Chapter 14 Lateral Earth Pressure – Curved Failure Surface 연세대학교 지반공학연구실

14.1 Retaining Walls with Friction  

14.1 Retaining Walls with Friction downward motion of the soil relative to the wall

14.1 Retaining Walls with Friction downward motion of the wall relative to the soil

upward motion of the soil relative to the wall

14.1 Retaining Walls with Friction upward motion of the wall relative to the soil

14.2 Properties of a Logarithmic Spiral Location of centroid

14.3 Procedure for Determination of Passive Earth Pressure, Pp (Cohesionless Backfill ) - procedure of evaluating the passive resistance by trial wedges (Terzaghi & Peck. 1967)

14.3 Procedure for Determination of Passive Earth Pressure, Pp (Cohesionless Backfill )

14.3 Procedure for Determination of Passive Earth Pressure, Pp (Cohesionless Backfill )

14.3 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 convenient 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

14.3 Procedure for Determination of Passive Earth Pressure, Pp (Cohesionless Backfill ) 4. + 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

14.4 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. 14.4 ,Table 14.1 참조  arc. of a circle (Packshaw, 1969) Passive Presure by the Method of Slices by Shields and Tolunay (1973) Table 14.2 참조  Example 14.1

14.5 Passive Force on Walls with Earthquake Forces   H Arc of a log spiral Logarithmic spiral failure surface for determination of Ppe

14.5 Passive Force on Walls with Earthquake Forces The passive force, Figure 14.6 shows variation of with and for Mononobe-Okabe solution and for the logarithmic spiral Type of failure surface analysis.

14.5 Passive Force on Walls with Earthquake Forces

14.5 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)

14.6 Braced Cuts (버팀 굴착) - Two Types of Braced Cuts  Soldier beam, wood lagging, wale, strut  Sheetpile, wale, strut

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

14.7 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.

14.7 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

14.7 Determination of Active Thrust on Bracing Systems of Open Cuts in Granular soil

14.7 Determination of Active Thrust on Bracing Systems of Open Cuts in Granular soil

14.8 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

14.8 Determination of Active Thrust on Bracing Systems for Cuts in Cohesive Soil 2. + 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

14.8 Determination of Active Thrust on Bracing Systems for Cuts in Cohesive Soil

14.8 Determination of Active Thrust on Bracing Systems for Cuts in Cohesive Soil   H Determination of active force on bracing system of open cut in cohesive soil(=0)

14.9 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)

14.9 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 to be 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

14.9 Pressure Variation for Design of Sheetings, Struts, and Wales