Investigation of Pulse Velocity-Strength Relationship of Hardened Concrete

INTRODUCTION

Some work in previous literature made use of the ultrasonic pulse velocity (UPV) of concrete to predict compressive strength and it is fundamental in such research work to study the relationship between UPV and compressive strength.1-6 At early age of concrete, the pulse velocity increases rapidly relative to strength.7,8 Previous research results indicated that the density of concrete ties positively to UPV and compressive strength. Pulse velocity is influenced by many variables, however, including mixture proportions, aggregate type, age of concrete, moisture content, and others.1 The factors significantly affecting the concrete strength might have little influence on UPV. As a result, a strength estimate made with the pulse velocity method is not reliable if a preestablished calibration curve is not available.2

Several previous studies1-5 concluded that, for concrete with a particular mixture proportion, there is a good correlation between UPV and the compressive strength; yet a relationship with a wide variation will be acquired if the data of UPV and the compressive strength of concrete having different mixture proportions are put together and analyzed. No clear rules have been presented to describe how the relationship between UPV and the compressive strength of concrete changes with its mixture proportion. Therefore, there exists a high uncertainty when one tries to make use of UPV to predict the strength of concrete in different mixture proportions.

A previous study9 showed that UPV of hardened concrete is predictable based on its mixture proportion. In addition, it has been known that the compressive strength of concrete corresponds with the mixture proportion; thus, this study tries to adopt the mixture proportion of concrete as a medium to investigate the relationship between UPV and the compressive strength of hardened concrete. This paper uses a mixture proportion of concrete with a paste content of 36% to make cylindrical concrete specimens and the specimen constituents vary widely in water/cement ratio (w/c) and coarse aggregate content by weight. The UPV measurement and compressive strength tests were carried out at the age of 1, 3, 7, 14, and 28 days. The influence of three factors-age, w/c, and coarse aggregate (CA) content-on UPV and the compressive strength of concrete is studied and used to determine how these factors affect the relationship between UPV and the compressive strength of concrete.

RESEARCH SIGNIFICANCE

Currently, the influence of mixture proportion on the relationship between UPV and the compressive strength of concrete is unclear. This study uses concrete mixture proportion as a medium to link the interrelated relationship between UPV and the compressive strength of concrete and to clarify its influence. Furthermore, this paper proposes a new direction to establish a clear relationship curve between UPV and the compressive strength of concrete to improve the application of the UPV method on nondestructive evaluation of concrete strength.

EXPERIMENTAL DETAILS

Materials

Materials used for making specimens include cement, fine aggregate (FA), CA, and high-range water-reducing admixture. The cement used was portland Type I. River sand with a saturated-surface dry (SSD) density of 2.62 and crushed stone with an SSD density of 2.60 were used as fine and coarse aggregates, respectively. Both sand and crushed stone were from the same source. The grading curves for fine and coarse aggregates are shown in Fig. 1. The pulse velocity of sand was measured by using the twophase model as discussed in a previous paper9 to be approximately 4960 m/s (16,273 ft/s). The pulse velocity of the coarse aggregate was measured to be approximately 5100 m/s (16,732 ft/s).

Experimental specimens

Fifteen concrete mixture proportions are used in the study. These mixture proportions are identified as Mixtures C1 to C15 in Table 1. The w/c ranges from 0.3 to 0.7. The cement paste occupies 36% of the total concrete volume (V^sub paste^ = 36%). The three volume ratios of FA to total aggregate (S/A: sand/ aggregate) are 30, 45, and 60% for each w/c. To improve workability of concrete, high-range water-reducing admixture was added into each group of concrete to control the slump of concrete above 13 cm (5.1 in.) and to prevent the occurrence of bleeding and segregation. The last column of Table 1 indicates the slump information of fresh concrete.

Fifteen concrete specimens were produced for each mixture proportion. All the specimens were cast in steel molds (100 mm [3.9 in.] in diameter and 200 mm [7.9 in.] in height) and kept in their molds for approximately 24 hours in the laboratory. After removing the molds, three concrete cylinders were tested at an age of 1 day and all other concrete cylinders were cured in water at 20 °C (68 °F) and tested at ages of 3, 7, 14, and 28 days, respectively. At each age, the pulse velocity and compressive strength of three SSD specimens were measured according to the specification of ASTM C 597 and ASTM C 39, respectively. In addition, cement paste specimens were also made with w/c of 0.3, 0.4, 0.5, 0.6, and 0.7. Each cement paste mixture proportion was determined by proportionally increasing the cement paste amount of the corresponding concrete mixture proportion to maintain a unit volume. The curing and experimental procedures of cement paste specimens were identical to those of concrete specimens.

Experimental equipment

Through a direct transmission mode, as illustrated in Fig. 2, ultrasonic pulse velocities were measured by a commercially available pulse meter with an associated transducer pair. The transducer pair had a nominal frequency of 54 kHz. The principle of ultrasonic pulse velocity measurement involves sending a wave pulse into concrete and measuring the travel time for the pulse to propagate through the concrete. The pulse is generated by a transmitter and received by a receiver. In the experimental studies, the transmitter and receiver were placed at the top and bottom surfaces of a cylinder specimen, respectively. As a result, the traveling length of the ultrasonic pulse was the length of the specimen, which was measured by using a vernier with a minimum reading of 0.01 mm (0.0004 in.). Knowing the path length, the measured travel time (Δt) can be used to calculate the pulse velocity (υ) as follows

υ = D/Δt (1)

where D is the travel path length of ultrasound in the cylinder. The concrete surface must be prepared in advance for a proper acoustic coupling. Light pressure is needed to ensure firm contact of the transducers against the concrete surface.

EXPERIMENT RESULTS

The experimental data presented in the figures discussed in this paper are from individual tests. The average coefficient of variation of UPV and compressive strength for a set of three concrete specimens are approximately 0.3% and 2.6%, respectively. Figure 3 shows the relationship between UPV and compressive strength of all the cement paste and concrete specimens (w/c between 0.3 and 0.7 and age from 1 to 28 days). In Fig. 3, one can easily find two well-separated data groups associated with the cement paste and concrete, respectively. These two groups differ little in compressive strength (vertical coordinate), but differ quite a lot in UPV (horizontal coordinate). The concrete group is on the right side of the cement paste group in the horizontal coordinate; this means that concrete shows quicker UPV than that of cement paste due to the addition of aggregate in concrete. In terms of strength, the strength of concrete was developed by hardening of the cement paste and the bond between cement paste and aggregate; therefore, as long as there is no occurrence of aggregate failure or the failure at the transition zone between cement paste and coarse aggregate particles, the strength of cement paste is equivalent to that of concrete. In other words, if the compressive strength of the concrete specimen reaches 50 MPa (7250 psi), the potential strength of the corresponding cement paste specimen should also reach 50 MPa (7250 psi). As an example, Fig. 4 is a plot of the data of hardened cement paste and concrete specimens (at the age of 28 days) taken from Fig. 3. Figure 4 shows that with the same w/c, cement paste and concrete specimens have similar levels of strength. Based on the aforementioned analysis, it is known that adding aggregate into cement paste (concrete) has significant influence on UPV, but it has less significant influence on strength.

To widely address the relationship between UPV and the compressive strength of concrete, this section first analyzes the development of UPV and strength of concrete along with age. Subsequently, the influence of age and mixture proportion on the UPV-strength relationship of concrete is investigated. In the end, equations for the relationship curves between UPV and strength of hardened concrete are developed.

Pulse velocity and compressive strength development of concrete

Figures 5(a) and (b) show the UPV and strength development, respectively, with the age of concrete having different w/c. Both the UPV and strength of concrete grow along with the advancement of age. At the same age, both UPV and strength of concrete with low w/c are higher than those with high w/c, as shown in Fig. 5(a) and (b) mainly because of the denser structure of concrete with a lower w/c.

To further discuss the growth rate of UPV and strength of concrete, Fig. 6(a) and (b) focus on specimens of Mixtures C6 (w/c = 0.7) and C10 (w/c = 0.3), respectively. Figure 6(a) indicates that concrete with a high w/c at the ages of 1 and 3 days has a UPV that is 80 and 90% of that at the age of 28 days, but the strength only grows 25 and 45%, respectively. Figure 6(b) indicates that, at the age of 1 and 3 days, concrete with low w/c has a UPV that is 90 and 95% of that at 28 days and the strength grows to 55 and 80%, respectively. To sum up, the UPV and strength growth rates of high and low w/c concrete have a significant difference at an early age. As a result, the relationship between UPV and strength of concrete becomes unclear when age and mixture proportion are taken into consideration simultaneously. This observation suggests that it should be better to separately consider the effects of age and mixture proportion on the UPV and strength relationship.

Relationship between UPV and strength of concrete at various ages

First, only consider the age of concrete as a variable. As an example, Fig. 7(a) shows the UPV and strength relationship for a particular mixture proportion of concrete (Mixture C8) at various ages. The exponential regression was applied to establish the UPV-strength relationship. It is found that the relationship between UPV and strength of concrete is pretty good for this particular mixture proportion with a very high coefficient of determination (the square of the Pearson product moment correlation coefficient, R^sup 2^ = 0.98). This result is consistent with the conclusion presented in the related literatures. Similar results are obtained for other concrete specimens such as Mixtures C4, C7, C9, C11, C12, and C13, as shown in Fig. 7(b). The correlation between the UPV and strength of each particular concrete is good and its corresponding coefficient of determination R^sup 2^ is larger than 0.95, as indicated in Fig. 7(b).

Glancing at the data in Fig. 7(b), however, one can find that the data are scattered and the fitting curves for different concrete mixtures intersect each other. This proves that by combining the experimental data of concrete with different mixture proportions at different ages, it is unlikely to clearly define the relationship between UPV and concrete strength due to the concern of significant differences in UPV and strength growth rates of concrete with different w/c (refer to Fig. 6(a) and (b)). To clearly define the relationship between UPV and the strength of concrete with different mixture proportions, it is necessary to eliminate the interference caused by the different UPV and strength growth rates of concrete at early ages. Thus, this paper subsequently investigates the relationship between UPV and strength of concrete at an age of 28 days (hardened concrete) and tries to find out the ruling factor in the relationship.

Relationship between UPV and strength of hardened concrete (age of 28 days)

Figure 8 shows the relationship between UPV and strength at the age of 28 days of concrete having 15 mixture proportions, as listed in Table 1, for a total of 45 data points (three data in each mixture proportion). A relationship curve is drawn by exponential regression of all data points and its coefficient of determination R^sup 2^ equals 0.84, as shown in Fig. 8. Because of the scattered distribution of data points, this relationship curve does not correlate the UPV with the strength of hardened concrete well, that is, a noticeable error may occur if one estimates the strength of concrete by using this relationship curve with a UPV value.

To improve the UPV-strength relationship of hardened concrete, it is inevitable to consider the influence of mixture proportion of concrete on the relationship. Recall that the strength of both hardened cement paste and concrete is dominated by the w/c, yet the UPV of concrete is much higher than that of cement paste due to the addition of aggregate in concrete as shown in Fig. 4. Therefore, the w/c and the amount of aggregate in concrete are two important variables affecting the UPV-strength relationship. To simplify the analysis task, concrete can be regarded as a composite of mortar and coarse aggregate and a new approach is proposed in this paper to discuss the UPV-strength relationship. The new approach treats the CA content as a ruling factor in establishing the UPV-strength relationship of hardened concrete based on the fact that, for a particular CA content, both UPV and strength of concrete are proportional to the density of hardened mortar as well as concrete.

The concrete specimens listed in Table 1 are classified into three groups according to the CA content (1165, 915, and 666 kg/m^sup 3^ [1961, 1540, and 1121 lb/yd^sup 3^]) and each group contains five w/c (0.3, 0.4, 0.5, 0.6, and 0.7). The exponential regression was applied to establish the UPV-strength relationship. Figure 9 shows the relationship between UPV and strength of hardened concrete having different CA contents. In Fig. 9, three regression curves are associated with CA contents of 1165, 915, and 666 kg/m^sup 3^ (1961, 1540, and 1121 lb/yd^sup 3^), respectively, and their corresponding coefficients of determination R^sup 2^ are 0.98, 0.97, and 0.97, indicating good relevance between data points and the regression curves. Figure 9 reveals that, for concrete with a particular CA content, both UPV and strength of hardened concrete increase with a decrease in w/c. This can be explained for concrete with a particular CA content, the denseness of mortar improves along with the decrease in w/c and so do concrete UPV and strength value. Thus, when introducing CA content as a key factor, one is able to better define the relationship between UPV and strength of hardened concrete.

General relationship between UPV and strength of hardened concrete with various coarse aggregate contents

Figure 9 shows that the relationship curves of the three CA content groups are almost parallel. Figure 9 also shows that for concrete with a high w/c (0.7), UPV of hardened concrete does not change significantly when CA content changes from 666 to 1165 kg/m^sup 3^ (1121 to 1961 lb/yd^sup 3^), but the strength of hardened concrete decreases with an increase in CA content. For concrete with a low w/c (0.3), UPV increases slightly (approximately 2%) with more CA content, but the strength decreases.

To further explain the aforementioned results, CA content (or S/A) and UPV are used as a horizontal and vertical coordinate, respectively, to draw Fig. 10(a). Figure 10(a) indicates that concrete with high w/c (0.7) receives less influence on UPV caused by a CA content change. When the w/c of concrete is low, UPV increases a little bit (less than 2%) with the increase of CA content. Figure 10(b) shows the change of strength of five w/c in different CA contents. Figure 10(b) indicates that with a certain w/c, concrete strength increases with the increase of S/A (lower CA content). This trend applies to both concrete with low and high w/c mainly because the lower CA content results in a higher FA content that improves the compactness as well as the strength of hardened concrete. The results shown in Fig. 10(a) and (b) can be used to explain the three relationship curves between UPV and strength in Fig. 9. Figure 9 shows that for concrete with a high w/c (0.7), the strength of hardened concrete changes significantly, but UPV maintains almost the same, as CA content varies. For concrete with relatively low w/c, UPV increases but strength decreases with an increase in CA content.

It is clear that CA content is the main influential factor of the relationship between UPV and strength of hardened concrete. For a given CA content, Fig. 10(a) and (b) can be used to acquire the UPV and strength values of hardened concrete having w/c of 0.3, 0.4, 0.5, 0.6, and 0.7, respectively. As a result, it is feasible to simulate the UPV-strength relationship curve for concrete with a particular CA content from Fig. 10(a) and (b). In this paper, five simulation curves of the relationship between UPV and strength are proposed for concrete with CA contents of 700, 800, 900, 1000, and 1100 kg/m^sup 3^ (1178, 1347, 1515, 1683, and 1852 lb/yd^sup 3^) as shown in Fig. 11. The equations for the simulation curves of these five CA contents are as follows

f^sup c(700)^ = 0.00440 × exp(0.00210 × υ) (2)

f^sup c(800)^ = 0.00294 × exp(0.00218 × υ) (3)

f^sup c(900)^ = 0.00183 × exp(0.00227 × υ) (4)

f^sup c(1000)^ = 0.00106 × exp(0.00237 × υ) (5)

f^sup c(1100)^ = 0.00055 × exp(0.00250 × υ) (6)

where f^sup c^ and υ represent the compressive strength (MPa) and the ultrasonic pulse velocity (m/s), respectively.

The aforementioned equations can be used to study the relationship between UPV and compressive strength of hardened concrete.

Verification of proposed UPV-strength relationship curves

To verify the validity of the proposed UPV-strength relationship based on CA content in concrete, additional specimens were constructed with concrete having 16 different mixture proportions named from C16 to C31, as listed in Table 2. The cement paste also occupies 36% of the total concrete volume. Four S/A ratios of 28, 36, 44, and 52% and four w/c of 0.4, 0.5, 0.6, and 0.7 were considered. Three specimens were produced for each mixture proportion. A total of 48 concrete specimens were prepared and cured in water and then tested at the age of 28 days. The measured pulse velocity υ of each saturated-surface dry specimen can be used to predict its compressive strength by using a suitable UPVstrength equation that is representative of the CA content of the specimen. For example, Eq. (6) was used to predict the strength of concrete having a CA content of 1175 kg/m^sup 3^ (1978 lb/yd^sup 3^) such as Mixtures C16 to C19 and Eq. (3) was adopted for concrete has a CA content of 783 kg/m^sup 3^ (1318 lb/yd^sup 3^) (Mixtures C28 to C31). The predicted strength was compared with the measured strength obtained from a compressive test on the specimen. The comparison results were plotted in Fig. 12. There are 48 comparison data points in Fig. 12 from the additional mixture proportions listed in Table 2. Figure 12 shows that almost all the comparison results are between +10% and -10% of the line of equality. This verifies the suitability of the proposed relationship curves for prediction of hardened concrete strength with a measured UPV value.

Further research

In this paper, a new approach to establishing the relationship between UPV and the strength of hardened concrete was presented and verified to be suitable for application. Although a wide variety of mixture proportions of concrete had been considered in the studies, the volume fraction of cement paste was constant. In addition, the coarse aggregate used in construction of specimens came from a single source. To extend the application of the new approach, further studies are under way to investigate how the changes in the volume fraction of cement paste and the type of coarse aggregate affect the UPV-strength relationship. It is also investigated whether the use of pozzolanic materials such as fly ash and slag in concrete influences the relationship between UPV and strength of hardened concrete.

CONCLUSIONS

The objective of this paper is to investigate the relationship between the ultrasonic pulse velocity (UPV) and the compressive strength of concrete as well as to understand the influence of the mixture proportion and the age of concrete on the relationship between UPV and compressive strength. Specific conclusions are as follows:

1. The UPV and strength growth rates of high and low w/c concretes have a significant difference at an early age. As a result, to clearly define the relationship between UPV and the strength of concrete with different mixture proportions, it is necessary to eliminate the interference caused by the different UPV and strength growth rates of concrete at early ages;

2. In this paper, to simplify the analysis task, the CA content is treated as a ruling factor in establishing the UPVstrength relationship of hardened concrete. For concrete with a particular CA content, both UPV and strength of hardened concrete increase with a decrease in w/c. This can be explained for concrete with a particular CA content, the density of mortar improves along with the decrease in w/c and so does concrete UPV and strength value;

3. When the content of cement paste is constant, the strength of concrete having a high w/c (0.7) changes significantly, but UPV maintains almost the same as CA content varies. For concrete having relatively low w/c, its UPV increases but strength decreases with the increase of CA content; and

4. In this paper, five simulation curves of the relationship between UPV and strength of hardened concrete are proposed for concrete with CA contents of 700, 800, 900, 1000, and 1100 kg/m^sup 3^ (1178, 1347, 1515, 1683, and 1852 lb/yd^sup 3^). These curves were verified to be suitable for prediction of hardened concrete strength with a measured UPV value.

ACKNOWLEDGMENTS

This work was sponsored by the National Science Council, Taiwan, R.O.C. under Grant No. NSC93-2211-E-005-003.