Interaction between tiered cantilever retaining walls

[GoodnightKiwi]

Hi all -

Long time listener, first time caller

I'm trying to find some advice / help / reference with respect to the attached problem, where the passive wedge asssociated with upper wall (Wall A) extends over the active wedge of the lower wall (Wall B). The design approach needs to be an Ultimate Limit State one. The uprights are timebr poles with the embedded portion encased in concrete. Upright spacing is at 1.2 metre centres.

Does anyone have any advice / reference sources etc etc

Do any of these options sound reasonable:

1. Designing Wall A as if wall B didn't exist (i.e. as a 4.8m high wall with 1 in 2.5 (v:h) toe slope. This would however require huge poles and big embedment depths
2. Look at what percentage of Pp is overlapping Pa and add this percentage of Pp into the loads applied to Wall B (say as a traffic load)
3. Treat the embedded portion of Wall A as a strip footing with applied load and look at how a Boussinesq type bulb would extend laterally from Wall A to Wall B, and add additional load to Wall B

Thanks in advance

 

[Ron]

Design the whole wall for the worst condition. Don't try to fine tune geotechnical stuff!

 

[FixedEarth]

I am assuming lower wall is the proposed new wall. If so, take the active earth pressure of Wall A multiplied by 1.2 m center spacing @ -2.4 m and apply is as a lateral load to top of Wall B. because Wall A is encased in concrete & is surrounded on all sides by soil and is same distance horizontally as the height of Wall B, there will be little concern for passive resistance erosion.

Also I would add a line or strip load to the loading of Wall B to account for the axial load of wall A. Check your embedment depths, usually we see buried depth that is about 1.2 to 1.4 times the exposed height.

 

[GoodnightKiwi]

Hi guys - both walls are proposed.

ka=0.333 & gamma = 16kN/m^3, so I calculate the active earth pressure for Wall A as 18.43kN per pole 0.5 x ka x gamma x height^2 x spacing). 18.43kN applied laterally to the top of Wall B with a lever arm of at least 3 metres will require some reasonable upgrading of pole size and embedment.

Ron - what is the worst condition?

Cheers

 

[RFreund]

FixedEarth - why apply active pressure of wall A and not passive? Also would you consider the weight of soil above the top of wall B as a strip load surcharge?

EIT

 

[GoodnightKiwi]

In looking at how much of Pp from Wall A is overlapping Pa from Wall B, I had considered a passive earth pressure wedge in front of the embedded portion of Wall A extending at 45-(phi/2) from the toe of the upright, while for the active earth pressure wedge behind Wall B I took 45=(phi/2) extending from the ground level in front of Wall B. The onsite soils have a cohesion component, albiet small (3 to 5kPa). Should any solution put forward take this into consideration also? Again, this is an ultimate limit state design.
For the scenario attached, the following was calulated:
Pp = 0.5 x kp x gamma x Embedment^2 x spacing (138.24 kN per pole)
% of Pp that overlaps or extends beyond Wall b = 35%
Therefore, 48.4kN per pole additional load applied to Wall B.
Kp was simply taken as (1+sin30)/(1-sin30), so there was no cohesion component.

 

[FixedEarth]

RF & GK - The active pressure is a force and it is directed towards the lower wall. The passive is a resistance and is directed toward the upper wall. See attached sketch. Some of the lateral force on lower wall due to upper wall will be resisted by the passive soils of the upper wall. However, some percentage, shall be applied horizontally to the lower wall. This is just one of many ways and reflects only my past experience.

 

[FixedEarth]

Not sure if the intended sketch opens. Let me try it again.

 

[RFreund]

FixedEarth - I see your method now. Thanks for that sketch I was thinking something slightly different more along the lines of a % of passive pressure and/or applying the soil above wall B as a uniform surcharge over a distance say 45 degrees up from the toe of wall B back to where it intersects the top grade above wall A. Similiar to what GK was proposing (sorta). However I think your solution is a good one (not that it needs to be validated by me!)

EIT

 

[kieran1]

agree with Ron don't over think

Kieran

 

[GoodnightKiwi]

Thanks FE.

Has anyone tried the method as attached?

 

[RFreund]

I was actually looking for that reference to post and I believe FixedEarth has posted it before.

FixedEarth - This seems to be slightly different than the method you proposed previously but I thought you have suggested the method as GNK attached. Any reason for using one or the other?

EIT

 

[FixedEarth]

Check with PEinc-he is more familiar with CivilTech. I see it as a different way to skin a camel.

I need to correct one assumption I made about the axial load caused by the upper wall. I believe the load path goes to the pole tip of the upper wall. We can then draw a 1:0.5 (V:H) and see where it intersects the lower wall. Not likely to be critical, but we also need to check for the global slope stability of the two wall system in static and if applicable in seismic region, the pseudo-static condition.

Given the generous setback distance between the two walls and the short exposed heights, I do not see it as very critical situation. By choosing embedded walls, you have eliminated a lot of additional analysis.

 

[GoodnightKiwi]

Thanks again FE.

We've already looked at static and seismic slope stability. Also, the timber uprights have been designed giving consideration to static and seismic loading.

Seismic loading does however raise another issue, being how the wall interaction occurs under seismic loading, but that's definitely starting to get into the realm of over-thinking the problem.

 

[FixedEarth]

Anytime GK. I agree, seismic loading shall be considered. However, since your walls are shorter than 12 ft (3.75 m), it is not a critical issue. You have good embedment depth and automatically will meet sliding and overturning factors of safety. Further, when dynamic loads are present, your required F.S. for Sliding & O.T. reduce to 1.15 You also have a cantilever and flexible wall which is able to take minor movements.