← Controller of Mines
Past Questions — 2022
Coal mines roof rating (CMRR) was given by:
A)
Z T Bieniawski
B)
Mark and Molinda
C)
Marinos and Hoek
D)
Laubscher and Taylor
The Coal Mine Roof Rating (CMRR) is a widely used empirical system specifically designed to evaluate the stability of coal mine roofs to determine the appropriate support requirements. It was developed by Mark and Molinda (specifically B.G. Mark and others at the National Institute for Occupational Safety and Health - NIOSH). The system uses parameters such as rock strength, bedding plane spacing, and moisture to assign a numerical rating to the roof rock.
Analysis of other options:
- Option (a) Z.T. Bieniawski developed the Rock Mass Rating (RMR) system, which is a general rock mass classification system used across various types of mining and civil engineering, not specifically for coal mine roofs.
- Option (c) Marinos and Hoek are known for their work on the Geological Strength Index (GSI), which focuses on the structure and surface condition of rock masses.
- Option (d) Laubscher developed the Mining Rock Mass Rating (MRMR) system, which is an adaptation of RMR specifically for caving and large-scale mining operations.
Development works are going on with 35% recovery from a coal seam. The pillars developed during development stage are having strength of 13.27 MPa with factor of safety 2.3. Considering the unit weight of rock 0.025 MPa/m, the depth of cover of the coal seam is:
A)
~200 m
B)
~250 m
C)
~150 m
D)
~100 m
FoS-based stress=13.27/2.3=5.77 MPa = gamma H/(1-e). With e=0.35 => H=5.77*0.65/0.025~150m.
If the porosity in rock mass is higher-
A)
Density will be also higher
B)
Modulus of elasticity will be lower
C)
Transmission of the sound waves will be higher
D)
Internal friction and rock stability will be higher
Porosity refers to the ratio of the volume of voids to the total volume of the rock mass. Here is the step-by-step analysis of the options:
1. **Density (Option a):** Density is mass per unit volume. Since voids (pores) are filled with air or water (which are much less dense than rock minerals), an increase in porosity leads to a decrease in the overall bulk density of the rock. Therefore, option (a) is incorrect.
2. **Modulus of Elasticity (Option b):** The Modulus of Elasticity (Young's Modulus) measures the stiffness of a material. Voids act as discontinuities and points of weakness within the rock matrix. As porosity increases, the effective cross-sectional area of the solid mineral skeleton decreases, reducing the rock's ability to resist deformation. Consequently, the rock becomes less stiff, and the modulus of elasticity decreases. This is a fundamental principle in rock mechanics. Therefore, option (b) is correct.
3. **Transmission of Sound Waves (Option c):** Sound waves (seismic waves) travel more efficiently through dense, continuous solid media. Pores act as scattering centers and barriers that attenuate the signal and slow down the wave velocity. Higher porosity generally leads to lower sound wave velocity and transmission. Therefore, option (c) is incorrect.
4. **Internal Friction and Stability (Option d):** Higher porosity generally weakens the structural integrity of the rock. It increases the likelihood of collapse under load and typically reduces the overall shear strength and stability of the rock mass. Therefore, option (d) is incorrect.
In which method of mining, slot raise are not required:
A)
VCR method
B)
Sublevel method
C)
Room and pillar method
D)
Cut and fill method
A 'slot raise' is a vertical or inclined opening created to provide a free face for blasting in underground mining, typically used in stoping methods to initiate the caving or slicing of the ore body.
1. **VCR (Vertical Crater Retreat) method**: This method relies heavily on the creation of a slot (often using large diameter holes) to create the initial free face for the crater blasting process.
2. **Sublevel method**: This is a bulk mining method where slot raises are essential to create the initial void (slot) from which the rest of the sublevel is blasted in slices.
3. **Cut and fill method**: In many variations of stoping (including cut and fill), slotting is used to initiate the extraction of a block of ore.
4. **Room and pillar method**: This is a horizontal mining method used for flat-lying deposits. It involves excavating 'rooms' while leaving 'pillars' of ore for support. The excavation is done horizontally using drilling and blasting against the face of the room; it does not involve vertical stoping or the need for a vertical slot raise to initiate the collapse or retreat of a block. Therefore, slot raises are not required in this method.
The incubation period in underground coal mine is used for deciding:
A)
Size of coal pillar
B)
Number of pillars in depillaring panel/size of depillaring panel
C)
Width of the gallery
D)
Diagonal line of extraction
In underground coal mining, specifically during depillaring operations, the 'incubation period' refers to the time interval between the initiation of a stress-induced change (such as the start of pillar extraction) and the actual occurrence of a spontaneous combustion event or a major strata failure (like a bump or cave-in).
1. Why Option (b) is correct: The incubation period is critical for planning the 'size of the depillaring panel' and the 'number of pillars' to be extracted. If the incubation period is short, the panel size must be kept small to ensure that the coal is extracted and the area is sealed or goafed before spontaneous combustion can ignite. If the panel is too large, the time taken to extract all pillars may exceed the incubation period, leading to hazardous fires.
2. Why other options are incorrect:
- Option (a) Size of coal pillar: Pillar size is determined by the depth of cover, strength of coal, and safety factors (e.g., using formulas like CMR guidelines), not by the incubation period.
- Option (c) Width of the gallery: Gallery width is decided based on the equipment used and the stability of the roof/sides (geotechnical properties).
- Option (d) Diagonal line of extraction: The line of extraction is decided based on the direction of the main dip, ventilation requirements, and the sequence of extraction to manage stress, rather than the chemical/thermal incubation period.
While determining the tri-axial compressive strength in the laboratory the lateral pressure acting of the rock sample known as:
A)
Atmospheric pressure
B)
Hydrostatic pressure
C)
Deviatric pressure
D)
None of these
In a tri-axial compressive strength test, a cylindrical rock sample is subjected to a constant lateral pressure (confining pressure) while an increasing axial load is applied until failure. This lateral pressure is typically applied using a fluid (oil or water) within a pressure chamber, which exerts an equal pressure in all lateral directions. This type of uniform pressure is known as hydrostatic pressure (or confining pressure).
Analysis of other options:
- Atmospheric pressure (a) is the pressure exerted by the weight of the atmosphere and is not the controlled lateral pressure used to simulate depth in rock mechanics tests.
- Deviatoric pressure (c), or deviatoric stress, is the difference between the axial stress (σ1) and the lateral confining stress (σ3). It is the 'extra' stress applied along the axis, not the lateral pressure itself.
- Therefore, the lateral pressure acting on the sample is the hydrostatic/confining pressure.
Which of the following excavator is preferred to be used for a bench height of 30 m or more?
A)
Bucket wheel Excavator
B)
Shovel
C)
Front and end loader
D)
Dragline
In open-cast mining, the choice of excavator depends heavily on the bench height and the nature of the material.
1. **Dragline (Option d):** Draglines are designed for very deep excavations and high bench heights. Because they cast their bucket and pull it back toward the machine using a cable system, they can reach depths and heights far exceeding those of shovels or loaders. They are typically used for overburden removal where bench heights can reach 30m to 60m or more.
2. **Shovel (Option b):** Electric or hydraulic shovels are highly productive but are limited by the reach of their boom and the stability of the face. They are generally preferred for bench heights ranging from 10m to 20m. A 30m bench would be unstable and unsafe for a standard shovel to operate from the floor.
3. **Bucket Wheel Excavator (Option a):** BWEs are used for continuous mining of soft materials. While they can be massive, they are typically used for specific terrace-mining methods rather than general high-bench excavation in the same manner as a dragline.
4. **Front and End Loader (Option c):** Loaders are used for loading material into haul trucks from a flat surface or low face. They have very limited vertical reach and are unsuitable for high benches.
Therefore, for a bench height of 30m or more, the Dragline is the preferred equipment due to its superior reach and digging depth.
Which is associated only with longwall mining?
A)
Hydraulic prop
B)
Powered support
C)
Shuttle car
D)
Roadheader
Step-by-step reasoning:
1. **Analyze the Question**: The question asks for the equipment associated *only* with longwall mining, meaning it is not typically used in other methods like Bord and Pillar or Room and Pillar mining.
2. **Evaluate Option (a) Hydraulic prop**: Hydraulic props are versatile support systems used in various mining methods, including Bord and Pillar, to support the roof temporarily or permanently.
3. **Evaluate Option (b) Powered support**: Also known as 'Shield Supports', these are massive, automated hydraulic supports specifically designed for longwall mining. They support the roof of the longwall face and advance automatically as the shearer moves forward, allowing the roof behind them to collapse (the goaf). They are not used in Bord and Pillar mining.
4. **Evaluate Option (c) Shuttle car**: Shuttle cars are primarily used in Bord and Pillar or Room and Pillar mining to transport coal from the working face to the feeder breaker or conveyor belt.
5. **Evaluate Option (d) Roadheader**: A roadheader is a versatile cutting machine used for developing galleries, tunnels, or in room and pillar mining. While it can be used in some longwall setups for development, it is not exclusive to longwall mining.
6. **Conclusion**: Powered supports (shields) are the defining characteristic of modern longwall mining systems.
When an open-pit mine reaches to its ultimate pit limit, the locked-up coal is extracted by:
A)
Punch longwall mining
B)
Highwall mining
C)
Augur mining
D)
Hydraulic mining
Step-by-step reasoning: 1. Understanding the Scenario: When an open-pit mine reaches its 'ultimate pit limit', it means that stripping any more overburden to reach the coal would be economically unviable (the cost of removing waste exceeds the value of the coal). However, there is still coal remaining in the seam extending horizontally from the pit wall. 2. Analyzing Highwall Mining: Highwall mining is a specialized technique used specifically for this scenario. It involves using a remotely operated cutter/borer from the surface (the top of the highwall) to extract coal from the exposed face of the pit without removing the remaining overburden. 3. Evaluating other options: (a) Punch longwall mining is an underground mining method used for thin seams, not specifically for recovering coal from an open-pit limit. (c) Augur mining is similar to highwall mining but typically refers to drilling holes from the surface into a seam that is not necessarily exposed by a pit wall (often used for recovery in abandoned mines). (d) Hydraulic mining involves using high-pressure water jets to dislodge material, which is not the standard method for extracting locked-up coal at a pit limit. Therefore, Highwall mining is the most accurate technical term for recovering coal from the face of an ultimate pit limit.
Filling up of mined area in Opencast mines is known as:
A)
OB removal
B)
Trenching
C)
Reclamation
D)
Salvaging
Step-by-step reasoning: 1. The question asks for the term used when a mined-out area in an opencast (open-pit) mine is filled back in. 2. 'Reclamation' is the process of restoring land that has been mined to a natural or economically usable state. This typically involves backfilling the void with overburden (OB) and topsoil, followed by revegetation. 3. Analyzing other options: (a) 'OB removal' is the initial process of removing waste rock to access the mineral, not filling it back. (b) 'Trenching' refers to digging narrow channels, usually for drainage or utility installation. (d) 'Salvaging' refers to the recovery of useful materials or topsoil before mining begins to be used later during reclamation. Therefore, 'Reclamation' is the only term that describes the filling and restoration of the mined area.
The fall which takes place soon after withdrawal of supports is called:
A)
Local fall
B)
Main fall
C)
Air blast
D)
Rock burst
In the context of underground mining and roof support systems, a 'Local fall' refers to the immediate detachment and falling of small pieces of rock or loose strata that occurs shortly after the supports (such as timber or hydraulic props) are withdrawn or shifted. This is typically caused by the redistribution of stress in the immediate roof.
Why other options are incorrect:
- b. Main fall: This refers to the larger, systemic collapse of the roof (goaf) that occurs once the critical span is reached, often involving the failure of the main roof strata.
- c. Air blast: This is a phenomenon where a large-scale roof collapse displaces a massive volume of air rapidly through the mine workings, creating a high-pressure wind blast; it is a result of a fall, not the fall itself.
- d. Rock burst: This is a violent, explosive failure of rock caused by the sudden release of accumulated elastic strain energy, typically occurring in deep mines under high geostatic pressure, rather than simply due to the withdrawal of supports.
Protodyakonov Index test is an indirect method for determination of:
A)
Shear strength of coal/rocks
B)
Young Modulus of coal/rocks
C)
Compressive strength of coal/rocks
D)
Tensile strength of coal/rocks
The Protodyakonov Index (also known as the Rock Strength Index or f) is a widely used empirical method in rock mechanics, particularly in mining engineering, to estimate the strength of rock masses. It is an indirect method used to determine the Uniaxial Compressive Strength (UCS) of the rock. The test involves measuring the amount of force required to crush a specific volume of rock or observing the fragmentation of the rock under a specific load. The index provides a numerical value that correlates directly to the compressive strength of the rock, allowing engineers to estimate support requirements for tunnels and mine galleries without performing expensive and time-consuming laboratory UCS tests on every sample.
Why other options are incorrect:
- Shear strength (a) is typically determined via direct shear tests or triaxial tests.
- Young's Modulus (b) is a measure of elasticity/stiffness, determined by the slope of the stress-strain curve during a compression test.
- Tensile strength (d) is usually determined via the Brazilian test (indirect) or direct tension tests.
For a circular opening of radius a, where the far –field stress value is P. The radial and tangential stresses at a distance r from the centre of the opening are
A)
σr = 0, σt = P(1 + a^2/r^2)
B)
σr = P(1 - a^2/r^2), σt = P(1 + a^2/r^2)
C)
σr = 2P(1 - a^2/r^2), σt = P(1 + a^2/r^2)
D)
σr = 3P, σt = 0
This problem refers to the Kirsch solution for a circular hole in an infinite elastic plate subjected to a hydrostatic (uniform) far-field stress P.
1. **Kirsch Equations for Hydrostatic Stress**: When a circular opening of radius 'a' is created in a rock mass subjected to a uniform far-field stress P (where σx = σy = P), the stress distribution around the hole is given by:
- Radial Stress (σr): σr = P(1 - a²/r²)
- Tangential/Hoop Stress (σt): σt = P(1 + a²/r²)
2. **Verification at Boundaries**:
- At the boundary of the opening (r = a):
σr = P(1 - a²/a²) = P(1 - 1) = 0. This is correct as the boundary of an unsupported opening is stress-free.
σt = P(1 + a²/a²) = P(1 + 1) = 2P. This shows the stress concentration factor is 2 at the wall.
- At the far-field (r → ∞):
σr = P(1 - 0) = P
σt = P(1 + 0) = P
This matches the given far-field stress condition.
3. **Evaluating Options**:
- Option (a) is incorrect because it suggests σr is always 0, which only happens at the boundary (r=a).
- Option (b) matches the derived Kirsch equations perfectly.
- Option (c) is incorrect as it introduces a coefficient of 2 for σr, which violates the far-field boundary condition.
- Option (d) is incorrect as it provides constant values regardless of the distance r.
Which of the following factor is considered for calculation of cycle time of excavating machine such as shovel, drag line etc.?
A)
Swell factor
B)
Bucket factor
C)
Swing factor
D)
Drill factor
Cycle time for excavating machinery (like shovels and draglines) is the total time taken to complete one full sequence of operations. A typical cycle consists of: 1. Digging/Loading, 2. Swinging (rotating the boom/arm to the dump point), 3. Dumping, and 4. Returning (swinging back to the digging point). The 'Swing factor' (or swing angle/time) is a critical component of the cycle time calculation because the time taken to move the material from the face to the haul truck or spoil pile depends directly on the angle of rotation.
Why other options are incorrect:
- a. Swell factor: This refers to the increase in volume of material when it is excavated from its natural state to a loose state. It affects the 'payload' or 'capacity' calculation, not the 'cycle time'.
- b. Bucket factor: This is a coefficient used to determine the actual volume of material a bucket carries relative to its rated capacity (fill factor). It affects productivity/volume per cycle, not the time taken for the cycle.
- d. Drill factor: This relates to drilling and blasting operations, which are separate processes from the excavation cycle of a shovel or dragline.
Passion’s ration can be expressed as:
A)
Lateral strain/ Longitudinal strain
B)
Longitudinal strain / Lateral strain
C)
Major principal stress/ Minor principal stress
D)
Normal stress/ Shear stress
The question contains a typographical error where 'Passion's ration' is written instead of 'Poisson's ratio'. Poisson's ratio (denoted by the Greek letter ν) is a fundamental material property in rock mechanics and elasticity. It is defined as the negative ratio of transverse (lateral) strain to axial (longitudinal) strain when a material is stretched or compressed in one direction. Mathematically, it is expressed as: ν = -(Lateral Strain / Longitudinal Strain). Since the options provide the ratios without the negative sign (which is standard in multiple-choice formats to indicate the magnitude of the relationship), option (a) is the correct definition.
Why other options are incorrect:
- Option (b) is the reciprocal of Poisson's ratio.
- Option (c) refers to the stress ratio, often used in Mohr-Coulomb failure criteria, but not Poisson's ratio.
- Option (d) describes the tangent of the angle of stress or is related to the definition of shear modulus, but not Poisson's ratio.
Tributary area method for stress estimation is valid for:
A)
Caving with Longwall
B)
Depillaring
C)
Development
D)
All cases
The Tributary Area Method (TAM) is a simplified approach used in rock mechanics to estimate the vertical stress acting on a pillar. It assumes that the pillar supports the entire weight of the rock column directly above it, plus a proportional share of the weight from the surrounding excavated areas (the 'tributary' area).
1. Why 'Development' is correct: During the development stage of a mine (e.g., creating a grid of pillars and galleries), the strata are generally assumed to be intact and the load is distributed statically. The TAM is most valid here because the pillars are designed to support the overburden without the complex dynamic stress redistributions associated with active caving.
2. Why 'Caving with Longwall' is incorrect: In longwall mining, the roof is intentionally collapsed (caved) behind the face. This creates a 'goaf' area. The stress is redistributed into a 'front abutment' and 'side abutment' pressure, which is far more complex than the simple vertical load distribution assumed by TAM.
3. Why 'Depillaring' is incorrect: Depillaring involves the systematic removal of pillars. This causes massive stress shifts, creating high-stress concentrations on the remaining pillars (abutment stresses) and potential instability. The static assumption of the Tributary Area Method fails to account for these dynamic stress transfers.
Therefore, the Tributary Area Method is a conservative estimation tool primarily valid for the initial development phase of pillar layouts.
Which of the following diagram can represent one aspect of bi-axial stress acting on a point with respect to a set of reference axes?
A)
Mohr’s circle diagram
B)
Rose diagram
C)
Intraformational shear diagram
D)
Goodman diagram
Mohr circle represents biaxial stress state w.r.t reference axes.
Mining method to protect the surface structure-
A)
Wide stall method
B)
Non effective width (NEW) of extraction method
C)
Both (a) & (b)
D)
None
In underground mining, surface protection is critical when mining beneath structures (like buildings, railways, or rivers). The 'Non-Effective Width' (NEW) concept is a specialized extraction method used to prevent surface subsidence. It involves leaving specific pillars or strips of coal/ore such that the width of the extracted area does not exceed a critical limit (the 'effective width'). If the width of the extraction is kept below this critical threshold, the overlying strata can bridge over the void, preventing the subsidence trough from reaching the surface and thereby protecting surface structures.
Option (a) 'Wide stall method' typically refers to a layout that increases the width of the extraction area, which generally increases the risk of surface subsidence rather than protecting against it. Therefore, the Non-Effective Width method is the technically correct approach for surface protection.
In longwall caving, the caving height is calculated from:
A)
Bulking factor and width of the longwall face
B)
Height of extraction and width of the longwall face
C)
Height of extraction and bulking factor
D)
Seam thickness and length of the panel
In longwall caving (also known as longwall collapse), the 'caving height' refers to the height of the strata that collapses into the goaf (the void left after coal extraction). The volume of the void created is determined by the height of extraction (the thickness of the seam being removed). However, as the overlying rock strata break and collapse, they undergo 'bulking'—meaning the broken rock occupies a larger volume than the original solid rock. The bulking factor is the ratio of the volume of the broken rock to the volume of the original solid rock. Therefore, the height to which the strata must cave to fill the void is a direct function of the height of extraction and the bulking factor of the material. Mathematically, if H is the height of extraction and B is the bulking factor (where B > 1), the caving height is related to the volume required to fill the void based on these two parameters.
Compressive strength of the rock can be expressed as:
A)
σ = Fc / A , where Fc is the failure load, and A is cross sectional area
B)
σ = A / Fc , where Fc is the failure load, and A is cross sectional area
C)
σ = Fc / V , where Fc is the failure load, and A is the Volume in m3
D)
σ = V / Fc , where Fc is the failure load, and A is the Volume in m3
In rock mechanics and materials science, compressive strength (σ) is defined as the maximum compressive stress that a material can withstand before failure. Stress is fundamentally defined as the force applied per unit area.
1. Formula derivation: Stress (σ) = Force (F) / Area (A).
2. In the context of compressive strength, the force used is the 'failure load' (Fc), which is the load at which the rock specimen breaks or yields.
3. The area (A) refers to the cross-sectional area of the specimen perpendicular to the direction of the applied load.
Evaluating the options:
- Option (a) correctly follows the formula σ = Fc / A.
- Option (b) is the reciprocal of the stress formula (Area/Force), which is incorrect.
- Option (c) divides load by volume, which does not represent stress (it would be load per unit volume).
- Option (d) divides volume by load, which is physically meaningless in the context of strength.
Punch shear test is used to determine:
A)
Tri-axial compressive strength
B)
Tensile strength
C)
Shear strength
D)
None of the above
The Punch Shear Test (also known as the Brazilian Test or Indirect Tensile Test in various contexts of rock mechanics) is specifically designed to determine the indirect tensile strength of rock samples. Because rocks are brittle and typically much weaker in tension than in compression, it is difficult to apply a direct uniaxial tensile load. In a punch shear or indirect tensile test, a cylindrical sample is loaded compressively along its diameter. This creates a transverse tensile stress perpendicular to the loading axis, causing the rock to split vertically. By measuring the load at which the sample fails, the indirect tensile strength can be calculated.
Why other options are incorrect:
- a. Tri-axial compressive strength is determined using a Tri-axial cell where the sample is subjected to confining pressure.
- c. Shear strength is typically determined using a Direct Shear Test or a Tri-axial test by analyzing the failure plane.
- d. This is incorrect as option b is the standard application of this test method.
With the increase in height, the strength of pillar:
A)
increases
B)
decreases
C)
is constant
D)
does not show any trend
In mining engineering and rock mechanics, the strength of a pillar is heavily dependent on its width-to-height (w/h) ratio. The strength of a pillar is inversely proportional to its height for a given width. As the height of the pillar increases, the w/h ratio decreases, making the pillar more slender. Slender pillars are more susceptible to buckling, lateral deformation, and the influence of structural discontinuities (joints/cleats) within the rock mass, which significantly reduces their overall load-bearing capacity. Most empirical formulas for pillar strength (such as the Obert-Duvall or Salamon-Munro formulas) incorporate the height in the denominator or as part of a ratio where an increase in height leads to a decrease in calculated strength.
The linear relationship between stress and strain can be represented by:
A)
σ = E * ε , where,ε is strain, is applied stress and E is modulus of elasticity
B)
ε = σ / E, where, is strain, is applied stress and E is modulus of elasticity
C)
E = σ / ε , where, is strain, is applied stress and E is modulus of elasticity
D)
σ = E / ε , where, is strain, is applied stress and E is modulus of elasticity
The question asks for the linear relationship between stress and strain, which is defined by Hooke's Law. Hooke's Law states that within the elastic limit of a material, the stress (σ) is directly proportional to the strain (ε). The constant of proportionality is known as the Modulus of Elasticity (E), also called Young's Modulus. Mathematically, this is expressed as σ ∝ ε, or σ = E * ε.
Analyzing the options:
- Option (a) σ = E * ε is the standard mathematical representation of Hooke's Law.
- Option (b) ε = σ / E is mathematically equivalent to σ = E * ε, but in the context of defining the 'relationship' (the governing law), the stress is typically expressed as a function of strain and the material property (E).
- Option (c) E = σ / ε is the formula used to calculate the Modulus of Elasticity, but it is a definition of the constant rather than the representation of the linear relationship between the two variables.
- Option (d) σ = E / ε is mathematically incorrect as it suggests an inverse relationship.
In engineering and rock mechanics textbooks, the primary linear constitutive equation is written as σ = Eε.
Rock mass classification is needed:
A)
For the assessment of stability of the mines
B)
For division of rock mass into group of similar behaviour
C)
For design of optimum support system in mines and tunnels
D)
All of the above
Rock mass classification systems (such as RMR - Rock Mass Rating, Q-system, and GSI - Geological Strength Index) are essential tools in rock mechanics and mining engineering for the following reasons:
1. **Assessment of Stability (Option a):** Classification systems provide a quantitative way to estimate the stand-up time of an unsupported excavation and the overall stability of the mine workings based on rock quality.
2. **Grouping by Behavior (Option b):** Because rock masses are heterogeneous, classification allows engineers to categorize different sections of a mine into groups with similar mechanical behaviors (e.g., 'Very Good', 'Fair', or 'Poor' rock), simplifying the engineering approach across large sites.
3. **Design of Support Systems (Option c):** The primary practical application of these systems is to determine the type and density of support required (e.g., rock bolts, shotcrete, or steel sets) to ensure the safety of tunnels and mine galleries, preventing over-design (which is costly) or under-design (which is dangerous).
Since all three statements are primary objectives of rock mass classification, option 'd' is the correct choice.
Dimension of modulus of elasticity (E) expressed with L, M and T is
A)
M L-1 T-2
B)
M L-1 T-1
C)
M L T-1
D)
M L T-2
The Modulus of Elasticity (E), also known as Young's Modulus, is defined as the ratio of tensile or compressive stress to the longitudinal strain.
1. **Formula**: E = Stress / Strain
2. **Stress**: Stress is defined as Force per unit Area.
- Force (F) = mass × acceleration = [M] × [L T⁻²] = [M L T⁻²]
- Area (A) = [L²]
- Therefore, Stress = [M L T⁻²] / [L²] = [M L⁻¹ T⁻²]
3. **Strain**: Strain is the ratio of change in length to original length.
- Strain = [L] / [L] = [Dimensionless] (or [M⁰ L⁰ T⁰])
4. **Calculation for E**:
- E = [M L⁻¹ T⁻²] / [1] = [M L⁻¹ T⁻²]
Comparing this result to the options:
- Option (a) M L⁻¹ T⁻² matches our derivation.
- Option (b) M L⁻¹ T⁻¹ is incorrect (incorrect time dimension).
- Option (c) M L T⁻¹ is incorrect (incorrect length and time dimensions).
- Option (d) M L T⁻² is the dimension of Force, not Modulus of Elasticity.