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# Residual strength: internal friction angle

## Residual strength: internal friction angle

(OP)
Dear all,
I have this doubt at the office. We considered an internal friction angle for a liquefied sand, let’s say 28 degrees. The residual internal friction angle (after liquefaction) must be a lower value, let’s say 10 degrees.
Structural engineers asked: why is that possible since liquefaction causes densification and that makes a greater friction angle.
So the question is: why is the residual (post-seismic) friction angle of a liquefied sand lower than the static friction angle? Is it a critical state soil mechanics topic or isn’t there always densification?
I appreciate your help on this.

### RE: Residual strength: internal friction angle

I have heard that argument before. One reason it doesn't always become denser (if true), is that many times there is liquefaction ejecta on ground surface. You are removing material from the ground so definitely reducing density. Although there is some settlement I dont think it has a tangible effect on densifying the soil.

I have done SPTs, maybe several months after a seismic event, where sites that have suffered liquefaction. SPTs can often be less than 5. If this is the densified version of ground, what was the SPT before!!!!

Residual liquefied strength is during the seismic event, or for a very short period after (less than days i would think). After the event there is a dissipation of pore pressure and the soil regains its strength.

Realistically, a sand cant have a phi of less than 28 deg.

### RE: Residual strength: internal friction angle

I would recommend your office reach out to a professional with an understanding of critical state soil mechanics and soils liquefaction before performing any analysis regarding liquefied sand using a friction angle of 28 or 10. Below are the images you will see in liquefaction study regarding cohesionless soil behavior dependent on a soils stress state.

When soil liquefies from seismic conditions it is assumed to follow an undrained path to the critical state line. If the soils void ratio is initially denser than its critical state it will increase in effective stress to reach the critical state line which requires more deviator stress. When you have looser soils it will decrease in effective stress to reach the critical state line which requires less deviator stress. Both of these paths will lead you to the soils critical state friction angle but at drastically different stresses.

You will see empirical correlations correlating the density state by corrected N values to liquefied strength ratios between 0.03 and 0.12 Sr/sigma', based on case histories.

### RE: Residual strength: internal friction angle

AS stated above, phi_cs, which is phi at the critical state (also called phi_cv or constant volume)for prevalently sandy soil, is usually 30° or above.
There is a discussion on this topic almost 10 years old....

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