Scientia Silvae Sinicae ›› 2021, Vol. 57 ›› Issue (12): 132-139.doi: 10.11707/j.1001-7488.20211213
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Zhongcheng Wang,Na Yang*
Received:
2020-10-28
Online:
2021-12-25
Published:
2022-01-26
Contact:
Na Yang
CLC Number:
Zhongcheng Wang,Na Yang. Applicability Analysis of Gerhards Model in Long-Term Life Prediction of Coniferous Wood[J]. Scientia Silvae Sinicae, 2021, 57(12): 132-139.
Table 2
8 sets of model parameters of Gerhards model"
编号 No. | 拟合使用的试验数据 Data used for fitting | 拟合使用的时间参数 Time used for fitting | 模型参数Model parameters | |
A | B | |||
G-1 | C | T | 24.613 4 | 20.890 9 |
G-2 | R,C,X* | Tc | 30.829 1 | 29.375 6 |
G-3 | C | Tc | 31.199 2 | 29.411 3 |
G-4 | R,C,X* | T | 31.424 7 | 30.302 5 |
G-5 | R* | Tr | 33.152 4 | 31.571 6 |
G-6 | R,C,X | Tc | 37.612 7 | 37.639 3 |
G-7 | R,C,X | T | 37.537 5 | 37.860 3 |
G-8 | R | Tr | 46.678 4 | 47.364 6 |
Table 3
Comparison between actual median failure time of Gerhards's experiment and predicted failure time"
编号 No. | 加载方式 Loading mode | 试样破坏时间中位数 Actual median failure time/min | 模型预测试样破坏时间Predicted failure time/min | |||||||
G-1 | G-2 | G-3 | G-4 | G-5 | G-6 | G-7 | G-8 | |||
1 | 线性加载 Ramp loading | 0.52 | 0.66 | 0.58 | 0.59 | 0.57 | 0.58 | 0.54 | 0.46 | 0.53 |
2 | 127.0 | 134.2 | 122.8 | 124.1 | 121.6 | 123.5 | 118.8 | 117.9 | 118.5 | |
3 | 24 336 | 24 203 | 23 707 | 24 018 | 23 584 | 24 256 | 23 935 | 23 746 | 24 746 | |
4 | 恒定加载 Constant loading | 2.50 | 57.1 | 6.73 | 9.08 | 4.9 | 7.8 | 1.73 | 1.3 | 1.1 |
5 | 670.5 | 457.2 | 125.4 | 170.5 | 100.2 | 181.1 | 73.4 | 56.34 | 119.1 | |
6 | 34 600 | 40 457 | 68 562 | 94 636 | 66 816 | 159 054 | 236 641 | 190 175 | 3 076 182 |
Table 4
Reference value of the physical and mechanical properties of the softwood used in the long-term load test"
树种 Tree species | 气干密度 Air-dry density/ (kg·m-3) | 顺纹抗压强度 Parallel-to-grain compressive strength/MPa | 抗弯强度 Bending strength/MPa | 抗弯弹性模量 Bending modulus of elasticity/MPa | 顺纹抗剪强度 Parallel-to-grain shear strength/MPa |
北美花旗松Pseudotsuga menziesii | 480 | 47.6 | 90.0 | 1 230 | 9.7 |
欧洲云杉Picea abies | 375 | 36.6 | 71.4 | 1 020 | 10.3 |
Table 6
Comparison of median failure time under similar SL between Gerhards's and Wood's experiments"
Gerhards试验Gerhards’s experiment | Wood试验Wood’s experiment | |||
恒定应力水平 SL | 破坏时间中位数 Median failure time/min | 相似应力水平 Similar nominal SL | 破坏时间中位数 Median failure time/min | |
SL≈98.46%(工况4 Loading condition No.4) | 2.5 | SL=95% | 14.4 | |
SL≈88.50%(工况5 Loading condition No.5) | 670.5 | 85%≤SL≤90% | 107.6 | |
SL≈67.04%(工况6 Loading condition No.6) | 34 600 | 65%≤SL≤70% | 188 210 |
Table 7
Statistics of Wood's experimental data"
统计量Statistic | SL-1 | SL-2 | SL-3 | SL-4 | SL-5 | SL-6 | SL-7 | SL-8 |
$\overline{{\rm{SL}}}$i | 94.77 | 90.37 | 85.17 | 80.03 | 75.04 | 70.02 | 65.10 | 60.03 |
Ni | 15 | 16 | 16 | 19 | 15 | 20 | 10 | 12 |
${\rm{\bar X}}$i | 2.69 | 4.69 | 4.63 | 8.22 | 9.85 | 11.71 | 13.20 | 13.52 |
Si | 0.78 | 1.56 | 1.65 | 1.81 | 1.89 | 1.17 | 0.93 | 0.81 |
ti | 2.14 | 2.13 | 2.13 | 2.10 | 2.14 | 2.09 | 2.26 | 2.20 |
Xi, u | 3.12 | 5.52 | 5.51 | 9.09 | 10.90 | 12.26 | 13.86 | 14.04 |
Xi, l | 2.26 | 3.85 | 3.75 | 7.34 | 8.80 | 11.16 | 12.54 | 13.00 |
Table 8
Comparison of parameters of two interval prediction model based on Wood's experimental data"
模型编号 No. | 模型统称 General name | 模型名称 Particular model | 参数Parameters | 校正决定系数 Adj. R2 | |
m | n | ||||
1 | T分布模型 T-distribution model | 均值模型Mean model | 102.21 | 2.88 | 0.962 |
2 | 下限模型Lower limit model | 99.95 | 2.86 | 0.962 | |
3 | 上限模型Upper limit model | 104.36 | 2.89 | 0.956 | |
4 | 分位数模型 Percentile model | 中位数模型Median model | 102.32 | 2.85 | 0.964 |
5 | 5%模型5% model | 96.20 | 2.81 | 0.955 | |
6 | 95%模型95% model | 109.14 | 3.01 | 0.891 |
Table 附表 1
Wood's long-term constant loading experimental data"
编号 No. | 名义应力水平Nominal SL(%) | ||||||||||
95 | 90 | 85 | 80 | ||||||||
SL(%) | FD/min | SL(%) | FD/min | SL(%) | FD/min | SL(%) | FD/min | ||||
1 | 96.2 | 15.4 | 91.2 | 50.3 | 86.1 | 224.9 | 81.0 | 5 014.8 | |||
2 | 95.2 | 33.8 | 91.2 | 173.8 | 85.4 | 45.1 | 80.3 | 3 182.8 | |||
3 | 95.2 | 14.3 | 91.2 | 92.7 | 85.2 | 213.3 | 80.2 | 10 435.1 | |||
4 | 95.2 | 15.7 | 90.2 | 1 834.4 | 85.2 | 567.1 | 80.2 | 1 884.8 | |||
5 | 95.2 | 6.1 | 90.2 | 159.1 | 85.2 | 81.6 | 80.2 | 5 663.1 | |||
6 | 95.2 | 18.3 | 90.2 | 21.0 | 85.2 | 21.3 | 80.2 | 9 074.5 | |||
7 | 95.2 | 11.2 | 90.2 | 122.4 | 85.2 | 18.2 | 80.2 | 11 587.8 | |||
8 | 95.2 | 8.4 | 90.2 | 225.6 | 85.2 | 2 253.1 | 80.1 | 6 399.2 | |||
9 | 95.2 | 7.1 | 90.2 | 880.9 | 85.2 | 421.4 | 80.1 | 5 280.8 | |||
10 | 95.1 | 5.6 | 90.2 | 46.1 | 85.2 | 27.2 | 80.1 | 4 755.5 | |||
11 | 94.2 | 33.7 | 90.2 | 14.3 | 85.2 | 14.5 | 80.1 | 3 856.5 | |||
12 | 94.2 | 17.7 | 90.2 | 1 513.7 | 85.2 | 287.0 | 80.1 | 72 493.2 | |||
13 | 94.2 | 110.6 | 90.1 | 9.1 | 85.2 | 47.5 | 80.1 | 14 288.5 | |||
14 | 93.2 | 7.9 | 90.1 | 64.2 | 85.1 | 6.1 | 80.1 | 137.3 | |||
15 | 93.1 | 12.9 | 90.1 | 30.3 | 85.1 | 188.7 | 80.1 | 184.7 | |||
16 | 90.1 | 176.7 | 84.1 | 629.2 | 80.1 | 328.7 | |||||
17 | 80.1 | 285.9 | |||||||||
18 | 79.1 | 110 145.0 | |||||||||
19 | 78.1 | 1 983.0 | |||||||||
20 | |||||||||||
编号 No. | 名义应力水平Nominal SL(%) | ||||||||||
75 | 70 | 65 | 60 | ||||||||
SL(%) | FD/min | SL(%) | FD/min | SL(%) | FD/min | SL(%) | FD/min | ||||
1 | 76.1 | 11 550.8 | 70.6 | 29 020.4 | 65.4 | 1 300 926.0 | 61.1 | 136 292.4 | |||
2 | 75.2 | 501 697.8 | 70.5 | 119 394.6 | 65.1 | 432 894.0 | 60.4 | 867 258.0 | |||
3 | 75.2 | 38 512.3 | 70.4 | 134 912.4 | 65.1 | 1 073 364.0 | 60.4 | 1 743 840.0 | |||
4 | 75.1 | 10 037.2 | 70.4 | 149 815.2 | 65.1 | 154 492.2 | 60.0 | 1 654 368.0 | |||
5 | 75.1 | 14 483.6 | 70.1 | 198 060.6 | 65.1 | 110 869.2 | 60.0 | 2 345 910.0 | |||
6 | 75.1 | 16 366.9 | 70.1 | 23 119.0 | 65.1 | 1 171 242.0 | 60.0 | 504 571.2 | |||
7 | 75.1 | 333.2 | 70.1 | 132 546.0 | 65.1 | 1 394 718.0 | 60.0 | 728 094.0 | |||
8 | 75.1 | 5 352.9 | 70.1 | 8 544.4 | 65.1 | 933 372.0 | 60.0 | 320 419.8 | |||
9 | 75.1 | 1 781.6 | 70.1 | 405 265.8 | 65.1 | 515 467.2 | 60.0 | 570 151.2 | |||
10 | 75.1 | 128 491.2 | 70.1 | 15 744.3 | 65.1 | 256 355.4 | 59.7 | 1 364 916.0 | |||
11 | 75.1 | 56 549.2 | 70.1 | 219 938.4 | 59.7 | 945 894.0 | |||||
12 | 75.1 | 4 495.2 | 70.1 | 178 358.4 | 59.0 | 416 056.2 | |||||
13 | 75.1 | 24 033.2 | 70.1 | 1 450 008.0 | |||||||
14 | 75.0 | 43 515.7 | 70.1 | 322 944.6 | |||||||
15 | 73.1 | 267 131.4 | 70.1 | 87 162.6 | |||||||
16 | 70.0 | 123 591.6 | |||||||||
17 | 70.0 | 142 122.0 | |||||||||
18 | 69.2 | 212 230.2 | |||||||||
19 | 69.1 | 160 488.0 | |||||||||
20 | 68.7 | 212 160.0 |
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