Outline - geo.cv.nctu.edu.tw

1 1 ChihChih--Ping LinPing LinNational National Mechanics Lateral Earth Pressure2 Outline Geotechnical applicationsGeotechnical applications KK00, active & passive states, active & passive states RankineRankine ssearth pressure theoryearth pressure theory CoulombCoulomb s earth pressure theorys earth pressure theory3 Lateral SupportIn geotechnical engineering, it is often necessary to prevent lateral soil movements. Cantilever retaining wallBraced excavationAnchored sheet pileTie rodSheet pileAnchor4 Lateral SupportWe have to estimate the lateral soil pressuresacting on these structures, to be able to design them. Gravity Retaining wallSoil nailingReinforced earth wall5 Soil Nailing6 Sheet PileSheet piles marked for driving7 Sheet PileSheet pile wall8 Sheet PileDuring installationSheet pile wall9 Reinforced Earth WallReinforced earth wallsare increasingly becoming WallCrib wallshave been used in stretchers and headersfilled with soilGood drainage & allow plant Pressure at Rest GLIn a homogeneous natural soil deposit,X h v the ratio h / v is a constant known as coefficient of earth pressure at rest (K0).

2 Importantly, at K0state, there are no lateral strains.''vhK =12 Estimating K0 For normally consolidated clays and granular soils, K0= 1 sin For overconsolidated clays, K0,overconsolidated= K0,normally elastic analysis, =10 KPoisson s ratio13 Example Earth Pressures-in granularsoilssmooth wallWall moves awayfrom soilWall moves towardssoilABLet s look at the soil elements A and B during the wall movement. 15 Active Earth Pressure-in granularsoilsA v h zAs the wall moves away from the soil, Initially, there is no lateral movement. v = z h = K0 v = K0 z v remains the same; and h decreases till failure stateActive state16 Active Earth Pressure-in granularsoils failure envelope v decreasing h Initially (K0state)Failure (Active state)As the wall moves away from the soil, active earth pressure17 Active Earth Pressure-in granularsoils v [ h ]active failure envelope ']'[vAactivehK =)2/45(tansin1sin12 =+ =AKRankine s coefficient of active earth pressureWJM Rankine(1820-1872)18 Active Earth Pressure-in granularsoils v [ h ]active failure envelope A v h 45 + /290+ Failure plane is at 45 + /2 to horizontal19 Active Earth Pressure-in granularsoilsA v h zAs the wall moves away from the soil, h decreases till failure movement h Active stateK0state20 Active Earth Pressure-in cohesivesoilsFollow the same steps as for granular soils.

3 Only difference is that c ']'[ = Everything else the same as for granular Earth Pressure-in granularsoilsB v h Initially, soil is in K0 the wall moves towards the soil, v remains the same, and h increases till failure state22 Passive Earth Pressure-in granularsoils failure envelope v Initially (K0state)Failure (Active state)As the wall moves towards the soil, increasing h passive earth pressure23 Passive Earth Pressure-in granularsoils v [ h ]passive failure envelope ']'[vPpassivehK =)2/45(tansin1sin12 += +=PKRankine s coefficient of passive earth pressure24 Passive Earth Pressure-in granularsoils v [ h ]passive failure envelope A v h 90+ Failure plane is at 45 - /2 to horizontal45 - /225 Passive Earth Pressure-in granularsoilsB v h As the wall moves towards the soil, h increases till failure movement h K0statePassive state26 Passive Earth Pressure-in cohesivesoilsFollow the same steps as for granular soils.

4 Only difference is that c ']'[+= Everything else the same as for granular Pressure Distribution-in granularsoils[ h ]passive[ h ]activeHhKA HKP hPA= KA H2PP= KP h2 PAand PPare the resultant active and passive thrusts on the wall28 Wall movement (not to scale) h Passive stateActive stateK0state29 Rankine s Earth Pressure Theory Assumes smooth wall Applicable only on vertical wallsPvPpassivehKcK2']'[+= AvAactivehKcK2']'[ = 30 Examples s Theory w/ Sloping Backfill'coscoscos'coscoscos2222 + =aK=0'coscoscos'coscoscos2222 +=pK35 Coulomb s Active Pressure(c)2001 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under s Passive Pressure(c)2001 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license.