Figure 1-3

Introduction
The objective of this article is to contribute to the development of a pragmatic method for the improved nondestructive determination of concrete strength in structures. Two novel approaches are discussed that seem promising for such development. In both approaches the velocity of ultrasonic waves in concrete is used. This feature is called pulse velocity in this article.

Concrete is unique in that it is the only engineering material in which strength determination is attempted from ultrasonic measurements. The reason for this unusual attempt is the need created by the acute infrastructure problem. If the concrete is not strong enough (for instance, it has deteriorated) the consequence can be excessive repair, shortened service life and, in extreme cases, collapse of the structure causing property loss, injuries and even loss of life. Once a reliable conclusion as to the condition of a structure has been reached, then, and only then, can a technically and economically sound selection be made among alternative repair strategies.

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There is no acceptable method at present for the nondestructive determination of concrete strength.

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The seriousness of the infrastructure problem is well known. According to the "ASCE 1998 Report Card for America's Infrastructure," 59 percent of our roadways are in poor, mediocre or fair condition. It will cost a total of $357 billion to eliminate the backlog of needs and produce modest improvement. In addition, 31.4 percent of our bridges are rated structurally deficient or functionally obsolete. It will require $80 billion to eliminate the current backlog of bridge deficiencies and maintain repair levels.

Yet there is unanimous agreement among engineers that the presently available test methods for nondestructive determination of concrete strength are, without exception, inadequate. Fifty years of research in this area could produce no better solution to the problem than empirical formulas obtained by elementary curve fitting for the calculation of the strength. In view of the complexities of the problem, discussed in the article, it would appear to be overly optimistic to attempt to formulate an ultrasonic test method for the determination of concrete strength. However, considering the seriousness of the infrastructure problem and the magnitude of the cost of rehabilitation, major advancement is desperately needed to improve the current situation. For instance, it has been demonstrated repeatedly that the standard ultrasonic method using longitudinal (or L) waves for testing concrete (ASTM C 597) can estimate the concrete strength only with ± 20 percent accuracy under laboratory conditions (Malhotra, 1980; Popovics, 1998). In the field the potential error is even greater. This is obviously not good enough. Yet, engineers are forced by necessity to use them. Unfortunately, improvement cannot come from science because there is no theoretically justifiable relation between strength and pulse velocity even for homogeneous, linearly elastic materials, let alone for concrete. Considerable value can, however, still be derived from formulas for improved nondestructive strength estimation obtained by circumventing the lack of scientific approach and selecting an engineering approach: mathematical modeling. Based on the analysis of previous work, formulas were developed and it was demonstrated that these new formulas are supported by experimental data better than anything available today for ultrasonic determination of concrete strength. This improvement and the importance of the problem in civil engineering are the justification of this article.

Longitudinal ultrasonic waves are an attractive tool for investigating concrete. Such waves have the highest velocity so it is simple to separate them from the other wave modes. The equipment is portable, usable in the field for in situ testing, is truly nondestructive and has been successful for testing materials other than concrete. In addition, none of the available nondestructive methods for testing concrete strength is better. Nevertheless, there are intrinsic and practical factors that may interfere with the determination of concrete strength by ultrasonic means. Therefore, the analysis of four of these interfering factors is appropriate with the anticipation that this improves future research on the ultrasonic determination of concrete strength. These factors are:

• the complexity of the internal structure of concrete
• that factors that affect the strength may affect the pulse velocity differently, especially since the strength of a typical structural concrete is controlled by the strength of the cement paste, whereas the pulse velocity is controlled by the properties of the aggregate
• the insensitivity of the longitudinal pulse velocity to small but important changes in the internal structure of concrete
• the lack of a theoretically justifiable relationship between strength and wave velocity.

Analysis of these factors forms the first half of this article. The second half is the demonstration that the proposed two approaches, the use of multivariable formulas developed by mathematical modeling and the use of surface waves for the calculation of concrete strength reduces these difficulties.

 

Concrete Composition
Concrete is a mixture of four materials: portland cement, mineral aggregate(s), water and air. It may also contain admixtures or other materials but we can disregard these in discussion. The aggregate particles in a hardened concrete are held together by porous hardened cement paste where the pores are filled with air, water or both. One can model concrete as a four phase composite material but this model is still a simplification. What makes the internal structure of concrete so complex is that

• the hardened cement paste itself is a highly complex multiphase material
• the mineral aggregate is also a porous composite material differing greatly from the hardening cement paste
• the interface between paste and aggregate particles has special properties of its own.

Thus, concrete can be aptly considered a composite of composites, heterogeneous at both microscopic and macroscopic levels. The multiphase composite nature of concrete justifies further the use of multivariable models for improved strength estimation.

 

Properties of Concrete
This complex structure results in complex properties. Hardened concrete

• is brittle in some respects and ductile in others is elastic in some respects, inelastic in others and the elasticity is not linear
• has some of the properties of a liquid (flow, for instance), and some of the properties of a solid (shear strength, for instance)
• shrinks to a significant extent during drying
• is full of pores and small cracks that may be filled with water, air or both
• has properties (strength, for instance) that change with time
• has properties that can be affected greatly by environmental conditions.

This complexity makes the behavior of ultrasonic waves in concrete highly irregular, which, in turn, hinders nondestructive testing. Some of the obstacles are:

• The fact that the attenuation of ultrasonic waves in concrete is high, higher than in most other solids. Attenuation coefficients of –0.7 dB/mm (-17.8 dB/in.) at 200 kHz and –2.7 dB/mm (-68.6 dB/in.) at 800 kHz have been measured in concrete (Carleton and Muratore, 1986). Thus, it is difficult, in many cases even impossible, to produce satisfactory wave penetration.
• The signal to noise ratio of the received signals frequently is so low that the noise masks the meaningful signals. In most cases the signal to noise ratio cannot be enhanced adequately by time averaging because the major portion of the noise is coherent.
• The present methods for ultrasonic testing of concrete require direct contact between the concrete surface and the transducers. Since the contact is not always perfect, the air trapped in between may cause variable errors in the measurements.

The problems with testing concrete with ultrasound are even more serious when there is no access to two opposing sides of the concrete for testing.

 

Differences in the Extent that Certain Factors Affect the Strength and Pulse Velocity
It is known that many factors that influence concrete strength (age, porosity, composition, curing and so forth) also influence the pulse velocity, though not necessarily in the same way or to the same extent. Such dissimilarities create ambiguity in the interpretation of the ultrasonic results. The age is such a factor. The differences in the effects of age on the compressive strength and on the longitudinal pulse velocity, respectively, are illustrated in Figure 1. It can be seen that the pulse velocity at the age of one day is about 4 km/s (2.5 mi./s) and at the age of 1095 days (3 years) it is 5.2 km/s (3.25 mi./s). That is, the velocity increases about 1.2 km/s (0.75 mi./s) during three years, an increase of 33 percent. The increase in the compressive strength during the same period is from 10 to 62 MPa (1450 to 8992 psi), an increase of more than 500 percent. Another case is the effect of wetting concrete before testing. This reduces its compressive strength but increases the pulse velocity (Popovics, 1986). In both cases appropriate selection of the supplementary test(s) may reduce the problem.

 

Insensitivity of Longitudinal Waves
For concrete testing, longitudinal pulse velocity (ASTM C 597) has been used exclusively due to the previously discussed practical advantages. It has been recognized, however, that longitudinal pulse velocity measurements are not sensitive enough to reveal small but important changes in the internal structure of concrete that can affect the strength. Consider, for instance, that an increase of one percent in the air content of the concrete causes about a one percent decrease in the pulse velocity but a decrease of almost ten times as much in the compressive strength (Popovics, 1969). This insensitivity is the reason that the ASTM C 666-97, Standard Test Method for Resistance of Concrete to Rapid Freezing and Thawing specifies the fundamental transverse frequency (ASTM C 215) for the laboratory characterization of the extent of frost damage in concrete, rather than the simpler longitudinal pulse velocity.

 

A Model for E versus v_L
Theoretical relationships between wave propagation in a material and certain properties exist. For instance, from the simplifying assumptions that the material is homogeneous (no porosity), isotropic and linearly elastic, the following theoretically correct formula (model) can be derived for the calculation of the dynamic modulus of elasticity:

(1)

where

E = the dynamic modulus of elasticity

v_L = the velocity of a pure longitudinal wave

d = density

µ = Poisson's ratio.

Simple Models for f versus v_L

No theoretical relationship between strength f and pulse velocity v exists even for homogeneous, linearly elastic materials. This is an intrinsic difficulty, not ascribable to ignorance. It is generally true that higher concrete strengths are usually associated with higher ultrasonic pulse velocity. However, efforts to convert this rule of thumb into a reliable numerical relationship have been unsuccessful. An example by Pessiki and Carino (1987) is the combination of Equation 1 with the empirical formula recommended by the American Concrete Institute (1992):

(2)

where

f = compressive strength of the concrete

= empirical parameter

If the left hand sides of Equations 1 and 2 are assumed to be identical, the right hand sides are also equal. From this equality

(3)

This mathematical model is not exact enough to calculate parameter c from µ and d; it is determined by curve fitting. This formula is also objectionable because it is not supported by experimental results. Therefore, the existing need has forced engineers to use other empirical formulas obtained by curve fitting for the calculation of the concrete strength solely from the longitudinal pulse velocity. The most popular such formula is

(4)

where

a and b are empirical parameters determined by curve fitting.

As mentioned before, Equation 4 can provide the concrete strength with the accuracy of ± 20 percent under laboratory conditions if reliable parameters are available. Since this is usually not the case, the potential error in the strength determination is significantly greater. This situation cannot be improved by increasing the accuracy of the ultrasonic measurement. The weakness is in the formula for the strength calculation. The question is how can the strength calculation be improved. In view of the lack of pertinent theory and other complexities discussed above, it would appear to be overly optimistic to attempt to devise a formula for the improved calculation of concrete strength from longitudinal pulse velocity. Nevertheless, it is suggested that useful inferences can be drawn from the multivariable structure of Equation 1 for improved strength calculation.

 

Multivariable Computational Models
The first inference from Equation 1 is that the strength versus pulse velocity formula should also be multivariable. Since the theory provides a multivariable solution for the ultrasonic determination of the modulus of elasticity of the simplest material, one cannot and should not expect that the much more complicated ultrasonic determination of the strength of concrete can have a satisfactory solution as rudimentary as Equations 3 or 4. This is an unrealistic expectation. Such strength formulas are oversimplifications; they violate the truism that a method must be as simple as possible, but not any simpler.

Thus, the first inference from Equation 1 is that one still can attempt to keep v_L with all its good features for strength determination but it should be supplemented by other measurement(s). It should be emphasized, however, that not every supplementary measurement is suitable for the improvement of ultrasonic strength estimation. For instance, strength formulas have already been published that contained supplementary variables, yet they did not improve the ultrasonic strength estimation (Pohl, 1969; Galan, 1990; Popovics 1998). The best known example is when longitudinal pulse velocity measurements are made along with the rebound number (ASTM C 805) on the same concrete. The two results are then substituted into an empirical formula obtained from cores or trial mixes to estimate the concrete strength. Unfortunately, analysis of such strength estimates suggests that the use of the rebound test, logical as it may have seemed several decades ago, contributes little, if any, to the increase of accuracy of the ultrasonic strength estimation (Malhotra and Carette, 1980; Popovics, 1998). The literature does not offer any reason for this failure. A possible explanation is that the same factor, the aggregate in the concrete, has the decisive influence on both the pulse velocity and the rebound number. Thus, the combination of these two tests cannot provide additional meaningful information, especially since the concrete strength is controlled by the hardened cement paste, not by the aggregate.

The second inference from Equation 1 is that finding promising supplementary measurements does not have to be a haphazard action. Since Equation 1 contains the density and Poisson's ratio of the material as supplement, it is logical to supplement the longitudinal pulse velocity measurement for strength also with material characteristic(s), rather than with something like the rebound number. An example below illustrates a good supplement.

Although only further research can establish the best supplementary tests, preliminary work has pinpointed the age of concrete as one of the promising candidates. After all, a young concrete is much more heterogeneous and much weaker than when it is matured. A literature search has produced no formula containing age for the f versus v_L relationship. The age can be included directly in the formula as a second variable t, or indirectly, developing the formula for a specified age t_i. The suitability of age as an indirect variable is illustrated by establishing a best fit model for f versus v_L by linear regression for the results published by Klieger (1957) for the age of t₁ = one day and a separate one for t₇ = seven days. For the one day strengths the following best fit was found:

(5)

for the seven day strengths

(6)

for the combination of the one and seven day strengths, that is when the age difference is disregarded

(7)

where

f_i = compressive strength of the concrete at the age of i days in megapascals.

The effect of age on the f versus v_L relationship is expressed by the difference between Equations 5 and 6 which is demonstrated graphically in Figure 2. This shows that the two straight lines representing Equation 5 for the one day and Equation 6 for the seven day strengths, respectively, fit the experimental data better than any single straight line representing Equation 7 would for the combination of the two ages. (The Equation 7 line is not shown in Figure 1 to preserve clarity, but the goodness of fit, or the lack of it, of Equation 7 is illustrated in Figure 3a.) This demonstrates, without any statistical calculation, that the accuracy of the strength estimation from ultrasonic pulse velocity (ASTM C 597) was improved by consideration of the age. The improvement is even better when the second age group is 28 days.

It is up to further research to develop a single, two variable formula that contains t directly and thus can calculate adequately strengths for a range of ages from v_L and t.

 

Use of Surface Waves
A different promising approach to reduce one of the interfering factors, the insensitivity of the longitudinal waves, is to find another, more sensitive ultrasonic mode for testing concrete. If there is one, the measurement of these other waves could provide the concrete strength adequately with a single variable formula. To obtain at least a preliminary answer to this question, the same experimental results (Klieger 1957) were used for a mathematical comparison of the use of ultrasonic longitudinal and surface (Rayleigh) waves, respectively, for strength estimation that were presented in Figure 2.

The best fit formula for the relationship between concrete strength and longitudinal pulse velocity for the one and seven day experimental results by Klieger is Equation 7. As shown in Figure 3a, the standard error of fit (SEF), that is the average of the absolute values of deviations between the experimental strengths and strengths calculated by Equation 7, is 3.569 MPa (518 psi).

When a similar formula with surface wave velocity v_R was used for the correlation with strength of the same specimens, the following best fit formula was provided:

(8)

This formula produced an SEF of only 2.658 MPa (386 psi), as shown in Figure 3b. That is, Equation 8 produced 25 percent improvement in strength estimation as compared to Equation 7.

A modified procedure was used for the development of Equation 8. Details of this modification are not presented here for the sake of brevity. The important point is that Equation 8, a single variable formula with v_R, is better for strength estimation than Equation 7. Despite this improvement, however, further research concerning more sensitive ultrasonic modes seems justified.

There was reason to think that surface waves may be more sensitive than longitudinal waves for testing strength. The propagation of surface waves is restricted to a region near the boundaries, that is to the free external surface of the material. The depth of the penetration is on the order of one wavelength thickness. The cement paste content of this layer is greater than the average paste content inside the concrete due to the so called wall effect. Therefore, the velocity of a surface wave v_R is influenced more by the paste properties than that of the longitudinal waves that travel through the whole mass of the concrete. Since the concrete strength is also controlled by the strength of the hardened cement paste, v_R may be a better indicator of the concrete strength than v_L. Nevertheless, only further research can establish the ultrasonic mode and/or feature that are the best for the in situ determination of concrete strength.

 

Conclusions
There is no acceptable method at present for the nondestructive determination of concrete strength. This is due to the complexity of the problem and because oversimplified approaches have been used in the past to find a solution. The novelty of this article is the recognition that concrete strength cannot be calculated with acceptable accuracy from the longitudinal pulse velocity v_L alone - supplementary tests are needed. It also shows that the supplementary test(s) should measure material characteristics of the concrete. That is, one approach for improvement is the use of multivariable formulas. Preliminary tests demonstrate that the consideration of the age of concrete as a supplement to the longitudinal pulse velocity does produce improvement in the strength estimation. Another promising approach, which provided 25 percent improvement in the strength estimation, is the use of surface waves instead of longitudinal waves. It is encouraging that not only the analysis of past results but also preliminary tests seem to support the proposed approaches. Thus, continued research in these two directions toward the development of a concrete strength versus ultrasonic pulse velocity relationship is justified.

 

References
American Concrete Institute, Building Code Requirements for Reinforced Concrete, ACI 318M-89, Farmington Hills, MI, ACI, 1992.

American Society of Civil Engineers, "Report Card for America's Infrastructure," New York, ASCE, 1998.

American Society for Testing and Materials, Standard Test Method for Fundamental Transverse, Longitudinal, and Torsional Frequencies of Concrete Specimens, ASTM C 215-91, West Conshohocken, PA, ASTM, 1991.

American Society for Testing and Materials, Standard Test Method for Pulse Velocity Though Concrete, ASTM C 597-83, West Conshohocken, PA, ASTM, 1991.

American Society for Testing and Materials, Standard Test Method for Resistance of Concrete to Rapid Freezing and Thawing, ASTM C 666-97, West Conshohocken, PA, ASTM, 1997.

American Society for Testing and Materials, Standard Test Method for Rebound Number of Hardened Concrete, ASTM C 805-94, West Conshohocken, PA, ASTM, 1994.

Carleton, H.R. and J.F. Muratore, "Ultrasonic Evaluation of Concrete," Proceedings of the 1986 IEEE Ultrasonic Symposium, pp. 1017-1020.

Galan, A., Combined Ultrasound Methods of Concrete Testing, Amsterdam, Elsevier, 1990.

Klieger, P., "Long-Time Study of Cement Performance in Concrete: Chapter 10, Progress Report on Strength and Elastic Properties of Concrete," ACI Journal, Proceedings, Vol. 54, December 1957, pp. 481-504.

Malhotra, V.M. and G.G. Carette, "In-Situ Testing: A Review," Progress in Concrete Technology, Ed., V. M. Malhotra, MOP/MEL 80-89 (TR), Ottawa, Canada, Energy, Mines and Resources, 1980, pp. 749-796.

Pessiki, S.P. and N.J. Carino, "Measurement of the Setting Time and Strength of Concrete by the Impact-Echo Method," NBSIR 87-3575, Gaithersburg, MD, National Bureau of Standards, July 1987.

Pohl, E., Zerstorungsfreie Pruf- und Messmethoden fur Beton, Berlin, VEB Verlag fur Bauwesen, 1969.

Popovics, S., "Effect of Porosity on the Strength of Concrete," Journal of Materials, JMLSA, Vol. 4, No. 2, June 1969. pp. 356-371.

Popovics, S., "Effect of Curing Method and Final Moisture Condition on Compressive Strength of Concrete," ACI Journal, Vol. 83, No. 4, April 1986, pp. 650-657.

Popovics, S., Strength and Related Properties of Concrete: A Quantitative Approach, New York, John Wiley & Sons, Inc., 1998.

 

* Department of Civil and Architectural Engineering, Drexel University, Philadelphia, PA 19104; (215) 895-2345; fax (215) 895-1363; e-mail <popovics@coe.drexel.edu>.

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