The Design and Shaking Table Test Verification of a Dynamic Model Box for Tunnels Crossing Multi-rupture Surface Fault
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摘要: 振动台模型试验是研究工程结构动力响应的重要手段，模型箱作为隧道工程振动台模型试验的关键因素，其设计的合理性成为确保振动台试验准确的关键。本文依托某高烈度地震区穿越大型断裂带隧道工程，以穿越多破裂面断层隧道为对象，根据多破裂断层相互作用力学机理，基于弹性地基理论构建了集中质量力学模型，并设计了针对穿越多破裂面断层隧道的动力模型箱。利用有限元软件对模型箱进行模态频响分析，得出模型箱-围岩-衬砌在地震动作用下不发生共振，各阶振型之间不会产生影响。运用该模型箱进行振动台试验并验证合理性，结果表明，围岩纵向范围同高度处，破碎带与上下盘交界处附近土体加速度峰值最大，显示出在地震作用下穿越多破裂面断层隧道与围岩的加速度响应特性；隧道衬砌共轭45°相对位移及围岩-衬砌拱顶接触应力峰值最大值出现在破碎带与上下盘交界处附近，最小值出现在破碎带内部破裂面处，破碎带边缘所受地震力最大；力学模型理论与试验的应力释放量相对差值仅为6.7%、0.5%，位移相差均在10%以内，验证了模型箱能较好地模拟穿越多破裂面断层隧道的错震特性；采用2-范数偏差μ对边界效应进行量化，μ总体小于0.2，并随着PGA的增大先增加后减小并趋于稳定，说明模型箱边界效应影响较小，能够模拟地震时多破裂面断层运动特性，验证了试验结果的可靠性，研究结果可为此类模型箱设计提供参考。Abstract: Shaking table model testing is a crucial method for investigating the dynamic response of engineering structures. In the context of tunnel engineering, the design of the model box plays a pivotal role in ensuring the accuracy and reliability of shaking table tests. This study focuses on a tunnel project located in a high-intensity seismic zone traversing a large fracture zone, where the tunnel intersects multiple fault surfaces. Based on the mechanics of multi-fault rupture interaction and employing elastic foundation theory, a concentrated mass mechanical model is developed to support the design of a dynamic model box tailored for tunnels crossing multiple fractured faults. A modal and frequency response analysis of the model box is conducted using finite element software, confirming that the model box–surrounding rock–lining system does not exhibit resonance under seismic excitation and that there is no coupling between different vibration modes. The designed model box is subsequently used in shaking table tests, validating its structural and dynamic rationality. The test results indicate that the peak acceleration of the soil near the junction between the fracture zone and the upper and lower rock plates is the highest at the same longitudinal elevation of the surrounding rock. This reveals the characteristic acceleration response of both the surrounding rock and the tunnel structure when subjected to seismic loading across a complex fracture zone. Additionally, the maximum relative displacement (along the 45° conjugate plane) of the tunnel lining and the peak contact stress between the surrounding rock and the lining vault occur near the interface of the fracture zone and the upper/lower planes. Conversely, the minimum values are observed within the interior of the fracture zone. The outer edges of the fracture zone experience the largest seismic forces. The relative error between the theoretical mechanical model and the experimental results is 6.7% for stress and 0.5% for stress release, while displacement discrepancies remain within 10%, confirming the model box’s capability to realistically simulate the seismic dislocation behavior of tunnels intersecting multiple fault surfaces. To assess boundary effects, the 2-norm deviation (μ) is introduced as a quantitative metric. The results show that μ generally remains below 0.2, and exhibits a trend of increasing, then decreasing, and stabilizing with rising peak ground acceleration (PGA). This behavior indicates minimal boundary effects, and demonstrates that the model box can accurately reproduce the kinematic characteristics of multi-fault rupture under seismic excitation. Overall, the model box design proves reliable and provides a practical reference for the development of similar shaking table testing systems for tunnel engineering in complex fault zones.
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图 4 走滑多破裂面断层地质力学模型
Figure 4. Geo-mechanical model of strike-slip multi-rupture surface fault
图 8 输入汶川波时x向测点的加速度时程及频谱图
Figure 8. Acceleration time histories and their spectrum at measurement points along x direction with the input of the Wenchuan earthquake wave
图 9 输入PGA为0.4 g的汶川波时的加速度时程曲线
Figure 9. Acceleration time histories at observation points along x direction with the input of the Wenchuan earthquake wave with PGA=0.4 g
图 10 隧道节段衬砌各断面相对位移
Figure 10. Relative displacement of tunnel segmental lining sections
图 11 隧道节段衬砌拱顶接触压力峰值
Figure 11. Peak contact pressure at tunnel segmental lining arch crown
表 1 断层错断模型箱类型及尺寸
Table 1. Type and dimensions of existing fault dislocation model box
单位 类型 错断形式 尺寸 破裂面 西南交通大学（仇文革等，2016） 刚性 无 1.0 m×0.5 m×1.0 m 无 西南交通大学（闫高明等，2019） 刚性 无 3.7 m×1.5 m×1.8 m 无 同济大学（Yan等，2016） 刚性 走滑断层 4 m×6 m×4.5 m 单 西南交通大学（杨长卫等，2023） 刚性 正/逆断层 8.3 m×3.1 m×2.5 m 单 中国地震局（孙海峰等，2012） 剪切 无 3.7 m×2.4 m×1.7 m 无 同济大学（伍小平等，2002） 剪切 无 2.0 m×1.5 m×2.0 m 无 西南交通大学（崔光耀等，2013，2018） 刚性 正/逆断层 2.5 m×2.5 m×2.0 m 单 西南交通大学（耿萍等，2020） 刚性 无 3.75 m×1.75 m×1.5 m 无 西南交通大学（赵建沣等，2019） 刚性 正/逆断层 2.5 m×2.5 m×1.5 m 单 
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表 2 模型箱材料与参数
Table 2. Materials and parameters of model boxes
动力模型箱 材料 规格/mm 侧壁 钢板 10 底板 钢板 16 外伸钢板 钢板 2 框架 H型钢 100×100×8×8 侧板连结 Π字型钢版 24×34.8×2
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表 3 模型箱材料参数
Table 3. Model box material parameters
材料 密度/(kg·m−3) 弹性模量/GPa 泊松比 Q345钢 7850 210 0.3
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表 4 模型箱各部频率表
Table 4. Model box frequency
类别 基频/Hz 位移图例（归一化） 一阶模态位移云图 二阶模态位移云图 模态分析曲线 下盘模型 28.07 
断层模型 19.56 
上盘模型 19.56 
整体模型 28.00 
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围岩+隧道 11.74 
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表 5 模型相似比量纲
Table 5. Model similarity ratios for the shaking table tests
物理量 量纲 相似比 泊松比μ 1 1.00 应力σ L−1MT−2 45.00 应变ε 1 1.00 时间t T 5.48 加速度a LT−2 1.00 频率f T −1 0.18
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表 6 围岩模型材料参数
Table 6. Material parameters of surrounding rocks model
弹性模量/GPa 密度/(kg·m−3) 黏聚力/kPa 摩擦角/° 上下盘（Ⅳ） 原型值 4 2200 400 33 模型值 0.089 1466.67 8.89 33 试验值 0.09 1467 11.7 32.3 断层破碎带（Ⅴ） 原型值 1 1800 100 24 模型值 0.022 1200.00 2.22 24 试验值 0.025 1200 4 25
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表 7 衬砌模型材料参数
Table 7. Material parameters of lining model
弹性模量/GPa 密度/(kg·m−3) 抗压强度/MPa 衬砌 原型值 32.5 2.3 26 模型值 0.72 1.53 0.58 试验型 1.16 1.48 1.18
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表 8 基于加速度时程计算的μ值
Table 8. μ-value distribution calculated based on acceleration time histories
偏差 PGA/g 0.1 0.2 0.3 0.4 μ5/3/% 11.76 12.73 10.75 11.00
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表 9 H=135 cm时各测点加速度峰值表
Table 9. Peak acceleration at measurement points at H=135 cm
工况 下盘 破碎带 上盘 A7 A2 A8 0.1 g 0.21 0.30 0.26 0.4 g 0.67 0.82 0.70
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表 10 H=170 cm时各测点加速度峰值表
Table 10. Peak acceleration at measurement points at H=170 cm
工况 下盘 破碎带 上盘 A9 A10 A3 A11 A12 0.1 g 0.20 0.23 0.22 0.23 0.23 0.4 g 0.61 0.67 0.68 0.71 0.64
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表 11 PGA为0.4 g时错动位移与应力降
Table 11. Misalignment displacement and stress drop at 0.4 g
项目 错动位移/cm 应力降/MPa u2 u3 u4 Δσ（U4-U3） Δσ（U3-U2） 试验 2.53 3.00 3.43 0.542 0.557 理论 2.42 2.8 3.17 0.508 0.560 相对差值/% 4.5 7.1 8.2 6.7 0.5
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