g Retaining Walls Lateral Earth Pressure Theory …

1 ENCE 461. Lateral Earth Pressure Foundation Analysis and Coefficient Design x '. K . z '. K = Lateral Earth Pressure coefficient x' = horizontal effective stress .. Retaining Walls .. Lateral Earth Pressure Theory Mohr's Circle Retaining and Lateral Earth Walls Pressures Necessary in situations where gradual transitions either take up too much space or are impractical for other reasons Retaining Walls are analysed for both resistance to overturning and structural integrity Two categories of Retaining Walls Gravity Walls (Masonry, Stone, Gabion, etc.). In-Situ Walls (Sheet Piling, cast in-situ, etc.). x' = = z '. Development of Lateral Earth Pressure P o 1 z 12 K o . b 2. Groundwater Effects Note Pore Water Effect! subtract vertically add horizontally Conditions of Lateral Earth Groundwater Effects Pressure Coefficient At-Rest Condition Steps to properly compute horizontal stresses Condition where wall movement is zero or minimal including groundwater effects: Ideal condition of wall, but seldom achieved in reality Compute total vertical stress Active Condition Compute effective vertical stress by removing groundwater effect through submerged unit weight.

2 Condition where wall moves away from the backfill plot on Po diagram The lower state of Lateral Earth Pressure Compute effective horizontal stress by multiplying Passive Condition effective vertical stress by K. Condition where wall moves toward the backfill Compute total horizontal stress by directly adding effect of groundwater unit weight to effective The higher state of Lateral Earth Pressure horizontal stress Estimates of At Rest Lateral Effect of Wall Movement Earth Pressure Coefficient Jaky's Equation K o 1 sin '. Modified for Overconsolidated Soils sin '. K o 1 sin ' OCR. Applicable only when ground surface is level In spite of theoretical weaknesses, Jaky's equation is as good an estimate of the coefficient of Lateral Earth Pressure as we have Example of At Rest Wall Wall Movements Necessary to Pressure Achieve Active or Passive Given Find States Retaining Wall as Shown PA, from At Rest Conditions Development of Passive Earth Pressure At Rest Pressure Example Compute at rest Earth Pressure coefficient K o 1 sin '.

3 K o 1 sin 30 Compute Effective Wall Force P o 1 z 12 K o 20. b 2. P o 120 20 2 h PA ft. 3. b 2. Po lbs kips (valid for all theories). 12000 12. b ft ft Development of Active Earth Earth Pressure Theories Pressure Rankine Earth Pressure Equations Rankine Coefficients with Level Backfills Inclined Backfills Inclined and level backfill equations are identical when = 0. Example of Rankine Active Wall Pressure Rankine Theory with Inclined Given Find Backfills Retaining Wall as Shown PA, from At Rest Conditions Rankine Passive Pressure Rankine Active Pressure Example Example Compute at rest Earth Pressure coefficient Compute at rest Earth Pressure coefficient 2 . 2 K A tan 45 . K P tan 45 2. 2. 2 2 1. K P tan 45. 15 3 K A tan 45 15 . 3. Compute Effective Wall Force Compute Effective Wall Force 2 2. P o 1 z 1 K p P o 1 z 1 K a . b 2 b 2. P o 120 20 2 3 P o 120 20 2 . b 2 b 2. Po lbs kips Po lbs kips 72000 72 8000 8. b ft ft b ft ft Summary of Rankine and At Rest Wall Pressures Rankine Passive Pressure Example 72,000 lbs.

4 12,000 lbs. 8000 lbs. 2. cos . K a 2.. Example of Coulomb Theory 2 sin . sin . cos cos 1.. cos cos . 2. cos .. K p 2. 2 sin . sin .. cos cos 1 . cos cos . Given Find Wall as shown above KA, KP, PA. Coulomb Theory Typical Solution for Coulomb Active Values Pressures of Wall Compute Coulomb Active Pressure Friction KA = Compute Total Wall Force PA = 8316 lb/ft of wall Theory of Cohesive Solution for Coulomb Passive Soils Pressures Compute Coulomb Passive Pressure 1. sin . tan 2 KP = 1 sin 4 2. Compute Total Wall Force Passive Case (Wall Driving). Active Case (Overburden PA = 96,470 lb/ft of wall driving). Rankine Pressures with Cohesion (Level Backfill) Walls with Cohesive Backfill Active . 3 1 tan 2 2 c tan . 4 2 4 2 Retaining Walls should generally have 1 H Overburden Driving cohesionless backfill, but in some cases cohesive backfill is unavoidable 2c . K A 3 tan 2 tan Cohesive soils present the following weaknesses as 1 4 2 H 4 2 backfill: Passive Poor drainage 2.

5 1 3 tan . 2 c tan Creep 4 2 4 2 Expansiveness 3 H Wall Driving Most Lateral Earth Pressure Theory was first 1 2c developed for purely cohesionless soils (c = 0). K P tan 2 . tan and has been extended to cohesive soils afterward 3 4 2 H 4 2. Valid if wall-soil Example of Equivalent Fluid Method Comments on friction is not taken in Rankine to account Equations Do not take into consideration soil above critical height 2c H c . Ka Given Find Do not take into Wall as shown above Forces acting on the consideration sloping KA = wall (both horizontal Walls and vertical). KP = For practical problems, should use equations as w = 3 degrees they appear in the book Example of Equivalent Fluid Equivalent Fluid Method Compute Equivalent Fluid Unit Weights (Active Case) Simplification used to guide the calculations of Lateral Earth pressures on Retaining Walls G h K a cos w Can be used for Rankine and Coulomb Lateral G h 120 cos 3 Earth pressures G h pcf Can be used for at rest, active and passive Earth pressures G v K a sin w Transforms the soil acting on the Retaining wall into an equivalent fluid G v 120 sin 3.

6 G v pcf Example of Equivalent Fluid Example of Equivalent Fluid Compute Wall Load (Passive Case) Compute Wall Load (Active Case). 2 2. P p Gh H Pa Gh H.. b 2 b 2. 2. P p 20 P a 202. 96338 lb/ft 8304 lb/ft b 2 b 2. 2 2. V p Gv H V a Gv H.. b 2 b 2. V p 202 V a 202. 5048 lb/ft 436 lb/ft b 2 b 2. Terzaghi Example of Equivalent Fluid Model Compute Equivalent Fluid Unit Weights (Passive Assumes log spiral Case). failure surface behind wall G h K p cos w Requires use of G h 120 cos 3 . suitable chart for KA. and KP. G h pcf Not directly used in G v K p sin w this course, but option in SPW 911. G v 120 sin 3 . G v pcf Effects of Homework Set 5 Surface Loading Reading McCarthy: Chapter 16. Coduto: Chapters 22, 23, 24 & 25. Homework Problems McCarthy: 16-1, 16-8, 16-12a, 16-17. Coduto: (Hand and Chart Solutions); (SPW. 911). Due Date: 17 April 2002. Surcharge and Groundwater Questions Loads