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Dear Sirs,
I am looking at the modelling of the segmental lining in Plaxis 2D. The dilemma I am facing is that should I use the reduced second moment of inertia (I effective) considering the number of segments (as proposed by Duddeck and Erdmann) or full stiffness without considering the joints.
Also, whilst considering reduced stiffness (with I effective), the plate thickness (d) also reduces in Plaxis plate properties. How this should be accommodated during the interpretation of results?
Many thanks.
Nadeem
Hi there.
There are multiple options. As you said, you can use Muir-Wood's approach to reduce the thickness to account the joints or you can model joints in Plaxis explicitly using connections.
For first option, as given in Reference Manual, 5.7.4, deq=sqrt(12EI/EA), so you should calculate the new moment of inertia using the Muir-Wood's equation, later on, you can calculate the equivalent thickness and use that thickness to calculate EI and EA.
Second option is connections to model joints. If you use free connections, the resulting structural forces will not correct and similar to first approach. You should use something like Janssen's approach to calculate connection rigidity. For example check "Kunst - Modelling construction phases of bored tunnels with respect to internallining forces", Author explains these in a detailed manner.
Lastly, segmantal tunnel linings are tricky. While modelling seems easy, there are many important points. Before even going into modelling, there are a lot to read.
The question still stands "If I am using parameters as such which gives a reduced deq, what impact it will have on the results". Should I multiply the output by 2 as the thickness used in the model was half?
What impact this will have if the lining is modelled as a solid element?
Thanks for your assistance.
Regards,
Dear Nadeem,
No, you should use the results as it is. In my experience, it is never the half of the original thickness, I can say something like 70-90%.
If you use your original thicknesses, your structural forces would be much higher than the case with joints. You can compare the solid case with joints modelled using Janssen theory. I have made this comparison and Wood's assumption is close enough to Janssens joints. If you model joints as free connections, moments would be much lower.
Short story: Reduce the thickness and use the forces as it is for practical purposes.
Many thanks, Berk
We got two types of linning, one with 6 segments and another with 8 segments. For 6 segments, the calculated reduced thickness is 67% which is close enough to 70% as you stated. However, for 8 segments, it reduces down to 50%.
I am wondering if you could share a paper or methodology on how you calculate the reduction due to joints? I have attached my calculation in the original post, above.
You may wish to drop me an email on mnkh@cowi.com.
Many thanks
The reduction factor is literally everywhere. I_red=I_joint+I_solid*(4/n)^2
As I said before, there are lot to read.