Friction and soil mechanics (wk 6)

What is the basic friction equation?

What is the friction angle?

• Maximum slope before soil slides

• Related to interparticle friction

• μ=tan⁡ϕ

What are two key properties of friction?

• Independent of apparent area → surface area

• Independent of velocity (magnitude)

Why is friction independent of apparent contact area?

According to bowden and tabor model

• True contact area is microscopic

  • in most materials σ_c is very high

    • E.g. in steel σ_c = 4000 Mpa

  • This means Atrue contact ÷ A surface area <<<< 1

    • i.e. out of total surface area, minimal is actually in contact

  • Surfaces touch only at asperities

• Friction arises from adhesion at true contact points

HOWEVER:

• Soft material friction depends on apparent contact area

• Bowden and Tabor model assumes hard surfaces

What did Bowden & Tabor discover?

• Normal force is directly proportional to true contact area

• Argued that the initial contact area is EXTREMELY small and there is a limiting normal stress (σ_c) at any asperity

• As the normal load is applied, ridges will be flattened until the load is spread over an area A_c such that N= σ_cA_c

  • As you increase the normal, more surface from each object comes into contact

  • Eventually each asperity is in contact with each other

What is the shear force needed to overcome friction?

• F=τA

• τ = shear strength of microscopic bonds

What is the physical meaning of the coefficient of friction?

a ratio of the shear strength of the bond to the limiting normal stress

Why do F1 cars have large tyres if friction is area‑independent?

• Bowden–Tabor applies to hard surfaces

• Tyres are soft materials

• Load spreads over full apparent area

• Friction depends on deformation, not µN

Surfers put wax on the top of the surfboard to enable them to stand up (to increase µ). Why do skiers put wax on the underside of their skis?

• Friction produces heat

• Melts snow directly under the ski, hence lubrication -> allows them to ski faster

• Ability of ski material to conduct heat is also critical. Metal skis would not work.

How does lubrication reduce friction?

• Adds fluid layer → hydrodynamic lubrication

• Reduces shear strength τc

• Prevents metal‑to‑metal contact

Avoids generation of excessive heat due to friction

What determines soil composition?

• Particle size (sand → clay)

  • Finest 25% of particles determines soil properties

    • Uniform distribution of fine particles in soil

      • Controls frictional properties

        • Affects strength and stiffness

      • Control pore size

        • Affects how easily soil drains

    • If more than 25% of soil are fine = less big particles in contact -> finer particles impact soil strength more than bigger particles

    • Movement of water moves through spaces between particles -> determined by finer particles

• Particle shape & mineral type

• Represented by grading curve

Why do fine particles control soil behaviour?

• Determine frictional strength

• Control pore size → drainage

• If >25% fines → fines dominate behaviour

• note: we assume soil has no tensile capacity

How do different soils drain?

• Clay: very slow (≈1×)

  • Construction in clay requires regular spaced drains to minimise time draining overall

  • Is fine and densely packed particles holds onto water -> can lead to waterlogging

• Sand & gravel: very fast

• Drainage time also depends on distance to free‑draining layer

Why use clay cores in earth dams?

• High friction → stability

• Low permeability → water barrier

  • point of a dam i

• Rockfill provides strength but cannot contain water

• Sand filter prevents mixing of clay & rockfill

What is effective stress?

 the difference between total stress and water pressure

• σ′=σ−u

• the actual stress carried by the soil skeleton (grain-to-grain contact)

• Controls strength & settlement

Why is effective stress zero at the seafloor (4000 m depth)?

• Total stress = water pressure

• Water supports the load

• No grain‑to‑grain contact stress

  • grain are actually hovering above each other

Why can sandcastles have slopes > friction angle?

• Suction (negative water pressure) increases effective stress

  • instead of particles being pulled away, they are pressed together

• Surface tension → negative pore pressure

• Stronger in finer soils (clay >> sand)

What is the angle of repose?

• Same as angle of friction

• Maximum stable slope angle for soil

• Slopes steeper than this are unstable

How does water affect the angle of repose?

• Water reduces effective stress

• Fills pore spaces → lowers friction

• Removes suction between grains

• Saturated soil has lower friction angle

What happens to friction angle when water flows out of a slope?

• Stable angle ≈ ½ of friction angle

Why are landslides associated with heavy rain?

• Rain increases pore water pressure

• Reduces effective stress

• Decreases frictional resistance

  • lubricates soil particles

What are rock discontinuities?

• Weakness planes separating rock blocks

• Examples: faults, joints, bedding planes, shear zones

• Control rock behaviour at shallow depth

What forces act on a rock block on a slope?

• Weight (W)

• Normal force (N)

• Frictional resistance (F = N tanθ)

• Water pressure force (F_water) → a distributed load (so need to calculate point load + the point from the base where it acts)

  • we draw water pressure as a right angle triangle since

    • Water pressure increases linearly with depth (height)

    • Water pressure = zero at the surface

calculate unknowns using equilibrium

When does sliding occur?

• When Fwater=friction=Ntan⁡θ

Why do we create ground models?

Identify soil types & depths

Predict ground behaviour

• Each layer is tested to identify its properties

  • Typical values of strength

  • Friction angle

  • Young's modulus (stiffness)

• Foundation design must consider

  • Stability -> is ground support enough?
    Serviceability -> how acceptable are deformations

Inform foundation design

• Columns transmit load to foundation -> foundation transmit load to ground

• column → (point load)→foundation pad → (pressure)→ ground

how to draw a geotechnical model

• Distance from point on x-axis

• Depth under ground on y-axis

What is the ground bearing requirement?

Ground bearing strength ≥ applied pressure

i.e. Strength of ground (kN) ≥ applied load (kN)

What is Poisson’s ratio?

• Ratio of lateral strain to axial strain

• When compressed vertically, soil expands laterally

What is the settlement formula for a circular loaded area?