Segmental tunnel lining

Question

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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

Berk Demir · Answer

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 internal lining 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.

Stefanos Papavasileiou · Answer

Dear Nadeem, 
 As mentioned very well by Berk Demir, there are different approaches you can use for this. 
 Unfortunately, this falls on the modeller's plate to test, verify and design, in order to achieve a behaviour as close to reality. 
 I would suggest to run a few simple models, e.g. one soil layer, simple tunnel cross-section, using the different approaches and determine which one gives a more realistic response. Note that typically a conservative solution is usually adopted by the designers, however, again this requires engineering judgement and using any experience from similar projects.

Segmental tunnel lining

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