^{1}

^{*}

^{2}

^{1}

^{1}

Due to the fact that the estimation of the triaxial parameters is very important in any geotechnical project, many attempts have become with the aim of their determination. In spite of its relative simplicity, triaxial tests are time consuming, expensive, and require a large number of well prepared (regularly shaped) rock specimens and suitable testing procedures. For this reason, they cannot be easily determined in rocks which are thinly bedded, highly fractured, weak, and so indirect, fast, practical, easy and economical ways should be used such as the correlation of them with some other characteristics which are calculated easily. The aim of this study is to apply correlation analysis to investigate the relationships between physical, dynamic and mechanical characteristics and triaxial parameters for ultramafic rocks. Thus, sixteen samples, taken from the western part of Othrysmt (ten samples) and the Kallidromomt (six samples, central Greece), were tested and the relations among the properties were described by simple regression analyses. The study reveals strong negative, logarithmic correlations between the effective porosity and triaxial parameters ( c , φ ). Positive, linear relationships are also indicated between wave velocities, apparent cohesion and friction angle, while the increase of serpentinization percentage causes decrease of the c , φ . Both dry unit weight and Schmidt Hammer Values are logarithmically affected with c , φ . The point load strength index and apparent cohesion and friction angle are strongly correlated by both logarithmic and linear functions, but logarithmic trends present higher determination coefficients.

The construction of geotechnical engineering projects like foundations, rock slopes and underground structures is based on the estimation of the rock mass properties. The determination of the triaxial parameters is very important because the rock-mass properties are estimated through them. Despite of its relative simplicity, triaxial tests are time consuming, expensive, and require a large number of well prepared (regularly shaped) rock specimens and suitabletesting procedures. Some rocks are thinly bedded, highly fractured, weak, present alterations such as ultramafic rocks with the result they are usually not suitable for preparing specimens and the determination of triaxial parameters is very difficult. On the other hand the fact that ultramafic rocks are met in many areas all over the world and especially south-eastern Europe has as a result many engineering geology projects to be constructed on/in them [

Ultramafic rocks are members of ophiolitic suite rocks which represent remnants of the Earth’s oceanic crust and upper mantle. Basic, hypabyssal and extrusive rocks cover ultramafic rocks. This succession is idealized and in most cases some members may be absent. This research focuses on ultramafic rocks. They include particular types of geological formation with both petrographic variety (harzburgites, lherzolites, plagioclastic peridotites, dunites, etc.) and structural complexity due to tectonic deformation and alteration. This ocean-floor metamorphism (serpentinization) lead to a modification of their petrographic characteristics (serpentinized varieties of them). Thus, they are from massive strong to weak rocks (peridotites and serpentinites, [

Within the framework of the present study, sixteen ultramafic rocks (six peridotites and ten serpentinites) were taken from the Kallidromomt and the western part of Othrysmt (Central Greece), the dry unit weight (γ_{d}), the effective porosity (n_{e}), the compressional wave velocity (V_{p}), the shear wave velocity (V_{s}), the Schmidt Hammer Values (SHV), the point load strength index (I_{s}_{50}) were determined and presented. The Uniaxial Compressive Strength (σ_{ci}) and the material constant (m_{i}) were estimated by the Hoek and Brown failure criterion and the triaxial characteristics (apparent cohesion, c and friction angle φ) were presented.

The main objective of this research is was to determine the predictability of apparent cohesion (c) and friction angle (φ) of ultramafic rocks (serpentinites and peridotites) with a simple, fast, practical and economical way through the physical, dynamic and mechanical properties at the preliminary site investigation stage. The results were statistically analyzed using the method of least-squares regression. The relationships among these parameters were described by the best fit equations and the highest correlation coefficient, in each relationship, was also determined. The same samples were subjected to petrographic studies with the aim of describing the main mineralogical composition and the serpentinization percentage of ultramafic rocks.

The study area is to be found in the central part of Greece (

at western part of Othrys Mt. (near the villages of Moschokarya, Mega Isoma, LoutraKaitsas and Domokos,

1) A carbonate sequence of Triassic-Jurassic age which constitutes the basement of the area.

2) A tectonic nappe, mainly ophiolitic (volcano-sedimentary formations, basaltic lavas, basic rocks and ultramafic masses, [

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

The present study research focuses on ophiolitic sequence and mainly on ultramafic masses. They are mainly represented by the peridotites whose degree of serpentinization varies.

The data pertains to ultramafic rocks sampled from sixteen sites in the study areas (eleven from Othrys and six from Kallidromo, _{p}, V_{s}) were calculated from the travel time with the application of ultrasonic compression wave pulses to the samples in accordance with test designations [_{3}) applied during the triaxial tests (fifty-eight specimens). Range of confining pressures of 0 < σ_{3}< 0.5σ_{ci}, proposed by [

Thin sections, from samples of the sixteen areas, were prepared and examined under the polarizing microscope, at the Mineralogy-Geology Laboratory of the Agricultural University of Athens, with the aim of describing the main mineralogical composition and the serpentinization percentage of ultramafic rocks. Fractures created by the tests, did not follow internal discontinuities and were always fresh. The tests were carried out in dry conditions for a better relation of the results.

The ultramafic rocks include rock types (peridotites) with large variability (harzburgites, lherzolites, plagioclasticperidotites, dunites, etc.), which due to their tectonic deformation and a low grade metamorphism (serpentinization, [

In this paper, sixteen thin sections were prepared and examined under a polarizing microscope. The studied rock samples are unaltered or slightly serpentinized (serpentinization < 30% by volume) ultramafic rock types, characterized as peridotites and partially to completely serpentinizedperidotites (serpentinization > 70% by volume) called as serpentinites. The investigated peridotites mainly comprised of olivines, ortho and clino pyroxenes which are characterised as parent-primary minerals (P_{m} > 74% by volume,

When the peridotites are influenced by the serpentinization, they transformed into Serpentinites. Serpentinites are mainly composed of secondary minerals (70% - 92%, by volume,

The dry unit weight (γ_{d}) and effective porosity (n_{e}) were determinedfor 6 peridotites and 10 serpentinites samples and their values are listed in _{d} and n_{e} for peridotites range from 31.67 to 33.17 KN/m^{3} and from 0.07 to 0.19 respectively. On the other hand, the values of γ_{d} and n_{e} for serpentinites fluctuate between 24.95 and 26.79 KN/m^{3} and from 0.39 to 3.59 respectively. The serpentinites present lower dry unit weight values and higher effective porosity than peridotites because they are mainly composed of secondary minerals (as it is afore-mentioned) which have lower specific gravity and more voids.

The compressional wave velocity (V_{p}) and shear wave velocity (V_{s}), which were determined as above-mentioned in chapter 3.1, are given in _{p} for peridotites and serpentinites fluctuate between 7412 and 7991 m/sec and from 4955 to 5645 m/sec respectively, while the mean values are 7781 m/sec (S.D. 211) and 5361

Sample No | Primary Minerals | Secondary Minerals | Degree of Serpentinization b (%) | |||||||
---|---|---|---|---|---|---|---|---|---|---|

Ol (%) | Opx (%) | Cpx (%) | Pl (%) | Sp (%) | Serp (%) | Chl (%) | Tc (%) | Act (%) | ||

KP01 | 71 | 22 | 6 | 1 | 7 | |||||

KP02 | 75 | 21 | - | - | 1 | 3 | - | - | - | 3 |

OP01 | 50 | 11 | 12 | - | 1 | 22 | 2 | 1 | 1 | 26 |

0P02 | 66 | 21 | - | - | 2 | 10 | 1 | - | - | 11 |

OP03 | 74 | 19 | 3 | - | - | 3 | 1 | - | - | 4 |

OP04 | 85 | 10 | - | - | 1 | 2 | 2 | - | - | 4 |

KS01 | 9 | 9 | 5 | - | 1 | 63 | 4 | 5 | 4 | 76 |

KS02 | 10 | 6 | 3 | - | 1 | 71 | 2 | 7 | - | 80 |

KS03 | 10 | 7 | 11 | - | 2 | 62 | 7 | 1 | - | 70 |

OS01 | 5 | 3 | - | - | - | 84 | 5 | 2 | 1 | 92 |

OS02 | 8 | 6 | - | - | - | 76 | 6 | 3 | 1 | 86 |

OS03 | 7 | 6 | - | - | - | 79 | 7 | 1 | - | 87 |

OS04 | 8 | 11 | 7 | - | 1 | 66 | 4 | 2 | 1 | 73 |

OS05 | 6 | 9 | - | - | 2 | 79 | 2 | 1 | 1 | 83 |

OS06 | 13 | 8 | - | - | 1 | 68 | 5 | 4 | 1 | 78 |

OS07 | 14 | 11 | - | - | 1 | 69 | 4 | 1 | - | 74 |

KP: Peridotite of Kallidromo, OP: Peridotite of Othrys, KS: Serpentinite of Kallidromo, OS: Serpentinite of Othrys.

Peridotites | Serpentinites | |
---|---|---|

Serpentinization percentage, β (%) | Serpentinization percentage, β (%) | |

Maximum value | 26 | 92 |

Minimum value | 3 | 70 |

Mean value | 9.17 | 79.90 |

Standard Deviation | 8.75 | 7.02 |

m/sec (S.D. 225) respectively. As far as V_{s} values are concerned, they vary between 4171 and 4539 m/sec for peridotites and from 2464 to 3044 m/sec for serpentinites. The mean values for serpentinites and peridotites are 2795 and 4392 m/sec respectively. According to [

Moreover, the Schmidt Hammer Values (SHV) range between 61.25 and 64.69 for peridotites (

Samples No | Effective Porosity, n_{e} | Dry Unit Weight, γ_{d} (KN/m^{3}) | Comp. Wave Velocity, V_{p} (m/sec) | Shear Wave Velocity, V_{s} (m/sec) | Schmidt Hammer Values, SHV | The point load strength index, I_{s}_{50} (MPa) |
---|---|---|---|---|---|---|

KP01 | 0.07 | 33.1 | 7959 | 4539 | 64.08 | 10.63 |

KP02 | 0.11 | 32.92 | 7850 | 4458 | 64.69 | 10.14 |

OP01 | 0.19 | 31.67 | 7412 | 4171 | 61.25 | 8.27 |

0P02 | 0.14 | 32.13 | 7704 | 4290 | 64.13 | 7.27 |

OP03 | 0.09 | 33.02 | 7769 | 4372 | 64.17 | 10.53 |

OP04 | 0.08 | 33.17 | 7991 | 4524 | 64.15 | 10.42 |

KS01 | 0.64 | 26.2 | 5442 | 2850 | 52.97 | 3.94 |

KS02 | 0.75 | 26.12 | 5473 | 2888 | 52.73 | 3.41 |

KS03 | 0.39 | 26.79 | 5646 | 3044 | 54.49 | 4.91 |

OS01 | 3.59 | 24.95 | 4955 | 2464 | 49.52 | 2.01 |

OS02 | 2.36 | 25.08 | 5152 | 2666 | 50.55 | 2.28 |

OS03 | 2.29 | 25.37 | 5154 | 2640 | 50.7 | 3.19 |

OS04 | 0.51 | 26.6 | 5637 | 3000 | 54.02 | 4.42 |

OS05 | 1.6 | 25.61 | 5313 | 2727 | 51.5 | 3.23 |

OS06 | 1.26 | 25.93 | 5320 | 2748 | 51.89 | 2.81 |

OS07 | 0.53 | 26.35 | 5520 | 2928 | 53.34 | 3.85 |

the other hand, in serpentinites the SHV vary from 49.52 to 54.49, the mean value is 52.17 and their standard deviation is 1.61 (

In this research, only diametrical point load tests were carried out on the samples. The point load strength index (I_{s}_{50}) (referred to a standard size 50 mm) values are listed in

In this research, the triaxial tests were carried out in fifty-eight specimens (three confining pressures at least in each sample ranging from 3 to 18 MPa, _{i}) and the σ_{ci} were estimated by the Hoek and Brown failure criterion (_{1} and σ_{3}) for intact rock are correlated by the following equation:

where,

σ_{1}, σ_{3}, the maximum and minimum (confining) total stresses at failure for intact rock,

Maximum value | Minimum value | Mean value | Standard Deviation | ||
---|---|---|---|---|---|

Peridotites | Effective Porosity, n_{e} | 0.19 | 0.07 | 0.12 | 0.04 |

Dry Unit Weight, γ_{d} (KN/m^{3}) | 33.17 | 31.67 | 32.67 | 0.62 | |

Comp. Wave Velocity, V_{p} (m/sec) | 7991 | 7412 | 7781 | 211 | |

Shear Wave Velocity, V_{s} (m/sec) | 4539 | 4171 | 4392 | 143 | |

Schmidt Hammer Values, SHV | 64.69 | 61.25 | 63.75 | 1.24 | |

The point load strength index, I_{s}_{50} (MPa) | 10.63 | 7.27 | 9.54 | 1.42 | |

Serpentinites | Effective Porosity, n_{e} | 3.59 | 0.39 | 1.39 | 1.06 |

Dry Unit Weight, γ_{d} (KN/m^{3}) | 26.79 | 24.95 | 25.90 | 0.63 | |

Comp. Wave Velocity, V_{p} (m/sec) | 5645 | 4955 | 5361 | 225 | |

Shear Wave Velocity, V_{s} (m/sec) | 3044 | 2464 | 2795 | 180 | |

Schmidt Hammer Values, SHV | 54.49 | 49.52 | 52.17 | 1.61 | |

The point load strength index, I_{s}_{50} (MPa) | 4.91 | 2.01 | 3.41 | 0.91 |

σ_{ci}, the uniaxial compressive strength of intact rock,

m_{i}, the material constant which depends on the properties of intact rock.

Finally the apparent cohesion (c) and the friction angle (φ) for intact rock were calculated using triaxial compressive strength test data (_{3} as abscissa and the σ_{1} as ordinates (

and

Furthermore, c and φ were calculated using the following equations:

Sample No | Axial Load, Ρ (kN) | Axial Stress, σ_{1} = P/A (MPa) | Confining Pressure, σ_{3} (MPa) | Material constant, m_{i} | Friction Angle, φ (˚) | Apparent Cohesion, c (MPa) | Estimated Uniax. Compressive Strength, σ_{ciestm} (Mpa) |
---|---|---|---|---|---|---|---|

KP01A | 520 | 224.66 | 3 | 26.58 | 54.13 | 32.18 | 184.43 |

KP01B | 605 | 261.39 | 6 | ||||

KP01C | 857 | 370.26 | 18 | ||||

KP01D | 651 | 281.26 | 9 | ||||

KP02A | 573 | 247.56 | 3 | 28.16 | 54.78 | 35.54 | 206.44 |

KP02B | 609 | 263.12 | 6 | ||||

KP02C | 906 | 391.43 | 18 | ||||

KP02D | 809 | 349.53 | 9 | ||||

KS01A | 220 | 95.05 | 3 | 14.27 | 44.10 | 16.98 | 73.97 |

KS01B | 269 | 116.22 | 6 | ||||

KS01C | 338 | 146.03 | 12 | ||||

KS02A | 232 | 102.11 | 3 | 14.39 | 44.64 | 17.94 | 79.95 |

KS02B | 276 | 121.47 | 6 | ||||

KS02C | 350 | 154.04 | 12 | ||||

KS03A | 337 | 148.87 | 3 | 16.04 | 46.58 | 24.48 | 115.37 |

KS03B | 344 | 151.96 | 6 | ||||

KS03C | 539 | 238.11 | 18 | ||||

KS03D | 406 | 179.35 | 9 | ||||

OP01A | 284 | 122.70 | 3 | 21.09 | 48.17 | 20.96 | 95.89 |

OP01B | 369 | 159.43 | 6 | ||||

OP01C | 534 | 230.71 | 18 | ||||

OP01D | 398 | 171.95 | 9 | ||||

OP02A | 486 | 214.69 | 3 | 25.20 | 53.37 | 30.33 | 170.27 |

OP02B | 531 | 233.70 | 6 | ||||

OP02C | 789 | 348.54 | 18 | ||||

OP02D | 596 | 263.29 | 9 | ||||

OP03A | 582 | 250.53 | 3 | 27.76 | 55.01 | 33.85 | 200.41 |

OP03B | 609 | 262.15 | 6 | ||||

OP03C | 918 | 395.16 | 18 | ||||

OP03D | 726 | 312.51 | 9 | ||||

OP04A | 520 | 229.71 | 3 | 26.69 | 54.09 | 32.84 | 187.52 |

OP04B | 567 | 250.48 | 6 | ||||
---|---|---|---|---|---|---|---|

OP04C | 837 | 369.75 | 18 | ||||

OP04D | 685 | 302.60 | 9 | ||||

OS01A | 116 | 50.12 | 3 | 12.76 | 38.05 | 9.88 | 33.55 |

OS01B | 163 | 70.42 | 6 | ||||

OS01C | 208 | 89.54 | 12 | ||||

OS02A | 133 | 57.25 | 3 | 13.10 | 39.59 | 10.44 | 37.96 |

OS02B | 168 | 72.32 | 6 | ||||

OS02C | 228 | 98.14 | 12 | ||||

OS03A | 161 | 69.30 | 3 | 13.52 | 39.44 | 12.54 | 45.00 |

OS03B | 174 | 74.90 | 6 | ||||

OS03C | 311 | 133.87 | 18 | ||||

OS03D | 222 | 95.56 | 9 | ||||

OS04A | 238 | 102.45 | 3 | 14.82 | 44.92 | 18.15 | 81.01 |

OS04B | 291 | 125.73 | 6 | ||||

OS04C | 362 | 155.83 | 12 | ||||

OS05A | 174 | 74.90 | 3 | 13.67 | 42.00 | 13.81 | 55.47 |

OS05B | 222 | 95.56 | 6 | ||||

OS05C | 282 | 121.39 | 12 | ||||

OS06A | 221 | 97.27 | 3 | 13.86 | 42.17 | 18.24 | 73.9 |

OS06B | 246 | 108.27 | 6 | ||||

OS06C | 391 | 172.08 | 18 | ||||

OS06D | 305 | 134.23 | 9 | ||||

OS07A | 268 | 117.95 | 3 | 15.52 | 44.64 | 21.21 | 92.32 |

OS07B | 297 | 131.20 | 6 | ||||

OS07C | 460 | 202.45 | 18 | ||||

OS07D | 365 | 160.05 | 9 |

where

a, the gradient of the Equations (2) and (3).

Least squares regression analysis was applied in order to describe the relationships among triaxial characteristics (c, φ), physical, dynamic, mechanical properties and the petrographic data of the ultramafic rocks. The equation of the best-fit line and the determination coefficient (R^{2}) were determined for each regression. Techniques from Excel 2003 software (Analysis ToolPak program) was used to process the data.

In this study, an attempt to correlate c and φ with dry unit weight is respectively presented in ^{2} = 0.84) the dry unit weight with the apparent cohesion while the relationship between φ and γ_{d} is better described by the linear equation (R^{2} = 0.92). The regression lines representing the best fit between effective porosity and c, φ are logarithmic (

Moreover, the plots of the apparent cohesion values as a function of sound velocities (V_{p}, V_{s}) values are shown in

relationship was found between the φ and the V_{p}, V_{s} (^{2} values, but better correlation is described by the linear trends (

As it is illustrated in

determination coefficient (R^{2} = 0.93) than that between c and β (R^{2} = 0.86).

In addition, ^{2} = 0.88). The plots of the friction angle as a function of the SHV are shown in ^{2} = 0.95).

As shown in _{s}_{50} and between φ and I_{s}_{50}. The logarithmic equations seem to fit better

the above-mentioned properties than the linear equations, exhibiting R-square values 0.87 and 0.93 respectively. The logarithmic functions are illustrated in

The estimation of the triaxial parameters is considered to be the most important component in any engineering geology project because the rock-mass properties are calculated through them. Despite of their simple, fast and easy determination, they require a

large number of well prepared (regularly shaped) rock specimens. But ultramafic rocks (especially serpentinites) are usually not suitable for preparing specimens. Thus, the immediate determination of the triaxial characteristics is usually difficult for these rocks. For this reason, this study mainly attempts to develop empirical equations between triaxial parameters and physico-mechanical properties.

In this paper ultramafic samples, taken from sixteen sites of central Greece (western part of Othrysmt and the Kallidromomt), were tested in laboratory and the triaxial properties were predicted through the wave velocities by simple regression analysis.

The research demonstrates that the friction angle (φ) exhibits strong linear correlation with the dry unit weight (γ_{d}) (R^{2} = 0.92) while the logarithmic equation seems to correlate better (R^{2} = 0.84) the dry unit weight with the apparent cohesion (c).

Significant negative logarithmic relationships exist between the triaxial parameters

and the effective porosity (n_{e}). The relation between φ and n_{e} presents higher determination coefficient (R^{2} = 0.96) than that between c and n_{e} (R^{2} = 0.91).

The wave velocities are positively correlated with c and φ and provide high determination coefficient. In particular, φ presents higher correlation with V_{p}, V_{s} (R^{2} = 0.91, R^{2} = 0.92 respectively) than c (R^{2} = 0.83, R^{2} = 0.84 respectively).

The effect of alteration on the physico-mechanical properties of ultramafic rocks can be characterized quantitatively by the serpentinization percentage (β). Strong inverse linear

Parameters to be related | Regression Equations | R^{2} |
---|---|---|

Apparent cohesion and point load strength index | 0.87 | |

Apparent cohesion and point load strength index | 0.85 | |

Friction angle and point load strength index | 0.93 | |

Friction angle and point load strength index | 0.91 |

relationships exist between the β and c, φ. The relationship between φ and β presents higher determination coefficient (R^{2} = 0.93) than that between c and β (R^{2} = 0.86).

The relations between c, φ and Schmidt hammer values (SHV) are also expressed by logarithmic functions. The SHV shows higher correlation (R^{2} = 0.95) with the friction angle than that with apparent cohesion (R^{2} = 0.88).

Both the c and φ exhibit negative relationships with the point load strength index (I_{s}_{50}). Τhe best fit trends are logarithmic and φ presents higher correlation with I_{s}_{50} (R^{2} = 0.93) than that c with I_{s}_{50} (R^{2} = 0.87).

Some observed deviations may be due to the petrographic variety, the different serpentinization degree, the structural complexity and the internally imprinted tectonic deformation of studied rocks.

All empirical methods evaluated in this study can be used for an assessment of the triaxial characteristics of ultramafic rocks, especially for serpentinites whose preparation in standard size cores, is quite difficult. However, it is commonly known that the prediction equations derived by different researches are dependent on rock types, quality, test conditions and different tectonic settings.

This study was funded by the State Scholarship Foundation of Greece (I.K.Y). The authors would also like to express their thanks to the Public Works Central Laboratory of Greece (KEDE) and to Ass. Professor Anastasios Tsagalidis for his help in petrography.

Diamantis, K., Exarhakos, G., Migiros, G. and Gartzos, E. (2016) Evaluating the Triaxial Charac- teristics of Ultamafic Rocks from Central Greece Using the Physical, Dynamic and Mechanical Properties. Open Access Library Journal, 3: e3214. http://dx.doi.org/10.4236/oalib.1103214