Lateral Earth Pressure and Retaining Walls
Vertical or near-vertical slopes of soil are supported by retaining walls, cantilever sheet-pile walls, bulkheads sheet-piles, braced cuts and other similar structures.
Lateral Earth Pressures
Lateral Support In geotechnical engineering, it is often necessary to prevent lateral soil movements. Tie rod Sheet pile Anchor Braced excavation Cantilever retaining wall Anchored sheet pile dr. isam jardaneh / foundation engineering 61303 / 2010
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 dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
Sheet Pile Sheet pile wall dr. isam jardaneh / foundation engineering 61303 / 2010
Soil Nailing dr. isam jardaneh / foundation engineering 61303 / 2010
Lateral Support Reinforced earth walls are increasingly becoming popular. dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
Lateral earth pressure is a function of several factors, such as: The proper design of those structures requires an estimation of lateral earth pressure. Lateral earth pressure is a function of several factors, such as: The type and amount of wall movement The shear strength parameters of the soil The unit weight of the soil The drainage conditions in the backfill dr. isam jardaneh / foundation engineering 61303 / 2010
Nature of Lateral Earth Pressure dr. isam jardaneh / foundation engineering 61303 / 2010
Passive At Rest Active dr. isam jardaneh / foundation engineering 61303 / 2010
Lateral Earth Pressure Lateral earth pressure is a function of effective vertical stress dr. isam jardaneh / foundation engineering 61303 / 2010
Ơh= f (Ơv)
K=coefficient of lateral earth pressure Ơh=kƠv K=coefficient of lateral earth pressure
Lateral Earth Pressure at Rest Lateral earth pressure is a function of effective vertical stress dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
Water Table dr. isam jardaneh / foundation engineering 61303 / 2010
q γ1 K0 γ1H1 H1 γ2 H2 γwH2 γ1H1 q γ2H2 K0 K0 K0
Ko = 0.4 + 0.007 (PI) for 0 > PI > 40 Ko = 1 - sinφ for NCC Ko = 0.95 - sinφ for NCC Ko = 0.4 + 0.007 (PI) for 0 > PI > 40 Ko = 0.46 + 0.001 (PI) for 40 > PI > 80 Ko = 0.19+0.233log(PI)
Active Lateral Earth Pressure Wall moves away from the soil
William John Macquorn Rankine 1820 – 1872 Scottish civil engineer, physicist and mathematician. He was a founding contributor to the science of thermodynamics, particularly focusing on the first of the three thermodynamic laws. Rankine developed a complete theory of the steam engine and indeed of all heat engines. He was an enthusiastic amateur singer, pianist and cellist who composed his own humorous songs. He was born in Edinburgh and died in Glasgow, a bachelor. Rankine's theory, developed in 1857
Assumptions No friction between the backfill soil and retaining wall. Angle of friction(δ) = 0 Retaining wall is vertical Surface of backfill is horizontal
Rankine Active Earth Pressure
σ`a = Rankine Active earth pressure σ`0 = Effective vertical stress C = Cohesion Φ = Angle of internal friction Ka = Rankine active pressure coefficient Ka =(1 – sin φ)/(1+sinφ) =
dr. isam jardaneh / foundation engineering 61303 / 2010
Zc = depth at which pressure = zero Zc = depth of tensile cracks dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
Example
Example dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
Use this dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
Example dr. isam jardaneh / foundation engineering 61303 / 2010
Charles Augustin de Coulomb Born in France. His studies included philosophy, language and literature. He also received a good education in mathematics, astronomy, chemistry and botany. He was involved in structural engineering , soil mechanics, as well as other fields of engineering. He discovered an inverse relationship of the force between electric charges and the square of its distance, later named after him as Coulomb's law. Coulomb leaves a legacy as a pioneer in the field of geotechnical engineering for his contribution to retaining wall design. His name is one of the 72 names inscribed on the Eiffel Tower. 1736 - 1806
Coulomb Active Earth Pressure
Comments: Coulomb considered friction δ Due to friction, the failure surface is NOT PLANE He considered it PLANE for easy solution No big difference in results When δ increases, the error in calculating Pp increases and the situation may be UNSAFE The REAL failure surface is LOGSPIRAL as shown
45+Ф/2 45+Ф/2 ACTIVE δ H/3 Pa 45 - Ф/2 45 - Ф/2 Pp PASSIVE δ H/3
dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
Example dr. isam jardaneh / foundation engineering 61303 / 2010
Passive Lateral Earth Pressure Wall moves towards the soil
Rankine Passive Earth Pressure
Use this dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
Passive Pressure Passive Force where dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
Solve this problem for passive case Example Solve this problem for passive case
Coulomb Passive Earth Pressure
* Passive means the wall moves into the backfill soil. * Coulomb 1776 assumes that there is friction between RW and backfill materials * Passive means the wall moves into the backfill soil. dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
dr. isam jardaneh / foundation engineering 61303 / 2010
Problem # 1 dr. isam jardaneh / foundation engineering 61303 / 2010
Problem # 2 Refer to problem # 1 above. For the retaining wall, determine the Rankine active force per unit length of the wall and the location of the line of action of the resultant. dr. isam jardaneh / foundation engineering 61303 / 2010
Problem # 3 dr. isam jardaneh / foundation engineering 61303 / 2010
Problem # 4 dr. isam jardaneh / foundation engineering 61303 / 2010