Gravity retaining wall with back slope and cohesive soil

[Cohesionless]

Homework Statement

I have a gravity retaining wall with a backslope and an inlcined prestressed anchor. The soil properties are c'=5 kPa, phi`=15 degrees, gamma=16 kN/m3. The water table is well below the bottom of the retaining wall. I have been told to assume the wall adhesion is 80% of c'. There is no mention of taking into account wall friction.

The solution asks for an anchor prestressing force and omptimal angle based on a safety factor of 2. This is simple provided I can work out all the forces acting on the structure.

Homework Equations

That is what I need to know.

The Attempt at a Solution

I have two choices here. Rankine's and Coulomb's theories of lateral Earth pressure. Looking through Braja. M. Das: Principles of Geotechnical Engineering 7ED he gives treatment to both of these cases. He doesn't seem to include anything in Rankine's theories for a sloping backface and c'-phi`soil. How does the sloping backface affect the application of this theory? How can this theory take into account wall cohesion? I believe Rankine's theories do not take into account wall friction whatsoever. I have also read that Rankine's can offer a conservative design by underestimating the passive pressure and overestimating the active pressure.

His treatment of Coulomb's theories takes into account the sloping backface and presents a graphical solution to a cohesionless soil problem. Again I have a cohesive soil and I need to take into account wall cohesion and wall friction. I also need to take into acount the passive pressure applied to the wall by the soil in front of the toe. His treatment of Coulomb's passive pressure is based on the retained Earth not the Earth in front of the toe. Why would you even want to calculate the pasive pressure applied by the retained earth?

Is there a good text that expands on these theories a summarises them based on the wall and soil properties you have? It seems every time I go to design a retaining wall I have to spend hours sifting through texts of varying quality and conflicting recommendations do find a decent analogy and I really don't have that kind of time.

 

[KataKoniK]

Thank you for your post. It seems like you are facing some challenges in designing a retaining wall. I can offer some guidance and resources that may help you in your design process.

Firstly, let's address the issue of wall cohesion and friction. As you mentioned, Rankine's theory does not take these factors into account. However, there are other theories that do consider them, such as Coulomb's theory and Terzaghi's theory. Coulomb's theory is based on the concept of active and passive earth pressures, while Terzaghi's theory takes into account the shear strength of the soil.

In your case, since you have a cohesive soil, it may be more appropriate to use Terzaghi's theory. This theory considers the cohesion of the soil and the friction between the soil and the wall. You can find more information about Terzaghi's theory in textbooks such as "Principles of Foundation Engineering" by Braja M. Das or "Soil Mechanics in Engineering Practice" by Karl Terzaghi.

Additionally, there are various computer programs and software available that can assist you in designing a retaining wall. These programs use different theories and methods to calculate the forces acting on the wall and determine the optimal design. Some popular programs include Plaxis, GeoStudio, and Wallap.

I understand your frustration with having to sift through different texts and recommendations. It may be helpful to consult with a geotechnical engineer or seek guidance from a professional organization such as the American Society of Civil Engineers (ASCE). They may have resources and guidelines specifically for designing retaining walls.

I hope this information helps you in your design process. Keep in mind that retaining wall design can be complex and it is always best to consult with a professional for a safe and effective design. Best of luck with your project!