K x ' Retaining. Walls ENCE 461. Foundation Analysis and Design. Mohr s Circle. and Lateral Earth. Pressures. Lateral Earth Pressure.

Transcription

1 Lateral Earth Pressure Coefficient K x ' z ' K = lateral earth pressure coefficient x = horizontal effective stress Mohr s Circle and Lateral Earth Pressures x ' = = z ' ENCE 461 Foundation Analysis and Design Retaining Walls Lateral Earth Pressure Theory Retaining Walls Necessary in situations where gradual transitions either take up too much space or are impractical for other reasons Retaining walls are analysed for oth resistance to overturning and structural integrity Two categories of retaining walls Gravity Walls (Masonry, Stone, Gaion, etc.) In-Situ Walls (Sheet Piling, cast in-situ, etc.)

2 Groundwater Effects Conditions of Lateral Earth Pressure Coefficient At-Rest Condition Condition where wall movement is zero or minimal Ideal condition of wall, ut seldom achieved in reality Active Condition Condition where wall moves away from the ackfill The lower state of lateral earth pressure Passive Condition Condition where wall moves toward the ackfill The higher state of lateral earth pressure Development of Lateral Earth Pressure 1 z 1 K o Note Pore Water Effect! sutract vertically add horizontally Groundwater Effects Steps to properly compute horizontal stresses including groundwater effects: Compute total vertical stress Compute effective vertical stress y removing groundwater effect through sumerged unit weight; plot on diagram Compute effective horizontal stress y multiplying effective vertical stress y K Compute total horizontal stress y directly adding effect of groundwater unit weight to effective horizontal stress

3 Estimates of At Rest Lateral Earth Pressure Coefficient Jaky s Equation K o 1sin ' Modified for Overconsolidated Soils K o 1sin 'OCR sin ' Applicale 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 Given Example of At Rest Wall Pressure Find Retaining Wall as Shown P A, from At Rest Conditions Effect of Wall Movement Wall Movements Necessary to Achieve Active or Passive States

4 Development of Passive Earth Pressure Earth Pressure Theories At Rest Pressure Example Compute at rest earth pressure coefficient K o 1sin ' K o 1sin 30º 0.5 Compute Effective Wall Force 1 z 1 K o ls 1000 ft kips 1 ft h PA ft. (valid for all theories) Development of Active Earth Pressure

5 Rankine Coefficients with Inclined Backfills Inclined and level ackfill equations are identical when = 0 Example of Rankine Active Wall Pressure Given Find Retaining Wall as Shown P A, from At Rest Conditions Rankine Earth Pressure Equations Level Backfills Rankine Theory with Inclined Backfills

6 Rankine Passive Pressure Example Compute at rest earth pressure coefficient K P tan 45º K P tan Compute Effective Wall Force 1 z 1 K p ls 7000 ft kips 7 ft Summary of Rankine and At Rest Wall Pressures 7,000 ls. 1,000 ls ls. Rankine Active Pressure Example Compute at rest earth pressure coefficient K A tan 45º K A tan Compute Effective Wall Force 1 z 1 K a ls kips ft ft Rankine Passive Pressure Example

7 Example of Coulom Theory Given Find Wall as shown aove K A, K P, P A Solution for Coulom Active Pressures Compute Coulom Active Pressure K A = Compute Total Wall Force P A = 8316 l/ft of wall K a cos cos1 cos sin sin coscos K p cos cos cos1 sinsin coscos Coulom Theory Typical Values of Wall Friction

8 Theory of Cohesive Soils 1sin 1sin tan 4 Passive Case (Wall Driving) Active Case (Overurden driving) Rankine Pressures with Cohesion (Level Backfill) Active 3 1 tan 4 c tan 4 1 H Overurden Driving K A 3 tan 1 4 c H tan 4 Passive 1 3 tan 4 c tan 4 3 H Wall Driving K P 1 tan 3 4 c H tan 4 Solution for Coulom Passive Pressures Compute Coulom Passive Pressure K P = Compute Total Wall Force P A = 96,470 l/ft of wall Walls with Cohesive Backfill Retaining walls should generally have cohesionless ackfill, ut in some cases cohesive ackfill is unavoidale Cohesive soils present the following weaknesses as ackfill: Poor drainage Creep Expansiveness Most lateral earth pressure theory was first developed for purely cohesionless soils (c = 0) and has een extended to cohesive soils afterward

9 Example of Equivalent Fluid Method Given Find Wall as shown aove K A = K P = Forces acting on the wall (oth horizontal and vertical) w = 3 degrees Example of Equivalent Fluid Compute Equivalent Fluid Unit Weights (Active Case) G h K a cos w G h cos 3º G h 41.5 pcf G v K a sin w G v sin 3º G v.18 pcf Comments on Rankine Equations Valid if wall-soil friction is not taken in to account Do not take into consideration soil aove critical height H c c K a Do not take into consideration sloping walls For practical prolems, should use equations as they appear in the ook Equivalent Fluid Method Simplification used to guide the calculations of lateral earth pressures on retaining walls Can e used for Rankine and Coulom lateral earth pressures Can e used for at rest, active and passive earth pressures Transforms the soil acting on the retaining wall into an equivalent fluid

10 Example of Equivalent Fluid Compute Wall Load (Passive Case) P p V p P p G h H V p G v H l/ft 5048 l/ft Terzaghi Model Assumes log spiral failure surface ehind wall Requires use of suitale chart for K A and K P Not directly used in this course, ut option in SPW 911 Example of Equivalent Fluid Compute Wall Load (Active Case) P a V a P a G h H V a G v H l/ft 436 l/ft Example of Equivalent Fluid Compute Equivalent Fluid Unit Weights (Passive Case) G h K p cos w G h cos 3º G h pcf G v K p sin w G v sin 3º G v 5.4 pcf

11 Homework Set 5 Reading McCarthy: Chapter 16 Coduto: Chapters, 3, 4 & 5 Homework Prolems McCarthy: 16-1, 16-8, 16-1a, Coduto: 5.3 (Hand and Chart Solutions); 5.5 (SPW 911) Due Date: 17 April 00 Questions Effects of Surface Loading Surcharge and Groundwater Loads