Seismic Performance Assessment of Terracotta Warriors Based on Fine Finite Elements
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摘要: 为了分析兵马俑的地震响应情况并探讨不同因素对兵马俑抗震性能的影响，对武士俑进行建模与有限元计算。通过时程分析确定兵马俑的运动状态和启动滑移、摇晃的地面峰值加速度临界值，并以刚体运动理论进行对比，得到了摩擦系数、重心高度、地震大小、地震方向对兵马俑的抗震响应影响。结果表明，兵马俑在地震中会发生静止、滑移、滑移摇晃、摇晃或倾覆5种运动状态。随着摩擦系数和地震加速度增大、宽高比降低，兵马俑更容易在地震中发生摇晃或者倾覆，反之则更倾向于滑移或静止。当兵马俑发生倾覆时，颈部与腿部将发生断裂破坏，其余运动状态材料均未出现失效。俑的前后向最易失稳，该方向宽高比也最小。兵马俑地震响应的数值模拟结果与刚体理论分析基本一致，可以将兵马俑看做刚体并采用理论公式进行快速评估。Abstract: In order to analyse the seismic response of the Terracotta Warriors and explore the influence of different factors on the seismic performance of the Terracotta Warriors, the warrior terracotta warriors were modelled and finite element computed. The motion state of the terracotta warrior and the critical value of the peak ground acceleration for initiating slip and shake are determined by time course analysis, and the effects of friction coefficient, height of the centre of gravity, magnitude of the earthquake, and direction of the earthquake on the seismic response of the terracotta warrior are obtained by comparing them with the theory of rigid-body motion. The results show that the Terracotta Warriors undergo five states of motion in earthquakes: rest, slide, slide-rock, rock and topple. As the friction coefficient and seismic acceleration increase, and the aspect ratio decreases, the terracotta warriors are more likely to rock or topple in an earthquake, and vice versa, they are more inclined to slide or rest. When the Terracotta Warriors topple over, the neck and legs would be fractured and damaged, and the rest of the kinematic state materials did not fail. The front-to-back direction of the terracotta is the most vulnerable to instability, and the aspect ratio in this direction is also the smallest. The numerical simulation results of the seismic response of the Terracotta Warriors are basically consistent with the theoretical analysis of the rigid body, and the Terracotta Warriors can be regarded as a rigid body and quickly evaluated by using the theoretical formulas.
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图 1 泥条盘筑法制作兵马俑躯干
Figure 1. The trunk of the terracotta warriors is made by clay strips
图 7 兵马俑模型M1地震响应情况
Figure 7. Earthquake response situation of the terracotta Warriors model M1
图 8 兵马俑模型M2地震响应情况
Figure 8. Earthquake response situation of the terracotta Warriors model M2
图 9 摩擦系数为0.1时模型M1的地震波加载结构响应
Figure 9. Failure sign of the seismic wave loading structure of model M1 when the friction coefficient is 0.1
图 10 摩擦系数为0.1时模型M1的应力剖面图
Figure 10. Stress profile of model M1 with a friction coefficient of 0.1
图 11 摩擦系数为0.55时模型M1的地震波加载结构响应
Figure 11. Failure sign of the seismic wave loading structure of model M1 when the friction coefficient is 0.55
图 12 不同摩擦系数下模型M1的位移时程图像
Figure 12. Displacement time-course image of the model M1 with different friction coefficients
图 13 不同摩擦系数下兵马俑最大安全地震峰值加速度地震响应
Figure 13. Peak acceleration seismic response of terracotta warriors under different friction coefficients
图 15 宽高比为0.15和0.25时的兵马俑地震响应方式的判据区域划分
Figure 15. Regional division of the seismic response mode of terracotta warriors with aspect ratio of 0.15 and 0.25
表 1 两个模型的几何参数
Table 1. The geometric parameters of the two models
模型 总高度/cm 实心部分高度/cm 重心离地高度/cm 网格数量 M1 186.13 25.40 73.028 404779 M2 186.13 45.21 78.173 668570 
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表 2 模型的计算参数
Table 2. The calculation parameters of the models
杨氏模量/MPa 密度/（kg·m−3） 泊松比 极限抗拉强度/MPa 1000 1900 0.2 11.5
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表 3 模型的宽高比
Table 3. The aspect ratio calculation of the model
模型 方向 宽高比 M1（实体高度最小） 0/180° 0.28 45°/225° 0.34 90°/270° 0.15 135°/315° 0.32 M2（实体高度最大） 0/180° 0.26 45°/225° 0.33 90°/270° 0.16 135°/315° 0.30
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