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Numerical modelling of centrifuge tests on tunnel–soil systems

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Abstract

The number of tunnels in seismic regions has grown significantly in recent decades. It has usually been assumed that tunnels perform better than surface structures during seismic events. However, recent cases have shown that tunnels can be significantly damaged by seismic events. Thus, an evaluation of their response to earthquakes has become increasingly necessary. This paper presents a FEM blind prediction of centrifuge tests on a reduced scale tunnel. The main objective of the paper is to evaluate the numerical model that reproduces the response recorded in the centrifuge. The centrifuge tests involved a tunnel in dry sand. The numerical simulation was performed on the physical-scale model of the transverse direction of the tunnel, which is of prime importance, as it can show large stress–strain levels in the tunnel lining. The tunnel behaviour was assumed to be visco-linear-elastic, while the soil behaviour was assumed to be visco-elastic-perfectly plastic. The soil model parameters were calibrated on the basis of laboratory tests performed on the sand used for the test. The comparison between the experimental and numerical results is presented in terms of acceleration in the time and frequency domains. The experimental and numerical settlements of the sand surface and displacements of the sand-tunnel system, as well as the bending moments and hoop forces acting in the tunnel are also compared. Increments of the bending moments and hoop forces are also evaluated using the closed-form solution proposed by Wang (Seismic design of tunnels: a simple state-of-the-art design approach. Parson Brinckerhoff, New York, 1993) and Penzien (Earthq Eng Struct Dyn 29:683–691, 2000). A very good agreement between the experimental and numerical results is achieved in terms of horizontal acceleration time-histories and their Fourier spectra, as well as in terms of vertical displacements of the sand surface. Moderate differences exist between the experimental and numerical bending moments and hoop forces; experimental, numerical and analytical increments of the bending moments and hoop forces are in a quite good agreement with each other.

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Abbreviations

\(a\) :

Acceleration

\(a_{max}\) :

Maximum value of acceleration

\(c\) :

Cohesion

\(C\) :

Cover of the tunnel

[C]:

Damping matrix

\(D\) :

Damping ratio

\(D_{r}\) :

Relative density

\(d\) :

Diameter of the tunnel

\(d_{10}\) :

Diameter of the soil particles for which 10 % of the particles are finer

\(d_{50}\) :

Diameter of the soil particles for which 50 % of the particles are finer

\(d_{60}\) :

Diameter of the soil particles for which 60 % of the particles are finer

\(e_{max}\) :

Maximum void ratio

\(e_{min}\) :

Minimum void ratio

\(E\) :

Elastic modulus

\(f\) :

Frequency

\(f_{max}\) :

Maximum input frequency

\(f_{y}\) :

Yield function

\(f_{yk}\) :

Tensile yield stress

\(f_{bk}\) :

Tensile strength

\(g^{\prime }\) :

Potential function

\(G\) :

Shear modulus

\(G_{0}\) :

Maximum shear modulus

\(G_{50}\) :

Shear modulus equal to 50 % of \(G_{0}\)

\(G_{s}\) :

Specific gravity

\(h\) :

Maximum size of FEM element

\(I_{1}\) :

First stress invariant

\(J_{2}\) :

Second deviatoric stress invariant

\(J_{3}\) :

Third deviatoric stress invariant

[K] :

Stiffness matrix

[M] :

Mass matrix

\(M\) :

Bending moment

\(N\) :

g-Level

\(p^{\prime }\) :

Mean effective stress

\(q\) :

Deviatoric stress

\(s\) :

Thickness of the tunnel

\(t\) :

time

\(V_{s}\) :

Soil shear velocity

\(w\) :

Vertical displacements

\(x\) :

Distance from the tunnel alignment

\(y\) :

Horizontal axis

\(z\) :

Vertical axis

\(\alpha \) :

Soil constant for \(G{-}\gamma \) curve by Yokota et al. (1981)

\(\beta \) :

Soil constant for \(G{-}\gamma \) curve by Yokota et al. (1981)

\(\alpha _{R}\) :

Rayleigh damping factor

\(\beta _{R}\) :

Rayleigh damping factor

\(\gamma \) :

Shear strain

\(\gamma _{m}\) :

Material unit weight

\({\varDelta } M_{pk}\) :

Peak bending moment increment

\(\varepsilon _{\alpha }\) :

Axial strain

\(\eta \) :

Soil constant for \(D-\gamma \) curve by Yokota et al. (1981)

\(\theta \) :

Lining angle, i.e.: angular position

\(\lambda \) :

Soil constant for \(D-\gamma \) curve by Yokota et al. (1981)

\(\lambda ^{*}\) :

Minimum wave length

\(\nu \) :

Poisson ratio

\(\sigma ^{\prime }\) :

Axial stress

\(\varphi \) :

Shear strength angle

\(\psi \) :

Dilatancy angle

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Acknowledgments

The authors acknowledge the support and cooperation of the RRTT organizers during the program.

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Authors and Affiliations

  1. Department of Civil Engineering and Architecture, University of Catania, Viale Andrea Doria 6, 95125, Catania, Italy

    Glenda Abate, Maria Rossella Massimino & Michele Maugeri

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  1. Glenda Abate
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  2. Maria Rossella Massimino
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  3. Michele Maugeri
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Correspondence to Maria Rossella Massimino.

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Abate, G., Massimino, M.R. & Maugeri, M. Numerical modelling of centrifuge tests on tunnel–soil systems. Bull Earthquake Eng 13, 1927–1951 (2015). https://doi.org/10.1007/s10518-014-9703-0

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