Seismic Damage Prediction Method for Lining Structures Based on the SEDR Principle

Abstract

The safety and stability of lining structures are core concerns of tunnel and underground engineering. It is crucial to determine whether a lining structure would crack and which direction the crack would expand with seismic excitation. In previous literature, the principle based on stress and strain has been widely used to predict the seismic damage of lining structures, whereas it cannot specify the cracking modes. Taking account of that deficiency, this paper introduces the strain energy density ratio (SEDR) principle and proposes a seismic damage prediction method for lining structures, which can precisely predict the crack positions and expansion directions. Moreover, numerical simulations of the typical seismic damage sections of two tunnels in the Great Wenchuan Earthquake and a calculating example of the theoretical equations are conducted to verify the proposed method. In summary, the numerical simulation results show that the arch springing cracks first, and the invert cracks next; then the cracks expand to the spandrel, and finally, they form oblique cracks, annular cracks, and longitudinal cracks, whose positions and patterns are in accordance with the field investigation results. In terms of the calculating example results, the obtained two-fold SEDR and cracking angle θ are 1.87 and −6.28°, respectively, which are consistent with the numerical simulation results. Therefore, one can see that the proposed seismic damage prediction method based on the SEDR principle is quite accurate. This method can be used to predict the seismic damage of lining structures and provide a reference for the research of the damage mechanism of tunnels.

Study on seismic dissipation mechanism of inter-story isolation structure based on phase

“…Here, the cumulative plastic deformation ratio η m is defined as the ratio of the cumulative plastic deformation δ pm to the yield deformation δ pm of the damper and the average plastic deformation ratio µ m is defined as the ratio of the maximum deformation δ 2 to the yield deformation δ ym [28]. Simultaneously, the coefficient n is introduced and its physical meaning is the ratio of the hysteretic energy dissipation of the damper to the work done by the vibration of the maximum deformation of the isolation layer in a week.…”

“…They noted that when the phase difference between the relative displacement of the TMD and the displacement of the main structure was 90 °, the energy transferred from the structure to the TMD system was the largest and the TMD damping effect was the best. Zhang et al [28] proposed that when the phase difference between the force of the TMD on the structure and the external excitation is 180 °, the force of the TMD on the structure is reduced; however, their research was limited to a sinusoidal load input. Zhang [18] proposed that TMD damping is most effective when the phase difference between the central structure velocity and TMD relative to the central structure displacement is 180 °.…”

Application of the Modified Mohr–Coulomb Yield Criterion in Seismic Numerical Simulation of Tunnels

“…e peak accelerations are introduced as the measurements [25][26][27][28][29]. By comparing the acceleration watch points of the two Mohr-Coulomb models with the results of the shaking table test, the peak acceleration similarity advantage of the modified Mohr-Coulomb yield criterion was assessed.…”

The Stability Analysis of Tunnel Lining Structure with Seismic Excitation Based on the Energy Evaluation Principle

“…Afterwards, the quasi-static stiffness principle based on the tangent stiffness matrix was proposed [9,10], which could evaluate the dynamic instability conditions of structures [11]. In terms of that principle, the motion equation was transformed to the differential equation of the first order [12], and its stability can be evaluated by the positive definite stability theory of the matrix in motion [13]. Moreover, in regard to the B-R principle, incremental dynamic analysis (IDA) curves were used to describe the relation of the strength and displacement [14], which could be effectively used for the dynamic stability analysis of structures.…”