mod7 Flashcards
three categories of failure
- planar, “infinite” slopes
- rotational failures
- wedge-type failures
F
Factor of Safety = available strength / actual stress
If F = 1
tan (phi’mob) = tan (phi’) – slope just at point of failure
If F > 1
tan ( phi’mob ) < tan (phi’) – slope is stable
If F < 1
the slope should fail as tan (phi’mob) cannot be greater than tan (phi’)
worst case scenario for infinite slope
fully saturated slope seepage parallel to slope
h = z cos^2 (beta)
steps in calculating a limit equilibrium mechanism solution
a) draw an arbitrary collapse mechanism of slip surfaces
b) calculate the statical equilbrium of the components of the mechanism to determine the strength mobilised in the soil or the external forces
c) examine other mechanisms to find the critical one for which the loading is the limit equilibrium load
Rotational failure of slopes assumes:
- that conditions of plane strain apply (conservative assumption)
- that failure occurs along a circular surface
(strong assumption for a fairly homogenous deposit)
(modification may be required for more inhomogenous slopes)
Assumptions of Taylor’s chart methods
- no cracks
- no surface loading
- constant shear strength with depth
- homogenous soil
Swedish Slip Circle Method
- used to examine more complex topography and situations where Cu is not constant throughout the slope
- can also include surface loads and tension cracks if need be
Total strain analysis methods
- Taylor’s chart methods
- Swedish slip circle method
Effective stress analysis methods
- Fellenius method
- Bishop’s simplified (or routine) method
Fellenius method
- assumed that the resultant of both the horizontal and vertical interslice forces is zero
- underestimates F by 5-20%
- simple but not very accurate (leads to an expensive design)
Bishop’s method
- assumed that vertical interslice forces have resultant of zero
ru
pore pressure ratio = pore water pressure / total vertical stress
ru = u / sigma
- can be calculated at the base of each slice