Method for seismic fragility analysis of shield tunnel considering surface surcharge effects

A method for seismic fragility analysis of a shield tunnel considering surface surcharge effects, comprising the steps of:

• S1, determining mechanical property parameters of tunnel materials and physical-mechanical parameters of soil layers;
• S2, investigating case studies of tunnels affected by surface surcharge to define reasonable locations, magnitudes, and extents of surface surcharge;
• S3, selecting appropriate seismic waves, and performing one-dimensional equivalent linear site response analysis on soil conditions obtained in step S1 to derive elastic modulus and Rayleigh damping parameters of soil;
• S4, establishing a dynamic finite element numerical model of a soil-tunnel system considering surface surcharge based on the physical-mechanical parameters of the tunnel and soil layers, the seismic waves, and surface surcharge scenarios, determined in Steps S1-S3;
• and designing various scenarios combining surface surcharge levels and seismic intensities, and obtaining dynamic responses of the soil-tunnel system through extensive numerical calculations;
• S5, choosing a maximum peak ground acceleration (PGA) of an input seismic wave as a ground motion intensity measure (TM);
• selecting a tunnel diameter deformation ratio as a damage measure (DM);
• and determining tunnel damage states (DSs) and DM thresholds corresponding to reaching the DSs;
• S6, establishing probabilistic seismic demand models for the tunnel under various surface surcharge effects based on the ground motion IM and DM selected in Step S5, as shown in Equation (3):
• ln
• ⁢
• DM
• =
• a
• ⁢
• ln
• ⁢
• IM
• +
• b
• (
• 3
• )
• where a and b are determined through regression analysis, and after the probabilistic demand model is established, key parameters for plotting the fragility curves are calculated:
• a median IM value and a logarithmic standard deviation βD for each DS.
• S7, establishing seismic fragility curves for tunnel structures under surface surcharge effects based on the key parameters, as shown in Equation (5):
• P
• f
• (
• d
• s
• ≥
• d
• s
• i
• ❘
• S
• )
• =
• Φ
• [
• 1
• β
• tot
• ·
• ln
• (
• S
• S
• mi
• )
• ]
• (
• 5
• )
• where βf is defined as a probability of exceeding a particular DS dsi when subjected to a seismic wave with a given IM;
• φ represents a cumulative probability function of standard normal distribution;
• Smi is a threshold value of the ground motion IM corresponding to each DS, obtained from Step S6;
• and βtot is a total logarithmic standard deviation.