Oxford Research Paper - Proceq Instruments for Rock Testing

EARTH SURFACE PROCESSES AND LANDFORMSEarth Surf. Process. Landforms 36, 320–333 (2011)Copyright © 2010 John Wiley & Sons, Ltd.Published online 05 July 2010 in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/esp.2040

The use of the Schmidt Hammer and Equotip for rock hardness assessment in geomorphology and heritage science: a comparative analysisHeather Viles,1,2* Andrew Goudie,1,2 Stefan Grab2 and Jennifer Lalley2

1 University of Oxford, Oxford, UK2 University of the Witwatersrand, Johannesburg, South Africa

Received 4 January 2010; Revised 1 April 2010; Accepted 15 April 2010

*Correspondence to: Heather Viles, University of Oxford, South Parks, Oxford, UK. E-mail: [email protected]

ABSTRACT: Rapid, fi eld-based measurements of rock hardness are of use in investigating many geomorphological and heritage science problems. Several different methods are now available for taking such measurements, but little work has been done to assess their comparability and strengths and weaknesses. We review here the capabilities of two types of Schmidt Hammer (Classic N type and Silver Schmidt BL type) alongside two types of Equotip (standard type D and Piccolo) for investigating rock hardness in relation to rock weathering on various types of sandstone and limestone, as well as basalt and dolerite. Whilst the two Schmidt hammers and the two Equotips show comparable results when tested at 15 individual sites, interesting differences are found between the Equotip and Schmidt Hammer values which may reveal information about the nature of weathering on different surfaces. Operator variance is shown to be an issue in particular for the Equotip devices, which also exhibit higher variability in measurements and necessitate larger sample sizes. Carborundum pre-treatment also has varying effects on the data collected, depending on the nature of the surface studied. The Equotip devices are shown to be particularly useful on smaller blocks and in situations where edge effects may affect Schmidt Hammer readings. We conclude that whilst each device contributes to geo-morphological research, they do not necessarily produce comparable information. Indeed, using Schmidt Hammer and Equotip in combination and looking at any differences in results may provide invaluable insights into the structure of the near-surface zones and the nature of weathering processes. Copyright © 2010 John Wiley & Sons, Ltd.

KEYWORDS: weathering; sandstone; limestone; rock strength; built environment; Schmidt Hammer; Equotip

Introduction

Rock hardness measurements allow geomorphologists to understand how rock type infl uences relief in a quantitative manner and also allow heritage scientists, concerned with buildings, structures and sites of cultural heritage importance (including rock art), to characterize materials as they deterio-rate. Various techniques have been developed to enable rock hardness to be determined, including those based on micro-drilling (Rodrigues et al., 2002), indentation tests (such as the Brinell, Rockwell, Knoop and Vickers tests) and on the rebound characteristics of rock surfaces [e.g. the Equotip, ball rebound (Hack et al., 1993), the Shore Scleroscope (Holmgeirsdottir and Thomas, 1998), the Duroscope (Török, 2003) and the Schmidt Hammer (Goudie, 2006)]. In this paper we evaluate two versions of the Schmidt Hammer (the ‘Classic Schmidt’ type N and the ‘Silver Schmidt’ type BL) and two versions of the Equotip (the standard version and the compact ‘Piccolo’), as shown in Figure 1, through a series of fi eld trials in Golden Gate Highlands National Park, South Africa and along the Dorset coast, England.

Geomorphological and Heritage Science Applications of Rock Hardness Measurements

One area where rock hardness determinations have proved to be important in geomorphology is in determination of rock mass strength (RMS) (del Potro and Hürlimann, 2008) and in relating this to such issues as slope instability (Borrelli et al., 2007), slope form (Selby, 1980; Synowiec, 1999) and coastal morphology (Trenhaile et al., 1998; Dickson et al., 2004). A RMS classifi cation involving the Schmidt Hammer was used in the Napier Range of Australia by Allison and Goudie (1990). They identifi ed seven main slope forms associated with differ-ent facies of a Devonian reef and found that it was possible to draw associations between slope profi le shape and RMS. Similarly, Placek and Migon (2007) investigated the relation-ship between Schmidt Hammer values and gross relief in the Polish Sudetes, whilst in central California, Hapke (2005) found some relationship between the yield of sediment from landslides and the Schmidt Hammer values of the catchments

USE OF THE SCHMIDT HAMMER AND EQUOTIP FOR ROCK HARDNESS ASSESSMENT 321

Copyright © 2010 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms, Vol. 36, 320–333 (2011)

from which they were derived. Augustinus (1992a, 1992b) and Brook et al. (2004) attempted to assess glacial trough morphology in relation to Schmidt Hammer values.

Rock bed river channel form, both in terms of cross and long profi les, is a topic of increasing interest geomorphologi-cally. Mitchell et al. (2005) found that in the Colorado River Schmidt Hammer rock hardness values correlated signifi cantly to channel width and gradient. In Idaho, Lifton et al. (2009) found a strong negative correlation existed between Schmidt Hammer values and valley width, with wide valley fl oors cor-responding to weak bedrock, and narrow valley fl oors with strong bedrock. They also found a statistically signifi cant dif-ference in Schmidt Hammer values between north- and south-facing slopes, indicating that aspect affects weathering intensity and bedrock strength. In Japan, Hayakawa and Matsukura (2003) investigated the relationship between recession rates of waterfalls and various rock properties, including Schmidt Hammer values.

Hardness can be used to indicate the degree of weathering of a rock or building stone, and by extension the date of surface exposure. Intuitively there should be a relationship between degree of weathering and the length that the rock surface has been exposed to weathering attack. This is the basis upon which the Schmidt Hammer has been used to estimate relative ages of various geomorphological phenom-ena including glacial moraine, rock glaciers, mass move-ments, talus, raised shorelines and platforms, and anthropogenic features. The technique was pioneered by Matthews and Shakesby (1984) and has recently been compared with Cosmogenic Nuclide absolute exposure ages (Sánchez et al., 2009; Winkler, 2009). The technique has also been used for

dating stones in archaeological sites (Betts and Latta, 2000) and for examining petroglyphs (Pope, 2000), and a similar combination of cosmogenic methods and Equotip measure-ments has been used to assess exfoliation rates in granite (Wakasa et al., 2006).

Hardness measurements have also been used to address other questions relating to weathering. For example, there is considerable controversy about the relationship between rock weathering and time, and whether rates are linear or non-linear. Sjöberg and Broadbent (1991) were able to obtain a measure of how weathering developed through time by exam-ining the Schmidt Hammer values of raised beaches at differ-ent elevations in Sweden. Spatial variations in hardness can also be used to investigate environmental infl uences on weathering, such as aspect (Hall, 1993; Waragai, 1999; Burnett et al., 2008) and seasonal snow patches (Ballantyne et al., 1989, 1990; Benedict 1993: Grab et al., 2005). Furthermore, hardness can be used to help infer the role of rock control in determining weathering rates and processes, as for example reported by Nicholson (2008, 2009) from peri-glacial sites in southern Norway.

Hardness measurements have also been used to investigate weathering process: form relationships. Matsukura and Matsuoka (1996) found that larger tafoni developed on bedrock with smaller Schmidt Hammer values and that smaller tafoni developed on those rocks with larger Schmidt Hammer values, while Matsukura and Tanaka (2000) found that the values on the backwall and ceiling of tafoni are smaller than those on the visor and outside the tafoni. Mellor et al. (1997) found rebound (R) values were signifi cantly higher on the outer roof of Spanish tafoni than on the inner cavern walls. In

a) b)

c) d)

1

2

3

4

Figure 1. (a) The four devices tested (1 = Silver Schmidt, 2 = Classic Schmidt, 3 = Piccolo, 4 = Equotip). (b) The Piccolo in action. (c) The Silver Schmidt in action. (d) Some of the blocks tested, note one small block has cracked after measurement with the Classic Schmidt.

322 H. VILES ET AL.


Jordan, Goudie et al. (2002) used the Schmidt Hammer to identify the signifi cance of case hardening in tafoni develop-ment. Aoki and Matsukura (2007a) used the Equotip to assess the role of rock strength in determining the rate and size of tafoni growth in Japan.

Various studies have related different landforms to hardness as measured with the Schmidt Hammer and Equotip. For example, Day (1981), Tang (1998), Haryono and Day (2004) and Goudie et al. (1989) investigated various karst features in relation to limestone hardness. Case hardening of limestone has also been identifi ed with Schmidt Hammer measurements and related to karst landforms (Yaalon and Singer, 1974; Day, 1980). For example, in Jamaica’s Cockpit Country, Lyew-Ayee (2004) found that fresh Montpelier limestone had Schmidt Hammer R values that averaged as little as 14, whereas case hardened zones had values as high as 38, enabling tower karst to form in otherwise weak material. The infl uence of rock hardness on the development of inselbergs has been studied by Pye et al. (1986) in Kenya. Here, Schmidt Hammer mea-surements showed no link between inselberg development and rock hardness, whilst geochemical analyses indicated potassium feldspar content to be the discriminating factor. Stephenson and Kirk (2000) working in New Zealand, found by using the Schmidt Hammer that weathering had reduced rock strength on some platforms by up to 50% and so played a major role in their development. Thornton and Stephenson (2006) found a relationship between rock hardness and shore platform elevation in Australia, while Kennedy and Dickson (2006) used the Schmidt Hammer to assess the importance of case hardening on shore platforms at Shag Point in southern New Zealand and found it less important than structural con-trols, notably jointing. Similarly, the Equotip has been used for assessing the importance of case-hardening in the develop-ment of raised rims on intertidal shore platforms in Japan (Aoki and Matsukura, 2008b).

Hardness measurements can be used to create quantitative weathering indices (Karpuz and Pasamehmetoglu 2004). For example, La Pera and Sorriso-Valvo (2000) were able to relate Schmidt Hammer R values and a weathering classifi cation to the biotite content of granites, while Arikan et al. (2007) used Schmidt Hammer values in a weathering classifi cation system of acidic volcanic rocks. Quantitative assessment of the degree of weathering is helpful in the identifi cation of nunataks, trimlines and glaciation extent, and the Schmidt Hammer can be used for this purpose (Ballantyne et al., 1997; Anderson et al., 1998; Rae et al., 2004). The R values tend to be lower above the glacial limit because of peri-glacial weathering.

Because of sulphation and other processes, the hardness of building stones may vary because of the development of weathering crusts composed of such minerals as gypsum and calcite. Török (2003, 2008a) investigated crusts on limestone and travertine buildings in Budapest, Hungary, using both the Schmidt Hammer and Duroscope rebound tests, and found signifi cant differences in hardness between the host rock and its weathering crusts. Koca et al. (2006) used the Schmidt Hammer to investigate changes to the properties of marble caused by an intense building fi re and to map the pattern of damage. Equotip hardness measurements have been used to investigate the spatial and temporal patterning of cavernous weathering of sandstone masonry (Aoki and Matsukura, 2007b). The micro-drilling technique has also been used to investigate alterations in surface hardness as a way of identify-ing the presence of past consolidants and other treatments (Rodrigues et al., 2002). For heritage science applications, techniques which are truly non-destructive and produce no damage are highly desirable.

The Classic Schmidt Hammer

The Schmidt Hammer was originally devised by E. Schmidt in 1948 for carrying out in situ, non-destructive tests on concrete hardness (Day and Goudie, 1977; Day, 1980).

The instrument measures the distance of rebound of a con-trolled impact on a rock surface. There are now a variety of versions of the hammer. The one most used by geomorpholo-gists is the ‘N’ type. This can provide data on a range of rock types from weak to very strong with compressive strengths that range from c. 20–250 MPa. The ‘L’ type hammer has an impact three times lower than the ‘N’ type (0·735 compared to 2·207 Nm). It is appropriate for weak rocks and those with thin weathering crusts. The ‘P’ type is a pendulum hammer for testing materials of very low hardness, with compressive strengths of less than 70 kPa.

When the Schmidt Hammer is pressed against a surface, its piston is automatically released onto the plunger. Part of the piston’s impact energy is consumed by absorption (i.e. the work done in plastic deformation of the rock under the plunger tip) and is transformed into heat and sound. The remaining energy represents the impact penetration resistance (i.e. the hardness) of the surface. This enables the piston to rebound. The distance travelled by the piston after it rebounds is called the rebound (R) value. Harder rocks have higher R values (Aydin and Basu, 2005). The R value is shown by a pointer on a scale on the side of the instrument (range 10–100).

The R values are infl uenced by gravitational forces to varying degrees so that non-horizontal R values must be nor-malized with reference to the horizontal direction (see Day and Goudie, 1977, table 2; Kolaiti and Papadopoulos, 1993; Aydin and Basu, 2005). Aydin (2009) also reported that unless the hammer impact direction remains roughly perpendicular to the tested surface, there is a danger of frictional sliding of the plunger tip, material removal by chipping and a partial transfer of energy to and from the hammer.

There remains a wide variation in the recommended testing procedures employed by different researchers (Goktan and Gunes, 2005) particularly with regard to the number of impacts used to obtain ‘R’ values. Aydin (2009) proposes a new ISRM (International Society for Rock Mechanics) method for the Schmidt Hammer which recommends 20 rebound values from single impacts separated by at least a plunger width. He also suggests that all values should be used to calculate summary statistics and no values (high or low) should be discarded. Other studies have championed different methods, such as Yavuz et al. (2006) who collected 20 values and only used the top 10, and Gupta (2009) who collected 50 samples per site and discarded the upper 10 and the lower 10. Kennedy and Dickson (2006) use Chauvenet’s criterion to discard anomalously low values. Recently, studies have been carried out to assess the minimum sample size required for Schmidt Hammer studies, based on a statistical method (Niedzielski et al., 2009).

The advantages of the Schmidt Hammer include portability, cheapness, lack of operator variance, simplicity, and the ability to take many readings in the fi eld (Goudie, 2006). However, the Schmidt Hammer has certain limitations and so should be used with care (McCarroll, 1987). It is extremely sensitive to discontinuities in a rock. Hence, fi ssile, closely foliated and laminated rocks cannot easily be investigated by this method. Ozbek (2009) found that there was a variation in Schmidt Hammer values with imbrications direction in clastic sedimentary rocks. Results may be infl uenced by surface texture, with smooth planar surfaces giving higher readings than rough or irregular surfaces (Williams and Robinson, 1983). Surface irregularities are often crushed before the



plunger tip reaches the rock surface, resulting in some loss of impact energy. Both the magnitude and repeatability of hammer readings increases with the degree of surface polish-ing. Indeed, many workers recommend cleaning the surface to be tested with a carborundum to remove surface irregulari-ties – especially when used in the fi eld. The Schmidt Hammer cannot be used on soft materials and is not non-destructive in that context (Aoki and Matsukura, 2007a). This may present particular problems for the testing of heritage structures and surfaces such as rock art panels. The test is sensitive to mois-ture contents, especially in weak rocks (Sumner and Nel, 2002). The block mass of the rock to be tested is signifi cant, and the test cannot be used on small, light blocks. Sumner and Nel (2002) suggest that block weight should exceed 25 kg for accurate and consistent rebound determinations, whilst Demirdag et al. (2009) have found experimentally that cubic blocks should have at least 11 cm edges. Finally, there may be between-hammer variation and deterioration of hammer performance with age.

Because of its speed, simplicity, portability, low cost and non-destructiveness, the Schmidt Hammer has been used as a means of estimating other rock properties, such as compres-sive strength (Sendir, 2002). Various researchers have studied the relationship between rock compressive strength and Schmidt Hammer R values (Yasar and Erdogan, 2004; Yagiz, 2009; Aydin, 2009). The regressions vary greatly between dif-ferent rock types, however (Dinçer et al., 2004), and so should be used only for particular lithologies (Sachpazis, 1990). Nonetheless, as Hack and Huisman (2002) point out, a large number of simple tests in the fi eld, including using the Schmidt Hammer, will tend to give a better estimate of the intact rock strength at various locations than a limited number of more complex tests. Various studies have indicated strong empirical relations between Schmidt Hammer R values and measured Young’s Modulus (Katz et al., 2000), with the coeffi cient of determination (R2) values as high as 0·99 (see also Aggistalis et al., 1996; Sachpazis, 1990; Yagiz, 2009). In addition to compressive strength and Young’s Modulus, attempts have been made to determine the correlation between R values and other measures of rock physical properties, including the point load index (Aggistalis et al., 1996) and the Shore Scleroscope (Yasar and Erdogan, 2004; Shalabi et al., 2007).

The Silver Schmidt

Recently, a new type of Schmidt Hammer, the Silver Schmidt, has been introduced (Figure 1c). It is lighter in weight than the classic Schmidt Hammer (weighing 600 g), and the readings are presented in a digital form and can be stored electronically and downloaded later. The measurements are also said to be independent of impact direction. In addition, it provides an automatic conversion to the required measurement units (kg/cm2, N/mm2, psi). There are two different versions: the stan-dard impact energy form (BN) (2·207 Nm), and the reduced impact energy form (BL) (0·735 Nm). These are the same as the impact energies of the N and L versions of the classic Schmidt Hammer.

The Equotip

The Equotip is an electronic rebound hardness testing device that was developed in the 1970s by Dietmar Leeb (Kompatscher, 2004). Originally it was designed for testing metals, but it has now been used extensively for testing rock hardness (e.g. Kawasaki et al., 2002; Aoki and Matsukura, 2007a) and the

effects of weathering on rock hardness (Kawasaki and Kaneko, 2004). The device fi res by spring force an impact body con-taining a permanent magnet and a very hard indenter sphere (a tungsten carbide ball with a diameter of 3 mm) towards the surface of the material to be tested. The velocity of the impact and the rebound phase is measured by the induction voltage generated by the moving magnet through a defi ned induction coil. The hardness value is expressed as the Leeb Number (L value) or Leeb Hardness (HL), which is the ratio of the rebound velocity to the impact velocity multiplied by 1000. Low hard-ness values are expressed by low L values. Values are expressed on a LCD, are stored electronically and can be downloaded later. Verwaal and Mulder (1993, table 1) provide data on L values for a range of rock types from gypsum (254·7) to granite (807·0), while Aoki and Matsukura (2008a) provide data on rocks that range from tuffs (408·8) to gabbro (890·0).

The instrument uses automatic compensation for impact direction. The device is light in weight (780 g plus a 120 g battery pack). The impact energy of the standard type (D) is 11 N mm, though versions with an impact value of 3 N mm (type C) and 90 N mm (type G) are also available (Verwaal and Mulder, 1993). The impact energy of the D type is approx-imately 1/200 that of the Schmidt Hammer N-type, and 1/66 that of the Schmidt Hammer L-type, so that less damage is caused to the surface being tested. Softer rocks can also be tested than is possible with the Schmidt Hammer (Aoki and Matsukura, 2007a). The device can be used on quite small samples and on those of limited thickness. However, the device cannot be used successfully on rough or friable sur-faces. Aoki and Matsukura (2008a) found good correlations could be achieved between L values and unconfi ned compres-sive strength. Various methods for collecting L values and calculating descriptive statistics have been suggested – for example, Aoki and Matsukura (2007a) use the Repeat Impacts Method (RIM) to calculate Lmax from the mean of the three largest of 20 impacts on exactly the same spot, as well as the Single Impacts Method (SIM) used to calculate Ls from 20 individual impacts in one small area. There appears to be no consensus over whether carborundum should be used to smooth surfaces in the fi eld before measurement, nor what size of area should be sampled, nor how many measurements should be taken and whether extremes need to be removed.

The Equotip Piccolo

Recently, a compact version of the Equotip has been produced (Figure 1b). This is called the Piccolo, and has a weight of only 110 g. The impact energy is low (11 N mm) and equiva-lent to that of the D type Equotip. It uses automatic compensa-tion for impact direction. Values are displayed on an LCD, stored electronically and can be downloaded later.

The Sampling Areas

The four instruments were tested in two locations: the Golden Gate Highlands National Park (GGHNP) in the Free State, South Africa, and along the Dorset coast in southern England. The GGHNP is situated in the upper catchment area of the Little Caledon River close to the border with Lesotho. The geological formations form part of the Karoo Supergroup (Late Triassic and Early Jurassic). These include the Elliot Formation which consists primarily of reddish sandstones and mudstones and was deposited primarily under fl uvial conditions (Eriksson et al., 1994; Bordy et al., 2004), the Clarens sandstone, which is primarily a yellowish aeolian/arid material (Holzförster,

324 H. VILES ET AL.


2007), and the basaltic lavas of the Drakensberg Formation (Groenwald, 1986). The Dorset coast in southern England is a World Heritage Site containing Jurassic age Portland and Purbeck limestones, and Cretaceous age chalk. We sampled these rock types at sites on the Isle of Portland and at Lulworth Cove.

Aims

We carried out a number of fi eld trials to investigate seven questions surrounding the use of four Schmidt Hammer and Equotip devices with particular focus on their use in projects investigating weathering, i.e.

• How do the devices compare? Do they give comparable results on a range of rock surfaces?

• What sample sizes (number of points tested) are required for each device as used on rock surfaces in the fi eld?

• How important is operator variance?• What effects does surface pre-treatment with carborundum

have on the values obtained?• Does moisture have an impact on the values obtained?• Does rock block size infl uence the values obtained?• How important are edge effects?

Each of these fi eld trials is described individually later with each section introducing the particular methods used for that trial, followed by a presentation of the results obtained.

How do the four devices compare?

At 15 sites, both in the GGHNP and in Dorset we took 50 measurements (except for the Clarens sandstone Block 1 and Block 17 in GGHNP where we took 30 measurements) with each device on vertical and horizontal surfaces of different rock types with varying degrees of hardness. Each set of mea-surements was collected from an area of 30 cm × 30 cm to avoid repeat blows to any single point (except Block 1 and Block 17 where the available surface areas were slightly smaller). Using each device it took around three minutes to take 50 readings. The Piccolo proved the hardest to use – as it was highly sensitive to surface irregularities and weaknesses, and often took several attempts around one point to get a successful reading. Similar, but less acute, problems were found with the Equotip and Silver Schmidt, whilst the Classic Schmidt proved extremely robust and reliable. The rock types studied were: dolerite, basalt, sandstone (with and without iron crust), which we sampled in GGHNP, and limestone sampled on the Dorset coast. For this experiment each surface was prepared with carborundum before using the devices. Classic Schmidt data were corrected for impact direction, using the graphical method of Basu and Aydin (2004), and then the mean hardness values from each set of 50 data points were compared (see Figure 2). Correlation analyses demon-strated strong positive correlations between Silver Schmidt and Classic Schmidt hammer data (R2 = 0·913) and between Piccolo and Equotip (R2 = 0·876). Correlations between mean hardness values collected by the two Schmidt Hammers and the Piccolo and Equotip mean values were less strong (as illustrated in Figure 2). All correlations were found, using one-tailed t-tests, to be signifi cant.

The Silver Schmidt tended to give lower values than the Classic Schmidt and, as shown in Figure 3 (which plots the coeffi cients of variation in terms of standard deviation/mean), the datasets are also characteristically more variable. This is

probably because the Silver Schmidt used was a type BL and the Classic Schmidt an N type, which has much greater impact energy. Conversely, the Piccolo tended to record higher mean values than the Equotip with similar levels of variability. Why do the Piccolo and Equotip values not correlate better with those of the two Schmidt Hammers? We hypothesize that this refl ects inherent differences in the impacts of the two types of device (as also suggested by Hack and Huisman, 2002). Whereas the Schmidt Hammers have a large impact force and volume, and thus record hardness within a broad near-surface zone, the Piccolo and Equotip with smaller impact force and volumes, record hardness within a narrow surface zone. On rock surfaces in the fi eld which may have thin and heteroge-neous weathered zones, these two measurements may be expected to be very different (as the Piccolo and Equotip measurements will be affected more than the Schmidt Hammer ones by conditions within the weathered zone). However, on cut homogeneous test rock blocks in the laboratory we would expect differences to be much less pronounced.

The Equotip has the highest mean coeffi cient of variation (0·18), and the Classic Schmidt has by far the lowest (0·05), with Piccolo (0·16) and Silver Schmidt (0·12) intermediate. The generally higher variability in Piccolo and Equotip values we hypothesize is a result of their smaller impact picking up micro-scale variations in surface conditions on natural rock surfaces which are not detected by the coarser Schmidt Hammers. The Silver Schmidt however, being a type BL with lower impact energy than the Classic Schmidt type N has almost as high variability as the two Equotips.

What is the appropriate sample size for each device?

The question here is ‘What is the appropriate number of impacts that are required to obtain a reasonable measure of the real hardness of the rock that is being sampled?’. In order to answer this we have assumed that 50 repeat measurements (sample size) represents the population mean and standard deviation. Then, choosing an acceptable level of error (5% or 10%), we have aimed to fi nd out how many samples we would need to take to get a sample mean and standard devia-tion that is equal to the population mean and standard devia-tion (based on 50 subsamples). We have tested how precise our sample mean (for sample sizes less than 50) is using an equation for the margin of error (the maximum difference between the observed sample mean and the true value of the population mean):

M n= ⋅ ( )1 96 σ sqrt

where 1·96 = the critical z value for the right tail of the stan-dard normal distribution (using a 95% degree of confi dence), and σ is the population standard deviation and n is the sample size.

We have rearranged the formula so that we can establish the sample size necessary to produce results accurate to a specifi ed confi dence level (e.g. 95%) and margin of error (e.g. a 5% and 10%):

n M= ⋅ ×( )[ ]1 96 2σ

The results using data from 13 sites for which we have 50 repeat measurements are shown in Table I.

Table I illustrates that, in general, the Piccolo and Equotip devices require much more sampling effort to obtain a good estimate of the true hardness on weathered natural rock



y = 0.863x + 12.908R² = 0.9133

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Piccolo Leeb hardness

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Silv

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a) b)

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Figure 2. Comparisons between mean hardness values at 15 different sites determined by Equotip, Piccolo, Silver Schmidt (SilverS) and Classic Schmidt (ClassicS). (a) ClassicS versus SilverS, (b) Equotip versus Piccolo, (c) Equotip versus SilverS, (d) ClassicS versus Piccolo, (e) ClassicS versus Equotip, (f) SilverS versus Piccolo. The signifi cance of the correlations has been tested using one-tailed student t-tests at the 95% signifi cance level, using N – 2 degrees of freedom.

326 H. VILES ET AL.


surfaces than does the Classic Schmidt, with the Silver Schmidt intermediate. However, because our experience shows that using each device it takes less than three minutes to obtain 50 samples, this is not a serious problem, but rather something that we recommend requires a pilot study in order to evaluate the required sample size for any particular surface. The Piccolo appears often to require less large sample size often than the Equotip, however this is to an extent an artefact of the inability of the Piccolo to take readings on rough or otherwise variable surfaces.

How important is operator variance?

At one location within the GGHNP, on a relatively smooth horizontal sandstone exposure close to a rock shelter (called Oribi Vulture site), four operators (two male, two female) each made 50 readings using each of the four devices within an area roughly 30 cm × 30 cm. Operators attempted to avoid repeat measurements on exactly the same spot. Each operator in turn carried out measurements using the Piccolo, then carried out the same procedure using the Equotip, followed by the Silver Schmidt and the Classic Schmidt. We used the devices in this order to minimize any surface disruption (as we moved from the softest rebound device to the hardest). After carrying out a total of 800 readings, the surface was then

treated with carborundum in order to remove any surface irregularities, weathered areas, etc. The devices were then tested again using the same procedures, generating a further 800 data points. Summary comparisons of the data from each operator are presented in Figure 4, whilst results of single factor analysis of variance (ANOVA) analyses of the datasets are presented in Table II.

The results in Table II imply that operator variance is an issue for the Classic Schmidt before carborundum treatment (but not afterwards), whereas it is an issue for the Piccolo and Equotip after carborundum treatment, but not before. The Silver Schmidt does not have signifi cant operator variance issues under either condition. Inspecting the datasets in Figure 4 allows us to hypothesize rather different causes of operator variance in the case of the Classic Schmidt, versus the Piccolo and Equotip. For the Classic Schmidt, the before carborundum datasets are highly infl uenced by signifi cantly higher readings by one operator (SG), whilst all other readings before and after carborundum taken with this device are extremely tightly grouped. However, looking at the values obtained from the Piccolo and Equotip it becomes clear that there is very high variance among all the datasets, especially those taken before carborundum. We hypothesize that this natural variability is masking the impact of operator variance for these two devices in the ‘before carborundum’ group. Our general conclusion from this test is that operator variance is an issue which needs

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Figure 3. Coeffi cient of variation for hardness values from 15 sites for all four devices (n=50 except for Block 1 and Block 17 where n=30).

Table I. Sample sizes necessary to produce a sample mean within a 5% and 10% error margin of the population mean (where the population is assumed to be/defi ned as that from 50 subsamples/repeat measurements)

Piccolo Equotip Silver Schmidt Classic Schmidt

5% 10% 5% 10% 5% 10% 5% 10%

Baboon ridge Clarens sandstone 30 7 50 15 14 3 4 1Baboon ridge dolerite 50 32 50 39 19 5 7 2Blesbok loop basalt 50 21 50 19 39 10 12 3Oribi vulture iron crusted Clarens Sandstone 7 2 4 1 13 3 2 0Mushroom rock Elliot Sandstone 6 1 8 2 16 4 2 0Oribi vulture Clarens sandstone 23 6 33 8 16 4 2 1Oribi vulture 2 Clarens sandstone (dry) 30 7 50 18 13 3 2 1Oribi vulture 2 Clarens sandstone (wet) 50 16 50 14 14 3 2 1Rockshelter caprock Clarens sandstone 11 3 11 3 13 3 1 0Rockshelter backwall Clarens sandstone 50 17 50 13 29 7 6 2Purbeck limestone 50 16 50 19 18 4 10 3Portland shelly limestone 50 17 50 19 50 12 12 3Portland limestone freestone 50 26 50 35 45 11 19 5



considering in geomorphological and heritage science uses of the Piccolo and Equotip and may also be an issue even for well-established techniques such as the Schmidt Hammer.

What impact does carborundum pre-treatment have on the results obtained?

Four sets of data can be used to evaluate the infl uence of car-borundum treatment on the results obtained. Firstly, the hori-zontal sandstone surface at Oribi Vulture site (details reported more fully in the testing operator variance section earlier) gave us 1600 ‘before and after’ comparisons based on four operators each carrying out 50 measurements before and 50 measure-ments after treatment using each device in turn. The surface studied appeared to have light iron staining and possible case-

hardening. Secondly, we ran a similar exercise with all four devices but with only a single operator, testing a further hori-zontal surface with obvious iron-staining, and possible case-hardening. Fifty points were tested at random within a 30 cm × 30 cm area, before and after carborundum treatment, produc-ing a dataset of 400 measurements. Thirdly, also at Oribi Vulture site, and as part of a larger study of a number of sand-stone boulders we took before and after measurements using all four devices (one operator only) on the top horizontal surface of a boulder measuring 30 cm × 30 cm × 22 cm (giving a maximum sampling area on the top of 30 cm × 30 cm). Thirty repeat measurements were taken using each device both before and after treatment, giving a total dataset of 240 measurements. Finally, two of the devices (Piccolo and Silver Schmidt) were tested before and after carborundum treatment of a vertical rock face, partly lichen covered, in Portland limestone in Dorset. For

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Figure 4. Summary of data (min, max and inter-quartile range) collected by four operators using (a) Piccolo, (b) Equotip, (c) Silver Schmidt and (d) Classic Schmidt devices on horizontal sandstone surface at GGHNP, South Africa. Data is given before and after carborundum.

Table II. Results of single factor ANOVA analyses (F and p values) illustrating whether or not there is signifi cant difference between the results obtained by different operators for Piccolo, Equotip, Silver Schmidt and Classic Schmidt devices

Before carborundum After carborundum

Piccolo Fcalc = 1·54, p = 0·21Not signifi cant at 0·05 level

Fcalc = 2·69, p = 0·05Signifi cant at 0·05 level

Equotip Fcalc = 0·90, p = 0·44 Not signifi cant at 0·05 level Fcalc = 3·57, p = 0·02Signifi cant at 0·05 level

Silver Schmidt Fcalc = 1·70, p = 0·17Not signifi cant at 0·05 level

Fcalc = 0·08, p = 0·97Not signifi cant at 0·05 level

Classic Schmidt Fcalc = 13·43, p = 0·00Signifi cant at 0·05 level

Fcalc = 2·07, p = 0·10Not signifi cant at 0·05 level

328 H. VILES ET AL.


this test, 50 repeat readings were taken each time, giving a total dataset of 200. In each case, carborundum treatment was carried out by one operator only using the same approach and time of treatment, to reduce any variability in results associated with different degrees of surface pre-treatment.

Figure 5 shows the impacts that carborundum treatment had on the results (pooling all data) from the sandstone surface at the Oribi Vulture site. Statistical analysis (using t-tests and assuming equal variance, with 0·05 signifi cance level) indi-cated that these differences were signifi cant, with Piccolo and Equotip recording higher values after carborundum and Silver Schmidt and Classic Schmidt showing higher values before carborundum.

Similar results were obtained in the second test, of the iron-stained surface, as illustrated in Figure 6. Statistical analysis using t-test (assuming equal variance, signifi cance level = 0·05) showed there to be signifi cant differences (again with Piccolo and Equotip recording harder values after carborun-dum, and Silver Schmidt harder values before carborundum) except for the Classic Schmidt which showed no signifi cant difference before and after the carborundum treatment.

Data from the other two fi eld experiments show rather dif-ferent trends, as pictured in Figure 7. Statistical analysis, using t-tests as before, indicated that for all devices in each case there were signifi cant differences in the values obtained before and after carborundum treatment, with the higher values recorded from the surfaces after treatment.

We interpret these results to indicate two different sets of conditions in the surface and near-surface zones of the Oribi

Vulture site sandstones and the sandstone boulder and lime-stone face. On the two Oribi Vulture iron-stained surfaces, the higher values after carborundum exhibited by Piccolo and Equotip, combined with the lower values shown by Silver and Classic Schmidt devices, are quite puzzling, but may indicate that a roughened, case hardened layer has been partially removed by the carborundum. The two types of devices appear to respond differently to the reduction in roughness and partial removal of the case hardening. The lower impact rebound devices record hardness within a much smaller near-surface volume than do the Schmidt Hammers and may pick up the impact of the carborundum on roughness. However, the Schmidt Hammer values may instead refl ect the removal of part of the case hardening. In distinction, the results from the other two sites (sandstone boulder and limestone outcrop) show increasing hardness on carborundum treatment in all the devices, implying that in these circumstances where the sur-faces are patchily weathered and lichen-covered, carborun-dum treatment removes a thin, weaker surface layer allowing all devices to record harder, less weathered rock below.

Does the wetness of the surface infl uence hardness values?

A small pilot experiment was carried out on a slightly iron-stained, relatively smooth horizontal sandstone surface at the mouth of Oribi Vulture cave (close to the location of the operator variance experiment). After carborundum

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Figure 5. The infl uence of carborundum on Oribi Vulture site hardness measurements (pooled data from all operators, n = 200).

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Figure 6. Hardness data for iron-stained Clarens sandstone surface at Oribi Vulture site, before and after carborundum.



pre-treatment, all four devices (single operator) were used to obtain 50 hardness values from a surface area 30 cm × 30 cm. Following this, 200 ml of water was applied using a pressure spray in a grid over the 30 cm × 30 cm area (in order to obtain approximately equal wetting across the whole surface). Each device was then used again (same operator) to collect a further 50 values. Whilst the mean values before and after wetting were similar (Figure 8), t-tests revealed statistically signifi cant differences (0·05 signifi cance level) for Piccolo and Classic Schmidt datasets with lower values recorded on the wet sur-faces. This pilot test indicates the potential importance of surface moisture levels, and illustrates the desirability of ensuring similar surface moisture conditions when comparing hardness data.

Does block size infl uence hardness data?

Previous work has shown that because of the high impact force, the Classic Schmidt Hammer should only be used on large masses, but such constraints do not necessarily apply to the lower impact Silver Schmidt and Equotip devices. We therefore obtained eight natural blocks of sandstone from Oribi Vulture site with volumes that ranged between under 200 cm3 to almost 20 000 cm3 and took 30 hardness measure-ments with each device, following carborundum pre-treat-ment. Each block was placed on a fabric mattress to reduce movement and vibration during measurement. The Classic Schmidt and Silver Schmidt were not able to record hardness values for the two smallest blocks, either failing to take a reading or, in one case, breaking the block in two on impact and for one of the larger blocks we could only obtain a Classic Schmidt sample of 13 measurements. For blocks ranging from almost 600 cm3 to 20 000 cm3 Classic Schmidt and Silver

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Figure 7. Hardness data before and after carborundum from Boulder 1, GGHNP and vertical face in Portland limestone, Dorset.

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Figure 8. Wet/dry surface hardness comparisons for all four devices.

Schmidt hardness values showed a clear correlation with block volume, whereas those of Piccolo and Equotip did not (see Figure 9). The effect is most pronounced for the Classic Schmidt. The signifi cance of this is that if for any reason samples of small volume require hardness evaluation, Piccolo and Equotip are the most suitable devices (e.g. in studies of rock fall debris for relative dating purposes or archaeological artefacts).

Edge effects

To test for the infl uence of edge effects on semi-constrained blocks (within a detaching rock pavement for example) we carried out an experiment using each of the four devices to measure hardness around 24 points on a 10 cm × 10 cm grid placed over a block within a sandstone pavement. Three faces were identifi ed as being unconstrained, and the distance of each measurement point from the nearest unconstrained face was measured. Three measurements were obtained around each point using each device, and a mean value calculated. Figure 10 illustrates correlations between distance from nearest unconstrained edge and hardness – showing the infl u-ence that this has on Schmidt Hammer but not Equotip or Piccolo values. This experiment again demonstrates the utility of Piccolo and Equotip devices in investigating hardness near edges.

Discussion and Conclusion

The data presented in this paper illustrate the need for care in using Schmidt Hammer and Equotip devices, in order to allow confi dence in the results collected and to ensure

330 H. VILES ET AL.


y = 0.2948x + 28.159R² = 0.2126

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Figure 9. Hardness values versus boulder size for all four devices. a) Silver Schmidt, b) Classic Schmidt, c) Piccolo, d) Equotip

Figure 10. Hardness data plotted against distance from edge for all four devices. a) Silver Schmidt, b) Classic Schmidt, c) Piccolo, d) Equotip

y = 0.0007x + 35.695R² = 0.4117

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comparability between studies. Whilst the literature records many uses of the Schmidt Hammer for fi eld and laboratory collection of hardness data for geomorphological and heritage science investigations, there is little agreement over methodol-ogy nor tests of the relative merits of type L versus type N. For the Equotip, which has not yet been used to anything like the same extent, there is also a pressing need for agreed method-ologies for fi eld and laboratory applications and greater knowledge of the comparability with Schmidt Hammers. Our investigations have demonstrated, for a range of rock types under fi eld conditions, that the two Schmidt Hammers and two Equotip devices give results of varying comparability – whilst on fresh, cut blocks within the laboratory the agreement between methods should be much closer. The difference between Schmidt Hammer and Equotip values could, we propose, be used to reveal information about the nature and degree of weathering on different surfaces. Differences in L and N type Schmidt Hammer values have previously been noted by Kennedy and Dickson (2006) from shore platforms, and Török (2008b) for building surfaces, whilst Aoki and Matsukura (2007a) utilized the varying difference between Equotip Lmax and Ls values to investigate the degree of weather-ing. However, no one has as yet utilized differences between Schmidt Hammer and Equotip to investigate degrees of weath-ering and case hardening.

Our data also illustrates the need for pilot studies to be undertaken for every investigation in order to work out the appropriate sample size – which generally speaking is higher for the Equotip and Piccolo than for the Schmidt Hammers. The required sample size will usually be larger for very weath-ered and inhomogeneous surfaces. Operator variance has also been shown to be a real issue under many circumstances for all devices except the Silver Schmidt (type BL). Again, this demonstrates the need for care to be taken when carrying out rock hardness measurements especially under variable condi-tions on rock surfaces in the fi eld. Our data also indicate that whether or not carborundum pre-treatment is required or valu-able depends greatly on the surfaces under study (as well as the aims and location of the project – carborundum treatment would simply be unacceptable for many heritage science proj-ects). Further studies, with progressive carborundum treat-ments during a sequence of hardness measurements, are hereby proposed as a way of extracting further information about the weathered zone. Whilst we only collected a small amount of data on the infl uence of moisture on hardness measurements, it is clear that our results back up those of previous researchers who have illustrated that moisture can infl uence Schmidt Hammer results. Whilst it did not signifi -cantly infl uence Equotip readings, the Piccolo values were signifi cantly different, showing that care should also be taken when using Equotip devices on wet and dry surfaces.

The value of the Equotip in comparison with the Schmidt Hammer was clearly illustrated by our experiment on blocks of different sizes, and on the edge effects associated with large blocks. The Equotip values have been shown to be insensitive to block size whilst our results confi rm the laboratory based studies of Demirdag et al. (2009) that block size is critical to Schmidt Hammer results – with volumes of around 1000 cm3 seen as the minimum required in both studies. Thus, the Equotip is the device of choice for any application that is interested in variations in hardness across the face of blocks (such as detaching blocks on rock platforms, boulders in rock-fall deposits or individual building stones within a wall).

Overall, we conclude that each device has its strengths and weakness depending on the purpose for which hardness data is being collected. Establishing rigorous protocols (normally through a pilot study at the start of a project) for their use for

every study in terms of sample size, calculation of test statis-tics, operator variance, conditions at the time of collecting the data (e.g. moisture levels) and the need for, and type of surface pre-treatment, will ensure that the data collected is of the best quality. All papers should make explicit mention of these protocols to ensure comparability between studies. Finally, we propose that the Schmidt Hammer (both L and N type) and Equotip (including Piccolo) have much potential to be used together for geomorphological and heritage science projects investigating weathering and surface crusting. Development of a simple coeffi cient of difference between Schmidt Hammer and Equotip values should enable identifi cation of case hard-ened or weathered surfaces.

Acknowledgements—We thank South Africa National Parks Service for granting us permission to work at GGHNP, the Oppenheimer Fund of the University of Oxford for fi nancial help, Dr Abi Stone for invalu-able help with data analysis, and Proceq for generously lending us the Piccolo and Silver Schmidt devices used in this paper.

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