Okay, lets continue on to Part 3 of Retaining walls. If you have not read Part 1 and Part 2, I would suggest you read those before continuing with this section. In this section we will take a simple cantilever retaining wall and discuss the concept of how they are affected by the loads and how you have to design them to resist these loads that they are subjected to.
What is a cantilever retaining wall? It is a wall that acts like a cantilever fixed at the bottom foundation. Here is a sketch of cantilever retaining wall and for the sake of understanding the basics lets assume an imaginary superman pushing the wall with all his strength. Notice that if he was not standing on the foundation or if the foundation was very short, then he could both push it or topple it over. Pushing force is represented by the left pointing arrow and toppling is represented by the curved arrow. But because he is standing on portion of the foundation and the foundation is large, he will have some difficulty making the wall topple. The forces shown in Yellow and Orange are the forces that will naturally cause the wall to slide (push) and overturn (topple). The force shown is yellow color is from soil pressure and the forces shown in orange color is from live load surcharge. Soil pressure can be “active” soil pressure or “At-rest” soil pressure. So what is the difference between the “active” and “at-rest” soil pressure and how can you tell which pressure you should design for?
You should always refer to the recommendations given by the soils engineer. When the wall is flexible (meaning if the top of the wall rotates by 0.001 to 0.003 radians or if the top of the wall deflects at the range of 0.001 h to 0.003 h where “h” is the height of the Retaining wall, then the wall deflects and moves away enough from the soil retained that the horizontal soil pressure decreases to the “active” pressure levels. You should never assume that walls are always designed for active pressure. If the wall is too stiff then you will be underestimating the soil pressure that the wall is subjected to. “At-rest” pressure is typically greater than “active” pressure.
If there is a roadway or buildings near by to the retaining wall then the wall will also be subjected to additional pressure called the Live load surcharge. This is shown in orange color in the sketch above. If there is any buildings or structures close to the retaining walls then the soils engineer will also recommend the loads coming from the foundation of those structures that the walls have to be designed for.
So what prevents these walls from being pushed and toppled? Well, see the small blue truncated triangle on the left side? That is the passive pressure. Passive pressure (in pcf) is usually pretty large but notice that the area of the actual structure that presses against the soil is pretty small so in reality the ability of passive pressure alone to resist these forces is unrealistic. So what else helps maintain the stability of the wall? The friction force between the bottom of the foundation and soil plays a big part in resisting this sliding force. In most text books coefficient of friction between soil and foundation is taken a 0.5 which is a relatively high number. In reality a lot of soils engineers define this value to be much less than that. Once again soils engineers play a big role in design of the retaining walls and often times they will not let the design engineer add the effects of 100% passive and 100% friction together. One additional item to keep in mind during design is that there is greater friction if the weight of the structure is large so if you are trying to design the most efficient section it will come back to give you problems in counteracting sliding forces. Once your design takes care of overturning and sliding, the third thing you have to check for is to make sure that the soil underneath the foundation can actually take these additional stresses. The soil fill underneath the foundation is rated for a certain amount of allowable bearing pressure. See the image below on how these overturning forces affect the soil underneath the foundation.
In Case 1, there is no eccentricity and hence the soil under the footing is uniformly loaded. fmax has to be less than Allowable bearing capacity. In Case 2, there is Moment that causes eccentric loading on the footing. As long as the eccentricity e<B/6, and fmax is less than allowable bearing capacity the footing size should be adequate. In Case 3, the moment is so large that the eccentricity of the footing is outside of the middle third of the footing or in other words e>B/6. What this indicates is that the footing size is not efficiently used. fmax should once again be less than the allowable bearing capacity but footing size can be adjusted to make the maximum use of it. When in any of the above cases fmax is greater than the bearing capacity of the soil, then the soil underneath the footing fails. This should be avoided at all costs.
Another important topic in the design of retaining walls is actual drainage details. Most retaining wall failures are caused due to improper drainage details. Imagine what happens if the soil on the right side of the wall in the picture above is water logged due to drains clogged or no drains at all? There is additional pressure on the wall due to water. The density of water is 62.4 pcf which is quite a big additional pressure on the wall.
If the height of soil to be retained above the footing is “h”. It is good practice to design the wall to be 6″ taller than the soil to be retained. The top of the footing also has to be a minimum of 12″ below the top of soil on the toe side (side that shows point “A”). In order for you to pictorially see what additional forces the wall could potentially be subjected to please see sketch below.
When there is an earthquake the wedge of soil above the failure plane will cause additional shear on the wall. This is an inverse triangle with larger forces acting on the top of the wall which means the moments due to seismic forces (inverse triangular force) on the base of the footing can be a huge addition to the moments due to the active pressure. The soils engineer will actually give you the value of the seismic forces that act on the wall.
In order to calculate the forces that cause the wall to overturn, moment and shear are calculated about the point “A” in the diagram above. Just from observation, you can tell that the passive pressure is very small force to counteract the active forces causing the footing to overturn and slide.
Your job as an engineer is to make sure that you design the wall and foundation to be strong enough to resist these forces shown by the red arrows. Designing retaining walls is a iterative process. Sometimes you are so close to your design working but not quite enough for sliding. In those instances you have to compare costs to see what is the best alternative. To add a shear key under the footing to engage more passive pressure or just make the footing big enough to increase the frictional forces? It is a trial and error process, but take into account what it will cost not just for materials but also labor to have to pour a shear key (additional trenching, additional concrete, additional steel).
I hate to say, we are still only scratching the surface of retaining wall design. There is so much to talk about. I will leave you with a video of retaining wall collapse in Baltimore, Maryland. After you watch the video, you can also read the blog post written by Dr. Dave Petley about this particular retaining wall collapse. I believe this particular collapse was due to heavy rains and lack of adequate drainage and the wall itself seems under designed for the loads that it was subjected to.
It is good that no one got hurt during that collapse.
Update: I have developed a short course on Design of Cantilever Retaining Walls. (Tieback, Drilled Pier, Soldier pile walls coming soon). Inside the course I discuss what the codes recommend and how to design the Cantilever retaining wall, how to write specifications, sample drawings, detailed example problems etc. I also show hand calculation and also step by step computer analysis using a commercial software. These are video courses so you can learn step by step how to do the calculations. You can obtain Continuing Education credits if you take the class and then pass the quiz at the end of the class. Click here to learn more about the different modules and try some for free. Once again thank you for reading and your support.