№85-14

Numerical simulation of the stress-strain state of a concrete tunnel lining under surface blast loading using the rht model

N. Zuievska¹,   https://orcid.org/0000-0002-1716-1447

R. Semchuk¹,   https://orcid.org/0000-0001-9635-1427

D. Darmostuk¹, https://orcid.org/0009-0002-3714-9821

I. Aleksieiev¹     https://orcid.org/0009-0004-7458-9468

¹National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine

Coll.res.pap.nat.min.univ. 2026, 85:175–187

Full text (PDF)

https://doi.org/10.33271/crpnmu/85.175

ABSTRACT

Purpose. Calculation of the stress-strain state of the concrete lining of a tunnel located at a depth of 10 m in a soil mass under surface blast loading, and substantiation of a methodology for the correct interpretation of the results taking into account dynamic effects.

Methodology. The calculation is performed using the ANSYS Explicit Dynamics software package with a fully coupled Eulerian–Lagrangian formulation. The behaviour of concrete C35/45 is described by the dynamic Riedel–Hiermaier–Thoma (RHT) model, and the behaviour of the soil is described by the Drucker–Prager Piecewise model. The influence of the strain rate on the strength of concrete is taken into account through the dynamic increase factor (DIF), defined as the ratio of the dynamic strength to the static strength.

Findings. The maximum principal stress σ₁ in the concrete lining amounts to the following values, respectively: the peak level at the monitoring point – 3.82 MPa at the moment t = 43.5 ms; the spatial maximum – 3.57 MPa at the moment t = 50 ms. The maximum soil displacement at the epicentre of the explosion is 4.21 m, and at the level of the tunnel – 0.2–0.5 m. The dynamic tensile strength of concrete is f_t,dyn ≈ 6.27 MPa, and the safety margin is about 76%.

Originality. Relationships between the peak stress level in the concrete tunnel lining and the time required for the shock wave to pass through the soil mass have been established; a two-stage scheme for strength assessment has been substantiated – comparison of the calculated stresses with the static strength, and then with the dynamic strength taking into account the actual strain rate ε̇ ≈ 10² s⁻¹. An RHT-model parameter f_t/f_с = 0.171 is proposed for a homogenised model of reinforced concrete C35/45 with reinforcement ratio ρ = 0.5% using class A500C steel.

Practical value. The obtained calculation data make it possible to assess the residual service life of tunnel linings under surface blast loading without the need to switch to computationally expensive discrete modelling of the reinforcement, as well as to formulate substantiated requirements for the thickness of the soil overburden and the concrete class for protective underground structures.

Keywords: physical and mechanical properties, stability safety factor, RHT model, ANSYS Explicit Dynamics, surface explosion, tunnel lining, dynamic increase factor, reinforced concrete.

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date of first submission of the article to the publication – 04/14/2026
date of acceptance of the article for publication after review – 05/15/2026
date of publication – 06/30/2026