50 YEARS OF EXPERIENCE WITH THE SCHMIDT REBOUND HAMMER   PDF

Paper published in Concrete Structures, 2009, Vol. 10., pp. 46-56. ISSN 1419-6441 link

Authors: Katalin Szilágyi, PhD and Adorján Borosnyói, PhD

Abstract: The Schmidt rebound hammer has the most widespread use in the non-destructive surface hardness testing of concrete. Compressive strength of structural concrete can be estimated by empirical relationships that can be found between rebound index (readings on the Schmidt rebound hammer) and compressive strength. Empirical formulae based on laboratory tests can be used only within their limits of application. Extension of the validity of the curves is usually not possible. The expected error of the strength estimation by the Schmidt rebound hammer under general service circumstances is about 30 percent. If users are not skilled well usually overestimate the reliability of the Schmidt rebound hammer. Present paper gives a summary of experiences with the Schmidt rebound hammer in the last more than 50 years. Detailed literature review reflects to the sensitive nature of the testing method. Authors’ intention is to give a general review to practitioners and engineers, to highlight special scientific questions in the field, and to help maintaining the widespread use of the Schmidt rebound hammer in the future.

Keywords: Schmidt rebound hammer, surface hardness, rebound index, strength estimation

1. INTRODUCTION

History of non-destructive testing (NDT) of concrete strength in structures goes back more than 70 years (Carino, 1994). Researchers adopted the Brinell method to cement mortar and concrete to find correlations between surface hardness and strength of concrete in the four decades following that Brinell (1901) introduced his ball indentation method for hardness testing of steel (Crepps, Mills, 1923; Dutron, 1927; Vandone, 1933; Sestini, 1934; Steinwede, 1937). The first NDT device for in-place testing of concrete strength was introduced in Germany in 1934 which also adopted the ball indentation hardness testing method, however, dynamic load was applied with a spring impact hammer (Gaede, 1934). Similar device was developed in the UK in 1936 (Williams, 1936). In the following decades several other NDT instruments were introduced adopting the same method (e.g. pendulum hammer by Einbeck, 1944) or different methods (e.g. pull-out testing and firearm bullet penetration testing by Skramtajew, 1938; drilling method by Forslind, 1944; ultrasound pulse velocity method by Long et al., 1945).

In Switzerland Ernst Schmidt developed a spring impact hammer of which handling was found to be superior to the ball penetration tester devices (Schmidt, 1950). The hardness testing method of Shore (1911) was adopted in the device developed by Schmidt, and the measure of surface hardness is the rebound index rather than ball penetration. With this development the hardness measurement became much easier, as the rebound index can be read directly on the scale of the device and no measurements on the concrete surface are needed (Schmidt, 1951). The original idea and design of the device was further developed in 1952 (using one impact spring instead of two) resulted in simpler use (Greene, 1954; Anderson et al, 1955). In 1954 Proceq SA was founded and has been producing the original Schmidt rebound hammers since then, without any significant change in the operation of the device (Proceq, 2005). Several hundred thousands of Schmidt rebound hammers are in use worldwide (Baumann, 2006). The latest development of the device was finalized in November 2007, since the Silver Schmidt hammers are available (Proceq, 2008a). The digitally recording Silver Schmidt hammers can also measure coefficient of restitution, CR (or Leeb hardness; see Leeb, 1986) of concrete not only the original Schmidt rebound index. Fig. 1 indicates the original Schmidt hammer and the Silver Schmidt hammer in use.

The gentle reader can find detailed information about further NDT methods for concrete in the technical literature (ACI, 1998; Balázs, Tóth, 1997, Borján, 1981; Bungey, Millard, Grantham, 2006; Carino, 1994; Diem, 1985; Malhotra, 1976; Malhotra, Carino, 2004; Skramtajew, Leshchinsky, 1964).

Fig. 1: The Schmidt rebound hammer
a) Original Schmidt hammer b) Silver Schmidt hammer

Fig. 2: Parts of the Schmidt rebound hammer
(see notation in the text)

2. OPERATION OF THE SCHMIDT REBOUND HAMMER

In the Schmidt rebound hammer (as can be studied in Fig. 2) a spring (1) accelerated mass (2) is sliding along a guide bar (3) and impacts one end (a) of a steel plunger (4) of which far end (b) is compressed against the concrete surface (c). The impact energy is constant and independent of the operator, since the tensioning of the spring during operation is automatically released at a maximum position causing the hammer mass to impinge with the stored elastic energy of the tensioned spring. The hammer mass rebounds from the plunger and moves an index rider before returning to zero position. Original Schmidt rebound hammers record the rebound index (R): the ratio of paths driven by the hammer mass before impact and during rebound; see Eq. (1). Silver Schmidt hammers can record also the square of the coefficient of restitution (referred as Q-value): the ratio of kinetic energies of the hammer mass just before and right after the impact (E₀ and E_r , respectively); see Eq. (2).

In Eqs. (1) and (2) x₀ and v₀ indicate path driven and velocity reached by hammer mass before impact, while x and v indicates path driven and velocity reached by hammer mass after impact.

3. INTERPRETATION OF HARDNESS MEASUREMENTS

Aim of Schmidt rebound hammer tests of concrete structures is usually to find a relationship between surface hardness and compressive strength with an acceptable error. For the rebound method no general theory was developed that can describe the relationship between measured hardness values and compressive strength. The existence of only empirical relationships was already considered in the earliest publications (Anderson et al, 1955; Kolek, 1958) and also recently (Bungey at al, 2006). To find a reliable method for strength estimation one should study all the influencing factors that can have any effect on the hardness measurement, and also that can have any effect on the variability of the strength of the concrete structure examined. The estimation should be based on an extensive study with the number of test results high enough to provide an acceptable reliability level. The estimation should take care of the rules of mathematical statistics. Indications are summarized in the topics above as follows.

3.1 Influences by the Schmidt rebound hammer

In the Schmidt rebound hammer mechanical parts (i.e. springs, sliding hammer mass, etc.) provide the impact load and mechanical (Original Schmidt hammer) or digital (DIGI- Schmidt hammer, Silver Schmidt hammer) parts are responsible for readings. The value of the Schmidt rebound index depends on energy losses due to friction during acceleration and rebound of the hammer mass and that of the index rider, energy losses due to dissipation by reflections and attenuation of mechanical waves inside the steel plunger; and of course, energy losses due to dissipation by concrete crushing under the tip of the plunger. The value of the coefficient of restitution (thus Q-value) depends on energy losses due to dissipation by reflections and attenuation of mechanical waves inside the steel plunger and energy losses due to dissipation by concrete crushing under the tip of the plunger. This latter loss of energy makes the Schmidt rebound hammer suitable for strength estimation of concrete. The energy dissipated in the concrete during local crushing initiated by the impact depends both on concrete compressive strength and Young’s modulus; therefore, depends on the stress- strain (σ-ε) response of the concrete tested.

The value of the Schmidt rebound index depends also on the direction of the hit by the hammer related to the direction of gravity force. The reading should be corrected accordingly (Proceq, 2006). The value of the coefficient of restitution (thus Q-value) can be considered to be independent from the direction of the hit by the hammer related to the direction of gravity force (Proceq, 2008b). Akashi and Amasaki (1984) studied the mechanical waves in the plunger of the Original Schmidt hammer during impact. The authors have found a relationship between concrete strength and the shape of the mechanical waves as well as the maximum stress values of the mechanical waves. The authors could also demonstrate that wave propagation behaviour is considerably different in the case of different ages of concrete, and also if different test materials (aluminium, copper, steel, concrete) are studied. Nevertheless, no general explanation of the behaviour was published.

The uncertainty of the average value of the reading (either R or Q) depends on three influences: 1. the variability of the strength of concrete in the structure; 2. the repeatability of the Schmidt rebound hammer test; 3. the number of individual readings. The term repeatability considers the inherent scatter associated with the NDT method and is often called within- test variation. For the characterization of repeatability either the standard deviation (s) or the coefficient of variation (V) of repeated tests by the same operator on the same material can be suitable. The repeatability for the Schmidt rebound hammer test was found to be appropriately described by the within-test coefficient of variation, rather than the within-test standard deviation (ACI, 2003b). Fig. 3 shows both parameters as a function of the average rebound index. A trend of increasing standard deviation with increasing average rebound index can be realized, consequently an almost constant coefficient of variation. The repeatability of the Schmidt rebound hammer test can be characterized by a V = 10 to 12 percent within-test coefficient of variation. No data are available concerning the repeatability of the Silver Schmidt rebound hammer tests for the time being.

Fig. 3: Repeatability of the Schmidt hammer test (ACI, 2003b)

a) within-test standard deviation as a function of average rebound index

b) within-test coefficient of variation as a function of average rebound index

3.2 Influences by the concrete structure

The energy dissipated in the concrete during local crushing initiated by the impact depends on the properties of the concrete in the very vicinity of the tip of the plunger. Therefore, the measurement is sensitive to the scatter of local strength of concrete due to its inner heterogeneity. For example, an air void or a bigger hard aggregate particle close to the surface is resulted in a much lower or a much higher local rebound value than can characterize to the concrete structure globally (Herzig, 1951).

The amount of energy dissipated in the concrete can be higher for a concrete of lower strength/lower stiffness compared to the lower energy dissipation in a concrete of higher strength/higher stiffness. As it is possible to prepare concretes of the same strength but having different Young’s moduli, it is also possible to measure the same rebound index for different concrete strengths or to measure different rebound indices for the same concrete strengths. Young’s modulus of the aggregate has considerable influence on the rebound index.

The most significant influence on strength of concrete was found to be the water-to-cement ratio (w/c) of the cement paste. Schmidt hammer test results available for hardened cement pastes of different w/c ratios are represented in Fig. 4 (Kolek, 1970b). Results indicate that the change of the rebound index due to the change of the w/c ratio is similar in nature to the relationships found between concrete compressive strength and w/c ratio, however, less pronounced. Even the compaction problems for low w/c ratios can be realized. It can be found that measuring the surface hardness of concrete by a rebound method could provide suitable result for strength estimation. However, it should be also noted that the w/c ratio of the cement paste is only one influencing parameter for the strength of concrete and several further influencing parameters should be taken into consideration in the strength estimation procedure (Granzer, 1970).

Fig. 4: Schmidt rebound hammer test results on hardened cement pastes of different w/c ratios (Kolek, 1970b)

Additional important influencing parameters are:

- the concrete mixture: type of cement, amount of cement, type of aggregate, amount of aggregate,

- the concrete structure: compaction of structural concrete, method of curing, quality of concrete  surface, age of concrete, carbonation depth in the concrete, moisture content of concrete, mass of the structural element, temperature and stress state.

Differences in the rebound index due to the application of different types and/or amounts of cement can reach 50 percent (IAEA, 2002). On the other hand, the influence of variation in fineness of cement is not considered to be significant, resulting in a scatter of about 10 percent (Bungey et al, 2006).

Type and grading of the aggregate have significant influence on the rebound index. The most considerable influence is attributed to the Young’s modulus of the aggregate. For example, the rebound index is always found to be higher for quartz aggregate than for limestone aggregate, both corresponding to the same concrete compressive strength (Grieb, 1958; IAEA, 2002; Neville, 1981).

Moisture content of the concrete influences the rebound index (Jones, 1962; Samarin, 2004; Victor, 1963; Zoldners, 1957). Increasing the moisture content of concrete from air dry condition up to water saturated condition can be resulted in a decrease of 20 percent in the rebound index (RILEM, 1977). The situation is similar for water saturated surface dry condition, too.

Influence of the age of concrete can be realized most significantly in the effect of carbonation of concrete (i.e. the forming of limestone from the hydrated lime due to carbon- dioxide ingress from ambient air). The surface hardness of concrete and thus the rebound index increases due to carbonation. Not taking this influence into account is resulted in an unsafe strength estimation. The error can be more than 50 percent (Gaede, Schmidt, 1964; Pohl, 1966; RILEM, 1977; Wesche, 1967). However, the use of a reduction parameter that is a function only of the age of concrete should be avoided. Age of concrete can be rather taken into consideration as the developed depth of carbonation thus with a parameter that takes into account porosity of concrete (the schematic relationship between porosity and depth of carbonation is represented in Fig. 5, after Bindseil, 2005). Such a parameter is introduced in Chinese Standard JGJ/T23-2001 that is adopted into the guidelines of Proceq SA (Proceq, 2003). Schematic representation is given in Fig. 6.

 Fig. 5: Schematic representation of depth of carbonation in time as a function of porosity (Bindseil, 2005)

 Fig. 6: Correction factor considering the depth of carbonation according to Chinese Standard JGJ/T23-2001 for rebound index R = 20-50 (after Proceq, 2003)

Authors of present paper do not intend to analyze mathematical statistical parameters of concrete strength in general. Only a short reference is given to the coefficient of variation due to the scatter of in-place compressive strength in concrete structures that was found to be V = 7 to 14 percent, depending on the type of structure and quality control (ACI, 2002; ACI, 2003a). The other source of variation in strength is the within-test coefficient of variation, as the measure of repeatability of strength tests. It was found experimentally that the within-test coefficient of variation is about V = 3% for moulded specimens and V = 5% for drilled cores (ASTM, 2004; ASTM, 2005). It was also demonstrated that the distribution of the within-test coefficient of variation is asymmetrical; the coefficient of variation of concrete strength is not constant with varying strength (Leshchinsky et al, 1990).

It should be mentioned that in the European practice usually the standard deviation is the measure for the variability of concrete strength, rather than the coefficient of variation (Rüsch, 1964; CEB-CIB-FIP-RILEM, 1974). It was found, however, that the coefficient of variation is less affected by the magnitude of the strength level, and is therefore more useful than the standard deviation in comparing the degree of control for a wide range of compressive strengths (ACI, 2002). A selection of references is given for further details to the gentle reader’s interest (Bartlett, MacGregor, 1994a; 1994b; 1994c; 1995; 1996; Neville, 1986; 2001).

3.3 Considerations about number of tests

Important question is that how many test repetitions are needed to be able to estimate concrete strength with acceptable error. Smaller number of repetitions affects the uncertainty of the average reading as it was indicated earlier. Generally, the number of repetitions depends on three influences: 1. the repeatability of the testing method (also called within- test variation); 2. the acceptable error between the sample average and the true average; 3. the desired confidence level that the acceptable error is not to be exceeded. The number of repetitions can be established from statistical principles or can be based upon usual practice.

The former RILEM Task Group suggested a minimum repetition number of 25 rebound indices for an acceptable representative value (RILEM, 1977). Borján (1968) proposed a minimum repetition number of 100 rebound indices for accuracy. The sufficiency of the collected data can be studied by an analysis of mathematical statistical parameters (average value, standard deviation, skewness and kurtosis). Asymptotic behaviour can be realized whenever the number of data is sufficient (Borján, 1968). Fig. 7 gives results for a concrete wall indicating the asymptotic behaviour for standard deviation (s) and kurtosis (k): after reaching a certain number of test repetitions the reliability of the sample size can not be increased further and the statistical parameters are found to be remaining constant.

 Fig. 7: Asymptotic behaviour of mathematical statistical parameters (standard deviation and kurtosis) by increasing sample size (number of test repetitions); Schmidt rebound hammer test results on a reinforced concrete wall (authors’ results)

Arni (1972) has demonstrated that the number of tests required to detect a strength difference of 200 psi (≈ 1.4 N/ mm²) with a 90% confidence level is 8 for standard cylinders and is 120 for rebound test readings. The technical literature demonstrates that if the total number of readings (n) taken at a location is not less than 10, then the accuracy of the mean rebound number is likely to be within ±15/√n % with a 95% confidence level (Bungey et al, 2006).

ACI suggests using a number of repetitions such that the average values of the NDT results provide comparable precision to the average compressive strength (Carino, 1993). If the coefficients of variation of the compressive strength test and of the NDT method are available, the ratio of the number of test repetitions can be given as:

  

In Eq. (3) n_i and V_i refer to the number of test repetitions and coefficient of variation corresponding to the NDT (i.e. in-place test), while n_s and V_s refer to the number of test repetitions and coefficient of variation corresponding to the strength test. As a numerical example, if the number of replicate compressive strength tests is n_s = 5 (higher uncertainty in the estimation) or n_s = 18 (lower uncertainty in the estimation) at a given strength level and the coefficient of variation is V_s = 3% (moulded specimens, see Chapter 3.2), one can find the required number of test repetitions in case of the Schmidt rebound hammer test (with an estimated coefficient of variation V_i = 12%, see Chapter 3.1) to be n_i = 5·(12/3)² = 80 or n_i = 18·(12/3)² = 288 at the given strength level. Results can be compared with the experimental data shown in Fig. 7. The user can decide which uncertainty is tolerated during Schmidt rebound hammer testing since the increase of the number of test repetitions does not have considerable economic impact but is resulted in more reliable strength estimation.

Leshchinsky et al. (1990) introduced a formula for the suggested number of NDT repetitions at a measuring location that is based on the use of empirical regression relationship from experiments as follows:

  

In Eqs. (4) and (5) V_f is the within-test coefficient of variation of the estimated concrete strength; p is the acceptable error for the evaluation of average value of concrete strength (with the preset probability P); t depends on P and the number of individual NDT repetitions; f=z(H) is the equation of the test measure vs. concrete strength correlation relationship; f is the concrete strength; H is the indirect measure (e.g. rebound index); r is the correlation coefficient of the correlation relationship; V_H is the within-test coefficient of variation of the indirect measure.

The exact confidence interval can be also given to any number of test repetitions using a suitable reliability analysis (ACI, 2003b; Leshchinsky et al, 1990).

3.4 Considerations about mathematical statistics

The rebound index vs. strength relationship can be determined if the experimental data are available. The usual practice is to consider the average values of the replicate compressive strength and NDT results as one data pair at each strength level. The data pairs are presented using the NDT value as the independent variable (along the X axis) and the compressive strength as the dependent variable (along the Y axis). Regression analysis is performed as a conventional least-squares analysis on the data pairs to obtain the best-fit estimate for the strength relationship. The technical literature calls the attention that the boundary conditions of the conventional least-squares analysis are violated in the case of rebound index vs. strength relationships (Carino, 1993), therefore it is not recommended because the uncertainty in the strength relationship would be underestimated. It is useful to summarize the findings here.

The two most important limitations of the conventional least-squares analysis are: 1) no error (variability) is considered to be existing in the X variable (here: the rebound index); 2) the error (i.e. standard deviation) is constant in the Y variable (here: the compressive strength) over all values of Y. Regarding the findings of Chapter 3.1 and 3.2, it is obvious that the first assumption is violated by the uncertainty of the NDT method – characterized by its within-test coefficient of variation (which, in fact, has a larger variability than that of the strength tests!); and the second assumption is violated because standard deviation increases with increasing compressive strength both for strength testing and NDT.

Mathematical statistics considers a data plot scatter to be heteroscedastic, when the error (i.e. standard deviation) is not constant in the Y variable; the variation in Y differs depending on the value of X (Tóth, 2007). Regression analysis of heteroscedastic data needs performing a Y variable transformation to achieve homoscedasticity (constant standard deviation in the Y variable). Conventional least-squares analysis regression can be used only if the data are homoscedastic. A suitable Y variable transformation is the Box-Cox Normality Plot (NIST, 2009) which is defined by a λ transformation parameter as:

  

For λ = 0, the natural logarithm of the data is taken; this is the most common estimation in the case of rebound index (R) vs. strength (f) relationships. If a linear relationship is used, it is formed as follows:

  

In Eq. (7) the exponent B determines the degree of nonlinearity of the power function. If B = 1, the strength relationship is a straight line passing through the origin with a slope of A. If B ≠ 1, the relationship has curvature.

Regarding the problem of error in the X variable the regression procedure proposed by Mandel is suggested instead of the conventional least-squares analysis regression (Carino, 1993; ACI, 2003b). Details are not given herewith. The most important difference to the conventional least-squares analysis is that Mandel’s method minimizes the sum of squares of the deviations from the regression line in both X and Y directions, on the contrary to the conventional least-squares analysis which minimizes only the deviations from the regression line in Y direction.

In the 1970’s Hungarian researchers (Talabér, Borján, Józsa, 1979) introduced an analysis method for the Schmidt rebound index vs. strength relationships as an adaptation of the Quantile function developed by. J. Reimann, Hungarian mathematician. Quantile function can provide an estimate of the relationship of two random variables which are in a stochastic relationship (i.e. they are not independent, but one can not exactly define the other) (Reimann, 1975; Koris, 1993). Quantile functions are used in hydrology for flood analyses (Reimann, V. Nagy, 1984). Coordinates of a Quantile function can be generated easily: if the cumulative distribution functions (CDF) of X and Y random variables (being in a stochastic relationship) are known and is F(x) and G(y), respectively, then the values of the variables which have the same probability of occurrences F(x_α) = G(y_α) = α can be plotted as data pairs (x_α , y_α) forming the Quantile function (Reimann, 1975). Use of Quantile functions can be advantageous in the regression analysis of Schmidt rebound index vs. strength relationships because this abstraction minimizes the deviations from the regression line in both X and Y directions, eliminating the problems of the conventional least-squares analysis (Borján, 1981). Scheme of generating a Quantile function is shown in Fig. 8. It should be noted that the abstraction of the Quantile function is resulted in fictitious data pairs and omits the use of data pairs of corresponding Schmidt rebound index vs. strength measured in reality. On the other hand, it should be also noted that if Quantile functions are separated for different influencing parameters then they can represent the differences in a much noticeable way as compared to conventional least-squares analysis. Therefore, the use of Quantile functions in the analysis of influencing parameters can be reasonable. Unfortunately, the results by the Hungarian researchers mentioned above were limited to a relatively small series of tests (1152 cube specimens) and the idea was not further developed. Future work is needed in this field.

4. ESTABLISHING THE STRENGTH RELATIONSHIPS

The concrete construction practice needs in-place NDT equipment provided together with simple, easy-to-use, generalized relationships (in the form of equations, graphs or tables) which express the measured value (e.g. rebound index) as a value of compressive strength of standard concrete specimens. Such relationships, however, usually could not accurately characterize the concrete in the structure being tested.

A rigorous analysis should cover all the influences introduced in Chapter 3 (within-test variation of the NDT method as well as of the standard strength testing; in-place variability of concrete strength in the structure; significance of the techniques of mathematical statistics both is sample size development and in regression analyses; acceptable error preset in the strength estimation) and should also take into consideration the economic impact of the decision taken by the results provided.

Generalized relationships are allowed to be used only if their validity has been established by tests carried out on concrete similar to that being investigated and with the same type of testing device that is intended to be used in the investigation.

One should accept as a global indicator that a rigorous analysis (based on tests carried out under ideal laboratory conditions) can provide an accuracy of ±15-20% in the strength estimation; however, in a practical situation it is unlikely that a strength prediction can be made to an accuracy better than ±30-40% (Malhotra, 1976; FHWA, 1997). In practice, it is advised to use the Schmidt rebound hammer as a device of assessing relative concrete quality and uniformity (for which purpose other NDT devices are not comparable in operation and economy), rather than a device for strength estimation.

In the followings a survey is given regarding the empirical relationships found by several researchers for concrete strength estimation in the last 50 years. Due to space limitations of present paper only 40 of the formulae is summarized in Table 1, however, more than 60 can be found in the technical literature.

 Table 1: Strength relationships in the technical literature         

Notations for mean concrete strength:

f_cm,100,cube      100 mm cube,

f_cm,150,cube      150 mm cube,

f_cm,200,cube      200 mm cube,

f_cm,cyl              Æ150/300 mm cylinder,

f_{cm,70×70,core}   Æ70/70 mm drilled core,

f_cm,core             drilled core (no geometry given),

Remark: certain references give only tabulated or graphical representation; for these cases regression curves are calculated and indicated in Table 1.

Formulae are usually given in their original form but the notation is unified. Data is given in a graphical representation in Fig. 9 with a correction to provide results for 150 mm standard cubes. For the sake of better visualization results are separated by their relation to the “B-Proceq” estimation curve (that is recommended by Proceq SA for the original Schmidt rebound hammers of N-type; Proceq, 2003) as follows: Proposal curves running continuously over the curve “B-Proceq” (Fig. 9a),

- Proposal curves running continuously under the curve “B-Proceq” (Fig. 9b),

- Proposal curves intersecting the curve “B-Proceq” coming from below (Fig. 9c),

- Proposal curves intersecting the curve “B-Proceq” coming from above (Fig. 9d).

Fig. 9: Strength relationships according to Table 1 (transformed to 150 mm standard cubes) 

Composition of the proposed empirical relationships can be summarized as follows (in which f_cm is the estimated mean strength; R is the rebound index; a…n are empirical values):

- linear relationships:

f_cm = a + b·R,

- power function relationships:

f_cm = a + b·R^c,

- polynomial relationships:

f_cm = a + b·R + c·R² + … + n·R^m,

- exponential relationships:

f_cm = a + b·e^c·R,

- logarithm relationships:

log_a(f_cm) = b + log_a(R),

- nonlinear relationships:

f_cm = z(R).

Results summarized are valid for 28 to 365 days of age, conventional, normal-weight concretes under air dry moisture condition. It can be realized that the concrete strength can be estimated at certain rebound indices by a ±40-60 N/mm² variation. Results clearly demonstrate that the validity of a proposal should be restricted to the testing conditions and the extension of the validity to different types of concretes or testing circumstances is impossible. It is also worth to mention that several linear estimations can be found among the proposals. This result contradicts the considerations introduced in Chapter 3.4 and calls the attention to that linear estimation can provide the best-fit regression if the strength range is chosen to be narrow in the experimental tests. Rigorous experiments were always resulted in nonlinear relationships since the very beginning of tests by the Schmidt rebound hammer (Schmidt, 1951; Gaede, 1952; Greene, 1954; Chefdeville, 1955; Zoldners, 1957; Kolek, 1958; Brunarski, 1963; Gaede, Schmidt, 1964; Granzer, 1970; Talabér, Józsa, Borján, 1979 etc.).

For the Schmidt rebound hammer tests no general theory has been developed that could describe the relationship between measured hardness values and compressive strength. Gaede and Schmidt (1964) have studied the performance in details and derived a model that can provide estimation with acceptable accuracy and can be fit to experimental data in a suitable way. Unfortunately, the model does not provide the general theory because the Brinell hardness of concrete is covered in the parameters applied to the model. For the Brinell hardness of cementitious materials very limited data have been published and neither acceptable relationships with strength nor accurate theory for the hardness of porous solids is available in the technical literature. Future work is needed in this field.

For a more detailed theoretical analysis the stress wave attenuation behaviour and structural damping capacity of cementitious materials should be also studied. The relationship between rebound index and concrete strength depends on the damping capacity of concrete in the vicinity of the tip of the plunger of the Schmidt rebound hammer. Damping capacity can be described by several parameters (damping ratio; damping coefficient; logarithm decrement; Q factor; decay constant etc.), but measurements are very sensitive to the heterogeneity of the concrete. Swamy and Rigby (1971) have found the logarithm decrement of cement mortar and concrete to be dependent on the w/c ratio, aggregate content and moisture condition. However, limited data are available in this field in the technical literature. Based on experiments with polymer bodies Calvit (1967) has demonstrated that a simple relationship can be derived between the rebound height (h_r) of an impacting ball (falling from height h₀) and the damping capacity of a homogeneous, isotropic, viscoelastic semi-infinite solid body. Assuming that the impact is a half cycle of a sinusoidal vibration then the ratio of the energy dissipated (E_d) to the energy stored and recovered (E_r) in the half a cycle is equal to π·tanθ, where θ is the phase shift (Ferry, 1961). The term π·tanθ is equal to the logarithm decrement (δ), therefore (Kolek, 1970a):

  

Of course, it is not possible to derive such a simplified relationship for concrete due to the inelastic deformations in the concrete and stress wave attenuation in the plunger and in the concrete. Analytical studies need future activities.

5. TODAY TRENDS

Rapid development of concrete technology can be realized recently. New types of concretes became available for concrete construction in terms of High Strength Concrete (HSC), Fibre Reinforced Concrete (FRC), Reactive Powder Concrete (UHPC), Self Compacting Concrete (SCC) and Lightweight Concrete (LC). The strength development of concretes in the 20^th century is schematically represented in Fig. 10 (after Bentur, 2002). Technical literature considering Schmidt rebound hammer test on special concretes is very limited (e.g. Pascale et al., 2003; Nehme, 2004; Gyömbér, 2004; KTI, 2005). Considerable development is expected in this field in the future.

Fig. 10: Development of concrete strengths in the last 50 years (after Bentur, 2002).

Shaded region indicates validity of use for the Original Schmidt rebound hammer 

Environmental impact on concrete structures also tends to be changed recently. For example, the rate of carbonation is expected to be increased due to the increasing CO₂ concentration of air in urban areas as a result of the accelerating increase of CO₂ emission worldwide. CO₂ concentration in the atmosphere is increasing by 0.5% per year on a global scale (Yoon et al, 2007). Development of CO₂ concentration in the atmospheric layer has been considerably increased in the last 50 years, as shown in Fig. 11. In the future, extensive studies are needed in this field to be able to develop relationships for the rate of carbonation considering special concretes available recently.

Fig. 11: Increase of CO₂ concentration in the atmosphere in the last 250 years (Yoon et al, 2007).  

6. CONCLUSIONS

The Schmidt rebound hammer was developed in 1950 by a Swiss engineer, Ernst Schmidt and became the most widespread surface hardness testing device of concrete in the last 50 years. Several thousand hundreds of Schmidt rebound hammers are in use worldwide recently. The apparently simple operation, easy and quick use and its economy made the device successful. On the other hand, if users are not skilled well usually overestimate the reliability of the Schmidt rebound hammer. If the estimation of the compressive strength of structural concrete is the purpose of the user, empirical relationships are available that are established between rebound index and compressive strength. Empirical formulae based on laboratory tests can be used only within their limits of application. Extension of the validity of the curves is usually not possible. In such cases the error of the strength estimation by the Schmidt rebound hammer can be higher than expected. The detailed literature review given in present paper reflects to the sensitive nature of the testing method. The widespread use of the Schmidt rebound hammer is expected to be maintained in the future. Rapid development of concrete technology makes special concretes available for the concrete construction industry. Several research programmes are expected to study the application of the Schmidt rebound hammer for novel types of concretes.

7. ACKNOWLEDGEMENTS

Authors gratefully acknowledge the support of the Bolyai János research scholarship by the Hungarian Academy of Sciences (MTA). Special thanks to Mr. Kurt Baumann (Proceq), Mr. Sándor Boros (ÉMI), Dr. Olivier Burdet (EPFL), Dr. Attila Erdélyi (BME), Dr. Zsuzsanna Józsa (BME), Mr. László Kutassy (MSZT) and Dr. István Zsigovics (BME) for their help provided in the literature review and to Dr. Lars Eckfeldt (TUD) for his ever initiative ideas.

8. REFERENCES

ACI (1998) „Nondestructive Test Methods for Evaluation of Concrete in Structures”, ACI 228.2R-98, American Concrete Institute, Farmington Hills, Michigan

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