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Mohr envelope for overconsolidated soil :common Yet puzzling

Mohr envelope for overconsolidated soil :common Yet puzzling

Mohr envelope for overconsolidated soil :common Yet puzzling

(OP)
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?



RE: Mohr envelope for overconsolidated soil :common Yet puzzling

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

RE: Mohr envelope for overconsolidated soil :common Yet puzzling

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

RE: Mohr envelope for overconsolidated soil :common Yet puzzling

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.

RE: Mohr envelope for overconsolidated soil :common Yet puzzling

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

RE: Mohr envelope for overconsolidated soil :common Yet puzzling

(OP)
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

RE: Mohr envelope for overconsolidated soil :common Yet puzzling

(OP)
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


RE: Mohr envelope for overconsolidated soil :common Yet puzzling

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.

RE: Mohr envelope for overconsolidated soil :common Yet puzzling

(OP)

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

RE: Mohr envelope for overconsolidated soil :common Yet puzzling

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).
cheers

RE: Mohr envelope for overconsolidated soil :common Yet puzzling

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).

RE: Mohr envelope for overconsolidated soil :common Yet puzzling

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

RE: Mohr envelope for overconsolidated soil :common Yet puzzling

Effective.

RE: Mohr envelope for overconsolidated soil :common Yet puzzling

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

RE: Mohr envelope for overconsolidated soil :common Yet puzzling

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.

RE: Mohr envelope for overconsolidated soil :common Yet puzzling

(OP)
Thank you GeoPaveTraffic

RE: Mohr envelope for overconsolidated soil :common Yet puzzling

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

RE: Mohr envelope for overconsolidated soil :common Yet puzzling

(OP)
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

RE: Mohr envelope for overconsolidated soil :common Yet puzzling

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.

RE: Mohr envelope for overconsolidated soil :common Yet puzzling

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

RE: Mohr envelope for overconsolidated soil :common Yet puzzling

Keep in mind for HOC soils that with equalization of pore pressures (i.e., sucking in of water), they will be weaker than initially. - Look at the stress paths for HOC and NC/LOC.  The latter curves are to the left of the drained stress path; the HOC is to the right - equalization is always to the drained line.

RE: Mohr envelope for overconsolidated soil :common Yet puzzling

(OP)
I have been able to know that this soil is sandy soil. The only justification for such results is that the sample subject to 20 KPa (highly dilative) confining stress is denser than the one subject to 50 KPa (lightly dilative) which is in turn denser than 100 KPa (contractive).
They are from the same soil but with different state parameters (e,P') it is common situation but assigning shearing strength through Mohr circle is not possible in this case. Shearing strength through Mohr Coulomb circle should be considered for soils having the same moisture contents (void ratios) ..should not it ? please answer me
The Dilative soils will have strain-stress curve continously hardening so it is better to look at the stress path curve and the points having minimum P' and drow the best line fitting them to get the strength parmateres that will be transfered to Mohr Coulomb strength parameters.
 NOw if the stress paths for these samples do not experience decrease in P' then one has no choice but to choose a specific level of strain E =15% (ASTM standard) to get the strength parameters at
Do you guys agree with me

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