强震作用下山岭隧道洞口段地震响应分析及减震措施研究
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摘要
随着我国经济建设和社会快速发展的需要，隧道建设已进入地震频发的高烈度地震区。受高山峡谷等复杂地形的限制，众多的山岭隧道在我国高烈度地震山区大量修建且有广泛的应用前景。而我国的公路、铁路隧道规范一直沿用不完全合理的静力法进行抗、减震计算，远远不能满足对隧道洞口段、浅埋、偏压等抗、减震重点地段的设计要求。本文以交通部西部交通建设科技项目（武-罐高速公路抗震优化设计及灾害防治技术研究）为依托，以武-罐高速公路在建麻崖子隧道为工程背景，从地下结构动力分析的基本原理出发，运用有限元软件，计算并分析了浅埋和偏压隧道的地震动力响应特点，确定了适用于隧道洞口段（浅埋和偏压）的减震措施。主要进行了以下方面的工作：
1）基于地层的弹塑性特点，从动力有限元分析原理出发，用增量形式推导了以地面加速度时程反算基岩地震动加速度时程的Wilson-θ法计算公式，由地面记录的加速度时程反算基岩地震动加速度。从计算结果可以看出，地层对地震动有放大作用，所以在对隧道及地下结构的抗震计算中，应该以基岩地震加速度作为输入，可以使计算结果更加合理。
2）考虑围岩的弹塑性特点，用Newmark-β法推导了非线性方程的计算公式。建立了山岭隧道洞口段（浅埋及偏压浅埋）的实体模型，计算并分析了该山岭隧道洞口段在强震（超越概率2%）作用下的地震响应，确定了对隧道最不利的地震波传播方向。同时分析了浅埋及偏压浅埋隧道衬砌在强震作用下的位移、内力及应力响应随埋深的变化规律，以及偏压侧衬砌的位移、内力及应力的分布规律与非偏压时的不同。确定了在该围岩条件下浅埋及偏压浅埋隧道抗震设防的重点部位。
3）针对浅埋及偏压浅埋隧道洞口段分别对围岩进行了注浆加固和对隧道洞口段衬砌采取抗震设防的数值模拟计算，分析了不同的注浆加固范围和不同的抗震设防长度对隧道衬砌抗震减震的效果。分别确定了该围岩级别下浅埋及偏压浅埋隧道的注浆加固范围和抗震设防长度。
4）通过建立偏压隧道洞口段横向平面模型，对处于偏压状态的隧道衬砌在不同厚度时进行了计算分析，得出厚度的增加可以有效减小衬砌的轴向应力，但是衬砌的弯曲应力则随厚度的增加而增加，组合应力则随衬砌厚度的增加而平缓减小。由此确定了偏压浅埋隧道洞口段应采取扩大注浆加固范围、高于标准要求的抗震设防长度、同时增加配筋来提高强度以及采用平滑过渡的断面形状以减小应力集中的综合抗震措施来保证偏压侧衬砌在地震动作用下的安全性。
5）运用振动理论，针对初衬-减震层-二衬体系简化后的力学模型，建立了振动方程。并结合麻崖子隧道实例给出相应的参数并用解析法进行了计算分析，从理论上确定了减震层与二衬的刚度比γ2在0.01~0.5范围时，减震层对衬砌有较好的减震效果。用麻崖子隧道浅埋洞口段的实例通过有限元计算进行验证分析，确定了减震层与二衬的刚度比2在0.05~0.15范围时，可以对衬砌起到较好的减震效果。
Lots of tunnels have been built in high seismic intensity regions in western of Chinawhere earthquake frequently happens. Many mountain tunnels have to be built in highmountains and gorges due to the limitation of the complicated topography. However, in ourcountry, the quasi-static method has been widely but unreasonably used for anti-seismic andshock absorption calculation in the the standards of roads and railways tunnels which can notmeet the requirements of key parts of mountain tunnel, such as portal sections, shallow-seatedsections and unsymmetrical loading sections. Supported by the Western traffic ConstructionTechnology&Science Project in China, based on the case study of Ma-Yazi tunnel of theWu-Guan Highway, the dynamic response of the shallow and unsymmetrical loading tunnellining was analyzed by using FEM. The characteristics of earthquake-induced dynamicresponse of shallow and unsymmetrical loading tunnel were obtained and the anti-seismic andshock absorption measures suitable for reducing the earthquake-induced dynamic responsesof the portal section of this tunnel was proposed. The main works are as follows：
1) Based on the characteristics of elasto-plasticity of ground, and by using the theory ofdynamic finite element, the equations for back-evaluating the seismic acceleration of thebedrock from the seismic acceleration of the ground surface were derived by using themethod of Wilson-θ. It is indicated that the ground has an obvious amplifying effect forground motion. Therefore, the seismic acceleration of the bedrock should be input foranti-seismic and shock absorption calculation of underground structures in order to obtainmore reasonable results.
2) With the consideration of the characteristics of elasto-plasticity of surrounding rock,the formulas of nolinear equations were deduced by using the method of Newmark-β. Themodels of the shallow and unsymmetrical loading tunnel lining were established and thedynamic responses of the tunnel portal section induced by intense earthquake were analyzed,the most unfavorable input direction of ground motion was determined too. Meanwhile, therelationships of the lining displacement, inner force and stress with the burial depth and thedifferences of those of the symmetrical loading&symmetrical loading were discussed. Thekey anti-seismic parts of the tunnel portal section in such kind of surrounding rock wereascertained.
3) The effects of different grouting areas of ground and different lengths of anti-seismicprotected section to the anti-seismic and shock absorption of tunnel lining were studied byusing numerical simulations. The proper grouting areas of ground and suitable length ofanti-seismic protected section for the shallow and unsymmetrical loading tunnel lining wereobtained respectively. γ
4) The transverse planar model of unsymmetrical loading tunnel portal was establishedto analyze the earthquake-induced dynamic responses of tunnel lining with different thickness.The conclusions show that the increasing of lining thickness can effectively reduce the axisstress in tunnel lining, but the bend stress in tunnel lining will increase with the increasing ofthickness, while the combined stress will gradually reduce with the increase of liningthickness. Thus, an integrated measure of increased grouting area of ground at tunnel portalsection, strengthened length of anti-seismic protected section, enhancing the intension byadding reinforcing bars in concrete and adopting a smoothed transition shape to reduce thestress concentration in the tunnel lining was proposed to ensure the safety of tunnel portalsection with unsymmetrical loadings under ground motion.
5) The vibration equations for simplified mechanical model of the tunnel lining systemcomposed of the primary lining, layer of shock absorption and second lining were derived byusing the vibration theory. Based on the case study of Ma-Yazi tunnel, the conclusionscalculated by analytical method show that the tunnel lining system can effectively reduce theearthquake-induced dynamic responses in the tunnel lining where the stiffness ratio of layerof shock absorption and second lining (γ2) is0.01~0.5. And the calculated results by usingfinite element method indicate that the shock absorption effect is much better if the stiffnessratio of layer of shock absorption and second lining (γ2) is0.05~0.15.
1）基于地层的弹塑性特点，从动力有限元分析原理出发，用增量形式推导了以地面加速度时程反算基岩地震动加速度时程的Wilson-θ法计算公式，由地面记录的加速度时程反算基岩地震动加速度。从计算结果可以看出，地层对地震动有放大作用，所以在对隧道及地下结构的抗震计算中，应该以基岩地震加速度作为输入，可以使计算结果更加合理。
2）考虑围岩的弹塑性特点，用Newmark-β法推导了非线性方程的计算公式。建立了山岭隧道洞口段（浅埋及偏压浅埋）的实体模型，计算并分析了该山岭隧道洞口段在强震（超越概率2%）作用下的地震响应，确定了对隧道最不利的地震波传播方向。同时分析了浅埋及偏压浅埋隧道衬砌在强震作用下的位移、内力及应力响应随埋深的变化规律，以及偏压侧衬砌的位移、内力及应力的分布规律与非偏压时的不同。确定了在该围岩条件下浅埋及偏压浅埋隧道抗震设防的重点部位。
3）针对浅埋及偏压浅埋隧道洞口段分别对围岩进行了注浆加固和对隧道洞口段衬砌采取抗震设防的数值模拟计算，分析了不同的注浆加固范围和不同的抗震设防长度对隧道衬砌抗震减震的效果。分别确定了该围岩级别下浅埋及偏压浅埋隧道的注浆加固范围和抗震设防长度。
4）通过建立偏压隧道洞口段横向平面模型，对处于偏压状态的隧道衬砌在不同厚度时进行了计算分析，得出厚度的增加可以有效减小衬砌的轴向应力，但是衬砌的弯曲应力则随厚度的增加而增加，组合应力则随衬砌厚度的增加而平缓减小。由此确定了偏压浅埋隧道洞口段应采取扩大注浆加固范围、高于标准要求的抗震设防长度、同时增加配筋来提高强度以及采用平滑过渡的断面形状以减小应力集中的综合抗震措施来保证偏压侧衬砌在地震动作用下的安全性。
5）运用振动理论，针对初衬-减震层-二衬体系简化后的力学模型，建立了振动方程。并结合麻崖子隧道实例给出相应的参数并用解析法进行了计算分析，从理论上确定了减震层与二衬的刚度比γ2在0.01~0.5范围时，减震层对衬砌有较好的减震效果。用麻崖子隧道浅埋洞口段的实例通过有限元计算进行验证分析，确定了减震层与二衬的刚度比2在0.05~0.15范围时，可以对衬砌起到较好的减震效果。
Lots of tunnels have been built in high seismic intensity regions in western of Chinawhere earthquake frequently happens. Many mountain tunnels have to be built in highmountains and gorges due to the limitation of the complicated topography. However, in ourcountry, the quasi-static method has been widely but unreasonably used for anti-seismic andshock absorption calculation in the the standards of roads and railways tunnels which can notmeet the requirements of key parts of mountain tunnel, such as portal sections, shallow-seatedsections and unsymmetrical loading sections. Supported by the Western traffic ConstructionTechnology&Science Project in China, based on the case study of Ma-Yazi tunnel of theWu-Guan Highway, the dynamic response of the shallow and unsymmetrical loading tunnellining was analyzed by using FEM. The characteristics of earthquake-induced dynamicresponse of shallow and unsymmetrical loading tunnel were obtained and the anti-seismic andshock absorption measures suitable for reducing the earthquake-induced dynamic responsesof the portal section of this tunnel was proposed. The main works are as follows：
1) Based on the characteristics of elasto-plasticity of ground, and by using the theory ofdynamic finite element, the equations for back-evaluating the seismic acceleration of thebedrock from the seismic acceleration of the ground surface were derived by using themethod of Wilson-θ. It is indicated that the ground has an obvious amplifying effect forground motion. Therefore, the seismic acceleration of the bedrock should be input foranti-seismic and shock absorption calculation of underground structures in order to obtainmore reasonable results.
2) With the consideration of the characteristics of elasto-plasticity of surrounding rock,the formulas of nolinear equations were deduced by using the method of Newmark-β. Themodels of the shallow and unsymmetrical loading tunnel lining were established and thedynamic responses of the tunnel portal section induced by intense earthquake were analyzed,the most unfavorable input direction of ground motion was determined too. Meanwhile, therelationships of the lining displacement, inner force and stress with the burial depth and thedifferences of those of the symmetrical loading&symmetrical loading were discussed. Thekey anti-seismic parts of the tunnel portal section in such kind of surrounding rock wereascertained.
3) The effects of different grouting areas of ground and different lengths of anti-seismicprotected section to the anti-seismic and shock absorption of tunnel lining were studied byusing numerical simulations. The proper grouting areas of ground and suitable length ofanti-seismic protected section for the shallow and unsymmetrical loading tunnel lining wereobtained respectively. γ
4) The transverse planar model of unsymmetrical loading tunnel portal was establishedto analyze the earthquake-induced dynamic responses of tunnel lining with different thickness.The conclusions show that the increasing of lining thickness can effectively reduce the axisstress in tunnel lining, but the bend stress in tunnel lining will increase with the increasing ofthickness, while the combined stress will gradually reduce with the increase of liningthickness. Thus, an integrated measure of increased grouting area of ground at tunnel portalsection, strengthened length of anti-seismic protected section, enhancing the intension byadding reinforcing bars in concrete and adopting a smoothed transition shape to reduce thestress concentration in the tunnel lining was proposed to ensure the safety of tunnel portalsection with unsymmetrical loadings under ground motion.
5) The vibration equations for simplified mechanical model of the tunnel lining systemcomposed of the primary lining, layer of shock absorption and second lining were derived byusing the vibration theory. Based on the case study of Ma-Yazi tunnel, the conclusionscalculated by analytical method show that the tunnel lining system can effectively reduce theearthquake-induced dynamic responses in the tunnel lining where the stiffness ratio of layerof shock absorption and second lining (γ2) is0.01~0.5. And the calculated results by usingfinite element method indicate that the shock absorption effect is much better if the stiffnessratio of layer of shock absorption and second lining (γ2) is0.05~0.15.
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