Eccentrically Loaded Footing Design Question 2

[MagicFarmer]

Good afternoon,

I am working through an eccentrically loaded footing problem and have some questions.

In Reinforced Concrete - Mechanics and Design (MacGregor and Bartlett), the book states:

"For the structural design of eccentrically loaded footings such as those for retaining walls or bridge abutments, the Ontario Highway Bridge Design Code requires that two pressure distributions be considered. The first of these is a uniform pressure over a portion, Ap, of the contact surface. The area Ap is chosen such that the centroid of Ap and the resultant of the applied loads coincides. The second pressure distribution is a linearly varying distribution, again, with the resultant soil pressure coincident with the resultant of the applied loads."

The clauses in the OHBDC state:
6.7.3 Pressure distribution
6.7.3.1 Effective area
For proportioning of concentrically loaded footings, a contact pressure of uniform intensity at the ULS shall
be assumed.
For eccentrically loaded footings, an equivalent effective area with a contact pressure of uniform
intensity shall be assumed such that the centroid of the area coincides with the vertical component of the
factored load.
6.7.3.2 Pressure distribution at the ULS for structural design
For the structural design of footings, the more critical of the following shall be considered:
(a) a uniform pressure distribution whose magnitude shall not be more than the factored geotechnical
resistance; or
(b) a linear pressure distribution where the maximum bearing pressure could be greater than the
factored geotechnical resistance.
6.7.3.3 Pressure distribution at the SLS
A linear distribution of contact pressure at the SLS shall be assumed. Tension at the interface between the
footing and the soil or rock shall not be assumed.
6.7.3.4 Eccentricity limit
In the absence of detailed analysis at the ULS for soil or rock, the eccentricity of the resultant of the
factored loads at the ULS acting on a foundation, as shown in Figure 6.4, shall not exceed 0.30 times the
dimension of the footing in the direction of the eccentricity being considered.


The "could be greater" in b) confuses me... I researched online, and there is a FEMA document online that uses the uniform pressure for plastic design only. I just spoke with a local soils engineer, and they stated that they don't assign plastic soil bearing pressure values. I have looked at this problem for a couple days now and can not find a case in which the triangular pressure distribution results in a lower bearing pressure. Could someone please explain how to implement or when to use the uniform soil pressure in design, and how this relates to standard engineering practice with the SLS and ULS bearing pressure values that would appear in a typical geotechnical report?

Thank you in advance.

 

[Shu Jiang PEng SE]

Hope the sketch help you

 

[MagicFarmer]

Thank you for the response Shu Jiang. I understand the physics of how the two pressure distributions function. My question was focused on the 'best engineering practice' and code compliance.

I have found a FEMA example where a plastic bearing pressures are given as a function of footing width. The document also states that "Where foundations will be subjected to short-term loads and inelastic response is acceptable (as for earthquake loading), plastic soil stresses may be considered."

No where in the Canadian concrete code (CSA A23.3) or teh Ontario building code does it mention that a plactice soil pressure can be used. I don't understand how a Canadian concrete design textbook, and the Canadian Bridge Design Code can mention the use of a soil pressure higher than ULS, and then there be no mention in the building code, or have a local soils engineer say that he has never heard of such a thing.

Thanks.

 

[Shu Jiang PEng SE]

I am not sure you can ever use soil plastic pressure. You just use the soil bearing capacity given by the geotechnical engineer. The two calculation methods are just two different interpretations of the interaction between soil and footing. The linear distribution assumes soil can take both compression and tension and which is not real situation. But the soil pressure obtained this way sometimes is larger than that of the other method. So conservatively two methods are used and the safe result is chosen for design.

The issue is not related to the soil plasticity. It is just two methods to calculate the pressure applied on the soil.

Anyway, this is my understanding.

 

[WARose]

The way I read 6.7.3.2.(b) is that (for the purposes of structural design) they are just basically telling you that you can use the non-linear pressure distribution (see "case b" in shu's post above) to figure footing moments. In some cases, geotech's will let a slightly excessive pressure at a tip slide as far as exceeding allowable bearing goes. In the real world, chances are you are not going to get that perfectly linear bearing distribution anyway. (It will vary based on soil stiffness, foundation stiffness, etc.)

 

[KootK]

I believe that this presupposes a geotechnical environment in which "failure" simply means a particular amount of settlement. In such a scenario, it is the average soil stress that is the relevant design parameter rather than the peak soil stress. As such, you could have a triangular soil pressure distribution that exceeds "allowable" at the peak but has an average stress within the specified geotechnical limits. While these two soil distributions are equivalent with respect to settlement, they are not equivalent with respect to the flexural demand required of the footing. With all of that in mind, my interpretation of the OHBDC clauses is as follows:

(a) a uniform pressure distribution whose magnitude shall not be more than the factored geotechnical resistance; or

I take this to mean that a soil pressure equal to the soil capacity should be applied to the entirety of the footing, regardless of the actual external loads applied to the footing. This is a conservative design practice that I was taught by my mentors long ago. In a buildings context especially, it is entirely plausible that someone may come along to renovate in the future and assume that the footings that were installed are capable of resisting an applied load equal to AREA x q_allow. And the difference in construction cost is usually trivial. It's a nice future proofing measure for the owner.

(b) a linear pressure distribution where the maximum bearing pressure could be greater than the factored geotechnical resistance.

I believe that this refers to the linearly varying soil pressure distribution that I mentioned in my first paragraph whereby a settlement neutral, linearly varying soil pressure might produce a greater flexural demand in the footing than (a). This, for the reason that WArose mentioned: who the hell knows what the actual soil stress distribution will be.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[MagicFarmer]

Thank you for the insightful replies.

I certainly have a far better understanding of the situation now. I didn't pick up on the nuance of the code clause that WARose did:
"6.7.3.2 Pressure Distribution at the ULS for STRUCTURAL DESIGN" and "6.7.3.3 Pressure distribution at the SLS." The implication being that one clause focuses on the structural design of the footing itself and the second focusing on the demand placed on the soil for settlement.

To clarify, you are interpreting this as, for the STRUCTURAL DESIGN of the footing, that:
a) One loading pattern be uniform, and of a magnitude equal to that of the ULS soil bearing resistance, and,
b) A second loading pattern be a linearly varying soil pressure where the AVERAGE soil pressure be that of the ULS soil bearing pressure.

Is this correct?

(For clarification, I am not currently implementing this on a design at the moment, it is something I came across while reading and has sent me down a rabbit hole to understand.)

Playing around with an excel sheet I quickly whipped up, scenario b may impart a moment twice as large as scenario b. This seems excessively conservative to me. Have I missed the mark again?

Again, I certainly appreciate your input on this topic. Thank you all.

 

[KootK]

Is this correct?

I'm not sure if you're addressing me here but, if you are...

b) A second loading pattern be a linearly varying soil pressure where the AVERAGE soil pressure be that of the ULS soil bearing pressure.

I disagree with this one slightly. I feel that this should be a pressure distribution based on the actual loading. It's average value would be the allowable soil pressure or less depending on the design. But yeah, for this kind of foundation it would not surprise me to see case (b) govern and, surely, that's in fact the spirit of the requirement.



I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[TLHS]

As far as Canadian codes go, the latest NBCC structural commentary actually has a diagram showing a plastic soil pressure distribution. I'll track it down.

 

[MagicFarmer]

Thank you all. This is all very helpful and interesting.

 

[Settingsun]

I've not used Canadian codes before, but I won't let that stop me...

I take this to mean that a soil pressure equal to the soil capacity should be applied to the entirety of the footing, regardless of the actual external loads applied to the footing.

I don't think that's what the code requires, although it might not cost much to be this conservative as you say. In 6.7.3.1, it says to size the footing according to the uniform pressure method. In 6.7.3.2a, it says that this uniform pressure must be not greater than the soil capacity (obviously, but codes have to state this). This appears to be the geotechnical basis of design.

For structural design, it requires that you determine bending moments, shear forces etc based on assumptions that match the geotechnical design (6.7.3.2a). However, it also says to check the linearly-varying soil pressure case as this may result in larger bending moments, shear forces etc (6.7.3.2b). Both of these may be based on the applied loads, and don't need to be increased based the soil capacity. If the uniform pressure case had to be based on the soil capacity, the code would say 'not less than' in 6.7.3.2a instead of 'not more than'.

The point of saying that the maximum pressure in the linearly-varying case may exceed the soil resistance is actually to say that this case isn't the basis of geotechnical design, eg if you have 100kPa soil but you have 110kPa in the linearly-varying case, you don't need to increase your footing size (provided the uniform pressure is less than 100kPa).

 

[KootK]

I don't think that's what the code requires...

Color me convinced. Nicely done.

Still, I'm pretty good with words, I've probably read the damn code blurb a dozen times now, and I'm still only about 80% sure that I understand the intent. They should consider a couple of clarifying sketches. Actual clarifying sketches as opposed to truth obfuscating ones such as the AISC web sidesway commentary figures.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.