Active static and seismic earth pressure for c φ soils

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1 Active static and seismic earth pressure for c φ soils Magued Iskander, PhD, PE, F.ASCE Professor & Head, Civil & Urban Engineering Department

2 Motivation Methods based on Mononobe-Okabe method: Require prior knowledge of failure surface Require assumption of lateral thrust inclination Difficult to apply in layered soils and presence of water table Stress based solutions are scarce and apply to limited cases Develop general Rankine (Stress-based) solution 2

3 Rankine Seismic Lateral Earth Pressure! Rigid retaining wall Frictional-cohesive soil Horizontal & vertical acceleration +ω +ω +β Cohesive Soil (γ, c, φ) Horizontal Acceleration (ah=khg) Inclined backfill Inclined wall Gravity (g) Vertical Acceleration (av=kvg) 3

4 Conjugate Stress If the stress on a given plane in a body be in a given direction, the stress on any plane parallel to that direction must be in a direction parallel to the first mentioned plane. Rankine (1858) 4

5 Modified Acceleration Field Modify acceleration field Modify density Conjugate element 5

6 Mohr circle used to derive stresses Conjugate element used to derive stress on a plane parallel to the wall σ'θ θ+β σ' β σ' β θ+β σ'θ

7 Formulation Stress acting on wall 7

8 One of the features of the method is that the obliquity angle on the wall can be analytically obtained: Obliquity Angle Computed (Not Assumed) Horizontal stress on the wall: 8

9 Importance of Obliquity (for vertical wall and horizontal backfill ) Variation of a with horizontal acceleration for different values of f Variation of a as a function of f for vertical walls, with horizontal backfill 9

10 Example Layered Backfill 8/10/

11 Tension Crack With depth of crack Without depth of crack 8/10/

12 Tension Crack With depth of crack Without depth of crack 8/10/

13 Formulation Depth of tension crack: Horizontal thrust on wall: More conservative 13

14 Example 8/10/

15 Example Undrained Cohesive Backfill 15

16 Comparison with Other Methods 8/10/2016 Without wall and backfill inclination With wall and backfill inclination 16

17 Comparison with Other Methods Normalization to facilitate comparison Frictional-cohesive backfill 17

18 Direction of Vertical Acceleration Upward vertical acceleration Downward vertical acceleration 18

19 Effect of Cohesion Natural soils often have some cohesion Cohesion reduces lateral earth pressure Conservative or unconservative? Huntington (1957) noted: For many years it was almost universal practice to compute the earth pressure against a retaining wall on the assumption that the soil was cohesionless and that the value of φ could be considered equivalent to the angle of repose... The most common assumption according to this practice was that the slope of the angle of repose was 1.5 horizontal: 1 Vertical (i.e., 33.41). 19

20 Design Charts Vertical Wall and Horizontal Backfill 20

21 Design Charts Inclined Wall and Backfill 21

22 Published Papers ASCE JGGE Soils and Foundations 22

23 Universal Earth Pressure Formulation Developed an expressions for the static and pseudo-static seismic analyses of c φ backfill. Results are identical to those computed with the Mononobe Okabe method for cohesionless soils, provided the same wall friction angle is employed. For c φ soils, the formulation yields comparable results to available solutions for cases where a comparison is feasible. +ω +ω Gravity (g) +β Cohesive Soil (γ, c, φ) Horizontal Acceleration (ah=khg) Vertical Acceleration (av=kvg) 23

24 Thank You Acknowledgments Mehdi Omidvar Chris Chen Omar Elsherif 24

UNIT V. The active earth pressure occurs when the wall moves away from the earth and reduces pressure.

UNIT V. The active earth pressure occurs when the wall moves away from the earth and reduces pressure. UNIT V 1. Define Active Earth pressure. The active earth pressure occurs when the wall moves away from the earth and reduces pressure. 2. Define Passive Earth pressure. The passive earth pressure occurs