Lateral Earth Pressure in Geotechnical Engineering

What you’ll learn

What is Lateral Earth Pressure in Geotechnical Engineering?

Lateral Earth Pressure is the horizontal stress exerted by soil against earth retaining structures like retaining walls, excavations, and foundations.

It varies based on wall movements and soil conditions, directly affecting structural stability and design requirements.

Why Lateral Earth Pressure matters?

Incorrect estimation of lateral earth pressure may lead to structural failures, collapse, wall deflection, safety hazards, or even worse fatalities.

Types of Lateral Earth Pressure?

There are three categories based on wall movement and soil response.

1. At Rest Pressure

Occurs when there is no lateral movement of the soil mass. The wall is completely rigid.

$p_a=k_a\gamma h$

For Normally Consolidated Soil (Jacky’s Equation)

$K_o=1-sin \phi '$

For Overconsolidated Soils

$K_o=(1-sin \phi ' ) \sqrt{OCR}$

2. Active Earth Pressure

Develops when the retaining structure moves away from the soil

$K_a=\frac{1-sin \phi }{1+sin \phi }$

$K_a = tan^2 (45 - \frac{\phi}{2})$

$\theta_{cr} =45 + \frac{\phi}{2}$

3. Passive Earth Pressure

$K_p =\frac{1+sin \phi}{1-sin\phi}$

$K_p = tan^2 (45+\frac{\phi}{2})$

Rankine’s Theory, 1857

Assumes a planar failure surface
Consider soil friction angle and soil weight

Active Earth Pressure

when $\beta = 0^o$

Passive Earth Pressure

when $\beta = 0^o$

Coloumb’s Theory, 1857

Assumes a planar failure surface inclined at angle θ to the horizontal
Accounts for friction between soil and wall (wall adhesion and friction)
More accurate for walls with significant friction

Active Earth Pressure

Passive Earth Pressure

Lateral Earth Pressure on Retaining Walls

What are the main types of retaining walls?

Retaining walls are structured designed to prevent lateral movement of earth or other materials, classified by their structural configuration and stability mechanism

1. Gravity Retaining Wall

Built of plain concrete or masonry
Depends only on its own weight for stability
Suitable for heights at 3-4 meters
Simple Construction

2. Semi Gravity Wall

Gravity wall with wider base (toe or heel)
Increased stability due to extended base
Less concrete compared gravity walls
Suitable for medium heights (4-6 meters)

3. T-Shaped Cantilever Wall

Most common cantilever wall design
Stem cantilevers from base slab
Backfill weight contributes to stability
Economical for heights of 3-8 meters

4. L-Shaped Cantilever Wall

Used when property line restrictions exist
No heel extension behind wall
Less stable than T-shaped walls
Requires larger toe for stability

5. Counterfort Retaining Wall

Has three main components
- Base
- Stem
- Counterforts
Counterforts provide additional support
Suitable for heights greater than 8 meters
Reduced material usage for tall walls

Lateral Earth Pressure Distribution

Pressure distribution describes how lateral earth pressure varies with depth along a retaining wall. Rather than a single force value, it is important to know:

How pressure changes from top to bottom
When maximum pressure occurs
The shape of the pressure diagram
The location of the resultant force

In general, lateral earth pressure behaves the same as hydrostatic pressure.

The deeper it is, the value is greater.
Zero value at the surface (assuming no surcharge)
Linear distribution between two boundaries

Lateral Earth Pressure in Retaining Walls

In this Linear Distribution where it is cohesionless soil, pressure increase linearly with depth.

The resultant location from base:

The line of action of this resultant is located at the centroid of the triangular distribution where it is H/3.

$P=\frac{1}{2}K\times \gamma \times H^2$

Lateral Pressure

$\sigma_h(z)=K\gamma z$

Where:
$\sigma_h(z) =\: lateral \: pressure \: at \: depth \: z$
$K = earth \: pressure \: coefficient$
$\gamma=unit \: weight \: of \: soil$
$z = depth \: below \: surface$

In most cases, the backfill is inclined in some angle with respect to the horizontal, therefore the pressure distribution and the resultant are also inclined at that same angle.

What factors of safety are required for retaining wall design?

Retaining walls must satisfy stability requirements against sliding, overturning, and bearing capacity failure.

a. Factor of Safety against Sliding

$FS_s=\frac{Resisting \: Forces}{Sliding \:Forces}$

b. Factor of Safety against Overturning

$FS_o=\frac{Stabilizing \: Moment}{Overturning \: Moment}$

c. Bearing Capacity

Ensure foundation soil can support wall loads

References:

Principles of Geotechnical Engineering. Braja M. Das

Essentials of Soil Mechanics and Foundations ( 7th Edition). David F. McCarthy

Geotechnical Enfgineering – Principles and Practices (2nd Endition). Coduto, Yueng, and Kitch.

CH 11: SLOPE STABILITY

lateral Earth Pressure in Geotechnical Engineering: Complete Guide for Civil Engineers (2025)