Retaining Wall Analysis

[Mireille Kreines]

Ourprevious article, Retaining Wall: A Design Approach discusses the principle and concept behind and when and where to consider a retaining wall in our design. We have learned the different checks against the mode of failures in the retaining wall should be considered in the design. To further understand the designed approach, here is a worked example of the design of the retaining wall.

This example is intended to be readily calculated by hand although a lot of structural spreadsheets and software such as Prokon are available. The purpose of this article is for the reader to fully understand the principle behind it.

The next thing to consider is the assumptions that we can make in terms of the geometry of the retaining wall that we are designing. Given the height, H of the retaining wall, we can assume or counter check our initial design considerations should at least according to the following geometric proportions:

Sketches of the retaining wall forces should be considered to properly distinguish the different forces acting on our retaining wall as tackled in the previous article, Retaining Wall: A Design Approach. Based on our example in Figure A.1, we have the forces due to soil pressure, due to water and surcharge load to consider. Figure A.3 below is most likely our analytical model.

Considering the Figure A.3, we can derive the following equation for the active pressures, Pa and passive pressure Pp. Notice that the pressures acting on the wall are equivalent to the area (triangle) of the pressure distribution diagram. Hence,

There are two checks to consider the stability of the retaining wall. One is the check for an overturning moment and the other one is the check for sliding. The weight of the retaining wall including the gravity loads within it plays a vital role in performing the stability check. Refer to Figure A.4 for the mass or weight calculations.

The sliding check should be carried out with reference to the Figure A.4 diagram and considering the summation of vertical forces for resisting force and horizontal forces for sliding force conservatively neglecting the passive pressure, hence:

The foundation bearing capacity usually governs the design of the wall. The soil, particularly under the toe of the foundation, is working very hard to resist the vertical bearing loads, sliding shear, and to provide passive resistance to sliding. The bearing capacity of the soil should be calculated taking into account the effect of simultaneous horizontal loads applied to the foundation from the soil pressure.

For the footing to be safe in soil pressure, the maximum soil pressure under working load shall be less than the allowable soil bearing capacity. The maximum soil bearing pressure under the footing considering 1m strip is:

The presented calculations above are actually too tiring to perform manually especially if you are doing a trial and error design. Thanks to structural design soft wares and spreadsheets, available nowadays, our design life will be easier.

What do you think about this article? Tell us your thoughts! Leave a comment on the section below. Subscribe to our newsletter to be updated with the latest posts or follow us on our social media pages on the below icons.

Thanks for pointing out. We have checked and found out that that is merely a typo error and it has been updated accordingly. We have also double-checked the attached spreadsheet and it is not affecting the results as we conservatively neglect the effect of passive pressure in the calculation.

Also ,would you be able to explain how is the d in critical shear calculated ? number 1.044 is used for similar triangles,however I struggle to find exact theory how you arrived to this number as I get different.

we have to learned the different checks against the mode of failures in the retaining wall should be considered in the design. Here some worked examples of the design of the retaining wall are described.I like the I have also found this resource Rfmasonry.co.nz useful and its related to what you are mentioning.

Hi Ruben, you can actually put your own logo on the space provided. Either editing some option setting on your excel or typing your company name on it. If none of these options are working, do it manually. Once you finish the design, convert the file to pdf and paste your logo from there.

Thanks, Aaron for pointing it out. We have checked and found out that that is merely a typo error and it has been updated accordingly. We have also double-checked the attached spreadsheet and it is not affecting the results in the calculation.

There is also a comment earlier about a typo of MoT = 57.91, the figure was right at 60.02, the weight of section 1 was not added to the equation. Though all of these moments are taken from the top of the toe and not the furthest point, thus moments are not accurate.

sir, Thank you for your valuable information. this is very much useful and one more plea that can we have any examples for considering wings & returns with head wall can be treated as a retaining wall any such kind of examples please post to mail if any thanks in advance

The shear strength is based on an average shear stress on the full effective cross section (bw x d). In a member without shear reinforcement, shear is assumed to be carried by the

concrete web. In a member with shear reinforcement, a portion of the shear strength is assumed to be provided by the concrete and the remainder by the shear reinforcement.

Thank for this detailed design to follow; It has been very helpful. One thing I noticed is that the calculation for the wall stem does not match the value you then indicated for the moment when checking for wall stem flexure. You have listed that Mu=19.40KNm again for tension, but the calculation comes out to the 29.33KNm you used. I believe it was just a typo but it made it a bit confusing to follow then. Thanks again, and God bless.

This package contains programs for the design of variety of retaining walls. Package also contains Slope Stability program for external stability check and Spread Footing program for bearing capacity analysis. You save 3737 % compared to buying individual programs.

I've only designed a few retaining walls but from what I realized using two perpendicular panels is the most optimal way to model it. The other major issue is simply adding hydro-static and soil loads which are all available in the loads drop-down. As for your checks I would suggest looking over this topic;

Lateral earth pressures are analyzed for either "Active," "Passive" or "At-Rest" conditions.

Active conditions exist when the retaining wall moves away from the soil it retains.

Passive conditions exist when the retaining wall moves toward the soil it retains.

At-Rest conditions exist when the wall is not moving away or toward the soil it retains.

Conditions for active, passive and at-rest pressures are usually determined by the structural engineer. Basically, at-rest pressures exist when the top of the wall is fixed from movement. Active and passive pressures are assumed when the top of the wall moves at least 1/10 of 1% of height of wall in the direction away from , and toward the soil it retains, respectively. Some theorize that at-rest pressures develop over time, when a retaining wall is constructed for the active case.

Basically, lateral earth pressures are derived from the summation of all individual pressure (stress)areas behind the retaining wall. These pressure areas are triangular in shape with the base of the triangle at the base of the wall for the soil component and pore water component. Pressure areas for surcharges are rectangular in shape, and earthquake pressures are usually analyzed with a nearly 'upside-down' triangle. See theRANKINE ANALYSIS link for an excellent presentation of determining lateral earth pressures using the Rankine Analysis.

Engineering judgment should allow for some pore water pressure behind a retaining wall due to stormwater or other water source. For a water table behind the wall, why would you analyze a partially submerged backfill? You could reasonably expect for almost every situation that a partially submerged backfill will become fully inundated during the life of the wall. The following lateral earth pressure equation is for a water table at the top of the wall. Thisequation is composed of a soil component plus a pore water component. Add the above surchargeand earthquake components if necessary.

NAVFAC 7.02 - Foundations and Earth Structures. This publication has a graphical solution for lateralearth pressure analysis. Other publications with Coulomb solutions may be found in the publicationssection of this website.

Since a planar slip surface, as assumed for both Rankine and Coulomb Methods, is reasonable for active earth pressure conditions, this assumption may yield unreasonable results forpassive earth pressure conditions. The Log Spiral Method assumes a curved slip surface, andtherefore should be used for all passive earth pressure conditions.

Geotechnical Info .Com does not currently have procedures and examples for the Log SpiralMethod. Please check the retaining wall publicationssection of this website for additional resources that may have information on the Log Spiral Method.

Overturning failure is a result of excessive lateral earth pressures with relation to retaining wall resistance thereby causing the retaining wall system to topple or rotate (overturn). Sliding governs the design of retaining walls most of the time, especially for walls less than 8 feet in height. However, overturning must be analyzed.

Bearing capacity and settlement for wall foundations can be determined in the same manneras building foundations. Technical guidance for these analyses can be found on this websiteunder the following headings:

Bearing Capacity

Settlement Analysis

Soil parameters,g and f, are determined from laboratory testing. Engineering soil properties from a known granular material source is sometimes used. Some engineers use conservative soil parameters based on the soil classification without laboratory testing. It is good practice to avoid cohesive soils, and use gravel type materials for retaining wall backfill.

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