Change in definition of k* in Soft Soil Creep model

Dear Matthew,

The factor 2 has been a typo for several years that was now corrected. If you would compare equations 258 and 260 in the latest version of the manual  (creep equation expressed in a,b,c vs  lambda*, kappa* and mu*) you would see that k* = a. Though I just noticed that in the text it still says k*=2a, so the table was corrected but the text not yet.

With kind regards,

Dennis Waterman

Dear Matthew,

The factor 2 has been a typo for several years that was now corrected. If you would compare equations 258 and 260 in the latest version of the manual  (creep equation expressed in a,b,c vs  lambda*, kappa* and mu*) you would see that k* = a. Though I just noticed that in the text it still says k*=2a, so the table was corrected but the text not yet.

With kind regards,

Dennis Waterman

Dear Mr. Dennis Waterman,

Yes, misconceptions about the definition of κ have taken on a very large scale all over the world. Let's deal with this issue together. I ask you to pay attention to the article by the authors of the SSC model P.A. Vermeer & H.P. Neher «A soft soil model that accounts for creep». In this article, the formula (10) is presented to describe the one-dimensional creep law,

according to which it is obvious that the parameter A is defined as the tangent of the reloading line inclination angle in the coordinates lnσ-ε.

When switching from a one-dimensional law to a three-dimensional one, the parameter κ* is introduced, which according to formula (22) is equal to А*3(1-νur)/(1+νur).

Where the Poisson's ratio vur has values of approximately 0.2. With this value of 0.2, the multiplier 3(1- vur)/(1+ vur) takes the value 2. Therefore, κ* is approximately equal to 2A. This is also presented in the description of the formula (30).

If you believe the article by the authors of this model, this is not an error, and κ* is indeed equal to 2A.

Could you please explain your position?

With great respect,

Julia

Dear Julia,

I fully agree that kappa* = 2A .... however, that is not the question here. In the Material Models Manual the Soft Soil Creep model is not defined in the parameters A, B and C as in the article. A few years ago it was rewritten using the parameters a, b and c ... and kappa* = 2A = a.  This is where the mistake started, since A, B and  C are not the same parameters as a, b and c when the manual was modified the "2" was by mistake left in.  
Please check equations 258 and 260 of the PLAXS V21 Material Models Manual and you'll see the definition in a, b and c and that kappa* must be a, not 2*a.

With kind regards,

Dennis Waterman

I believe there may be further inconsistencies in the text and equations which could add to this confusion. For example Eqn 259 and the text at in Section 11.6 in the v22 Material Models manual, repeated below for clarity.

Dear Matthew,

I agree that it's not clear, so we will have to work on that. 
But reading the text carefully it says that kappa*=a is valid for normally consolidated state, but for overconsolidated state it's not. The problem with moving from 1D to 3D is that there is no linear relation between kappa* and a.  So for slightly overconsolidated state kappa* » a still holds, but for heavily overconsolidated clay with K0=1 or higher kappa* would be more in the order of 2a or even larger. Since we can enter only 1 value for the entire calculation, usually we choose what is the most suitable. Since the SSC model is best used for loading or normally consoldiated clay kappa*=a is a good choice. If we would only unload (for instance in an excavation problem) we could choose the relation kappa* vs a based on the average K0 value. But to have an average K0=1 it requires to unload from normally consolidated state K0=K0nc down to the overconsolidated state K0=1/K0nc ... which is a lot of unloading, more than often is done.
Unless you're working with overconsolidated clay from the beginning, but then the question is whether one would use the SSC model since creep deformation is very small for overconsolidated clays and can often be neglected.

But all these considerations should be at least briefly mentioned in the manual.....which right now is not the case.

With kind regards,

Dennis Waterman

Dear Dennis Waterman,

I agree with you that the parameters for one-dimensional creep in the Plaxis manual are interpreted somewhat differently, but this applies only to parameter B (b), which is responsible for the slope of the normal compaction line.
I ask you to pay more attention to the article by P.A. Vermeer & H.P. Neher "A soft soil model that accounts for creep".
Comparing the one-dimensional creep law presented in the article:

and presented in the PLAXIS versions (I have three of them v20, v21 and v22. I will be focusing on the latest version of v22)

Parameter A (from the article) fully corresponds to the parameter a (from the manual) and characterizes the slope of the reloading line. Obviously, A = a.
But B (from the article) is not equal to b (from the manual).
This can be seen in the graphical representation, comparing the drawings
from the article:

and from the user manual:

In the article, the primary loading line angle tangent is quite rightly equal to A+B. In the manual, apparently, to simplify perception, the parameter b is adopted as the tangent of the angle, i.e. B = b-a. And further, where the parameter B appears in the article, the expression b-a is in the manual-and until the parameters of the three-dimensional model are introduced.
I ask you to compare the formulas from the article (21, 22, 23)

And the corresponding formulas of the manual 258, 259, 260 (version V22)

Further, paragraph 6 of the article describes the transition from a one-dimensional law to a three-dimensional one

I think that here we are not talking about the characteristics of the soil (OCR), but about its work under load. Whatever the over-compacted soil is, there is a pressure value, above which it will work as a normally compacted soil and its behavior will be described by the normal compaction line, and before this pressure is reached, by the reloading line.
As I understand it here (in the description before formula 29), we are talking about a normal compaction line, i.e. if the kappa parameter described the process of normal compaction, it would be fair to assume that k* = a, since the change in stresses (both vertical and average) during the transition from 1-D to 3-D occurs the same for a normally compacted state (i.e. when the behavior of the soil is described by a normal compaction line). But the parameter k* describes the processes of reloading, i.e. in fact, the over-compacted state, and in the process of unloading and reloading, the stress changes (vertical and average) in the 1D model and in the 3-D model do not occur in the same way, hence the conclusion of this formula:

And if νur=0,2 parameter k* will be equal ≈ 2А, and since А is а, then k* is approximately equal to 2а.
Moreover, please pay attention to the relationship with the alternative parameters Сс, Сs (or Cr), Cα, which are determined by the dependence of the porosity coefficient on the decimal logarithm of stresses:
According to user manual v22

Which corresponds to the formulas 32 from the article

Where 1/(2.3 (1+e)) is a transition to other coordinates.
The formula describing the relationship between k* and Cs also has this multiplier of 2.
It is also easy to check in the PLAXIS program itself. When entering parameters k*, λ*, μ*, please pay attention to the values of alternative parameters Сс, Сs, Cα, which are recalculated automatically. You will see that

the condition is met.
From all of the above it follows that А=а, а k*=2А=2а.

With kind regards,

Julia