Numerical simulation on the influence of wall wood column defects on the safety of ancient building
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摘要:目的 墙体木柱作为木结构古建筑最重要的承重构件之一，容易出现裂纹、腐朽等缺陷，而各类缺陷会影响墙体木柱顺纹压应力的分布，导致其承载力降低，进而影响其安全性，直接威胁整个建筑的稳定性。因此，研究不同类型的缺陷对古建筑墙体木柱安全性影响是很有必要的。方法 首先建立了墙体木柱裂纹缺陷、腐朽缺陷以及复合缺陷几何模型，并定义了墙体木柱的受压安全性系数kc，然后使用Abaqus有限元软件分别模拟分析了裂纹缺陷模型、单侧腐朽缺陷模型、环形腐朽缺陷模型和复合缺陷模型最大顺纹压应力的大小和位置，探究了不同尺寸的缺陷对墙体木柱安全性的影响，并进行了实例验证。结果 单侧腐朽缺陷以及复合缺陷会使墙体木柱在径向上出现较大偏移，对木柱的稳定性产生较大影响，而裂纹缺陷和环形腐朽缺陷在径向、顺纹方向和切向上偏移较小；裂纹缺陷、单侧腐朽缺陷、环形腐朽缺陷和复合缺陷都对墙体木柱最大顺纹压应力和安全性有较大影响，最大顺纹压应力总是出现在有效截面面积最小处，且均随各缺陷程度的增大呈指数增加，而安全性系数呈指数下降，同时复合缺陷对墙体木柱安全性的影响要大于单一缺陷对墙体木柱的安全性影响。半露明柱与暗柱在腐朽深度相同时，安全性相差不大，在腐朽面积相同时，半露明柱的安全性要远低于暗柱。结论 裂纹缺陷和腐朽缺陷会降低墙体木柱的安全性，而有限元数值模拟能够计算出墙体木柱的顺纹压应力最大值，进而量化墙体木柱的安全性，其结果可以为墙体木柱的修缮提供依据。Abstract:Objective As one of the most important load-bearing components of wooden structure ancient buildings, the wall wood columns are prone to occur the defects such as cracks and decay. All kinds of defects will affect the distribution of longitudinal compressive stress of wall wood columns, leading to a reduction in its bearing capacity, which then affects its safety and directly threatens the stability of the whole building. Therefore, it is necessary to study the influence of different types of defects on the safety of wall wood columns of ancient buildings.Method Firstly, in this paper, the geometric models of wall wood columns with crack, decay defects and composite defects were established, and the compression safety factor kc of wall wood column was defined. Then, the magnitude and location of the maximum longitudinal compressive stress were simulated and analyzed using Abaqus finite element software for the crack defect model, the unilateral decay defect model, the ring decay defect model and the composite defect model, respectively. The influence of defects of different sizes on the safety of wall wood columns was investigated and verified by an example.Result The unilateral decay defects and composite defects caused large deflections in the radial direction of the wall wood columns, which had a greater influence on the stability of wood columns, while wall wood columns with crack defects and ring decay defects had smaller deflections in the radial direction, longitudinal direction and tangent direction. Crack defects, unilateral decay defects, ring decay defects and composite defects had a significant influence on the maximum longitudinal compressive stress and the safety of wall wood columns. The maximum longitudinal compressive stress always occurred at the minimum effective sectional area. The longitudinal compressive stress in wall wood columns increased exponentially with the increase of defect degree and the safety factor decreased exponentially with the increase of defect degree, while the impact of composite defects on the safety of wall wood columns was greater than that of a single defect on the wall wood column safety impact. The difference in safety between semi-exposed columns and concealed columns was not much when the decay depth was same, and the safety of semi-exposed columns was much lower than that of concealed columns when the decay area was same.Conclusion The crack defects and decay defects can reduce the safety of wall wood columns, and the finite element numerical simulation can calculate the maximum longitudinal compressive stress of wall wood columns, and then quantify the safety of wall wood columns, and the results can provide a basis for the repair of wall wood columns.
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Keywords:
- wall wood column /
- defect /
- numerical simulation /
- safety
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《北京林业大学学报》（原名《北京林学院学报》）创刊于1979年，由教育部主管、北京林业大学主办，国内外公开发行。历任主编分别为我国6位著名林学家汪振儒、沈国舫、关毓秀、王九龄、贺庆棠、尹伟伦。
《北京林业大学学报》是中文核心期刊、中国科技核心期刊、中国科学引文数据库统计源期刊、中国科技论文统计源期刊。荣获第二届国家期刊奖提名奖、第三届国家期刊奖百种重点期刊、中国精品科技期刊、中国高校精品科技期刊、中国国际影响力优秀学术期刊、“中国科技论文在线优秀期刊”一等奖等。
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为保持学科特色，《北京林业大学学报》重点报道以林木遗传育种学、森林培育学、森林经理学、森林生态学、树木生理学、森林土壤学、森林植物学、森林保护学、自然保护区学、园林植物与观赏园艺、风景园林、水土保持与荒漠化防治、森林工程、木材科学与技术、林产化学加工工程、其他学科在林学上的应用等方面的论文。
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《北京林业大学学报》自2015年起由原来的双月刊改为单月刊，大16开本，每月月底出版。每期定价50元。各地邮局发行，邮发代号：82−304。国内统一刊号：CN 11−1932/S。如当地邮局订阅不便或错过征订时间，也可直接汇款向本刊编辑部订阅。
地址：北京市海淀区清华东路35号《北京林业大学学报》编辑部
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图 3 墙体木柱裂纹缺陷模型
α是裂纹扭转弧度；d1是裂纹深度；w是裂纹宽度；l是裂纹高度。α is crack torsion radian; d1 is crack depth; w is crack width; l is crack height.
Figure 3. Crack defect models of wall wood column
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图 4 墙体木柱腐朽缺陷模型
d2是腐朽深度；h是腐朽高度；点A和点B是墙体内外的交界点。d2 is decay depth; h is decay height; point A and point B are the junction points inside and outside the wall.
Figure 4. Decay defect model of wall wood column
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图 6 墙体木柱模型施加荷载与设定边界条件示意图
UR 为径向位移，UL 为顺纹方向位移，UT 为弦向位移，RL 是顺纹方向的转动。UR is radial displacement. UL is longitudial displacement, UT is tangential displacement, RL is rotation in longitudinal direction.
Figure 6. Schematic diagram of applying load and setting boundary conditions of wall wood column model
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图 7 墙体木柱模型网格划分示意图
Figure 7. Schematic diagram for mesh generation of wall wood column model
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图 8 完好墙体木柱模型数值计算结果
σc 表示顺纹压应力，MPa；PS表示最大压应力位置。UL 表示顺纹方向位移，mm；PL 表示最大顺纹位移位置。σc is longitudinal compressive stress, MPa；PS is the position of maximum compressive stress. UL is the displacement in longitudinal direction, mm. PL is the position of maximum displacement in longitudinal direction.
Figure 8. Numerical calculation results of intact wall wood column model
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图 9 裂纹缺陷模型顺纹压应力云图
Figure 9. Cloud diagram for longitudinal compressive stress of crack defect models
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图 11 单侧腐朽缺陷模型顺纹压应力云图
Figure 11. Cloud diagram for longitudinal compressive stress of unilateral decay defect models
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图 12 单侧腐朽对数值模拟结果的影响
Figure 12. Effects of unilateral decay on numerical simulation results
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图 13 环形腐朽缺陷模型顺纹压应力云图
Figure 13. Cloud diagram for longitudinal compressive stress of annular decay defect models
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图 14 环形腐朽对数值模拟结果的影响
Figure 14. Effects of annular decay on numerical simulation results
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图 15 复合缺陷模型顺纹压应力云图
Figure 15. Cloud diagram for longitudinal compressive stress of composite defect models
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图 16 复合缺陷对数值模拟结果的影响
Figure 16. Effects of composite defect on numerical simulation results
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图 17 北京某木结构古建筑墙体木柱
Figure 17. Wall wood column of an ancient wooden building in Beijing
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图 18 某古建筑墙体木柱数值计算结果
UR 表示径向位移，mm；PR 表示最大径向位移位置；σc 表示顺纹压应力，MPa；PS表示最大压应力位置。UR is the displacement in radial direction, mm. PR is the position of maximum displacement in radial direction；σc is the longitudinal compressive stress, MPa. PS is the position of maximum compressive stress.
Figure 18. Numerical calculation results of wall wood column of an ancient building
表 1 清式带斗拱建筑檐柱尺寸
Table 1 Dimensions of eave columns of Qing style buildings with bucket arches
等级
Grade尺寸
Size檐柱径
Eave column
diameter/mm檐柱高
Eave column
height/mm一等材
First grade material6.0 1 152 11 520 二等材
Second grade material5.5 1 056 10 560 三等材
Third grade material5.0 960 9 600 四等材
Fourth grade material4.5 864 8 640 五等材
Fifth grade material4.0 768 7 680 六等材
Sixth grade material3.5 672 6 720 七等材
Seventh grade material3.0 576 5 760 八等材
Eighth grade material2.5 480 4 800 九等材
Ninth grade material2.0 384 3 840 十等材
Tenth grade material1.5 288 2 880 十一等材
Eleventh grade material1.0 192 1 920 注：数据引自文献[11]，尺寸的单位为寸。Notes: data is cited from reference [11]，dimensions are in inches. 
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表 2 裂纹缺陷模型几何参数
Table 2 Geometric parameters of crack defect models
模型编号
Model No.裂纹斜度
Crack slope (θ)/(°)裂纹深度
Crack depth (d1)/mm裂纹宽度
Crack width (w)/mm裂纹高度
Crack height (l)/mmC0 0 0 0 0 CC1 0 100 10 3 840 CC2 4.5 100 10 3 840 CC3 8.9 100 10 3 840 CC4 13.3 100 10 3 840 CC5 17.4 100 10 3 840 CC6 21.4 100 10 3 840 CC7 25.2 100 10 3 840 CC8 28.8 100 10 3 840 CC9 32.1 100 10 3 840
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表 3 腐朽缺陷模型几何参数
Table 3 Geometric parameters of decay defect models
模型编号
Model No.腐朽深度
Decay depth
(d2)/mm腐朽高度
Decay height
(h)/mm腐朽面积占比
Proportion of
decay area (η)/%C0 0 0 0 CE1-1 38.4 384 5 CE1-2 76.8 768 14 CE1-3 96.0 960 20 CE1-4 128.0 1 280 29 CE1-5 153.6 1 536 37 CE1-6 192.0 1 920 50 CE1-7 230.4 2 304 63 CE1-8 256.0 2 560 71 CE2-1 4.8 48 5 CE2-2 19.2 192 20 CE2-3 38.4 384 36 CE2-4 48.0 480 44 CE2-5 57.6 576 50 CE2-6 64.0 640 56 CE2-7 76.8 768 64 CE2-8 96.0 960 75
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表 4 复合缺陷模型几何参数
Table 4 Geometric parameters of composite defect model
模型编号
Model No.裂纹斜度
Crack slope
(θ)/(°)裂纹深度
Crack depth
(d1)/mm裂纹宽度
Crack width
(w)/mm裂纹高度
Crack height
(l)/mm腐朽深度
Decay depth
(d2)/mm腐朽高度
Decay height
(h)/mm腐朽面积占比
Proportion of
dacay area (η)/%CD1-1 0 100 10 3 840 38.4 384 5 CD1-2 0 100 10 3 840 96.0 960 20 CD1-3 0 100 10 3 840 192.0 1 920 50 CD1-4 0 100 10 3 840 256.0 2 560 71 CD2-1 8.9 100 10 3 840 38.4 384 5 CD2-2 8.9 100 10 3 840 96.0 960 20 CD2-3 8.9 100 10 3 840 192.0 1 920 50 CD2-4 8.9 100 10 3 840 256.0 2 560 71 CD3-1 17.4 100 10 3 840 38.4 384 5 CD3-2 17.4 100 10 3 840 96.0 960 20 CD3-3 17.4 100 10 3 840 192.0 1 920 50 CD3-4 17.4 100 10 3 840 256.0 2 560 71
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表 5 顺纹抗压强度设计值折减系数
Table 5 Reduction coefficient for design value of longitudinal compressive strength
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表 6 落叶松木材材性参数
Table 6 Wood property parameters of larch
EL/MPa ER/MPa ET/MPa μLR μLT μRT GLR/MPa GLT/MPa GRT/MPa 14 190 1 419 709.5 0.03 0.02 0.43 1 064.25 851.4 255.42 注：表6引自参考文献[21]和[22]。EL为木柱顺纹方向弹性模量；ER为径向弹性模量；ET为弦向弹性模量；μLR为径面的泊松比；μLT为弦面的泊松比；μRT为端面的泊松比；GLR为径面内的剪切模量；GLT为弦面内的剪切模量；GRT为端面内的剪切模量。Notes: Tab. 6 is cited from reference [21]
and [22]. EL is the longitudinal elastic modulus of wood column; ER is radial elastic modulus; ET is tangential elastic modulus; μLR is the Poisson’s ratio of radial plane; μLT is the Poisson’s ratio of tangential plane; μRT is Poisson’s ratio of end plane; GLR is shear modulus of radial plane; GLT is shear modulus of tangential plane; GRT is shear modulus of end plane.
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表 7 裂纹缺陷模型数值模拟结果
Table 7 Numerical simulation results ofcrack defect models
模型
编号
Model
No.顺纹最大
位移
Maximum
displacement
in longitudinal
direction
(ULmax)/mm径向最大
位移
Maximum
displacement
in radial
direction
(URmax)/mm弦向最大
位移
Maximum
displacement
in tangent
direction
(UTmax)/mm最大顺纹
压应力
Maximum
longitudinal
compressive
stress
(σcmax)/MPa安全性
系数
Safety
coefficient
(kc)C0 0.19 0 0 0.84 7.43 CC1 0.19 0.03 0 0.86 7.24 CC2 0.20 0.09 0.08 1.19 5.24 CC3 0.21 0.21 0.10 1.67 3.74 CC4 0.22 0.29 0.13 2.02 3.09 CC5 0.22 0.32 0.22 2.25 2.77 CC6 0.24 0.36 0.24 2.49 2.51 CC7 0.26 0.44 0.26 3.76 1.66 CC8 0.27 0.50 0.27 3.91 1.60 CC9 0.28 0.51 0.28 4.17 1.50
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表 8 单侧腐朽模型数值模拟结果
Table 8 Numerical simulation results ofunilateral decay models
模型编号
Model No.ULmax/mm URmax/mm UTmax/mm σcmax/MPa kc C0 0.19 0 0 0.84 7.43 CE1-1 0.20 0.09 0 1.45 4.30 CE1-2 0.22 0.41 0 2.20 2.84 CE1-3 0.23 0.71 0 2.79 2.24 CE1-4 0.29 1.51 0 3.80 1.64 CE1-5 0.37 2.55 0 4.18 1.49 CE1-6 0.57 5.12 0 6.13 1.02 CE1-7 0.94 9.49 0.01 11.40 0.55 CE1-8 1.28 13.53 0.02 18.32 0.34
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表 9 环形腐朽模型数值模拟结果
Table 9 Numerical simulation results ofannular decay models
模型编号
Model No.ULmax/mm URmax/mm UTmax/mm σcmax/MPa kc C0 0.19 0 0 0.84 7.43 CE2-1 0.19 0 0 0.86 7.26 CE2-2 0.19 0 0 1.37 4.55 CE2-3 0.20 0 0 1.37 4.55 CE2-4 0.20 0 0 1.64 3.80 CE2-5 0.20 0 0 1.87 3.34 CE2-6 0.21 0 0 1.98 3.15 CE2-7 0.22 0 0 2.42 2.58 CE2-8 0.24 0 0 3.21 1.94
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表 10 复合缺陷模型数值模拟结果
Table 10 Numerical simulation results ofcomposite defect models
模型编号
Model No.ULmax/mm URmax/mm UTmax/mm σcmax/MPa kc CD1-1 0.19 0.06 0 1.48 4.22 CD1-2 0.24 0.68 0 2.84 2.20 CD1-3 0.58 5.24 0 6.36 0.98 CD1-4 1.30 13.77 0.02 19.03 0.33 CD2-1 0.21 0.13 0.21 1.84 3.39 CD2-2 0.25 0.77 0.22 2.85 2.19 CD2-3 0.60 5.41 0.22 6.42 0.97 CD2-4 1.35 14.35 0.22 19.38 0.32 CD3-1 0.22 0.31 0.32 2.18 2.86 CD3-2 0.27 0.97 0.34 2.92 2.14 CD3-3 0.63 5.76 0.36 6.46 0.97 CD3-4 1.38 14.61 0.37 20.65 0.30
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