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# Cantilever retaining wall design2

## Cantilever retaining wall design

(OP)
Hey everyone:

Trivial question here, but I asked my colleague and didn't get a convincing answer :(

So I've recently started designing a conventional cantilever retaining wall while working through the preliminary calcs, I became aware of the K(active) and K(passive) coefficients that I'm using. I mean, I've always been taught to use these coefficients to calculate the earth pressures acting on the wall. But will the retaining wall reach these limiting states, because according to Rankine, the wall has to undergo some degree of deformation before the K(At rest) reaches one of these limiting states.

I'm not sure whether this is more conservative, because when K(At rest) approaches K(active), the active pressure gradually reduces, so wouldn't it be more conservative to design the wall at a higher "K(active)" pressure? Why do we design the wall at its failure point?

Any advice would be greatly appreciated :) thx

### RE: Cantilever retaining wall design

It does not take much movement to achieve active earth pressure. According to Terzaghi, a lateral movement equal to 0.001 times the height of the wall results in active earth pressure. For a 10' high wall, this means the top of the wall must only move 1/8". So active earth pressure is used for design of cantilever retaining walls.

DaveAtkins

### RE: Cantilever retaining wall design

To DaveAtkins: 1" of rotation on the top of a 10-ft wall is the guide for mobilization of active earth pressure. No clue how you got 1/8"?

To the OP: Movement is required to engage friction. At rest earth pressure does not mobilize friction in the same manner. If you don't want ANY movement, you really have to design for base shear and at rest earth pressures. Of course there's also the weight to help in the moment stability.

f-d

ípapß gordo ainÆt no madre flaca!

### RE: Cantilever retaining wall design

I understood that the amount of movement to reach the lower active pressure condition depends on the retained soil type, with clayey materials requiring much larger movements.

As fattdad noted, if there are no adverse effects from the wall moving the amount that it will take to mobilize the internal friction of the retained soil and reduce the pressure from at-rest to the active condition, then it can be designed using the active pressure.

If it can move the additional amount required to mobilize the passive resistance (which is typically much larger than required to achieve active) of the soil in front of the wall, and that soil can be confidently assumed to be in place for the service life of the wall, passive resistance can be used to supplement the external stability (typically only helps for sliding).

### RE: Cantilever retaining wall design

Avoid all this and design for "at rest".

### RE: Cantilever retaining wall design

Kereo, design of cantilevered retaining walls is covered extensively in many text books and design manuals. These references will cover when to use active and at-rest pressures and how much wall movement is required to develop these pressures for different soil types. I suggest that you check one or more of these references; then ask questions in ET.

### RE: Cantilever retaining wall design

(OP)

To summarise, we don't always assume the wall will reach limiting state and so before applying the relevant Earth pressure coefficients, it is important to know the approximate deformation that the wall will undergo through its service life?

Also with reference to HotRod10's comment - "If it can move the additional amount required to mobilize the passive resistance (which is typically much larger than required to achieve active) of the soil in front of the wall, and that soil can be confidently assumed to be in place for the service life of the wall, passive resistance can be used to supplement the external stability (typically only helps for sliding."

If the cantilever wall deforms such that the active limiting state is achieved, does that mean the passive limiting state on the other side of the wall (resisting) is not achieved? Because it'll require an additional amount of movement which will cause the active side to fail?

### RE: Cantilever retaining wall design

Kereo - I think you should avoid calling it the "active limiting state" as it might just confuse things (well for me at least). Just call it Ka and Ko. Earth pressure on the retained side will be somewhere between.

If the cantilever wall deforms such that the active limiting state is achieved, does that mean the passive limiting state on the other side of the wall (resisting) is not achieved? Because it'll require an additional amount of movement which will cause the active side to fail? - Yes in short. If the wall can not move enough to mobilize (full) passive resistance then it means that the reaction that you relied upon in your calculations is not there. This is one reason why passive is ignored or sometimes factored by half. The additional active side will not "fail" as it depends what your definition of failure is. If the area is a landscaped area then movement required to reduce Ko pressure to Ka pressure is not a big deal as the grass etc will move with it, however if it was a basement wall supporting full height glazing (or something very sensitive to excessive movement) the the movement could be an issue and in this instance you would design for Ko pressures. Ko pressures increase structural forces on your wall by approximately 40%.

I have always worked off the rule of thumb:

Wall supporting landscaping, temporary works, no structural elements - Ka

Walls supporting structural elements - Ko

f-d

Where did you get 1 inch for a 10ft wall from? That equates to 0.83% of H. Ill guess and say someone told you it long ago, you took it on board, applied it to everything and havent had any problems?

I was told above 1% of the wall height will be active.

Bowels recommends a range between 0.001H to 0.004 for cohesionless which is 0.1 to 0.4% and 0.01 to 0.05H for cohesive , which is a 1 to 5% range

EC7 recommends greater and 0.05% of H is active. See below

I suppose mine and your 1 and 0.83% is conservative at it would result in more walls being designed to Ko pressures.

### RE: Cantilever retaining wall design

"If the cantilever wall deforms such that the active limiting state is achieved, does that mean the passive limiting state on the other side of the wall (resisting) is not achieved?"

Correct.

"Because it'll require an additional amount of movement which will cause the active side to fail?"

No. The passive resistance is unrelated to what's happening behind the wall. Without movement, the soil pressure on the retained side of the wall may be as high as Ko, depending on how it was backfilled. Usually, that is the assumption. If that level of pressure causes the wall to move, the movement allow the pressure to decrease as the retained soil particles begin to interlock and become partially self-supporting. This fully mobilized internal resistance is the difference between Ko and Ka. Additional movement will not reduce the pressure behind the wall below that corresponding to Ka, since it is the remaining pressure after the soil's internal resistance capacity has been reached.

In front of the wall, it takes significantly more movement to fully mobilize the interlock of particles within the wedge of soil resisting movement.

### RE: Cantilever retaining wall design

Make life easy (both for you, and the financial health of your project) and just design for k0.

Get it out the door.

### RE: Cantilever retaining wall design

Although easier to design to Ko, like my above post if its just supporting landscaping above it would be an over design in my opinion.

OP- whats the context of the wall?

### RE: Cantilever retaining wall design

(OP)

Thx for the contribution everyone!

### RE: Cantilever retaining wall design

Hi EireChch: 0.83 rounds up to 1.

Good post!

f-d

ípapß gordo ainÆt no madre flaca!

### RE: Cantilever retaining wall design

Can anyone provide a reputable reference for using at-rest earth pressure for designing a cantilevered retaining wall?

I have never seen a reference or design manual recommending use of at-rest earth pressure for anything other than a restrained wall. Even anchored, non-gravity walls are usually designed using active pressure. Only rarely have I have seen people recommend using at-rest earth pressure when they wanted to be extra careful and wanted to limit wall movement.

### RE: Cantilever retaining wall design

At-rest pressure is used where movement of the wall would be detrimental to the wall or another part of the structural system. If you want a specific directive, I found it in the AASHTO LRFD bridge design spec, at the beginning of Article 3.11.5, where it states that Ko should be used "for walls that do not deflect or move". That seems clear enough to me, so for the situation at hand, designing for Ko would be conservative.

### RE: Cantilever retaining wall design

0.001 times 10' or 120" is 1/8" (approximately).

I agree with PEinc. Designing a cantilever retaining wall for at rest pressure is unnecessarily conservative. The minute the wall moves a tiny amount, you have active pressure.

DaveAtkins

### RE: Cantilever retaining wall design

DaveAtkins: Your math is correct. However; if you use 1% of 10 ft you'd actually get 0.83".

f-d

ípapß gordo ainÆt no madre flaca!

### RE: Cantilever retaining wall design

So, depending on the material, for a 10ft tall wall the movement to reach the active soil pressure condition is between 1/8" and 1". Even an inch of movement won't cause any issues for a typical landscape retaining wall (unless you're building it 1/2" away from the property line).

OTOH, a few of the retaining walls we've done couldn't move at all because there was a sidewalk poured right up against it. For those we used Ko.

We've even done a couple of walls restraining landslides, or subject to the loading of one, so we've used Kp (passive pressure coefficient) to calculate the retained soil pressure. I just depends on the site conditions and design requirements.

### RE: Cantilever retaining wall design

I would never assume that a sidewalk was supporting or even could support a retaining wall. Sidewalks may be here today, gone tomorrow. In my experience, few cantilevered retaining walls need to be designed for at-rest earth pressure.

HotRod10 said above that "If you want a specific directive, I found it in the AASHTO LRFD bridge design spec, at the beginning of Article 3.11.5, where it states that Ko should be used 'for walls that do not deflect or move.'" Cantilevered walls are meant/expected to move and deflect a reasonable amount. As far as HotRod10's above mention of AASHTO as a reference, I interpret what AASHTO says as, if the wall will not be able to move or deflect, it should be designed for at-rest pressure. AASHTO did not say or recommend that cantilevered retaining walls be designed for at-rest pressure. I'm still waiting for a clear and reputable reference for requiring at-rest pressure for cantilevered walls.

### RE: Cantilever retaining wall design

It's fairly straightforward that a wall that is only designed for Ka may move, or may try to move, at least some amount, when the backfill is compacted. If this is unacceptable from a serviceability standpoint, then the wall should be designed for Ko, so that it doesn't move or load whatever is restraining it.

### RE: Cantilever retaining wall design

"I would never assume that a sidewalk was supporting or even could support a retaining wall."

I wasn't assuming that the sidewalk would support the wall. I was assuming the sidewalk would restrain the wall from the movement necessary to relieve the at-rest pressure and reach the active pressure condition. If I designed it for Ka, it would likely rotate forward at the top to reach the Ka pressure condition, since it would not be able to slide because the bottom was not able to move. It would also put pressure on the sidewalk, which might cause the sidewalk to slide or crack.

### RE: Cantilever retaining wall design

Couldnt agree anymore with Hotrod, oldestguy and Fatdad really.

In my view designing for k0 earth pressures is a simple, conservative (but not unreasonably) so way of designing relatively stiff RC retaining walls e.g. bridge abutments (obviously more flexibile types are a completely different matter).

Also:

1. (Eurocode specific) - it saves a lot of the hassle of designing for DA1 C1/C2 particularly at the tender design stage.

2. You can only optimise the design so much (its really either B20s/25s/32's @ 150 centres - theres really only so much economy you're going to get out of using K0=0.33 vs 0.5 in a lot of cases for phi'=30, in a lot of instances you might allow a slight overstress by inspection to use a smaller bar diameter if its a very long wall.

3. We're to make a bit of cash at the end of the day

### RE: Cantilever retaining wall design

For the soil pressure on a bridge abutment, I would certainly agree with using Ko, at a minimum. If we have soil against our integral abutments, we design for the high end of the passive pressure to account for movement of the abutment into the soil.

We also do some fairly massive retaining walls supporting fill slopes for roadways. For those we use Ka and sometimes find it cost-effective to use select backfill rather than native fill. Although, on one recent project, the native fill was slightly better than our crusher run...

I can certainly appreciate your perspective of simplifying and shortening the design. I have a somewhat different financial setup, since I work for the agency responsible for paying for the construction (the DOT), so if I take the time to 'sharpen my pencil' and cut a significant amount out of the construction costs, the bosses like that. It's similar to designing for a design-build project. Also, it sounds like design for Ka comes with some extra headaches under the Eurocode; it's fairly straightforward under AASHTO. It's a long equation to calculate Ka, but once I had it programmed in Excel, it takes no time at all to use it again.

### RE: Cantilever retaining wall design

There may be reason for designing some walls and abutments for higher earth pressures, but Kereo's original question was about "designing a conventional cantilever retaining wall."

### RE: Cantilever retaining wall design

For the design of conventional retaining walls (unrestrained and which can move or rotate freely without significant impact on ancillary structures), I learned to use the following earth pressure coefficients:
- wall equilibrium (sliding and overturning): ka
- structural design of wall: (ka + k0)/2

As we aim for a stability safety factor larger than 1, it is foreseeable that the wall will sustain earth pressures larger than ka before it slides or rotates. In this way, we try to establish a failure hierarchy, guaranteeing that structural collapse won't occur before any stability issues.

### RE: Cantilever retaining wall design

full passive pressure generally required only a very small movement (0.003 or less for half passive), so if you can stand any movement, you may be able to justify using it. For your 10 foot wall, that would be about 1/3 inch.

### RE: Cantilever retaining wall design

avscorreia, AASHTO LRFD puts a load factor of 1.5 on lateral earth pressure for the structural design of flexible walls, probably for the reason you mentioned.

### RE: Cantilever retaining wall design

According to your graph as I read it, cvg, you don't get anywhere near full passive until 0.02*H, which for the case of the 10' (120") wall would be 2.4".

### RE: Cantilever retaining wall design

HotRod10, I forgot to mention: I use the Eurocodes so I use a 1.35 load factor on lateral earth pressure, so you're probably right regarding AASHTO LRFD.

### RE: Cantilever retaining wall design

check again, you are misreading the graph. 1.0 Kp is at about .003 for loose sand and less for dense sand

### RE: Cantilever retaining wall design

What I considered "full" passive pressure for loose sand would be Kp = 3; half would be Kp = 1.5, corresponding to movement of nearly 0.01 ---> 1.2" for the 10' wall. It's similar for dense sand, with full passive being Kp = 8 and half being Kp = 4, crossing at a value slightly over 0.01.

From the AASHTO LRFD bridge design spec, Section C3.11.5.4: "The movement required to mobilize passive pressure is approximately 10.0 times as large as the movement needed to induce earth pressure to the active values. The movement required to mobilize full passive pressure in loose sand is approximately five percent of the height..."

Of course, that's only for sand. Mix in a little silt, clay, or larger granular material, and it changes considerably. From the same section: "For poorly compacted cohesive soils, the movement required to mobilize full passive pressure is larger than five percent of the height..."

In any case, I'd be hesitant to count on any amount of passive resistance on something where movement would be detrimental.

### RE: Cantilever retaining wall design

nobody is recommending that full passive pressure be used. corps of engineers and navfac recommend no more than .5kp and only if you cant achieve stability using at rest pressure or you have a deep structure. according to the chart, .5kp would require very little movement, about .001 or .002.

### RE: Cantilever retaining wall design

Well, I won't be hanging my hat on that supposition, especially since we rarely have clean sand as backfill material.

### RE: Cantilever retaining wall design

Eurocode (EC) 7 provides some very different numbers!

For 0.5kP, EC7 indicates 1.1 to 4% of wall height for loose to dense sand, 0.011 to 0.04 x H. Thats 10 times more than cvg's Department of Navy reference.

I am sure that both methods were developed based on retaining wall monitoring at some point in time, but my gut says that 0.001 to 0.002 x H for 0.5Kp is too small a movement! For a 10ft wall thats 1/8" to 2/8" or 3 - 6mm.

In saying that, that's just my gut feeling and i have never actually measured pressures in a retaining wall!

Its after sparking my interest so I may look into it a bit more and see what i can find. If anyone has any references, let me know.

### RE: Cantilever retaining wall design

EireChch, your Eurocode values are similar to what's in my soil mechanics textbook. Anyway, in the rare circumstance where we include passive resistance in a design, it's only used for sliding resistance, and the depth (Height) is generally 2' or less and we're counting on it to mobilize a wedge of soil in front of the wall. I can't see how any graph value or anything multiplied by the height would be applicable.

As I said, I won't be counting on any passive resistance for anything where the movement is, or needs to be, limited.

### RE: Cantilever retaining wall design

I’m with PEinc, been doing this a long time and have never designed a conventional retaining wall for an at-rest condition. I’ve only used at-rest for the design of foundations related to thrusts from arch type superstructures on bridges.
Soil Mechanics 101 will cover the design of a retaining wall. Of course if you do design for an at-rest condition it’s just conservative.

### RE: Cantilever retaining wall design

Again, deciding on at-rest or active pressure for design is not complicated - if an inch or so of movement of the wall will not cause problems, designing for active pressure is generally acceptable. If it makes for simpler design calculations or the designer wants to be conservative, using at-rest pressure will usually require a more substantial wall. For walls that are not very long, the cost difference may be negligible.

For walls, abutments, etc. where movement would be detrimental, or external restraint doesn't exist or isn't adequate for the forces, design for at-rest pressure is generally recommended and prudent.

### RE: Cantilever retaining wall design

I don't see how designing for the at-rest condition is a simpler design. Same calcs required, just a bigger triangular base pressure.

### RE: Cantilever retaining wall design

"I don't see how designing for the at-rest condition is a simpler design."

Under the AASHTO code that I design to, it's a minimal difference. Calculating Ka is accomplished using a fairly large formula, but once I programmed into Excel, it takes no extra time now. I was referencing a comment by ukbridge, posted on Feb. 9th, indicating there were additional requirements to design for Ka under the Eurocode.

### RE: Cantilever retaining wall design

Whatever pressure is used, I hate leaning walls, so I want the front face to be built sloping back to the earth.

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