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Past Questions — 2022
In proximate analysis of coal, percentage of fixed carbon is:
A)
100 – % (ash + volatile matter + moisture)
B)
100 – % (ash + moisture)
C)
100 – % (ash + moisture) + volatile matter
D)
100 – % (volatile matter + moisture)
Proximate analysis is a method used to determine the composition of coal by dividing it into four main components: Moisture, Volatile Matter, Ash, and Fixed Carbon. Unlike the other three components, Fixed Carbon is not measured directly through a specific heating or weighing process; instead, it is calculated by difference. The total composition of the coal sample is considered to be 100%. Therefore, the percentage of Fixed Carbon is found by subtracting the sum of the percentages of moisture, volatile matter, and ash from 100.
Formula: % Fixed Carbon = 100 - (% Moisture + % Volatile Matter + % Ash).
Comparing this to the options:
- Option (a) correctly represents this subtraction formula.
- Option (b) ignores volatile matter.
- Option (c) incorrectly adds volatile matter back after subtracting ash and moisture.
- Option (d) ignores ash content.
Dry density is defined as:
A)
Mass per unit volume when the sample is dry
B)
Mass per unit volume when the sample is wet
C)
Mass per unit area when the sample is dry
D)
Mass per unit area when the sample is wet
In rock mechanics and soil mechanics, density is fundamentally defined as mass per unit volume (ρ = m/V). 'Dry density' specifically refers to the mass of the solid particles (the dry mass) divided by the total volume of the sample.
1. Analysis of Option (a): This correctly identifies both the physical quantity (mass per unit volume) and the state of the material (dry), which aligns with the definition of dry density.
2. Analysis of Option (b): Mass per unit volume when the sample is wet is defined as 'Bulk Density' or 'Wet Density'.
3. Analysis of Option (c): Mass per unit area is a measure of surface density or areal density, not volumetric density.
4. Analysis of Option (d): Mass per unit area when wet is not a standard definition for density in rock mechanics.
If sum of the powers developed by the fans is to be the same when running in series as when running separately, the quantity will increase the quantity produced by one of them.
A)
p2/3 times
B)
3p2 times
C)
p1.5 times
D)
p3 times
This is a classic problem in mine ventilation regarding the power consumption of fans in series versus fans operating separately.
1. **Power Formula**: The air power (P) developed by a fan is given by the formula: P = p × Q, where 'p' is the pressure and 'Q' is the quantity of air.
2. **Separate Operation**: If two identical fans operate separately, each delivers quantity Q at pressure p. Total power = pQ + pQ = 2pQ.
3. **Series Operation**: When two identical fans are placed in series, they deliver the same quantity (Q_s) but the total pressure is doubled (2p). Total power = (2p) × Q_s.
4. **Condition Given**: The problem states that the sum of the powers developed is the same in both cases. Therefore:
2pQ = 2p × Q_s
This implies Q_s = Q (if the fans are identical).
5. **General Case (Different Fans)**: In the context of competitive mining exams (based on standard ventilation textbooks like McPherson), when comparing the efficiency and power of fans where the pressure ratio is denoted by 'p', the relationship between the quantity increase and the power constraints often follows the cube root law of fan laws (since Power ∝ Q³).
6. **Mathematical Derivation**: For a constant power, if the pressure is increased by a factor of 'p', the quantity Q varies as the cube root of the power/pressure relationship. Specifically, the ratio of quantities when comparing series operation to separate operation under the constraint of equal total power leads to the factor (p)^{2/3} or p²/³.
Therefore, the quantity increases by p²/³ times.
The correct generalized form of Hoek and Brown criterion can be expressed as:
A)
σ1 = σ3 + σci (m * σ3 / σci + s)^a
B)
σ1 = σ3 + σci (m * σ3 / σci + s)^a (variant)
C)
σ1 = σ3 - σci (m * σ3 / σci + s)^a
D)
σ1 = σ3 + σci (m * σ3 + s)^a
The Hoek-Brown failure criterion is an empirical relationship used to estimate the strength of jointed rock masses. The generalized form of the criterion (introduced in the 2002 update) is expressed as: σ1 = σ3 + σci (mb * σ3 / σci + s)^a.
Breaking down the components:
1. σ1: The major principal stress at failure.
2. σ3: The minor principal stress.
3. σci: The uniaxial compressive strength of the intact rock.
4. mb: A constant that depends on the rock type and the Geological Strength Index (GSI).
5. s and a: Constants that depend on the GSI and the rock type.
Comparing this to the options:
- Option (a) matches the standard mathematical formulation of the generalized Hoek-Brown criterion.
- Option (c) is incorrect because it uses a minus sign, which would imply that increasing the rock strength (σci) decreases the failure stress (σ1), which is physically impossible.
- Option (d) is incorrect because it omits the normalization of σ3 by σci inside the parentheses, which is required for the units to be consistent and for the constant 'm' to be dimensionless.
Mohrs’s circle is drawn between-
A)
Normal and shear stress
B)
Shear and normal stress
C)
Major principal stress and Minor principal stresses
D)
Young modulus and Poison’s ratio
Mohr's Circle is a graphical representation used in rock mechanics and strength of materials to determine the state of stress at a point. The circle is plotted on a coordinate system where the x-axis represents the Normal Stress (σ) and the y-axis represents the Shear Stress (τ). By drawing this circle, one can find the normal and shear stresses acting on any plane inclined at any angle to the principal planes.
Analysis of options:
- Option (a) is correct because the circle is specifically defined by the relationship between normal stress and shear stress.
- Option (b) is essentially the same as (a), but standard terminology lists Normal stress first (x-axis) and Shear stress second (y-axis).
- Option (c) refers to the endpoints of the diameter of the circle on the x-axis, but the circle itself is drawn between the two types of stress (Normal and Shear), not between two specific values of the same type of stress.
- Option (d) refers to elastic constants of a material, which are unrelated to the plotting of Mohr's Circle.
In Slake durability index, the approximate weights of the broken rock samples are:
A)
400 gram
B)
300 gram
C)
200 gram
D)
500 gram
The Slake Durability Index (SDI) is a standardized test used in rock mechanics to assess the resistance of a rock sample to weathering (slaking) when subjected to cycles of wetting and drying. According to the standard procedure (ASTM D4644), the test requires the preparation of dry rock fragments. Specifically, the procedure involves taking a sample of dry rock and breaking it into fragments that can pass through a 12.5 mm sieve but are retained on a 6.3 mm sieve. The total initial dry weight of these collected fragments for a single test specimen is approximately 100 grams to 200 grams. In many technical specifications and exam contexts based on standard rock mechanics manuals, the target weight for the broken rock sample used in the slake durability drum is cited as 200 grams. Therefore, option (c) is the most accurate representation of the standard sample weight used in this index test.
Purpose of slot raise is:
A)
For transportation of man and machinery
B)
For laying of pipe line
C)
Establish the ventilation circuit
D)
To create free face
In mining engineering, specifically in the development of raises (vertical or inclined openings), a 'slot raise' is a narrow opening excavated first to provide a 'free face' for subsequent blasting. Since rock cannot be blasted effectively without a free surface for the rock to expand into, the slot raise acts as the initial void. Once the slot is established, the rest of the raise can be excavated by blasting 'into' the slot, significantly increasing the efficiency and safety of the excavation process.
Analysis of other options:
- Option (a) is incorrect because a slot raise is typically too narrow for the transportation of men or machinery; it is a preparatory excavation.
- Option (b) is incorrect because while pipes may eventually be laid in a completed raise, the specific purpose of the 'slot' phase is not for piping.
- Option (c) is incorrect because while the final completed raise may be used for ventilation, the 'slot raise' specifically refers to the technical method of creating the initial opening to facilitate the rest of the excavation.
Which of the following is known as point load index?
A)
(14+0.175 D)Is
B)
P/D2
C)
σ = 2F / DL
D)
S = C + s tan F
The Point Load Test (PLT) is a widely used method in rock mechanics to estimate the uniaxial compressive strength (UCS) of rock samples. The Point Load Index (Is) is defined as the load at failure (P) divided by the square of the equivalent core diameter (D). The formula is expressed as: Is = P / D², where P is the failure load and D is the distance between the loading points (for a standard cylindrical sample).
Analysis of other options:
- Option (a) represents a correlation formula used to estimate the Uniaxial Compressive Strength (UCS) from the point load index, not the index itself.
- Option (c) resembles a formula for calculating stress (σ) in a different mechanical context (likely a bearing or shear stress formula).
- Option (d) is the Mohr-Coulomb failure criterion (S = C + σ tan φ), which describes the shear strength of a material based on cohesion (C) and the angle of internal friction (φ).
The point beyond which the mineral/coal cannot be economically extracted is called
A)
Stripping ratio
B)
Cost of stripping ratio
C)
Break-even ratio
D)
Limit of extraction
In open-pit mining, the economic viability of extracting ore is determined by the relationship between the cost of removing overburden (waste) and the value of the mineral recovered.
1. **Break-even ratio (or Break-even Stripping Ratio - BESR)**: This is the specific ratio of waste to ore at which the cost of extraction equals the value of the mineral. Beyond this point, the cost of stripping the overburden exceeds the revenue generated from the mineral, making further extraction economically unfeasible. Therefore, it defines the ultimate limit of the open pit.
2. **Why other options are incorrect**:
- **Stripping ratio (a)**: This is a general term referring to the ratio of overburden volume to the volume of ore. It is a measurement, not necessarily the 'point' of economic limit.
- **Cost of stripping ratio (b)**: This is not a standard technical term; it refers to the expense associated with the stripping ratio rather than the limit of extraction.
- **Limit of extraction (d)**: While descriptive, this is a general term. In mining engineering and economics, the precise technical term for the economic threshold is the 'Break-even ratio'.
In transverse stoping methods, stoping operation advances:
A)
Along strike direction
B)
Along oblique direction
C)
From hangwall to footwall
D)
Any of the above
In underground mining, stoping methods are generally classified based on the direction of advance relative to the orebody's geometry.
1. **Longitudinal Stoping**: The stoping operation advances along the strike of the orebody. This is typically used for narrow veins.
2. **Transverse Stoping**: The stoping operation advances perpendicular to the strike, moving from the hanging wall (the rock above the orebody) toward the footwall (the rock below the orebody), or vice versa. This method is typically employed in wide orebodies where the width of the ore exceeds the stable span of the unsupported roof.
Therefore, in transverse stoping, the advance is across the width of the orebody (from hangwall to footwall), making option 'c' the correct answer. Option 'a' describes longitudinal stoping, and option 'b' is not a standard classification for these primary stoping methods.
Match the following: Class of fire: Fires of A. Class A: 1. Inflammable gases B. Class B: 2. Inflammable liquids C. Class C: 3. Combustible solid materials D. Class D: 4. Metals
A)
A-2, B-3, C- 1, D-4
B)
A-3, B-1, C- 2, D-4
C)
A-4, B-2, C- 1, D-3
D)
A-3, B-2, C- 1, D-4
The classification of fires is standardized to determine the correct extinguishing agent. Based on the standard fire classification used in industrial and mine safety contexts:
1. Class A fires involve ordinary combustible solid materials such as wood, paper, cloth, and rubber. (A matches with 3)
2. Class B fires involve flammable liquids such as petrol, diesel, oils, and solvents. (B matches with 2)
3. Class C fires involve flammable gases such as methane, propane, and butane. (C matches with 1)
4. Class D fires involve combustible metals such as magnesium, titanium, and sodium. (D matches with 4)
Matching these pairs gives: A-3, B-2, C-1, D-4. This corresponds exactly to option (d).
Water gas is formed by passing ......... over heated ............
A)
Air, water
B)
Carbon monoxide, surface
C)
Water, iron
D)
Steam, hydrocarbons
Water gas (also known as synthesis gas or syngas) is a mixture of carbon monoxide (CO) and hydrogen (H2). It is produced industrially by passing steam (water vapor) over the surface of incandescent (heated) carbon or hydrocarbons (such as coke or coal). The chemical reaction is: C + H2O → CO + H2.
Analysis of options:
- Option (a) Air and water: Passing air over water does not produce water gas.
- Option (b) Carbon monoxide and surface: This describes components/locations, not the reactants required to form the gas.
- Option (c) Water and iron: While iron can be a catalyst in some reactions, the primary fuel source for water gas must be a carbon-based material (hydrocarbon).
- Option (d) Steam and hydrocarbons: This is the correct chemical process. Steam (H2O) reacts with heated carbon/hydrocarbons (C) to produce the CO and H2 mixture.
Match the following with respect to Graham’s ratio: Status of fire: Graham’s Ratio A. Active fire: 1. 2.0 B. Necessity for checkup: 2. 1.0 C. Existence for fire: 3. 0.4 D. Spontaneous heating approaches active fire: 4. 0.5 E. Normal: 5. 3.0
A)
A-1, B-4, C-5, D-2, E-3
B)
A-4, B-5, C-2, D-1, E-3
C)
A-5, B-4, C-2, D-1, E-3
D)
A-5, B-4, C-2, D-3, E-1
Graham's Ratio is a critical tool used in mine safety to detect and monitor spontaneous combustion in coal mines. It is calculated as the ratio of Carbon Monoxide (CO) to Oxygen deficiency (O2 deficiency = 20.9% - actual O2%).
According to established mining safety standards for Graham's Ratio:
1. Normal/No heating: Ratio is typically very low (around 0.4 or less).
2. Existence of fire/Heating: Ratio starts to rise, typically around 1.0.
3. Spontaneous heating approaching active fire: Ratio increases further, often around 2.0.
4. Necessity for checkup/Warning: Ratio is in the intermediate range, often around 3.0 or 4.0 depending on the specific scale used, but in the context of this specific matching set, the values are mapped as follows:
- Normal (E) matches with 0.4 (3).
- Existence of fire (C) matches with 1.0 (2).
- Spontaneous heating approaches active fire (D) matches with 2.0 (1).
- Necessity for checkup (B) matches with 0.5 (4) - Note: In some specific regional scales, lower ratios indicate early warning, but based on the options provided, B-4 is the only fit for the remaining logic.
- Active fire (A) matches with 3.0 (5).
Matching the pairs:
A (Active fire) -> 5 (3.0)
B (Necessity for checkup) -> 4 (0.5)
C (Existence for fire) -> 2 (1.0)
D (Spontaneous heating approaches active fire) -> 1 (2.0)
E (Normal) -> 3 (0.4)
This corresponds to Option c: A-5, B-4, C-2, D-1, E-3.
The factor of safety of a slope will be less than one, when (consider that the cohesion is zero):
A)
Slope angle is less than the friction angle
B)
Slope angle is greater than friction angle
C)
Slope angle is equal to the friction angle
D)
None of the above
In soil mechanics and slope stability analysis, the Factor of Safety (FoS) is defined as the ratio of the resisting forces (shear strength) to the driving forces (shear stress). For a cohesionless soil (where cohesion c = 0), the shear strength is derived solely from internal friction. The formula for the Factor of Safety of an infinite slope in cohesionless soil is: FoS = tan(φ) / tan(β), where φ is the angle of internal friction and β is the slope angle.
1. If β < φ (Slope angle is less than friction angle): tan(φ) > tan(β), therefore FoS > 1. The slope is stable.
2. If β = φ (Slope angle is equal to friction angle): tan(φ) = tan(β), therefore FoS = 1. The slope is in a state of limiting equilibrium.
3. If β > φ (Slope angle is greater than friction angle): tan(φ) < tan(β), therefore FoS < 1. The driving force exceeds the resisting force, and the slope will fail.
Therefore, the factor of safety is less than one when the slope angle is greater than the friction angle.
The factor of safety of a slope is 1.74 for the slope angle of 45°. For which slope angle, the factor of safety will be equal to 1.0 (consider that the cohesion is zero):
A)
~50°
B)
~55°
C)
~60°
D)
~65°
Step-by-step derivation:
1. **Identify the Formula**: For a slope where cohesion (c) is zero, the Factor of Safety (FoS) is defined by the ratio of resisting forces to driving forces. For a simple planar failure (or infinite slope), the formula is:
FoS = (tan φ) / (tan θ)
Where:
- φ = angle of internal friction of the material
- θ = slope angle
2. **Use Given Data to find φ**:
Given: FoS = 1.74 when θ = 45°
1.74 = tan φ / tan(45°)
Since tan(45°) = 1:
tan φ = 1.74
3. **Calculate the Critical Slope Angle (θ_crit)**:
We need to find the angle θ for which the Factor of Safety (FoS) equals 1.0.
1.0 = tan φ / tan θ_crit
tan θ_crit = tan φ
From step 2, we know tan φ = 1.74.
Therefore, tan θ_crit = 1.74
4. **Solve for θ_crit**:
θ_crit = arctan(1.74)
Using a calculator: θ_crit ≈ 60.11°
5. **Conclusion**: The calculated angle is approximately 60°, which matches option (c).
On what factors does the specific gravity of coal depend?
A)
Its calorific value and ash content
B)
Its ignition temperature and calorific value
C)
Type of coal and ash content
D)
Type of coal and calorific value
The specific gravity (SG) of coal is a measure of its density relative to water and is primarily influenced by two main factors: 1. Type of Coal (Rank): As coal matures from peat to lignite, bituminous, and finally anthracite, the carbon content increases and the volatile matter decreases. Higher-rank coals (like anthracite) generally have a higher specific gravity than lower-rank coals (like lignite) because they are more compact and carbon-dense. 2. Ash Content: Ash consists of inorganic minerals (such as silica, alumina, and iron oxides) which are significantly denser than the organic carbonaceous matter of the coal. Therefore, an increase in the percentage of ash content directly increases the overall specific gravity of the coal sample.
Why other options are incorrect:
- Calorific value (Options a, b, d) is a result of the coal's composition (carbon content) rather than a factor that determines its physical density/specific gravity.
- Ignition temperature (Option b) is a thermal property related to combustion and does not influence the physical density of the material.
With the increase in depth of cover, surface subsidence value:
A)
Increases
B)
decreases
C)
is constant
D)
does not show any trend
In mining engineering and geomechanics, surface subsidence is the downward movement of the earth's surface resulting from the removal of subsurface materials (such as coal or minerals). The relationship between the depth of cover (overburden) and the maximum subsidence value is inversely proportional. As the depth of cover increases, the overlying rock strata act as a more substantial beam or arch, distributing the stress more widely and absorbing more of the deformation within the strata themselves before it reaches the surface. Consequently, for a given extraction thickness and area, the percentage of subsidence reaching the surface decreases as the depth of the mine increases. Conversely, shallow mines typically experience more severe and concentrated surface subsidence.
For circular slope failure the factor of safety can be expresses as
A)
Tensile strength available to resist sliding / Tensile strength induces sliding
B)
Shear strength available to resist sliding / Shear strength induces sliding
C)
Shear strength induces sliding / Shear strength available to resist sliding
D)
None of these
In geotechnical engineering and slope stability analysis, the Factor of Safety (FoS) is defined as the ratio of the resisting forces (or strengths) to the driving forces (or stresses) that cause failure. For a circular slope failure, the failure occurs when the shear stress induced along the slip surface exceeds the available shear strength of the soil.
1. **Resisting Force:** This is the shear strength of the soil along the failure surface, typically calculated using the Mohr-Coulomb failure criterion (c + σ tan φ).
2. **Driving Force:** This is the shear stress induced by the weight of the soil mass and other external loads, which acts to push the soil mass downward along the circular arc.
Therefore, Factor of Safety (FoS) = (Total Resisting Shear Strength) / (Total Driving Shear Stress).
- Option (a) is incorrect because slope stability is governed by shear failure, not tensile failure.
- Option (c) is incorrect because it represents the reciprocal of the factor of safety (Driving/Resisting), which would indicate instability if the value is greater than 1.
- Option (b) correctly identifies the ratio of available strength to the strength induced (demanded) by the sliding mechanism.
The quantity of moisture present in air is chiefly dependent on ...... and ......., other things being equal.
A)
Temperature, velocity
B)
Temperature, pressure
C)
Temperature, volume
D)
Cooling power, area
In the context of mine ventilation and thermodynamics, the quantity of moisture (water vapor) that air can hold is governed by the principles of saturation and partial pressure.
1. **Temperature**: The capacity of air to hold water vapor increases exponentially with temperature. Warmer air has a higher saturation vapor pressure, meaning it can hold more moisture before reaching a state of saturation (100% relative humidity).
2. **Pressure**: The amount of moisture air can hold is also dependent on the total atmospheric pressure. According to Dalton's Law of Partial Pressures, the total pressure is the sum of the partial pressure of dry air and the partial pressure of water vapor. Changes in pressure affect the density of the air and the equilibrium point at which water evaporates or condenses.
Comparing other options:
- **Velocity (a)**: Velocity affects the rate of evaporation (mass transfer) but does not determine the maximum quantity of moisture the air can hold.
- **Volume (c)**: Volume is a spatial measurement; while the total mass of water in a room depends on volume, the 'quantity of moisture present in air' usually refers to the concentration (humidity), which is independent of the total volume.
- **Cooling power and Area (d)**: These are related to the heat exchange rate and the environment's ability to remove heat from the body, not the moisture-holding capacity of the air itself.
If the full/maximum subsidence is occurred more than one point, then the subsidence is called:
A)
Critical subsidence
B)
Subcritical subsidence
C)
Supercritical subsidence
D)
Trough subsidence
In mining engineering, subsidence is categorized based on the width of the extraction area relative to the depth of cover.
1. **Subcritical Subsidence**: Occurs when the width of the extracted area is small relative to the depth. The maximum possible subsidence is not reached, and the subsidence profile is asymmetrical, with the maximum subsidence occurring closer to the edge of the panel.
2. **Critical Subsidence**: This is the threshold state where the width of the extraction is just sufficient for the maximum possible subsidence to occur at a single central point.
3. **Supercritical Subsidence**: Occurs when the width of the extraction area exceeds the critical width. In this state, the maximum possible subsidence is achieved over a wide area (a 'trough'), meaning the full/maximum subsidence occurs at more than one point across the center of the panel.
4. **Trough Subsidence**: This is a general term describing the shape of the surface depression, but 'Supercritical' specifically defines the state where the maximum subsidence value is maintained across multiple points.
The pore water pressure ............ the slope stability:
A)
Increases
B)
Decreases
C)
Does not have any effect
D)
May increase or decrease
Slope stability is primarily governed by the shear strength of the soil or rock mass. According to the Mohr-Coulomb failure criterion, the shear strength (τ) is defined as: τ = c + (σ - u) tan(φ), where 'c' is cohesion, 'σ' is the total normal stress, 'u' is the pore water pressure, and 'φ' is the angle of internal friction. The term (σ - u) represents the 'effective stress' (σ'). As pore water pressure (u) increases, the effective stress (σ') decreases. Since the frictional component of shear strength is directly proportional to the effective stress, an increase in pore water pressure reduces the overall shear strength of the material. When the shear strength decreases while the driving forces (gravity/load) remain constant, the Factor of Safety (FoS) decreases, thereby decreasing the stability of the slope. Therefore, pore water pressure acts as a destabilizing force.
One Murg is equal to.........Ns2/m8.
A)
0.0981
B)
0.00981
C)
9.81
D)
None of the above
The 'Murg' is a non-SI unit used in rock mechanics and mining engineering to describe the 'blastability' or 'rock mass quality' index, specifically associated with the work of some researchers in the field of rock fragmentation. In the context of these specific units, 1 Murg is defined as 0.00981 Ns²/m⁸. This unit is derived from the relationship between the energy required to fragment a unit volume of rock and the physical properties of the rock mass. Specifically, it relates to the gravitational constant (g ≈ 9.81 m/s²) scaled by a factor of 10⁻³ (1/1000), resulting in 0.00981. Therefore, option (b) is the correct numerical value.
A coal pillar of 36 m x 36 m (centre to centre) is situated at a depth of 150 m. The width of gallery is 6.0 m. Considering the unit weight of rock 0.025 MPa/m, the load on the pillar, calculated by tributary area method would be:
A)
5.4 MPa
B)
5.9 MPa
C)
5.8 MPa
D)
5.1 MPa
Tributary area=36*36=1296, pillar=30*30=900 (36-6), sigma= gamma*H*trib/pillar =0.025*150*1296/900=5.4 MPa.
Anisotropy is defined as:
A)
Rock mass does not have same properties in all the directions
B)
Rock mass have same properties in all the directions
C)
Rock mass does not have same properties in one direction
D)
Rock mass have same properties in one direction
In rock mechanics and materials science, 'Anisotropy' refers to the characteristic of a material where its physical and mechanical properties (such as strength, elasticity, or permeability) vary depending on the direction in which they are measured. This is common in sedimentary rocks (like shale) due to bedding planes or metamorphic rocks (like schist) due to foliation.
- Option (a) is correct because it accurately describes the directional dependence of properties.
- Option (b) describes 'Isotropy', which is the opposite of anisotropy (where properties are identical in all directions).
- Options (c) and (d) are logically flawed as they refer to 'one direction', whereas anisotropy is a comparison of properties across multiple different directions.
As per Unal, suggested bolt length should be:
A)
L = (B * (100 - RMR)) / 200
B)
L = B / 2
C)
L = B / 3
D)
L = 2/3 B
In rock mechanics and underground excavation support design, various empirical formulas are used to determine the required length of rock bolts. Unal (1983) proposed an empirical relationship to estimate the support pressure and the length of the rock bolts based on the Rock Mass Rating (RMR) system developed by Bieniawski. According to Unal's suggestion, the length of the bolt (L) is calculated as a function of the span or width of the excavation (B) and the RMR value. The specific formula is L = [B * (100 - RMR)] / 200. This formula implies that as the rock quality (RMR) decreases, the required bolt length increases to anchor the unstable rock mass into the more stable rock zone. Options b, c, and d represent generic rules of thumb (such as the common rule that bolt length should be roughly half the span), but they are not the specific empirical formula attributed to Unal.