tunnel liner in FLAC 2

Hello Luca

Unfortunately I have never used FLAC (except for ver. 1.0 !) and so I am not familiar with its capabilities, apart from what I 've read in the brochures. Never-the-less the problem you mention is common in practically all codes dealing with tunnelling.

I have used on such occasions gap elements available in other codes (perhaps also in FLAC ?) that can show a non-linear stress-strain behavior with modulus aproaching infinity as the width of the element tends to zero. These are like 2D shell elements that can accept initial gap, slip etc. They are usually used to model faults or spring foundation. The initial stiffness of such elements, that starts to function increasing after the initial gap has closed, may be chosen as normal K0=E/d and tangent Ks=G/d where E,G moduli of soil and d usually at 0.01m. That is if FLAC is able to accept non-linear relations and increase element stifness as soon as the gap tends to close. After this phase you can initialise the lining and change the properties of the gap elements to match the properties of the mortar.

On some occasions I have seen (and experimented) with usual 2d elements with low modulus of deformation but have run against numerical instability problems.

But my initial thought is not how to model it but the problems related to the usefulness of this modelisation. The properties involved are far from exact for such a refined approach. You will have numerical results but their correspondence with real values is open to questions. In my opinion working first with the lining in contact with the soil will provide you with upper limits as to the stresses that may be presented in the lining accepting your estimation as to the part of the stress relief that has occured before the TBM reaches the section. A second analysis with gap (or eventually soft) elements with wdth equal to the estimated gap in the border of the excavation section and boundary conditions of dr=0, will provide you with a set of displacements. Although filosophically not correct, this approach should provide you with some limits for your design.

Please, consider the above with critical view as I just want to share my thoughts when dealing with this problem, and I am sure that FEM experts should have much more to say on (or even reject) the above.

Regards
Dimitrios

Hallo Dimitrios,

I thank you very much for your exaustive answear.
To "avoid" my problem I already did what you suggested.
That means, I worked with the lining in direct contact to the soil (but not bounded to it).
The results saw realistic.

Thanks again,

Regards
Luca

Hello Luca

Just one tip that might be usefull. Bear in mind that assuming only radial/normal connection between the lining and the soil will give you higher bending moments as the lining is forced by the radial bond condition into the same deformation shape as that of the surrounding soil, than in the case when the lining participates in taking full or part of the tangential soil pressure component. Whether this actually takes place or not as well as an estimation of a percentage of the tangential component to be carried by the lining, depends on the nature of your problem and data available.

Regards
Dimitrios

Hallo Dimitrios,

you are right!
Anyway working with a TBM-Mixshield the gap will be filled with mortar during the excavation-stage. Of course the E-Modul and poissons-number of mortar and rock are different (but probably not so much), so that the lining won't take the whole 100% of loads. I think that it will take anyway a good part of load, say 80 to 90 % depending on the welll known parameters. On the other hand, in the dimensioning process I have to use a safety factor of 1.3, what shoud cover part of insicurities. In conclusion, as you say, the lining shoud take higher bending moments so that the computed results are on the safety side.

I have appreciated your Tips.
Thanks
Luca