Principles of Foundation Engineering
Braja M. Das
Chapter 8 Retaining Walls
1 Moments
Review Moments
2 Types of retaining walls
3 Dimensions
Approximate dimensions for various components of retaining wall for initial stability checks: cantilever wall
4 Active Earth Pressure
5 Stability Issues
Overturning Sliding
Failure of retaining wall: (a) by overturning (b) by sliding Bearing Capacity Global Stability (c) by bearing capacity failure (d) by deep-seated shear failure
6 Deep-seated shear failure
Traditional Slope Stability Analysis
7 Check for overturning, assuming that the Rankine pressure is valid
Forces at Work
Overturning • Active Earth Pressure Using H’ • Any load along top – q
Resisting • Weight of Soil (1 & 2) • Weight of Structure (3, 4 & 5) • Bearing Capacity of Base • Passive Pressure Against Base
Point of Rotation
8 Moment Table
Procedure for Calculating MR Weight per unit Moment arm Moment Section Area length of wall measured from C about C 12 3 4 5
M1 1A1W1 = 1•A1 X1 2A2W2 = 2•A2 X2 M2 X3 M3 3A3W3 = 3•A3 X4 M4 4A4W4 = 4•A4
5A5W5 = 5•XA5 X5 M5 6 X6 M6 6A6W6 = 6•A6 Pv B Mv V MR
Pv = Vertical Component of Pa if sloped ground
Pp neglected in overturning
Always build the moment table C = Point of Rotation
9 Check Overturning
Sw
Ws1 = weight of soil over heel Ws1 Pa = total lateral earth pressure force Ignore BC = weight of concrete base
C1 = weight of rectangular section of stem 1 C = weight of triangular section of stem 2 Ws = weight of soil over toe C1 2
C2 Ws2 Pa
Moment Arm for Pa =z+T z is the location of the z total force Pa determined BC from the earth pressure L1 L 2 L3 diagram B T
Moment Arm for Ws11212 = (L +L )+(B-(L +L ))/2
Point of Rotation Moment Arm for C112ww = (L +(L -S )+S /2
Moment Arm for C21 = L +2•(L 2w -S )/3
Moment Arm for Ws21 =L /2 Moment Arm for BC=B/2
10 Overturning (Continued)
Overturning Moment Sw
Moa = P(z+T)• Resisting Moments Ms = •• H [(L12 +L )+(B-(L 12 +L ))/2] Ws1 1 Mc 1 = c• H•• Sw [(L12ww +(L -S )+S /2] Ignore C Mc = •• 0.5H [L12w +(L -S )/2] 1 2c 1 MBC = c •BTB/2 • • C a Unit Width Omitted Ws2 P Ms2 = 2••• (D-T) L11 [L /2] BC z Mr L3 D L1 L2 FS FS = 2 to 3 M T o • B
MMs Ms MC MC MB Point of Rotation r 1 2 1 2 c
11 Check for sliding along the base
Sw
Resisting Forces Ws1 R Vtan Bc P Ignore f a p Driving Forces C1 1 Df Pa C a Ws2 P Vtan Bc P BC a p FSsliding Pa P 1 2 p B T Pp D K 2c D K • 2 2 1 p 2 1 p
Point of Rotation s tan ca FS >1.5 = angle of friction between soil & slab
12 Coefficient of Friction
Coefficient of Friction for Cohesionless Soil
Material tan Wood 0.40 22° Rough concrete, cast against soil tan Smooth, formed concrete 0.3-0.4 17° Clean steel 0.20 11° Rusty steel 0.40 22° Corrugated metal tan
13 Alternatives for increasing the factor of safety with respect to sliding
14 Check for bearing capacity failure
Resultant Force R acting on base
R VP a Location of Resultant Force “R” Net Moment Mnet Mnet Mr Mo CE= X V Pressure on Base So Eccentricity “e” y Ve B V q Mnet 2 e X
15 Bearing Capacity
Note you use only the lowest fill height over the footing. BN 2 qu cN c Fcd DNqFqd 2 2 2
BB2e D Fcd 10.4 B 2 D Fqd 12tan 2 1sin 2 B Fd 1 For inclined surface, add inclination factors F , F , F qu ci qi i FS 2 2 ° ° qmax Fi 1 Fci Fqi 1 ° 90° 1 Pa cos FS >3 tan [ V ]
16 Example
Review Example 8.1 on Page 390-393
17 MSE Walls
Mechanically Stabilized Earth (MSE) Walls
18 Geogrid Reinforcement for MSE
19 How Geogrids Work
20 Similar Checks to Retaining Wall
21 Types of MSE Walls
22 Geogrid Reinforced Walls
23 Comments
Active Versus At-Rest Pressures You must have sufficient movement to get active pressure Creep Prolonged Rainfall & Groundwater Fluctuations Vibrations Due to Traffic and Other Sources Temperature Tides and Wave Action Seismic Events
24 Homework
CE 430 CE 530 8.1 All of CE 430 plus 8.2
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