Analysis of the main controlling factors of weathering rates in Yungang Grottoes sandstones
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摘要:
分析岩石风化速率的变化特征与主控因子是进行石质文物保护工作的基础工作。文章以云冈石窟砂岩为研究对象，将裂隙宽度扩展速率、石窟立柱倾斜角度变化速率、石窟洞门沉降变化速率作为表征石窟砂岩风化速率的定量指标，使用因子分析方法研究了主要环境因素（壁温、环境温度、环境湿度、气压、风速、积雨量）对石窟砂岩风化速率的影响，使用多元线性回归方法得到了影响石窟风化速率的主控因子。结果表明：对裂隙宽度扩展速率来说，夏季是环境湿度、壁温、积雨量影响最大的季节，春季是环境温度、风速影响最大的季节，主控因子是湿度；对石窟立柱风化速率来说，夏季时壁温、环境温度、环境湿度、气压、风速、积雨量的影响最大，其他季节时影响较小，主控因子是壁温；对石窟洞门风化速率来说，夏季时壁温、环境温度、环境湿度、积雨量影响最大，春季时气压、风速影响最大，主控因子是环境湿度。文章结果对砂岩风化速率分析与石窟文物保护具有一定的参考价值。
Abstract:Analyzing the weathering rates and their main environmental controlling factors is fundamental in conserving rocky relics. In this study, using the sandstones of the Yungang Grottoes as a case study, the rock weathering rates were quantitatively expressed by the expansion rates of crack widths, changes in the column inclination angles and door settlements. Factor analysis was employed to explore the influences of environmental factors, including wall temperature, ambient temperature, ambient humidity, air pressure, wind speed, and accumulated rainfall, on the weathering rates of these sandstones. Multivariate linear regression techniques were subsequently used to identify the main controlling factors affecting these weathering rates. It was found that ambient humidity, wall temperature, and accumulated rainfall have the greatest influences on the expansion rates of crack widths during summer, while ambient temperature and wind speed are more influential in spring, with environmental humidity as the main controlling factor. For the changes in column inclination angles, wall temperature, ambient temperature, ambient humidity, air pressure, wind speed, and accumulated rainfall exert the greatest impacts in the summer, with smaller effects in other seasons, and wall temperature acting as the controlling factor. Regarding the change rates in door settlement, wall temperature, ambient temperature, ambient humidity, and accumulated rainfall have the most substantial effects in the summer, while air pressure and wind speed are more influential in spring, with environmental humidity again being the main controlling factor. These findings may provide useful references for both the analysis of weathering rates and the conservation of the grottoes.
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Key words:
- Yungang Grottoes /
- weathering rate /
- environmental conditions /
- main controlling factors
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表 1 环境影响因子的KMO度量值和显著性水平p
Table 1. KMO measures and significance levels (p-values) for environmental factors
石窟编号 KMO p 9 0.93 0.002 10 0.95 0.006 12 0.92 0.004 13 0.90 0.001 25 0.88 0.003 
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表 2 不同洞窟裂隙处环境因子的载荷值
Table 2. Loadings of environmental factors on fissures in different caves
石窟编号 公共因子 X1 X2 X3 X4 X5 X6 9 F1 0.82 0.32 0.91 0.25 0.47 0.75 F2 0.39 0.84 0.33 0.21 0.77 0.20 F3 0.36 0.31 0.54 0.75 0.25 0.57 10 F1 0.84 0.49 0.90 0.22 0.46 0.75 F2 0.39 0.92 0.29 0.37 0.79 0.16 F3 0.46 0.32 0.20 0.82 0.23 0.19 12 F1 0.85 0.41 0.89 0.25 0.36 0.71 F2 0.39 0.82 0.34 0.31 0.78 0.19 F3 0.46 0.38 0.24 0.71 0.22 0.26 13 F1 0.75 0.49 0.92 0.23 0.31 0.79 F2 0.41 0.89 0.15 0.21 0.72 0.13 F3 0.48 0.41 0.19 0.9 0.16 0.09 25 F1 0.82 0.44 0.86 0.26 0.36 0.77 F2 0.32 0.75 0.29 0.51 0.68 0.16 F3 0.36 0.49 0.17 0.66 0.19 0.24
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表 3 不同洞窟公共因子特征值与方差贡献率
Table 3. Eigenvalues and variance contributions of common factors in different caves
石窟
编号公共
因子载荷平方和 旋转载荷平方和 合计 方差/% 累计值/% 合计 方差/% 累计值/% 9 F1 2.81 40.37 40.37 2.78 39.94 39.94 F2 1.71 24.57 64.94 1.52 21.84 61.78 F3 1.42 20.40 85.34 1.64 23.56 85.34 10 F1 3.87 39.33 39.33 3.53 35.91 35.91 F2 2.67 27.15 66.48 2.89 29.36 65.27 F3 2.06 20.94 87.42 2.18 22.15 87.42 12 F1 3.56 40.98 40.98 3.23 37.18 37.18 F2 2.45 28.21 69.19 2.12 24.41 61.59 F3 1.32 15.2 84.39 1.98 22.8 84.38 13 F1 2.81 40.25 40.25 2.78 39.74 39.74 F2 1.71 24.49 64.74 1.52 21.82 61.56 F3 1.42 20.33 85.07 1.64 23.51 85.07 25 F1 3.71 43.95 43.95 3.29 38.92 38.92 F2 2.28 27.01 70.97 2.15 25.47 64.39 F3 1.02 12.08 83.05 1.57 18.66 83.05
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表 4 第9窟裂隙扩展速率的公共因子得分
Table 4. Scores of common factors for fissure expansion rates in Cave 9
月 F1 F2 F3 F 数值 排名 数值 排名 数值 排名 数值 排名 1 0.17 12 0.31 6 0.06 12 0.22 12 2 0.36 9 0.48 2 0.14 9 0.67 9 3 0.47 8 0.54 1 0.15 7 0.69 8 4 0.62 6 0.42 3 0.19 6 0.83 6 5 0.76 5 0.39 4 0.23 4 0.81 5 6 1.02 2 0.36 5 0.26 1 1.37 2 7 1.34 1 0.22 8 0.25 2 1.56 1 8 0.98 3 0.11 11 0.23 3 1.23 3 9 0.84 4 0.16 9 0.20 5 1.06 4 10 0.59 7 0.06 12 0.15 8 0.70 7 11 0.29 10 0.13 10 0.09 10 0.41 10 12 0.20 11 0.26 7 0.08 11 0.34 11 总和 7.64 3.44 2.03 9.89
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表 5 裂隙宽度扩展速率与环境参数的回归关系
Table 5. Regression relationships between environmental parameters and fissure expansion rates
石窟编号 回归关系式 R2 9 $ {v_\omega } = 0.40X_2' + 0.54X_3' + 0.10X_4' - 0.116 $ 0.83 10 $ {v_\omega } = 0.34X_2' + 0.66X_3' + 0.16X_4' + 0.084 $ 0.90 12 $ {v_\omega } = 0.39X_2' + 0.68X_3' + 0.19X_4' + 0.035 $ 0.86 13 $ {v_\omega } = 0.46X_2' + 0.62X_3' + 0.08X_4' - 0.091 $ 0.82 25 $ {v_\omega } = 0.46X_2' + 0.62X_3' + 0.08X_4' - 0.091 $ 0.89
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表 6 第9窟立柱倾斜角度变化速率的公共因子得分
Table 6. Scores of common factors for changes in column tilt angles in Cave 9
月 F1 F2 F3 F 数值 排名 数值 排名 数值 排名 数值 排名 1 0.12 12 0.17 10 0.15 11 0.25 12 2 0.34 9 0.30 9 0.21 9 0.61 9 3 0.37 8 0.31 8 0.27 7 0.68 8 4 0.67 7 0.42 7 0.38 5 1.08 7 5 0.95 6 0.57 2 0.39 4 1.38 6 6 1.58 2 0.49 4 0.48 2 2.00 2 7 2.05 1 0.64 1 0.52 1 2.46 1 8 1.38 3 0.43 11 0.43 3 1.80 3 9 1.12 4 0.51 9 0.37 6 1.53 4 10 1.06 5 0.48 12 0.24 8 1.42 5 11 0.30 10 0.13 10 0.19 10 0.46 10 12 0.13 11 0.10 7 0.13 12 0.30 11 总和 10.07 4.55 3.76 13.97
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表 7 立柱倾斜角度变化速率与环境参数的回归关系
Table 7. Regression relationships between changes in column tilt angles and environmental parameters
石窟编号 回归关系式 R2 9 ${v_\theta } = 0.77X_1' + 0.30X_3' + 0.13X_5' + 0.036$ 0.95 10 ${v_\theta } = 0.64X_1' + 0.26X_3' + 0.24X_5' - 0.051$ 0.90 12 ${v_\theta } = 0.59X_1' + 0.42X_3' + 0.26X_5' + 0.113$ 0.93 13 ${v_\theta } = 0.68X_1' + 0.33X_3' + 0.24X_5' - 0.102$ 0.96 25 ${v_\theta } = 0.71X_1' + 0.25X_3' + 0.17X_5' - 0.068$ 0.95
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表 8 第9窟洞门沉降变化速率的公共因子得分
Table 8. Scores of common factors for the settlement rate of the cave door in Cave 9
月 F1 F2 F3 F 数值 排名 数值 排名 数值 排名 数值 排名 1 0.15 12 0.11 12 0.35 5 0.26 12 2 0.43 10 0.26 9 0.42 2 0.56 10 3 0.49 9 0.28 8 0.49 1 0.62 9 4 0.68 6 0.35 6 0.39 3 0.82 6 5 0.84 5 0.39 5 0.35 4 0.87 5 6 1.01 2 0.48 2 0.31 6 1.26 2 7 1.23 1 0.58 1 0.24 8 1.35 1 8 0.92 3 0.43 3 0.13 11 1.06 3 9 0.91 4 0.42 4 0.15 10 0.99 4 10 0.65 7 0.34 7 0.06 12 0.8 7 11 0.62 8 0.19 10 0.21 9 0.75 8 12 0.22 11 0.16 11 0.3 7 0.47 11 总和 8.15 3.99 3.40 9.81
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表 9 洞门沉降变化速率与环境参数的回归关系
Table 9. Regression relationships between environmental parameters and the settlement rate of the cave door
石窟编号 回归关系式 R2 9 ${v_s} = 0.29X_2' + 0.56X_3' + 0.14X_4' + 0.125$ 0.86 10 $ {v_s} = 0.38X_2' + 0.73X_3' + 0.04X_4' - 0.034 $ 0.90 12 ${v_s} = 0.21X_2' + 0.62X_3' + 0.19X_4' + 0.095$ 0.89 13 $ {v_s} = 0.49X_2' + 0.65X_3' + 0.15X_4' - 0.152 $ 0.92 25 $ {v_s} = 0.40X_2' + 0.59X_3' + 0.17X_4' - 0.128 $ 0.84
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