Rock Mech Rock Eng DOI 10.1007/s00603-016-0930-3
ORIGINAL PAPER
Determination of the Geotechnical Characteristics of Hornfelsic Rocks with a Particular Emphasis on the Correlation Between Physical and Mechanical Properties Davood Fereidooni1
Received: 24 June 2015 / Accepted: 9 February 2016 Springer-Verlag Wien 2016
Abstract Geotechnical characteristics and relationships between various physical and mechanical properties were assessed for eight types of hornfelsic rock collected from southern and southwestern parts of the city of Hamedan in western Iran. Rock samples were subjected to mineralogical, physical, index, and mechanical laboratory tests and found to contain quartz, feldspar, biotite, muscovite, garnet, sillimanite, kyanite, staurolite, graphite, and other finegrained cryptocrystalline matrix materials. Samples had a porphyroblastic texture, and the mineral contents and physical properties influenced various rock characteristics. Some rock characteristics were affected by mineral content, while others were affected by porosity. Dry unit weight, primary and secondary wave velocities, and slakedurability index were noteworthy characteristics affected by mineral content, while porosity had the greatest influence on water absorption, Schmidt hardness, point load index, Brazilian tensile strength, and uniaxial compressive strength. Empirical equations describing the relationships between different rock parameters are proposed for determining the essential characteristics of rock, such as secondary wave velocity, slake-durability index, point load index, Brazilian tensile strength, and uniaxial compressive strength. On the basis of these properties, the studied rocks were classified as being strong or very strong.
Abbreviations cd Dry unit weight (g/cm3) csat Saturated unit weight (g/cm3) Gs Specific gravity n Porosity (%) Wa Water absorption (%) vp Primary wave velocity (m/s) vs Secondary wave velocity (m/s) Id Slake-durability index (%) Hs Schmidt hardness Is(50) Point load index (MPa) BTS Brazilian tensile strength (MPa) UCS Uniaxial compressive strength (MPa) HDR Heydareh ABD Abbas-Abad CMK Cheshmeh-Malek FGR Faghireh PSK1 Piste-Eski1 PSK2 Piste-Eski2 SHR1 Shahrestaneh1 SHR2 Shahrestaneh2 E Elasticity modulus (dynamic) (GPa) G Shear modulus (dynamic) (GPa) m Poisson’s ratio (dynamic) K Bulk modulus (dynamic) (GPa)
Keywords Hornfels Correlation Physical properties Mechanical properties Strength Durability
1 Introduction & Davood Fereidooni
[email protected] 1
School of Earth Sciences, Damghan University, Damghan, Iran
The geotechnical properties of intact rock are important in civil engineering studies if interaction will occur between the rock and construction materials, underground structures, dams, or foundations on rock and rock slopes. The
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geotechnical behavior of rock depends on various factors, such as grain size, mineral composition, rock origin, degree of weathering, porosity, and loading direction (Singh et al. 2001). In recent years, different methodologies and testing techniques have been developed and implemented to determine the geotechnical properties of intact rock. ISRM and ASTM have published standard procedures for measuring various geotechnical properties of different types of rock, and these sources provide an excellent review of many available techniques in both laboratory and field investigations. The laboratory techniques fall within two major groups, static techniques and dynamic methods. Static techniques, which measure the deformation of a rock specimen in response to quasi-static stress or stress increment and dynamic techniques, are based on the passage of ultrasonic body waves through representative specimens (cited by Khanlari et al. 2014a). Static methods include uniaxial, triaxial, or multiaxial compression tests and point load, Brazilian, hollow cylinder, torsion, and bending tests. Dynamic methods include the resonant bar and the ultrasonic pulse methods. In recent years, relationships between some rock characteristics have been identified and used for interpreting the engineering properties of rocks. Strength properties always require careful test setups and specimen preparation, and index tests are useful only if the results are reproducible from laboratory tests of other properties and can be measured inexpensively. In previous literature reviews, the bases for the relationships are obtained through two separate processes: microscopic observations and physical tests that identify the mineralogical and physical properties of rocks and laboratory mechanical tests that measure the mechanical properties. The two data sets are then correlated by using statistical regression analyses. For example, some researchers (e.g., Tugrul and Zarif 1999) found a strong positive correlation between quartz content and compressive strength, which suggests a relationship between the physical and mechanical properties of rocks. However, Shakoor and Bonelli (1991) found no significant relationship between these parameters and determined that the types of grain contacts can be more important than the total amount of quartz. Brattli (1992) used multiple regression analysis to investigate the causality between the mineral composition and the mechanical properties of mafic igneous rock aggregates and found that the mechanical properties were affected by the mineral types and amounts. Using simple regression analyses, Tugrul and Zarif (1999) identified a relationship between the mineral composition and uniaxial compressive strength (UCS) of granitic rocks, concluding that a linear relationship exists between the quartz to feldspar ratio and the UCS. Vernik et al. (1993) reported an inverse relationship between bulk porosity and ultimate strength for siliciclastics and pure
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sandstones. Ersoy and Waller (1995) used a texture coefficient to represent the principal texture characteristics of rock, such as grain size, grain shape, grain orientation, relative proportion of grains, and matrix material, and then correlated the coefficient with the mechanical properties of specific rock types. Other researchers (e.g., Khanlari et al. 2014a, b; Fereidooni et al. 2015) have suggested equations to define the relationship between index and mechanical properties such as point load index, cylindrical punch index, BTS, Hs, and UCS. Hornfelsic rock is widely distributed in the Hamedan region, west of Iran. It frequently serves as construction material in foundations and facades and in the production of aggregate, curb, and flooring stones in nearby cities such as Hamedan, Tuysekan, and Asad-Abad as well as other important cities within Iran. This widespread use is the main impetus for the present research. Investigation into the mineralogical, physical, and mechanical properties of the rock and the relationships between these properties is important. It is evident that the texture and type of rock greatly affect its geotechnical properties. The present research has general significant because petrographic and physical properties, such as mineral content, grain size, density, porosity, and water absorption, are the primary factors that determine the mechanical properties of rock, weathering processes, stone decay of cultural heritage structures, and so forth. Determination of the petrographic and physical properties of rock is simple, inexpensive, and faster than testing mechanical properties, and can subsequently be used to estimate mechanical properties of rocks. In this research, we determine the geotechnical characteristics of Hamedan hornfelsic rocks and then attempt to identify correlations between different properties to enable estimating values for some parameters from others.
2 Site Description and Geology The southern and southwestern parts of the city of Hamedan in western Iran composed the study area (48100 E to 48350 E, 34300 N to 34520 N). Figure 1 depicts the area’s geology and shows the sampling locations. The study area is part of the country’s most important and interesting plutonic rock mass, and its metamorphic aureole. This granitic rock mass, called Alvand, is bordered by Hamedan in the north and east, by Touyserkan in the south, and by Assad-Abad in the west. It covers approximately 400 km2, making it the largest plutonic rock mass in Iran. This region has an irregular morphology due to its geological history, tectonics, and lithology. From a geological perspective, the study area is within the Sanandaj-Sirjan structural zone, which is the most active tectonic zone in Iran. The regional metamorphism of the Sanandaj-Sirjan
Determination of the Geotechnical Characteristics of Hornfelsic Rocks with a Particular… Fig. 1 Geological map of the study area indicating sampling locations and its location on the general map of Iran
zone is due to the activity of the Zagros orogenic belt, and the contact metamorphism in this area is caused by the intrusion of the Alvand plutonic rock mass. The Alvand batholith consists of a mafic part (gabbro, diorite, and tonalite), an intermediate part (granite-granodiorite), and a felsic part (hololeucocratic granitoids). The metamorphic rock masses adjacent to this batholith are pelitic hornfelses. Materials bordering the north and east sides of the study area are Quaternary alluvial deposits. The area is 1950 m above sea level and has a typical continental climate.
3 Methods and Materials This research was based on field and laboratory investigations. During the field investigation, lithological characteristics of eight types of hornfelsic rocks were determined, and samples were collected from quarries, road cuttings, and excavated foundations. Sampling locations included Heydareh (HDR), Abbas-Abad (ABD), Cheshmeh-Malek (CMK), Faghireh (FGR), Piste-Eski1 (PSK1), Piste-Eski2 (PSK2), Shahrestaneh1 (SHR1), and Shahrestaneh2 (SHR2). Block samples were prepared during the field investigation and then transferred to the laboratory. The laboratory investigations determined mineralogical and petrographic properties, physical properties,
ultrasonic wave velocity, Id, Hs, point load index, BTS, and UCS. Polished thin sections were prepared for optical microscopy to identify the mineral composition, petrographic properties, and texture of the rock samples. Laboratory specimens were prepared in three shapes; irregular or lump, disc, and cylinder. Irregular or lump specimens were used for the slake-durability test, and disc specimens were used for the Brazilian test. Cylindrical specimens were used for measuring physical properties through the UCS test. Cylindrical specimens were also used for the ultrasonic wave velocity, point load, and UCS tests. The cut end faces of cores were smoothed and made perpendicular to the core axes with a polishing and lapping machine. The diameters of the prepared rock cores were 54 mm. The ratio of length to diameter of prepared specimens for different tests was in accordance with ISRM (2007). A total of 320 specimens were used for various destructive and nondestructive tests.
4 Results and Discussions 4.1 Mineralogical and Petrographical Properties Thin sections were used to investigate the mineralogical composition, texture, and petrographic properties of the
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hornfelsic rocks by optical microscopy based on ISRM (2007). The rock samples were commonly composed of quartz, feldspar, biotite, muscovite, garnet, sillimanite, kyanite, staurolite, graphite, and other fine-grained cryptocrystalline matrix materials. Minerals such as andalusite, garnet, sillimanite, kyanite, staurolite, and graphite were crystallized under metamorphic conditions. The rock textures were porphyroblastic, and garnet, kyanite, and staurolite porphyroblasts were the dominant types, with sizes ranging from 0.2 to 1 mm (Fig. 2). The matrix consisted of quartz, feldspar, biotite, and muscovite (50–100 lm dimensions). This pattern defines the characteristic composition of contact metamorphic rocks. The mechanical behavior of rock is closely related to its mineral content and internal structure. According to Bandini and Berry (2013), rock texture influences its mechanical properties. In addition, hard or weak minerals may be present. When the grains of rock consist of resistant, hard, and more rounded materials, the rock can absorb significant force without breaking. However, when fragile material makes up the rock, it undergoes fragmentation in response to applied pressure because of the shearing of the asperities and the cracking of the grains (Melbouci et al. 2008). Quartz is a very stable mineral during the weathering process, while muscovite, orthoclase, biotite, amphibole, pyroxene, plagioclase, and olivine are less stable. Merriam et al. (1970) found a correlation between the strength of rocks and their quartz content. The
Fig. 2 Microscopic fabric images of the rocks
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investigated rock types and the average modal abundance of the minerals in them are presented in Table 1. The mineral content of the samples was quantified based on point counting from the thin section studies. Figure 2 shows the microscopic composition of the samples from HDR, ABD, CMK, and FGR as representative rock samples. 4.2 Physical Properties The assessment of the physical properties of rock is critical in civil, mining, and geological engineering applications. These properties depend on the mineral content and the microstructures of the intact rock. Willard and McWilliams (1969) found that microstructures, including mineral cleavage, grain boundaries, and microfractures, have a definitive impact on rock strength. Onodera and Asoka Kumara (1980) reported that rock strength decreases linearly with an increase in grain size. The physical properties of intact rock are strongly influenced by the type, texture, percentage, and composition of minerals forming it (Shalabi et al. 2007). In the current research, the physical properties of the rock samples, including the dry and saturated unit weights (cd and csat), specific gravity (Gs), the ratio of solid unit weight of rock to unit weight of water, porosity (n), and water absorption (Wa), were determined using standard testing methods (ISRM 2007). These tests involved five
Determination of the Geotechnical Characteristics of Hornfelsic Rocks with a Particular… Table 1 Mineral composition of the rocks
Rock mark
Rock type
Minerals content (%) Qtz.
Fld.
Bt.
Mt.
Gt.
Slt
Kt.
St.
Gpt.
HDR
Hornfels
32
8
30
5
13
12
–
–
–
ABD
Hornfels
32
7
20
8
15
4
10
4
–
CMK
Hornfels
23
7
25
5
15
–
–
–
25
FGR
Hornfels
35
5
25
11
11
–
8
5
–
PSK1
Hornfels
32
5
30
5
13
5
5
5
–
PSK2
Hornfels
32
5
25
8
12
6
7
5
–
SHR1
Hornfels
35
4
30
15
10
–
3
3
–
SHR2
Hornfels
36
4
30
10
8
4
4
4
–
Qtz. quartz, Fld. feldspar, Bt. biotite, Mt. muscovite, Gt. garnet, Slt. sillimanite, Kt. kyanite, St. staurolite, GPt. graphite
Table 2 Values of physical properties for the rocks cd (g/cm3)
csat (g/cm3)
Gs
n (%)
Wa (%)
HDR
2.85
2.87
2.90
2.00
0.70
ABD
2.85
2.86
2.87
0.92
0.32
CMK
2.81
2.82
2.84
0.97
0.45
FGR
2.78
2.81
2.86
2.78
1.00
PSK1
2.80
2.81
2.82
0.56
0.20
PSK2
2.76
2.77
2.79
0.42
0.15
SHR1
2.70
2.70
2.72
0.49
0.18
SHR2
2.68
2.69
2.70
0.54
0.20
sets of experiments that were performed on prepared cylindrical specimens. Thus, a total of 40 tests were performed for characterizing the physical properties, and average values for the parameters are presented in Table 2. Table 2 shows that dry unit weights of tested rocks were high, but porosity and water absorption values were quite low. The SHR2 and HDR samples had the lowest and highest values for dry unit weight, while the PSK2 and FGR samples had the lowest and highest values for porosity, respectively. Figure 3 shows the correlations between different physical properties of the tested rocks. A linear relationship exists between dry and saturated unit weights, which are highly correlated (0.99); however, dry unit weight is poorly correlated with porosity and water absorption. Figure 4a shows that dry unit weight was influenced by the presence of dense metamorphic minerals such as garnet, which overshadowed the effect of porosity on dry unit weight. Figure 4b shows good linear correlations between water absorption and porosity in the tested rocks. In other words, the extent of water absorption was influenced by porosity. 4.3 Ultrasonic Wave Velocity The ultrasonic wave velocity was determined in the laboratory based on ISRM (2007) and ASTM-D-2845 (1996).
γsat (g/cm3) n (%) Wa (%)
4
3
γsat, n, Wa
Rock sample
y = 1.05x - 0.14 R² = 0.99
2
y = 5.52x - 14.25 R² = 0.17 1
y = 1.99x - 5.13 R² = 0.17 0 2.65
2.70
2.75
γd
2.80
2.85
2.90
(g/cm3)
Fig. 3 Correlations between different physical properties for the rocks
This technique is often used to determine and characterize the dynamic properties of rocks. Since this method is nondestructive and relatively easy to apply, it is being increasingly used in geological and geotechnical engineering. Based on ASTM-D-2845 (1996), ultrasonic wave velocity testing is the best method for determining the dynamic elastic constants of rock. The ultrasonic wave velocity depends on various parameters such as elastic properties, mineral content and orientation, density, porosity, presence of cracks and microfractures, and the degree of weathering (Goodman 1989). In this study, the average ultrasonic wave velocity was determined from five tests for each sample. The ultrasonic wave velocities and the different dynamic elastic constants of the rock samples are presented in Table 3. The primary or P-wave velocity values ranged from 3015 to 5529 m/s, and the secondary or S-wave velocity values were 2011 to 3480 m/s. The SHR2 and HDR samples had the lowest and highest wave velocities, respectively. Based on IAEG (1979), the P-wave velocity values of the rocks ranged from low to very high. A direct linear
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D. Fereidooni
(a) 3.0
(b)
1.5
y = 0.02x + 2.50 R² = 0.79
2.9
1.0
2.8
Wa (%)
γd (g/cm3)
Fig. 4 Correlation between a dry unit weight and garnet content, b water absorption and porosity for the rocks
2.7
y = 0.35x + 0.02 R² = 0.98
0.5
2.6 0.0
2.5 7
8
9
10
11
12
13
14
15
0.0
16
1.0
Garnet (%)
2.0
3.0
n (%)
Table 3 Values of ultrasonic wave velocities and different dynamic elastic constants for the rocks Rock sample
vp (m/s)
vs (m/s)
E (GPa)
G (GPa)
m
K (GPa)
Description of vp (IAEG 1979)
HDR
5529
3480
80.89
31.51
0.17
41.10
Very high
ABD
5065
3149
66.97
28.25
0.19
35.44
Very high
CMK
5225
3263
70.63
29.92
0.18
36.83
Very high
FGR
3912
2325
36.87
15.02
0.23
22.50
Moderate
PSK1
4078
2527
42.49
17.88
0.19
22.72
High
PSK2
3873
2432
38.35
16.32
0.17
19.63
Moderate
SHR1
3123
2125
26.06
12.19
0.07
10.08
Low
SHR2
3015
2011
23.83
10.84
0.10
9.91
Low
relationship was observed between primary and secondary wave velocities in the rock samples (Fig. 5a). In addition, a direct linear relationship was found between primary wave velocity and dry unit weight of the samples (Fig. 5b). Therefore, the main factor affecting the primary wave velocity was the mineral content of the rocks (because dry unit weight is affected by mineral content of the rocks), and their porosities did not have an effect. Figure 5c shows a three-dimensional view of the correlations between dry unit weight and the primary and secondary wave velocities. Based on this research, as shown by Fig. 5a, the empirical correlation between primary and secondary wave velocities is as follows: vs ¼ 0:58vp þ 217:44
ð1Þ
where vp and vs are in meters per second. 4.4 Slake-Durability Index The slake-durability test was primarily designed for argillaceous rocks by Franklin and Chandra (1972), and the test method was standardized by ISRM (2007) and ASTM-D-4644 (1990). The slake-durability of rocks is well known to be an important consideration in evaluating the engineering behavior of rock masses and rock materials in geotechnical practices (Franklin and Chandra 1972; Dhakal et al. 2002). The durability of rock is a
123
measure of its ability to resist weathering and to retain its original size, shape, strength, and appearance over an extensive period of time (Bell 1993). This property represents the degradability of rock due to chemical and mechanical breakdown processes (e.g., exfoliation, hydration, solution, oxidation, and abrasion), and it is closely related to the rock’s mineralogical composition (Gupta and Ahmed 2007). To perform the test, rock lumps (ten pieces of about 40–60 g for each sample) were prepared and rotated for 10 min in a test drum made of a standard sieve mesh so that slaking products would be finer than 2 mm and pass through the drum. The drum was half immersed in water at 20 C. The slake-durability index (Id) corresponding to each cycle was calculated as the percentage ratio of final to initial dry weights of rock lumps in the drum after the drying and wetting cycles. The slake-durability test was carried out in two cycles, and the results are presented in Table 4. Based on Gamble (1971), the tested rocks were classified as durable and very durable. The CMK and SHR2 samples had the highest and lowest slake-durability index values in the second cycle (Id2), respectively. As the number of cycles increased, the rate of sample weight loss decreased for all rocks. In other words, the rate of decrease in the slake-durability index in the first cycle was higher than in the second cycle (see Fig. 6).
Determination of the Geotechnical Characteristics of Hornfelsic Rocks with a Particular…
(a) 4000
(b) 6000 5500
3500 3000
y = 14,104.78x - 34,966.23 R² = 0.88
5000
y = 0.58x + 217.44 R² = 0.98
vp (m/s)
vs (m/s)
Fig. 5 Correlations between a primary and secondary wave velocities, b primary wave velocity and dry unite weight; c a three-dimensional view of the correlations between dry unit weight with primary and secondary wave velocities for the rocks
2500
4500 4000 3500 3000
2000
2500 1500 2500 3000 3500 4000 4500 5000 5500 6000
2000 2.60
2.70
vp (m/s)
2.80
2.90
γd (%)
(c)
100.5
Table 4 Results of the slake-durability test for the rocks Id1 (%)
Id2 (%)
100.0
Description of Id2 (Gamble 1971)
HDR
99.49
99.22
Very durable
ABD
99.55
99.32
Very durable
CMK
99.57
99.40
Very durable
FGR
98.70
98.04
Very durable
PSK1
99.12
98.58
Very durable
PSK2
98.92
98.27
Very durable
SHR1
98.23
97.41
Durable
SHR2
98.01
97.18
Durable
The slake-durability index values for tested rocks indicated that this parameter is highly influenced by the mineral content of rock. With an increasing amount of soft minerals such as mica (biotite and muscovite), the value of slake-durability index was decreased (Fig. 7a). However, as hard minerals such as garnet increased, the value was likewise increased (Fig. 7b). In addition, as the dry unit weight increased, the value of the slake-durability index also increased (Fig. 7c). As stated before, the dry unit weight values for the tested rocks were affected by mineral content. Figure 7d shows a three-dimensional representation of the correlations between slake-durability index with mica and garnet present in the rock samples. Based on this research, the empirical correlation between slake-durability index in cycle two and dry unit weight, as shown by Fig. 7c, is
Id (%)
Rock sample
99.5
CMK
99.0
ABD HDR
98.5
PSK1 PSK2
98.0
FGR
97.5
SHR1 SHR2
97.0 96.5 0
1
2
No. of cycles Fig. 6 Correlation between slake-durability index and number of the test cycles
Id2 ¼ 12:89cd þ 62:61
ð2Þ
where slake-durability index and dry unit weight are percentage and grams per cubic centimeters, respectively. 4.5 Schmidt Rebound Hardness The Schmidt hammer test was performed according to ISRM (1981) and ASTM-D-5873 (2001c). In the context of rock mechanics, Hs is perhaps the most frequently used index for estimating the UCS and the elasticity modulus (E) of intact rock in both laboratory and field conditions. Hs is also widely used for estimating discontinuity wall strength and assessing the workability, excavatability, and boreability of rock
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D. Fereidooni
(a) 100.0
(b) 100.0
99.5
99.5
99.0
y = -0.14x + 103.21 R² = 0.73
98.5 98.0
y = 0.34x + 94.29 R² = 0.92
99.0
Id2 (MPa)
Id2 (MPa)
Fig. 7 Correlations between slake-durability index in cycle two and a mica present, b garnet present and c dry unit weight; d a three-dimensional view of the correlations between slakedurability index in cycle two (Id2) with mica and garnet present in the rocks
98.5 98.0
97.5
97.5
97.0
97.0
96.5
96.5 24
29
34
39
44
49
6
8
10
Mica (%)
12
14
16
18
Garnet (%)
(c) 100.0 99.5
Id2 (%)
99.0
y = 12.89x + 62.61 R² = 0.90
98.5 98.0 97.5 97.0 96.5 2.65
2.70
2.75
2.80
2.85
2.90
γd (%)
(d)
Table 5 Values of Schmidt rebound hardness for the rocks
Rock sample
Hs
HDR
40.10
ABD
49.10
CMK
45.40
FGR
40.50
PSK1
58.40
PSK2
59.70
SHR1
58.90
SHR2
53.70
masses (Aydin 2009). Empirical correlations between Hs and UCS and E were found by different researchers for various rock types and were summarized by Yilmaz and Sendir (2002). These correlations can be classified into three categories: exponential, power, and linear. In the current research, the Schmidt hammer was used on rock blocks of approximately 30 9 40 9 50 cm to determine Hs. Based on the results (Table 5), the tested samples were classified as
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hard rocks. The HDR and PSK2 samples had the lowest and highest values for the parameter, respectively. Based on Fig. 8, an inverse power relationship exists between Hs and porosity; however, no correlation has been found between Hs and dry unit weight or mineral content. Therefore, for the tested rock samples, the Hs values were affected by porosity. 4.6 Point Load Index The point load test is commonly used owing to the ease of testing, simplicity of specimen preparation, and feasibility of field application (Kahraman and Gunaydin 2009). This test method was standardized by ISRM (1985) and ASTMD-5731 (2001a), and it is often used as an indirect measure of the compressive or tensile strength of rocks (Kahraman and Gunaydin 2009). In this test, cylindrical, prismatic, or irregular rock specimens that are loaded between two conical platens (of stipulated geometry and hardness) fail
Determination of the Geotechnical Characteristics of Hornfelsic Rocks with a Particular…
45
The relationship between point load index and porosity is inverse exponential (Fig. 9a). No correlation was found between the point load index value and mineral content of the rock samples. Therefore, the point load index values were mainly influenced by porosity. The relationship between point load index and Hs is directly exponential (Fig. 9b). Figure 9c shows a three-dimensional view of the correlations between point load index and porosity and Hs for the tested rocks.
40
4.7 Brazilian Tensile Strength
65 60
y = 48.48x-0.23 R² = 0.92
Hs
55 50
35 0.0
0.5
1.0
1.5
2.0
2.5
3.0
n (%) Fig. 8 Correlation between Schmidt rebound hardness and porosity for the rocks
Table 6 Values of point load index for the rocks Rock sample
Is(50) (MPa)
Description of Is(50) (Broch and Franklin 1972)
HDR ABD
4.13 6.88
Very strong Very strong
CMK
5.38
Very strong
FGR
4.00
Very strong
PSK1
8.20
Very strong
PSK2
11.08
SHR1
10.60
SHR2
5.08
Extremely strong Extremely strong Very strong
when they develop one or more extensional planes along the line of loading. The applied force (P) and the distance (De) between the platens at failure (or equivalent core diameter) were measured, and the point load index (Is) was calculated, using the following equation (ISRM 1985; ASTM-D-5731 2001a): Is ¼
P D2e
ð3Þ
The point load index for a core diameter equal to 50 mm (Is(50)) was calculated from following expression (ISRM 1985; ASTM-D-5731 2001a): 2 De Isð50Þ ¼ Is ð4Þ 50 In this research, ten tests were undertaken for each rock sample, and the results are presented in Table 6. Based on these results, the FGR and PSK2 samples had the lowest and highest point load index values, equal to 4.00 and 11.08 MPa, respectively. Based on Broch and Franklin (1972), the tested samples were classified as very to extremely strong rocks.
The Brazilian test is a simple indirect testing method for obtaining the tensile strength of brittle materials such as concrete, rock, and rock-like materials (Barla and Innaurato 1973; Li and Wong 2013). Following ISRM (1978) and ASTM-D-3967 (2001b), this test was carried out on specimens with length to diameter ratios between 0.5 and 0.75. The BTS was determined using the following equation: BTS ¼
2P pDt
ð5Þ
where P is the maximum load recorded in the experiment, and D and t are diameter and thickness of the specimen, respectively. In this research, ten tests were undertaken for each rock sample. The average BTS values calculated for the rocks are presented in Table 7. Based on the results, the FGR and PSK2 samples had the lowest and highest BTS values, equal to 3.84 and 20.48 MPa, respectively. Empirical exponential correlations between BTS values and point load index have been reported by some researchers, such as Kilic and Teymen (2008). For the studied rocks, the BTS was related to parameters such as porosity, point load index, and Hs. BTS and porosity exhibited an inverse exponential relationship (Fig. 10a), but no correlation was found between BTS and the mineral content of the rocks. The relationship between BTS and Hs and point load index are directly power and linear equations, respectively (Fig. 10b, c). Figure 10d shows a threedimensional view of the correlations between BTS and porosity and Hs for the rocks. In this research, due to the high correlation coefficient of the equations between BTS with Hs and point load index, the following equations are proposed for determining BTS: BTS ¼ 3:5 106 Hs3:80
ð6Þ
BTS ¼ 2:28Isð50Þ 4:66
ð7Þ
where BTS and Is(50) are in MPa. The relationship between experimental results and calculated BTS values using Eqs. (6) and (7) for all tested samples is shown in Fig. 11. For a comparison of the
123
D. Fereidooni
(a) 14
(b)
15
12
y = 6.22x-0.53 R² = 0.89
10 8
Is(50) (MPa)
Is(50) (MPa)
Fig. 9 Correlations between point load index and a Porosity and b Schmidt rebound hardness; c a three-dimensional view of the correlations between point load index with porosity and Schmidt rebound hardness for the rocks
6 4
y = 0.64e0.05x R² = 0.95
10
5
2 0
0 0.0
0.5
1.0
1.5
n (%)
2.0
2.5
3.0
35
40
45
50
55
60
65
Hs
(c)
Table 7 Values of Brazilian tensile strengths for the rocks
Rock sample
BTS (MPa)
HDR
3.97
ABD
12.61
CMK
8.17
FGR
3.84
PSK1
16.26
PSK2
20.48
SHR1
18.13
SHR2
10.11
results, a 45 line (y = x) has been plotted in this figure. It is clear that the two lines fully overlap each other and closely fit to the 45 line. This finding confirms the validity of the equations. 4.8 Uniaxial Compressive Strength UCS test is very commonly used in rock engineering. ISRM (1979) and ASTM-D-2938 (1995) describe the recommended method for determining UCS. Application of Schmidt rebound, point load, slake-durability, and Los Angles indexes may be used for indirect determination of UCS (Cargill and Shakoor 1990). Andrade and Saraiva (2010) proposed linear and exponential correlation equations between UCS and point load index for phyllites and meta-greywackes in central Portugal. Kahraman and
123
Gunaydin (2009) suggested an equation between UCS and point load index for 17 igneous, 16 metamorphic, and 19 sedimentary rocks. They also presented a list of the correlation equations between UCS and point load index proposed by other researchers. In the current research, five prepared cores with a 2:3 length to diameter ratio were tested for each sample to determine UCS. The average UCS values obtained for the rocks are presented in Table 8. As with the point load index and BTS, the FGR and PSK2 samples had the lowest and highest UCS values, respectively. Based on ISRM (1979) and Broch and Franklin (1972), the tested samples were classified as moderately to extremely strong rocks. The results showed that the UCS was not related to the mineral content of the tested rocks. Therefore, this parameter was affected by porosity and related to parameters such as Hs, point load index, and BTS. The correlation between UCS and porosity, Hs, point load index, and BTS are presented in Fig. 12. There are inverse and direct power correlations between UCS and porosity and Hs, respectively. For point load index and BTS, the relationships can be depicted as direct linear equations. Figure 12e shows a three-dimensional view of the correlations between UCS and point load index and BTS for the tested rocks. In the current research, because of the high correlation coefficient, the equations between UCS and Hs, point load index, and BTS are as follows:
Determination of the Geotechnical Characteristics of Hornfelsic Rocks with a Particular… Fig. 10 Correlations between Brazilian tensile strength and a porosity, b Schmidt rebound hardness and c point load index; d a three-dimensional view of the correlations between Brazilian tensile strength with porosity and Schmidt rebound hardness for the rocks
(a)
20
(b)
15
y = 8.73x-0.89 R² = 0.89
10
BTS (MPa)
BTS (MPa)
15
20
10
5
y = 0.000004x3.795624 R² = 0.922968
5
0 0.0
0.5
1.0
1.5
2.0
2.5
0
3.0
35
40
45
n (%)
(c)
55
60
65
Hs 22
y = 2.28x - 4.66 R² = 0.95
17
BTS (MPa)
50
12
7
2 2
4
6
8
10
12
Is(50) (MPa)
(d)
25
y=x
BTS from Equ. 6
BTS (MPa) (Calculated)
BTS from Equ. 7
20
Linear (BTS from Equ. 6) Linear (BTS from Equ. 7)
15
UCS ¼ 0:02Hs2:28
ð8Þ
UCS ¼ 24:36Isð50Þ 2:14
ð9Þ
UCS ¼ 10:03BTS þ 55:19
ð10Þ
where UCS, Is(50), and BTS are in MPa. The equation between UCS and point load index is close to the one proposed by ISRM (1979):
10
UCS ¼ 24Isð50Þ
5
0 0
5
10
15
20
25
BTS (MPa) (Experimental) Fig. 11 Correlation between experimental and calculated values of Brazilian tensile strength for the hornfelsic rocks
ð11Þ
The relationships between experimental results and calculated UCS values based on Eqs. (8–10) for all tested samples are shown in Fig. 13. For comparison of the results, a 45 line (y = x) has been plotted in this figure. It is clear that the three lines closely fit the 45 line, which confirms the validity of the equations.
123
D. Fereidooni
UCS (MPa)
Description of UCS ISRM (1979)
Broch and Franklin (1972)
HDR
99.22
Moderately strong
Very strong
ABD
165.21
Very strong
Very strong
CMK
129.22
Very strong
Very strong
FGR
95.93
Moderately strong
Very strong
PSK1
183.14
Strong
Very strong
PSK2
272.83
Very strong
Extremely strong
SHR1
256.20
Very strong
Extremely strong
SHR2
178.01
Strong
Very strong
(b) 300
(a) 300
250
250
y = 149.33x-0.53 R² = 0.89
UCS (MPa)
Fig. 12 Correlations between uniaxial compressive strength and a porosity, b Schmidt rebound hardness, c point load index and d Brazilian tensile strength; e a three-dimensional view of the correlations between uniaxial compressive strength with point load index and Brazilian tensile strength for the rocks
Rock sample
UCS (MPa)
Table 8 The values of uniaxial compressive strength for the rocks
200 150 100
y = 0.02x2.28 R² = 0.92
200 150 100 50 0
50 0.0
0.5
1.0
1.5
2.0
2.5
35
3.0
40
45
50
UCS (MPa)
250
250
y = 24.36x - 2.14 R² = 0.99
200 150
65
y = 10.03x + 55.19 R² = 0.92
200 150 100
100
50
50 2
4
6
8
Is(50) (MPa)
(e)
123
60
(d) 300
300
UCS (MPa)
(c)
55
Hs
n (%)
10
12
2
6
10
14
BTS (MPa)
18
22
Determination of the Geotechnical Characteristics of Hornfelsic Rocks with a Particular… UCS from Equ. 8 UCS from Equ. 9 UCS from Equ. 10 Linear (UCS from Equ. 8) Linear (UCS from Equ. 9) Linear (UCS from Equ. 10)
UCS (MPa) (Calculated)
325
275
y=x
Acknowledgments The author gratefully acknowledges Professor V. R. Vidal-Romani and Professor L. G. Collins for having greatly improved the English.
References
225
175
125
75 75
125
175
225
275
325
UCS (MPa) (Experimental) Fig. 13 Correlation between experimental and calculated results of uniaxial compressive strength for the rocks
5 Conclusions The hornfelsic rocks studied in this research showed a high degree of metamorphism because of the presence of metamorphic minerals such as garnet, andalusite, sillimanite, and staurolite as porphyroblasts in their composition. The matrix of the rocks consisted of quartz, feldspar, biotite, and muscovite. The mineral content influenced the dry unit weight, wave velocity, and slake-durability index. The dry unit weights for the tested rocks were high, but the porosity and water absorption values were fairly low. Linear relationships existed between different physical properties, with various correlation coefficients. Water absorption, Schmidt hardness, point load index, BTS, and UCS of the rocks were influenced by porosity. The sonic velocity values of these rocks ranged from low to very high, and a direct linear relationship was found between primary and secondary wave velocities. The slakedurability index values for the tested rocks were greatly influenced by the rocks’ mineral content and dry unit weight. With a higher content of soft minerals such as mica (biotite and muscovite), the slake-durability index value was reduced, and with a higher content of hard minerals such as garnet, the slake-durability index was increased. Based on the Schmidt hammer test results, the tested samples were classified as hard rocks. The rocks were classified as very to extremely strong rocks based on their point load strength indexes. The correlation between point load index and Hs is directly exponential. BTS values of the rocks were related to parameters such as porosity, point load index, and Hs. The correlation between Brazilian strength and porosity was inversely exponential. The samples were classified as moderately to extremely strong rocks based on their UCS, which was affected by porosity and related to Hs, point load index, and BTS. An inverse power relationship was found between UCS and porosity.
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