Pseudo-Static vs Pseudo-Dynamic Methods: A General Comparison and Their Application to Underground Tunnel Stability

Two categories of methods are available to represent seismic acceleration in the medium: pseudo-static or Mononobe-Okabe (M-O) and pseudo-dynamic methods. The first part of the study provides a critical comparison of these methods, focusing on amplitude and phase changes. The M-O approach ignores amplitude and phase change effects. The conventional pseudo-dynamic method disregards the frequency-dependent amplification, underestimating the acceleration magnitude, especially near the fundamental frequency, and overestimating otherwise. This method results in a negative phase difference, indicating some levels are accelerated before the base, which is impractical. The second part of the study evaluates the implications of using the M-O and harmonic base excitation methods for seismic stability analysis of underground tunnels. Two cases of seismic acceleration coefficients were considered for the Mononobe-Okabe approach—acceleration coefficients matching the base acceleration amplitude and peak ground acceleration from harmonic input. For the first case, the Mononobe-Okabe approach underestimated the peak dynamic stability factor compared to the harmonic input. On the other hand, this approach overestimates the above-said quantity by a maximum of 81% when peak ground accelerations from the harmonic case are used. However, it has been found that the Mononobe-Okabe approach using the peak ground acceleration can be considered against the harmonic base excitation to estimate the maximum dynamic stability factor for tunnels placed at a lower cover depth in soils with higher shear strength. 

Keywords: Tunnel, Mononobe-Okabe, Harmonic, Seismicity, Granular, Cohesive-frictional

Gowtham, G., and Sahoo, J.P. (2026). Pseudo-Static vs Pseudo-Dynamic Methods: A General Comparison and Their Application to Underground Tunnel Stability. Soil Dynamics and Earthquake Engineering, 200. https://doi.org/10.1016/j.soildyn.2025.109888