1. Lateral Earth Pressure
John Sturman
Rutgers University 180:473

2. Lateral Earth Pressure- Introduction
We calculate vertical effective stress using the effective stress equations and principles we have previously discussed
In many cases we need to consider the horizontal (or lateral) pressures that a soil mass places on a wall, a pile, a braced cut or other structure

3. Coefficient of lateral earth pressure, k
We use the term k to refer to the ratio of lateral to vertical earth pressure.
K = σhorizontal / σvertical
(Do not confuse this k with the term for hydraulic conductivity)

4. K is a function of several factors, primarily
The ability of the structural member to move toward or away from the soil mass, and
The shear strength properties of the soil

6. We refer to the three different cases as
Ko for the at-rest condition, where there is no or insufficient movement
Ka for the active case where the structure can move or flex away from the soil mass
Kp for the passive case where the soil moves toward the structure (or vise versa)

7. At-rest pressure

8. At-rest lateral earth pressure
σv = γz + q
σh = ko σv + u
where σv = the vertical overburden
q = the surcharge pressure
ko = the at-rest earth pressure coefficient, and
u = the pore water pressure

9. At-rest lateral earth pressure
For most normally consolidated soils:
ko = ~ 1 - sinØ
For normally consolidated clays:
ko = ~ sinØ
For overconsolidated clays:
ko (overconsonsol) = ko(norm consol) (OCR) -2

10. Active Earth Pressure - Rankine

12. Active Earth Pressure - Rankine
Use ka equations in Das Sec. 7.3
Note that ka is only a function of the
friction angle but the lateral earth pressure includes the effect of cohesion on the structure

15. Passive Earth Pressure - Rankine
Use Relationships in Das 7.7

16. Lateral Earth Pressure - Coloumb
Coloumb developed a set of theories for lateral earth pressure that presume a failure surface to then consider wedges
Coloumb also assumed no friction force between the wall and the soil mass behind it

18. Rankine and Coloumb’s theories are remarkably similar
They result in similar resultant pressures
They have the ability to include inclined backfill
Rankine is simpler and is probably more commonly used for that reason
The same deflections to mobilize the earth forces are used

20. Stability Analyses on Retaining Walls
Overtuning
Sliding
Bearing Capacity Failure
Deep Shear Failure
Settlement

22. Check For Overturning

23. Check For Sliding

24. If the FS against sliding is too low

25. Check Against BC Failure