GATE Mining Engineering Geomechanics and Ground Control Syllabus

Geomechanics and Ground Control syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Geomechanics and Ground Control in GATE Mining Engineering, not a summary of it.

1. 1

   Engineering Mechanics

   7 topics

   • Equivalent force systems
   • Equations of equilibrium
   • Two dimensional frames and trusses
   • Free body diagrams
   • Friction forces
   • Particle kinematics and dynamics
   • Beam analysis
2. 2

   Geomechanics

   8 topics

   • Geo-technical properties of rocks
   • Rock mass classification
   • Instrumentation and in-situ stress measurement techniques
   • Theories of rock failure
   • Ground vibrations
   • Stress distribution around mine openings
   • Subsidence
   • Slope stability
3. 3

   Ground Control

   4 topics

   • Design of pillars
   • Roof supporting systems
   • Mine filling
   • Strata Control and Monitoring Plan

Geomechanics and Ground Control flashcards for GATE Mining Engineering

19 of 51 cards from the Geomechanics and Ground Control deck — real questions with worked answers.

1. What is an equivalent force system, and what two conditions must two force systems satisfy to be equivalent?

   Two force systems are equivalent if they produce the same external effect on a rigid body. The conditions are equal resultant forces and equal resultant moments about any point: $\sum \vec{F}_1 = \sum \vec{F}_2$ and $\sum \vec{M}_{O,1} = \sum \vec{M}_{O,2}$.

2. How is a force $\vec{F}$ applied at point A replaced by an equivalent force-couple system at point B?

   Move the force $\vec{F}$ to B unchanged and add a couple moment $\vec{M} = \vec{r}_{B \to A} \times \vec{F}$, where $\vec{r}_{B \to A}$ is the position vector from B to A. This keeps both the resultant force and net moment identical.

3. State the three scalar equations of equilibrium for a rigid body in two dimensions (the xy-plane).

   $$\sum F_x = 0, \quad \sum F_y = 0, \quad \sum M_z = 0$$ The sum of forces in the x and y directions and the sum of moments about any point (perpendicular to the plane) must each be zero.

4. How many independent equilibrium equations exist for a general three-dimensional rigid body, and what are they?

   Six: $\sum F_x = 0$, $\sum F_y = 0$, $\sum F_z = 0$, $\sum M_x = 0$, $\sum M_y = 0$, $\sum M_z = 0$.

5. What is a free body diagram (FBD) and why is it essential in statics?

   An FBD is a sketch of a body isolated from its surroundings showing all external forces, reactions, and moments acting on it. It is essential because it allows correct application of the equilibrium equations by accounting for every force on the chosen system.

6. In a two-dimensional truss, what assumptions are made about members and joints?

   Members are straight, two-force members carrying only axial load (tension or compression); joints are frictionless pins; and all loads are applied only at the joints. Member weights are neglected or applied at joints.

7. State the equation for static determinacy of a plane truss with $m$ members, $r$ reactions, and $j$ joints.

   $$m + r = 2j$$ If $m + r = 2j$ the truss is statically determinate; if $m + r > 2j$ it is indeterminate; if $m + r < 2j$ it is a mechanism (unstable).

8. What is the difference between the method of joints and the method of sections for truss analysis?

   The method of joints applies $\sum F_x = 0$ and $\sum F_y = 0$ at each pin joint to find all member forces. The method of sections cuts through the truss and applies all three equilibrium equations to one part to directly find forces in selected members.

9. How is a frame distinguished from a truss in structural analysis?

   A frame contains at least one multi-force member (a member loaded at more than two points or carrying transverse loads), so members can develop axial force, shear, and bending moment. A truss has only two-force members carrying pure axial force.

10. State the law of dry (Coulomb) friction relating the maximum static friction force to the normal force.

    $$F_{s,\max} = \mu_s N$$ where $\mu_s$ is the coefficient of static friction and $N$ is the normal reaction. Once sliding begins, the kinetic friction is $F_k = \mu_k N$, with $\mu_k < \mu_s$.

11. Define the angle of friction $\phi$ and relate it to the coefficient of friction.

    The angle of friction $\phi$ is the angle the total reaction makes with the normal when sliding is impending: $$\tan \phi = \mu_s$$ It also equals the angle of repose, the steepest incline angle at which a block just begins to slide.

12. Write the basic kinematic equations for a particle undergoing constant acceleration $a$.

    $$v = u + at, \quad s = ut + \tfrac{1}{2}at^{2}, \quad v^{2} = u^{2} + 2as$$ where $u$ is initial velocity, $v$ is final velocity, $s$ is displacement, and $t$ is time.

13. State Newton's second law for a particle and its work-energy theorem form.

    Newton's second law: $\vec{F} = m\vec{a}$. The work-energy theorem states that net work equals change in kinetic energy: $$W_{net} = \Delta KE = \tfrac{1}{2}mv^{2} - \tfrac{1}{2}mu^{2}$$

14. For a beam, define shear force and bending moment at a cross-section.

    Shear force is the algebraic sum of all transverse (vertical) forces on one side of the section. Bending moment is the algebraic sum of the moments of all forces on one side of the section about that point.

15. State the differential relationships between distributed load $w$, shear force $V$, and bending moment $M$ along a beam.

    $$\frac{dV}{dx} = -w, \quad \frac{dM}{dx} = V, \quad \frac{d^{2}M}{dx^{2}} = -w$$ Shear is the slope of the moment diagram; the bending moment is maximum where shear is zero.

16. Write the flexure (bending) formula relating bending stress to bending moment in a beam.

    $$\frac{M}{I} = \frac{\sigma}{y} = \frac{E}{R}$$ where $M$ is bending moment, $I$ is the second moment of area, $\sigma$ is bending stress at distance $y$ from the neutral axis, $E$ is Young's modulus, and $R$ is the radius of curvature.

17. What is the maximum bending moment for a simply supported beam of span $L$ carrying a central point load $W$, and for a uniformly distributed load $w$?

    Central point load: $M_{\max} = \dfrac{WL}{4}$ at midspan. Uniformly distributed load: $M_{\max} = \dfrac{wL^{2}}{8}$ at midspan.

18. Define porosity and dry density as geotechnical properties of rocks, and give the relationship between porosity and void ratio.

    Porosity $n$ is the ratio of void volume to total volume; void ratio $e$ is void volume to solid volume, with $n = \dfrac{e}{1+e}$. Dry density is the mass of solids per unit total volume of the rock.

19. How is the Point Load Strength Index $I_{s(50)}$ used to estimate uniaxial compressive strength (UCS)?

    The point load index corrected to a 50 mm core gives $I_{s(50)}$, and UCS is estimated as approximately $$\sigma_c \approx 22\,I_{s(50)} \ \text{to}\ 24\,I_{s(50)}$$ (a factor of about 22-24 depending on rock type).

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