LATERAL EARTH PRESSURE AND RETAINING STRUCTURES
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1 Topic Outline LATERAL EARTH PRESSURE AND RETAINING STRUCTURES Types of retaining structures Lateral earth pressure Earth pressure at rest Rankine s Theory Coulomb s Theory Cullman s graphic solution Braced Cuts Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 1 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures Use of Retaining Walls (from Murthy, 003) Use of Retaining Walls (from Murthy, 003) Embankment Cut Bridge Abutment Water Storage Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 3 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 4 1
2 Use of Retaining Walls (from Murthy, 003) Types of Retaining Walls Flood Wall Sheet Pile Wall 1. Gravity walls a) Coherent gravity wall monolithic, unitary b) Stacked, articulated blocks resist local shear failure (gabions). Non-gravity walls a) Anchored or tie back walls b) Cantilever pile walls c) Braced cuts Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 5 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 6 Types of Rigid Retaining Walls (from Murthy, 003) Types of Rigid Retaining Walls (from Murthy, 003) Gravity Wall Semi-Gravity Wall Cantilever Wall Counterfort Wall Buttressed Wall Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 7 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 8
3 Anchored Soldier Piles Soil Mixing and Soldier Piles Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 9 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 10 Soil Mixing and Soldier Piles Bridge Abutment Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 11 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 1 3
4 Sheet Pile Wall Anchored Sheet Pile Wall Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 13 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 14 Soil Nailing Reinforced Soil Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 15 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 16 4
5 Reinforced Earth Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 17 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 18 Reinforced Earth Gabions Gravity Wall Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 19 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 0 5
6 Gabions Articulated Blocks Walls Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 1 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures Braced Cut External Stability Considerations for Walls Sliding Overturning PAH PAH N V N tan 15. P AH Reaction moment. Overturning moment 15 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 3 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 4 6
7 External Stability Considerations for Walls Lateral Earth Pressure at Rest and Active (from Das, 00) Tilting/bearing failure Mass stability failure PAH q ult av base. 5 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 5 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 6 Passive Earth Pressure (from Das, 00) Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 7 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 8 7
8 Development of Active and Passive Pressures (from Das, 003) Typical Displacement Values for Active and Passive States (from Das, 003) Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 9 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 30 Rotation of Frictionless Wall About the Bottom (from Das, 00) Rotation of Frictionless Wall About the Bottom (from Das, 00) Active State Passive State Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 31 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 3 8
9 Lateral Earth Pressure at Rest (from Das, 00) Lateral Earth Pressure at Rest When there is no soil movement K where K 0 is the coefficient of lateral earth pressure at rest. Jaky (1944), for granular soils H 0 Brooker and Ireland (1965), for normally consolidated clays K sin V K 0 1 sin Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 33 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 34 Lateral Earth Pressure at Rest Coefficient of Lateral Earth Pressure at Rest (from Murthy, 003) Sherif and Fang (1984), for dense sand backfill g d K0 ( 1 sin ) g d (min) where g d is the actual dry unit weight. For overconsolidated clays K K OCR 0( overconsolidated ) 0( normally consolidated ) Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 35 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 36 9
10 Distribution of Earth Pressure at Rest (from Das, 00) Distribution of Earth Pressure at Rest (from Das, 00) Effective stress Pore water pressure Moist soil Partially submerged soil Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 37 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 38 Distribution of Earth Pressure at Rest (from Das, 00) Rankine s Theory of Lateral Earth Pressure Key assumptions: Total horizontal pressure 1. Frictionless wall => V and H are principal stresses (for vertical wall and horizontal backfill).. Sufficient deformation or yielding occurs to develop a state of plastic equilibrium in the soil mass. Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 39 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 40 10
11 Rankine s Active Earth Pressure (Das, 00) Rankine s Active Earth Pressure From the geometry it can be derived that a gz tan 45 c tan 45 Coefficient of active earth pressure is K a tan Active state At rest leading to gzk c K a a a Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 41 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 4 Rankine s Active State (from Das, 00) Rankine s Passive Earth Pressure (Das, 00) At rest Passive state Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 43 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 44 11
12 Rankine s Passive Earth Pressure Rankine s Passive State (from Das, 00) From the geometry it can be derived that p gz tan 45 c tan 45 Coefficient of passive earth pressure is 0 0 K p tan 45 0 leading to gzk c K p p p Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 45 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 46 Typical Values for Active and Passive Rankine Coefficients for Sand Backfill Calculation of Rankine s Active Pressure c=0 (after Das, 00) K 0 K a K p K p 1 K a K gz a a Pa 1 KagH Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 47 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 48 1
13 Calculation of Rankine s Passive Pressure c=0 (after Das, 00) Calculation of Rankine s Active Pressure c=0 and GWT (after Das, 00) p K gz p a Ka ( q gz) Ka v ' Use moist unit weight K q g H g z H K a a 1 b 1 a v ' Pp 1 K pgh Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 49 Use submerged unit weight Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 50 Calculation of Rankine s Active Pressure c=0 and GWT (after Das, 00) Calculation of Rankine s Passive Pressure c=0 and GWT (after Das, 00) Active pressure Pore water pressure Total horizontal pressure K ( q gz) K ' p p p v Use moist unit weight K q g H g z H K p p 1 b 1 p v ' Use submerged unit weight Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 51 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 5 13
14 Calculation of Rankine s Passive Pressure c=0 and GWT (after Das, 00) Passive pressure Pore water pressure Total horizontal pressure From soil weight Rankine s Active Pressure for Cohesive Soil From cohesion gzk c K a a a After Das (00) Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 53 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 54 Rankine s Active Pressure for Cohesive Soil Rankine s Passive Pressure for Cohesive Soil (after Das, 00) Tensile cracks develop to a depth z 0 c g K a In calculation of the total active force, common practice is to take tensile cracks into account. This will lead to a reduced active force. gzk c K p p p Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 55 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 56 14
15 Rankine s Active and Passive Pressures with Sloping Backfill (from Das, 00) Coefficient of Active Pressure with Sloping Backfill (from Das, 00) cos cos cos K a cos cos cos cos cos cos cos K p cos cos cos cos Note: equations are for c=0. For cohesive soils K a and K p use different expressions. Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 57 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 58 Rankine s Active Pressure Example (Das 1.4) Rankine s Active Pressure Example (Das 1.4) Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 59 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 60 15
16 Rankine s Active Pressure Example (Das 1.4) Rankine s Active Pressure Example (Das 1.4) Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 61 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 6 Rankine s Active Pressure Example (Das 1.5) Rankine s Active Pressure Example (Das 1.5) Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 63 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 64 16
17 Coulomb s Active Pressure Theory (from Das, 00) Coulomb s Active Earth Pressure Rutgers University Active force Resultant on the failure plane Assumes wall friction and a planar failure surface. Weight of soil wedge Soil Mechanics Lateral Pressure & Retaining Structures 65 From the equilibrium of forces P a 1 cos( b) cos( ) sin( b ) gh 0 cos sin( b ) sin( 90 b ) dpa The critical value of b from leads to db 0 K a cos cos( ) 1 cos ( ) sin( ) sin( ) cos( ) cos( ) Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 66 Coulomb s Active Earth Pressure For =0 (no slope) and =0 (vertical wall) K a cos 1 cos sin( ) sin cos For =0 (no wall friction), Rankine s Coulomb s K a for b=0 and =90 0 (from Murthy, 003) K a cos 1 sin 1 sin 1 sin 1 sin 1 sin Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 67 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 68 17
18 Coulomb s K a for =0, b= and = (from Murthy, 003) Culmann s Solution for P a (from Das, 00) Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 69 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 70 Approximate Procedure to Find the Position of P a (from Das, 00) Coulomb s Passive Pressure Theory (from Das, 00) Wedge centroid Failure plane Passive force Weight of soil wedge Resultant on the failure plane Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 71 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 7 18
19 Coulomb s Passive Earth Pressure Culmann s Method Example (Das 1.8) Coulomb s coefficient of passive earth pressure cos ( ) K p sin( ) sin( ) cos cos( ) 1 cos( ) cos( ) For no slope and wall friction, and a vertical wall, equal to Rankine s K p cos 1 sin 1 sin 1 sin 1 sin tan 45 1 sin 0 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 73 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 74 Culmann Example (Das 1.8) Culmann s Method Example (Das 1.8) Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 75 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 76 19
20 Braced Cuts Frequently used in construction of trenches for utilities. Magnitude of pressures influenced by the deformation condition of sheeting. Braced Cut (from Das, 00) The deformation differs from the retaining wall, it is about the top. => Neither Rankine s nor Coulomb s theories will give actual earth pressures. Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 77 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 78 Braced Cut Chicago Subway Construction (R. Peck) Braced Cut Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 79 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 80 0
21 Braced Cut Seoul, South Korea (Richard Tsai) Earth Pressure Distribution Against the Wall (from Das, 00) At rest Deformation line Failure surface Active n a >1/3 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 81 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 8 Laboratory Observation of Lateral Pressure (Das, 00) Determination of Active Force on Bracing System (from Das, 00) Determined from the spiral equation r r e 1 tan 1 0 r O b r O B O b, O B Sand Known P 1 from the sum of moments about O 1 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 83 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 84 1
22 Determination of Active Force on Bracing System (from Das, 00) Normalized Active Force for Braced Cuts (after Kim and Preber, 1969) Solution Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 85 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 86 Active Pressure for Cuts in Cohesive Soils Pressure Variation for Design of Bracing (after Peck, 1969) The procedure is the same as for a cohesionless, except that point O is on the surface and the failure surface becomes circular. Das and Seeley (1975) P a N c KN c H ( 1 n ) (. )g a u ch and K f ca g c u c a adhesion along the face of sheet pile Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 87 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 88
23 Strut Loads (after Peck, 1969) Braced Cut Example (Das 13.) Assumed that vertical members are hinged at each strut, except top and bottom. Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 89 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 90 Braced Cut Example (Das 13.) Braced Cut Example (Das 13.) Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 91 Rutgers University Soil Mechanics Lateral Pressure & Retaining Structures 9 3
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