ROCK MECHANICS The study of rock behavior in the solid state under varying environmental and internal conditions Main focus is how rocks respond to applied stresses, especially those that naturally occur due to: –Gravity –Mantle Convection –Plate Tectonics –Diapiric Movements: magma, salt diapirs

Stress Same as Pressure = Force/Area Units in Earth Sciences are MPa = 10 6 Pa = 10 bars =10 atm = 147 psi

STRAIN Response to or result of applied stress Linear strain is defined as (L 1 – L 0 )/L 0 Units are ???? (unitless) Volumetric strain = (V 1 -V 0 )/V 0 Units are ????? Areal Strain = (A 1 -A 0 )/A 0 Strain is usually expressed as a percent change

ENVIRONMENTAL CONDITIONS affecting rock behavior Stress Factors: –Applied Stress –Stress History Duration How stress applied over time –Temperature –Pore Fluids and Pressure

Lithospheric Pressure Aka Confining Pressure The vertical component can be calculated as Pc =  gz, Where  = average density in g/cc, g= grav. constant, z = depth In the Lithosphere Pc increases at about MPa/km In general Pc increases at  *10 MPa/km

Pressure vs. Depth in Earth

Geothermal Gradient T increases in the Lithosphere at 25 0 C/km T continues to increase all the way to the core, but at a lower rate The melting T of Quartz is C The melting T of Feldspar >1100 The melting T of calcite is 910

Temperature vs. Depth in the Earth

Horizontal Stresses in the Earth do not equal vertical load,  gz, but are about of  v depending on composition, porosity, pore fluids

INTERNAL CONDITIONS affecting rock behavior Composition ( silicates and oxides most resistant to strain ) Texture/Fabric ( phaneritic most resistant ) Pores, cracks, flaws Previous stresses stored in grains Degree of Weathering ( minerals that weather from oxides and silicates to other compounds are weakened ) Presence of fluids in pores or cracks

Rock Texture/Fabric Grain size Interlocking or grains in cement? Sorting Foliation/ non-foliated Sedimentary layering

Textures Note: Most Strain is not due to breaking bonds, but is due to slip of grains against each other, or between grains and cement

Porosity vs. Depth

Rigid and Brittle Behaviors Rigid: No strain, no response Most rocks show rigid behavior at room T and no Pc, and at stresses below Pa – Brittle: No strain before failure In ideal brittle behavior, if stress is removed before rock fails, there will be no internal signs of strain