Pseudo-static vs pseudo-dynamic methods: A general comparison and their application to underground tunnel stability

Abstract

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.