# Lateral Earth Pressures

## Presentation on theme: "Lateral Earth Pressures"— Presentation transcript:

Lateral Earth Pressures
N. Sivakugan Duration: 18 min

Contents A 2-minute break Geotechnical applications
K0, active & passive states Rankine’s earth pressure theory A 2-minute break Design of retaining walls A Mini Quiz

Lateral Support In geotechnical engineering, it is often necessary to prevent lateral soil movements. Tie rod Sheet pile Anchor Cantilever retaining wall Braced excavation Anchored sheet pile

Lateral Support We have to estimate the lateral soil pressures acting on these structures, to be able to design them. Soil nailing Gravity Retaining wall Reinforced earth wall

Soil Nailing

Sheet piles marked for driving

Sheet Pile Sheet pile wall

Sheet Pile Sheet pile wall During installation

Lateral Support Reinforced earth walls are increasingly becoming popular. geosynthetics

Lateral Support filled with soil Crib walls have been used in Queensland. Good drainage & allow plant growth. Looks good. Interlocking stretchers and headers

Earth Pressure at Rest In a homogeneous natural soil deposit, v’ h’
GL v’ h’ X the ratio h’/v’ is a constant known as coefficient of earth pressure at rest (K0). Importantly, at K0 state, there are no lateral strains.

Estimating K0 For normally consolidated clays and granular soils,
K0 = 1 – sin ’ For overconsolidated clays, K0,overconsolidated = K0,normally consolidated OCR0.5 From elastic analysis, Poisson’s ratio

Active/Passive Earth Pressures
- in granular soils Wall moves away from soil Wall moves towards soil A B smooth wall Let’s look at the soil elements A and B during the wall movement.

Active Earth Pressure - in granular soils v’ = z
Initially, there is no lateral movement. h’ = K0 v’ = K0 z As the wall moves away from the soil, v’ remains the same; and h’ decreases till failure occurs. Active state

Active Earth Pressure - in granular soils
As the wall moves away from the soil, failure envelope Initially (K0 state) Failure (Active state) v’ decreasing h’ active earth pressure

Rankine’s coefficient of active earth pressure
- in granular soils failure envelope WJM Rankine ( ) [h’]active v’ Rankine’s coefficient of active earth pressure

Active Earth Pressure - in granular soils    A v’ h’ [h’]active
failure envelope Failure plane is at 45 + /2 to horizontal A v’ h’ 45 + /2 90+ [h’]active v’

Active Earth Pressure - in granular soils
As the wall moves away from the soil, h’ decreases till failure occurs. wall movement h’ K0 state A v’ h’ z Active state

Active Earth Pressure - in cohesive soils
Follow the same steps as for granular soils. Only difference is that c  0. Everything else the same as for granular soils.

Passive Earth Pressure
- in granular soils Initially, soil is in K0 state. As the wall moves towards the soil, v’ remains the same, and B v’ h’ h’ increases till failure occurs. Passive state

Passive Earth Pressure
- in granular soils As the wall moves towards the soil, failure envelope Initially (K0 state) Failure (Active state) passive earth pressure v’ increasing h’

Passive Earth Pressure
- in granular soils failure envelope v’ [h’]passive Rankine’s coefficient of passive earth pressure

Passive Earth Pressure
- in granular soils failure envelope Failure plane is at 45 - /2 to horizontal A v’ h’ 45 - /2 90+ [h’]passive v’

Passive Earth Pressure
- in granular soils As the wall moves towards the soil, h’ increases till failure occurs. wall movement h’ Passive state B v’ h’ K0 state

Passive Earth Pressure
- in cohesive soils Follow the same steps as for granular soils. Only difference is that c  0. Everything else the same as for granular soils.

Earth Pressure Distribution
- in granular soils [h’]active PA and PP are the resultant active and passive thrusts on the wall H [h’]passive PA=0.5 KAH2 h PP=0.5 KPh2 KPh KAH

Wall movement (not to scale)
h’ Passive state Active state K0 state

Rankine’s Earth Pressure Theory
Assumes smooth wall Applicable only on vertical walls

Retaining Walls - Applications

Retaining Walls - Applications
highway

Retaining Walls - Applications
High-rise building basement wall

Gravity Retaining Walls
cement mortar plain concrete or stone masonry cobbles They rely on their self weight to support the backfill

Cantilever Retaining Walls
Reinforced; smaller section than gravity walls They act like vertical cantilever, fixed to the ground

Design of Retaining Wall
- in granular soils 1 2 3 Block no. toe Wi = weight of block i Analyse the stability of this rigid body with vertical walls (Rankine theory valid) xi = horizontal distance of centroid of block i from toe

Safety against sliding along the base
soil-concrete friction angle  0.5 – 0.7  to be greater than 1.5 H 1 2 3 PA PP h S toe R y PP= 0.5 KPh2 PA= 0.5 KAH2