泥塑文物历史悠久、价值高，天津独乐寺山门天王像是辽代木骨泥塑的代表，但因处于京津冀地震带且已出现一定破损，对其进行抗震分析和损伤诊断十分紧迫。本研究从泥塑构造和泥塑土材料力学性能角度出发，探究天王像抗震性能，涵盖天王像构造、粗泥层材料性能、本构模型、抗震稳定性分析等方面，亦为塑像修复和其他泥塑文物保护提供参考。主要研究如下：

（1）通过现场调研与多种技术手段，明确了独乐寺天王像的历史沿革、形制构造、文物价值及破损状况。利用三维激光扫描技术，采用华测导航公司手持式GEO SLAM三维激光扫描仪，以封闭路径对天王像进行扫描，获取分辨率达2mm、近330万个孤立点组成的点云数据，经处理得到多边形拟合模型，并精准还原天王像外部几何特征。运用以加速器为射线源的 X 射线探测技术获取内部木骨数据，虽因结构复杂等因素导致部分成像受限，但仍大致勾勒出主要支撑结构形状，获取木骨走向等信息，最后组合形成天王像的几何模型供后期的抗震评估。

（2）对天王像粗泥层掉落残块进行分析，采用扫描电镜、悬浮沉淀法、粒径分析以及 XRD 分析等多种方法，确定粗泥层由土、砂和麦秆纤维组成，其中土占比57.05%，砂占比36.21%，纤维占比6.74%。对比残块土与当地土，发现两者粒径曲线相似，矿物成分相近，证实了当地土适合作为后续试验材料。按所得比例制得样品后，通过无侧限抗压试验和巴西劈裂试验，研究粗泥层在不同应力状态下的力学行为。在无侧限抗压试验中，发现粗泥试样呈现塑性破坏特征，其平均抗压强度为3.54MPa，平均弹性模量为189.57MPa，在巴西劈裂试验中表明，测得粗泥平均抗拉强度约为0.28MPa。

（3）基于粗泥层材料的力学性能，构建粗泥层材料弹塑性损伤本构模型。该材料在受压和受拉时应力-应变关系不同，受压时分弹性、弹塑性和破坏三个阶段，受拉时分弹性、裂缝出现和发展阶段。采用ABAQUS的塑性损伤模型，基于连续性、均匀性、小变形和各向同性假设，引入损伤因子描述材料在拉伸和压缩过程中的刚度退化现象。通过能量法则计算损伤因子，考虑材料在拉压不同状态下的力学特性差异，引入受拉刚度恢复系数和受压刚度恢复系数。经拟合计算，得到材料塑性状态时损伤因子等相关参数，绘制出拉压损伤关系图，验证了模型的有效性，为天王像有限元抗震性能研究提供可靠的计算参数和本构模型。

（4）运用Hypermesh和ABAQUS软件建立天王像有限元模型，考虑其表面拓扑关系复杂的特点，选用四面体单元进行网格划分，确定合适的网格种子尺寸，生成四面体实体网格单元。综合室内试验、现场踏勘和相关文献资料，考虑天王像残损情况，确定模型材料物理性能参数，利用ABAQUS软件进行模态分析，得到天王像前六阶固有频率、自振周期以及振型。依据相关规范，结合场地情况，选用 El-Centro 波、Taft 波、唐山波三条地震波，在设防烈度为8度的背景下，对地震波加速度时程最大值进行调幅处理，截取前15秒用于地震时程分析。结果表明，不同地震波对天王像破坏程度不同，天王像主要受拉损伤破坏，7度小震调幅时就可能出现损伤，8度中震调幅时存在破坏甚至有可能倒塌。位移反应方面，腿部、手臂等部位位移明显；应力集中主要出现在腿部、颈部及与木骨连接部位；损伤多由腿部单元失效引发，其中Taft波对天王像的破坏最为严重。

（5）基于天王像抗震计算结果从材料增强、结构加固和隔震减震三方面对天王像提供可行的抗震加固方法。认为可以对天王像泥塑部分注入特殊修复材料，对内部木骨进行防腐处理；在不影响外观和文物价值的前提下，增加辅助支撑结构，检查修复拉铁构造。并可以在基础部分设置隔震层，安装隔震装置，在内部或表面安装减震装置，施工时遵循文物保护原则，避免对天王像造成二次损伤。

Clay sculptures have a long history and high value. The Heavenly King Statues at the entrance of Dule Temple in Tianjin is a representative example of wooden framework and clay sculpture from the Liao Dynasty. However, due to its location in the Beijing-Tianjin-Hebei seismic zone and the presence of certain damage, it is urgent to conduct seismic analysis and damage diagnosis. This study explores the seismic performance of the Heavenly King Statues from the perspectives of clay structure and mechanical properties of clay materials. It covers aspects such as the construction of the statue, material properties of coarse clay layers, constitutive models, and seismic stability analysis. The findings also provide references for the restoration of the statue and other clay sculptures. The main research points are as follows:

 (1) Through on-site research and various technical means, the historical evolution, structural composition, cultural value, and damage status of the Dule Temple Heavenly King Statue have been clarified. Using 3D laser scanning technology, a handheld GEO SLAM 3D laser scanner from Huace Navigation Company was employed to scan the statue along a closed path, obtaining point cloud data with a resolution of 2mm and nearly 3.3 million isolated points. After processing, a polygonal fitting model was generated, accurately reconstructing the external geometric features of the statue. X-ray detection technology using an accelerator as the radiation source was applied to obtain internal wooden bone data. Although some imaging was limited due to structural complexity, it still roughly outlined the main supporting structure shapes and obtained information on the direction of the wooden bones. Finally, these elements were combined to form a geometric model of the Heavenly King Statue for subsequent seismic assessment.

(2) The analysis of residual fragments from the coarse mud layer of the Heavenly King statue involved multiple methods, including scanning electron microscopy, suspension sedimentation, particle size analysis, and XRD analysis. These methods confirmed that the coarse mud layer consists of soil, sand, and wheat straw fibers, with soil accounting for 57.05%, sand for 36.21%, and fibers for 6.74%. Comparing the soil from the residual fragments with local soil, it was found that their particle size curves were similar and their mineral compositions were comparable, confirming that the local soil is suitable as a material for subsequent experiments. After preparing samples according to the obtained proportions, unconfined compressive strength tests and Brazilian split tests were conducted to study the mechanical behavior of the coarse mud layer under different stress conditions. In the unconfined compressive strength test, the coarse mud sample exhibited plastic failure characteristics, with an average compressive strength of 3.54MPa and an average elastic modulus of 189.57MPa. The Brazilian split test revealed that the average tensile strength of the coarse mud was approximately 0.28MPa.

(3) Based on the mechanical properties of coarse mud layer materials, a viscoplastic damage constitutive model for these materials is constructed. The stress-strain relationship varies under compression and tension. Under compression, the material undergoes three stages: elastic, viscoplastic, and failure. Under tension, it progresses through an elastic stage and a crack initiation and propagation phase. The plastic damage model from ABAQUS is adopted, assuming continuity, uniformity, small deformation, and isotropy. A damage factor is introduced to describe the stiffness degradation during tension and compression. The damage factor is calculated using the energy principle, taking into account the differences in mechanical properties under different states of tension and compression. Tensile stiffness recovery coefficients and compressive stiffness recovery coefficients are introduced. After fitting calculations, parameters related to the damage factor under plastic conditions are obtained, and a tension-compression damage relationship diagram is plotted. This validates the effectiveness of the model, providing reliable computational parameters and constitutive models for the seismic performance study of the Heavenly King Statue finite element.

(4) Using Hypermesh and ABAQUS software to establish a finite element model of the Heavenly King statue, considering its complex surface topological relationships, tetrahedral elements were selected for meshing, and appropriate grid seed sizes were determined to generate tetrahedral solid mesh units. Based on indoor tests, field surveys, and relevant literature, taking into account the damage condition of the Heavenly King statue, material physical properties parameters were established, and modal analysis was conducted using ABAQUS software to obtain the first six natural frequencies, self-vibration periods, and modes of vibration of the Heavenly King statue. According to relevant standards and site conditions, three types of seismic waves: El-Centro wave, Taft wave, and Tangshan wave were used. Under a design intensity of 8 degrees, the maximum acceleration time history of the seismic waves was amplitude-modulated, with the first 15 seconds used for seismic time-history analysis. The results show that different seismic waves cause varying degrees of damage to the Heavenly King statue, primarily through tensile damage. Damage can occur at a small magnitude of 7 when the amplitude is adjusted, and even collapse may happen at a moderate magnitude of 8 when the amplitude is adjusted. In terms of displacement response, significant displacements are observed in the legs and arms; stress concentration mainly occurs in the legs, neck, and areas connected to the wooden framework. Most damage is caused by the failure of the leg units, with the Taft wave causing the most severe damage to the Heavenly King statue.

(5) Based on the seismic calculation results of the Heavenly King statue, feasible seismic reinforcement methods are provided from three aspects: material enhancement, structural reinforcement, and seismic isolation. It is suggested that special restoration materials can be injected into the clay parts of the Heavenly King statue, and anti-corrosion treatment can be applied to the internal wooden framework; auxiliary support structures can be added without affecting its appearance or cultural value, and the iron tie structure should be inspected and repaired. Additionally, a seismic isolation layer can be set up in the foundation, and seismic isolation devices can be installed, as well as vibration reduction devices on the inside or surface. Construction should follow the principles of cultural relic protection to avoid causing secondary damage to the Heavenly King statue.

[1]王进玉.中国古代石窟寺彩塑的种类、分布及其彩绘研究[C]//云冈石窟研究院.2005年云冈国际学术研讨会论文集（保护卷）.文物出版社,2005,11.

[2]刘雪.晋北地区韦陀塑像遗存研究[D].山西大学,2023.

[3]高燕,杨秋颖,张芳等.陕西蓝田水陆庵壁塑制作工艺与结构稳定性调查研究[J].文物鉴定与鉴赏, 2023, 16, 68-71.

[4]张铁山,彭金章.敦煌莫高窟北区B77窟出土木骨上的回鹘文题记研究[J].敦煌学辑刊,2018(02):37-43.

[5]穆静,康小花.陇南石窟群雕塑材质与造型手法研究[J].美术大观, 2014, 5, 65.

[6]成军鹏.甘肃武山木梯寺石窟调查与研究[D].西北师范大学,2022.

[7]杨传宇.克孜尔和库木吐喇石窟内现存泥塑的制作方法[J].明日风尚, 2017, 14, 307-308.

[8]王晨,陈钧锴.场景根植与群体生产：从泥塑技艺演变看传统工艺传承[J].艺术百家, 2023, 39(5), 38-45.

[9]马赞峰,汪万福,唐伟,等.不同土沙比壁画地仗性能测试[J]. 敦煌研究, 2009, 6, 36-39.

[10]Luczanits C. Buddhist sculpture in Clay-Early Western Himalayan Art late 10th to 13th Centuries[M]. Serindia Publications, 2004.

[11]杜建国,谢冰,刘洪丽,等. 莫高窟壁画地仗试件物理力学性能分析[J]. 文物保护与考古科学, 2016, 28(2), 38-43.

[12]赵凡,王冲,陈尔新,等. 四川广汉龙居寺中殿壁画制作材料与工艺研究[J]. 文物保护与考古科学, 2020, 32(4), 8-15.

[13]李娜,苏伯民,冯雅琪,等. 山西大同观音堂观音殿壁画制作材料与工艺分析[J]. 敦煌研究, 2021, 1, 128-136.

[14]张亚旭. 莫高窟196窟壁画保存现状研究[D]. 西北大学, 2018.

[15]胡可佳,白崇斌,马琳燕,等. 陕西安康紫阳北五省会馆壁画制作工艺研究[J]. 敦煌研究, 2015, 1, 124-132.

[16]陶忠,潘兴庆,潘文,等. 云南农村民居土坯墙单块土坯力学特性试验研究[J]. 工程抗震与加固改造, 2008, 30(1), 99-104.

[17]吴锋,李钢,贾金青,等. 传统土坯抗压强度的试验研究[J]. 工程抗震与加固改造, 2012, 34(5), 56-61.

[18]吴锋. 土坯房屋基本力学和抗震性能的试验研究[D]. 大连理工大学,2013.

[19]阿肯江·托呼提,沙吾列提·拜开依,曹耿. 土坯砌体单轴受压本构模型研究[J]. 工程力学, 2012, 29(12), 295-301, 315.

[20]曹耿. 土坯砌体墙抗震性能研究[D]. 新疆大学, 2011.

[21]外力·艾比不拉,阿肯江·托呼提,哈斯亚提·哈里丁,等. 植物纤维单块土坯抗压试验研究[J]. 建筑科学, 2012, 28(5), 61-64.

[22]王毅红,张建雄,兰官奇,等. 标准试件、土坯及土坯砌体强度关系研究[J]. 建筑科学, 2020, 36(7), 60-66.

[23]Vargas J, Bariola J, Blondet M. Seismic strength of adobe masonry[J]. Materials and Structures, 1986, 19(4), 253-258.

[24]B. V Venkatarama Reddy, Ajay Gupta. Strength and elastic properties of stabilized mud block masonry using cement-soil mortars[J]. Journal of Materials in Civil engineering, 2006, 18(3), 472-476.

[25]B. V. Venkatarama Reddy, Richardson Lal, K. S. Nanjunda Rao. Influence of Joint Thickness and Mortar-Block Elastic Properties on the Strength and Stresses Developed in Soil-Cement Block Masonry[J]. Journal of Materials in Civil engineering, 2009, 21(10), 535-542.

[26]Davorin Penava, Vasilis Sarhosis, Ivica Kožar, Ivica Guljaš, Contribution of RC columns and masonry wall to the shear resistance of masonry infilled RC frames containing different in size window and door openings[J], Engineering Structures, 2018, 172, 105-130.

[27]Torelli, Giacomo, D'Ayala, Dina, Betti, Michele, Bartoli, Gianni, Analytical and numerical seismic assessment of heritage masonry towers[J], Bulletin of Earthquake Engineering, 2020, 18, 15-20.

[28]Poiani, Minh, Samir Khatir, Magd Abdel Wahab, Thanh Cuong-Le, A concrete damage plasticity model for predicting the effects of compressive high-strength concrete under static and dynamic loads[J], Journal of Building Engineering, 2021, 44, 103-139.

[29]Papadopoulos, K., Vintzileou, E., Psycharis, I.N. Finite element analysis of the seismic response of ancient columns[J]. Earthquake Eng. Struct. Dynam, 2019, 48(13), 1432-1450.

[30]Zambas, C. Study for the restoration of the parthenon[M]. Committee for the Conservation of the Acropolis Monuments (in Greek), 2004.

[31]Masi F, Stefanou I, Vannucci P. A study on the effects of an explosion in the Pantheon of Rome[J]. Engineering structures, 2018, 164, 259-273.

[32]Gu X, Zhang Q, Huang D, et al. Wave dispersion analysis and simulation method for concrete SHPB test in peridynamics[J]. Engineering Fracture Mechanics, 2016, 160, 124-137.

[33]Arbace L, Sonnino E, Callieri M, et al. Innovative uses of 3D digital technologies to assist the restoration of a fragmented terracotta statue[J]. Journal of Cultural Heritage, 2013, 14(4), 332-345.

[34]葛静. 石砌结构抗震性能与加固技术研究[D]. 兰州理工大学, 2010.

[35]李秋蓉. 藏式石木结构像的抗震性能及设防对策[D]. 西南科技大学, 2015.

[36]Bagnéris M, Cherblanc F, Bromblet P, et al. A complete methodology for the mechanical diagnosis of statue provided by innovative uses of 3D model. Application to the imperial marble statue of Alba-la-Romaine (France)[J]. Journal of Cultural Heritage, 2017, 28, 109-116.

[37]欧阳东.探访蓟县千年名刹独乐寺[J].建筑, 2020, 20, 42-43.

[38]丁垚.发现独乐寺[J].建筑学报, 2013, 5, 1-9.

[39]王南.规矩方圆，度像构屋——蓟县独乐寺观音阁、山门及塑像之构图比例探析[J].建筑史, 2018, 1, 103-125.

[40]郭宏,李最雄,宋大康等.敦煌莫高窟壁画酥碱病害机理研究之一[J].敦煌研究, 1998, 3, 153-163,188.

[41]冯圆媛.奉国寺大雄殿元代壁画颜料层起甲病害研究[D].西北大学, 2020.

[42]白琳.三维扫描技术在博物馆中的应用[J].文物鉴定与鉴赏, 2025, 6, 125-128.

[43]徐子鹏.三维激光扫描建筑物点云特征提取方法[J].科学技术创新, 2025, 6, 65-68.

[44]杨雪,王龙帅,殷文彦,等.点云建模技术在部件级古建筑构件三维可视化中的应用[J].北京测绘, 2025, 39(1), 54-60.

[45]赵利民,王瀚斌,姜涛,等.三维多站点云拼接新技术在文物保护中的应用[J].北京测绘, 2024, 38(9), 1295-1299.

[46]鲁冬冬,邹进贵.三维激光点云的降噪算法对比研究[J].测绘通报, 2019, S2, 102-105.

[47]张雪雁,段佩权,刘瀚文,等.X射线技术在故宫博物院藏景泰款铜胎掐丝珐琅研究中的应用[J].核技术, 2025, 48(1), 53-61.

[48]姚强,朱晓林,朱宇宏.微区X射线荧光光谱分析技术研究进展[J].计量与测试技术, 2025, 51(1), 30-32.

[49]陈彪,朱玥玮,谭静,等.X射线衍射技术在纸张、纸质文物分析和保护研究中的应用[J].复旦学报(自然科学版), 2024, 63(5), 567-573.

[50]耿焕然,李晓静.X射线检测分析技术在文物保护修复中的应用[J].理化检验-物理分册, 2024, 60(9), 74-78.

[51]王旭艳.现代仪器分析方法在文物保护和文物研究中的应用[J].化学世界,2024, 65(4), 205-218.

[52]秦立科,王猛,贾甲,等.独乐寺观音阁辽代十一面观音像的材质分析[J].文物保护与考古科学, 2024, 36(2), 119-127.

[53]秦立科,周效丞,孔德翊,等.温度循环下壁画地仗层与支撑体接触面力学性能[J].西安科技大学学报, 2025, 45(1), 153-160.

[54]中华人民共和国住房和城乡建设部.土工试验方法标准:GB/T 50123-2019[S].中国计划出版社, 2019.

[55]侯云瀚.高温作用花岗岩巴西劈裂及断裂韧度试验研究[D].重庆交通大学, 2024.

[56]侯鹏,高峰,杨玉贵等. 黑色页岩巴西劈裂破坏的层理效应研究及能量分析[J].岩土工程学报, 2016, 38(5), 930-937.

[57]苏承东,张盛,唐旭. 砂岩巴西劈裂疲劳破坏过程中变形与强度特征的试验研究[J].岩石力学与工程学报, 2013, 32(1), 41-48.

[58]刘港平.应力-应变曲线系数与塑性损伤因子无量纲计算模型研究[D].湖南大学, 2023.

[59]姜晨.岩石塑性损伤模型理论研究与工程应用[D].西安石油大学, 2020.

[60]江一博.钙质砂颗粒破碎弹塑性损伤本构模型构建及验证[D].湘潭大学, 2020.

[61]Lee J, Fenves G L. Plastic-Damage Model for Cyclic Loading of Concrete Structures[J]. Journal of Engineering Mechanics, 1998, 124(8), 892-900.

[62]Lubliner J, Oliver J, Oller S, et al. A Plastic-Damage Model for Concrete[J]. International Journal of Solids and Structures, 1989, 25(3), 299-329.

[63]Damian Kachlakev, Thomas Miller, et al. Finite Element Modeling of Reinforced Concrete Structures Strengthened with FRP Laminates[R]. Washington DC, 2001.

[64]建筑抗震设计规范GB50011-2010[M].中国建筑工业出版社,2010.