Chapter 12 Lateral Earth Pressure AtRest Rankine and
- Slides: 73
Chapter 12 Lateral Earth Pressure : At-Rest, Rankine, and Coulomb 연세대학교 지반공학연구실 Soil Substructure Interaction Lab.
Introduction - Retaining Structures : retaining walls, basement walls, bulkhead, temporary retaining wall - 구조물에 작용하는 토압의 분포는 구조물과 흙의 상대적인 변위에 따라 달라짐 변위 토압 - 토압의 크기 : 배면지반의 강도정수와 관련(cu, u or c , ), 배수조건 Soil Substructure Interaction Lab.
12. 1 At-Rest, Active, and Passive Pressure at rest Soil Substructure Interaction Lab.
12. 1 At-Rest, Active, and Passive Pressure Active Pressure Soil Substructure Interaction Lab.
12. 1 At-Rest, Active, and Passive Pressure Soil Substructure Interaction Lab.
12. 1 At-Rest, Active, and Passive Pressure : Variation of the magnitude of lateral earth pressure with wall tilt Soil Substructure Interaction Lab.
12. 2 Earth Pressure at Rest - Assume • frictionless wall : No shear stress on the vertical & Horizintal planes • Elastic equilibrium : horizontal strain is ZERO Fig. 12. 3 Earth pressure at rest Soil Substructure Interaction Lab.
12. 2 Earth Pressure at Rest - h = K 0 v = K 0 ( z), - K 0= Coeffi. of earth pressure at Rest Soil Substructure Interaction Lab.
12. 2 Earth Pressure at Rest -Elasticity Soil Substructure Interaction Lab.
12. 2 Earth Pressure at Rest Soil Substructure Interaction Lab.
12. 2 Earth Pressure at Rest - Soil is elasto-plastic behavior Jaky, 1944) : 사질토, NC clay (OC clay) Comments on Earth PR. Increase caused by Compaction - Jaky’s eq. : good results for loose sand backfill - For a dense sand backfill (Sherif, Fang, 1984) Soil Substructure Interaction Lab.
12. 2 Earth Pressure at Rest where, d : actual compacted dry unit wt. of the sand d, min : the loosest dry unit wt. Soil Substructure Interaction Lab.
12. 2 Earth Pressure at Rest (total force per unit length of the wall) Fig. 12. 4 Distribution of earth pressure at rest on a wall Soil Substructure Interaction Lab.
12. 3 Earth Pressure at Rest for Partially Submerged Soil - Partially submerged soil (ground W. T) z < H 1 z > H 1 Soil Substructure Interaction Lab.
12. 3 Earth Pressure at Rest for Partially Submerged Soil Substructure Interaction Lab.
12. 3 Earth Pressure at Rest for Partially Submerged Soil Fig. 12. 5 Distribution of earth pressure at rest for partially submerged soil Example 12. 1 Soil Substructure Interaction Lab.
12. 4 Lateral Pressure on Retaining Walls from Surcharges Based on Theory of Elasticity - Point load Surcharge, Q - Line load Surcharge, q (load/unit length) - Strip load Surcharge, q/unit area Example 12. 2 Soil Substructure Interaction Lab.
12. 5 & 12. 6 Rankine’s Theory of Active & Passive Earth Pressures - Rankine Theory(1857)-Limiting Plastic Equilibrium - Assume : No Friction between wall and soil smooth wall z H Soil Substructure Interaction Lab.
12. 5 & 12. 6 Rankine’s Theory of Active & Passive Earth Pressures Fig. 12. 9 Rankine’s active earth pressure Soil Substructure Interaction Lab.
12. 5 & 12. 6 Rankine’s Theory of Active & Passive Earth Pressures -Rankine’s Active state where, (Rankine’s active earth pressure) Soil Substructure Interaction Lab.
12. 5 & 12. 6 Rankine’s Theory of Active & Passive Earth Pressures If c=0 (for cohesionless soils) : Coefficient of active earth Pressure. Soil Substructure Interaction Lab.
12. 5 & 12. 6 Rankine’s Theory of Active & Passive Earth Pressures Active state Soil Substructure Interaction Lab.
12. 5 & 12. 6 Rankine’s Theory of Active & Passive Earth Pressures Z 0 + = H Pa Fig. 12. 11(a) Rotation of frictionless wall about the bottom Soil Substructure Interaction Lab.
12. 5 & 12. 6 Rankine’s Theory of Active & Passive Earth Pressures <tension crack depth> Total active force Soil Substructure Interaction Lab.
12. 5 & 12. 6 Rankine’s Theory of Active & Passive Earth Pressures Acting at Soil Substructure Interaction Lab.
12. 5 & 12. 6 Rankine’s Theory of Active & Passive Earth Pressures - Rankine’s passive state Soil Substructure Interaction Lab.
12. 5 & 12. 6 Rankine’s Theory of Active & Passive Earth Pressures where, (Rankine’s passive earth pressure) Soil Substructure Interaction Lab.
12. 5 & 12. 6 Rankine’s Theory of Active & Passive Earth Pressures If, c=0 : coefficient of passive earth pressure Soil Substructure Interaction Lab.
12. 5 & 12. 6 Rankine’s Theory of Active & Passive Earth Pressures Passive Soil Substructure Interaction Lab.
12. 5 & 12. 6 Rankine’s Theory of Active & Passive Earth Pressures ＋ ＝ Ｈ Fig. 12. 11(b) Rotation of frictionless wall about the bottom Soil Substructure Interaction Lab.
12. 7 Yielding of Wall of Limited Height Soil Substructure Interaction Lab.
12. 7 Yielding of Wall of Limited Height Figure 12. 11 Rotation of frictionless wall about the bottom Soil Substructure Interaction Lab.
12. 8 Diagrams for Lateral Earth Pressure Distribution against Retaining Walls Backfill-Cohesionless soil with Horizontal ground Surface -Active case Soil Substructure Interaction Lab.
12. 8 Diagrams for Lateral Earth Pressure Distribution against Retaining Walls -Passive case Fig. 12 Pressure distribution against a retaining wall for cohesionless soil backfill with horizontal ground surface Soil Substructure Interaction Lab.
12. 8 Diagrams for Lateral Earth Pressure Distribution against Retaining Walls Backfill - Partially Submerged Cohensionless Soil Supporting a Surcharge - Active case Soil Substructure Interaction Lab.
12. 8 Diagrams for Lateral Earth Pressure Distribution against Retaining Walls Fig. 12. 13 Rankine’s active earth pressure distribution Soil Substructure Interaction Lab.
12. 8 Diagrams for Lateral Earth Pressure Distribution against Retaining Walls at z=0, z=H 1, z=H, at z=H, u= w · H 2 c Soil Substructure Interaction Lab.
12. 8 Diagrams for Lateral Earth Pressure Distribution against Retaining Walls - Passive case Soil Substructure Interaction Lab.
12. 8 Diagrams for Lateral Earth Pressure Distribution against Retaining Walls Fig. 12. 14 Rankine’s passive earth pressure distribution Soil Substructure Interaction Lab.
12. 8 Diagrams for Lateral Earth Pressure Distribution against Retaining Walls Backfill-Cohesive Soil with Horizontal Backfill - Active case a is negative in the upper part of retaining wall because of the cohesion effect Soil Substructure Interaction Lab.
12. 8 Diagrams for Lateral Earth Pressure Distribution against Retaining Walls (undrained condition) , Soil Substructure Interaction Lab.
12. 8 Diagrams for Lateral Earth Pressure Distribution against Retaining Walls for =0 for taking the tensile cracks into account Soil Substructure Interaction Lab.
12. 8 Diagrams for Lateral Earth Pressure Distribution against Retaining Walls for =0 - Passive case at z=0 at z=H Soil Substructure Interaction Lab.
12. 8 Diagrams for Lateral Earth Pressure Distribution against Retaining Walls for =0, Kp=1 Example 12. 3~ 12. 6 Soil Substructure Interaction Lab.
12. 9 Ranking Active and Passive Pressure with Sloping Backfill where Rankine’s active pressure coefficient Soil Substructure Interaction Lab.
12. 9 Ranking Active and Passive Pressure with Sloping Backfill where 12. 57 참조 Soil Example 12. 7 Soil Substructure Interaction Lab.
12. 10 & 12 & 14 Coulomb’s Earth Pressure Theory - Coulomb’s Theory(1776) : Stability of soil wedge · Consider wall friction · Coulomb assumes failure lines is straight · Force equilibrium only considered (Not moment dquilibrium, point of load application may not be coincide) Soil Substructure Interaction Lab.
12. 10 & 12 & 14 Coulomb’s Earth Pressure Theory - Active case Find maximum Pa Soil Substructure Interaction Lab.
12. 10 & 12 & 14 Coulomb’s Earth Pressure Theory Fig. 12. 22 Coulomb’s active pressure: (a) trial failure wedge; (b) force polygon Soil Substructure Interaction Lab.
12. 10 & 12 & 14 Coulomb’s Earth Pressure Theory If = = = 0 Same as Rankine’s earth PR. coeffi - Ka (Table 12. 5 참조) Soil Substructure Interaction Lab.
12. 10 & 12 & 14 Coulomb’s Earth Pressure Theory - Passive case Soil Substructure Interaction Lab.
12. 10 & 12 & 14 Coulomb’s Earth Pressure Theory Fig. 12. 34 Coulomb’s passive pressure: (a) trial failure wedge; (b) force polygon Soil Substructure Interaction Lab.
12. 10 & 12 & 14 Coulomb’s Earth Pressure Theory Pp의 최소값 Where, Kp = <Eq. 12. 89> -Kp is increased with the wall friction Kp (Table 12. 7) - Overestimates the passive resistance of walls, especially for > /2 Soil Substructure Interaction Lab.
12. 11 Graphic Solution for Coulomb’s Active Earth Pressure - Culmann’s Solution(1875) : Graphic Solution of Coulomb’s Earth PR. Theory Consider for ant Wall friction, regardless of irregularity of backfill and surcharge Active Earth PR. with granular backfill(c=0) Soil Substructure Interaction Lab.
12. 11 Graphic Solution for Coulomb’s Active Earth Pressure Steps 1. Draw retaining wall and backfill to a convenient scale 2. Determine = 90 - - , , 3. Draw a line BD ( with the horizontal) 4. Draw a line BE ( with line BD) 5. Draw lines BC 1, BC 2, BC 3, … BCn Soil Substructure Interaction Lab.
12. 11 Graphic Solution for Coulomb’s Active Earth Pressure Fig. 12. 23 Culmann’s solution for active earth pressure Soil Substructure Interaction Lab.
12. 11 Graphic Solution for Coulomb’s Active Earth Pressure 6. Determine the weight of soil, W W 1=area(ABC 1) 1 Wn=area(ABCn) 1 7. Adopt a convenient load scale and plot the weight W 1=BC 1, W 2=BC 2, … Wn=BCn 8. Draw C 1 C 1 , … Cn. Cn parallel to the line BE Soil Substructure Interaction Lab.
12. 11 Graphic Solution for Coulomb’s Active Earth Pressure 9. Draw a smooth curve through points c 1 , c 2 , c 3 , … cn called the “Culmann line” 10. Draw a tangent B D parallel to line BD 11. load scale -Culmann Solution : provides only the magnitude of the active force per unit length of the retaining wall Soil Substructure Interaction Lab.
12. 11 Graphic Solution for Coulomb’s Active Earth Pressure Fig. 12. 24 Approximate method for finding the point of application of the resultant active force Soil Substructure Interaction Lab.
12. 12 Active Force on Retaining Walls with Earthquake Forces FIGURE 12. 26 Active force on a retaining wall with earthquake forces Soil Substructure Interaction Lab.
12. 12 Active Force on Retaining Walls with Earthquake Forces • • Where • • Soil Substructure Interaction Lab.
12. 12 Active Force on Retaining Walls with Earthquake Forces Mononobe-Okabe Eq. Force polygon Soil Substructure Interaction Lab.
12. 12 Active Force on Retaining Walls with Earthquake Forces Where If no inertia force from E. Q , ¨Location of Line of Action of Resultant Force, Pae - Seed & Whitman (1970) : Location of the 1. Let • = E. Q effect Soil Substructure Interaction Lab.
12. 12 Active Force on Retaining Walls with Earthquake Forces 2. Calculate (Eq. 12. 68) , 3. Calculate (Eq. 12. 72) , 4. 5. from the base of the wall 6. Calculate the location of Soil Substructure Interaction Lab.
12. 12 Active Force on Retaining Walls with Earthquake Forces Soil Substructure Interaction Lab.
12. 12 Active Force on Retaining Walls with Earthquake Forces FIGURE 12. 28 Location of the line of action of Pae Soil Substructure Interaction Lab.
12. 12 Active Force on Retaining Walls with Earthquake Forces ¨ Deign of Retaining Wall Based on Tolerable Lateral Displacement - Richards & Elms (1979) Proposed a procedure for designing gravity retaining wall for E. Q conditions that allows limited lateral displacement of the walls. Soil Substructure Interaction Lab.
12. 12 Active Force on Retaining Walls with Earthquake Forces (11. 13) where (11. 14) • Determined the weight of the retaining wall ( ) 1) Determine the tolerable displacement, Soil Substructure Interaction Lab.
12. 12 Active Force on Retaining Walls with Earthquake Forces 2) Determine : effective acceleration coefficients. 3) Determine based on calculated in step 2 4) Determine =0, by applying a S. F Soil Substructure Interaction Lab.
12. 13 Pae for c’- Soil Backfill 12. 15 Passive Force on Retaining Walls with Earthquake Forces FIGURE 12. 35 Passive force on a retaining wall With earthquake forces Soil Substructure Interaction Lab.
12. 15 Passive Force on Retaining Walls with Earthquake Forces (12. 91) Where Soil Substructure Interaction Lab.
12. 15 Passive Force on Retaining Walls with Earthquake Forces FIGURE 12. 36 Variation of with for (after Davies, Richards, and Chen, 1986) Soil Substructure Interaction Lab.
12. 16 Summary and General Comments Soil Substructure Interaction Lab.
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