兩層岩層中隧道受簡諧P波與S波作用之反應

Response of a Tunnel in Two Layered Rocks Subjected to Harmonic P- and S- Waves

許瑞慈(Jui-Tsu Hsu)

指導教授 ： 黃燦輝

國立臺灣大學/工學院/土木工程學研究所/碩士(2012年)

https://doi.org/10.6342/NTU.2012.01922

摘要

岩石隧道受震發生嚴重損害後，其修復作業需時頗長，交通與民生需求影響甚鉅，故隧道受震課題亟待進一步深入探討，且岩石隧道結構受震行為未臻完全瞭解，目前多數研究集中於震後災損案例調查、統計受震損害比例與其他影響因素等，而對於隧道本體受震破壞之機制仍尚未釐清。
本研究採用商用有限元素分析軟體(ABAQUS)進行兩層岩層中隧道之動態簡諧歷時分析，在考慮平面應變條件下，比較解析解並驗證數值模式之正確性後，模擬S波及P波垂直入射於不同硬度地層(Impedance ratio)、不同隧道位置(h/λ)和頻率(Hz)進而引發隧道襯砌應力變化之情形。研究中，記錄入射波所引發之襯砌軸應力、剪應力與撓曲應力增量，並針對襯砌每一角度位置(θ)選取歷時過程中軸應力、剪應力與撓曲應力增量之最大值(σ_(N,max)^θ、σ_(V,max)^θ、σ_(M,max)^θ)與最小值(σ_(N,min)^θ、σ_(V,min)^θ、σ_(M,min)^θ)，並分別對入射波或折射波之初始最大應力值 (σ_0或σ_n)進行正規化並繪製襯砌周緣受震歷時過程應力增量包絡線。
研究結果顯示，隧道受震引致襯砌正規化動態應力增量歷時變化頻率與襯砌位置有關，襯砌位置可分為四類；第一類位於襯砌頂拱與仰拱(θ = 0˚、180˚)，第二類位於襯砌兩側壁(θ =±90˚)，第三類位於角度45o之奇數倍位置(θ = ±45˚、±135˚)，第四類則為襯砌其他角度位置。依據隧道受震引致襯砌周緣受震歷時過程應力增量包絡線圖，簡諧S波入射引致之襯砌軸應力與撓曲應力增量於兩側肩部與兩側壁下方(θ = ±45˚、±135˚)達到最大及最小值，襯砌剪應力增量於隧道頂拱、起拱線及底部位置(θ = 0˚、±90˚、180˚)達到最大及最小值；簡諧P波入射引致之襯砌軸應力於兩側壁(θ =±90˚)達到最大及最小值，襯砌剪應力增量於隧道兩側肩部與兩側壁下方(θ = ±45˚、±135˚)達到最大及最小值，襯砌撓曲應力增量於隧道頂拱、起拱線及底部位置(θ = 0˚、±90˚、180˚)達到最大及最小值。
震波引發隧道襯砌最大正規化軸應力、剪應力與撓曲應力增量隨正規化覆蓋深度(h/λ)、頻率(Hz)與波長( λ )有關，當正規化覆蓋深度(h/λ)為0.25之奇數倍時襯砌應力增量存在最大值；正規化覆蓋深度(h/λ)為0.25之偶數倍時存在最小值。同時研究分析發現相同正規化覆蓋深度(h/λ)，其阻尼比( ξ )越大，正規化應力增量則越小。阻抗比(α)主要連結上下層岩層性質關係，隧道位於上層岩層時其阻抗比(α)折減或放大入射波，進而影響正規化動態應力增量值。圍岩與隧道襯砌之相對勁度也會影響正規化動態應力增量值。

關鍵字

岩石隧道 ； 受震行為 ； 兩層岩層 ； 簡諧波 ； 阻抗比

並列摘要

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.

並列關鍵字

rock tunnels ； seismic behavior ； two layered rocks ； simple harmonic wave ； Impedance ratio

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