Sliding Stability, Coefficient of friction given soils angle of internal friction

[T.Burke]

Looking at the sliding stability of a retaining wall. Soils are sandy (cohesion = 0). I have soil boring's which provide the soil angle of internal friction (Φ),which is 26 degrees.

My question is, is there a way to determine the coefficient of friction for the soil from the soil angle of internal friction (Φ)? Reading through Das's Principles of Foundation engineering, which has an equation that includes the passive force, cohesion, and Φ in the lateral resistance. they multiply the sum of vertical forces by tanΦ, which leads me to believe the coefficient of friction (f)= tanΦ. This would yield a value of .49, however the international building code, table 1806.2 assumes f=.25 ford sandy soil.

Any ideas / thoughts?

 

[lexeng18]

I can't cite the source (I'm positive someone else that comes along can)...but I've always used (2/3)tanΦ for coefficient of friction. So in your case... 0.666*tan(26) = 0.325.

 

[T.Burke]

After some more reading, it looks like the friction angle is further reduced by k, which are usually in the range of 1/2 to 2/3, so lexeng18 that makes sense.

Thanks!

 

[BridgeSmith]

We generally take tanΦ as the nominal coefficient of friction between foundation soil and granular backfill or concrete cast directly against the foundation soil, using factored loads. Other interface materials (precast concrete, etc.) would have a reduction factor applied. We also use 2/3tanΦ for the interface of reinforced backfill and geogrid for MSE wall design, in accordance with the AASHTO bridge design spec (the geogrid manufacturers have verified somewhat higher values for their products, in the range of .8 to .9, but we haven't compiled the documentation from all of our approved suppliers yet).


As far as the .25 value you mentioned, presumably that would be a lower bound value when Φ is unknown, so you would expect it to be lower than a calculated value if Φ is known.

 

[LRJ]

This is a duplicate thread:

https://www.eng-tips.com/viewthread.cfm?qid=442513

I'm unsure what you mean by 'coefficient of friction'.

Friction is just shear stress (τ). The soil internal friction angle (φ) relates normal effective stress (σ'_n) to shear stress in the soil (tanφ = τ_soil/σ'_n). When there is a different interface roughness, the relationship between normal effective stress and shear stress changes, and is represented by an interface friction angle (δ) (i.e. tanδ = τ_interface/σ'_n).

The ratio of tanδ/tanφ is equal to the ratio of τ_interface/τ_soil. The ratios of 0.5 to 0.67 stated above are commonly applied for designs with a soil-steel interface, though these ratios are just common approximations. For soil-concrete interfaces I've seen ratios as high as 1 used before. Really this ought to be tested as the ratio is dependent on the soil as well.

For many foundation applications (e.g. walls, piles, etc.) the stress normal to the foundation friction is the radial effective stress, σ'_r. The radial effective stress is related to the vertical effective stress (σ'_v) by the coefficient of lateral earth pressure, K (i.e. K = σ'_r/σ'_v). The value of K depends on soil conditions (it is higher for higher overconsolidation ratio), though also depends on some other factors.

To calculate σ'_v all that is required is the soil effective unit weight (γ') with depth (z) profile (i.e. σ'_v = γ'.z). So the common equation for interface friction is: τ_interface = K.σ'_v.tanδ.

Which of the above factors are the 'coefficient of friction' which you refer to?

 

[BridgeSmith]

"I'm unsure what you mean by 'coefficient of friction'."

Some codes (AASHTO, for one) use the coefficient of friction, μ (greek letter Mu) to to define the relationship between vertical force or pressure and lateral sliding resistance force or pressure. It's also the typical notation used in engineering Statics and Dynamics courses, at least when I went to school. From your description, your K value may be the same thing.

The 0.5 and 0.67 reductions are common approximations used for materials that do not conform to soil interface. Granular backfill and wet concrete conform to and interlock with the foundation soil, and so have a higher friction value, apparently close enough to the internal friction angle of the soil, Φ, thus the μ equal to tanΦ.

 

[T.Burke]

In my case, we have a rectangular concrete tank, cast against and at grade, holding back full height water pressure and obviously no lateral soil resistance.We have a full length engineering joint that basically divides the tank into pieces, so lateral movement could be possible. The equation at the end of your reply shows that at a depth of 0 ft, the interface friction would be 0. Am i looking at that correctly?

The coefficient of friction would be the coefficient multiplied by the sum of the vertical forces to determine the total lateral restraining force due to friction.