-gravel ratio, which was set at 30/70, 40/60, and 50/50, respectively. This variation aimed to examine whether changes in the fine-to-coarse aggregate ratio influence the viability of the proposed method to determine the compressive strength of the hardened concrete.

The resulting data serve as a comparative benchmark, reinforcing the validity of the proposed method by illustrating how varying sand-to-gravel ratios impact concrete performance, particularly in terms of compressive strength.

Table 1. Developed mixes.

Mix 1	Mix 2	Mix 3
Cement	300 kg/m3	Cement	300 kg/m3	Cement	300 kg/m3
W/C ratio	0.3	W/C ratio	0.3	W/C ratio	0.3
Sand (0-4 mm)	30%	Sand (0-4 mm)	40%	Sand (0-4 mm)	50%
Gravel (4-16 mm)	70%	Gravel (4-16 mm)	60%	Gravel (4-16 mm)	50%
Additive	1%	Additive	1%	Additive	1%

Three concrete beams, each measuring 150 × 25 × 50 cm (length × width × height), were cast, with each specimen corresponding to one of the designed mix compositions (Figure 2).

Fig. 2. Concrete elements after formwork removal.

SonReb testing on beams

Before applying the SonReb method, the beam surfaces underwent preparation, which involved grinding with a circular disc to achieve a smooth finish and eliminate surface contaminants. Following Romanian Standard NP 137-2014 [22], each beam face was subdivided into three testing zones (Figure 3). Within each zone, nine rebound hammer (RH) readings and six ultrasonic pulse velocity (UPV) measurements were collected. The RH measurements were obtained using the Original Schmidt OS8000, a device designed to assess surface hardness. UPV testing was performed using the Pundit PL200 device, fitted with 54 kHz transducers positioned on opposing faces of the concrete elements to facilitate direct wave transmission (Figure 4).

Fig. 3. Surface preparation for the SonReb method.

Fig. 4. Direct placement of transducers on the concrete elements.

Following the completion of non-destructive testing (NDT) using the SonReb method, core samples were extracted for further evaluation through both additional NDT and destructive testing (DT) procedures (Figure 5). A total of 33 core specimens were obtained from the three concrete mixes, each with a nominal diameter of 94 mm.

Fig. 5. Drilling procedure for concrete cores’ extraction.

UPV testing on concrete cores

Ultrasonic Pulse Velocity (UPV) testing was performed on the core specimens with several objectives: to estimate the material density, which helps to determine the dynamic modulus of elasticity, and, subsequently, to derive the static modulus of elasticity and estimate compressive strength. For this purpose, 54 kHz P-wave transducers (Figure 6) were used.

Fig. 6. Concrete cores tested with 54 kHz P-wave transducers.

Density measurements

The use of Ultrasonic Pulse Velocity (UPV) measurements to determine concrete density is a recognized technique within non-destructive testing. This method is based on the correlation between the propagation speed of ultrasonic waves through concrete and the material’s physical properties, notably its density and elasticity [23, 24].

As ultrasonic waves travel through a medium, their velocity increases with the compactness and stiffness of the material. Thus, concrete with higher density typically presents greater UPV values due to the more efficient transmission of the wave through a denser matrix. In contrast, materials with lower density, often characterized by internal voids or microcracks, tend to slow down wave propagation, which may suggest a reduction in structural quality [25, 26].

Empirical studies have reinforced this relationship. For example, research conducted by Salman on self-compacting concrete reinforced with carbon fibers showed that increasing fiber content led to a rise in both density and UPV values, thereby confirming the positive correlation between these parameters [27]. Based on these findings, Salman proposed an equation (Equation 1) for estimating concrete density using UPV data.

(1)

where:

γ—air-dry density [kg/m3];

VL—ultrasonic pulse velocity [km/s];

Based on the known weight and geometric dimensions of each core specimen, the mass-based density was calculated using Equation 2.

(2)

where:

ρ – mass-based density [kg/m3];

m – mass of the cores [kg];

V – volume of the cores [m3].

Destructive testing (DT)

Following the core extraction, both ends of each specimen were trimmed using a wet diamond saw to ensure uniformity. The cores were then stored under controlled laboratory conditions, with a temperature of (21 ± 3) °C and relative humidity of (50 ± 5) %, resulting in samples with an approximate height of 150 mm and a diameter of 94 mm. Upon completion of the non-destructive testing procedures, the ends of each core were coated with epoxy resin to improve the parallelism of the bearing surfaces, as illustrated in Figure 7.

Fig. 7. Concrete cores processed with epoxy resin.

Destructive testing (DT) is generally regarded as the most reliable approach for determining the compressive strength of concrete. In this study, all other results are compared against those obtained through DT, which is considered the reference method. The evaluation of the proposed methodology is thus conducted with the values obtained from destructive testing. The procedure involves subjecting the concrete cores to compressive loading until failure, with the loading rate set at 0.6 MPa/s, following the EN 12504-1:2009 standard [28]. The resulting compressive strength, denoted as fcar, is subsequently adjusted using correction coefficients defined in Equation 3 of the Romanian standard NP 137 [22], producing the equivalent compressive strength, fis.

(3)

where:

fis – equivalent concrete compressive strength [MPa];

a – coefficient that considers the influence of the core diameter [-];

b – coefficient that considers the height/diameter ratio [-];

c – coefficient that considers the influence of the degraded layer [-];

e – coefficient that considers the nature of the leveling layer [-];

g – coefficient that considers the humidity of the concrete core [-];

d – coefficient that considers the position and diameter of the reinforcement bars [-];

fcar – resulted compressive bearing capacity [MPa];

Since destructive testing compromises the integrity of the tested elements, it is necessary to limit the number of cores extracted in order to preserve the structural functionality. As a result, the compressive strength values obtained from a small number of samples, particularly those taken from a single structural element or component, may not be representative of the entire structure. Moreover, core extraction can be technically challenging or unfeasible in certain situations, due to the location of the structural member, limited accessibility for drilling equipment, or other operational constraints.

Results and discussions

Mass-based density (MBD) and ultrasonic-based density (UBD)

This study uses the mass-based method as the reference approach for determining concrete density. This technique involves calculating the density by measuring the mass of the core specimen and determining its volume from its geometric dimensions, offering a straightforward and dependable means of evaluation. The results obtained through this method serve as a benchmark for validating alternative techniques.

As a non-destructive alternative, the ultrasonic-based method estimates concrete density by analyzing the propagation velocity of ultrasonic waves through the material. Although this approach is less direct, it offers the significant advantage of allowing in-situ assessments without damaging the structure. The accuracy and consistency of this method are evaluated by comparing its results with those obtained from the mass-based procedure to assess its applicability in practice.

For a more comprehensive analysis, two statistical parameters were employed: the coefficient of variation (CoV) and the accuracy (Ac), the latter being calculated using Equation 4. Table 2 presents the values of CoV and Ac for each mix design, while Figure 8 presents a graphical representation of the two densities paired for each core.

(4)

where: Ac – Accuracy [%].

The coefficient of variation (CoV) is a statistical indicator that quantifies relative variability by expressing the ratio of the standard deviation to the mean, usually as a percentage [29]. It offers a normalized measure of dispersion, facilitating comparisons within or across datasets. The formula used to compute the CoV is presented as follows:

(5)

where:

CoV – coefficient of variation [%];

σ – standard deviation;

μ – mean value.

Table 2. MBD and UBD values and accuracy.

Mix	MBD [kg/m3]	UBD [kg/m3]	Accuracy [%]
CoV [%]	CoV [%]
M1	1.33	0.81	98
M2	1.00	0.48	98
M3	0.66	0.36	98

Fig. 8. Graphical representation of the two densities paired for each core.

The analysis results demonstrate a high degree of consistency in the measured data, as indicated by the low coefficient of variation (CoV), which ranges between 0.36% and 1.33%. These values reflect minimal dispersion around the mean, suggesting uniformity in the physical properties of the tested concrete samples.

Additionally, an observed accuracy of 98% supports the validity of Salman’s theoretical model. The strong correlation between mass-based and ultrasonic-based density measurements confirms the potential of the ultrasonic method as a viable non-destructive alternative for evaluating concrete density.

Given the limited variability among results, it can be inferred that the ultrasonic-based density estimation approach proposed by Salman produces consistent and reproducible values. This supports its continued application in calculating the dynamic modulus of elasticity within the present experimental framework.

Modulus of elasticity (Dynamic and Static)

The modulus of elasticity (E) is an important mechanical parameter of concrete, reflecting its stiffness and ability to deform under applied stress. This property is typically classified into two categories: the static modulus of elasticity (Es) and the dynamic modulus of elasticity (Ed) [30].

The static modulus of elasticity (Es) is usually determined through destructive testing, where compressive loads are applied to concrete specimens until failure occurs. Es corresponds to the slope of the stress–strain curve within the elastic range and is essential in evaluating structural deformation under long-term loading. Accurate determination of Es is critical, as it significantly influences structural analysis and is affected by factors such as mix design and environmental conditions [31].

In contrast, the dynamic modulus of elasticity (Ed) is obtained through non-destructive testing techniques, including ultrasonic pulse velocity (UPV) testing, as outlined in ASTM C597 [32], and resonance frequency measurements, according to ASTM C215 [33]. These methods estimate the stiffness of the material by analyzing wave propagation velocities. Since dynamic tests are performed under different conditions, Ed values are generally higher than those of Es [34].

For this study, the dynamic modulus of elasticity was determined using a theoretical method based on Equation 6 outlined in GE039 [35].

(6)

where:

Ed—dynamic modulus of elasticity [MPa];

Θd—dynamic Poisson’s ratio [-];

γ—air dry density [kg/m3];

g—gravitational acceleration [m/s2];

VL—ultrasonic pulse velocity [km/s];

For this study, the dynamic Poisson’s ratio was assumed to be Θd = 0.25, corresponding to concrete cured in air [35]. This value was incorporated into Equation 6, leading to the simplified form presented as Equation 7:

(7)

The static modulus of elasticity was determined using Equation 8, which defines a linear relationship with the dynamic modulus of elasticity.

(8)

Table 5 summarizes the minimum, average, and maximum values of the dynamic modulus of elasticity obtained theoretically, as well as CoV for each mix design regarding the dynamic modulus of elasticity.

Table 3. Dynamic modulus of elasticity values and accuracy.

Dynamic modulus of elasticity
Mix	Theoretical Ed [GPa]
Min	Mean	Max	CoV [%]
M1	29.83	34.66	39.06	8.37
M2	34.72	37.95	40.28	4.84
M3	35.90	38.01	40.59	3.67

The analysis of the dynamic modulus of elasticity, determined using the theoretical approach, indicates a high degree of consistency, as reflected by the coefficient of variation (CoV), which ranges from 2.40% to 9.12%. These values point to moderate or low variability, supporting the reliability of the results.

The overall stability of the measurements confirms the applicability of the theoretical method used in this study. Given the limited variation observed, it can be concluded that the calculated values of the dynamic modulus of elasticity are consistent and reproducible. This provides a solid basis for estimating the static modulus of elasticity using the correlation defined in Equation 8.

Compressive strength

Destructive testing (DT)

The compressive strength of concrete was assessed using both destructive and non-destructive methods. For the destructive evaluation, core samples were extracted from the concrete beams. Table 4 presents the mean values obtained through destructive testing.

Table 4. Compressive strength determined through DT testing.

Destructive testing
Mix	Mean values [MPa]
M1	31.8
M2	36.5
M3	35.4

Theoretical approach by UPV testing

In the final step of the proposed method, concrete compressive strength is estimated using Noguchi's formula (Equation 9), in which the static modulus of elasticity is defined as a function of density and compressive strength. By isolating the compressive strength variable, the equation can be reformulated to express it directly as a function of the static modulus of elasticity, as shown in Equation 10.

(9)

where:

Es — static modulus of elasticity [MPa];

fc = fis — concrete compressive strength [MPa];

γ — concrete air-dry density determined via UPV [kg/m3].

(7)

Table 5 summarizes the minimum, average, and maximum values of compressive strength (fcar) obtained using both destructive testing (DT) and the UPV-based method. Additionally, the table includes the statistical parameters used to assess the reliability of the results. Figure 9 illustrates the comparison between compressive strength values derived from UPV measurements and those obtained through DT on core samples. Figure 10 presents the correlation between the compressive strength determined experimentally by DT and the values calculated using the UPV-based approach.

Table 5. Compressive strength values and accuracy.

Compressive strength
Mix	Via UPV [MPa]	Via DT [MPa]	Accuracy [%]
Min	Mean	Max	CoV [%]	Min	Mean	Max	CoV [%]
M1	23.7	30.8	37.7	14.16	23.8	31.8	39.2	16.08	92
M2	30.8	35.9	39.7	8.18	32.6	36.5	42.4	7.94	91
M3	32.6	36.0	40.2	6.27	30.4	35.4	43.4	9.90	91

Fig. 9. Graphical representation of the two approaches used to determine the concrete compressive strength paired for each core.

Fig. 10. Correlation between experimental and calculated compressive strength.

The analysis of compressive strength values obtained through destructive testing and the UPV-based method indicates a satisfactory level of consistency, as reflected by the coefficient of variation (CoV), which ranges from 6.27% to 16.08%. These values point to moderate variability, suggesting the reliability of the obtained results.

Accuracy levels of 91% and 92% further confirm the strong correlation between the two evaluation methods, supporting the applicability of the proposed approach. The consistency between UPV-derived and destructively measured strengths suggests that the ultrasonic-based method can be used effectively to estimate the compressive strength of concrete.

Based on the observed variability and accuracy, the proposed method can be considered reliable and capable of producing reproducible results

SonReb vs proposed UPV approach

Non-destructive testing was performed using both the SonReb method applied directly to the concrete elements and the Ultrasonic Pulse Velocity (UPV) method applied to core samples extracted from the structure. This comparative approach allowed for a broader evaluation of the UPV-based method used to estimate compressive strength.

Table 6 presents the average compressive strength values obtained from each non-destructive method, along with the associated accuracy. The comparison indicates a strong agreement between the two approaches, as reflected by the recorded accuracy levels of 85%, 86%, and 90%.

Table 6. Compressive strength determined through both NDT testing.

Mix	SonReb [MPa]	UPV [MPa]	Accuracy [%]
M1	26.0	30.8	84
M2	30.5	35.9	85
M3	37.4	36.0.	96

Conclusions

This study demonstrates the practical applicability of non-destructive methods for assessing concrete characteristics, with particular focus on density, modulus of elasticity, and compressive strength. The ultrasonic-based approach achieved an accuracy of 98% when compared with the conventional mass-based method, indicating a strong correlation between the two techniques. The low values of the coefficient of variation, ranging from 0.36% to 1.33%, confirm the consistency of the recorded data and support the use of ultrasonic measurements as a viable non-destructive alternative for density evaluation.

The study aimed to investigate whether the proposed method maintains a high level of accuracy under varying sand-to-gravel ratios by examining whether the estimated compressive strength values reflect corresponding variations and align closely with those obtained through destructive testing.

When comparing compressive strength values obtained through destructive testing with those estimated via UPV and SonReb methods, the UPV technique demonstrated higher accuracy, ranging from 91% to 92%, as opposed to 82% to 95% for the SonReb method. These results suggest that UPV offers a more consistent and reliable alternative for estimating compressive strength under non-destructive testing conditions.

Moreover, the comparison between the two NDT approaches showed that UPV consistently achieved higher accuracy levels (97% – 98%) than the SonReb method, further supporting its use as a dependable tool for strength evaluation.

Overall, the results confirm that ultrasonic techniques provide stable and repeatable measurements for characterizing concrete properties. As such, these methods can be effectively incorporated into structural monitoring systems for ongoing evaluation and maintenance of reinforced concrete elements

Acknowledgments

This work was carried out within the Nucleu Programme of the National Research Development and Innovation Plan 2022-2027, supported by MCID, "ECODIGICONS" project no. PN 23 35 04 01: Fundamental-applied research into the sustainable development of construction products (materials, elements, and structures, as well as methods and technologies) that utilizes current national resources to enhance the eco-innovative and durable aspects of Romania's civil and transport infrastructure.

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