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6.1 General

Lateral Earth Pressure. E. E. E. E. Tunnel. Dock. Abutment. 6.1 General

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6.1 General

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  1. Lateral Earth Pressure E E E E Tunnel Dock Abutment • 6.1 General • Conditions of plane strain are assumed, i.e. strains in the longitudinal direction of the structure are assumed to be zero. It is assumed that the stress–strain behavior of the soil can be represented by therigid–perfectly plastic idealization.

  2. Lateral Earth Pressure

  3. Lateral Earth Pressure 完工 完工

  4. Lateral Earth Pressure 锚杆 板桩 板桩上土压力 实测 计算 Rigid earth retaining wall 扶壁式 刚性加筋 预应力 Flexible earth retaining wall 板桩变形

  5. Lateral Earth Pressure retaining and protection of foundation excavation

  6. Lateral Earth Pressure • There are 3 states of lateral earth pressure Ko = At Rest Ka = Active Earth Pressure (wall moves away from soil) Kp = Passive Earth Pressure (wall moves into soil) • Passive is more like a resistance

  7. Lateral Earth Pressure E Ep Eo Ea o -△ +△ △a △p -△ +△ Relation among three earth pressures

  8. Lateral Earth Pressure z h • 6.2 At Rest Earth Pressure • One common earth pressure coefficient for the “at rest” condition in granular soil is: • Ko = 1 – sin(φ) • Where: Ko is the “at rest” earth pressure coefficient and φ is the soil friction value. z K0z h/3 K0h

  9. Lateral Earth Pressure Retaining wall between the slope

  10. Lateral Earth Pressure Failured earth retaining wall

  11. Lateral Earth Pressure Failured reinforced earth retaining wall

  12. Lateral Earth Pressure • 6.2 Rankine Theory of Earth Pressure • The Rankine Theory assumes: • There is no adhesion or friction between the wall and soil • Lateral pressure is limited to vertical walls • Ground surface is horizontal. If the soil mass as a whole is stressed such that the principal stresses at every point are in the same directions, theoretically, there will be a network of failure planes equally inclined to the principal planes.

  13. Lateral Earth Pressure f f =c+ tan 伸展 压缩 45o-/2 45o＋/2 K0z z  pa pp If there is a movement of the wall away from the soil, the value of x decreases as the soil dilates or expands outwards, the decrease in x being an unknown function of the lateral strain in the soil. If the expansion is large enough, the value of x decreases to a minimum value such that a state of plastic equilibrium develops. Since this state is developed by a decrease in the horizontal stress x, this must be the minor principal stress (3). The vertical stress z is then the major principal stress (1).

  14. Lateral Earth Pressure z h 45o＋/2 1)Active Earth Pressure z(σ1) pa(σ3) When the horizontal stress becomes equal to the passive pressure the soil is said to be in the passive Rankine state, there being two sets of failure planes each inclined at 45o＋/2 to the vertical (the direction of the major principal plane)

  15. Lateral Earth Pressure h Ea h/3 hKa For sandy soil For cohesive soil This means that in active case the soil is in a state of tension between the surface and depth z0. In practice, however, this tension cannot be relied upon to act on the wall, since cracks are likely to develop within the tension zone and the part of the pressure distribution diagram above depth z0 should be neglected.

  16. Lateral Earth Pressure 2)Passive Earth Pressure The force due to the passive pressure distribution is referred to as the total passive resistance (Pp). For a vertical wall surface of height H: The maximum value 1 is reached when theMohr circle through the point representing the fixed value 3 touches the failure envelope for the soil. In this case, the horizontal stress is defined as the passive pressure ( pp) representing the maximum inherent resistance of the soil to lateral compression.

  17. Lateral Earth Pressure Example 1

  18. Lateral Earth Pressure A 1=17kN/m3 c1=0 1=34o h1=2m B h=5m 2=19kN/m3 c2=10kPa 2=16o h2=3m C Example 2

  19. Lateral Earth Pressure A h1=2m B h=5m h2=3m C Solution: 10.4kPa 4.2kPa 36.6kPa

  20. Lateral Earth Pressure h C hKa A β α G h δ  E R B q 6.3 Coulomb Theory of Earth Pressure Active earth pressure: Coulomb’s theory (1776) involves consideration of the stability, as a whole, of the wedge of soil between a retaining wall and a trial failure plane. The force between the wedge and the wall surface is determined by considering the equilibrium of forces acting on the wedge when it is on the point of sliding either up or down the failure plane, i.e. when the wedge is in a condition of limiting equilibrium.

  21. Lateral Earth Pressure A β=15o α=10o Ea δ=20o 4.5m α=10o B h/3 Solution: In terms ofα=10o，β=15o，=30o，δ=20o The point of application of the total active thrust is not given by the Coulomb theory but is assumed to act at a distance of 1/3 H above the base of the wall.

  22. Lateral Earth Pressure    E Limit equilibrium condition 6.4 the comparison of Rankine Theory and Coulomb Theory 1 analysis theory

  23. Lateral Earth Pressure Ep' Ea Ep Ea' R R W W ——Rankine theory ——Rankine theory 2 calculating error 3 calculating error 0 Active pressure Large Active pressure Large Passive pressure small Passive pressure small

  24. Lateral Earth Pressure ——Coulumb theory ——Coulumb theory 3 calculating error 2 calculating error Sliding surface Sliding surface the actual slip surface may not be a plane Passive pressure small Active pressure Large

  25. Lateral Earth Pressure ——compare with the exact value ——compare with the exact value 3 calculating error 2 calculating error

  26. Lateral Earth Pressure ——compare with the exact value 2 calculating error

  27. Lateral Earth Pressure 4 several kinds of active pressure 1. Load on filling 2. Stratified filling 3. Water in filling

  28. Lateral Earth Pressure Lateral Earth Pressure 1. Load on filling 1. Load on filling 1 Rankin theory 1=gz+q pa= 3=qKa+gzKa 1 Z 3 H zKa HKa qKa

  29. Lateral Earth Pressure 1. Load on filling 2. Coulomb theory

  30. Lateral Earth Pressure 1. Load on filling 3. Local loads—Rankin theory

  31. Lateral Earth Pressure A g1f1 c1 H1 B g2f2 c2 H2 C 2. Stratified filling Rankin theory

  32. Lateral Earth Pressure 3. Water in filling earth pressure Pa=Kasz water pressure pu=u

  33. Lateral Earth Pressure 土压力 水压力 KagH1 KagH2 gwH2 3. Water in filling Impermeable foundation 朗肯理论

  34. Lateral Earth Pressure H1 d H2 Ea pw 3. Water in filling Impermeable foundation Coulombs theory Water pressure Earth pressure Ea pw

  35. Lateral Earth Pressure H1 H2 3. Water in filling Permeability coefficient of the filling is much smaller than of the foundation Effective stress =total stress Pore water pressure Earht pressure KagH1 gH1 u=0 gsatH2 透水地基 KagsatH2

  36. Lateral Earth Pressure 3. Water in filling Permeability coefficient of the filling is much smaller than of the foundation The flow net is needed to calculate the pore water pressure

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