Rankines Undrained Case Flashcards
Active side undrained
When sigma_v’< 2Su that sigma_h becomes -ve, leading to tension cracks up to the depth where sigma_h = 0
- Angle of max obliquity at 45 degrees
Passive side undrainded
The two circles intersect with sigma_v being less than sigma_h from the start
- sigma_h/sigma_v varries with Su/sigma_v
- Angle of max obliquity at 45 degrees
Factors that limit the application of Rankine
- Initial stress state
- Soil properties
- Layering
- Wall properties (roughness and flexibility)
- Different pore pressure conditions
Experiment vs Rankines
- Small disp/H0 for active failure while large for passive
Active:
- Wall friction exerts an upwards F on the soil which makes layers bend up at the wall
- Wedge with angle approximating the inclination of the surface for max obliquity formed with the bottom part curved
- Forces reached are 10% lower than the rankine prediction
-Base not impactful
Passive:
-Wall friction exert downward force
-2 part rupture surface while there was only on for active
* One sliding and 1 wedge with angle approximating the inclination of the surface for max obliquity formed with the bottom part curved
- Several times higher than predicted
- Base had a big impact
Limitations of rankines method from experiments
- Doesnt account for wall friction
- Incorrect force estimation
- Cant account for sloped ground
- No consideration for concentrated surcharges
- Can handle non uniform PWP
Wall Friction
Always less than or equal to phi’
- lowest for high plasticity clays where sometimes its even less that phi_res’
- high for fine sand on rough conc
- low for clay against a coated wall
Affects
- Smaller active circle since sigma_v’ < (gamma.z - u) making sigma_h’ lower than the rankine prediction
- Bigger passive cricle since sigma_v’ > (gamma.z - u) making sigma_h’ higher than the rankine prediction
- For both
* Poles move to the friction failure surface so angle to planes of max obliquity changes
* Effects concentrated near the wall with Rankine applied far away
Wedge method
Coulomb is an example of a limit equilibrium method
- Assumes soil-soil failure along with wall-soil failure
-Equilibrium used to get wall F and wedge angle theta as well as the magnitude of the force normal to the soil-soil surface
* Theta is varries
* Solution is when Qa’ is at a max or Q’p is at the min
Accounts for:
- Irregular geometry
- Point loads
- Surcharges
- Wall friction
- Adhession
Wedge with cohesion and PWP
- Conditions
- Short term: undraind PWP strong and likely negative
- Active presssure increases at delta U dissipates
- can cause tension cracks which can be critical when filled with water
- Hc is the critical slope height for an unsupported cut and this falls will increased 50% with the addition of tension cracks and further falls when its filled with water
- Long term is drained in which can U must be known
Wedge with cohesion and PWP force set
-Only the forces @ the base are unknown since others can be found using earth pressures or PWP calcs
-The base forces are found using force equilibrium but the moment should also be satisfied
Wedge with cohesion and PWP stability checks
Forward sliding:
F = Q_bv’Tan(delta’)/Q_bh’ , with the numerator being the friction resistance being available at the base
Forward overturning:
F = Moment Resistance/Moment Mobilised, with F=1 being indicative of toppling for a rigid wall
- Apply momnet abount the corner of the foundation
-Q_bv’ should act in the middle third of the base so the leaver arm is taken as B/3
-Also check bearing capacity using the eccentricity of loading which can cause overturning/toppling at low loads
Bearing pressure:
-Max and min values found through moments, equations in terms of e are given
-Q_bv’ outside the middle third gives e>B/6 making q_min -ve and a non trapz distribution
-Check local failure under q_max
