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Where does in-situ stress come from
Excavations disrupt the stress field and induce new stresses in the rock surrounding the opening.
Importance of rock mechanic stress
- 1.) Pre-existing stress state in the ground
- 2.) Engineering activities change the stress fields in rock masses – change of stress leads to instability; almost all failure criteria are expressed as a function of stress quantities.
- 3.) Stress is complex: it is a tensor (Note the difference between a scalar, a vector and a tensor).
- a.) normal & shear forces
- b.) normal & shear stresses (sigma = Force/Area)
Normal and Shear stress calculations
- 1.To have a basic knowledge of the stress state for engineering, e.g. in what direction and with what magnitude is the major principal stress acting? In what direction is the rock most likely to break? For such basic and direct engineering questions, a knowledge of the stress state is essential.
- 2. To have a specific knowledge of the boundary conditions for stress analyses conducted in the design phase of rock engineering projects.
- Can be measured by flat-jack, USBM gauge, CSIRO gauge
k value for horizontal stress calculation
- Shallow: k < than unity k = 1 – sin f’ (f’ = effective internal friction angle) e.g. when f’ = 35°, k=0.43
- Deep: k = 0.25+7Eh (0.001+1/H) Where Eh in GPa is the average deformation modulus of the overlying material, and H is the depth
Subduction zones cause high in-situ stress
Rock masses cooling at different rates will produce locked in local stresses
- Fracture is the mechanical response to large imposed stress
- Stresses are re-distributed as the rock strains. Discontinuities break the rock mass up into relatively small volumes, each with its own stress regime.
In-situ vs Induced stress
Point Load Test
Refer lab notes
- the maximum resistance that can be developed to external and internal stresses tending to cause failure. (Joint shear strength and UCS)
The stress-strain curve in uniaxial compression
Deformation, strength and failure of rock masses
- The properties of the mass depend not only on the properties of the intact material and the discontinuities, but also on the way in which they are combined.
- If a rock mass is loaded, its stress/strain curve will not be the same as that of intact rock — its modulus of deformation will be lower than the Young’s modulus for the intact rock, and its peak strength will also be lower.
Rock Mass Strength
method for obtaining estimates of the strength of jointed rock masses, based upon an assessment of the interlocking of rock blocks and the condition of the surfaces between these blocks. (p44, lecture 11)
- sigma prime 1 and 3 are max & min effective principal stresses at failure
- mb is Hoek-Brown constant
- s & a constants based on rock mass characteristics
- sigma ci is unaxial compressive strength of intact rock pieces
3 properties of rock mass estimated to use Hoek-Brown criterion for estimating the strength and deformability of jointed rock masses
- • Uniaxial Compressive Strength (UCS) of the intact rock pieces
- • Value of the Hoek-Brown constant mi for these intact rock pieces
- • Value of the Geological Strength Index GSI for the rock mass.
A rock pillar fails in compression when...
roof pressure exceeds UCS of the rock.
Shear failure takes place when...
shear stress exceeds shear strength.
Shear box test
- measure the strength of a material against failures in shear
- τ = σ tan(φ)
- σ is the stress applied normal to the shear plane
- φ = the angle of shearing resistance (in soil mechanics, φ is called the internal friction angle)
- For a single test, plot
- (a) Shear stress (kPa) vs Strain or
- (b) Shear resistance (kN) vs displacement (mm)or
- (c) Shear stress (kPa) vs displacement (mm)
Shear strength of rock joints in relation to rock slopes