Indian Journal of Science · The rock samples consisted of igneous, sedimentary and metamorphic origins like basalt, granite, sandstone, rhyolite, dolerite and granulite. The dynamic
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Undergraduate Dual BS-MS Student, Indian Institute of Science Education & Research, Kolkata, Email: [email protected] Received 09 July; accepted 22 August; published online 01 September; printed 16 September 2013
ABSTRACT The laboratory measurements of physical properties such as density, porosity, ultrasonic P-wave and S-wave velocities, Poisson’s ratio, Young’s modulus, Bulk modulus, and Shear modulus have been carried out of some of the different types of rocks of southern part of geographical Indian sub-continent. The rock samples consisted of igneous, sedimentary and metamorphic origins like basalt, granite, sandstone, rhyolite, dolerite and granulite. The dynamic elastic moduli were calculated using density, P-wave and S-wave velocity data’s. The compressional P-wave and shear S-wave velocities increases with increase in density, young’s modulus, shear modulus and Bulk modulus. Based on observed experimental results the rock samples which can be classified under excellent quality rocks are NK19AY2 (Granulite) and JDP-20B (Sandstone) can be classified under good quality rocks for engineering applications. Key Words: P-wave velocity, S-wave velocity, density, elastic waves, modulus of elasticity.
To Cite This Article: Abhilash Borah. Characteristic Study of Dynamic Elastic Modulii, Physical properties of rocks in geographical South India. Indian Journal of Science, 2013,4(11),76-84
1. INTRODUCTION Rock mechanics is the discipline of engineering science that involves the relation between geology, geophysics, mathematical sciences, physical sciences, mining and civil engineering. Rock Mechanics deals with the theoretical and applied behavior of rocks: it is the branch of mechanics concerned with the response of rock to the force fields of its environment (Jumikis, 1979). Rock is a natural substance which functions under the environmental processes of load, water, temperature, pressure, plate tectonics of the earth’s crust etc which ultimately depends upon the physical and mechanical properties of those rock materials. Rock mechanics is a division of a broader discipline, Geomechanics, which is classified under geotechnical engineering. This subject basically deals with the physical and mechanical reactions of all geological elements like soil, rock, ice etc. in geographical fields. A naturally occurring material, rock has many uses and application. For example, rock is used: For laying structural foundations and to support structures. For constructing vehicular and equeous tunnels, underground power plants, and other underground openings and
cavities. As facing stone for buildings, bridges, and hydraulic structures to protect these structures from weathering. For making artificial sand from rock in regions poor in sand but rich in suitable rocks.
1.1. Rock Mechanics According to the definition put forwarded by the Committee on Rock Mechanics of the Geological Society of America in 1964, viz., of the National Academy of Sciences committee on Rock Mechanics in 1966: “Rock Mechanics is the theoretical and applied behavior of rock; it is that branch of mechanics concerned with the response of rocks to the force fields of its environment”. Some of the features of Rock Mechanics are as follows (Jumikis, 1979): Mechanically, rock is a “Multiple-body” system. In a large, solid, sound rock mass. Rock may be considered to be a continuum. In its geologic environment, rock is principally characterized by the fact that rock is not a continuum but a regulated
discontinuum because of joints, fissures, shistosity, cracks, cavities, and other possible discontinuities. Objectives of Rock Mechanics are: To carry out engineering rock surveys. To develop rational rock sampling, identification and classification methods. To collect and classify information on rocks and their physical properties in the light of fundamental knowledge of rock
mechanics, foundation engineering and hydraulic structures engineering.
RESEARCH • GEOSCIENCE Indian Journal of Science, Volume 4, Number 11, September 2013
Characteristic Study of Dynamic Elastic Modulii, Physical properties of rocks in geographical South India
To study rock performance under thermal conditions and water regimen. To perform research on the mechanisms of failure in rocks. To apply the knowledge of rock mechanics for the solution of practical
engineering problems. 1.2. Physical Properties Rock is a natural substance having structural features which are not encountered in most other engineering materials. For safe and economical design of structure on and in rock, adequate knowledge about the technological properties of rock is indispensible. Some of the main technological properties of rocks necessary to consider in the design of concrete dams, rock slopes, and underground structures are (Jumikis, 1979): Unit weight Movements and deformations under load Static and dynamic strength Young’s modulus of elasticity Poisson’s ratio Density against water absorption Permeability to water Resistance to weathering Thermal properties Electrical properties etc.
The physical properties of rocks affecting design and construction in rock are: Mineralogical composition, texture, and structure Specific gravity Density Porosity Void ratio
Permeability to water Elastic waves (P-wave and S-wave) Saturation moisture content etc.
2. OBJECTIVES OF PRESENT STUDY 2.1. Determination of physical properties like density, Compressional P-wave velocity, Shear S-wave velocity of different rock types 2.1.1. Density It is the characteristic property of a substance. The density of a substance is the relationship between the mass of the substance and how much space it takes up (volume). The mass of atoms, their size, and how they are arranged determine the density of a substance. Density equals the mass of a substance divided by its volume; ƥ = m/V. Objects with the same volume but different mass have different densities (Understanding Earth- Grotzinger, Press, Jordan, Siever). A great many common rock-forming minerals, however, are too similar in density. A standard measure of density is specific gravity, which is equal volume of pure water at 40C. Density depends on the atomic mass of mineral ion’s and how closely they are packed in its crystal structure. Increase in density caused by increases in pressure affect the way minerals transmit light, heat, and earthquake waves. Rock densities are very sensitive to the minerals present in it which compose a particular rock type. Covalently bonded materials have more open packed and so have lower densities. Sedimentary rocks and granite, which are rich in quartz and feldspar, tend to be less dense than volcanic rocks while the more mafic a rock is, the greater is its density. Some of the standard density ranges are mentioned in Table 1.
2.1.2. Elastic Waves It is the motion in medium in which, when particles are displaced, a force proportional to the displacement acts on the particles to restore them to their original position. If a material has the property of elasticity and the particles in a certain region are set in vibratory motion, an elastic wave will propagate. An elastic wave is a type of mechanical wave that propagates through, or on the surface of a medium. Elastic waves are fairly common in nature. For example, sound propagating through the air or water waves propagating across the surface of a pond are elastic waves. The elasticity of the material provides the restoring force of the wave. Elastic waves occurring in the Earth as a result of an earthquake or any other disturbance, are usually called seismic waves. Earthquake shaking and damage is the result of three basic types of elastic waves. Two of the three propagates within a body of rock. The faster of these waves is called the Primary wave (P-Wave). Its motion is the same as that of a sound wave in that, as it spreads out, it alternately pushes (compresses) and pulls (dilates) the rock. These P-Waves are able to travel through both solid rock, such as Granite Mountains, and liquid material, such as volcanic magma and the water of the oceans (Lama et al. 1978). The slower wave through the body of rock is called the Secondary or S-Wave. As an S-Wave propagates, it shears the rock sideways at right angles to the direction of travel. If a liquid is sheared sideways or twisted, it will not spring back; hence S-waves cannot propagate in the liquid parts of the earth, such as oceans and lakes. The actual speed of P and S seismic waves depends on the density and elastic properties of the rocks and soil through which they pass. In most earthquakes, P waves are felt first. The effect is similar to a sonic boom that bumps and battles and rattles windows. Some seconds later, S waves arrive with their up-and-down and side-to-side motion, shaking the ground surface vertically and horizontally. This is the wave motion that is so damaging to structures. P-wave and S-wave have a characteristic which effects shaking: when they move through layers of rocks in the crust, they are reflected or refracted at the interfaces between rock types. Whenever either wave is reflected or refracted, some of the energy of one type is converted to waves of the other type.
3. EXPERIMENTAL PROTOCOL 3.1. Sample Details The samples collected were in the shape of blocks of 25*25*25 cm for laboratory studies from different geographical areas of Southern India. The samples are of hard Basalt, vesicular Basalt, Dolerite, pink Granite, gray Granite, Sandstone, Quartzite and granulites. The cylindrical specimens 60 mm length and 30 mm diameter were prepared. The two ends of each rock cylinder were ground and lapped parallel to attain an accuracy of 0.2 mm and the ends were polished. Also, the cylindrical sides are made straight to the accuracy of 0.3 mm over the full length of each specimen.
3.2. Density The density of each core samples was measured after the removal from it. The moisture was removed by placing the rock samples in an electric oven at ~800C for about one hour and they were dried at the room conditions. The diameter and the length of each the cylindrical rock samples were measured using digital Vernier calipers for four observations, and the values were averaged for computing the volume. Several measurements were made along the core and the average values of length and diameter were used for calculating the cross-sectional area and volume of the samples. The weight (Mass) of each of the dried core was measured using an electronic balance. The density is calculated using the following equation:
Table 4 Summary of physical properties and dynamic modulii of different rock types used in present study
Table 5 Physical properties that show maximum and minimum values of density, P-wave velocity, S-wave velocity, Shear Modulus, Young’s Modulus and Bulk Modulus of the different rock types in present study
Properties Maximum Minimum Density NK19AY2: 3.348 g/cc JDP20B: 2.009 g/cc
P-wave velocity NK19AY2: 6962 m/s JDP20B: 3023 m/s S-wave velocity NK19AY2: 4187 m/s JDP20B: 3023 m/s Shear Modulus NK19AY2: 58.6937 GPa JDP20B: 18.35933 GPa
Table 6 Classification of different rock types under our present study (Reference: Barton N. Rock quality, seismic velocity, attenuation, and anisotropy, Taylor & Francis, 2007)
Rock types Samples No. Classification of rocks based on dynamic
young’s modulus data (Barton,N./2007,taylor & francis)
3.3. Velocity Ultrasonic velocities of P-Wave and S-Wave measurements have been carried out using a high-energy pulser receiver on the driving side and a 2-channel digital storage oscilloscope on the receiving side. We determined the velocity of compressional (Vp) waves and shear waves (Vs) using the time-of-flight measurement technique at 1MHz frequency as described in detail. In this technique the test sample is placed between the transmitting transducer and receiving transducer. We have two different sets of transducers to measure P-wave and S-wave velocity measurements separately. The pulser will generate a high power DC electric pulse which is converted by the transmitting transducer into an elastic wave. This stress wave passes through the test sample and when it enters the receiving transducer the stress wave is converted back into an electric transient pulse. The electric transient pulse is viewed and stored on the receiving side with the help of a digital storage oscilloscope for the measurement of travel time and pulse width. The velocity is computed using the formula: VP
(m/sec) = length the sample/time
The Poisson’s ratio and dynamic moduli have been computed using P-wave and S-wave velocities and density data. The relation between them is given in the table below,
Figure 1 Density and P-Wave velocity relationship of different rock types
Figure 2 Density and S-Wave velocity relationship of different rock types
Figure 3 Young’s Modulus and P-Wave velocity relationship of different rock types
Figure 4 Youngs Modulus and S-Wave velocity relationship of different rock types
Poisson’s Ratio() 1/2 *((VP/VS)2 –2))/((VP/VS)2 –1)) Young’s Modulus(E) (1+)(1-2)VP 2/(1- ) Bulk Modulus(K) E/3(1-2) Shear/Rigidity Modulus(G) E/2(1+) Where, VP =P-wave velocity in rock sample (cm/sec) VS =S-wave velocity in rock sample (cm/sec) =Density of rock sample (gm/cc)
4. OBSERVATIONS Observations are listed and shown in Table 2-6 and Figure 1-6.
5. RESULTS AND DISCUSSION The densities of different rock samples of the geographic southern India were determined. The rock sample densities found are similar to the standard values by comparing. From the measurement of elastic wave velocity measurements it is seen that the velocities depend on the elastic modulii and density. The elastic constants, and densities, in turn depend on the properties that the geologist or engineer use to characterize the rock such as porosity, fluid saturation, texture etc. It is observed from the Table-5 Rock sample, Granulite NK19AY2 has the highest maximum value of density, compressional P-wave velocity, shear S-wave velocity, Young’s Modulus, Bulk Modulus & Shear Modulus while the rock sample, Sandstone JDP20B has the lowest minimum value of density, compressional P-wave velocity, shear S-wave velocity, Young’s Modulus, Bulk Modulus & Shear Modulus. It is evident that as P-Wave velocity increases, the youngs’s modulus increases simultaneously (Figure 3) and as S-Wave velocity increases, the young’s modulus increases (Figure 4). Density is also increasing with increase in compressional P-wave velocity and shear S-wave velocity (Figure 1 & Figure 2 respectively). It is also seen that as Poisson’s ratio increases P-Wave velocity & S-Wave velocity both increases (Figure 5 & Figure 6 respectively). The density of all rock types of the present study varies from 2.009 g/cc to 3.348 g/cc with an average value of 2.774 m/s. The compressional P-Wave velocity shows a wide variation from 4863 m/s to 6962 m/s with an average value of 6024 m/s (Figure 3). The shear S-Wave velocity too shows a wide variation from 3023 m/s to 4187 m/s with an average value of 3559.143 m/s (Table 3). The physical properties are essential for classification of rock materials and judgments about their suitability for various construction purposes.
6. CONCLUSIONS Hence, from the experimental measurements of elastic waves measurement it shows that the velocities depend on the
elastic modulii and density. It is inferred from the experimental results that velocity increases with increase in density, Young’s modulus and Poisson’s
ratio. On the basis of experimental data evidences, Granulite (NK19AY2) rock is an excellent strong rock group for engineering
applications while sandstone (JDP20B) come under somewhat good quality rock. Classification of rocks based on dynamic young’s modulus data (Barton, 2007)
SUMMARY OF RESEARCH The research project analysis helped to see the various physical properties of rocks found in geographical South India. DISCLOSURE STATEMENT I thank to IAS-NASI-INSA for the research funding as a part of Research Fellowship Programme-2013
Figure 5 Poisson ratio and P-Wave velocity relationship of different rock types
Figure 6 Poisson’s ration and S-Wave velocity relationship of different rock types
ACKNOWLEDGEMENT Thanks and appreciation to IISER-Kolkata, IAS(Banglore)-NASI(Allahabad)-INSA(New Delhi), NGRI-Dr.K.Lakshmi, Hyderabad. REFERENCE
1. Barton N. Rock quality, seismic velocity, attenuation, and anisotropy, Taylor & Francis, 2007 2. Jumikis AR. Rock Mechanics, Trans Tech Publications, Rockport USA, 1979 3. Lama RD, Vutukuri VS. Handbook on Mechanical Properties of rocks-Testing Technique and Result-Volume I Trans Tech
publications Aedermannsdorf, Switzerland, 1978 4. Lama RD, Vutukuri VS. Handbook on Mechanical Properties of rocks-Testing Technique and Result-Volume II Trans Tech