The various types of retaining walls are given as below: 1. Masonry Retaining Wall 2. Semi-Gravity Type Retaining Wall 3. Canti Lever Type Retaining Wall 4. Counter Fort Type Retaining Wall 5. Buttressed Walls.
Type # 1. Masonry Retaining Wall:
These retaining walls are constructed by using the stone blocks or bricks as masonry materials. The constructional feature of this wall is exactly similar to the masonry dam. The only difference between them is that, a masonry dam retains the water behind it, while the retaining wall retains the earth materials at its back. The distribution of pressure along its height is also same to the masonry dam.
Masonry structures are very weak regarding their tensile strength, but are very strong for compressive strength. The masonry walls are so weak to bear tension that, they are not capable to withstand a very low tension. Due to this fact, the design of masonry structures requires a great care so that no tension should be developed anywhere in the body of structure under any circumstances.
Design of Masonry Retaining Wall:
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The retaining wall is predominantly subjected to following two forces:
(i) Weight of the wall acting vertically downward; and
(ii) Horizontal pressure due to earth materials acting at the distance of one-third height of the retaining wall from the base.
Fig. 19.1. Masonry retaining wall with trapezoidal cross-section
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In order to make analysis of above two forces acting on the wall, the retaining wall has been assumed to be in trapezoidal cross section, as shown in Fig. 19.1, with ‘a’ as the top width; b as the base width and H as the height. If soil is filled behind it up to the full height of the wall, (i.e. h = H) then,
(i) Weight of Retaining Wall:
It is given by –
In which, W is the weight of retaining wall; λr is the density of Masonry materials and H is the height of wall. The weight of retaining wall acts at a distance ‘x’ from the vertical face of the wall. The value of ‘x’ can be computed by using the following equation –
(ii) Horizontal Pressure due to Earth Fill:
The distribution of horizontal pressure on retaining wall is similar to that of the retaining dam, i.e. in triangular form, but in case of retaining wall the maximum pressure exerted by the earth fill is somewhat different. It is given by the following expression –
Where,
P = horizontal pressure acting at the distance h/3 from the base of retaining wall.
λe = density of earth fill.
ɸ = internal frictional angle of the soil.
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Maximum and Minimum Stresses:
Referring Fig. 19.2, let R is the resultant force of weight of retaining wall (W) and the horizontal pressure (P) acting at the distance Z from the point A.
Now, taking the moment of all forces acting on retaining wall, about the point A.
The moment of R about point A is given by –
W. Z + P. O due to component W and P.
The moment of component P about point A is zero, because its line of action passes through point A.
Thus, the equation (19.4) can be rewritten as –
Eccentricity (e) of weight (W) at the base = [Z – (b/2)]
Direct stress on the base of retaining wall is given as –
The bending moment is developed at the base of the wall due to horizontal pressure caused by the earth fill. This tends to shift the line of action of weight (W) of the retaining wall from the centre of the base to the right side, at the distance Z from the vertical face. In this condition, the eccentricity (e) at the base is equal to [Z – (b/2)].
Since, the maximum stress is developed at point B and minimum at the point A, therefore the nature of this stress will be compressive so long as the values of the stresses obtained by equations 19.6 and 19.7, are positive. The maximum stress obtained by the equation 19.6 will always be positive, which indicates the stress to be in compressive nature.
On the other hand, the minimum stress obtained by equation 19.7 may not be always positive, but negative also. The negative value of stress indicates to be in tensile nature. The tensile stress developed in masonry retaining wall causes failure. This situation must be avoided. To avoid the possibilities of development of tension in retaining wall, the value of e should always be less than b/6, which can be obtained by equating the minimum stress equals to zero. i.e.
The equation 19.8 states that, if the value of e is less than b/6, then fmin will be in compressive nature, and when e is equal to b/6, then fmin will be 0. But when the value of e exceeds b/6, then minimum stress acts in tensile nature. Thus, to avoid the possibilities of development of tension in Masonry retaining wall, the eccentricity should always be less than bl6 or at most it should be equal to b/6.
Specific Cases of Earth Fill behind Retaining Wall:
The following are the specific cases regarding earth fill behind the retaining wall:
Case (1):
When earth fill is saturated up to the top of the retaining wall (Fig. 19.5).
In this condition the lateral earth pressure developed on the wall is due to following reasons:
1. Due to Saturated Soil:
The horizontal pressure acting on the wall due to saturated soil is given by the following equation –
It acts at the distance h/3 from the base of retaining wall.
2. Due to Water:
The horizontal pressure acting on the retaining wall due to water filled up to the top of the wall is given by the following equation (Fig. 19.6) –
It acts at the distance h/3 from the base of the wall. In this equation w stands for density of water.
Combining the above two horizontal pressures –
Case (2):
When a superimposed load is acting on the earth fill, as shown in Fig. 19.7. In this case, it is assumed that the height of soil filled behind the retaining wall is imaginarily increased. Let, if the superimposed load on the soil is W per unit area and λe is the density of the soil fill, is supposed to increase by a height h’, then it will be equal to W/λe meters.
The distribution of horizontal pressure can be determined by considering the imaginarily increased height (h’) and the actual height of earth fill. The pressure distribution along the fill height of retaining wall consists of two parts, i.e. one is rectangular part due to superimposed load and second is triangular part due to the earth fill. These pressures are given by the following equations –
In which, P1 is the horizontal pressure caused by superimposed load and P2 is the horizontal pressure due to earth fill behind the wall (i.e. triangular part).
Case (3):
When surcharge soil is behind the wall.
The surcharged retaining wall is shown in Fig. 19.8. In this case the horizontal pressure ‘P’ can be computed by using the following formula –
In which, α is the surcharge angle and ɸ is the internal friction angle of the soil. The pressure P acts at the distance H/3 from the base of retaining wall, acting in the direction parallel to the surface of the surcharge fill. The pressure P can be divided into two components, one as vertical component (Pv) and other as horizontal component (PH), given as –
Pv = P sin α … [19.14(a)]
PH = P cos α … [19.14(b)]
The vertical component (Pv) increases the load of the retaining wall in downward direction, whereas the horizontal component (PH) increases the horizontal pressure, which causes overturning of the structure.
Stability Conditions for Masonry Retaining Wall:
The following conditions must be satisfied for making the masonry retaining wall safe and stable against various causes of failures:
1. The development of tensile force in masonry retaining wall should not be there. This can be achieved by maintaining the value of eccentricity (e) less than b/6.
2. The maximum compressive stress developed at the base of the structure should not be greater than the permissible limit of the stress for the masonry materials, i.e.
3. In order to make the structure safe against sliding from its base, the value of horizontal pressure (P) should always be less than the resisting force offered by the structure, i.e.
P < μW
In which, μ is the coefficient of friction between the retaining wall and the foundation or in between any adjacent horizontal section of the retaining wall.
4. To avoid the possibilities of overturning of the wall, the magnitude of resisting moment about the toe of the structure should always be greater than the overturning moment about the same point.
Type # 2. Semi-Gravity Type Retaining Wall:
This type of retaining wall involves a greater toe to increase the base width to prevent the development of tension in the retaining wall. In addition, the semi-gravity type retaining wall also needs a fairly heavy section of stem. However, by providing the reinforcement in toe and stem, the heavy section of wall can be reduced.
Type # 3. Cantilever Type Retaining Wall:
This type of retaining wall consists of a base slab and a vertical slab, which are jointed together. The front portion of the base slab is termed as toe, and rear is known as heel. All these components are designed as cantilever. Sometimes to prevent the wall against sliding a vertical projection known as key, is also provided to its base; it increases the resistance of the wall.
The position of key can be fixed at following points of the base:
i. Near the toe
ii. Near the heel; and
iii. Middle of the base.
Type # 4. Counter Fort Type Retaining Wall:
The cantilever type retaining walls are economical for the height of 6 m, only. When their height exceeds 6 m, then they become uneconomical. Under such condition, the counter fort type retaining walls are preferred for construction.
The construction of this type of retaining wall can be made more economical by making the stem and heel as a continuous slab over the counterforts. However, to construct this retaining wall additional amount of concrete, reinforcement and framework are required for constructing the counter forts as an additional part of the wall.
Type # 5. Buttressed Walls:
Buttressed walls are similar regarding constructional feature to that of counter fort type retaining walls. The only difference is that the buttressed wall has counter forts in front of the wall as shown in Fig. 19.12 while in others it is not so. Due to this reason its name becomes as buttressed wall. In this wall, the projection of the heel is very small, as a result the backfill contributes very little stability to the wall; and therefore, the buttress retaining walls are rarely used.
