drained vs/ undrained strength 4

[Jordan2]

Dear Friends,
I have the following theoretical doubt and maybe I am doing a stupid question: let you suppose that by means of triaxial CU tests the effective shear strength parameters (c' & phi') of a saturated clay have been derived. Could I derive from the effective envelope the undrained strength (cu) for the examined stress condition? Is this undrained strength coincident with the available effective shear strength?
Please, let you notice that I am not referring to the values of c(CU) and phi(CU) that I could derive from the same CU test, but as I said to the cu (i.e. with phiu=0).
Thank you in advance for your comments..

 

[jdonville]

Jordan2,

Maybe you could use the total stress measurements to back something out of the data.

Jeff

 

[fattdad]

One-half the maximum deviator stress at failure, represents the undrained shear strength for a given confining stress providing the shear forces were applied in an undrained state (i.e., you measured pore pressures for later determining the effective strength envlope). This assumes phi=0.

pretty sure I got this right. . . . .

f-d

¡papá gordo ain’t no madre flaca!

 

[Jordan2]

Thank you for your answers, but I am not sure that the concept of my question was clear: I am not generally asking how to determine the undrained strength (it is clear what Fattdad says..), but if it may be theoretically derived from the effective shear envelope (for a certain stress condition). More in detail, I have seen some pubblications from which it seems that the undrained strength is taken coincident with the available effective shear strength for a certain stress condition.
Jordan

 

[moe333]

The undrained strength is used for a loading (or unloading) condition where the shearing occurs over a period of time where drainage cannot take place. The effective stress envelope is for the condition where the shear occurs over a period of time where drainage does occur. You cannot combine these strengths.

 

[fattdad]

O.K. if you have an effective strength envelop and you want to derive the undrained shear strength for a given confining stress (sigma 3) couldn't you just convert phi to alpha (ala stress path) and plot a 45 degree intercept from a sigma 3 value to the alpha line and then look to the left (horizontally) to get the appropriate Su for that confining stress?

I just thinking out loud here so forgive me in advance. . . .

f-d

¡papá gordo ain’t no madre flaca!

 

[Jordan2]

I have to think in detail to your suggestion, but my first impression is that it is not so far from what I have seen in the pubblications as I have reported in my first post. If I am understanding, this seems in contrast to the opinion of Moe333 (that, incidentally, was also my original convinction..).
Is it correct?

 

[fattdad]

I'm in agreement with Moe333. You cannot combine a total strength analyis and an effective stress analysis in the same evaluation. You can use one CU test to acquire both total and effective stress parameters. Essentially the total stress circle of a CU test can be interpreted as the undrained shear strength for that confining stress. If you take an undisturbed sample from the depht of 10 ft and replace it into a triaxial cell at the in-situ confining stress, consolidation is unnecessary. If you further lock off the drainage it's an undrained test. You get a total stress circle and then derive the undrained shear strength.

I enjoy this discussion and may be off-track somewhere. Maybe I'll be further informed by others.

f-d

¡papá gordo ain’t no madre flaca!

 

[BigH]

Might I suggest that you find a copy of Lambe and Whitman's excellent book on "Soil Mechanics" (originally published by Wiley in 1968 with the SI version published in 1979). Section 28.3 is entitled "Relationshipo between Drained and Undrained Strength". This explains the relationships of Su vs c'-phi'.
(Quote): ". . . for a given clay with a given stress history, there is a unique qf..p'f..wf relation which applies independent of the type of loading and the degree of drainage during loading. (new para) The foregoing result provides a complete unity for the shearing resistnace of clay under a variety of loading conditios. That is, regardless of how the soil is sheared, the relationsip between strength and effective stress remains the same. However, if two specimens of a given clay are consolidated to the sae stress, p'o, and one then is sheared with full drainage and the other without further drainage, different values of srength qf will result. This difference is explained by the difference in the pore pressures, and hence effective stresses, existing within the two specimens. (new para) By using the pore pressure parameter Af, it is possible to dervie an expression connecting undrained shear strength and intial consolidation stress. . . . the undrained shear strength depends upon the conditions existing before shear, i.e., upon p'o and also upon Af, phi' and c' which are functions of stress history. For normally consolidated Weald clay with Af=0.89, c'=0 and phi'=22, qf = 0.29p'o."
For c'=0, qf/p'o = ( (sin phi')/(1+(2Af-1)sin phi') ) (see equation 28.2. In your case, having the effective stress parameters (and the test results), you can determine Af at failure - then compute qf using these values. Equation 28.1 of Lambe and Whitman can be used if c'o does not equal zero.
I hope this helps you - but it is better to think in terms of stress paths than Mohr's circles per se.

 

[fattdad]

I agree with BigH (for what that's worth). I'll also recommend Bishop and Henkel for further reference on triaxial strength testing.

f-d

¡papá gordo ain’t no madre flaca!

 

[Jordan2]

Thank you very much to BigH, Fattdad and to all of you for the very interesting discussion. I am in some way conforted that maybe my question was not so banal as I was afraid.
Ciao!

 

[GTeng]

Following on to BigH's response, you could theoretically ( based on critical state soil mechanics principles) estimate the undrained strength if in addition to the effective stress phi you know the OCR of the soil. But, if you knew that you could do your calculations much more easily based the ratio to the vertical effective stress, as in SHANSEP calculations.

 

[fattdad]

Isn't SHANSEP to determine the undrained shear strength as a function of confining pressure (i.e., Su/P)?

f-d

¡papá gordo ain’t no madre flaca!

 

[Jordan2]

A request to BigH: unfortunately I did not find the book of Lambe & Whitman. Please, have you any possibility to report the equation 28.1 that you have mentioned for c' different than zero?
Thank you very much in advance..
Jordan

 

[BigH]

I'll find it when I get home - am out of station for a few more days. Cheers.

 

[Mccoy]

Jordan2,
here's L&W's equation 28.1:

qf = [c*cosPhi + (po-2Af*qf)sinPhi ] / (1 - sinPhi)

Phi, po and c are barred (effective stress values)

 

[Jordan2]

Thank you to Maccoy (as well as to BigH).
I found also in the Book "Soil Mechanics" (Verruijt, 2001) the following similar equation:
su = c' [cos phi'/(1 ? (1/3)sin phi')] + p0' [sin phi'/(1 ? (1/3)sin phi')]
In this equation there is Af=1/3 and then a more general formulation should be obtained by substituing -1/3 with (2Af-1).
Coming back to my original question, I have derived the following conclusions:
1) in the case when the drained parameters are known, it is possible to derive the undrained strength only if the preconsolidation pressure is known.
2) in the opposite case when the undrained strength is known, it is possible to derive the drained parameters only if the deltaU is known (or eventually the OCR, given that the Af can be empirically derived).
Do you agree?

 

[BigH]

Jordan2:
I disagree that you need to know Pc' in order to determine Su if you know effective stress parameters (I am presuming that you have the back-up data from which the parameters are derived). If the soil is overconsolidated, its Af value will differ from that of normally consolidated clay - and heavily overconsolidated soil will have a very very different Af since the stress path of the HOC soil is to the "right" of the drained condition line (HOC soils are less conservative in the long term and you design not for Su but for c'-phi'. In other words, if you have Af, then you have enough information to determine Su.

 

[dgillette]

Walked in on this late due to two weeks out of hemisphere.

You can find Su from the effective-stress envelope and Af, but it's a heck of a lot easier if you have Pc', and probably more reliable, because of sampling disturbance, stress path issues (CIUC vs CAUC vs DSS vs CAUE), etc. One of the main reasons SHANSEP was created was dealing with sampling disturbance. If I could only have one test run on the soil in question, I would ask for oedometers, then look at typical Su/sigma-vc' ratios, such as published in CC Ladd's Terzaghi lecture on SHANSEP in the ASCE JGGE in about 1989. (The lecture was actually in 1986, but he and the editors had a disagreement over number of pages, etc. There is too much meat in the paper for the JGGE's standard number of pages.) I think this would be easier and better than using Af from a CIUC test, and it would allow consideration of CAUC vs DSS vs CAUE.

Are we talking about a real case where somebody has 3x tests but not Pc'? Why would somebody go to the trouble of "undisturbed" sampling, but not do oedometer tests?

 

[Jordan2]

I am examining a case in which there are not available undisturbed samples and I got just some indication of under-consolidation of a clay-bearing breccia (very low undrained strength with reference to effective in situ stress, as well as the analysis of some compression curves for swelling test by odometer). Evidently, the reliability of such indication is strongly conditioned by the sampling disturbance. In addition, from some triaxial CU tests, the effective parameters have been derived (again with disturbed samples). My original question arose from this anomalous situation, to evaluate also if a crossing check (drained vs undrained) could give some additional information about the soil properties.