Analysis of the composite mechanical properties of the substructure of a masonry pagoda
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摘要: 為研究古塔子結構的受力性能，設計制作了3件不同樓層的子結構縮尺模型試件，進行低周反復加載試驗，觀察試件的開裂、變形及破壞現象；建立數值模型進行計算，得到了試驗荷載作用下各試件的等效塑性應變、荷載?位移曲線，將計算結果與試驗結果進行對比，分析豎向壓應力對古塔砌體抗震性能的影響。結果表明，特征荷載的計算值相對試驗值的誤差均小于21%，等效塑性應變的分布與試件開裂破壞區域一致；當豎向壓力保持恒定時，隨著水平荷載的增大，塔體沿砌筑縫逐漸開裂破壞，裂縫寬度亦隨之增大，在塔體洞口周圍的破壞更為明顯，且試件殘余變形增大；隨著壓剪比的增大，古塔砌體開裂破壞的范圍減小，抗剪承載力、剛度以及耗能能力均有所提高，但延性和變形能力略有降低。研究結果為磚石古塔建筑結構損傷及抗震能力評定提供參考。Abstract: Brick wall tubes, a popular form of ancient masonry pagoda, can be seen as a spatial lateral force resistance system. The masonry of the ancient pagoda is a case of compression and shear developed due to earthquakes. This composite compression and shear behavior is one of the key issues in the seismic capacity of masonry tube structure. In order to study the mechanical properties of the substructure of masonry pagodas, three sub-structural models were designed and constructed. Low cyclic loadings tests were conducted on the models and the crack, deformation, and failure phenomena were surveyed during the loading process. Simulation models were then developed for calculation, and results were obtained about the equivalent strain and load-displacement curve. Comparing the calculated results with the experimental results, the effects of vertical compressive stress on the masonry in the ancient tower were analyzed. Results showed that the error was less than 21% for the calculated value of the characteristic load relative to the test value. The distribution of equivalent plastic strain was consistent with the crack failure area of the specimens. When the vertical pressure remained constant with increasing horizontal load, the tower body gradually cracked, damage occurred along the masonry joints, and the width of cracks also increased. The failures around the structure opening were more obvious, and the residual deformation of specimens increased. With the increase in the ratio of compression to shear, the range of cracking and damage to the masonry of the ancient tower decreased, while shear bearing capacity, stiffness, and energy dissipation capacity were increased. However, ductility and deformation capacity slightly decreased. These results can provide references for the assessment to structural damage and seismic capability of ancient masonry pagodas.
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圖 1 古塔原型及其子結構模型。（a）興教寺玄奘塔；（b）子結構模型
Figure 1. Prototype of ancient pagoda and its substructure model: (a) Xuanzang Pagoda in Xingjiao Temple; (b) substructure model
圖 2 子結構試件尺寸（單位：m）。（a）頂部結構；（b）中部結構；（c）底部結構
Figure 2. Dimensions of substructure specimens (Unit: m): (a) top structure; (b) central structure; (c) bottom structure
圖 4 測點布置示意圖。（a）南立面；（b）東立面；（c）北立面
Figure 4. Loading test scheme: (a) south facade; (b) east facade; (c) west facade
圖 5 試件局部破壞。（a）加載初期開裂；（b）北立面X型裂縫；（c）磚塊脫落；（d）交叉貫通裂縫；（e）X型貫通裂縫；（f）南立面開裂錯層
Figure 5. Local failure of substructure specimens: (a) cracking at initial loading stage; (b) X-type crack in north facade; (c) brick fell off; (d) cross through fracture; (e) X-type through fracture; (f) cracking and staggered floor of south facade
圖 6 子結構試件壓剪比曲線。（a）T1試件；（b）T2試件；（c）T3試件
Figure 6. Compression-shear ratio curve of substructure specimen: (a) T1 specimen; (b) T2 specimen; (c) T3 specimen
圖 7 子結構試件滯回曲線。（a）T1試件；（b）T2試件；（c）T3試件
Figure 7. Hysteresis curve of substructure specimen: (a) T1 specimen; (b) T2 specimen; (c) T3 specimen
圖 11 應力?應變曲線。（a）灰漿試塊；（b）磚砌體試塊
Figure 11. Stress strain curve: (a) mortar test block; (b) brick masonry test block
圖 12 子結構試件模擬骨架曲線。（a）T1試件；（b）T2試件；（c）T3試件
Figure 12. Simulation skeleton curve of substructure specimen: (a) T1 specimen; (b) T2 specimen; (c) T3 specimen
圖 13 極限位移下子結構等效塑性應變云圖。（a）T1，10 kN，11 mm；（b）T1，20 kN，12 mm；（c）T2，10 kN，13 mm；（d）T2，20 kN，20 mm；（e）T3，20 kN，13 mm；（f）T3，30 kN，18 mm
Figure 13. Equivalent plastic strain nephogram of substructure at ultimate displacement: (a) T1，10 kN，11 mm; (b) T1，20 kN，12 mm; (c) T2 ，10 kN，13 mm; (d) T2，20 kN，20 mm; (e) T3，20 kN，13 mm; (f) T3，30 kN，18 mm
圖 14 荷載?位移曲線對比。（a）T1, 10 kN；（b）T1, 20 kN；（c）T2, 10 kN；（d）T2, 20 kN；（e）T3, 20 kN；（f）T3, 30 kN
Figure 14. Load-displacement curve comparison: (a) T1, 10 kN; (b) T1, 20 kN; (c) T2, 10 kN; (d) T2, 20 kN; (e) T3, 20 kN; (f) T3, 30 kN
表 1 試件特征點荷載值
Table 1. Load value of characteristic point of specimen
Specimen number Vertical pressure /kN Loading mode Critical load, $ {P_{\text{y}}} $/kN Peak load, $ {P_{\text{m}}} $/kN Limit load, $ {P_{\text{u}}} $/kN T1 10 Push（+） 3.82 4.32 3.96 Pull（?） 2.36 2.61 2.28 20 Push（+） 4.75 5.16 4.39 Pull（?） 3.76 4.13 3.18 T2 10 Push（+） 4.52 7.32 7.26 Pull（?） 2.22 2.19 1.89 20 Push（+） 7.85 9.04 6.47 Pull（?） 3.92 4.23 2.03 T3 20 Push（+） 5.13 7.37 6.43 Pull（?） 4.91 6.40 5.47 30 Push（+） 7.58 8.89 7.46 Pull（?） 7.01 7.45 5.68 
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表 2 試件特征點位移值與延性系數
Table 2. Displacement and ductility of specimen characteristic points
Specimen number Vertical pressure /kN Critical displacement, $ {\varDelta _{\rm{y}}} $/mm Peak displacement, $ {\varDelta _{\rm{m}}} $/mm Limit displacement, $ {\varDelta _{\rm{u}}} $/mm Ductility coefficient, $ \eta $ T1 10 5.02 7.99 11.02 2.20 20 5.99 7.92 11.92 1.99 T2 10 4.91 10.80 12.80 2.61 20 8.08 9.91 19.97 2.47 T3 20 10.05 8.99 12.98 2.58 30 7.05 10.02 17.94 2.54
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表 3 耗能及等效黏滯阻尼系數
Table 3. Energy consumption and equivalent viscous damping coefficient
Specimen number Vertical pressure/kN W/(kN·mm) ηe Crack Peak Limit Crack Peak Limit T1 10 8.75 15.89 34.32 0.090 0.091 0.104 20 14.72 22.18 45.42 0.092 0.095 0.115 T2 10 6.85 23.42 59.48 0.065 0.071 0.088 20 24.75 41.34 85.00 0.084 0.090 0.081 T3 20 14.45 31.93 77.35 0.092 0.082 0.091 30 25.12 42.42 118.26 0.078 0.075 0.087
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表 4 試驗與模擬峰值荷載對比
Table 4. Comparison of test and simulated peak load
Specimen number Vertical pressure /
kNTest value /
kNSimulated value /
kNError /
%T1 10 4.32 4.66 7.9 20 5.16 5.61 8.7 T2 10 7.32 6.94 5.5 20 9.04 7.99 11.6 T3 20 7.37 8.33 13.0 30 8.89 10.76 21.0
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