As a civil engineer, you know the importance of a good foundation to the stability of any structure. Its job is to receive all the loads from the structure and safely transfer them to the ground.
For this to happen, not only does the foundation need to be able to take on such loads without collapsing, but the soil itself upon which the foundation lies also needs to be able to take on such loads without “failing” — that is, without settling excessively.
The Tower of Pisa is a great example. It started tilting even before construction was completed. Why?
After it reached a certain height, the pressure applied by the tower’s self-weight to the soil via the foundation’s base was bigger than the pressure the soil could handle, which caused the soil to “move” and led to a settling of the foundation on one side.
That’s when the concept of bearing capacity comes into play. Not only is it an important concept in the real world, but it’s also a huge part of both the Civil FE and PE Exam. If you plan on passing any of them, then you need to truly understand it and know how to apply it.
The problem?
There's a lot of confusion about the different types of bearing capacity and which ones to use. Ultimate bearing capacity, net bearing capacity, allowable bearing capacity, etc.
Even worse, there’s the most asked bearing capacity question ever: “Should I use Ultimate Bearing Capacity or Net Bearing Capacity to find the Allowable Bearing Capacity?”
If you’re confused about this already, worry no more!
This article dives into what you need to know about the different types of bearing capacity for the Civil FE and PE Exam and puts an end to this dilemma that test-takers face in their exam prep.
What is Bearing Capacity?
Bearing capacity, in general, is the capacity of the soil to support the pressure created by the total load coming from the foundation. In other words, it’s a measure of the soil’s load-carrying ability — how much it can take on.
This important piece of information about the soil allows civil engineers to design appropriate foundations with the right dimensions and shapes, as well as make better decisions regarding construction materials and load paths.
Various factors influence the bearing capacity of the soil, such as soil type and cohesion, moisture content, presence of groundwater, relative compaction, as well as the type of foundation.
As you know, there are two different types of foundation:
- Shallow Foundations. A foundation is considered shallow if its depth is less or equal to its width, and it transfers loads almost exclusively by end bearing. Examples include strip footings and mat foundations.
- Deep Foundations. A foundation is considered deep if its depth is greater than its width, and it transfers loads via both end bearing and lateral friction. Examples include piles and caissons.
Deeper foundations indeed reach stronger layers of soil with higher bearing capacities and can rely on end bearing, but most of them rely heavily on lateral friction. So, most of the bearing capacity theories have been developed to apply to shallow foundations — and that’s what this article focuses on.
For these shallow foundations to perform as intended, they need to (1) be safe against what’s called shear failure in the soil that supports them, and (2) not undergo settlement that’s greater than what’s allowed for it.
To meet these criteria, civil engineers use the concept of bearing capacity of soil — to make sure it can withstand the pressure created at the base of the foundation due to the total load coming from the structure.
What is Ultimate Bearing Capacity?
Ultimate Bearing Capacity, denoted by qu, is the maximum theoretical pressure at the base of the foundation at which shear failure in the soil occurs. That is, it’s the maximum load per unit area of the foundation the soil can handle before it shears — and one load value you should steer clear of.
When the ultimate bearing capacity of the soil is reached, shear failure happens in one of three ways, depending on the type of soil:
- General shear failure → Dense sand or stiff cohesive soil
- Local shear failure → Sand or clayey soil of medium compaction
- Punching shear failure → Fairly loose soil
Even though all three types of shear failure can occur in real life depending on the soil you’re dealing with, the one type most commonly used both in the bearing capacity theories and on the Civil FE and PE Exam is the general shear failure.
In this type of shear failure, if the load applied to the soil by the foundation increases, then the settlement increases as well. At a certain point, when the load per unit area equals the Ultimate Bearing Capacity value (qu), a sudden failure in the soil supporting the foundation takes place.
A downward movement of the footing then happens along with a bulging of the soil around the footing, causing the foundation to be heaved up on only one side and leading to tilting of the structure.
As mentioned before, this is one value you should stay away from because the consequences of reaching it are catastrophic. In fact, you don’t operate on this ultimate value at all. As you’ll see, you should use a factor of safety to make sure you do not get even close to qu.
In Principles of Foundation Engineering, Braja M. Das mentions that, for general shear failure, the ultimate bearing capacity value may occur at a settlement of 4% to 10% of the foundation's width (B).
Now that you know what Ultimate Bearing Capacity is, how do you calculate it?
Karl Von Terzaghi was the first person to come up with a theory to evaluate the ultimate bearing capacity of soil. His theory, however, only applies to shallow foundations of the type of strip (or continuous) footings subjected to vertical loads only.
After doing an equilibrium analysis of the foundation-soil configuration, he expressed the Ultimate Bearing Capacity as shown below:
In the equation above, you have that:
- c = cohesion of soil
- γ = unit weight of soil
- q=qappl+γDf = total surcharge at the base of the footing
- B = width of the footing
- Nc, Nq, and Nγ = non-dimensional bearing capacity factors found in a table based on the soil friction angle φ
Despite the various simplifying assumptions, Terzaghi’s equation still provides fairly good results, being used by many design engineers in the real world — and it’s what NCEES will want you to use on exam questions involving strip footings.
However, to account for other possible shapes, depths, and types of load rather than vertical loads (e.g., inclined loads), there is a more general form of Terzaghi’s equation.
You can find that more general equation in any Geotechnical textbook and you’ll be good to go. However, for the Civil FE and PE Exam specifically, the most common additional factors that show up are the shape factors sc, sq, and sγ.
Each one of these additional shape factors can be calculated based on the friction angle φ by the equations included in a table that can be found in both the FE Reference Handbook and the PE Reference Handbook.
So, when you get a bearing capacity question for a foundation that’s not a strip footing, for example, in addition to the bearing capacity factors, you need to find the shape correction factors sc, sq, and sγ, and then add each of them to their respective terms in Terzaghi’s equation.
To wrap up this section, remember that the above equations are based on the assumption that the groundwater table of the soil is located well below the foundation.
In the cases in which the water table is close to the foundation, you’ll also need to include the correction factors Cwq and Cwγ to their respective terms in the equation as well, in addition to the shape correction factors, if it’s not a strip footing.
Please, don’t forget this! These correction factors for the location of the groundwater table can be calculated based on another table found in your Reference Manual.
So, for example, the Ultimate Bearing Capacity equation you’d use for a foundation that’s not a strip footing and is impacted by the location of the groundwater table would be like this:
What is Net Bearing Capacity?
Now, that’s when things start getting a bit confusing. Why?
The Civil Engineering Reference Manual (CERM) and other Geotechnical Engineering books touch on what’s called Net Bearing Capacity, while the FE and PE Reference Handbooks don’t specify it explicitly.
So, what is Net Bearing Capacity?
Simply put, it consists of subtracting the pressure applied by the weight of the soil located above the base of the footing from the Ultimate Bearing Capacity value.
That is, it tells you the maximum pressure the soil can withstand from the loads applied on it by the foundation alone (and consequently, the structure) before it shears. It’s denoted by qnet and is given by the following equation:
In his equation, Terzaghi included the soil above the footing by using an equivalent surcharge q=γDf. That means the Ultimate Bearing Capacity value qu includes the pressure created at the footing’s base by the weight of the soil above it.
The reason why the CERM and other Geotechnical books mention Net Bearing Capacity is because this pressure created by the soil itself is in addition to the pressure created by the loads of the structure being transferred to the soil via the foundation.
In reality, the maximum pressure that the total load of the structure can create on the soil via the foundation’s base is less than the Ultimate Bearing Capacity value — simply because the soil is already subjected to pressure from upper layers of soil. Got it?
For example, if the Ultimate Bearing Capacity value is 35 psi, but the weight of the soil above the footing already creates a pressure of, say, 3 psi, then the maximum pressure the foundation itself (and the structure or building) can apply to the soil before it shears is 32 psi.
That’s why most textbooks and the CERM mention Net Bearing Capacity. It’s the “realistic” ultimate value civil engineers should consider. That is, the maximum pressure the structure alone can apply to the soil via the foundation before it shears — and what they would probably consider to design and size the foundation.
Now the question is, do civil engineers really use Net Bearing Capacity instead of Ultimate Bearing Capacity in real practice?
Keep reading.
What is Allowable Bearing Capacity?
Regardless of whether you use Ultimate Bearing Capacity or Net Bearing Capacity, do you remember that you do not operate on this maximum value at all?
Yes, you don’t. And the reason is that this is the load per unit area of your foundation that causes shear failure in the soil to occur — and consequently, your structure to tilt, if not collapse.
So, you need to add a Factor of Safety (FS) to this failure load and use this lower, safer value instead.
This lower value is the Allowable Bearing Capacity, and it tells you how much pressure (load per unit area) your foundation is, you guessed it, “allowed” to apply to the soil so it doesn’t go anywhere near failing and collapsing.
If you think of it in terms of supply and demand, the Allowable Bearing Capacity is how much supply you’ve got, how far you can go. The “pressure demand” made on the soil by the foundation, then, must be lower or at most equal to the Allowable Bearing Capacity for it to be safe.
Braja M. Das suggests in his textbook a factor of safety of at least 3 in all cases, but it generally varies from 2 to 3. So don’t worry that much.
Now comes the interesting (and confusing) part.
While the Allowable Bearing Capacity is calculated the exact same way, it can take on two forms. They are:
- Ultimate Allowable Bearing Capacity (qall(u)). Here, the most common form, the factor of safety is applied to the Ultimate Bearing Capacity (qu).
- Net Allowable Bearing Capacity (qall(net)). Some engineers, on the other hand, prefer to apply the Factor of Safety to the Net Bearing Capacity (qnet).
“Which one should I use,” you ask?
Well, that’s hands down the most asked question about bearing capacity ever! But as promised, let’s put an end to this dilemma once and for all.
Should You Use Qu or Qnet?
First of all, if you’re already confused about this, don’t worry; you’re definitely not alone.
This is the most asked question that students of both our FE review course and PE review course have when they get to the Soil Mechanics section — and that’s totally understandable.
Why? Even reputable textbooks and reference manuals get it mixed up!
For example, the CERM states to find the Net Bearing Capacity first and then use it to calculate the Allowable Bearing Capacity. However, in the solutions to the problems, it finds the Ultimate Bearing Capacity and then divides it by the Factor of Safety to find the Allowable Bearing Capacity.
Gosh, even Braja M. Das, in his textbook, explains Net Bearing Capacity and then, in the example right below it, uses the Ultimate Bearing Capacity to find the Allowable Bearing Capacity. Like, “What?!”
So, now that question is, what do you do? How do you make sure you’re using the right value to find the Allowable Bearing Capacity on your Civil FE or PE Exam so you get the question right?
There’s one little hint the question will give you. Whether it’s a practice problem, a question you run into while taking a practice exam, or a question during the real deal, you should be on the lookout for this hint whenever you get a Bearing Capacity question.
What is that hint?
Here it is: You’ll only use the Net Bearing Capacity to find the Allowable Bearing capacity if, and only if, the problem statement explicitly directs you to do so by including pieces of information such as “consider the weight of the soil above the footing” or “consider correction for overburden.”
If you see anything like that in the problem statement, go with Net Bearing Capacity, as this is the value that accounts for it. If such pieces of information are not given, use the Ultimate Bearing Capacity. Period.
Now you may be thinking, “If we use Ultimate Bearing Capacity, why even mention Net Bearing Capacity?”
Well, first, every engineer works differently. Remember what was mentioned before: “Some engineers” prefer to use the Net Bearing Capacity. Others, on the other hand, go with the Ultimate Bearing Capacity.
Second, each and every project is different. In actual practice, the tendency is to use the Ultimate Bearing Capacity for most projects, while the weight of the soil is usually taken into account only when calculating overturning cases.
But all in all, when it comes to passing the civil FE or PE exam once and for all, follow the rule above, and you’ll be all set.
Conclusion
There you have it. Of course, there’s a lot more to it than what was covered here (e.g., eccentricity), but this was intended to be an overview of the basic Bearing Capacity concepts and to put an end to the Ultimate vs. Net Bearing Capacity dilemma for the FE and PE exams.
Now, for you to truly learn everything you’ve read, you need to practice it. Seriously, it’s one of the most important things in your exam prep, but according to a 13-year study covered here before, only 11% of test-takers do it — and those were the people who aced their exams!
To help you be part of those 11%, we have an entire playlist on YouTube with FREE Geotechnical practice problems, each with step-by-step video solutions. The best part? We constantly add new problems there! So check them out and practice as much as you can — that’s really the key to passing!
If you need help in your journey to pass your Civil FE or PE Exam, we at the Civil Engineering Academy have your back!
If you’re planning on becoming an E.I.T., here’s the 5 Best FE Resources Guide. That’s a list of the best resources you must use when preparing for the Civil FE exam for you to pass it. No matter if you’re going about it alone or using an FE review course, these can truly help.
In case you’re planning on tackling the Civil PE Exam instead, here’s The Ultimate Civil PE Exam Startup Guide. It covers everything you need to start your exam prep on the right foot. From the prerequisites you need to meet and how to register for the exam to the must-have resources to get and the best PE review courses out there that can make it a lot easier for you.
Author: Allan Cardec
Allan is the Content Manager at Civil Engineering Academy. He’s a former civil engineering undergraduate who’s now one part content creator and one part civil engineering geek. Outside of content, you can find him staring at piles of books trying to decide which one to pick up next.