How to Design Retaining Walls? | Civil Engineering

In this article we will discuss about how to design retaining walls.

Design of Cantilever Type Retaining Wall:

The following points are considered for design of retaining wall:

1. The design of vertical wall should be such that, it can resists the bending moment as well as shearing force, developed at the junction point of the base slab.

2. The design of base slab should also be such that, the load coming on the soil should be within the range of safe limit.

3. The retaining wall must be safe against sliding. It can be achieved by making the base slab of wider width to increase the frictional resistance between the soil and foundation of the wall.

4. The design of toe and heel of the wall should be carefully done, so that they can resist the bending moment, significantly.

5. The width of base slab should be so kept as it can bear the load coming on the soil, safely.

6. There should be provided temperature steel on the exposed face of the retaining wall, so that it can withstand against the effects of temperature. Generally, 0.2% of the total concrete volume, is provided as the temperature steel. The steel should be provided in form of bars, both in horizontal and vertical directions.

7. The top thickness of stem should be kept within the range of minimum 15 cm to maximum 45 cm, provided that there should be heavy surcharge load on the retaining wall.

8. The base width should be kept in the range of 0.4 to 0.6 of the total height of the retaining wall, above the foundation.

9. The maximum length of toe should be 0.3 of the base width and minimum length can be up to 0.2 of the base width.

10. The average thickness of base should be equal to the stem at the bottom of the wall. Sometimes, 5 cm additional thickness is also given to the base, depending on the height of the retaining wall.

11. In case of masonry retaining wall, the development of tension must be checked, which-can be achieved by creating a condition to make the eccentricity value either equal to or less than b/6; in which ‘b’ is the base width of the retaining wall.

Design of Cantilever Retaining Wall:

In this type of retaining wall, the stem acts as cantilever and is subject to lateral earth pressure.

The design consists of determining the following parameters:

1. Intensity of Total Earth Pressure (P):

Let ‘h’ is the height of the stem; α is the surcharge angle and ɸ is the internal frictional angle. Also assume the length of retaining wall as 1 m.

Total earth pressure acting on the wall at height ‘h’ is given by the equation –

2. Maximum Bending Moment:

Maximum Bending Moment is given by following equation,

The thickness of stem at the junction point of base slab is designed according to the above value of bending moment. The minimum 15 cm thickness at the top of stem is generally used.

3. Weight of Retaining Wall:

It includes the following weights:

i. Weight of earth material supported on the heel

ii. Weight of the stem; and

iii. Weight of the base.

(Weight of earth fill at the toe of the wall is neglected)

The resultant force of the above weights should pass through the point at middle third of the base width, so that the base may not be lifted up.

4. Maximum and Minimum Stress at the Base.

It can be estimated by using the following equation –

The maximum stress should not exceed the permissible limit of bearing capacity of the soil.

5. Design of Toe:

The toe of the retaining wall is subject to the pressure caused by the weight of earth fill and self-load acting vertically downward. The design of toe should be such that the maximum shearing force and bending moment can concentrate at the stem face. To make the toe safe, an adequate amount of reinforce­ment should be provided to resists the shearing force and bending moment.

6. Design of Heel.

The heel of the wall is subject to two types of load, in which one is the upward pressure from the soil and other is downward load due to its own weight and earth fill above the heel. Considering these forces into account the design of heel should be such that, the bending and shearing moments would be maximum at the junction point of the heel and stem.

The combine effect of bending moment caused by earth fill behind the wall and self-load should be more than the upward pressure of the soil. In this condition, there should be provided an adequate depth and amount of reinforcement to resists the bending moment and shearing force for making the heel stable.

Design of Base Width.

An approximate formula for determining the base width of cantilever type retaining wall can be derived by assuming the following points:

i. The density of earth material retained behind the wall is same to the concrete, and

ii. The weight of the toe and soil above it, is negligible.

Let, if H is the height of retaining wall; B is the base width; kB is the width of toe and λe is the density of soil, then,

This equation estimates the minimum value of the ratio of toe width to base width, when pressure lies within the allowable limit.

For finding the approximate value of base width of the retaining wall, first the value of σ_b, /λ_e is determined by using the graph, and also the value of k corresponding to H is determined. Again by using another graph B/H for the obtained value of k and internal frictional angle (ɸ) of given soil, is obtained; and in this way the value of B is determined.

Design of Counterfort Retaining Wall:

Counterfort type retaining walls are more economical, when height of wall is equal to 6 m.

The design involves the determination of following parameters:

1. Base Width:

For level top surface, the base width of wall is determined in the same way as the cantilever type retaining wall. However, in counterfort type wall the base width is kept from 0.5H to 0.7 H, in which H is the total height of the retaining wall.

2. Spacing of Counterfort:

The spacing of counterforts to be fixed, depends on several factors such as height of the wall, permissible limit of pressure acting on the soil, cost of concrete, frame work etc. If the counterforts are kept at closer spacing from the vertical wall and heel slab, then amount of concrete and steel is reduced.

The spacing should be such that, the total cost would be minimum. The most economical spacing of counterfort varies from one-third of the height of retaining wall. The thickness of counterfort is governed by the space required to adjust the steel.

3. Design of Vertical Slab:

The vertical slab is supported by counterforts and base. The counterforts are spaced at 2.5 to 4 m from each other. The design of vertical slab is similar to continuous slab. The lower part of stem is subject to maximum horizontal earth pressure. The procedure to calculate the bending moment is given below, considering one meter as length of vertical slab and ‘h’ as its height –

Max^m ending moment = (λehl/12) ke

Where, l is the distance between the counterforts for all intermediate panels. Similarly, the bending moment for end panel is equal to ke. (λehl/ 10). There should be less reinforcement in the stem towards the top.

4. Design of Heel Slab:

The heel of the retaining wall is the same to that of the continuous slab supported by the counterforts. Heel is subject to downward load due to earth and its own weight. The upward load is also subject to the heel due to earth pressure. The thickness of heel slab can be estimated, using the following equation –

Where,

d = effective depth

I = distance between the counterforts

H = total height of retaining wall.

The above equation is derived on the basis of maximum bending moment, and considering the density of earth fill as 1600 kg/m³.

The equation of effective depth (d) can also be derived using the shear force, given as under –

5. Design of Toe Slab:

The toe slab of counterfort type retaining wall is designed as cantilever, which subject to downward and upward forces due to self-weight and earth pressure, respectively in the condition when no front counterforts are provided. On the contrast, when the front counterforts are provided to the retaining wall, then toe slab is designed as a continuous slab supported by the counterforts.

6. Design of Counterforts:

Its design is similar to that of a cantilever beam, considering the loads from stem portion between two counterforts. The effective depth is taken as the distance between the junction of stem and base. The reinforcement is given to its inclined side. In addition, two lagged stirrups are also provided horizontally and vertically for connecting the counterforts to the stem and base, respectively.