Mohr envelope for overconsolidated soil :common Yet puzzling

[MCC1966]

Triaxial (consolidated-undrained) under the confining stresses (sigma3) show (note that 15% is the failure criterion according to ASTM standard):

sigma3 axial strain sigma1-sigma3 pore p
20 15 289.772839 -87.31215224
50 15.00151 172.5743 -15.5049
100 15.00212432 106.3252557 45.87678529

I want to get the total strength parameters phi and c for this overconsolidated soil. However, when drowing Mohr circles I'am getting a circle completely inside a circle.(try it if you do not beleive) How can I get the Mohr envelope in this case?

 

[fattdad]

In addition to the deviator stress at 15 percent, what was the maximum deviator stress for each consolidation interval? You may have a maximum deviator stress prior to 15 percent that shows a higher value then what you have at 15 percent.

f-d

 

[MCC1966]

No f-D the material behaves with unidentifiable peak.. that is why we are going by this 15% criterion

 

[GeoPaveTraffic]

Have you looked at the P-Q plots? Generally this a better way of looking at R-Bar traix data. It is very helpful when some of the data points may be at over consolidated pressures and some at under normally consolidated.

You should be able to draw a line somewhat "along" the P-Q plot. This becomes the failure envelope. Note that with this method you are measuring an angle (zeta) defining a line through the top of the Mohr circle and there for the value needs to be corrected. sin(phi) = tan(zeta) similarly the intercept (d) is converted to cohesion by c = d*(tan(phi)/tan(zeta)).

If you want to post the P-Q data I'll be happy to take a look.

 

[fattdad]

The slope of the P-Q plot defines the angle "Alpha", which is not the same as Phi. This is only appropriate for effective stress analyses. There is some trig correlation between these two, that I don't have at my fingertips right now. For total stress analyses, the slope of the P-Q plot is a 45 degree angle (positive) beginning at (sig1-sig3)/2 and zero sheer.

My suspecion is that the three samples were not uniform or had a defect. The circles that you are describing don't conform to what we know about soil srength.

f-d

 

[MCC1966]

Traditionally (and for a specific void ratio(e)) one gets higher deviatoric stress at critical state (q) for higher confining pressure sigma 3 , but here we have to remember that we are taking failure criterion at q15 % strain (before critical state)
Also, if one has two samples each has different void ratios e1>e2 and test these samples at two different confining stresses P2>P1 then is not possible that one will get (looking at strain 15%) q1>q2;i.e Mohr circle inside the other..? I beleive yes
I will forward the data to Geopavetraffic as soon as I get home

 

[MCC1966]

Here are the results of the test I am talking about

At confining Stress =50 KPa

e (%) (s>1-s>3) Du (kPa)
0 0 0
0.000347859 3.177182332 4.521912
1.062629329 38.77673253 29.072761
2.069896972 48.75427377 24.55082783
3.802321975 66.16516677 18.41364483
5.490123026 81.66157984 13.56787417
6.856265054 93.45943792 7.43067
7.979247898 108.5499343 6.137183
9.214847666 120.5975511 -1.615271
10.44312389 130.727035 -6.461084
11.69944387 147.408024 -4.84583417
12.76657617 159.8906973 -6.461084
15.00151 172.5743 -15.5049

At 100 Kpa confining stress
e (%) (s>1-s>3) Du (kPa)
0 0 0
0.002 2.802888442 3.058220971
0.003 6.132649642 2.253319931
0.004 8.939964893 3.86315366
0.004913818 11.90718198 5.311562001
0.055023284 34.43466899 14.48733259
0.104221982 45.76449679 20.60382728
0.160546257 53.67767598 29.13505674
0.236687168 58.26574312 34.44767367
0.288391649 59.92736706 38.31082733
0.355714219 61.68052196 43.62238933
0.420759086 62.04759459 45.23222306
0.486877641 62.09909854 49.73993895
0.553322022 61.87328779 50.54485054
0.607986895 62.02936862 52.79818102
0.676350569 62.33409662 55.85643364
0.754834349 62.07851105 57.46624627
0.831267735 61.78284389 58.27114731
0.911735972 61.68519398 60.52448834
0.978212938 61.61447176 60.52448834
1.05721727 61.08012488 60.52448834
1.144648947 61.49016471 63.58273041
1.224238222 61.56415663 63.58273041
1.291528985 61.49717242 64.387642
1.369328524 61.7133538 64.387642
1.434699224 61.78462448 65.03220423
1.501436077 62.19130802 65.83711582
1.571687233 62.35378115 65.83711582
1.649585299 62.72585515 65.83711582
1.717720892 63.09224697 65.03220423
1.784458519 63.23556989 64.387642
1.8549044 63.87247869 65.83711582
1.923008186 64.24958375 65.03220423
1.992315988 64.39365193 67.44588407
2.061135048 64.67012001 67.44588407
2.139976464 64.74410952 68.0904463
2.221225918 65.07584161 65.83711582
2.299774864 65.5407662 65.03220423
2.382715526 65.78747936 65.03220423
2.450949646 66.0659506 67.44588407
2.563793692 66.13136534 67.44588407
2.630270658 66.31158098 65.83711582
2.710120597 67.22325804 66.64097248
2.777248446 66.93469264 65.83711582
2.871675374 67.22636722 64.387642
2.954552032 67.62469074 65.83711582
3.039966284 67.7300263 65.83711582
3.13410074 67.92577712 65.83711582
3.22215072 68.29769089 66.64097248
3.302911815 68.55630396 65.83711582
3.383542968 69.15291678 64.387642
3.470063489 69.75941098 66.64097248
3.550206283 70.32540218 65.03220423
3.634124045 70.58252713 64.387642
3.714461952 71.24808211 65.83711582
3.786080041 71.51442364 63.58273041
3.874064468 72.0495838 64.387642
3.939857967 72.68842485 65.83711582
4.016323934 73.21549322 66.64097248
4.092074237 74.07372403 65.03220423
4.155394924 74.42072123 63.58273041
4.235082335 74.67134214 63.58273041
4.312980011 75.36715889 64.387642
4.389836586 75.71984559 62.77782937
4.536000573 77.09822318 64.387642
4.68857487 78.34947213 64.387642
4.835389739 79.35313818 64.387642
4.987964036 80.08305514 62.77782937
5.136666004 81.13814478 62.77782937
5.257124376 81.62641497 63.58273041
5.426098366 82.6549044 61.97289668
5.567999808 84.38728518 61.32938938
5.735509115 86.02374518 61.32938938
5.878094024 87.36668831 60.52448834
6.043358599 88.55016527 60.52448834
6.187824007 89.16604357 59.71957675
6.354005951 90.02052405 57.46624627
6.476143508 90.46654559 58.27114731
6.623954099 91.20148425 59.71957675
6.772011776 92.44018543 58.91467571
6.942261156 92.8254598 58.10974302
7.072344492 93.48172644 59.71957675
7.220600965 93.90728856 57.46624627
7.371785831 94.51103445 58.10974302
7.500378886 95.64549731 55.05150095
7.630761673 96.43564888 55.85643364
7.761290892 96.67460933 54.40799365
7.896388607 97.19455659 55.85643364
8.028359328 97.68499452 54.40799365
8.158442762 98.19133117 55.05150095
8.288080408 98.82782141 52.79818102
8.420796176 99.21518404 53.60309261
8.553957822 99.41902618 51.99327998
8.671282803 99.42197516 51.34975158
8.823609767 99.91212465 51.99327998
8.956273508 100.2437659 51.99327998
9.090626033 100.2577048 50.54485054
9.244791401 100.5985224 49.73993895
9.378201611 101.1354754 50.54485054
9.532812444 101.0675816 51.34975158
9.655845705 101.3513643 49.73993895
9.760210526 101.8704392 48.93503791
9.88791019 101.974936 50.54485054
10.01238393 102.1317524 51.34975158
10.15641999 102.6303281 49.73993895
10.27845985 102.92403 50.54485054
10.42229745 103.1735416 51.34975158
10.56439419 103.5219916 49.73993895
10.70609723 104.057247 49.73993895
10.8493881 104.2462905 49.73993895
10.99436776 104.9647401 48.93503791
11.1362661 105.2758277 45.87678529
11.32047125 105.5516365 48.93503791
11.48500989 105.400127 50.54485054
11.65218425 105.7771849 48.93503791
11.81746823 105.9837402 48.29046513
11.96522664 106.045213 47.48556409
12.13691743 106.173575 46.68169688
12.28681372 106.5483273 46.68169688
12.43586402 106.2243884 48.29046513
12.58694803 106.3883183 47.48556409
12.73898858 106.1965046 47.48556409
12.89175799 105.9191954 45.87678529
13.04521086 105.8501776 46.68169688
13.17891265 105.9869632 48.93503791
13.33633521 105.819816 48.93503791
13.49310688 105.7994043 45.87678529
13.64945537 106.1755723 46.68169688
13.8069431 106.2537324 46.68169688
13.91887638 106.2193364 47.48556409
14.07587575 106.0683781 45.23222306
14.23407952 106.1105089 46.68169688
14.38925657 106.0695543 46.68169688
14.5479809 106.1776813 48.29046513
14.70006684 106.1646732 48.93503791
14.82885519 106.1939834 48.29046513
15.00212432 106.3252557 45.87678529
15.154308 106.7137747 47.48556409
15.28316153 107.2793028 45.87678529
15.41305615 107.2812052 45.87678529
15.47670189 107.5440134 47.48556409
15.48662612 103.15882 45.87678529


At confining Stress 20 KPa
e (%) (s>1-s>3) Du (kPa)
0 0 0
0.006 1.53505237 1.44947382
0.03 9.732903015 0.804901041
0.277004224 10.78519067 1.44947382
0.466458607 10.720949 1.44947382
0.49545963 10.65707334 0.804901041
0.714011344 11.14755396 1.44947382
0.742014354 16.74706108 3.86315366
0.771369151 20.83513948 3.058220971
0.919881685 30.18383182 6.117528521
1.067042049 34.63056194 4.50771589
1.213043631 37.52282567 6.922429561
1.360236228 40.21613308 5.312616931
1.524294861 43.25860095 6.922429561
1.666241089 45.45392752 5.312616931
1.803809654 47.95505658 8.37086955
1.963748471 50.43462669 6.117528521
2.096424825 52.35055749 5.312616931
2.255462323 54.64766473 5.312616931
2.384823103 56.57391372 3.058220971
2.515600128 58.4179012 4.50771589
2.671644363 60.36978801 4.50771589
2.805286111 62.46714639 3.058220971
2.962456513 64.50048068 3.058220971
3.089757574 66.57067292 0.804901041
3.221532226 68.19551896 0
3.36003434 69.90512441 -0.804932689
3.493805014 71.506632 -3.05824207
3.625583119 73.3025353 -0.804932689
3.762218134 75.43184734 -1.609833729
3.899049796 77.40110234 -1.609833729
4.036373748 79.18284071 -4.668075799
4.173746048 80.56295443 -5.472987389
4.341126396 83.0884948 -7.726328419
4.479921466 85.47344052 -6.116494689
4.64248999 88.61493921 -6.92139573
4.78329969 90.5639151 -8.531229459
4.924602065 93.00453216 -8.531229459
5.095124173 95.86305951 -8.531229459
5.235493 98.61802199 -8.531229459
5.380281217 101.8974866 -11.58947153
5.549625165 105.1320452 -12.23297883
5.693724541 108.1471281 -12.23297883
5.838071788 112.0238391 -14.64772415
6.009282595 116.7904772 -13.84279146
6.175336964 120.0017334 -15.29226528
6.315705885 123.3529191 -16.09719797
6.47969706 126.432429 -17.70596622
6.617265335 129.5712889 -19.96034108
6.746140531 132.8319695 -21.40875997
6.905859422 136.3390268 -22.21366101
7.034587138 139.4612396 -25.27190308
7.169796408 142.0615918 -23.82349474
7.193177287 142.6347559 -21.40875997
7.351519568 146.5785835 -23.01858315
7.477645586 148.9919765 -25.27190308
7.603523734 152.0990165 -26.07683577
7.731072477 154.6230816 -26.88173681
7.858131902 157.1216599 -26.07683577
7.988429394 159.5540348 -29.93997888
8.143041171 162.9145309 -31.38839777
8.273193813 165.7241458 -29.93997888
8.407666087 168.5994056 -32.19329881
8.56601158 172.7393339 -32.19329881
8.700535271 175.4695434 -35.25260636
8.836481541 178.4571158 -36.05645247
8.970316483 182.0431944 -36.86137461
9.104643718 185.5982764 -37.50594739
9.267653308 189.6952393 -39.92066106
9.40384745 192.2898958 -39.92066106
9.538812013 195.6641539 -42.97891368
9.674072796 198.8012733 -46.03715575
9.835704701 202.8179904 -44.42733257
9.999860032 206.4545445 -46.03715575
10.16913318 210.6436421 -47.48557464
10.31104718 214.3815442 -49.09539782
10.46535324 219.0647557 -49.73890512
10.60346897 222.2807493 -51.3487283
10.74477134 225.5251067 -52.79820212
10.88626672 227.5065077 -55.21188196
11.02637808 230.8717062 -56.66135578
11.16771269 233.8283005 -57.46626737
11.30495932 236.8786008 -58.91468626
11.47104583 240.2115833 -57.46626737
11.60871108 242.6612141 -61.97292833
11.74627965 244.7208452 -62.77783992
11.85459011 245.9834671 -63.58275151
12.02305825 249.2987888 -63.58275151
12.12975947 250.8777575 -67.44590517
12.26359422 253.0932672 -68.08941247
12.39720374 255.0592667 -66.64099358
12.55987835 256.9707787 -68.89432406
12.69503305 259.9501201 -69.69923565
12.82954388 261.6340691 -70.50414724
12.96431218 263.5840824 -71.30905883
13.09592606 264.3821273 -72.75853265
13.22992197 266.5709832 -74.3673009
13.3704838 268.3398335 -74.3673009
13.50740889 269.9252689 -77.4265979
13.51980096 270.3570642 -76.62168631
14.5 283.3077087 -83.34144309
15 289.772839 -87.31215224
16.5 308.5898243 -99.22427968
18 326.5392012 -111.1364071

 

[Panars]

If you look at this data in p-q space, you can see a very distinct yield envelope. From this you can determine the zeta and d for the effective strengths and convert them to cohesion and phi, as Geopavetraffic stated above (he also included the trig conversions between the two).

However, the other thing the p-q graph can tell you is the strain level that the sample began to yield. This would be the appropriate failure criterion for total stress analysis. From your data, I would estimate that the strain level at yield was about 1.5%, 1%, and 1.5% for the 20, 50, and 100 kPa confining stresses. This is significantly different than the arbitrary 15% failure criterion, and in my opinion, more appropriate for an overconsolidated soil.

 

[MCC1966]

I will try to locate the conversion formula that give you the undrained shearing strength knowing the drained ones. I think such formula were obtained for specific soils and i donot know if they are vaild for the soil at hand

 

[BigH]

How fast did you run the tests? You did give pore p in your initial post. Did you actually measure the porewater pressures? In Asia, I have seen Consolidated undrained with pwp measurements failed in 20 minutes - in such cases the porewater pressure has no time to stabilize and is hence not reliable.

Normal practice (Lambe and Whitman) - is to use alpha for the slope of the line in p'-q' space. As GeoPaveTraffic indicated, tan(alpha)=sin(phi'); cohesion' is intercept (a)/cos(phi'). Of course, this is for 2-D; 3-D has the "M" relationships: the r'-s' space if I remember correctly.

Su = {p'+c'cot(phi')} x V/W where V= sin(phi')[Ko+Af(1-Ko)] and W=1-(1-2Af)sin(phi'). Af is the A factor at failure and Ko is at rest k value (usually taken as 0.5).

 

[GeoPaveTraffic]

Ok, had a chance to look at and plot the data you posted.

Here is my take on the data. First, the 20KPa sample appears to be a different soil than the other two. The p-q line plots significantly different than the other two. Second, the 50KPa and 100 KPa appear to be from the same soil, however, the tests have a problem. Not knowing more about you lab setup and how the tests were ran, not much more I can say about what the problem was. BigH may have hit it with the rate of testing, but I just don't know.

If I were to assume that the data was all correct...Then I would draw the following conclusions.

For the 20KPa test, phi =~37 degrees, choesion = 2.4 KPa
For the 50 & 100 KPa tests,
phi =~35 degrees, choesion = 0 (note that the data plot results in a choesion of -5 KPa).

 

[MCC1966]

Thank you Big H and GeoPaveTraffic.
GeoPaveTraffic: are these total or effective parameters?

 

[GeoPaveTraffic]

Effective.

 

[MCC1966]

what about total which i am particularly concerned about in this situation?

 

[GeoPaveTraffic]

I can't make any sense out of your total stress data. Don't think I'm missing something, but ... The data is showing a decrease in shear stress with an increase in confining pressure.

Based on what I'm seeing I think there is a problem with how the test was set up and ran or in the data collection.

The data for 20 and 50 KPa shows numorous negative pore water pressure readings. While some may be ok, I think it is at least possible that the samples were not saturated prior to shearing at those confining pressures. Looking back at the plots for effective stress, I think the satuation problem would also help explain that data as well. I would go back to the test paperwork and check the B coeficients and how the back pressure of the samples was done.

 

[MCC1966]

Thank you GeoPaveTraffic

 

[GTeng]

Haven't charted the data, but it appears to me that the results are should be as expected considering the apparently widely varying OCRs. The sample tested at 100 kPa appears to be lightly overconsolidated, based on the A value. Therefore, the sample at 20 kPa may have an OCR greater than 5. This would explain why they looked like different soils.
Based on CAM CLAY or SHANSEP, the value at the low confining stress would be expected to have a higher shear strength, which is consistent with the results presented.
I agree with Panars that using an arbitrary strain value as a failure criteria is poor practice. You really have to consider the stress path behavior.
In my opinion you can't really understand the shear strength behavior if you don't know the stress history

 

[MCC1966]

GTeng

So can I say that assigning shearing strength through Mohr-Coulomb is not applicable in this case. My concern is to get the undrained strength Parameters.(what we should do in this case to get undrained shear strength.?)
BY the way GeoPaveTRaffice also suggested that the soil could not fully saturated. OC soils (or let us say heavily over consolidated soils) in most cases implies partially saturated soil. DO you guys agree with me..?
Your answer is affirming to us that our understanding of critical state theory is good

 

[GeoPaveTraffic]

While the soils may have been partially saturated when collected, they should have been completly saturated before shearing in a triaxial test. While there has been considerable work done on partially saturated soils in the last 20 years or so, I don't know of anyone who purposely conducts triax tests without saturating them first.

If the tests were not saturated, then without A LOT of research I do not how to use the results.

 

[GTeng]

Can you check with the lab to find if they checked B values after consol and prior to shearing? That should answer the questions about saturation.
It sounds like the effective stress phi from your p-q diagram should be reliable. However, it sounds like you are worried about the undrained case, which would mean you either have to estimate the pore pressures that will occur in the field during loading, or you need to know a little more about the stress history of the in-situ deposit, and the variation of undrained strength with stress history