9Lateral SupportReinforced earth walls are increasingly becoming popular.geosynthetics
10Interlocking stretchers and headers Lateral Supportfilled with soilCrib walls have been used in Queensland.Good drainage & allow plant growth.Looks good.Interlocking stretchers and headers
11Earth Pressure at Rest In a homogeneous natural soil deposit, v’ h’ GLv’h’Xthe ratio h’/v’ is a constant known as coefficient of earth pressure at rest (K0).Importantly, at K0 state, there are no lateral strains.
12Estimating K0 For normally consolidated clays and granular soils, K0 = 1 – sin ’For overconsolidated clays,K0,overconsolidated = K0,normally consolidated OCR0.5From elastic analysis,Poisson’s ratio
13Active/Passive Earth Pressures - in granular soilsWall moves away from soilWall moves towards soilABsmooth wallLet’s look at the soil elements A and B during the wall movement.
14Active Earth Pressure - in granular soils v’ = z Initially, there is no lateral movement.h’ = K0 v’ = K0 zAs the wall moves away from the soil,v’ remains the same; andh’ decreases till failure occurs.Active state
15Active Earth Pressure - in granular soils As the wall moves away from the soil,failure envelopeInitially (K0 state)Failure (Active state)v’decreasing h’active earth pressure
16Rankine’s coefficient of active earth pressure - in granular soilsfailure envelopeWJM Rankine( )[h’]activev’Rankine’s coefficient of active earth pressure
17Active Earth Pressure - in granular soils A v’ h’ [h’]active failure envelopeFailure plane is at45 + /2 to horizontalAv’h’45 + /290+[h’]activev’
18Active Earth Pressure - in granular soils As the wall moves away from the soil,h’ decreases till failure occurs.wall movementh’K0 stateAv’h’zActive state
19Active 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.
20Passive Earth Pressure - in granular soilsInitially, soil is in K0 state.As the wall moves towards the soil,v’ remains the same, andBv’h’h’ increases till failure occurs.Passive state
21Passive Earth Pressure - in granular soilsAs the wall moves towards the soil,failure envelopeInitially (K0 state)Failure (Active state)passive earth pressurev’increasing h’
22Passive Earth Pressure - in granular soilsfailure envelopev’[h’]passiveRankine’s coefficient of passive earth pressure
23Passive Earth Pressure - in granular soilsfailure envelopeFailure plane is at45 - /2 to horizontalAv’h’45 - /290+[h’]passivev’
24Passive Earth Pressure - in granular soilsAs the wall moves towards the soil,h’ increases till failure occurs.wall movementh’Passive stateBv’h’K0 state
25Passive Earth Pressure - in cohesive soilsFollow the same steps as for granular soils. Only difference is that c 0.Everything else the same as for granular soils.
26Earth Pressure Distribution - in granular soils[h’]activePA and PP are the resultant active and passive thrusts on the wallH[h’]passivePA=0.5 KAH2hPP=0.5 KPh2KPhKAH
27Wall movement (not to scale) h’Passive stateActive stateK0 state
28Rankine’s Earth Pressure Theory Assumes smooth wallApplicable only on vertical walls
32Gravity Retaining Walls cement mortarplain concrete or stone masonrycobblesThey rely on their self weight to support the backfill
33Cantilever Retaining Walls Reinforced; smaller section than gravity wallsThey act like vertical cantilever, fixed to the ground
34Design of Retaining Wall - in granular soils123Block no.toeWi = weight of block iAnalyse the stability of this rigid body with vertical walls (Rankine theory valid)xi = horizontal distance of centroid of block i from toe
35Safety against sliding along the base soil-concrete friction angle 0.5 – 0.7 to be greater than 1.5H123PAPPhStoeRyPP= 0.5 KPh2PA= 0.5 KAH2
36Safety against overturning about toe to be greater than 1.5H123PAPPhStoeRy
37Points to PonderHow does the key help in improving the stability against sliding?Shouldn’t we design retaining walls to resist at-rest (than active) earth pressures since the thrust on the wall is greater in K0 state (K0 > KA)?