Failure Criterion: (Sigma1- Sigma3)max Vs (Sigma1/Sigma3)max

[soildynamics]

Which should be our failure criterion

(Sigma1- Sigma3)max or
(Sigma1/Sigma3)max
they do not coincide when having undrained case
Please refeer me to specialized paperes or texts if you can

 

[GeoPaveTraffic]

failure can be defined in many ways. what are you trying to accomplish?

 

[fattdad]

Plot the stress path. That may tell you more than just looking at the stress strain curves. If you are concered about failure at too great of strain, you can limit the stress path to some measure of strain. If the failure shows a peak strength this may not be relavent.

f-d

¡papá gordo ain’t no madre flaca!

 

[fattdad]

maybe I should retract my post: For undrained saturated triaxial testing the stress path will just be a 45 degree line, so your question is one of failure criteria. I guess I'd have to see how the data differ and to what extent your curve shows a peak.

Sorry for any confusion.

f-d

¡papá gordo ain’t no madre flaca!

 

[dgillette]

fattdad - Maybe you should retract your retraction; your first post was entirely correct if you are referring to effective stress. The total-stress path is just a 45, but the effective-stress path can give you phi', c', dilation/contraction, etc.

Soildynamics - You should explain what you are using the results for and what the stress-strain curve and effective-stress path look like. Otherwise, people here can't really be very helpful. The answers to these questions are very often context-dependent.

 

[BigH]

The following excerpts are from K. H. Head’s book “Manual of Laboratory Testing, Volume 3, Effective Stress Tests”, Pentech Press: London, 1986, pages 761-762. (Note that I have used [green]s[/green] instead of lower case sigma for stress so this will be readable in the thread; the use of [blue]1, 3[/blue] and [blue]f[/blue] should be subscripted immediately afterwards; [green]e[/green] has been used for lower case epsilon – strain; [green]u[/green] is pore pressure; bolded text is my doing.)

“Five different criteria of “failure”, from which the shear strength of a soil is determined are . . .
• Peak Deviator Stress
• Maximum principal stress ratio
• Limiting Strain
• Critical State
• Residual State

“(1) Maximum Deviator Stress
The maximum or ‘peak’ deviator stress criterion is the one that is traditionally associated with ‘failure’ in the testing of soil samples. . . . If the vertical and horizontal principal stresses are denoted by [green]s[/green][blue]1[/blue] and [green]s[/green][blue]3[/blue], the peak deviator stress is written ([green]s[/green][blue]1[/blue] - [green]s[/green][blue]3[/blue])f and the corresponding strain is denoted by [green]e[/green][blue]f[/blue]. In an undrained test the pore pressure at that strain is denoted by [green]u[/green][blue]f[/blue], from which the principal effect stresses at peak can calculated. . . .

“(2) Maximum Principal Stress Ratio
If the principal effect stresses [green]s[/green][blue]1’[/blue] and [green]s[/green][blue]3’[/blue] are calculated for each set of readings taken during an undrained test, values of the principal stress ratio [green]s[/green][blue]1’[/blue] / [green]s[/green][blue]3’[/blue] can be calculated and plotted against strain. . . .The ratio is equal to 1 at the start of the test because at that point [green]s[/green][blue]1[/blue] = [green]s[/green][blue]3[/blue], and therefore [green]s’[/green][blue]1[/blue] = [green]s[/green][blue]3’[/blue]. The maximum value of the ratio occurs at about the same strain as the peak deviator stress in many undrained tests on normally consolidated clays.
“The maximum stress ratio criterion . . . is preferable to the peak stress criterion in some ways because it can provide a better correlation of shear strength with other parameters, or between different types of test. It is particularly useful for clays in which the deviator stress continues to increase at large strains. It can also be used as a criterion in multistage undrained triaxial tests.
“The stress ratio is not used for drained tests, except perhaps to quote the value at ‘peak’ deviator stress, because the effective stress changes are equal to the total stresses changes, and the stress ratio curve is the same shape as the deviator stress plot.”

Sorry for the long post, but I thought this was a good and clear explanation.

 

[soildynamics]

thanks bigh
it is valuable stuff.

 

[BigH]

soildynamics - I thank you, sincerely, for using the word "stuff". I remember when I first started out in geo (1975) - we had a sort of pedantic type and I used the word "stuff" once - and he rapped my knuckles for being "imprecise" - you know what I mean. I thought about it - but me, being a Yank, and he a Canadian (but unlike any other I met) - I didn't care too much. I was, in my mind, exonerated when I heard Henry Ford II (CEO of Ford at the time and a Elini (Yalie)) use it during a formal speech he gave to a high faluting group of American businessmen!! Go STUFF!!! (I also got "rapped" when I told him and his wife that I thought Big Bird was silly and not something I wanted my kids to emulate - and that only "Mighty Mouse" would do for my kids!!!)

 

[emmgjld]

BigH

You are the contrary one.