Introduction

The physico-mechanical properties of rocks are the most important parameters in any geotechnical application and in the classification of rocks for engineering purposes. They are mainly influenced by the mineral composition, texture (size, shape and arrangement of mineral grains, nature of grain to grain contacts and degree of grain interlocking), degree of alteration, weathering and deformation of the source rock (Hartley 1974; Irfan and Dearman 1978; Shakoor and Bonelli 1991; Grönholm 1994; Haney and Shakoor 1994; Tugrul and Zarif 1999; Akesson et al. 2001; Lundqvist and Göran 2001; Miskovsky et al. 2004; Zorlu et al. 2004; Al-Oraimi et al. 2006; Pomonis et al. 2007; Tamrakar et al. 2007; Rigopoulos et al. 2010).

Owing to the fact that ophiolitic complexes have become important earth crust components in some areas like south-eastern Europe, they are used extensively as engineering materials and many works are constructed on/in them. Ophiolitic suite rocks represent remnants of the Earth’s oceanic crust and upper mantle and are fundamentally characterized by underlying ultrabasic rocks, which are covered by basic, hypabyssal and extrusive rocks. This succession is idealized and in most cases some members may be absent.

This research concentrates on ultrabasic rocks. They include a wide range of rock types (harzburgites, lherzolites, plagioclastic peridotites, dunites, etc.) which, due to ocean-floor metamorphism (serpentinization), lead to a modification of their petrographic characteristics (serpentinized varieties of them). Variations in mineralogical and textural characteristics as well as the serpentinization affect their physico-mechanical properties, which vary from excellent to fair, becoming poor to very poor when extensive alteration and/or intense deformation is present (Christensen 1966, 2004; Ramana et al. 1986; Escartin et al. 2001; Marinos et al. 2006; Diamantis 2010; Ozsoy et al. 2010).

The aim of this study is to quantify the relationships of the dry and saturated unit weight (γ d , γ s), effective porosity (n e), uniaxial compressive strength (UCS) and static tangent modulus (E st) with the petrographic characteristics (serpentinization percentage, mineral composition, grain size and the micro-petrographic index I ps: ratio between primary and secondary minerals) of 33 serpentinite and 14 peridotite samples, taken from central Greece. Physico-mechanical tests were performed according to ISRM and ASTM specifications and petrographic characteristics were described from one polished thin section per sample using a polarizing microscope. Point counting was carried out to quantify the mineralogical data. Furthermore, X-ray diffractions (XRDs) were used to estimate the mineral composition, while textural characteristics were studied using scanning electron microscope (SEM).

Geological setting-tectonics

The study area is situated in central Greece and specifically in the Kallidromo and Othrys Mountains, consisting mainly of Alpine formations (Mountrakis et al. 1983; Katsikatsos et al. 1986). From bottom to top, the following formations can be distinguished (Marinos 1974; Ferriere 1982; Migiros 1990):

  1. (a)

    A carbonate sequence of Triassic-Jurassic age which constitutes the basement of the area;

  2. (b)

    A tectonic nappe, mainly ophiolitic (Katsikatsos et al. 1986), and

  3. (c)

    An unconformable sequence of Cretaceous limestones, which passes upward to flysch.

The ophiolitic formations have thrusted over the Triassic-Jurassic carbonate sequence and belong to the Subpelagonian geotectonic unit consisting of volcano-sedimentary formations, basaltic lavas, basic rocks and ultrabasic masses. The present research focusses only on the ultrabasic rocks. They are comprised of harzburgites, lherzolites, plagioclastic peridotites and dunites which vary in their degrees of serpentinization.

According to Migiros (1990), the tectonic analysis of the geological formations exhibits the following prominent tectonic features in the ultrabasic rock masses:

  1. (a)

    Schistosity: NW–SE direction and NE dip less than 30°.

  2. (b)

    Low thrusts: E–W direction and N dip between 30° and 45°.

  3. (c)

    Thrusts: NW–SE direction and NE dip between 45° and 60°.

  4. (d)

    Faults: E–W, NW–SE, NE–SW directions and dips more than 60°.

Petrographic properties of ultrabasic rocks

The mineralogical and textural characteristics of the samples were studied, as described above, by optical microscopy, XRD and SEM analyses. Point counting under a polarizing microscope was used to determine grain size, grain shape and the modal composition. Approximately 300 equally distributed points were counted in each polished thin section. The mineralogical analysis results, the structure and the name of each rock type are given in Table 1.

Table 1 Mineralogical composition and structures of the ultrabasic rocks investigated (Diamantis 2010)
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Peridotites

The peridotites investigated are unserpentinized or slightly serpentinized (serpentinization <30 % by volume) ultrabasic rock types. They are mainly medium-grained homogeneous isotropic rocks and, in general, present a granular or porphyritic structure (Fig. 1a) and compact texture without preferred mineral orientation. In some samples, the structure is characterisized as porphyroclastic because both the crystals of olivine and orthopyroxene are broken in many pieces (Fig. 1b). Olivine, which is the main constituent of these rocks, ranges between 50 and 85 % (by volume). The orthopyroxene (mainly enstatite, Fig. 1a, b, d) varies from 4 % to 24 %, while opaque minerals (mainly chromite) are present in small amounts (1–3 %, by volume, Fig. 1b, c). The mentioned above minerals are characterized as primary (parent) minerals (Table 1). They are influenced by the serpentinization (low-temperature, metamorphic process) and transformed into secondary minerals. The secondary mineral constituents (Table 1) are serpentine (2–22 % by volume), chlorite, talc and actinolite comprising up to 5 %. Using the classification system of Streckeisen (1976), these peridotites are classified as unserpentinized or slightly serpentinized harzburgites. In some samples, except for the above minerals, clinopyroxene phenocrysts (3–12 %) are present, while in sample OP12 collected from Othrys, subhedral to euhedral plagioclases (up to 2 %, by volume) are also found. According to the Streckeisen classification system (1976), these peridotites are characterized as lherzolite and plagioclastic lherzolite, respectively. Finally, when the percentage of olivine is higher than 90 %, then the rocks are classified as dunites (Table 1).

Fig. 1
figure 1

a–d Peridotite with allotriomorphic olivines (Ol), phenocrysts of orhopyroxenes and clinopyroxenes (Opx, Cpx), opaque minerals (mainly chromite, Sp) and serpentines (Serp) in the fractures (corss Nicols). e orthopyroxene crystals are secondarily replaced by actinolite (Act)

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The olivine grains are mainly allotriomorphic (Fig. 1a–d), while sometimes they appear as neoblasts. Their size ranges from 0.3 to 0.8 mm, and they show intense microcracking and undulose extinction. The orthopyroxenes appear as porphyroclasts with the form of hypidiomorphic to allotriomorphic prisms and their mean size is 1.7 mm (varies from 0.6 to 2.8 mm, Fig. 1a, b, d). Most of them show exsolution lamellea of clinopyroxene (Fig. 1a, d). Plastic deformation is manifested by the undulose extinction and the deformation of the exsolution lamellea (Fig. 1d). Clinopyroxene porphyroclasts appear as hypidiomorphic prisms and their size is between 0.4 and 1.8 mm (Fig. 1a, c). The plagioclases (An-rich) appear as very small (<0.2 mm) allotriomorphic crystals between the grains of olivine, pyroxene and opaque minerals.

The olivine, as mentioned, is the first mineral that undergoes serpentinization. This alteration is mainly initiated along cracks in the olivine, but, as the process continues, the remaining olivine decreases. Serpentinization moves inwards to the centers of the grains often leaving concentric rings of serpentine around the grains which may represent pauses in the process. The orthopyroxenes then get serpentinized, while the clinopyroxenes are preserved in significant amounts, as they are less influenced by the serpentinization. The serpentinization of orthopyroxenes mainly occurs along the cracks and cleavage and progressively moves inwards. Thus, in a crystal which is not completely altered, the fresh orthopyroxene is in the centre. The alteration products, called bastites, often show zoning in thin sections with the central parts of the pseudomorph being in extinction at a different position to the edges. Some orthopyroxene and clinopyroxene crystals are secondarily replaced by talc, chlorite, and actinolite (uralitization, Fig. 1e).

The study of representative samples using X-ray Diffraction (XRD) shows that the serpentines are lizardite and antigorite (Fig. 2a, b) and that in most of the samples lizardite prevails. The X-ray analyses also show that in some samples basic plagioclases occur (Fig. 2a).

Fig. 2
figure 2

a, b X-ray graphs show that serpentines, detected, are lizardite (Liz) and antigorite (Ant) and there are chlorite (Chl) and plagioclase (Pl)

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Serpentinites

As far as the serpentinites are concerned, they constitute the majority of the ultrabasic rocks and occur in both western Othry and in Kallidromo. They are mainly composed of secondary minerals (69–97 %, by volume), while the presence of the primary (parent) minerals is limited to <30 %. Serpentine is the dominant (secondary) mineral phase (62–84 %, Table 1, Diamantis 2010) and is usually found in the form of antigorite or lizardite (leaf form, SEM-Fig. 3a), while fibrous structures like chrysotile are absent. Other ocean-floor metamorphic products are chlorite, actinolite, and talc (Fig. 3b). The serpentinites are mainly fine-grained (they form fine-grained matrix grains), dark green coloured, isotropic, homogeneous rocks and show mesh structures (Fig. 3c, d), while in some cases, an interpenetrating structure is observed without any preferred orientation of serpentine minerals (Fig. 3a, e, SEM). The hour-glass shape is scarce, and where they do appear, they are not well developed. The polygonal-shaped cells are mainly generated by serpentinized olivine grains, so in some samples in the center of the cell, a residual olivine crystal is observed (Fig. 3c–e). The involvement of the residual mineral phases in the paragenesis is important for the determination of the protoliths of serpentinites. The length of serpentines is <0.3 mm, while their thicknss and width are <0.015 and <0.05 mm, respectively.

Fig. 3
figure 3

a Leaf form of serpentine (SEM), b participation of chlorite, actinolite, and talc in serpentinites, c–e mesh structure (residual olivine crystals)

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The values of serpentinization percentage are given in Table 1.

Physical and mechanical properties of ultrabasic rocks

Physical properties

A variety of laboratory tests was used to obtain physical indices expressing the characteristics of ultrabasic samples. The rock blocks were cored to give cylindrical test specimens and the dry (γ d ) and saturated unit weight (γ s ), as well as the effective porosity (n e) were determined using the following functions (ISRM 2007):

$$ \gamma_{\text{d}} = \frac{{W_{d} }}{{V_{t} }}\frac{{M_{s} *g}}{{(M_{\text{sat}} - M_{\text{sub}} )/\rho_{\text{w}} }} {\text{kN}}/{\text{m}}^{ 3}, $$
(1)
$$ \gamma_{\text{sat}} = \frac{{W_{\text{sat}} }}{{V_{t} }}\frac{{M_{\text{sat}} *g}}{{(M_{\text{sat}} - M_{\text{sub}} )/\rho_{\text{w}} }} {\text{kN}}/{\text{m}}^{ 3}, $$
(2)
$$ n_{\text{e}} = \frac{{V_{v} }}{{V_{t} }}\frac{{(M_{\text{sat}} - M_{s} )/\rho_{\text{w}} }}{{ ( {\text{M}}_{\text{sat}} - M_{\text{sub}} )/\rho_{\text{w}} }}\%, $$
(3)

where, W d, is the dry weight of the specimen (kN/m3), W sat, is the saturated weight of the specimen (kN/m3), V t, is the total volume of the specimen (m3), V v, is the volume of the voids (m3), M s, is the dry mass of the specimen (gr), M sat, is the saturated mass of the specimen (dry on the surface, gr), M sub, is the submerged mass of the specimen (gr), g is the gravitational acceleration (m/s2), ρ w, is the density of water (gr/cm3).

At least three tests were carried out on each sample for each property and the average values were then obtained (Table 2). As shown, the total volume was obtained from saturation and buoyancy techniques and not from the measurements of their dimensions.

Table 2 Dry, saturated unit weight and effective porosity values using saturation and buoyancy techniques
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The dry and saturated unit weight (γ d , γ s ) range from 24.53 to 26.79 and from 25.00 to 26.83, respectively, in serpentinites, while in the peridotites γ d and γ s vary between 30.86 and 33.27 and between 30.88 and 33.28, respectively (Tables 2, 3). In general, it is commonly known that unit weight is related to the mineralogical and textural characteristics of the rocks. Serpentinites are mainly composed of minerals (secondary) that have smaller specific gravities than those of peridotites, and, thus, serpentinites show lower values of unit weight than peridotites. The effective porosity varies from 0.39 % to 4.74 % in serpentinites and between 0.07 % and 0.26 % in peridotites. Porosity is an important factor in rock strength, since a small change in pore volume can have an appreciable effect on the mechanical properties. The ranges, the mean values and the standard deviations of the mentioned above properties for serpentinites and peridotites are given in Table 3. The big differences in unit weight and porosity values between serpentinites and peridotites are due to their different degress of serpentinization .

Table 3 Statistical analysis of physical properties and serpentinization percentage
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Mechanical properties

The mechanical properties of the ultrabasic rocks were determined by a variety of laboratory tests. The uniaxial compressive strength (UCS) of the ultrabasic rocks was determined using a uniaxial compression testing machine in accordance with ASTM (1986), while the static tangent modulus (E st) was determined using stain gauges. Samples cored for these properties had length/diameter ratios of 2–2.5 (ASTM 2001). Test results obtained for this range do not suffer from sample size effects (Hoek and Brown 1980; Hawkins 1998). The cylindrical rock specimens’ diameters ranged between 53 and 55 mm. The specimens were inspected macroscopically and only the isotropic, homogeneous, unweathered (or slightly weathered) ultrabasic rocks free of visible joints were considered. The UCS was measured by axial loading of specimens, while the static tangent modulus was derived from the slope of the stress–strain curves. Fractures created by the tests did not follow internal discontinuities and were always fresh. The mechanical tests were carried out in dry conditions for a better correlation of the results.

The UCS values vary from 19.21 to 125.73 MPa in serpentinites and from 79.31 to 241.56 MPa in peridotites (Tables 4, 5, Diamantis et al. 2009; Diamantis 2010) exhibiting a large variation. In general, peridotites are stronger than serpentinites (Table 4). This big difference may be attributed to the different degrees of serpentinization and/or to the internal fractures/cracks, macroscopically undetected and/or petrographic variety and/or the structural complexity of ultrabasic rocks. Peridotites present greater variations (standard deviation, Table 5) than serpentinites because according to Escartin et al. (2001) and Shimada et al. (1983) small amounts (>9 %) of lizardite and chrysotile reduce the strength of the unaltered peridotite by more than a factor of two. Thus, the strength of these peridotites is similar to that of pure oceanic serpentinites. The strength of peridotite, which contains <9 % of a serpentine phase, is intermediate between that of pure serpentinite and unaltered peridotite. In accordance with ISRM (1981), the majority of peridotites are characterized as rocks with very high strength, while the majority of serpentinites range in strength between 50 and 100 MPa (rocks with high strength). The mean value for peridotites is 138.94 MPa, while for serpentinites the mean is 64.06 MPa. The mean value for both of them is 86.37 MPa. Similar values were given by several authors: Rao and Ramana (1974) found that for highly serpentinized peridotites and under a confining pressure of 75 MPa, the UCS values vary between 70.5 and 156.2 MPa. According to Koumantakis (1982), for slightly, moderately and highly serpentinised peridotites, the mean value of UCS was 95.44 MPa.

Table 4 Uniaxial compressive strength, static tangent modulus and modulus ratio values
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Table 5 Statistical analysis of mechanical properties
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The E st varies from 5.2 to 27.8GPa in serpentinites and between 29.1 and 69.3 GPa in peridotites (Tables 4, 5). The modulus ratio (MR) was calculated as the ratio of tangent modulus to uniaxial compressive strength and ranges between 180 and 413 in serpentinites and from 264 to 403 in peridotites. Deere and Miller (1966) classificated rocks into three categories: (a) High Ratio, (b) Medium Ratio and (c) Low Ratio. The values of MR for the rocks studied are illustrated in Fig. 4 using the diagram of Deere and Miller (1966).

Fig. 4
figure 4

a, b The results of this study plotted on the Deere and Miller diagram for peridotites and serpentinites, respectively

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From Fig. 4 it is obvious that the peridotites all plot in the Medium Ratio Zone (M), while serpentinites mainly plot in the lower portion of the Medium Ratio Zone (M) with a few results in the Low Ratio Zone (L). The results are reasonable because, according to Deere and Miller (1966), igneous rocks plot in the Medium Ratio Zone. The values, which plot in the Low Ration Zone, indicate that these serpentinite samples may not be homogeneous and isotropic.

Correlations of petrographic characteristics with physical and mechanical properties

Simple regression analyses with confidence limits of 95 % were applied to check whether petrographic variables could significantly explain the physical and mechanical properties. Selected petrographic, physical and mechanical properties were plotted against each other in order to predict one parameter from another. The equations of the best fit curves (e.g., linear, logarithmic, exponential, power) and the coefficients of determination (R 2) were calculated by the “least squares” method.

In order to determine the influence of the petrographical characteristics on the engineering properties, correlations were attempted between the serpentinization (β), the percentages of minerals, their grain size, the micro-petrographic index (I ps) and the physico-mechanical properties.

Some researchers (Christensen 1966, 2004; Escartin et al. 2001; Diamantis 2010, Rigopoulos et al. 2010) have studied the relationships between the degree of serpentinization and physical characteristics and have concluded that these properties are closely related. Unit weight decreases with increasing serpentinization, while effective porosity decreases with the reduced low-temperature metamorphic process.

In this paper, an attempt to correlate degree of serpentinization with physical characteristics is presented in Fig. 5. The dry unit weight decreases linearly as the serpentinization increases, while the increase of secondary minerals increases the effective porosity (exponentially in serpentinites, linearly in peridotites). The empirical equations and the determination coefficients (R-square) are given in the same figures. Both of these functions give strong correlations.

Fig. 5
figure 5

Variation of serpentinization degree versus physical properties

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The uniaxial compressive strength (UCS) and the static tangent modulus (E st) are two of the most fundamental engineering parameters, but they require a large number of high quality core samples and use of expensive laboratory equipment. Thus, indirect, simpler, faster and more economical tests are usually used to estimate UCS and E st. For this reason, in this study, empirical equations have been investigated to correlate the uniaxial compressive strength and the static tangent modulus with petrographic parameters. The relationship between the percentage of secondary minerals (serpentinization) and the uniaxial compressive strength is given in Fig. 6a, b. As can be seen in this figure, the secondary minerals play a very important role in strength reduction. The regression line representing the best fit between UCS and β is logarithmic for peridotites (R 2 = 0.69) and exponential (R 2 = 0.87) for serpentinites. The estimated UCS using the β values can be expressed by the empirical equations:

$$ {\text{UCS}} = - 56.06{\text{Ln}}\left( \beta \right) + 273.93\quad {\text{ for peridotites}}, $$
(4)
$$ {\text{UCS}} = 10989\exp^{ - 0.065\beta } \quad {\text{for serpentinites}}. $$
(5)

Serpentinites present higher determination coefficients than peridotites because as above-mentioned, small amounts (>9 %) of serpentine reduce the strength of the unaltered peridotite by more than a factor of two. So the strength values of these peridotites are much lower than those of unaltered peridotites.

Fig. 6
figure 6

Correlation between serpentinization and mechanical properties

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Similar correlations have been obtained by Rao and Ramana (1974), Koumantakis (1982), Escartin et al. (2001) and Diamantis et al. (2009) studied the mentioned above parameters.

The plots of the E st values as a function of serpentinization percentage values are also shown in Fig. 6c, d. The logarithmic trend seems to fit better (R 2 = 0.68) the β with the E st in peridotites, while the same relationship is better described by the exponential equation in serpentinites (R 2 = 0.78). The determined correlations are described by the functions:

$$ E_{\text{st}} = - 16.71{\text{Ln}}\left( \beta \right) + 84.18\quad {\text{ for peridotites}}, $$
(6)
$$ E_{\text{st}} = 1060\exp^{ - 0.0544\beta } \quad {\text{for serpentinites}}. $$
(7)

The correlations of the physico-mechanical parameters with (a) mineral percentage and (b) grain size were also determined. The relation between the percentage of the main minerals (serpentine, olivine, ortho and clinopyroxene, etc.) and the physico-mechanical properties is illustrated in Fig. 7. As is commonly known, dry unit weight is negatively affected (Fig. 7a, b) by an increase in serpentine (decrease of primary minerals), while a decrease in serpentine, evidently decreases the effective porosity (Fig. 7c, d). Moreover, in the majority of samples, serpentine has a very important role in strength and elasticity modulus reduction, while the primary minerals have a smaller effect on the mechanical properties (Fig. 7e–h). Serpentine is softer and results in lower strength and elasticity modulus values than the primary minerals.

Fig. 7
figure 7

Bar chart showing the relationship between the percentage of minerals and the physicomechanical characteristics

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The graphs of the test result values between the serpentine percentage and the physico-mechanical properties are illustrated in Fig. 8. The serpentine percentage and the γ d are better related by a positive linear function (Fig. 8a, R 2 = 0.96) in peridotites and by a logarithmic equation in serpentinites (Fig. 8b, R 2 = 0.74). The functions of the two regression lines are:

$$ \gamma_{d} = - 0.11{\text{Serp }} + \, 33.28\quad {\text{ for peridotites}}, $$
(8)
$$ \gamma_{\text{d}} = - 5.30{\text{Ln}}\left( {\text{Serp}} \right) + 48.49\quad {\text{ for serpentinites}}. $$
(9)

The regression lines representing the best fit between serpentine percentage and effective porosity are linear in peridotites and exponential in serpentinites (Fig. 8c, d). The estimated n e using the serpentine percentage can be expressed by the empirical equations:

$$ n_{\text{e}} = 0.009{\text{Serp}} + 0.059 \, \left( {R^{2} = 0.93} \right)\quad {\text{for peridotites}}, $$
(10)
$$ n_{\text{e}} = 0.001\exp^{{0.0965{\text{ Serp}}}} \left( {R^{2} = 0.66} \right)\quad {\text{for serpentinites}}. $$
(11)

From Fig. 8c, d and the above functions, it is obvious that the n e is less influenced by the serpentine percentage in serpentinites than in peridotites.

Fig. 8
figure 8

Relationship of serpentine percentage with physicomechanical properties

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Strong positive correlations of quartz content with (a) compressive strength and (b) dry unit weight have been obtained by Gunsallus and Kulhawy (1984), Tugrul and Zarif (1999), while some authors (Pomonis et al. 2007; Zorlu et al. 2004; Tamrakar et al. 2007) have suggested an inverse relationship between quartz content and effective porosity.

The UCS and E st decrease logarithmically with the increase of serpentine percentage in peridotites (Fig. 8e, g) while in serpentinites the relationships of serpentine percentage with UCS and E st are logarithmic (Fig. 8f) and exponential, respectively (Fig. 8h). The determination coefficients are not very high (Table 6) indicating that the serpentine percentage does not influence the mechanical properties as significantly as the other above-mentioned petrographic characteristics.

Table 6 Regression equations and determination coefficients (R 2)
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Several investigators have studied the effect of grain size on the mechanical properties of rock. In general, the strength and elasticity modulus of rocks are greater for fine-grained than coarse-grained rocks (Brace 1961). Onodera and Asoka Kumara (1980) and Tugrul and Zarif (1999) reported that the strength decreased significantly as the grain size increased in igneous rocks. They determined a linear relationship between the grain size and strength, that is, as the grain size of the granite decreased, the strength increased.

In this study, an attempt has been made to correlate the maximum grain size (Table 7) with UCS and E st. As shown in Figs. 9, 10, there is a very poor relationship between strength and the static tangent modulus with mineral size (except clinopyroxene) in peridotites, while in serpentinites, there is no correlation between these characteristics. This means that in ultrabasic rocks, the mechanical properties are much more affected by the other petrographic parameters than the mineral size and the low-temperature metamorphic process plays the greatest role. Only the correlations of clinopyroxene size with the UCS and E st (in peridotites) presents high determination coefficients (R 2 = 0.77 and R 2 = 0.88, respectively). That may be due to clinopyroxenes that are less influenced by the serpentinization than the other primary minerals. The logarithmic trends describe better the correlation between the above-mentioned parameters and the functions of the two regression lines are:

$$ {\text{UCS}} = - 73.98{\text{Ln}}\left( {\text{Cpx}} \right) + 114.98\quad {\text{ for peridotites}}, $$
(12)
$$ E_{\text{st}} = - 23.03{\text{Ln}}\left( {\text{Cpx}} \right) + 40.28\quad {\text{ for peridotites}}. $$
(13)

We cannot be absolutely based on the above-mentioned equations because we have only four points. Additional data may result in similar trends as other minerals.

Table 7 Grain size of minerals
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Fig. 9
figure 9

Bar chart showing the relationship between the minerals maximum size and the mechanical properties

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Fig. 10
figure 10

Correlation between the minerals maximum size and the mechanical characteristics

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Onodera and Asoka Kumara (1980) and Tugrul and Zarif (1999), as mentioned above, suggested strong inverse equations between grain size and strength because they examined granite samples, which as is commonly known, do not undergo the phenomenon of serpentinization.

Particular emphasis was also given to the degree of dependence between the micropetrographic index I ps (ratio between primary and secondary minerals) and the physical and mechanical parameters of the studied samples. The I ps forms good to strong correlations with almost all the engineering parameters (R 2 = 0.74–0.94). As can be seen in Fig. 11a, b, significant negative correlations (logarithmic in peridotites and exponential in serpentinites) exist between the micropetrographic index and effective porosity, indicating that with increase of the I ps, the voids decrease according to the following equations:

$$ n_{\text{e}} = - 0.073{\text{Ln}}\left( {{\text{I}}_{\text{ps}} } \right) + 0.30\quad {\text{ for peridotites}}, $$
(14)
$$ n_{\text{e}} = 5.37\exp^{{ - 6.73\,{\text{I}}_{\text{ps}} }} \quad {\text{for sepentinites}}. $$
(15)

As it is illustrated in Fig. 11c, d, the dry unit weight presents visible correlations with the micropetrographic index. The γ d increases logarithmically with the increase of I ps in peridotites, while the same relationship in serpentinites is better described by a linear equation. The logarithmic function presents a higher determination coefficient (R 2 = 0.94) than the linear trend (R 2 = 0.84). Moreover, the plots of the mechanical properties as a function of the micropetrographic index are shown in Fig. 11e–h. The estimated empirical equations indicate linear correlations among these variables except for the relation between E st and I ps in serpentinites which is obviously expressed by an exponential function. The empirical equations and the determination coefficients (R 2) of the mentioned above relations are given in Table 8. Rigopoulos et al. (2010) suggested strong inverse equations between I ps and UCS.

Fig. 11
figure 11

Variation between micropetrographic index and physicomechanical properties for the studied rocks

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Table 8 Regression equations and determination coefficients (R 2)
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As shown in Fig. 11, the relationship between the physical characteristics and the micropetrographic index presents better correlation in peridotites than in serpentinites, while the mechanical properties with the I ps are better correlated in serpentinites than in peridotites. That happens because as mentioned above, small amounts (>9 %) of serpentine reduce the strength and elasticity modulus of the unaltered peridotite by more than a factor of two. So the strength and static tangent modulus values in peridotites are much lower than those of unaltered peridotites.

Conclusions

During the last decades, a number of researchers have attempted to ascertain the influence of petrographic characteristics on the physico-mechanical properties of various rock types; however, only a few have been devoted to the ultrabasic rocks. These rocks have become important earth crust components in some areas like south-eastern Europe, especially in the countries of the former Yugoslavia, and Albania, Greece, and Turkey. Furthermore, estimation of the rock physico-mechanical properties is considered to be the most important component in any engineering geology project. In spite of their easy and simple determination, they require a large number of well prepared (regularly shaped) rock specimens. But ultrabasic rocks (especially serpentinites) are usually not suitable for preparing specimens. The immediate determination of physico-mechanical characteristics is usually difficult for these rocks. For this reason, this study mainly attempts to develop empirical equations between petrographic characteristics and physico-mechanical properties.

Thus, in this paper, ultrabasic rock samples taken from central Greece (western part of Othrys mountain and the Kallidromo mountain), were tested in the laboratory and the physico-mechanical properties were predicted from the petrographic characteristics by simple regression analysis.

The effect of alteration on the physico-mechanical properties of ultrabasic rocks can be characterized quantitatively by the serpentinization percentage (β). Strong inverse linear relationships exist between the β and the dry unit weight (γ d ) for both peridotites (R 2 = 0.98) and serpentinites (R 2 = 0.83), while the increase of secondary minerals (serpentinization percentage) increases the effective porosity (n e) exponentially in serpentinites (R 2 = 0.81) and linearly in peridotites (R 2 = 0.92).

Serpentinization generally results in mechanically weaker rocks. The uniaxial compressive strength (UCS) values extend from 19.21 to 125.73 MPa in serpentinites and from 79.31 to 241.56 MPa in peridotites, while the static tangent modulus (E st) varies from 5.2 to 27.8 GPa and between 29.1 and 69.3 GPa, respectively. The variation of the mechanical properties is related to the degree of preservation of the primary subophitic texture and the development of soft minerals during alteration. The relatively high strength of the fresh peridotites is a result of the low proportions of soft minerals, along with the preservation of primary textures. In accordance with ISRM (1981), the majority of studied peridotites are characterized as rocks with very high strength, while the majority of serpentinites range between 50 and 100 MPa (rocks with high strength). As far as the modulus ratio values are concerned, the peridotites plot in the Medium Ratio Zone (M) in the Deere and Miller (1966) diagram. On the other hand, serpentinites mainly plot in the lower portion of the Medium Ratio Zone (M) with a few results in the Low Ratio Zone (L). This difference indicates that some serpentinite samples may not be homogeneous and isotropic. It may also be attributed to the internal fractures/cracks that are macroscopically undetected.

Both the UCS and E st exhibit negative relationships with the degree of serpentinization. Τhe best fit equations are logarithmic for peridotites and exponential for serpentinites.

The correlations of the physico-mechanical parameters with mineral percentage are also determined. Significant linear relationships exist between the serpentine percentage and the physical properties (γ d , n e ) in peridotites, while the increase of serpentine exponentially increases (R 2 = 0.66) the effective porosity and decreases linearly (R 2 = 0.74) the dry unit weight in serpentinites. The UCS and E st are negatively correlated with the percentage of serpentine. Τhe best fit equations are logarithmic in peridotites and logarithmic and exponential, respectively, in serpentinites. The determination coefficients are not very high indicating that the serpentine percentage has a smaller influence on the mechanical properties than the other petrographic characteristics.

Contrary to several investigations suggestions (Brace 1961; Onodera and Asoka Kumara 1980; Tugrul and Zarif 1999), that the strength decreases significantly as the grain size increases in rocks, a very poor relationship between UCS and E st with size of the minerals (except clinopyroxene) was found in this research. This due to that, in the mentioned above researches, the examined rocks have not undergone the phenomenon of serpentinization, contrary to this study in which serpentinization plays an important role. The relations of clinopyroxene size with UCS and E st are expressed by logarithmic equations. They present high determination coefficients (R 2 = 0.77 and R 2 = 0.88, respectively) because clinopyroxenes are much less influenced by the serpentinization than the other primary minerals.

Finally, significant positive correlations (logarithmic in peridotites, R 2 = 0.94 and linear in serpentinites, R 2 = 0.84) exist between the micropetrographic index and dry unit weight, indicating that with increasing I ps, the density also increases. The relationship between n e and I ps is better described by a logarithmic relationship (R 2 = 0.89) in peridotites and an exponential relationship (R 2 = 0.80) in serpentinites. Moreover, the mechanical characteristics and I ps correlated well by linear functions apart from the relation between E st and I ps in serpentinites, which is obviously expressed by an exponential function.

In summary, the correlation between petrographic and mechanical properties present a higher determination coefficient in serpentinites than in peridotites, because small amounts (>9 %) of serpentine reduce the strength of the unaltered peridotite by more than a factor of two. So the strength values in peridotites are much lower than those of unaltered peridotites.

The relationships between the petrographic parameters and the engineering properties show that they can be used for an assessment of the physico-mechanical characteristics of ultrabasic rocks. However, it is commonly known that the prediction equations derived by different researches are dependent on rock types, quality and test conditions. Further research is necessary in order to investigate if ultrabasic rocks taken from different locations will present different physico-mechanical values than those which are determinate in this study.