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For the structural design using the bedding modulus method of the linings of tunnels to be driven by shield machines in granular soil, the surrounding ground is normally discretised with radially arranged extension springs, the stiffness of which is derived from the load-displacement behaviour of the surrounding ground (stiffness modulus E s ). The precondition for this is that the properties of the mortar used to fill the annular gap at least correspond to those of the surrounding soil. If this is not the case -for example, if the grout is softer than a densely bedded non-cohesive soilcorresponding negative effects on the deformation of the tunnel lining are to be expected. This can even lead to damage to the segments in the form of spalling or leaks. In order to be able to quantify such effects and consider them in future structural calculations, the results of a parameter study using the finite-element method (FEM) for a tunnel in water-saturated granular soil are presented and a simply applied, modified bedding approach is proposed on this basis.

The increasing use of polymer solutions as support fluids in pile drilling, diaphragm walling or tunnelling applications demands a more detailed discussion of their penetration behaviour and prediction thereof. In this context, the capillary bundle approach can be a useful tool. However, while it is widely discussed in the oil and gas application, the subject is currently addressed only scarcely with regard to support fluid penetration targeting stagnation, where small flow velocities and non-cohesive soil environments are of relevance. In these boundary conditions, the applicability of capillary bundle approaches is not yet sufficiently confirmed and substantiated. The current paper thus reviews current capillary bundle models based on Hagen–Poiseuille in combination with a power-law rheological model and discusses their applicability with respect to support fluid application in the context of experimental soil permeation tests for small gradients ($$i\le 10$$ i ≤ 10 ). Two granular materials of similar grain size, but different angularity (glass beads and sand), and four polymer solutions varying in polymer chain length and concentration are investigated, and the impact of model assumptions and bulk material input variables is systematically discussed. The experimental results show that the theoretical models are generally able to predict the filter velocity qualitatively for values above $${\bar{v}}=5\times 10^{-7}$$ v ¯ = 5 × 10 - 7 m/s and also quantitatively, when an empirical shift factor $$\alpha ^*$$ α ∗ is introduced and water permeability values are determined experimentally. With respect to the influence of soil parameters, it was found that the soil particle roughness decreases the flow velocity of the polymer solution despite similar hydraulic conductivity in water. Polymer chain length and concentration were observed to control the degree of possible dilution ($$\alpha ^*<1$$ α ∗ < 1 ) in the porous system compared to bulk rheological characteristics. It can therefore be concluded that capillary bundle models can indeed be applied in the targeted fields even though they are unable to predict a complete stagnation for $$i>0$$ i > 0 . However, rather than specific model assumptions for tortuosity, taking into account the specific soil-polymer interaction has shown to be of primary importance to ensure no under- or over-prediction of penetration velocities solely based on bulk rheology.

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