1. Chapter 13 Lateral Earth Pressure – Curved Failure Surface
연세대학교 지반공학연구실

2. 13.1 Retaining Walls with Friction
In reality, retaining walls are rough
 shear forces develop bet/the face of the wall & the backfill
- For practicality
 loose granular backfill
 dense granular backfill

3. 13.1 Retaining Walls with Friction

4. 13.1 Retaining Walls with Friction

5. 13.1 Retaining Walls with Friction

6. 13.1 Retaining Walls with Friction
Figure 13.1 Effect of wall friction on failure surface

7. 13.2 Properties of a Logarithmic Spiral
Location of centroid
Fig 13.2 General parameters of a logarithmic spiral

8. 13.3 Procedure for Determination of Passive Earth Pressure, Pp (Cohesionless Backfill )
procedure of evaluating the passive resistance by trial wedges
(Terzaghi & Peck. 1967)
Steps
1. Draw retaining wall to a convinient scale
2. Draw line C1A (45-/2) degrees with the surface of the backfill
3. Consider the stability of the soil mass ABC1C1 for equilibrium)
Rankine’s
passive force
F1 = resultant of the shear and normal forces
P1 = passive force per unit length of the wall

9. 13.3 Procedure for Determination of Passive Earth Pressure, Pp (Cohesionless Backfill )
5. Trial passive force per unit length of the wall is repeated for several trial wedges
6. P1 (trial wedge 1)
P2 (trial wedge 2)  Plotted to a same scale 
P3 (trial wedge n)
Find the low point of the smooth curve
That is actual passive force, Pp

10. 13.3 Procedure for Determination of Passive Earth Pressure, Pp (Cohesionless Backfill )

11. 13.3 Procedure for Determination of Passive Earth Pressure, Pp (Cohesionless Backfill )

12. 13.3 Procedure for Determination of Passive Earth Pressure, Pp (Cohesionless Backfill )
Fig Passive earth pressure against retaining wall with curved failure surface

13. 13.4 Coeffi. of Passive Earth Pressure (Kp)
Proposed the curved failure surface like as
 arc. of a logarithmic spiral (Terzaghi & Peck, 1967 : Janbu, 1957)
 arc. of an ellipse (Caquot & Kerisel, 1948)
; Fig ,Table 13.1 참조
 arc. of a circle (Packshaw, 1969)
Passive Presure by the Method of Slices
by Shields and Tolunay (1973)
Table 13.2 참조
 Example 13.1

14. 13.5 Passive Force on Walls with Earthquake Forces
FIGURE Logarithmic spiral failure surface for determination of Ppe

15. 13.5 Passive Force on Walls with Earthquake Forces
The passive force,
Figure 13.6 shows variation of
with
and
for Mononobe-Okabe solution and for the logarithmic spiral
Type of failure surface analysis.

16. 13.5 Passive Force on Walls with Earthquake Forces( )
FIGURE Variation of
with
and

17. 13.5 Passive Force on Walls with Earthquake Forces( )
FIGURE Variation of
with
and

18. 13.5 Passive Force on Walls with Earthquake Forces
As we can see from the figure, for a given value of ,
the magnitude of is always larger when the failure
surface is assumed to be plane (Mononobe-Okabe solution)

19. 13.6 Braced Cuts (버팀 굴착) - Two Types of Braced Cuts
 Soldier beam, wood lagging, wale, strut
 Sheetpile, wale, strut
Figure 13.8 Braced cut : (a) cross section ; (b) plan (section at X-X )

20. 13.6 Braced Cuts (버팀 굴착) 정지토압 (변형이 작음) 탄성변형 횡토압 < Rankine 토압
(변형이 크다)
소성평형

21. 13.7 Determination of Active Thrust on Bracing Systems of Open Cuts in Granular soil
- Active thrust on the bracing system of open cuts :
Terzaghi’s general wedge theory (1941)
General Procedures
1. A point b1 is selected.
2. From b1, a line b1b1 that makes an angle of  with the ground surface is drawn.
3. The arc. of the logarithmic spiral, b1B is drawn with the center of the spiral (pt. O1)
4. Consider the stability of the soil mass ABb1 for equilibrium.
W1 =  · area(ABb1)·(1)
P1 = the active trust acting at a point na·H
F1 = the resultant of the shear and normal forces acting along
with the trial failure surface.

22. 13.7 Determination of Active Thrust on Bracing Systems of Open Cuts in Granular soil+
6. Trial active thrust is repeated for several trial wedges
P1 (trial wedge 1)
P2 (trial wedge 2) Plotted to a same scale 
Pn (trial wedge n)
 Find the maximum point of the smooth curve
 That is actual active force, Pa

23. 13.7 Determination of Active Thrust on Bracing Systems of Open Cuts in Granular soil

24. 13.7 Determination of Active Thrust on Bracing Systems of Open Cuts in Granular soil
Fig Determination of active force on bracing system
of open cut in cohesionless soil

25. 13.8 Determination of Active Thrust on Bracing Systems for Cuts in Cohesive Soil
- Undrained condition, =0
 The equation of the logarithmic spiral
(circle)
1. Consider force for equilibrium of the wedge ABb1
W1 =  · area(ABb1)·(1)
P1 = the active trust acting at a height of na·H
F1 = the resultant acting along the surface of sliding
cur11 = force from cohesion acting along the surface of sliding
caH = force from adhesion between the soil and the sheeting

26. 13.8 Determination of Active Thrust on Bracing Systems for Cuts in Cohesive Soil
3. Trial active thrusts is obtained from several trial wedges
P1 (trial wedge 1)
P2 (trial wedge 2) Plotted to a same scale 
Pn (trial wedge n)
 the highest point of the smooth curve
 That is actual active thrust, Pa

27. 13.8 Determination of Active Thrust on Bracing Systems for Cuts in Cohesive Soil

28. 13.8 Determination of Active Thrust on Bracing Systems for Cuts in Cohesive Soil
Fig. (3rd ed.) Determination of active force on bracing system
of open cut in cohesive soil(=0)

29. 13.9 Pressure Variation for Design of Sheetings, Struts, and Wales
- Calculation using general wedge theory does not explain the veriation of the earth PR with depth
- Empirical lateral PR. diagrams (Peck, 1969)
Fig Peck’s pressure diagrams for design of bracing systems

30. 13.9 Pressure Variation for Design of Sheetings, Struts, and Wales
- Limitation for Pressure Envelopes
1. PR. envelopes : apparent PR. envelopes
2. applied depth  20(6m)
3. W.T. : below the bottom of the cut
4. Sand : assumed th bd drained
5. Clay : assumed to be undrained and pwp is not considered
 Strut load determination
- Soldier piles are assumed to be hinged at the strut level, except for the top & bottom ones
- Strut loads

31. 13.9 Pressure Variation for Design of Sheetings, Struts, and Wales
Figure Determination of strut loads from empirical lateral pressure diagrams
 Example 13.2

32. 13.10 Dynamic Earth Pressure Distribution Behind a Wall Rotating about the Top
Figure Dynamic lateral earth pressure distribution
behind a rigid model retaining wall rotating