Lateral Earth Pressure
John Sturman
Rutgers University 180:473

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

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

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

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)

At-rest pressure

At-rest lateral earth pressure
σ v
= γz + q
σ h
= ko σ v
+ u where σ v
= the vertical overburden q = the surcharge pressure ko = the at-rest earth pressure coefficient, and u = the pore water pressure

At-rest lateral earth pressure
For most normally consolidated soils: ko = ~ 1 sinØ
For normally consolidated clays: ko = ~ 0.95 sinØ
For overconsolidated clays: ko
(overconsonsol)
= ko
(norm consol)
(OCR) -2

Active Earth Pressure - Rankine

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

Passive Earth Pressure - Rankine
 Use Relationships in Das 7.7

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

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

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

Check For Overturning

Check For Sliding

If the FS against sliding is too low

Check Against BC Failure