Dear all,
When conducting plaxis analysis the elastic modulus of soils is used as an input in Mohr Coulomb and Hardning Soil models, E´and E50 in drained conditions, respectively. The pressuremeter tests conducted in the fields gives us the Menard modulus of deformatio. Can these values be used as E´ and E50?
The pressuremeter test is a rapid test and therefore there is no possibility of drainage. Consequently, the pressuremeter modulus is used for undrained conditions. There are correlations in the literature which relate E and E'.
Dear Ahmed Hussein Olat
E50 is Secant modulus, it is modulus of elasticity at 50% strength. E50 can be produced from triaxial test at drained as well as undrained conditions.
E' or E0 is initial tangent modulus.
Elastic modulus of soil has various types and use of it depend upon structure and loading type.
I would suggest that the strain at which is pressuremeter modulus is determined is estimated using the cylindrical cavity expansion strain dR/R. Accordingly, the modulus at 50% of the strength, E50, can be determined. Please refer to this article:
Article Assessment of Undrained Nonlinear Stiffness of Clays using R...
Dear Ahmed Hussein Olat
The pressuremeter modulus has been related empirically to the elastic modulus of the soil as EM/E = α, in which α is termed by Menard as the rheological coefficient and has a value between 0 and 1.
For more details, please refer directly to :
Article A Study of the Pressuremeter Modulus and Its Comparison to t...
http://www.soil-rock.ir/pm/wp-content/uploads/2017/05/Using-pressuremeter-to-obtain-parameters-to-elastic-plastic-models-for-sands.pdf
Thank you Youssouf Chalabi Pankajkumar Yadav Sayed Mohamed Ahmed Soufyane Aissaoui for your replies.
In the case of HS the module is based on a triaxial test analysis so using a Menard test parameter is a priori incorrect. The selection of the parameters also depends on the problem being analyzed, especially in the case of MC model. In your case, and if you do not have soil parameters from tests more associated to MC and HS models, you would try to make some kind of calibration and compare the different available parameters from tests and literature.
E50 is very very imprecise. Bare that in mind. The "line" is not "real", it's just a parameter, used to distribute loads within an elastic mesh. Then the elastic mesh gets deformed further by plastic components... even plastic simulations are just an elastic mesh, elastic springs, pulled and pushed towards some parametric curve.
The methods using E50 are merely a "compromise". A campromise, used to approximate ultimate strength, failure mechanism, etc... So, try using 10x bigger and 10x smaller E50, see how that changes your peak strength estimates in simulation. From that, you can draw conclusions about importance of getting E50 correctly, how "sensitive" the solution is to E50 values. Then you decide how much time and energy you are willing to waste in this trivial pursuit of "perfect E50" - which might as well not exist at all.
It can even be wrong to take E50 from lab tests. Sand can have infinite different stiffness curves at the same density. F.x.: liquefying specimen have near constant density (undrained), but every loading cycle produces a different stiffness hysteresis loop. There is no "unique" stiffness path for a given density. The best we can aim for is getting the "ultimate strength" right.
The stiffness part depends on disturbed soil states which are not accounted in any existing soil models. In tests, you can generate denser sand with lower stiffness, looser sand with higher stiffness - for both drained and undrained tests... As soon as you stop closing your eyes to the test results, as soon as you take care to look at anomalies - you start noticing how shallow, imprecise, unreliable, and outright wrong our current interpretation of soil stiffness is.
Peak strength estimates, though... they ain't too bad. The stiffness path doesn't have to be perfect, to get a diecent peak strength estimate. Just "test a range" of values, see how much influence it is having...
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