Analysis of circular tunnels due to seismic P-wave propagation, with emphasis on unreinforced concrete liners
Introduction
The need to reduce infrastructure costs has led to the adoption of unreinforced concrete for the construction of final tunnel lining sections, at least for tunnel sections bored through a competent rock mass where long-term external loads are expected to be generally low in occurrence and magnitude. Modern guidelines and code provisions, such as the French AFTES [1], the German DIN 1045-1 [2] and Eurocode EN-1992 [3], offer methodologies applicable to the design of unreinforced concrete tunnel liners. These are based on two fundamental design requirements: (a) compressive stresses in the liner must remain low compared to the concrete design strength, and (b) crack depths must be limited, generally up to 50% of the cross-section height for high axial force load cases [1]. The latter requirement is quantified by imposing restrictions on the maximum developing eccentricity elim = Mmax/Tmax, where Mmax is the bending moment in the cross-section and Tmax is the axial hoop force.
Unlike conventional reinforced concrete liners, which have been proven to suffer less from earthquakes compared to above-ground structures [4], [5], significant damage to unreinforced tunnel linings has been recorded during the Kobe (1995) and the Niigata-Chuetsu (2004) earthquakes in Japan, which has a long tradition in using unreinforced concrete for tunnel linings [6], [7], [8]. Although the damage distribution in the tunnel networks suggested that unreinforced tunnel linings can indeed survive earthquake effects under certain conditions, transient seismic wave propagation is recognized to be an important load case to be considered during their analysis and design.
Section snippets
Existing closed-form solutions for the calculation of internal forces due to S-wave propagation and limitations of current state-of-practice
Taking into account rock mass-structure interaction effects, a series of elastic closed-form solutions have been proposed for determining the internal forces in the lining of a circular tunnel due to the deformation generated by seismic shear or S-wave propagation [9], [10], [11], [12]. Here we focus on one of the most widely-used ones, proposed by Wang [9] and also discussed by Hashash et al. [13]. The validity of Wang’s solution under specific conditions has been verified more recently by
Internal forces considering P-wave propagation under no-slip and full-slip interface conditions
A closed-form elasticity solution is proposed to calculate the axial forces and bending moments in an annular tunnel lining, resulting from the deformation imposed by compressional P-wave propagation. The expressions resulted from adapting the well-established elasticity solution for rock mass-lining interaction of Ranken et al. [22], [23].
The Ranken et al. solution for static loads is based on the following assumptions: (a) the rock mass surrounding the tunnel is an infinite, elastic,
Numerical verification and effect of separation at the liner-rock mass interface
Verification of the expressions derived previously, and an investigation of the fundamental assumption of an infinite tensile bond strength at the liner-rock mass interface, was carried out using a dynamic finite element model which simulates a circular tunnel geometry, harmonic cyclic excitation, and free-field geometry conditions (Fig. 5). The input data for the example case study considered are summarized in Table 2.
The finite element code ABAQUS/Standard [28] was employed for the analyses,
Summary and conclusions
A new set of analytical expressions is proposed in this study to quantify the effect of compressional P-seismic wave propagation on the final tunnel lining. It is shown that P-waves impinging at the rock mass-liner interface can result in significant axial hoop forces, even under full-slip conditions, which are considerably higher than the corresponding forces due to shear S-waves of similar, or even lower amplitude. This finding is of practical importance for tunnels that are constructed near
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2022, Journal of Applied GeophysicsCitation Excerpt :However, the rock mass in the sidewall does not experience vertical displacements, which could be attributed to the constraints in vertical direction. This result is consistent with the previous rock damage study under P-wave (Kouretzis et al., 2014). Under the disturbance of S-wave (0.2–0.632 s), the rock mass in the sidewall experienced considerable displacements in both horizontal and vertical directions, as shown in Fig. 15a. However, the rock mass in the roof (Fig. 15b) only shows significant displacements in the vertical direction.