ISRM Suggested Method for Determination of the Schmidt Hammer Rebound Hardness: Revised Version

Abstract

With its portable, simple and affordable attributes, the Schmidt hammer (SH) is an ideal index apparatus, which underlies its increasing popularity and expanding range of applications. The SH rebound hardness value (R) is perhaps the most frequently used index in rock mechanics practice for estimating the uniaxial compressive strength (UCS) and the modulus of elasticity (E) of intact rock both in laboratory conditions and in situ. The SH is also widely used for estimating the (UCS) of discontinuity walls and assessing the workability, excavatability and boreability of rocks by mechanical means (cutting, polishing, milling, crushing and fragmentation processes in quarrying, drilling and tunneling).

Please send any written comments on this “ISRM Suggested Method” to Prof. Resat Ulusay, President of ISRM Commission on Testing Methods (resat@hacettepe.edu.tr).

Reprinted from International Journal of Rock Mechanics & Mining Sciences, 46, A. Aydin, ISRM Suggested Method for Determination of the Schmidt Hammer Rebound Hardness: Revised Version, 627–634, 2009, with permission from Elsevier.

Appendix A: UCS and E Versus Rebound Value Correlations in the Light of Indentation Mechanisms

As the number of studies proposing new correlations estimating the uniaxial compressive strength (UCS) and the modulus of elasticity (E) of intact rock based on the SH rebound hardness determination are rapidly increasing, it is important for the users of these correlations to be aware of the fact that high correlation coefficients presented in these studies do not necessarily guarantee better point estimates. Contrary to common assumption, the scatter in the original datasets of these correlations may be such that correlation coefficients for smaller ranges of rebound values may actually be lower than those for wider ranges. It should also be noted that the type of correlation functions varies with the range for which the correlations are established. This appendix is aimed to provide an insight into the nature of these correlations in the light of indentation mechanisms and help users to select appropriate functions and interpret them for their particular cases.

Three correlation functions (Fig. A.1) were selected from the literature to facilitate this discussion. All three functions were derived for variably weathered granites using the L-type hammer. Striking differences in these correlations (Fig. A.1) may be partly due to different testing, data gathering and reduction procedures adopted in these studies as well as different microstructures of the granites tested. For example, Hong Kong granites [2] had noticeably high microcrack densities even at fresh state resulting in lower UCS values than those of hydrothermally altered granites of Southwest England [7].

Fig. A.1

Comparison of predictions of the uniaxial compressive strength (UCS) of granites based on their rebound hardness values (R_L) using the L-type hammer. (Dotted [7]—Grade I–IV; dashed [8]—Grade I; solid [2]—Grade I–IV)

Interestingly, the linear correlation proposed in [8] for a wide variety of fresh to slightly weathered granitic rocks from Turkey is quite consistent with the trends of the other correlations in the same UCS range. Thus at the outer ends of the rock weathering spectrum (Grade I–IV) when the microstructures are relatively uniform, linear correlations may be expected. The fact that most of the linear correlations were proposed for coal [2] proves the role of microstructural consistency as well as surface smoothness in shaping these correlations.

The presence of two different linear correlation domains joined with a transitional domain suggests that indentations mechanisms change as rock microstructure is altered through weathering processes. Understanding how these mechanisms operate or how different microstructures control these mechanisms are crucial in selecting most appropriate data gathering and reduction methods and improving plunger tip shape and diameter in order to develop better correlations with well-delineated ranges of applicability.

Momber [6] applied classical Hertzian contact mechanics theory [9] to explain different modes of indentation of four rock types (granite, rhyolite, limestone and schist) by two spherical indenters (1.0 and 5.0 mm in dimater) at contact forces between 0.1 and 2.45 kN using a classical Rockwell hardness tester. He observed that elastic response (formation of an array of ring cracks or Hertzian cracks surrounding a damaged core zone) is limited to granite and rhyolite, whereas limestone and schist displayed plastic response. Indentation of limestone surface was in the form of collapse (sink-in) due to its porous structure and that of schist was in the form of pile-up (characterized by wall formation around periphery of the plunger tip, presumably due to sliding along the schistosity planes). However, according to Hertzian theory, yielding starts at a depth equal to about half of the contact radius beneath the contact point, and thus most of the deformation may be hidden in the elastic-to-plastic transition domain. Static hardness tests might also result in different indentation modes than impact tests. For example, grain crushing and fragmentation is a common occurrence under impact, especially when grains are coarse and/or weak, and plastic flow (pile-up) behavior is not observed unless the material is highly viscoelastic.

Taking such differences into account, it is now possible to interpret the nonlinear nature of most UCS versus R correlations more systematically. Looking at Fig. A.1 again, it becomes obvious that in the lower end of the weathering spectrum, where rock porosity substantially increased due to leaching and feldspar grains are at least partly weakened by pseudomorphic replacement by clay [10], indentation is mainly through the collapse of the pore space and grain crushing. In the upper end of the spectrum, the linear response is caused by the domination of an elastic-brittle response at the grain scale. The degree of scatter is also expected to be lesser in the elastic domain. In the transitional region, the response to hammer impact is mixed (elastoplastic) and the scatter is bound to be much larger than both domains.

1.1 A.1 Guidelines for the Correlations

From the preceding discussion, it becomes obvious that correlations should ideally be established for a given rock type whose response falls within a single response domain. Nonlinear correlations simply indicate significant micro- structural changes in that seemingly identical rock type. This is well-illustrated in Fig. A.1 for weathering-induced microstructural changes in granite. When the aim is to derive a generic correlation function involving a large group of rock types (e.g. carbonates, mudrocks) it is essential to ensure that there are no large gaps across the entire range and all distinct microstructural varieties of each rock type are represented.

In terms of data gathering and reduction procedures, it also becomes evident that averaging single impact readings is the only rational approach. Note that data gathering procedures based on multiple (or repeated) impact at a single point alter the original microstructure of the test surface resulting in the loss of invaluable information.

The UCS or E versus R correlations should be established using the mean rebound value using the entire set of measurements. The structure of each rebound value data set reflects the nature of surface heterogeneity and it is not immediately obvious which microstructural element or feature (corresponding to average, median or most repeated rebound value) controls or dominates UCS and E of the corresponding rock. Therefore, median and mode (with the number of repetition) values should also be plotted along the range bars on the correlation graphs to facilitate interpretation of overall significance of the correlation and potential variability in UCS and E values of each sample.

On the other hand, the UCS and E of a given rock type are highly sensitive to slight changes in its microstructural state (e.g. degree and style of weathering, density and orientation of microcracks, grain size distribution, mineralogy). However, a systematic analysis of the potentially large variability in these basic mechanical properties is not always feasible due to the difficulties of laboratory testing (justifying the search for indirect predictions using index tests). As a result, in establishing correlations (especially those involving a mixture of rock types), only a few UCS or E values are often available to represent full range of variability in each rock type. This important limitation in constraining potential scatter in UCS and E values can be partly offset by careful evaluation of the variability in rebound values, which should be depicted on the correlation plots by range bars. The reliability of the correlation coefficient and variance can also be better evaluated in this context.

For the identification of weathering grade in granites, Aydin and Basu [2] showed that changes in rebound values between first and second impact provide the best correlation. This procedure is supported in the light of the indentation mechanisms discussed above.

In order to capture overall trends among different rock types or across the weathering spectrum of a given rock type, one of the following pairs of generalized expressions can be used to establish the UCS and E versus rebound value (R) correlations [2]:

$$ UCS = ae^{bR} ,\,E_{t} = ce^{dR} $$

(A.1)

$$ UCS = aR^{b} ,\,E_{t} = cR^{d} $$

(A.2)

where a, b, c and d are positive constants that depend on the rock type. However, as a final note on the validity of generalizing expressions for a mixture of rocks or for a given rock across the weathering spectrum, Aydin and Basu [2] cautioned that these correlations are valid “assuming similar style and sequence of microstructural changes”. This is probably the key consideration in selecting appropriate functions for estimating point values of the UCS and E, and hence, such generalized expressions are not recommended for use in practice when more specific expressions becomes available for the corresponding rock microstructures.

It was demonstrated that when the SH tests are conducted using the recommendations outlined in this suggested method, the rebound values (R) obtained by using standard L- and N-type Schmidt hammers are almost perfectly correlated with a very limited scatter for the range of R _L > 30 or R _N > 40 [2]:

$$ R_{\text{N}} = 1.0 6 4 6\;R_{\text{L}} + 6. 3 6 7 3 { }\left( {r = 0. 9 9} \right) $$

(A.3)

Note, however, that this relationship has been derived on granitic core samples with relatively smooth surfaces in laboratory conditions and the degree of correlation and data scatter may be expected to deteriorate in case of field applications and testing weak porous rocks due to the differences in the impact energies.