The use of the Schmidt Hammer and Equotip for rock

Transcription

EARTH SURFACE PROCESSES AND LANDFORMS
Earth 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 analysis
Heather Viles,1,2* Andrew Goudie,1,2 Stefan Grab2 and Jennifer Lalley2
University of Oxford, Oxford, UK
2
University of the Witwatersrand, Johannesburg, South Africa
1
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, field-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 geomorphological 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 influences 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 deteriorate. Various techniques have been developed to enable rock
hardness to be determined, including those based on microdrilling (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 field 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 classification involving the Schmidt Hammer was used
in the Napier Range of Australia by Allison and Goudie (1990).
They identified seven main slope forms associated with different facies of a Devonian reef and found that it was possible
to draw associations between slope profile shape and RMS.
Similarly, Placek and Migoń (2007) investigated the relationship 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
1
2
3
4
a)
b)
c)
d)
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.
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 profiles, is a topic of increasing interest geomorphologically. Mitchell et al. (2005) found that in the Colorado River
Schmidt Hammer rock hardness values correlated significantly
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 floors corresponding to weak bedrock, and narrow valley floors with
strong bedrock. They also found a statistically significant difference in Schmidt Hammer values between north- and southfacing 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 phenomena including glacial moraine, rock glaciers, mass movements, 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 measurements 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 nonlinear. Sjöberg and Broadbent (1991) were able to obtain a
measure of how weathering developed through time by examining the Schmidt Hammer values of raised beaches at different elevations in Sweden. Spatial variations in hardness can
also be used to investigate environmental influences 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 periglacial 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 significantly higher on the
outer roof of Spanish tafoni than on the inner cavern walls. In
Earth Surf. Process. Landforms, Vol. 36, 320–333 (2011)
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H. VILES ET AL.
Jordan, Goudie et al. (2002) used the Schmidt Hammer to
identify the significance of case hardening in tafoni development. 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 identified 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 influence of rock
hardness on the development of inselbergs has been studied
by Pye et al. (1986) in Kenya. Here, Schmidt Hammer measurements 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 controls, notably jointing. Similarly, the Equotip has been used for
assessing the importance of case-hardening in the development 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 Paşamehmetoğlu 2004). For
example, La Pera and Sorriso-Valvo (2000) were able to relate
Schmidt Hammer R values and a weathering classification to
the biotite content of granites, while Arikan et al. (2007)
used Schmidt Hammer values in a weathering classification
system of acidic volcanic rocks. Quantitative assessment of
the degree of weathering is helpful in the identification 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
significant 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 fire 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 identifying 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 controlled impact on a rock surface. There are now a variety of
versions of the hammer. The one most used by geomorphologists 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 influenced by gravitational forces to
varying degrees so that non-horizontal R values must be normalized 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 field (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, fissile, 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 influenced 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
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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 polishing. Indeed, many workers recommend cleaning the surface
to be tested with a carborundum to remove surface irregularities – especially when used in the field. 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 moisture contents, especially in weak rocks (Sumner and Nel,
2002). The block mass of the rock to be tested is significant,
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 compressive strength (Sendir, 2002). Various researchers have studied
the relationship between rock compressive strength and
Schmidt Hammer R values (Yaşar and Erdoğan, 2004; Yagiz,
2009; Aydin, 2009). The regressions vary greatly between different 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 field, 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 coefficient 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
(Yaşar and Erdoğan, 2004; Shalabi et al., 2007).
effects of weathering on rock hardness (Kawasaki and Kaneko,
2004). The device fires by spring force an impact body containing 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 defined 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 hardness 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 approximately 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 surfaces. Aoki and Matsukura (2008a) found good correlations
could be achieved between L values and unconfined compressive 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 field 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 Silver Schmidt
The Equotip Piccolo
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 standard 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.
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 equivalent to that of the D type Equotip. It uses automatic compensation for impact direction. Values are displayed on an LCD,
stored electronically and can be downloaded later.
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
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 fluvial conditions (Eriksson
et al., 1994; Bordy et al., 2004), the Clarens sandstone, which
is primarily a yellowish aeolian/arid material (Holzförster,
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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 field 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 field?
• 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 influence the values obtained?
• How important are edge effects?
Each of these field 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 measurements 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 demonstrated 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 onetailed t-tests, to be significant.
The Silver Schmidt tended to give lower values than the
Classic Schmidt and, as shown in Figure 3 (which plots the
coefficients 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
reflects 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 field which may have thin and heterogeneous 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 coefficient 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 find out how many samples we
would need to take to get a sample mean and standard deviation that is equal to the population mean and standard deviation (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 = 1⋅ 96 (σ sqrt n)
where 1·96 = the critical z value for the right tail of the standard normal distribution (using a 95% degree of confidence),
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
specified confidence level (e.g. 95%) and margin of error (e.g.
a 5% and 10%):
n = [(1⋅ 96 × σ ) M ] 2
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
b)
65
60
y = 0.863x + 12.908
R² = 0.9133
55
Equotip Leeb hardness
ClassicS (corrected) R values
a)
50
45
40
650
600
y = 0.9955x - 20.915
R² = 0.876
550
500
450
35
400
30
25
25
35
45
55
350
65
350
450
d)
65
60
y = 0.0827x + 3.2088
R² = 0.4145
55
50
45
40
35
65
60
55
y = 0.0614x + 17.272
R² = 0.2852
50
45
40
350
450
550
30
650
350
450
SilverS R values
f)
55
SilverS R values
60
y = 0.0612x + 18.826
R² = 0.3201
50
45
50
45
40
35
35
30
25
450
550
650
y = 0.0842x + 0.4985
R² = 0.3796
55
40
350
650
65
65
60
550
Piccolo Leeb hardness
e)
30
650
35
30
25
550
SilverS R values
c)
325
400
450
500
550
600
650
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 significance of the correlations has been tested using one-tailed student t-tests at the 95% significance
level, using N – 2 degrees of freedom.
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H. VILES ET AL.
0.35
Piccolo
0.3
0.25
Equotip
0.2
0.15
SilverS
0.1
ClassicS
0.05
0
Figure 3. Coefficient 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/defined as that from 50 subsamples/repeat measurements)
Piccolo
Baboon ridge Clarens sandstone
Baboon ridge dolerite
Blesbok loop basalt
Oribi vulture iron crusted Clarens Sandstone
Mushroom rock Elliot Sandstone
Oribi vulture Clarens sandstone
Oribi vulture 2 Clarens sandstone (dry)
Oribi vulture 2 Clarens sandstone (wet)
Rockshelter caprock Clarens sandstone
Rockshelter backwall Clarens sandstone
Purbeck limestone
Portland shelly limestone
Portland limestone freestone
Equotip
Classic Schmidt
5%
10%
5%
10%
5%
10%
5%
10%
30
50
50
7
6
23
30
50
11
50
50
50
50
7
32
21
2
1
6
7
16
3
17
16
17
26
50
50
50
4
8
33
50
50
11
50
50
50
50
15
39
19
1
2
8
18
14
3
13
19
19
35
14
19
39
13
16
16
13
14
13
29
18
50
45
3
5
10
3
4
4
3
3
3
7
4
12
11
4
7
12
2
2
2
2
2
1
6
10
12
19
1
2
3
0
0
1
1
1
0
2
3
3
5
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
Silver Schmidt
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 significant 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 influenced by significantly 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
a)
327
b)
800
700
600
500
400
300
200
100
0
800
700
600
500
400
300
200
100
0
c) 65
d) 65
60
60
55
55
50
50
45
45
40
40
35
35
30
30
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 significant 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 = 0·21
Not significant at 0·05 level
Fcalc = 2·69, p = 0·05
Significant at 0·05 level
Equotip
Fcalc = 0·90, p = 0·44 Not significant at 0·05 level
Fcalc = 3·57, p = 0·02
Silver Schmidt
Fcalc = 1·70, p = 0·17
Fcalc = 0·08, p = 0·97
Classic Schmidt
Fcalc = 13·43, p = 0·00
Fcalc = 2·07, p = 0·10
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 influence of carborundum treatment on the results obtained. Firstly, the horizontal 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 measurements after treatment using each device in turn. The surface
studied appeared to have light iron staining and possible caseCopyright © 2010 John Wiley & Sons, Ltd.
hardening. Secondly, we ran a similar exercise with all four
devices but with only a single operator, testing a further horizontal surface with obvious iron-staining, and possible casehardening. Fifty points were tested at random within a 30 cm
× 30 cm area, before and after carborundum treatment, producing a dataset of 400 measurements. Thirdly, also at Oribi
Vulture site, and as part of a larger study of a number of sandstone 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
328
H. VILES ET AL.
a) 800
b) 70
700
600
500
60
50
400
300
200
100
0
40
30
20
Figure 5. The influence of carborundum on Oribi Vulture site hardness measurements (pooled data from all operators, n = 200).
a) 800
b) 60
700
50
600
500
40
400
30
300
20
200
10
100
0
0
Figure 6. Hardness data for iron-stained Clarens sandstone surface at Oribi Vulture site, before and after carborundum.
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 significance level) indicated that these differences were significant, 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 ironstained surface, as illustrated in Figure 6. Statistical analysis
using t-test (assuming equal variance, significance level =
0·05) showed there to be significant differences (again with
Piccolo and Equotip recording harder values after carborundum, and Silver Schmidt harder values before carborundum)
except for the Classic Schmidt which showed no significant
difference before and after the carborundum treatment.
Data from the other two field experiments show rather different trends, as pictured in Figure 7. Statistical analysis, using
t-tests as before, indicated that for all devices in each case
there were significant 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 limestone 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 nearsurface volume than do the Schmidt Hammers and may pick
up the impact of the carborundum on roughness. However,
the Schmidt Hammer values may instead reflect 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 surfaces are patchily weathered and lichen-covered, carborundum treatment removes a thin, weaker surface layer allowing
all devices to record harder, less weathered rock below.
Does the wetness of the surface influence
hardness values?
A small pilot experiment was carried out on a slightly ironstained, relatively smooth horizontal sandstone surface at
the mouth of Oribi Vulture cave (close to the location of
the operator variance experiment). After carborundum
a) 800
b) 70
700
600
500
400
300
200
100
0
60
50
40
30
20
10
0
329
Figure 7. Hardness data before and after carborundum from Boulder 1, GGHNP and vertical face in Portland limestone, Dorset.
a) 800
b) 70
700
60
600
50
500
400
300
200
40
30
20
100
10
0
0
Figure 8. Wet/dry surface hardness comparisons for all four devices.
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 significant
differences (0·05 significance level) for Piccolo and Classic
Schmidt datasets with lower values recorded on the wet surfaces. 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 influence 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 measurements with each device, following carborundum pre-treatment. 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
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 significance 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 influence 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 identified 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 influence 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
confidence in the results collected and to ensure
330
H. VILES ET AL.
a)
b)
70
60
50
40
y = 0.0007x + 35.695
R² = 0.4117
30
20
mean ClassicS R value
mean SilverS R value
60
50
40
y = 0.0021x + 19.985
R² = 0.7713
30
20
10
10
0
70
0
10000
20000
0
30000
0
Boulder volume (cm3)
c)
30000
d)
700
600
500
y = 0.0025x + 497.75
R² = 0.0683
400
300
200
100
0
0
10000
20000
mean Equotip Leed hardness
700
mean Piccolo Leeb hardness
10000
20000
600
500
300
200
100
0
30000
y = 0.0019x + 486.16
R² = 0.05
400
0
10000
20000
30000
Figure 9. Hardness values versus boulder size for all four devices. a) Silver Schmidt, b) Classic Schmidt, c) Piccolo, d) Equotip
a)
b)
50
35
30
25
20
y = 0.2948x + 28.159
R² = 0.2126
15
10
0
35
y = 0.7416x + 26.365
R² = 0.4813
30
25
20
15
10
d)
600
500
400
300
y = -0.9407x + 431.92
R² = 0.0343
200
100
0
0
10
20
30
Distance from nearest edge (cm)
0
10
20
30
mean Equotip Leed hardness
mean Piccolo Leeb hardness
c)
40
5
5
0
50
45
40
mean ClassicS R value
mean SilverS R value
45
0
10
20
30
600
500
400
300
y = -1.3992x + 401.53
R² = 0.0387
200
100
0
0
10
20
30
Figure 10. Hardness data plotted against distance from edge for all four devices. a) Silver Schmidt, b) Classic Schmidt, c) Piccolo, d) Equotip
comparability between studies. Whilst the literature records
many uses of the Schmidt Hammer for field and laboratory
collection of hardness data for geomorphological and heritage
science investigations, there is little agreement over methodology 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 methodologies for field and laboratory applications and greater
knowledge of the comparability with Schmidt Hammers. Our
investigations have demonstrated, for a range of rock types
under field 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 weathering. However, no one has as yet utilized differences between
Schmidt Hammer and Equotip to investigate degrees of weathering 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 weathered 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 conditions on rock surfaces in the field. Our data also indicate that
whether or not carborundum pre-treatment is required or valuable 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 projects). Further studies, with progressive carborundum treatments 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 influence of moisture on hardness
measurements, it is clear that our results back up those of
previous researchers who have illustrated that moisture can
influence Schmidt Hammer results. Whilst it did not significantly influence Equotip readings, the Piccolo values were
significantly 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 confirm 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 rockfall 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
331
every study in terms of sample size, calculation of test statistics, 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 coefficient of difference between Schmidt Hammer
and Equotip values should enable identification of case hardened 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 financial help, Dr Abi Stone for invaluable help with data analysis, and Proceq for generously lending us
the Piccolo and Silver Schmidt devices used in this paper.
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The use of the Schmidt Hammer and Equotip for rock

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