Friction "f" and coefficient "Ks" relation for Rankine formula 2

[Iasonasx]

I have ran into this problem of solving for a safety factor for a retaining wall using the Rankine formula, but instead of having the angle of friction "φ" I had only a coefficient of cohesion Ks. I am unaware of the relationship between the two. I might manage to extrude it but I would rather get the opinion of a specialist instead of playing Magellan!

 

[Iasonasx]

Got it. I guess I found this in my own notes.

http://www.avant-garde-engineering.com/K-to-phi.png

 

[hokie66]

No, you don't have it. Cohesive soils and granular soils are very different in the way they apply lateral loading to structures. There is no relationship between the two variables, as they are for different soils.

 

[Iasonasx]

So this formula with the phi and beta angles for active soil pressure is for which one of the two types of soil?

 

[hokie66]

Granular, non-cohesive.

 

[Iasonasx]

Thanks hokie66. So for cohesive I only consider the moisture content to be my Ks (such as 35% moisture means Ks=0.35)? And to put it in practice: if I want to calculate the lateral load I do P=Ks*0.5*(gamma soil)*L^2. Right?

But in case I have granular that is moist? It may be a bit too tricky for a structural, I should probably just let the geotech do it all the way.

 

[hokie66]

Moisture content and cohesion coefficient are completely different things. I don't agree that earth pressure analysis is "too tricky for a structural" engineer, but you need better grounding in the fundamentals. In your case, ask your geotechnical engineer for assistance. Make sure the geotech knows not only the material and ground water parameters, but also the type structure, e.g. cantilevered wall, basement wall, which is involved.

 

[RFreund]

I thought we discussed this:

http://www.eng-tips.com/viewthread.cfm?qid=325411

Do you have Ks 'a coefficent of cohesion' or do you have Ks the coefficient for lateral soil pressure?
If Ks is the latter.
If you have Ks then the pressure for the soil at a depth H is Ps= Ks*gamma*H
The force is Fs=1/2*Ps*H.

EIT

http://www.HowToEngineer.com

 

[hokie66]

That's still drawing a long bow, RF. That's likely good enough for active soil pressure on a cantilevered retaining wall with no surcharge and no hydrostatic pressure, but the OP hasn't defined his problem well enough for us to know. What if he is dealing with an unyielding basement wall where a trapezoidal pressure distribution would be more correct?

 

[RFreund]

Hmmm, Good point.

EIT

http://www.HowToEngineer.com

 

[Iasonasx]

I was referring to a cantilever wall, not a basement, sorry for not clarifying that. Surcharge would be a simple addition of Ks*gamma*S*L (S being the height of the surcharge for the analogous gamma) to the triangular configuration of stress that RF quotes. I assume that is the trapezoid hokie refers to. The issue to me was actually how that Ks was established. Once it is given though I do not know if it is worth analyzing it and going backwards. The question that lingers is on the hydrostatic component actually and how it affects the behavior of granular and non granular soils.
Thank y'all for your tips.

 

[hokie66]

A trapezoidal pressure distribution is often used for cohesive soils against an unyielding wall.

If you have a water level part way up the wall, the pressure increment below that level is the hydrostatic pressure plus the buoyant soil pressure. The buoyant soil pressure is just the triangular pressure obtained in the same way as you outlined above, but with the density of the soil reduced by the density of water. Any good soils book will have an explanation.

 

[Iasonasx]

The water level is way below. However, in winters there is snow that sits there for months. I expected that to cause the hydro component as the consistency of the soil will fluctuate (and that means varying levels of moisture and specific weight) but not to the point of considering buoyancy to be a real threat, unless no proper drainage is specified in the construction I guess. It is a sloped area to become terraced with walls of heights up to 14 ft max.