General presentation
A retaining wall is a structure that retains (holds back) any material (usually earth) and prevents it from sliding or eroding away. It is designed so that to resist the material pressure of the material that it is holding back.
from Wikipedia
Gravity retaining wall relies on their huge weight to retain the material behind it and achieve stability against failures. Gravity Retaining Wall can be constructed from concrete, stone or even brick masonry. Gravity retaining walls are much thicker in section. Geometry of these walls also help them to maintain the stability. Mass concrete walls are suitable for retained heights of up to 3 m. The cross section shape of the wall is affected by stability, the use of space in front of the wall, the required wall appearance and the method of construction.
Piling wall – Steel sheet pile walls are constructed by driving steel sheets into a slope or excavation upto the required depth. Their most common use is within temporary deep excavations. They are considered to be most economical where retention of higher earth pressures of soft soils is required. It cannot resist very high pressure.
Cantilever retaining wall is one that consists of a wall which is connected to foundation. A cantilever wall holds back a significant amount of soil, so it must be well engineered. They are the most common type used as retaining walls. Cantilever wall rest on a slab foundation. This slab foundation is also loaded by back-fill and thus the weight of the back-fill and surcharge also stabilizes the wall against overturning and sliding.
Anchored retaining wall uses facing units tied to rods or strips which have their ends anchored into the ground is an anchored earth wall. The anchors are like abutments. The cables used for tieing are commonly high strength, prestressed steel tendons. To aid anchorage, the ends of the strips are formed into a shape designed to bind the strip at the point into the soil.
Wall analysis
The magnitude of stress or earth pressure acting on a retaining wall depends on:
- height of wall
- unit weight of retained soil
- pore water pressure
- strength of soil (angle of internal friction)
- amount and direction of wall movement
- other stresses such as earthquakes and surcharges
Lateral earth pressures are analyzed for either „Active,” „Passive” or „At-Rest” conditions.
Active conditions exist when the retaining wall moves away from the soil it retains.
Passive conditions exist when the retaining wall moves toward the soil it retains.
At-Rest conditions exist when the wall is not moving away or toward the soil it retains.
Basically, lateral earth pressures are derived from the summation of all individual pressure (stress) areas behind the retaining wall. These pressure areas are triangular in shape with the base of the triangle at the base of the wall for the soil component and pore water component. Pressure areas for surcharges are rectangular in shape, and earthquake pressures are usually analyzed with a nearly ‘upside-down’ triangle.
There are several methods used for the computation of the active thrust.
Coulumb‘s method is based on global limit equilibrium theory of a system whose components are the wall and the wedge of homogeneous terrain behind the work assuming rough surface.
Where terrain is dry and homogeneous the pressure diagram is expressed linearly by the following:
Pt = Ka × γt × z
Thrust St is applied at 1/3 H with the value:
Having
Limit value of Ka:
δ < (β-ϕ-ε) according to Muller-Breslau
γt = Terrain unit weight
β = Inside wall surface inclination to horizontal plane of footing
ϕ = Terrain shear resistance angle
δ = Angle of friction terrain to wall
ε = Field level inclination to horizontal – Positive if anticlockwise
H = Wall height
If ε = δ = 0 e β = 90° (wall with smooth surface and backfill with horizontal surface) thrust St is simplified to:
that coincides with Rankine‘s equation that gives active thrust where backfill is horizontal.
Effectively Rankine used the same hypothesis as Coulumb except that he ignored wall-terrain friction and cohesion. Rankine’s expression for Ka in general form is as follows:
After determining lateral earth pressures, retaining wall analysis and design also includes: sliding check, overturning check, bearing capacity and settlements, global stability analysis and structural design of the wall.
Checks
Sliding
Sliding failure is a result of excessive lateral earth pressures with relation to retaining wall resistance thereby causing the retaining wall system to move away (slide) from the soil it retains.
Overturning
Overturning failure is a result of excessive lateral earth pressures with relation to retaining wall resistance thereby causing the retaining wall system to topple or rotate (overturn). Sliding governs the design of retaining walls most of the time, especially for walls less than 8 feet in height. However, overturning must be analyzed.
Global stability
Global Stability verification is calculated with the classical DEM and Limit Equilibrium methods. Verification can be performed both with circular and free form slip surfaces.
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