Note from Andy:
In this post, Ian gives a very detailed overview for the design of retaining walls. If this topic is not one of the things that you come across regularly, you should definitely check it out!
Earth pressure and retaining wall are one of the few subjects that may appear on both days of the structural engineer (SE) exam per the 2011 to 2014 SE exam specifications. That said, as best as I can tell, you will only have to design a full retaining wall during the vertical portion of the exam.
Some of the relevant items for retaining walls you should be familiar with according to the SE exam specification:
- Settlement loads, fluid/hydrostatic loads, and static earth pressure loads for the vertical exam. Also, dynamic earth pressure loads specifically for the lateral exam.
- Use of design pressure coefficients (e.g., active, passive, at rest, bearing coefficient of friction, cohesion).
- Selection of foundation systems (e.g., based on geotechnical information, boring logs, settlement, and groundwater table).
- Overturning, sliding, and bearing.
- Piles (concrete, steel, timber).
- Drilled shafts/drilled piers/caissons.
- Gravity walls.
- Anchored walls.
- Basement walls for buildings.
- Effect of adjacent loads.
- Use of modulus of sub-grade reaction.
In addition, remember the note at the end of the vertical, depth (afternoon) exam specifications: “…and at least one problem includes a foundation.” This could be a pile cap, a combined footing, or any of a number of problems that could take about an hour to solve. Since retaining walls generally would take about an hour to design, it makes an attractive option if I were designing the SE exam so it’s a good idea to know it well.
General Study Strategy
This is a good time to note a test study strategy that I don't often see mentioned. Consider this one of my “secret pro tips”, and would have saved my derrière had I known it the first time I took the vertical exam.
Ian's SE Exam Pro Tip #1: While you are studying, make some observations of items that would be good afternoon test problems. Try to identify problems that incorporate a large section of engineering principles and that can be solved in an hour, to an hour and a half (or more for the bridge exam, 2 hour problem).
As an example for the lateral exam; steel or concrete special moment frames present a number of options that can be done in an hour. Thus, try to gather resources (or create your own resources) to help increase your speed on this and other items you feel have a decent chance of appearing on the exam.
Make sure you practice using them as well! A cheat-sheet isn't any good if you have to take time during the exam learning how to use it.
However, a note of caution – You can never guess what will be on the exam and I would highly advise you not to skip sections just because you think they won't be on the exam. Remember my tip at the end of my previous post: “if you didn't study something, then it's going to be on the exam.”
Design Handbooks for the SE Exam
With the above tip in mind, we know that there will be at least one foundation problem on the vertical, depth section of the SE exam. Therefore, try to gather as much resources to help increase your speed with foundation problems of all types. One of the references that I used often during the exam was the 2008 CRSI Design Handbook, 10th Edition.
The CRSI Handbook is kind of like the AISC Design Manual except it’s for the 2008 ACI building code. It provides tabulated designs for common concrete design problems. Round and square columns, beams, development and lap splice lengths, slabs, footings and pile caps, and cantilevered retaining walls all have tabulated design sections in the CRSI Handbook.
For the morning “multiple choice” session of the exam, tabulated design handbooks such as the AISC manual and CRSI handbook are invaluable. The obvious problem is these handbooks do not help you with the long-answer afternoon problems as you are expected to show your calculations.
What this and other handbooks do provide for the afternoon is quick verification of your calculations. For example, if I had to design a lap splice on the exam I would open up ACI 318 to 12.2.2 and 12.15 and write out my design. I would then open up CRSI to the lap splice tables and verify my numbers. If time was critical I could just skip ACI and just write out the numbers from CRSI; probably worth at least partial credit.
This is definitely true for any retaining wall structures, the CRSI handbook provides detailed tables for most cantilevered retaining wall structures you would see. Below is an example of one of the tables from the CRSI handbook for cantilevered retaining walls.
You can see that if we were asked to size the required width of base for a cantilevered retaining wall, the CRSI handbook would do a good job of getting us close and makes an excellent verification of our design.
OK enough about the CRSI handbook though. I didn't originally intend to spend this entire post advertising for a concrete handbook, but whatever. I'll bill CRSI later. My point is that handbooks, flowcharts, design guides, and other quick reference materials are essential to rapid problem solving during the exam, use them wherever possible.
Retaining Wall Design
Let's actually talk about designing retaining walls now! Since both masonry and concrete retaining walls are likely to appear on the exam, I will only focus on the general design requirements for retaining walls.
For the design specific calculations and details of each retaining wall design, I leave up to the reader for their own studying. If you're taking the SE exam, you should make sure to practice at least one design of each type of retaining wall.
I'm also going to only briefly touch on each area without going into too much detail. There are plenty of other good references on retaining wall design that will do a much better job than I can on explaining the detailed design of a retaining wall. The goal of this section is to familiarize yourself with the basic principles and make sure you cover all the bases during your studies.
Retaining walls generally have little vertical load other than self-weight and weight of any soil on a footing. However, this isn't the case if the retaining wall is also a bearing wall. If the retaining wall is, for example, the basement foundation wall of a building, then it likely has a beam or other lateral support at the top as well as the cantilevered support at the bottom. Thus, the wall acts somewhere between a simple span beam and a fixed cantilever.
With the above in mind, let's limit our discussion to non-bearing walls for the remainder of this article (the principles are similar for both bearing and non-bearing retaining walls). Either way, the design will likely be one of the four structures shown above: gravity wall, piling wall, cantilever wall, and an anchored wall.
Of note, I would consider cantilever walls to be a subsection of gravity walls. This is important because the SE exam specifications list three types of walls that may show up on the exam:
- Gravity walls
- Anchored walls
- Basement walls for buildings
You may also see some mentioning of piling walls or mechanically stabilized earth walls but they aren't specifically called out in the exam specification so I believe you can reasonably ignore these during your studies. I'd just be aware that they exist and understand the fundamentals of how those retaining structures work prior to the exam.
Loads and Reactions on Retaining Walls
Loads on a retaining wall are generally as follows:
- Self-weight of the retaining wall.
- Vertical weight of the soil, both in front and behind the wall (as applicable).
- Lateral soil load, generally modeled as an equivalent fluid pressure. (Note: If the backfill is sloped there will be a vertical component to this load as well.)
- Surcharge loads from adjacent structures or loads near the wall.
Reactions on a retaining wall depend on the type of wall being designed but will generally include some of the following:
- Vertical base soil pressure reaction, in response to overturning moments.
- Passive soil pressure on the front of the wall and footing (sometimes ignored).
- Friction forces between the footing of the wall and the soil.
- Anchorage forces from any soil anchors in the wall.
I've borrowed the image above from Alan Williams’ excellent Structural Engineering Reference Manual. Copyright? What's that? Just kidding, fair-use laws are good to know and I was too lazy to redraw it, so be quiet.
In the above image we can see all the loads on a cantilevered retaining wall. Many of these loads are applicable to all types of retaining walls. I've listed the loads below:
- F is the frictional force at the underside of the wall bearing surface.
- HA is the total active earth pressure behind wall (HA may also include a hydrostatic component but note that any hydrostatic load will reduce the active earth pressure ).
- HL is the total pressure behind the wall due to live load surcharge (if present).
- HP is the total passive earth pressure in front of the wall.
- WB is the weight of the base.
- WK is the weight of the key (if present).
- WL is the weight of the surcharge (if present).
- WS is the weight of the backfill.
- WW is the weight of wall stem.
The primary method to solve these problems is statics: sum of the forces and sum of the moments equal to zero. With that you can solve for all of the forces on a retaining wall.
Often you will be given the retaining wall geometry and the soil properties of the backfill. You then usually are tasked with finding the resulting bearing pressures under the retaining wall. Or perhaps you have to find the length of the heel of the retaining wall (LH in the image above). Some design of the structural components will also likely be involved.
The easiest way to speed up the analysis of a retaining wall is to break the vertical weights into rectangular sections, as the above image has done. You can quickly calculate and tabulate the centroid and weight of each section based on given densities and dimensions.
After that, you can then sum the moments about a “point” to obtain the total moment in the wall. The “point” typically chosen is the furthest forward, lowest part of the toe of the wall's footing (bottom left corner for the example image above); but any point will serve as long as you're consistent.
I often choose the typical “point” such that the vertical loads will cause a clockwise moment (in the wall orientation shown above) and the soil pressures will cause a counter-clockwise moment. See the picture below from the 2008 CRSI Handbook for details, note they have separated the overturning moment Mo and the resisting moment Mr as you are often given one and must design for the other.
After tabulating these moments you can then calculate the required length of heel for overturning resistance, the soil pressure from the soil below the footing of the wall, and any anchorage forces required, depending on the wall type being designed. Anchorage loading for an anchored wall should be much simpler to calculate so I'll leave that for another time.
For cantilevered and other gravity walls, you have to first calculate the centroid of the required soil bearing force (see “e” in the picture above). If it is outside of the kern (middle third of the footing) then you will have the soil pressure truncated to zero at some point on the footing. This will require a more complicated analysis and should be avoided if possible due to the time required for analysis. Remember that soil is typically assumed to have zero tensile capacity, though some very small amount does exist.
Once the centroid is determined, you can then calculate the pressure distribution using the equations shown on page 2-1 of the Structural Engineering Reference Manual. After that, you can compare soil pressure demand v.s. capacity.
If the exam question asks you to size the footing, most likely you will need to do an iterative analysis to come up with a satisfactory soil pressure. (Note: if you run into an iterative design like this, don't focus on an efficient design unless required to.)
For example, sure you think you can make the foundation work with only a 4-foot long heel but what if you find it needs 4.5 feet? You just wasted 10 minutes writing out a design that's no good. Instead, just find a rough idea of what will work (remember those CRSI tables I mentioned?) and then exceed it.
As far as I know you don't lose points for an inefficient design unless they specifically mention it. Watch out for wording that might read something like “find the smallest bar diameter that can adequately reinforce the wall”.
You'll note that I have not discussed passive soil resistance so far. This is because of two very important reasons. The first being that it's unreliable. In practice, some engineers (and myself) tend to ignore it as it may not exist in certain circumstances (unless the soil report specifically indicates it). For instance, if the wall toe is excavated for repairs or future construction then there will be no passive soil resistance to sliding or overturning. Additionally, it's possible for the wall to “push” the soil away leaving a gap or at least a reduced passive soil pressure.
Passive soil is a real force though so it can be included if required for a design to work. For example, if a shear key is added below the wall for sliding resistance then passive soil is almost certainly being used. In the case of a shear key, excavation is unlikely and the weight of the wall confining the soil will help ensure that the passive soil pressure is likely to be present.
The other issue with passive soil is it's generally not required. Frictional forces below a wall can often be sufficient to resist sliding and are very quick to calculate. Thus, not including passive soil can speed up your design process. This can save precious time during the exam.
In the end, both in real practice and on the exam, only use passive soil pressure if you require it and understand its limitations.
Structural Design of Wall Components
After you've calculated the forces on the wall you can then design the individual components for the loads on them. Sum the forces and moments on each member in a free-body diagram and find the internal forces that need to be resisted. Typically it's all cantilevers but you'll see others as well. For example, a counterfort retaining wall spans continuously between the counterforts, assuming no construction joints.
From here, you will design the components typically as reinforced concrete, reinforced masonry, or steel structural members, whichever is applicable. Most of these will be simple designs in nature and should be of little difficulty. Note that shear in the walls will likely not control but don't forget to check it as some minimal shear reinforcement may be required. If possible, break the retaining wall up into 12 inch sections. This will simplify your design and loads mathematically.
Further details about design of the wall components is highly dependent of the material of the retaining wall and I leave it up to the reader to study those further. See the previous blog post from Andy regarding design of reinforced concrete members for a quick refresher as much of that will apply to a concrete retaining wall.
Note that the governing section of the codes for masonry and concrete will be the wall and foundation sections of those codes. Make sure to check their sections for specific requirements for walls and foundations.
There's much more to cover but I fear that this blog post is getting too long as it is. I will conclude this by broadly addressing some of the other items the reader should be familiar with regarding retaining walls.
Remember that if there is a sloped backfill there will be both a vertical and horizontal component to the active pressure from the backfill (where there was just horizontal with a level backfill before).
Also, remember that if they don't give you soil data for lateral soil loads (which is unlikely), then in ASCE 7, chapter 3, there are minimum soil and hydrostatic pressure loads. Glance over Table 3-1 Design Lateral Soil Loads on page 7 and be familiar with that table and the footnotes given there. Under AASHTO most retaining walls that are subject to vehicle loads require some amount of additional “backfill” to be included to simulate a vehicle surcharge load.
Bearing pressure and other service related design aspects are typically done with un-factored loads under LRFD. Some other service failures that must be checked are sliding of the wall, lateral deflection of the wall, lateral tilt of the wall due to differential settlement, and crack control. However, I would expect that any question regarding serviceability failures will likely be related to “how would one fix it” and not include much in the way of actual design. This is entirely my own opinion, though – be prepared either way.
Finally, remember that retaining walls are just spread footings that are trying to tip over. Much of the same design applies to both, and both will likely be encountered in either a large or small portion of the exam. Shear in the footings, anchorage of the reinforcement, flexure in the walls, temperature and shrinkage reinforcement, these are all going to be similar in both retaining walls and typical footings and foundations. Make sure you can do these sorts of problems quickly because any unfamiliarity will cause issues during both morning and afternoon portions of the exam. Foundation problems require much tabulation and multiple simple calculations at each step. Thus, being able to rapidly solve these sorts of problems through familiarity with the design steps is crucial to success.
I hope you've enjoyed this blog post. It took me a little longer to finish it than I hoped but that was partly due to my lax attitude to beginning my own studies for the exam. However, that time is upon us and study we must. I plan to study hard over the next few months to pass this exam and I hope you will too. Don't let good opportunities to study pass you by; you will miss them as October gets closer.
Thanks for reading.
Standard disclaimer: The above blog post is offered as a helpful reference for studying for the NCEES Structural Engineering exam. However, no warranty is given or implied for the accuracy or correctness of the information presented and any use of this material is at the users own risk. I am not a licensed engineer in any state nor a subject matter expert in the areas discussed. I write these blogs for Andy Lin and Engineering HQ to allow myself and others to better prepare for the SE exam in the hope that we can all learn to be better engineers together.