Response of a Tunnel in Two Layered Rocks Subjected to Harmonic P- and S- Waves
Date Issued
2012
Date
2012
Author(s)
Hsu, Jui-Tsu
Abstract
Seismic problem plays an important role in rock tunnels for the recondition time after earthquake is long and the effects on traffic and civil needs are great. In the past few years, efforts surge on investigation of seismic damage cases, statistics of damage proportion and main influence factors affecting tunnel seismic behavior. Only few understandings focus on the seismic behavior of tunnels, hence the mechanisms causing seismic damages remains obscure.
This study investigates the response of a tunnel in two layered rocks subjected to harmonic P- and S- waves using commercial finite element method software “ABAQUS”. First of all, assume the whole model is in plane strain condition. The numerical model is then verified by comparing the results with an analytic solution. Harmonic S-wave and P-wave with vertical incidence in different Impedance ratio strata (hard /soft strata), tunnel positions (h / λ) and frequencies (Hz) are simulated, and the maximum and minimum increments in axial-, shear- and flexural stress of tunnel lining (σ_(N,max)^θ, σ_(V,max)^θ, σ_(M,max)^θ and σ_(N,min)^θ, σ_(V,min)^θ, σ_(M,min)^θ) in selected angles are recorded. Envelops of these seismic induced stresses are depicted according to the normalized values of stress increments with respect to the initial maximum stress of the incident or the refractive waves (σ_0 or σ_n).
The results showed that the frequencies of seismic induced normalized tunnel lining stress increments differ from point to point on the lining. According to the location on tunnel lining, four types can be defined: the first one on tunnel roof and floor (θ = 0˚, 180˚), the second on two sidewalls of tunnel (θ =±90˚), the third includes odd multiples of 45 degree (θ = ±45˚, ±135˚), others are classified as the fourth type. Harmonic S-wave-induced axial- and flexural stress increments reach their maximum and minimum in shoulders and below sidewalls (θ = ±45˚, ±135˚), respectively; shear stress increments attain to its maximum on tunnel roof and spring lines (θ = 0˚, ±90˚), and to its minimum on floor (θ = ±180˚). Harmonic P-wave-induced axial stress increments are found to maximize and minimize on two sidewalls (θ = ±90˚), the shear stress increments reach its peak and valley on tunnel shoulders and below sidewalls (θ = ±45˚, ±135˚), and the flexural stress increments approach its maximum on tunnel roof and spring lines (θ = 0˚, ±90˚) and minimum on floor (θ = ±180˚).
The results revealed that the ratio of tunnel depth to wavelength (h/λ), frequency (Hz) and wavelength ( λ ) significantly affect the maximum values of seismic induced axial-, shear- and flexural stress increments of tunnel lining. The lining stress increment reach its maximum at depths odd times of 0.25(h/λ) and minimum at depths even times of 0.25(h/λ). With the same ratio of tunnel depth to wavelength (h/λ), the normalized stress increments decrease as the damping ratio ( ξ ) is larger. In this research, the impedance ratio (α) is used to define the relative magnitude of rock mass properties of the two layers. While a tunnel locates at the upper rock layer, the impedance ratio may induce a decline or grow of the incident wave, thus influence the normalized stress increments. The relative stiffness of surrounding rock and the tunnel lining would also affect the seismically induced normalized stress increments.
Subjects
rock tunnels
seismic behavior
two layered rocks
simple harmonic wave
Impedance ratio
Type
thesis
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