RETAINING WALL

UNIT V RETAINING WALLS Plastic equilibrium in soils – active and passive states – Rankine‟s theory – cohesionless and cohesive soil – Coulomb‟s wedge theory – Condition for critical failure plane – Earth pressure on retaining walls of simple configurations – Culmann Graphical method – pressure on the wall due to line load – Stability analysis of retaining walls.

Lateral Support We have to estimate the lateral soil pressures acting on these structures, to be able to design them. Soil nailing Gravity Retaining wall Reinforced earth wall

Soil Nailing

Sheet Pile Sheet piles marked for driving

Sheet Pile Sheet pile wall

Sheet Pile Sheet pile wall During installation

Lateral Support Reinforced earth walls are increasingly becoming popular. geosynthetics

Lateral Earth Pressure There are 3 states of lateral earth pressure Ko = At Rest Ka = Active Earth Pressure (wall moves away from soil) Kp = Passive Earth Pressure (wall moves into soil) Passive is more like a resistance σv z H σh

Earth Pressure at Rest In a homogeneous natural soil deposit, v’ h’ GL v’ h’ X the ratio h’/v’ is a constant known as coefficient of earth pressure at rest (K0). Importantly, at K0 state, there are no lateral strains.

Estimating K0 For normally consolidated clays and granular soils, K0 = 1 – sin ’ For overconsolidated clays, K0,overconsolidated = K0,normally consolidated OCR0.5 From elastic analysis, Poisson’s ratio

Active/Passive Earth Pressures - in granular soils Wall moves away from soil Wall moves towards soil A B smooth wall Let’s look at the soil elements A and B during the wall movement.

Active Earth Pressure Active earth pressure occurs when the wall tilts away from the soil (a typical free standing retaining wall)

Active Earth Pressure Active earth pressure occurs when the wall tilts away from the soil (a typical free standing retaining wall)

Active Earth Pressure Active earth pressure occurs when the wall tilts away from the soil (a typical free standing retaining wall)

Active Earth Pressure - in granular soils v’ = z Initially, there is no lateral movement. h’ = K0 v’ = K0 z As the wall moves away from the soil, v’ remains the same; and h’ decreases till failure occurs. Active state

Active Earth Pressure Active earth pressure occurs when the wall tilts away from the soil (a typical free standing retaining wall) Ka can be calculated as follows: Ka = tan2 (45 – φ/2) thus: σa‘ = Ka σv’ – 2 c (Ka)1/2 Soil sliding down pushing the wall Failure wedge H 45 + φ/2

Active Earth Pressure - in granular soils As the wall moves away from the soil,   failure envelope Initially (K0 state) Failure (Active state) v’ decreasing h’ active earth pressure

Active Earth Pressure - in granular soils    [h’]active v’ failure envelope  WJM Rankine (1820-1872) [h’]active v’ Rankine’s coefficient of active earth pressure

Active Earth Pressure - in granular soils    A v’ h’ [h’]active failure envelope  Failure plane is at 45 + /2 to horizontal A v’ h’ 45 + /2 90+ [h’]active v’

Active Earth Pressure - in granular soils As the wall moves away from the soil, h’ decreases till failure occurs. wall movement h’ K0 state A v’ h’ z Active state

Active Earth Pressure - in cohesive soils Follow the same steps as for granular soils. Only difference is that c  0. Everything else the same as for granular soils.

Passive Earth Pressure - in granular soils Initially, soil is in K0 state. As the wall moves towards the soil, v’ remains the same, and B v’ h’ h’ increases till failure occurs. Passive state

Passive Earth Pressure Passive earth pressure occurs when the wall is pushed into the soil (typically a seismic load pushing the wall into the soil or a foundation pushing into the soil) Kp can be calculated as follows: Kp = tan2 (45 + φ/2) thus: σp‘ = Kp σv’ + 2 c (Kp)1/2 Soil being pushed up the slope H Failure wedge 45 - φ/2

Passive Earth Pressure - in granular soils As the wall moves towards the soil,   failure envelope Initially (K0 state) Failure (Active state) passive earth pressure v’ increasing h’

Passive Earth Pressure - in granular soils   failure envelope  v’ [h’]passive Rankine’s coefficient of passive earth pressure

Passive Earth Pressure - in granular soils   failure envelope  Failure plane is at 45 - /2 to horizontal A v’ h’ 45 - /2 90+ [h’]passive v’

Passive Earth Pressure - in granular soils As the wall moves towards the soil, h’ increases till failure occurs. wall movement h’ Passive state B v’ h’ K0 state

Passive Earth Pressure - in cohesive soils Follow the same steps as for granular soils. Only difference is that c  0. Everything else the same as for granular soils.

Earth Pressure Distribution - in granular soils [h’]active PA and PP are the resultant active and passive thrusts on the wall H [h’]passive PA=0.5 KAH2 h PP=0.5 KPh2 KPh KAH

Rankine’s Earth Pressure Theory Assumes smooth wall Applicable only on vertical walls

Active Stress Distribution (c = 0) γ c = 0 Φ dry soil H Pa = ? ? - What is this value σa‘ = Ka σv’ – 2 c (Ka)1/2 σa‘ = Ka σv’ σa‘ is the stress distribution Pa is the force on the wall (per foot of wall) How is Pa found?

Passive Stress Distribution (c = 0) γ c = 0 Φ dry soil H Pp = ? ? - What is this value σp‘ = Kp σv’ – 2 c (Kp)1/2 σp‘ = Kp σv’ σp‘ is the stress distribution Pp is the force on the wall (per foot of wall) How is Pp found?

Stress Distribution - Water Table (c = 0) H1 Effective Stress Pore Water Pressure Ka γ H1 H2 Pa Ka γ H1 Ka γ’ H2 γw H2 or Ka (γ H1 + γ’ H 2) Pa = Σ areas = ½ Ka γH12 + Ka γH1H2 + ½ Ka γ’H22 + 1/2γwH22

Stress Distribution With Water Table Why is the water pressure considered separately? (K) H1 Effective Stress Pore Water Pressure Ka γ H1 H2 Pa Ka γ H1 Ka γ’ H2 γw H2 or Ka (γ H1 + γ’ H 2)

Active Stress Distribution (c ≠ 0) zo γ c ≠ 0 Φ dry soil H _ - = Ka γH 2 c (Ka)1/2 Ka γH – 2 c (Ka)1/2 Find zo: Ka γzo – 2 c (Ka)1/2 = 0 Zo = 2c / γ (Ka)1/2 Pa = ?

Passive Stress Distribution (c ≠ 0) γ c ≠ 0 Φ dry soil H + - = Kp γH 2 c (Kp)1/2 Kp γH + 2 c (Kp)1/2 Pp = ?

COULOMB'S EARTH PRESSURE THEORY FOR SAND FOR ACTIVE STATE Coulomb made the following assumptions in the development of his theory: 1. The soil is isotropic and homogeneous 2. The rupture surface is a plane surface 3. The failure wedge is a rigid body 4. The pressure surface is a plane surface 5. There is wall friction on the pressure surface 6. Failure is two-dimensional and 7. The soil is cohesionless

Importance of Drainage for Retaining Walls Drains, Filters & Weep holes Granular zone or geofabric drain Weep holes

Kind of loads Soil a) Rest b) Active c) Passive Surcharge Water Static Finite Infinite Dynamic Water Dynamics

Design of Retaining Wall 1- External Stability 2- Internal Stability

External Stability External Stability 1- Sliding 2- Overturning 3- Bearing Capacity 4- Overall Failure

Sliding FR = Pp + Friction & Cohesion FD = Pa

Overturning MR = Pp.yp + W1 a1 + W2 a2 +W3 a3 +W4 a4 MD = Pa . ya Moment About o

Bearing Capacity

Bearing Capacity

Bearing Capacity

Overall Failure

Check for Overturning

Check for Overturning

Check for Overturning

Check for Sliding

Check for Sliding

Internal Stability

Internal Stability

Internal Stability