Physical Properties of Rock, Soil and Water

Soil and Rock Mechanics

Resistance of soil and rock to

1. tensile, compressive and shear stresses
   • is the most important type of resistance governing the stability of rock masses
   • stress: force/unit area (Nm^-2), same units as pressure
   • tensile stress: pulling apart causing a change in volume (strain, e.g. angular deformation)
   • compressive stress: crushing or collapsing causing a change in volume
   • shear stress: deformation involves sliding within a body causing no change in volume but a change in shape (strain)
   • tectonic stresses (isostasy, orogenesis) are often tensile and compressive; but exogenic stresses (gravity and fluid stresses) are shear stresses
2. abrasion by solids moving over a rock surface (ice or rock fragments carried in wind, water, snow, ice or under the force of gravity; is controlled by the harness of constituent minerals and cementing agents
3. transport by fluids, i.e. bed shear stress

Behavior of rock

1. Elastic
   • a given stress always produces the same strain
   • maintaining a given stress results in constant strain
   • removal of stress results in complete recovery of strain
   • stress and strain are proportional (Hooke's law) up to the proportional limit
   • for rocks, the practical definition of the proportional and elastic limits are the same point
2. Plastic
   • plastic deformation does not occur until the yield stress is exceeded and bonds between mineral crystals are broken
   • beyond the yield stress, a uniform stress causes a constant rate of strain
   • typical behavior of most rocks (except dense fine grain rocks like basalt) is initially plastic as voids and fractures are closed, then elastic up to the elastic limit then plastic deformation up to the fracture point as shearing occurs between crystals
3. Brittle
   • rupture, complete failure, fracturing of rock

Strength of rock masses

Controls on resistance of rock to stress: lithology and structure

• lithology: mineral composition determines intact rock strength and susceptibility to weathering, especially chemical weathering
• structure: the spacing and orientation of discontinuities and rock units controls factors 3-8 below
• maximum relief = compressive strength (resistance to crushing) in Nm^-2/ unit weight in Nm^-3 = 1000's of meters for most rock
• but, cliffs of this height are rare, because rock mass strength is << than intact rock strength; strain is concentrated along discontinuities

Controls on rock mass stability

1. Strength of intact rock: cohesion and friction between mineral crystals and grains within rock blocks
2. Extent of weathering: from negligible discoloration and disaggregation to total disaggregation where the rock has weathered to sediment or soil
3. Spacing of joint and fractures: no cohesion along open joints, so the denser is jointing the weaker is the rock mass; failure in nearly always long preexisting discontinuities
   • caprocks in flat lying strata may have intact rock strength but often are more massive, i.e. have fewer fractures
4. Orientation of discontinuities (joints, bedding planes): those dipping out of a slope favour sliding of rock blocks
5. Width and roughness of fractures: no cohesion across open joints and friction only at points of contact between crystals or grains
6. Continuity of fractures: governs the likelihood that a fracture will form a failure surface; also circulation of water promotes deeper weathering
7. Amount of infill: strength along a joint is that of the infill
8. Water flow: excess cleft water pressure in a saturated joint applies a buoyant force on the overlying rock

Soil strength

shear strength (S)

resistance to shear force = f(normal force, friction, cohesion, pore pressure)

friction

mechanical resistance

• internal friction (phi) = plane friction (between plane surfaces) + interlocking friction (resistance due to roughness of surfaces)
• angle of repose : angle of rest of dry sediment,typically 25-40^o depending on particle size
• sliding angle: angle at which dry sediment fails, up to 10^o greater than the angle of repose
• angle of static friction > angle of dynamic friction, because failing material has momentum and usually comes to rest at angles < the angle of repose

cohesion (c)

• produced in rock by fusion of minerals or cementing of grains; eliminated by fracturing (brittle failure)
• in sediment results from electrostatic forces among fine particles (especially clay) and water
• with a surface area >> than mass, clay particles carry a negative charge and thus cohere in the presence of water (bipolar molecules)
• y-intercept on the plot of normal stress versus shear strength
• cohesion increases with soil moisture but only to a threshold above which porewater pressure forces particles apart counteracting normal force and reducing friction

pore pressure (p)

portion of the normal stress supported by air and water in interstitial spaces

• when soil is saturated, p = porewater pressure (u) > 0
• effective normal stress = normal stress - u, the stress exerted at grain contacts producing internal friction

positive porewater pressure is a buoyant force, that is, is supports part of the weight of the soil and therefore wet sediment has very low shear strength

Coulomb equation

1. dry soil
   • u is atmospheric
   • c = 0
   • S = normal stress * tan phi
2. wet soil
   • c > 0, u <0
   • effective normal stress = normal stress - (-u) = normal stress + u, that is water increases the normal stress (adds weight to the soil)
   • s = c + normal stress * tan phi
3. saturated soil
   • u > 0
   • S = c + (normal stress - u) tan phi

Note

• when c = 0 (# 2 above), tan phi = shear strength/ normal stress, when shear strength = shear stress, i.e. at the critical stability threshold (failure is imminent)
• therefore, tan phi = shear stress/ normal stress = W sin theta / W cos theta = tan theta
• or tan phi = tan theta, i.e. slope angle (theta) is governed by friction (phi)

Factor of Safety

shear strength/ shear stress

• = 1, critical threshold
• < 1, slope instability
• > 1, slope stability

Atterberg limits

behavoir of fine sediment:

plastic limit

water content at the transition from solid to plastic behavior, measured when a wet thread of fine soil begins to crumble

liquid limit

water content at transition from plastic to solid behavior, measured when soil in a shallow dish flows to close a 12.5 mm groove after 25 drops from 1 cm

plasticity index

liquid limit - plastic limit, that is the range of water content over which sediment behaves

Sensitive clay

• marine clays cemented with Na⁺
• "house of cards" or honeycomb structure
• Na+ is leached when the clays are exposed to subaerial conditions
• high porosity such that natural moisture contents can exceed the liquid limit
• sensitivity = undisturbed strength / disturbed strength
  • 2-4 for most clays
  • 8-16 for sensitive (quick) clays
• sensitive clay fails and flows when disturbed by erosion, heavy rain, heavy traffic, river ice breakup, etc.
• earth flows in Norway have been slowed by applying NaCl to the slope restoring the Na⁺ bonds
• earthflows are common in the glaciomarine (Leda) clay of the St. Lawrence lowlands
  • St. Jean-Vianney, Quebec, 1971; 31 deaths as retrogressive slumps engulfed 40 houses
  • Lemieux, Ontario 1993; a large landslide temporarily blocked the South Nation River

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