What is so special about the letter ‘L’?

Photo by Brina Blum on Unsplash

Believe it or not, but the letter that gives us some of the most existential words in the world, like Love and Life, deserves more praise than one would think. The letter that comprises merely two lines — one that goes from top to bottom and the other that continues from left to right — is interestingly part of a widely used geotechnical design. The shape ‘L’ governs the design of a structure that you may have seen or even leaned against, aka the L-shaped retaining wall. So, what is so special about this letter that enables it to Lure more Lauding?

Before we talk about an L-shaped retaining wall, let us first understand what retaining walls are. Simply speaking, retaining walls are structures that hold soil or earth behind them. Basically, granular materials, like soil and rocks, generate horizontal pressures that increase linearly with depth. Retaining walls must resist these pressures. They withstand the forces exerted by the retained ground, on one side, and transmit these forces safely to the foundation. The structure supports the soil behind it laterally so that the soil can be retained at different levels on the two sides.

Few different types of retaining walls (Photo credit: Retaining Wall Solutions)

There are different types of retaining walls, such as gravity retaining walls (which include mass concrete retaining walls, crib walls, gabion walls, and reinforced fill structures); cantilevered retaining walls, like pipe pile and bored pile walls; and reinforced concrete (R.C.) retaining walls, which include R.C. L-shaped and inverted T-shaped cantilever, counterfort, and buttressed retaining walls. However, in this piece, we will only discuss the L-shaped retaining walls.

Let’s Design a Wall

If you were to use an L-shaped retaining wall to retain a volume of soil on one side, how would you place the L structure? Should the bottom leg of the L be towards or away from the soil volume? Or does it make no difference? We will refer to a demonstration video here, using a wooden L-shaped model and some marbles, to better understand what will happen.

An image still from the demonstration video

When deciding how to place the L-shaped structure, some might decide to point the base of the said shape away from the mass. Assuming the entire structure to be rigid, one can well argue that by placing this L-shaped wall in this manner, it would be difficult for the wall to tip over, with the base providing some stability against any toppling. This tipping over is critical, and an engineer needs to be wary about this form of failure, formally referred to as an overturning failure.

Sliding failure of the wall (Excerpt from the demonstration video)

Let’s start filling in the volume of soil (depicted by marbles in the demonstration video) behind the wall then. Once the soil starts to be filled on one side, unbalanced forces start to come into play. Eventually, the wall would be seen to slide as more and more soil is added since the increasing volume of soil pushes the wall away, causing the structure to fail in serving its role. We call this type of failure, sliding failure.

Overturning failure of the wall (Excerpt from the demonstration video)

Even if we try to prevent sliding failure by increasing friction between the retaining wall and the base, we will notice that the wall would still eventually fail (albeit with a greater retained height). But this time it would fail due to overturning about the corner base of the structure.

If we were to turn the wall around, however, what can we expect? The bottom leg now points to the same side where the soil will be poured. It is interesting to note that a higher retained height will be achieved now. So, why is the wall able to retain more soil when the bottom leg points the other way round, without possibly undergoing any sliding or overturning failures?

Greater retained height achieved upon placing the bottom leg of the structure towards the retained side (Image still from the demonstration video)

Bring Back Some High School Physics!

Resistance against overturning (Image still from the demonstration video)

When the bottom leg is oriented away from the mass, the resistance to the overturning and sliding is only provided by the actual weight of the L-shaped wall. However, when the bottom leg is on the same side, the weight of the soil volume that the structure retains provides additional assistance in keeping the wall upright. This surcharge load, that acts downwards, in the area over the bottom leg of the L-shaped retaining wall helps in producing stabilizing moments against overturning.

Resistance against sliding (Image still from the demonstration video)

The weight of the soil (acting on the bottom leg of the wall) also increases the friction between the wall base and the ground, thereby providing a higher resistance against sliding.

Simple loading diagram of L-shaped retaining wall structure (Image still from the demonstration video)

Hence, when engineers design L-shaped retaining walls, they check against overturning and sliding, among other failures, by calculating how strongly the lateral pressure from the soil will destabilize the wall and make it, a) slide away, and b) overturn about the base corner (Point Q) of the wall. They then check the sliding force and overturning moments (Mo) against the resistance force and restorative moments (Ms) provided by the weight of the structure as well as the vertical pressure from the mass of soil acting downward on the horizontal leg of the wall.

While this is an overly simplistic (and even incomplete) depiction when it comes to the actual design of this popular geotechnical structure, it is worth appreciating how the understanding of fundamental physics governs the way a structure behaves to serve its role!

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Saad Ali Faizi

Saad Ali Faizi

Engineer by day, writer by night, thinker at all times