地震研究

工程振动对馆藏大型石造像文物的影响评估与减振控制

(1.青岛理工大学土木工程学院,山东青岛 266033; 2.山东建筑大学,山东济南 250010; 3.青岛市博物馆,山东青岛 266061; 4.青岛鼎泰常容创新科技有限公司,山东青岛 266799)

Assessment of the Impact of Engineering Vibrations on the Large Stone Statue in Museum and Anti-vibration Control

XU Weixiao¹,HAN Donglin¹,YU Dehu²,QIU Yusheng³,QIU Lingling⁴

(1.School of Civil Engineering,Qingdao University of Technology,Qingdao 266033,Shandong,China)(2.Shandong Jianzhu University,Jinan 250010,Shandong,China)(3.Qingdao Museum,Qingdao 266061,Shandong,China)(4.Qingdao Dingtai Changrong Innovation Technology Co.,Ltd.,Qingdao 266799,Shandong,China)

Keywords：stone statue relics; engineering vibrations; vibration response; protection of cultural relics; the Finite Element Analysis

DOI: 10.20015/j.cnki.ISSN1000-0666.2025.0048

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为了解决在实际施工活动中工程振动对馆藏石造像文物的潜在危胁,基于ABAQUS有限元分析,建立了青岛市博物馆4尊大型石造像的有限元模型。对石造像有限元模型基底施加实测施工振动,通过有限元逐步增量动力时程分析,结合石造像抗拉强度本构关系、长期振动监测,得到合理的石造像文物振动安全阈值。提出大型石造像文物的数值建模方法,开展了修缮材料水硬性石灰抗拉强度试验。结果表明:4尊石造像的脖颈处、足部为振动敏感区域,可采用有针对性的保护措施。右侧石佛造像因其体量及本构参数的不同,对工程振动最为敏感,建议工程振动安全阈值设为1.5 mm/s。

To address the possible influence to the four stone Buddha statues in the Qingdao Museum brought by construction activities,we use the Finite Element Analysis software,ABAQUS,to build the Finite Element models of these statues. Then we apply the measured vibration to the bases of the Finite Element models,and do incremental dynamic analysis. Referring to the tensile-strength constitutive relations of the statues and the results from their long-term vibration monitoring,we propose vibration safety threshold for these stone statues. In addition,we put forward a numerical modeling method for large-scale stone statues,and carry out a tensile-strength test of hydraulic lime,a kind of restoration material. The results indicate that the neck and the feet of the stone Buddha statues are vulnerable to vibration,and need special protective measures. The Buddha statue on the right side is most sensitive to engineering vibration due to its unique volume and special constitutive parameters. The recommended safety threshold of engineering vibration for this statue is 1.5 mm/s.

引言
1 石造像文物及其工程概况
2 典型施工工况振动测试
3 石造像有限元模型建立
4 模态分析
5 石造像模型逐步增量动力时程分析
6 结论

图1 青岛市博物馆馆藏石佛造像(a)和菩萨造像(b)示意图<br/>Fig.1 Photos of stone Buddha statues(a)and Bodhisattva statues(b)in Qingdao Museum

图1 青岛市博物馆馆藏石佛造像(a)和菩萨造像(b)示意图
Fig.1 Photos of stone Buddha statues(a)and Bodhisattva statues(b)in Qingdao Museum

图2 石佛造像(a)和菩萨造像(b)病害图<br/>Fig.2 Distribution of disease of stone Buddha statues(a)and Bodhisattva statues(b)

图2 石佛造像(a)和菩萨造像(b)病害图
Fig.2 Distribution of disease of stone Buddha statues(a)and Bodhisattva statues(b)

图3 各工况施工现场情况<br/>Fig.3 Construction sites of different working conditions

图3 各工况施工现场情况
Fig.3 Construction sites of different working conditions

表1 龙门石窟力学参数<br/>Tab.1 Mechanical parameters of the rock mass of the Longmen Grottoes

表1 龙门石窟力学参数
Tab.1 Mechanical parameters of the rock mass of the Longmen Grottoes

图4 各工况施工水平向(a)和垂向(b)振动速度时频曲线<br/>Fig.4 Time-frequency curves of vibration velocity in horizontal(a)and vertical(b) directions under various working conditions

图4 各工况施工水平向(a)和垂向(b)振动速度时频曲线
Fig.4 Time-frequency curves of vibration velocity in horizontal(a)and vertical(b) directions under various working conditions

图5 组合工况施工水平向(a)和垂向(b)振动速度时频域曲线<br/>Fig.5 Time-frequency cruves of vibration velocity in horizontal(a)and vertical(b) directions under working conditions

图5 组合工况施工水平向(a)和垂向(b)振动速度时频域曲线
Fig.5 Time-frequency cruves of vibration velocity in horizontal(a)and vertical(b) directions under working conditions

图6 左侧(a)和右侧(b)石佛造像、大势至(c)和观世音(d)菩萨造像有限元模型<br/>Fig.6 Finite element model of stone Buddha statues on the left(a)and right(b)side,Mahasthamaprapta(c)and Arya Avalokiteshvar(d)Bodhisattva statues

图6 左侧(a)和右侧(b)石佛造像、大势至(c)和观世音(d)菩萨造像有限元模型
Fig.6 Finite element model of stone Buddha statues on the left(a)and right(b)side,Mahasthamaprapta(c)and Arya Avalokiteshvar(d)Bodhisattva statues

图7 左侧(a)和右侧(b)石佛造像、大势至(c)和观世音(d)菩萨造像弹性波速测点布置<br/>Fig.7 Distribution of the test points for the elastic wave around stone Buddha statues on the left(a)and right(b)side,Mahasthamaprapta(c)and Arya Avalokiteshvar(d)Bodhisattva statues

图7 左侧(a)和右侧(b)石佛造像、大势至(c)和观世音(d)菩萨造像弹性波速测点布置
Fig.7 Distribution of the test points for the elastic wave around stone Buddha statues on the left(a)and right(b)side,Mahasthamaprapta(c)and Arya Avalokiteshvar(d)Bodhisattva statues

图8 4尊石造像弹性波波速测试结果<br/>Fig.8 Results from the measurement of the elastic wave velocity for four stone Buddha statues

图8 4尊石造像弹性波波速测试结果
Fig.8 Results from the measurement of the elastic wave velocity for four stone Buddha statues

表2 水硬性石灰砂浆劈裂抗拉强度试验结果<br/>Tab.2 Results from the split tensile strength test of hydraulic lime mortar

表2 水硬性石灰砂浆劈裂抗拉强度试验结果
Tab.2 Results from the split tensile strength test of hydraulic lime mortar

图9 4尊石造像拉应力-应变关系<br/>Fig.9 Tensile stress-strain of four stone Buddha statues

图9 4尊石造像拉应力-应变关系
Fig.9 Tensile stress-strain of four stone Buddha statues

图10 石佛造像自振频率测点布置<br/>Fig.10 Measuring points for the natural frequency of the stone Buddha statues

图10 石佛造像自振频率测点布置
Fig.10 Measuring points for the natural frequency of the stone Buddha statues

图11 左侧(a)和右侧(b)石佛造像1阶振型<br/>Fig.11 The first-order modes for the stone Buddha statues on the left(a)and right(b)side

图11 左侧(a)和右侧(b)石佛造像1阶振型
Fig.11 The first-order modes for the stone Buddha statues on the left(a)and right(b)side

图12 左侧(a)和右侧(b)石佛造像沿面向自振频率实测结果<br/>Fig.12 Measured facing natural frequencies of stone Buddha statues on the left(a)and right(b)side

图12 左侧(a)和右侧(b)石佛造像沿面向自振频率实测结果
Fig.12 Measured facing natural frequencies of stone Buddha statues on the left(a)and right(b)side

图13 左侧(a)和右侧(b)石佛造像、大势至(c)和观世音(d)菩萨造像应力云图<br/>Fig.13 Stress nephograms of the stone Buddha statues on the left(a)and right(b)side,Mahasthamaprapta(c)and Arya Avalokiteshvar(d)Bodhisattva Statues

图13 左侧(a)和右侧(b)石佛造像、大势至(c)和观世音(d)菩萨造像应力云图
Fig.13 Stress nephograms of the stone Buddha statues on the left(a)and right(b)side,Mahasthamaprapta(c)and Arya Avalokiteshvar(d)Bodhisattva Statues

图14 左侧(a)和右侧(b)石佛造像、大势至(c)和观世音(d)菩萨造像输入强度-最大拉应力关系<br/>Fig.14 The relationship between the input intensity and the maximum tensile stress of the stone Buddha statues on the left(a)and right(b)side,Mahasthamaprapta(c)and Arya Avalokiteshvar(d)Bodhisattva Statues[JZ)]

图14 左侧(a)和右侧(b)石佛造像、大势至(c)和观世音(d)菩萨造像输入强度-最大拉应力关系
Fig.14 The relationship between the input intensity and the maximum tensile stress of the stone Buddha statues on the left(a)and right(b)side,Mahasthamaprapta(c)and Arya Avalokiteshvar(d)Bodhisattva Statues[JZ)]

图15 冲击钻拆除现场情况<br/>Fig.15 Demolition of the jointing structure between the arch and the main structure of the Museum

图15 冲击钻拆除现场情况
Fig.15 Demolition of the jointing structure between the arch and the main structure of the Museum

图16 冲击钻拆除竖向(a)、水平向(b)振动时程<br/>Fig.16 Time-history of the vibration caused by the impact drill during the demolition:vertical diretion(a)and horizontal direction(b)

图16 冲击钻拆除竖向(a)、水平向(b)振动时程
Fig.16 Time-history of the vibration caused by the impact drill during the demolition:vertical diretion(a)and horizontal direction(b)