Simplified analysis of seismic in-plane stresses in composite and jointed tunnel linings

Simplified Analysis of the Lining Behavior During Earthquakes in Deep Rock Tunnels

“…Simplifiedload scheme of the rock around the tunnel, to simulate the dynamic effects of the presence of an earthquake on the lining of a circular and deep tunnel. Key: q dyn is the normal stress that simulates the presence of an earthquake; R: The tunnel radius (El Naggar et al, 2008;Penzien and Wu, 1998) where, * 2 a is a dimensionless coefficient: According to the Einstein and Schwartz analytical method (Einstein and Schwartz, 1979) and for the assumptions made, in particular for the eligibility of lining-tunnel wall relative displacements (full slip case), the normal forces induced by the earthquake in the lining are everywhere equal to zero. That fact is a consequence of the simplified calculation model adopted: Actually values of normal force, even if low and negligible, can be detected even when it is allowed a lining-rock relative displacement.…”

Dynamic interaction of two circular lined tunnels with imperfect interfaces under cylindrical P-waves

“…Due to the existence of underground tunnels, the response of the surrounding rock mass to the static or dynamic loadings will show great variation, especially when the dynamic interaction between the tunnels is considered. Because of the large dynamic stress resulting from the interaction between the tunnels, many rock tunnels have been damaged by earthquakes in recent years 3,4 .…”

Behaviour of segmental tunnel linings under seismic loads studied with the hyperstatic reaction method

“…As far as circular tunnels are concerned, El Naggar et al [13] developed a closed-form solution for moments and thrusts in a jointed composite tunnel lining, on the basis of external load scheme that was proposed by Peinzen and Wu [3], which is also used in this study. This solution has been adapted to evaluate the effect of in-plane shear stresses induced by ovaling deformation.…”

“…This method has been developed on the basis of the HRM that was proposed by Oreste [14], and then developed by Do et al [15,16]. Seismic loads are determined on the basis of in-plane shear stresses which were introduced in the works of Peinzen and Wu [3] and El Naggar et al [13]. The parameters that are necessary to calculate the tunnel lining under seismic loads are presented.…”