BE Civil Engineering (IOE, TU) Engineering Geology I (IOE, CE 552) Question Paper 2077 Nepal

Definition of a mineral

A mineral is a naturally occurring, inorganic, homogeneous solid with a definite (but not always fixed) chemical composition and an ordered internal atomic arrangement (crystalline structure). Examples: quartz ($SiO_2$), calcite ($CaCO_3$), orthoclase ($KAlSi_3O_8$).

Why minerals are the building blocks of rocks

A rock is an aggregate of one or more minerals (plus sometimes mineraloids/glass). The identity, proportion, grain size and bonding of the constituent minerals control the rock's strength, durability, permeability and weathering response. Hence rock engineering behaviour is ultimately rooted in mineralogy.

Principal physical properties (with engineering relevance)

Mohs scale and relative hardness

Mohs scale (1 talc -> 10 diamond) is an ordinal, relative scale: a mineral can scratch any mineral of equal or lower Mohs number and is scratched by any mineral of higher number. It does NOT give absolute hardness (the absolute hardness gap from 9 corundum to 10 diamond is very large).

Quartz (H = 7) vs Orthoclase (H = 6):

Since $7 > 6$, quartz will scratch orthoclase, and orthoclase cannot scratch quartz. This is consistent with the durability of quartz-rich rocks (quartzite, quartz sandstone) as engineering aggregate.

Folds

Folds are wave-like bends produced in originally planar rock layers (bedding, foliation) by compressive tectonic stress (ductile deformation). They are primary indicators of crustal shortening.

Principal parts of a fold

        axial plane
            |
  limb \    | hinge   / limb
        \   v        /
   ------ \----.----/ ------  (crest of anticline)
           \__/
            fold axis (line of max curvature)

• Limbs: the two sloping sides of the fold.
• Axial plane: the plane (or surface) that bisects the inter-limb angle, passing through hinge lines of successive beds.
• Hinge: the zone/line of maximum curvature on a folded surface.
• Fold axis (hinge line): line of intersection of the axial plane with a bedding surface.
• Crest: highest point of an upfold (anticline).
• Trough: lowest point of a downfold (syncline).

Classification (i): by attitude of axial plane

• Symmetrical (upright): axial plane vertical, limbs dip equally in opposite directions.
• Asymmetrical: axial plane inclined, limbs dip unequally.
• Overturned: axial plane strongly inclined, one limb rotated past vertical.
• Recumbent: axial plane nearly horizontal.
• Isoclinal: both limbs parallel (axial plane parallel to limbs).

Classification (ii): by inter-limb angle

Apparent dip calculation

Given: true dip $\delta_{true} = 30^{\circ}$, angle between cliff face and strike $\beta = 40^{\circ}$.

$$\tan(\delta_{app}) = \tan(\delta_{true})\cdot\sin\beta$$ $$\tan(\delta_{app}) = \tan(30^{\circ})\cdot\sin(40^{\circ}) = 0.57735 \times 0.64279 = 0.37113$$ $$\delta_{app} = \tan^{-1}(0.37113) = 20.36^{\circ}$$

The apparent dip in the cliff face is approximately $20.4^{\circ}$. (Note: apparent dip < true dip, as expected since the cliff is oblique to the strike.)

Plate tectonics theory

The Earth's rigid outer shell (lithosphere) is broken into about a dozen major plates that move (a few cm/yr) over the weaker, partly ductile asthenosphere. The driving mechanisms are mantle convection, ridge-push and slab-pull. Plates interact at their boundaries, producing earthquakes, volcanism and mountain building.

Three types of plate boundaries

1. Divergent (constructive): plates move apart; new oceanic lithosphere forms (mid-ocean ridges, e.g. Mid-Atlantic Ridge). Shallow earthquakes, basaltic volcanism.
2. Convergent (destructive): plates move together. Sub-types:
   • Ocean-continent / ocean-ocean: subduction, deep trenches, volcanic arcs (e.g. Andes).
   • Continent-continent: collision, no subduction of buoyant crust, fold mountains (e.g. Himalaya).
3. Transform (conservative): plates slide laterally past each other; lithosphere is neither created nor destroyed (e.g. San Andreas Fault). Shallow strike-slip earthquakes.

Origin of the Himalaya

About 50-55 million years ago the northward-drifting Indian Plate collided with the Eurasian Plate after the intervening Tethys Ocean was consumed by subduction. Because both are buoyant continental crust, the collision caused intense crustal shortening, stacking and uplift, raising the Himalayan range. Convergence continues today (~18-20 mm/yr of India-Tibet shortening), so the mountains are still rising.

High seismicity of Nepal

Nepal lies on the active collision front. The continuing underthrusting of India beneath Tibet builds elastic strain that is released as large earthquakes (e.g. 1934 Bihar-Nepal, 2015 Gorkha). Stress concentrates along major thrusts (MFT, MBT, MCT) and along the locked Main Himalayan Thrust ramp, making Nepal one of the most seismically hazardous regions in the world.

Principal underthrusting feature

The Indian Plate underthrusts beneath the Tibetan Plate along the Main Himalayan Thrust (MHT) - the basal decollement to which the surface thrusts MFT, MBT and MCT merge at depth.

Physical (mechanical) weathering breaks rock into smaller fragments without changing its chemical composition. Processes:

1. Frost wedging (freeze-thaw): water in cracks freezes, expands ~9%, prising rock apart.
2. Thermal expansion/insolation: repeated heating-cooling causes differential expansion and exfoliation.
3. Unloading (pressure release): removal of overburden allows expansion -> sheet jointing.
4. (Also: salt crystallisation, root/biological wedging.)

Chemical weathering alters the mineral composition, producing new (usually clay) minerals. Processes:

1. Hydrolysis: feldspar + water/acid -> clay minerals (kaolinite). The dominant decay of silicates.
2. Oxidation: $Fe^{2+}$ minerals react with oxygen -> iron oxides (rust staining).
3. Carbonation/dissolution: $CO_2 + H_2O -> H_2CO_3$, dissolving carbonates (karst).
4. (Also: hydration.)

Effect on engineering properties

Weathering reduces intact strength and stiffness, increases porosity and water absorption, lowers durability, transforms hard minerals into weak clays (reducing shear strength, increasing plasticity and swelling), and opens discontinuities - all of which degrade foundation, slope and aggregate quality.

Numerical solution

Porosity $n = 1 - \dfrac{\rho_{dry}}{\rho_{solid}}$ (the dry bulk density reflects solids in the total volume; assuming negligible bound water in the dry state).

Fresh granite:

$$n_{fresh} = 1 - \frac{2650}{2700} = 1 - 0.98148 = 0.01852 = \mathbf{1.85\%}$$

Weathered granite:

$$n_{weath} = 1 - \frac{2120}{2700} = 1 - 0.78519 = 0.21481 = \mathbf{21.48\%}$$

Percentage increase in porosity:

$$\frac{n_{weath} - n_{fresh}}{n_{fresh}}\times 100 = \frac{0.21481 - 0.01852}{0.01852}\times 100 = \frac{0.19630}{0.01852}\times 100 = \mathbf{1060\%\ (\approx 10.6\times)}$$

The porosity rises from about 1.85% to about 21.5%, an increase of roughly 1060% (about an 11-fold rise), reflecting severe weakening of the rock.

Major fluvial landforms

• Erosional: V-shaped valleys, gorges/canyons, waterfalls and rapids, potholes, river terraces, meander cut-banks.
• Depositional: alluvial fans, flood plains, natural levees, point bars, braided bars, deltas, ox-bow lakes.

Cycle (stages) of river erosion

(In Nepal the Himalayan rivers are largely youthful/mature due to active uplift, giving deep gorges ideal for high dams.)

Engineering significance for dams and bridges in Nepal

• Narrow youthful gorges (e.g. on the Trishuli, Karnali) give short, strong dam axes but pose problems of high sediment load, debris flows and bank instability.
• River terraces provide founding levels for bridge abutments but may be undercut.
• Meandering/braided reaches in valleys require careful scour-depth design for bridge piers.
• Aggradation/degradation trends, sediment yield and active faulting near river courses must be assessed for reservoir life and structure safety.

Gradient calculation

Vertical drop $= 1500\,\text{m}$, horizontal length $= 50\,\text{km} = 50000\,\text{m}$.

(i) As a ratio:

$$\text{gradient} = \frac{1500}{50000} = \frac{1}{33.33} \approx \mathbf{1:33.3}$$

(ii) In m/km:

$$\frac{1500\,\text{m}}{50\,\text{km}} = \mathbf{30\ m/km}$$

(iii) In percent:

$$\frac{1500}{50000}\times 100 = \mathbf{3\%}$$

The average channel gradient is 1:33.3, i.e. 30 m/km, i.e. 3% - a steep, youthful-stage gradient typical of Nepal's Himalayan rivers.

Three major rock groups

1. Igneous rocks: form by cooling and solidification of molten magma/lava. Intrusive (slow, coarse, e.g. granite) or extrusive (fast, fine, e.g. basalt).
2. Sedimentary rocks: form by weathering, transport, deposition and lithification (compaction + cementation) of sediments, or by chemical/organic precipitation. E.g. sandstone, limestone, shale.
3. Metamorphic rocks: form by solid-state alteration of pre-existing rocks under heat and/or pressure. E.g. gneiss, schist, slate, marble, quartzite.

Rock cycle (described sketch)

   Magma --cooling--> IGNEOUS
     ^                    |
     |              weathering/erosion
   melting               v
     |              SEDIMENT --lithification--> SEDIMENTARY
     |                                              |
  METAMORPHIC <----heat & pressure-----------------+
     |                                              |
     +----------heat & pressure---------------------+

Any rock can be transformed into another: igneous, sedimentary and metamorphic rocks are continuously recycled through melting, uplift, weathering, deposition and metamorphism, driven by internal (tectonic) and external (surface) energy.

Engineering examples in Nepal

• Igneous: granite - dimension stone, aggregate.
• Sedimentary: limestone/sandstone - limestone for cement (e.g. Udayapur, Chobhar), sandstone for masonry.
• Metamorphic: gneiss/slate - gneiss as aggregate and building stone; slate for traditional roofing.

Fault: a fracture (or fracture zone) in rock along which there has been appreciable relative displacement of the two sides.

Main elements

• Fault plane: the surface along which movement occurs (described by dip and strike).
• Hanging wall: the block resting above the inclined fault plane.
• Foot wall: the block lying below the inclined fault plane.
• Slip (net slip): total relative displacement measured along the fault plane.
• Throw: vertical component of the dip-slip displacement.
• Heave: horizontal component of the dip-slip displacement.

Classification by relative movement

1. Normal fault: hanging wall moves down relative to foot wall (tensional/extensional).
2. Reverse fault: hanging wall moves up relative to foot wall (compressional); a low-angle reverse fault is a thrust.
3. Strike-slip (transcurrent) fault: horizontal movement parallel to strike (dextral/sinistral).
4. Oblique-slip fault: combination of dip-slip and strike-slip.

Numerical solution

For dip-slip on a plane dipping at angle $\theta$ with net slip $S$:

$$\text{Throw} = S\sin\theta, \qquad \text{Heave} = S\cos\theta$$

Given $S = 40\,\text{m}$, $\theta = 60^{\circ}$:

$$\text{Throw} = 40\times\sin 60^{\circ} = 40\times 0.86603 = \mathbf{34.64\ m}$$ $$\text{Heave} = 40\times\cos 60^{\circ} = 40\times 0.5 = \mathbf{20.0\ m}$$

Check: $\sqrt{34.64^2 + 20.0^2} = \sqrt{1199.9 + 400.0} = \sqrt{1599.9} \approx 40\,\text{m}$ = net slip. Correct.

Throw = 34.64 m and heave = 20.0 m.

Joints: fractures in rock along which there has been no appreciable displacement parallel to the fracture surface (essentially opening/tensional or shrinkage cracks).

Joints vs faults

Effect on rock-mass behaviour

• Slope stability: joints oriented adversely (daylighting out of a slope, dip < slope angle) create planar/wedge/toppling failures.
• Permeability: joints are the main flow paths in hard rock; closely spaced, open joints raise mass permeability and seepage/leakage (important for dams, tunnels).
• Excavation: spacing and orientation control blockiness, overbreak, support needs and ease of ripping/blasting.

Volumetric joint count $J_v$

$$J_v = \frac{1}{S_1}+\frac{1}{S_2}+\frac{1}{S_3}$$ $$J_v = \frac{1}{0.50}+\frac{1}{0.40}+\frac{1}{0.25} = 2.0 + 2.5 + 4.0 = \mathbf{8.5\ joints/m^3}$$

Comment: By the standard $J_v$ description, $J_v$ of $3-10$ indicates a blocky / medium-sized block rock mass (roughly $J_v=8.5$ is at the small-to-medium end). Approximate block volume $\approx 0.50\times0.40\times0.25 = 0.05\,\text{m}^3$, i.e. blocks about half a metre across - a moderately fractured mass requiring attention to block stability in slopes and tunnels.

From south to north, Nepal is divided into five major physiographic-tectonic zones, separated by major thrust faults:

Principal boundary faults (thrusts), from south to north:

• MFT (Main Frontal Thrust / Himalayan Frontal Thrust): separates Terai from Siwalik.
• MBT (Main Boundary Thrust): separates Siwalik from Lesser Himalaya.
• MCT (Main Central Thrust): separates Lesser Himalaya from Higher Himalaya.
• STDS (South Tibetan Detachment System): separates Higher Himalaya from the Tethys Himalaya (a normal-sense detachment).

These zones and bounding thrusts reflect the southward propagation of the India-Asia collision and control Nepal's seismicity, slope stability and rock-engineering conditions.

Mass wasting: the downslope movement of rock, soil and debris under the direct action of gravity, without a primary transporting medium such as a stream or glacier.

Classification of main types

Principal causes in Nepal's hills + one mitigation each

Mass wasting is the dominant geohazard along Nepal's hill roads and settlements, and integrated drainage + bio-engineering + structural support is the standard control strategy.

Specific gravity (G): the ratio of the weight (or density) of a mineral to the weight of an equal volume of water at $4^{\circ}C$. It is dimensionless.

Engineering significance: G controls the unit weight of rock, hence dead loads on foundations and dams, the design of mineral-processing and the identification of heavy (ore) versus light (rock-forming) minerals; it also feeds into porosity/void calculations.

Numerical solution (Archimedes' principle)

Using the submerged-weight method:

$$G = \frac{W_{air}}{W_{air} - W_{water}}$$

The denominator $W_{air}-W_{water}$ equals the weight of water displaced (the buoyant force).

Given $W_{air} = 0.085\,\text{N}$, $W_{water} = 0.053\,\text{N}$:

$$W_{air} - W_{water} = 0.085 - 0.053 = 0.032\,\text{N}$$ $$G = \frac{0.085}{0.032} = 2.656$$

Specific gravity $\approx 2.66$.

Identification: $G = 2.66$ matches quartz (G $\approx$ 2.65) most closely (calcite is a bit higher at 2.71, galena is far heavier at 7.5). The specimen is most likely quartz.