Hi all,
I have a couple of questions related to some parameters that are required for the soil hardening model. I would appreciate it if you can provide some insight.
1. Stress dependent stiffness parameter m
How do I actually derive it? I have seen two approaches online and their y and x axis labels are different, which make it confusing. I understand that you need double log scale. Then on the y-axis, do you have E50? Do you need to do E50/pref on y-axis? On x-axis, do you have (confining pressure) sigma'3/pref or something else? Then I know the gradient of the line is parameter m right?
2. Determining confining pressures for triaxial tests
My understanding is that pref does not have to be 100kPa but it is the default setting in PLAXIS since 100kPa is commonly used in triaxial test.
Following the above, I now have two samples, I'm planning to schedule three tests at different confining pressures for each of them. Since these samples are fairly deep so their effective overburden is expected to be >100kPa. As a result none of the confining pressures that I'm specifying will be 100kPa.
Now, since I need a reference pressure, my approach is to choose one confining pressure that is the same for both samples.
For example, confining pressures for Sample A: 250kPa, 500kPa, 1000kPa; for Sample B: 250kPa, 700kPa, 1400kPa.
In which case, I have a pref of 250kPa. Is this the correct approach?
Hi Teng,
To determine the stiffness stress dependency parameter m, at least three triaxial test curves are needed. The process to determine it is the following:
The following graph demonstrates the process:
Reference stress, pref is used to scale stiffness moduli E0,ref , Eur,ref , E50,ref to current values with respect to a current minor principal stress σ’3.
Although 100 kPa is the default pref value that people are commonly using, however, it is a user defined input value, which allows you to specify a different value based on your experimental data. Typically, it can be the confining pressure in the triaxial test that best corresponds to in situ conditions.
Since HS and HSsmall models take the stress dependency for the stiffness into account, practically, using a different value for pref will only tell the software that the reference pressure at which the stiffness values are determined is different. The equations to calculate a stiffness at a different pressure levels (σ'3) are given in Chapter 6.1 of the Material Models Manual, e.g.
Hopefully an example can make this clearer:
Let’s assume that you are performing drained triaxial compression tests for a soil by unloading and reloading your samples at cell pressures of σ’3 = 250, 500, 1000 and 1400 kPa, respectively. Depending on the expected in-situ minor principal stresses, you can select one of the above cell pressures as your reference stress. For example, you could choose 250 kPa, but it could be any of the other three values. The secant modulus, E50 and the unloading-reloading modulus Eur determined for that particular reference value, will also correspond to the reference moduli values E50,ref and Eur,ref.
Thank you, this is very helpful.
If I have a lot of samples for the same type of soil, and I want to use their data to derive a suitable parameter to be used in PLAXIS. Does it mean that when I specify the confining pressures for their triaxial tests, they have to have one confining pressure that is the same?
For example, confining pressures for Sample A: 250kPa, 500kPa, 1000kPa; for Sample B: 250kPa, 700kPa, 1400kPa. Because then I can compare the E50 for pref=250kPa and use the average or something?
Hi Teng,Not necessarily, but it helps to keep one parameter constant (in this case, the confining pressure).Sample A and Sample B should give similar results for the same confining pressure depending on the sampling process. As you said, you can calculate the average stiffness and strength parameters.