Scalar- and vector-valued vulnerability analysis of shallow circular tunnel in soft soil

This paper presents a scalar- and vector-valued vulnerability analysis of shallow circular tunnel in soft soil. Numerous dynamic analyses were firstly performed to capture seismic response of the tunnel lining under transversal seismic shaking. Subsequently, a series of 15 intensity measures (IMs) are selected and tested to find the optimal IM used in the scalar-valued vulnerability analysis. The selected IMs are all tested based on their correlation, efficiency, practicality and proficiency, according to the regression analyses between the IMs and the damage measure (DM) for the examined tunnel. The peak ground acceleration (PGA) at the ground surface was demonstrated to be optimal IM, followed by peak ground velocity (PGV) and acceleration spectrum intensity (ASI). The scalar-valued vulnerability function was then developed in terms of optimal IM (PGA). Finally, the vulnerability functions based on vector-valued IMs were developed to obtain the exceeding probability of various damage states as a function of two IMs (PGA, ASI). This study reveals that the use of vector-valued IMs in the vulnerability analysis can significantly improve the correlation and efficiency with the seismic demand DM compared to the scalar-valued IM, thus reducing the uncertainties in evaluating earthquake risk. The scalar-valued vulnerability curves cannot represent the effect of a second IM on the seismic behavior of the tunnel, and it may either underestimate or overestimate the damage probability. Hence, the use of the second IM in vulnerability analysis and the development of vector-valued vulnerability functions lead to more proper evaluations of seismic risk.