Doctormo
Geotechnical
- Jul 20, 2011
- 150
I would like to revisit lateral earth pressure from surcharges as it pertains to classical earth pressure theory (Coulomb/Rankine) and elastic theory (Bousinesseq) since it has bothered me for years. At the same time, I want to look at the argument for doubling Bousinesseq values.
When I look at a simple uniform surcharge condition on a vertical wall with a phi = 30 granular material, the lateral pressure relationship is Q x K with K being defined by the phi angle and wall displacement condition whereas Bousinesseq is typically simplified based on a Poisson's ratio of 0.50 and the phi angle is not part of the calculation. If the Bousinesseq strip load formula is run with no setback from a wall and an infinite depth to simulate a uniform load, a K value can be calculated also. So here goes:
Coulomb Ka = 0.297
Rankine Ka = 0.333
Ko condition = 0.500
Bousinesseq = 0.500
2xBousinesseq = 1.00
By this comparison, doubling Bousinesseq is twice the Ko condition and three times the typical active earth condition which seems to be unreasonable for most conventional retaining structures. I have never been able to accept the 2X factor for conventional retaining walls for that reason alone.
It sure seems to me that doubling the Bousinesseq values would be a function of a non-yielding wall that essentially pushes back against the load imposed and does not allow the soil to do any work (worse than Ko condition in some way?). You could use compacted crushed stone for backfill and the simplified Bousinesseq formulas in all the handbooks and textbooks would yield the same pressure increase so there is certainly a limitation to the simple formulas in practice.
Equally perplexing is that most retaining walls would be designed for active earth pressure for the base soil pressure then the surcharge would be added based on some sort of higher Ko condition or more which seems to be a little bit of adding apples and oranges together. If one was to use Bousinesseq then should the wall be designed for the Ko condition starting out?
It is not that I don't like Bousinesseq theory in concept but it fights with classical active earth pressure theory and wedge theory which is lot simpler to understand than elastic theories and of course, calculus. Both theories coexist in the same section of almost all text books yet they have never agreed in magnitude (or force location). Bowles made a stab at explaining some of the differences (such as with Spangler's testing) but everyone else leaves all the theories in the books with no comparison.
Just like to see what you all think about this since it never seems to get resolved.
When I look at a simple uniform surcharge condition on a vertical wall with a phi = 30 granular material, the lateral pressure relationship is Q x K with K being defined by the phi angle and wall displacement condition whereas Bousinesseq is typically simplified based on a Poisson's ratio of 0.50 and the phi angle is not part of the calculation. If the Bousinesseq strip load formula is run with no setback from a wall and an infinite depth to simulate a uniform load, a K value can be calculated also. So here goes:
Coulomb Ka = 0.297
Rankine Ka = 0.333
Ko condition = 0.500
Bousinesseq = 0.500
2xBousinesseq = 1.00
By this comparison, doubling Bousinesseq is twice the Ko condition and three times the typical active earth condition which seems to be unreasonable for most conventional retaining structures. I have never been able to accept the 2X factor for conventional retaining walls for that reason alone.
It sure seems to me that doubling the Bousinesseq values would be a function of a non-yielding wall that essentially pushes back against the load imposed and does not allow the soil to do any work (worse than Ko condition in some way?). You could use compacted crushed stone for backfill and the simplified Bousinesseq formulas in all the handbooks and textbooks would yield the same pressure increase so there is certainly a limitation to the simple formulas in practice.
Equally perplexing is that most retaining walls would be designed for active earth pressure for the base soil pressure then the surcharge would be added based on some sort of higher Ko condition or more which seems to be a little bit of adding apples and oranges together. If one was to use Bousinesseq then should the wall be designed for the Ko condition starting out?
It is not that I don't like Bousinesseq theory in concept but it fights with classical active earth pressure theory and wedge theory which is lot simpler to understand than elastic theories and of course, calculus. Both theories coexist in the same section of almost all text books yet they have never agreed in magnitude (or force location). Bowles made a stab at explaining some of the differences (such as with Spangler's testing) but everyone else leaves all the theories in the books with no comparison.
Just like to see what you all think about this since it never seems to get resolved.
