Most important output of pore pressure-deformation analyses

[slam00000]

Hello All

I have done staged construction deformation analyses of earth/tailings dams using advanced numerical modelling ( no ready FOS can be given) . I can get all kinds of output(related to hydrology ore pressures,saturation, flow velocity.. and mechanical outputs: stresses , strains, displacemnets,void ratio....
My objective is to investigate the stability of the dams during staged construction
These are the outputs that I beleived ultimately will dictate the safety of the system

1- I took some horizontal profiles and plot the settelment along them to see if there are remarkable differential movements that could cause vertical cracks

2- I took vertical profiles at each satge and plotted
a: the horizontal displacement to see if there is big differential movement that could lead to horizontal cracks
b: the operating friction angle (t/P'):where t is the operating shear stress , and p' is effective pressure) and compare it with the stregnth friction angle to check the FOS at each point along the considered profiles (my materials are almost cohesionless)

DO you recommend me to plot any other outputs that are practically important to evaluate the response of the dam during construction.. and why..?

 

[BigH]

slam00000:

First of all, before we go any further, please provide information as to the stratigraphy encountered beneath your dam/embankment. Is the dam being construted on soft clay? Firm clay? sand and gravel? glacial till? rock? Please provide how many strata are encountered and how thick. Please provide any geodata that you have (undrained shear strength, CIU tests with pwp measurements, consolidation test results, permeability of strata. Please provide height of dam; anticipated design side slopes? Please provide make up of dam - single material, clay core? with filters, etc. In other words, give some details so that members of the forum can provide you some useful guidance.

 

[dgillette]

If you haven't already, get ahold of Chuck Ladd's Terzaghi lecture, "Stability Evaluation During Staged Construction," published in the ASCE JGE in the August 1991 issue. Also, S.G. Vick's discussion and Ladd's closure in the August(?) 1992 issue. They both have some useful discussion of tailings dams with fine-grained material, where undrained shear strength was the critical issue, as I suspect it is for your situation.

DRG

 

[slam00000]

I have attached an interesting page showing the system with some results. Any fedback is hugely appreciated
BigH My question is very general for just a parameteric study on my own that doesnot represent an actual case
The question again what is useful to get as an output that could indicate failure

Any way the hypothetical dam (40 m height) is assumed to be founded on very stiff clay (20 m) of very low permeability that is underlain by bedrock.(refer to the figure)
The dam has three zones (1 dykes : dense sand
dgillette
: thanks I red the materials twice
Please see attachment and comments are helpful

 

[dgillette]

Your dam resembles the copper tlgs dam in Ladd's paper, but yours doesn't have a design flaw that one does. There, they filled slimes or maybe whole tailings almost up to the crest of the starter dam before they started building a shell of sand (which as I recall was separated from the whole tailings by cyclone). Therefore, the shell is very thin just above the starter dam, which made a pretty significant difference in the stability. That dam has a sister at the same mine with a thick shell for the full height, more like yours, and stability was never an issue for it.

By "operating friction angle" you mean the actual shear stress over actual p' or Sigma'v? If so, in the US that would generally be called "mobilized shear strength ratio." Arctangent of that would be "mobilized friction angle." Just want to be sure I understand the terms you are using. You're using undrained strengths for the slimes, right? What do your limit-equilibrium analyses show for FS?

Do your computed pore pressures include the excess pressure from undrained shearing of the contractive materials? At first I thought maybe they do because of that sharp point of red that sticks out under the shell, but it doesn't reach all the way to where the sheared slimes are, so I concluded that there are only hydrostatic and the excess from underconsolidation - correct? Does that red point correspond to a looser, more compressible layer in the model, or just a younger layer with similar properties?

By the way, for anyone who is hunting through the JGE for Ladd's paper and not finding it, it's actually in APRIL 1991, not August 1991. Please pardon the goof.

 

[slam00000]

Hello dgillette
Yes you are right the friction angle
So the FOS at a point level for my almost non-cohesive materials is the Shear friction angle/ mobilized friction angle.
-Please note that this FOS considers the increase in the operating friction angle (strength gain due to the actual 2D consolidation taking place during staged construction) unlike Other analyses such as Ladd's (1991) who considers the gain in strength due to the 1D consolidation.
- I am considering the undrained friction angle/residual of the slimes (most left hand materials which are clay-like materials: no liquefaction behavior) and the friction angle at liquefaction for the loose sandy beach, and the drained peak friction angle of the Shell dam(dense sand)
-Yes my pore pressure includes excess pore pressure it decreases when you go toward the higher permeable materials and also by moving toward the drainage layer (my design section tries to minimize it under the upstream shell of the dykes.
If I understood your question right: The red zone is highly under-consolidated (also it is relatively very far from drainage and has the highest excess pore water)
I have not done LE yet but I think these analyses are much more accurate. Do you recommend me to extract other outputs that could be beneficial to judge the response or stability of the system..?
Thanks

 

[dgillette]

OK, the u values in the plot include the effect of underconsolidation, but NOT the effect of excess pore pressure due to undrained shearing.

Tell me again, in different words please, the definition of "operating friction angle." Apparently I did not understand it, because what I thought I understood doesn't fit with "the increase in the operating friction angle (strength gain due to the actual 2D consolidation taking place during staged construction)" Wouldn't it be the UNDRAINED STRENGTH that is increasing due to the consolidation, rather than the friction angle (whether mobilized friction angle, effective stress friction angle, or the so-called 'consolidated-undrained friction angle,' called Phi-cu). If you maintain constant shear stress and increase the effective stress by consolidation, the mobilized friction angle, i.e., arctan(tau/sigma'), would decrease. The others would stay essentially the same.

Another thing I did not understand is whether your shearing resistance accounts for the excess pore pressure due to undrained shearing, and not just due to underconsolidation. If not, I don't think you can get a realistic answer from this or any other analytical method.

 

[slam00000]

This pore pressure is due to:
Gravity and loading (the load is carried by both the soil grains and the pore pressure: partial drained loading case).

(strength gain due to the actual 2D consolidation taking place during staged construction)"
I meant : it accounts for the increase in the confining stress(P') due to the 2D consolidation. As you are assuming the material governed by Mohr-Coluomb then with increasing P'(updated) shear strength will increase. You check the FOS at a specific point as follows: if the updated mobilized friction angle q(updated)/p'(updated)> phi(failure) then the point has failed. If you want to see if this point is shearing under drained or undrained so that you can compare with the appropriate Phi(failure), then plot the effective stress and the pore pressure with time at this point and see:
if the rate of increase of pore pressure is much higher the that of the effective confining pressure, then your point will shear under undrained situation and it is better to compare your operating friction angle with Phi (Failure-undrained).
If the rate of increase of effective confining stress is much higher than that of the rate of increase of pore water pressure then the point is being sheared under drained loading and compare your mobilized friction angle with
Phi (Failure-drained).
If I understood you :"The excess pore pressure due to undrained shearing": that is the pore pressure generated after the stress path (p', q) hits the failure line and therefore it is post failure response. I am doing design analyses and hence looking at the behavior prior to failure or at the impedance of failure and not at the post failure behavior.
Plesae defend your point of view as this discussion is very important

 

[dgillette]

Increased u can occur in loose granular material or NC fine-grained material long before the effective-stress path hits the failure line (if by that you mean the phi'-c' line). It's like a load-controlled [not displacement-controlled: an important difference] triax or DSS test. In theory, you can load it slow enough that it reaches full static consolidation (anisotropic) with no excess pore pressure remaining. However, if you load too fast, the shear strain causes the material to contract and generate excess pore pressure. Once that happens, it may not be possible for the system to "recover," in which case the excess pore pressure can cause strain softening which sheds load onto neighboring elements, which causes them to strain, and so on. The consolidation pore pressures don't tell the whole story.

Extremely slow load-controlled shearing is hard enough to do in a lab, and you probably can't expect to do it at all in a working mine without frequent shutdowns. Somewhere I saw a paper (from Japan?) in which the researchers did semi-drained tests with very slow load-controlled shearing. Basically, they tried to test very slowly, with the drainage ports open. In displacement-controlled tests, which are more familiar, there is no excess u. However, in the load-controlled tests, at the beginning there was full dissipation of excess u, giving resistance like a drained test, but then they hit a point where the material suddenly began to contract, strain-soften, etc., and basically collapsed because the excess u couldn't dissipate fast enough to maintain the shearing resistance. Clearly, your hypothetical tailings dam is not being hypothetically loaded slowly enough, because your yellow and red zones extend under the shell.

Regardless of the drained FS, if the undrained FS is below 1.0, the dam is metastable, and vulnerable to instability triggered by slight disturbance from foundation movements (similar to Ft. Peck Dam), minor earthquake, erosion by storm runoff or careless direction of spigots delivering slimes, etc. If this were a real tailings dam, the regulatory agency would almost certainly require an undrained stability analysis. Even if there was no regulatory agency, I would not think of presenting a design without checking undrained stability, whether by simple SHANSEP method or with FEM analysis that accounts for u-excess from shearing, explicitly modeled or with input from lab shear testing. This is why Ladd's undrained approach is so important for tailings dams, regardless of whether the consol analysis is 1D or 2D.

 

[slam00000]

Let us be clear about pore pressure generation:

"However, if you load too fast, the shear strain causes the material to contract and generate excess pore pressure"
The shear strain doesn’t cause the material to contract. It just leads to distortion. It is volumetric strain which causes the material to contract.(plesae send me a reference about your statement if you have)
As you know the stress affecting a point can be divided into a deviatoric shear stress part (q) and consolidation stress part (p'). In frictional materials such as tailings (q) will cause both distortion and volume change at a point (researchers call this non associative behavior: coupling behavior: Note that purely cohesive soils under undrained will not show this behavior).
1-Do you mean by shear pore pressure is that excess pore water pressure that caused by the contraction caused by q
or
2- In loose sand-like materials (low plasticity index) when you load the sample under undrained condition, at a specific stage much earlier than the classic failure line , when the stress path (p',q) hits what is called instability line (Sladen et.al,1985) ,the sample will experience dramatic pore pressure increase accompanied by large strain
This is the liquefaction pore pressure. Sample now may recover (temporary liquefaction) or may continue this behavior until hitting the classic Failure line (point is finished). Please note that my strength friction angle is considered at the instability line and not at the failure line accounting for the scenario that the loose materials under the Embankment shell will mostly fail under undrained case. So in fact I am considering the material will fail at the instability line this is much more realistic than the undrained analyses considering the undrianed friction angle that is too conservative and hence doesn’t appreciate the economic factor [note that Phi(instability)=50 Phi(effective at failure)>>> Phi(total at failure)]. See the attached figure please.
Which pore pressure are you talking about 1 or 2 above
In Case 2: I am not considering the pore pressure increase after hitting the instability line (liquefaction generated pore pressure): post failure response.
Answering your statement "regardless of whether the consol analysis is 1D or 2D":
a-If you consider only 1d consolidation will get mistaken P' during the staged construction and that will wrongly change the case even toward the conservative side
b- total friction angle at classic failure implies is not realistic
c- steady state friction angle (post liquefaction friction angle in case of sands in the beach zone) or (residual friction angle in case of hugely soft plastic slimes existing in pond) both represent post failure response: meaning that you assume that the points will 100% failure under undrained and you are taking the strength post the failure
.
-Remember please that flattening the slope unnecessarily by a small fraction could result in loss of millions of $ in huge systems as tailings facilities. a, b, and c above would contribute to this loss.

Waiting you comments

 

[slam00000]

Sorry: typing mistake above :
[note that Phi(instability)=50% Phi(effective at failure)>>> Phi(total at failure)].

 

[dgillette]

Slam00000:

You wrote "The shear strain doesn’t cause the material to contract. It just leads to distortion. It is volumetric strain which causes the material to contract."

I think you are just playing word games here. Strictly speaking, it is the shear strain that causes the distortion of the soil structure that softens the structure, allowing the normal stress to cause the contraction in drained shearing, or shedding of the confining pressure onto the pore water causing increased pore-water pressure, in undrained shearing. So, yes, it is true that the shear strain only causes the distortion, but the end result is either contraction or excess pore pressure resulting from the contractive tendency of the disrupted soil structure. One can quite reasonably speak of excess u caused by shear strain in a contractive material, or by changes in q – the two go together.

The answer to the question is 'either one,' and I don't really understand why you ask it. The need to account for excess pore pressure from shear strain (or if you prefer, from changes in q) exists in loose or low-OCR soils whether the material is plastic or not, whether there is an instability line or not. In either plastic or nonplastic materials, there can be pore pressure increase due to change in q long before the effective stress path hits the effective-stress Mohr-Coulomb strength envelope, which is apparently what you mean when you use the term 'failure line.' You see that frequently in tx and DSS tests on low-OCR clays and silts, when the effective stress path starts to veer off to the left before q even gets very large. The main difference is that plastic materials generally do not display an instability line like loose sands sometimes do. From your previous descriptions, I could not tell whether you were accounting for the excess pore pressure that results from changing q (or from shear strain), and whether you were applying the pore-pressure conditions from consolidation analysis with the EFFECTIVE-STRESS strength envelope, rather than to an UNDRAINED strength envelope. (The latter is the SHANSEP way; the former would be acceptable if the material is not contractive.)

It is irrelevant to the shear-strength principles whether you use 1d or 2d consolidation analysis. The only difference is how quickly the excess u (that part resulting from the change in p) dissipates. For Ladd's tailings dam (low PI in slimes), they used a combination of 1d large-strain consolidation analysis (with parameters of the slimes adjusted slightly to help match field data in the pond, away from the shell) and piezometers under the shell to estimate the pressure contours shown – data beat theory! (These were used to determine the effective-stress conditions at the base of each slice to apply with the undrained strength envelope for the stability analysis).

A tailings dam has to be "robust," in the sense of being able to withstand small disturbances that could push the material to a collapse state even if just locally, such as minor earthquake, erosion by storm runoff or misdirected spigots, excavation of a road into the shell, changes in raise rate, etc. Flattening slopes is much less expensive than cleaning up after a failure. (Even if the collapse state occurs only locally, the shear load can be "shed" onto other areas, which then reach collapse state, which then shed their load...) For this reason, it is important to show that the structure is at least marginally stable with strengths at higher strains (post-peak, steady state, or whatever), unless you have a very generous factor of safety with respect to the undrained peak strength (so that disturbances cannot push the material past the peak into strain softening, and possibly to the instability state for materials that have one). I heard Steve Poulos make this point some years ago at a conference on tailings and hydraulic fills, and I agree with him, in principle if not in all the specifics of determining the strength. It is not at all unreasonable for a regulatory agency to require you to show FS slightly greater than 1 assuming steady-state strengths for materials with instability lines. (Since the strain that would constitute “failure” in a tailings dam is quite large [not just 1 or 2 percent], one may be able to take advantage of phase transformation and strength recovery after instability. Also, there may be some advantage for the undrained strength from anisotropic consolidation – see Duncan, Wright, and Wong’s analysis for rapid-drawdown stability in the HB Seed memorial volume for explanation.)

You may now consider me to be "non associative." I’ve said about all I’m going to about this.

 

[slam00000]

Hello dgillette

See.. when you are doing 1D consolidation analysis, the excess pore pressure resulted will not include any shear stress-induced pore pressure (coupling herein is only between the pore pressure and the effective confining stress component). However, when you perform 2D consolidation analyses (or in a research language: coupled analysis based on Biot's theory, the shear-induced pore pressure is accounted for automatically. 2D consolidation analysis implies a full coupling between the stress field pressure (including both shear component q and effective confining stress component p') and pore water pressure. More clearly, any influence of q on the pore pressure generation will be captured by the simultaneous coupled equations representing the porous soil medium.(I have a simplified version of these equations [originally derived from Biot's formulations] but they are still a bit scary for the geotechnical practitioners to see). This is regardless of the material behavior: elastic, plastic. and so on. But the more realistic your considered material behavior considered in this equation is , the more accurate your resulted effective stress field is and thus the more accurate your predicted pore pressure will be.
-However, for the liquefaction-induced pore pressure (post instability line behavior), your material behavior (realistic effective stress-strain curve observed in liquefaction: dramatic drop in the shear strain accompanied with large strain [which my model cannot produce]) is very critical for producing the stress path (the one I have previously attached you). I want to say that the correctness of the stress path is driven by the material (soil solid grains) behavior and not the other way around. It is shown that liquefaction can happen under a dry condition. The water during liquefaction process is merely a medium ensuring a vanished volume change.
So I am stressing on the significance of performing 2D coupled consolidation analysis not only for computing accurate p’(because in reality [specially at the slime-beach interface] the consolidation is hugely 2D) but also for prediction of more accurate pore water pressure field.
-During my staged construction analysis (that embodies both consolidation and stability) I am considering that the system, which is in reality under a partial drainage case, could be exposed to any trigger that can lead to developing an undraind case: the point will collapse immediately when the stress path at this point touches the instability line and thus my analysis considered the strength parameters at the instability line.
-I think this is more logical considering the shearing strength at the instability line than considering the total strength parameters (used in Limit equilibrium analyses) that considers that there is no dissipation of pore pressure at all during staged construction.
-Any way, separately, at different profiles and at the end of each stage, I am going to plot the mobilized friction angle q/p’ along the undrained strength ratio of the materials (cu/p’) which is smaller than the strength ratio at the instability line (liquefaction strength ratio) . If q/p’> cu/p’ at a point, you have failure what about that..?

Hope this discussion is useful. Please defend your points or suggest some points regarding this matter (if any)

 

[dgillette]

"2D consolidation analysis implies a full coupling between the stress field pressure (including both shear component q and effective confining stress component p') and pore water pressure."

Now I understand your point. This is the first I've seen a fully coupled consol analysis, and it is also the first time in your communication that coupling was mentioned. Hence, I assumed that the 2D consolidation analysis was not coupled to shear strain. I have seen 2D stability analysis before, but it considered only 2D dissipation of excess PWP from changes in p' or sigma-v'. Had you said that earlier, it would have saved a lot of effort on both of our parts.

As I said before, I need to sign off from this communication, as it is taking too much of my time. There are several other points I would like to discuss, but this sort of discussion is only a hobby for me, not my job, and I have billable work to get back to.

Best regards,
DRG

 

[slam00000]

Hello DRG
I know that this discussion is terminated. You seem to have good insight about tailings dams slopes.
I just want to take your opinion about a phreatic surface issue in these systems this matter:
Vick (1990) stated that the permeability should decrease in the direction toward the embankment dykes.. That is fine.. also he added that it is the relative permeabilities of the tailings in terms of each other that dictate the phreatic surface level rather than the absolute permeabilities.

consider that you have two systems identical in everything but with one difference as follows
1- First system is with embankment dyke of permeability
KD = 100 and a talings beach with very low permeability Kb= 1
2- The second system is with embankment dyke of permeability KD = 100 and a talings beach with permeability Kb= 50
Does this mean that the first system will have lower phreatic surface..?
Please comment about this ..
Thanks

 

[dgillette]

Just to be sure we're talking the same language, by "dike" you mean the coarse material that forms the shell, as well as the starter dike, right? By "beach" do you mean a zone of middle gradation that forms between the finer slimes and the shell by separation of hydraulically placed tailings (whether naturally or by cycloning)? I don't have the 1990 edition of Vick's book, but in the 1983 version it would look like Fig. 7.1, "Effect of internal zoning on phreatic surface." Or are you considering beach and slimes to be the same material.

If I understand the question properly, yes, it should cause a lower phreatic line if the dike is more pervious, although there are other things that could affect it. If there are three zones (dike, beach, slimes), and K-slime is << K-beach, there may not be much effect from varying K-Beach/K-Dike.

Do I understand the question correctly? ?

DRG

 

[slam00000]

Yes you understood it. My first attachment above in this thread shows indeed that I have three zones (plesae visit it again)
1-Dykes forming the shell
2-Beach zone
3-Slime zone
My second system (whose K-beach is low) shows lower phreatic surface. Do you think that is because in my model K-slime is << K-beach ( by 1 orders[ten times])

By the way please explain to me why
"If there are three zones (dike, beach, slimes), and K-slime is << K-beach, there may not be much effect from varying K-Beach/K-Dike"
Thanks for help

 

[dgillette]

If K-Slime << K-Beach, practically all of the head loss occurs in the slimes, and the phreatic line will be very low in the beach already, so it can't be too much lower in the dike even if the dike is much more pervious. Another way for me to say this is that the quantity of seepage exiting the slimes into the beach is quite small with respect to the permeability of the beach, and it only requires a small depth of flow to continue through the beach. Roughly speaking, Q=K i a, and if you increase K, the area a decreases in response - hence, the much lower phreatic line in the beach than in the slimes. If K-Dike is 10 times K-Beach, then a is smaller by a factor of 10 in the dike, but it's already quite low, so it makes no difference for stability analysis. Either way, the beach and dike are mostly unsaturated.

 

[slam00000]

PLease see the attachment. Does it make sense to you.. any comment..?

 

[dgillette]

Interesting. My first thought was that it can't be like that, and there must be a problem with boundary conditions. Then, I saw that there is a big difference in the progress of consolidation when the slimes are changed from 1e-8 to 1e-7 (cm/sec, right?). Qualitatively, this makes sense. K-Dike is practically infinite.

Do consider that Kv-beach may be << Kh-beach because of mode of deposition causing layering. I expect this would tend to reduce the benefit of the increase in the K values.