未來方向與建議 - 在簡單應力狀態下探討具有空間變異性土壤的整體彈性模數

1. 無限硬之束制板其作用為控制邊界較為平整，但實際上無法完全平整，此現

象將會造成計算整體彈性模數時有其誤差存在，且無限硬之束制板會不會對研究主體有應力之影響也是另一個問題，因此模型之邊界需加以改善，目前有提出改用位移控制之模型，即強制讓模型之邊界位移一單位，如圖 5. 1 所示，在求出其應力後，算出整體彈性模數，此方法即無邊界不平整之問題。

圖 5. 1 位移控制示意圖

109

2. 從結果可以發現不論是等向性或是異向性，當 V 值變大時，整體彈性模數之

期望值與標準差皆與隨機場特定之數學平均(等向性為幾何平均，異向性為算數平均或倒數平均)差異很大，表示當變異系數變大時，用隨機場特定之數學平均較無法準確預估整體彈性模數，經過討論，推估可能是是因為 E 值較大者，對整體彈性模數較無貢獻，如圖 5. 2 所示，較深色塊體為 E 值較大，灰色塊體為 E 值較小，當具有空間變異性之物體受壓時，E 值較大者如被 E 值較小者包圍，雖 E 值較大者位移較小，卻會與 E 值較小者一起移動，因此 E 值較大者之 E 值不應該一起放入計算幾何平均，而當 E 值多大時可以忽略不考慮，又是另一個值得討論之課題。

圖 5. 2 空間變異性之如有 E 值較大特例之現象

3. 基礎模型中，1.5 單位寬之基礎與 3 單位寬之基礎皆可以與 5 倍深度之隨機

場比較，但 7.5 單位寬之基礎板與 15 單位寬之基礎板，最大也只能與 4 倍寬之深度和 1 倍寬度深度比較，因此也無法證實基礎版選取五倍深度寬為最為恰當之結果，而分佈相似性範圍不一定也值得另外探討。

110

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113

Arithmetic average /

0.5 1 1.5

E x/

Geometric average /

0.5 1 1.5

E x/

Harmonic average /

0.5 1 1.5

Ez/

Arithmetic average /

0.5 1 1.5

E z/

Geometric average /

0.5 1 1.5

E z/

Harmonic average /

0.5 1 1.5

G /

Arithmetic average /

0.5 1 1.5

G /

Geometric average /

0.5 1 1.5

G /

Harmonic average /

114

Quantile for ( Arithmetic average )/ 0.50.5 1 1.5 1

1.5

Quantile E x/

Quantile for ( Geometric average )/ 0.50.5 1 1.5 1

1.5

Quantile E x/

Quantile for ( Harmonic average )/

0.5 1 1.5

Quantile E z/

Quantile for ( Arithmetic average )/ 0.50.5 1 1.5 1

1.5

Quantile E z/

Quantile for ( Geometric average )/ 0.50.5 1 1.5 1

1.5

Quantile E z/

Quantile for ( Harmonic average )/

0.5 1 1.5

Quantile G/

Quantile for ( Arithmetic average )/

0.5 1 1.5

Quantile G/

Quantile for ( Geometric average )/

0.5 1 1.5

Quantile G/

Quantile for ( Harmonic average )/

115 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

116 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

117 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

118

雙隨機場-等向性

圖 A. 3 Ex/μ 之期望值與幾何平均理論值比較

圖 A. 4 Ex/μ 之變異系數與幾何平均理論值比較

10^-1 10⁰ 10¹

0 0.2 0.4 0.6 0.8 1 1.2

Sample mean of E x/

/L

V = 0.1 V = 0.5 V = 1 Geometric av erage

10^-1 10⁰ 10¹

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Sample COV of E x/

/L

V = 0.1 V = 0.5 V = 1

Geometric av erage

119

圖 A. 5 Ez/μ 之期望值與幾何平均理論值比較

圖 A. 6 Ez/μ 之變異系數與幾何平均理論值比較

10^-1 10⁰ 10¹

0 0.2 0.4 0.6 0.8 1

Sample mean of E z/

/L

V = 0.1 V = 0.5 V = 1 Geometric av erage

10^-1 10⁰ 10¹

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Sample COV of E z/

/L V = 0.1

V = 0.5 V = 1

Geometric av erage

120

圖 A. 7 G/μ 之期望值與幾何平均理論值比較

圖 A. 8 G/μ 之變異系數與幾何平均理論值比較

10^-1 10⁰ 10¹

0 0.2 0.4 0.6 0.8 1

Sample mean of G/

/L

V = 0.1 V = 0.5 V = 1 Geometric av erage

10^-1 10⁰ 10¹

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Sample COV of G/

/L V = 0.1

V = 0.5 V = 1

Geometric av erage

121

Arithmetic average /

0 1 2

Geometric average /

0 1 2

Harmonic average /

0 1 2

Arithmetic average /

0 1 2

Geometric average /

0 1 2

Harmonic average /

0 1 2

Arithmetic average /

0 1 2

Geometric average /

0 1 2

Harmonic average /

122

Quantile for ( Arithmetic average )/

0.5 1 1.5

Quantile E x/

Quantile for ( Geometric average )/

0.5 1 1.5

Quantile E x/

Quantile for ( Harmonic average )/

0.5 1 1.5

Quantile E z/

Quantile for ( Arithmetic average )/

0.5 1 1.5

Quantile E z/

Quantile for ( Geometric average )/

0.5 1 1.5

Quantile E z/

Quantile for ( Harmonic average )/

0.5 1 1.5

Quantile G/

Quantile for ( Arithmetic average )/

0.5 1 1.5

Quantile G/

Quantile for ( Geometric average )/

0.5 1 1.5

Quantile G/

Quantile for ( Harmonic average )/

123 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

124 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

125 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

126

雙隨機場-異向性

圖 A. 11 Ex/μ 之期望值與算術平均理論值比較

圖 A. 12 Ex/μ 之變異系數與算術平均理論值比較

10^-1 10⁰ 10¹

0 0.2 0.4 0.6 0.8 1

S a m p le m e a n o f E

/ 

 /L

V = 0.1 V = 0.5 V = 1 Arithmetic av erage

10^-1 10⁰ 10¹

0 0.2 0.4 0.6 0.8 1

S a m p le C O V o f E

/ 

 /L

V = 0.1 V = 0.5 V = 1

Arithmetic av erage

127

圖 A. 13 Ez/μ 之期望值

圖 A. 14 Ez/μ 之變異系數

10^-1 10⁰ 10¹

0 0.2 0.4 0.6 0.8 1

S a m p le m e a n o f E

/ 

 /L

V = 0.1 V = 0.5 V = 1

10^-1 10⁰ 10¹

0 0.2 0.4 0.6 0.8 1

S a m p le C O V o f E

/ 

 /L

V = 0.1 V = 0.5 V = 1

128

圖 A. 15 μ/Ez之期望值與倒數平均理論值比較

圖 A. 16 μ/Ez之變異系數與倒數平均理論值比較

10^-1 10⁰ 10¹

0 0.5 1 1.5 2 2.5

S a m p le m e a n o f



/E



/L

V = 0.1 V = 0.5 V = 1 Harmonic av erage

10^-1 10⁰ 10¹

0 0.2 0.4 0.6 0.8 1

S a m p le C O V o f



/E



/L

V = 0.1 V = 0.5 V = 1

Harmonic av erage

129

圖 A. 17 G/μ 之期望值

圖 A. 18 G/μ 之變異系數

10^-1 10⁰ 10¹

0 0.2 0.4 0.6 0.8 1

Sample mean of G/

/L

V = 0.1 V = 0.5 V = 1

10^-1 10⁰ 10¹

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Sample COV of G/

/L V = 0.1

V = 0.5 V = 1

130

圖 A. 19 μ/G 之期望值與倒數平均理論值比較

圖 A. 20 μ/G 之變異系數與倒數平均理論值比較

10^-1 10⁰ 10¹

0 0.5 1 1.5 2 2.5

S a m p le m e a n o f



/G



/L

V = 0.1 V = 0.5 V = 1 Harmonic av erage

10^-1 10⁰ 10¹

0 0.2 0.4 0.6 0.8 1

S a m p le C O V o f



/G



/L

V = 0.1

V = 0.5 V = 1

Harmonic av erage

131

132

133

134

135

136

137

138

139

表 B. 1 等向性

3 單位基礎寬下楊氏模數與不同範圍之數學平均總相差值 (1B，2B，V = 0.1)

 = 1  = 2  = 5  = 10  = 100 V = 0.1

1B*1B

E /μ-AM /μ 16.819 24.942 32.614 32.514 17.090 E /μ-GM /μ 16.438 24.433 32.376 32.368 17.086 E /μ-HM /μ 16.493 24.231 32.240 32.252 17.083

1B*2B

E /μ-AM /μ 11.910 17.811 24.997 24.577 11.362 E /μ-GM /μ 11.194 17.486 24.653 24.399 11.350 E /μ-HM /μ 11.175 17.669 24.525 24.338 11.346

1B*5B

E /μ-AM /μ 9.995 16.000 24.532 25.512 14.225 E /μ-GM /μ 9.217 15.404 24.176 25.310 14.204 E /μ-HM /μ 9.407 15.467 24.188 25.291 14.188

2B*1B

E /μ-AM /μ 11.086 16.884 25.017 27.342 15.753 E /μ-GM /μ 10.523 16.219 24.590 27.028 15.736 E /μ-HM /μ 10.678 16.117 24.421 26.870 15.721

2B*2B

E /μ-AM /μ 8.169 11.817 17.797 17.675 9.294 E /μ-GM /μ

7.109 11.332

17.179 17.342 9.257 E /μ-HM /μ 7.217 11.662

16.910 17.260

9.234

2B*5B

E /μ-AM /μ 8.421 12.841 20.156 21.736 12.583 E /μ-GM /μ 7.478 12.013 19.683 21.567 12.569 E /μ-HM /μ 7.624 12.095 19.721 21.654 12.566 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

140

表 B. 2 等向性

3 單位基礎寬下楊氏模數與不同範圍之數學平均總相差值 (5B，10B，V = 0.1)

 = 1  = 2  = 5  = 10  = 100 V = 0.1

5B*1B

E /μ-AM /μ 9.838 16.028 22.920 27.430 16.752 E /μ-GM /μ 9.076 15.367 22.637 27.085 16.718 E /μ-HM /μ 9.234 15.372 22.814 26.958 16.712

5B*2B

E /μ-AM /μ 8.914 12.810 19.136 20.916 11.622 E /μ-GM /μ 7.839 12.050 18.648 20.489 11.599 E /μ-HM /μ 7.982 12.177 18.713 20.419 11.606

5B*5B

E /μ-AM /μ 8.904 13.604 21.939 24.096 13.358 E /μ-GM /μ 7.993 12.689 21.475 23.674 13.334 E /μ-HM /μ 8.209 12.783 21.632 23.632 13.339

10B*1B

E /μ-AM /μ 9.975 15.944 26.738 33.854 21.381 E /μ-GM /μ 9.155 15.318 26.315 33.589 21.372 E /μ-HM /μ 9.281 15.405 26.308 33.608 21.391

10B*2B

E /μ-AM /μ 9.549 14.693 24.798 31.352 18.079 E /μ-GM /μ 8.555 14.031 24.370 31.044 18.117 E /μ-HM /μ 8.668 14.125 24.377 30.991 18.208

10B*5B

E /μ-AM /μ 9.447 15.086 25.860 31.430 19.592 E /μ-GM /μ 8.592 14.249 25.586 31.046 19.612 E /μ-HM /μ 8.885 14.207 25.831 30.995 19.716 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

141

表 B. 3 等向性

3 單位基礎寬下楊氏模數與不同範圍之數學平均總相差值 (1B，2B，V = 0.5)

 = 1  = 2  = 5  = 10  = 100 V = 0.5

1B*1B

E /μ-AM /μ 112.844 145.917 179.625 172.389 79.648 E /μ-GM /μ 69.195 108.990 154.726 157.609 79.036 E /μ-HM /μ 68.439 101.906 142.327 147.877 78.536

1B*2B

E /μ-AM /μ 106.252 128.549 149.533 142.380 56.544 E /μ-GM /μ 50.955 80.070 114.335 120.835 55.039 E /μ-HM /μ 55.179 74.876 101.996 109.603 53.931

1B*5B

E /μ-AM /μ 101.894 122.068 138.061 135.920 63.570 E /μ-GM /μ 42.750 69.064 103.779 111.736 62.461 E /μ-HM /μ 55.315 72.288 101.294 107.552 62.201

2B*1B

E /μ-AM /μ 104.389 123.513 150.997 148.360 73.250 E /μ-GM /μ 48.469 73.210 114.076 126.812 71.868 E /μ-HM /μ 56.213 73.207 103.276 118.006 71.123

2B*2B

E /μ-AM /μ 103.026 119.133 129.346 118.380 48.301 E /μ-GM /μ 35.748 52.886 80.144 87.717 46.050 E /μ-HM /μ 49.397 55.559

72.303 80.765

44.962

2B*5B

E /μ-AM /μ 103.109 116.324 123.708 116.889 55.572 E /μ-GM /μ

35.550 52.225

83.482 92.506 54.939 E /μ-HM /μ 52.158 64.426 88.152 94.573 55.243 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

142

表 B. 4 等向性

3 單位基礎寬下楊氏模數與不同範圍之數學平均總相差值 (5B，10B，V = 0.5)

 = 1  = 2  = 5  = 10  = 100 V = 0.5

5B*1B

E /μ-AM /μ 105.506 127.386 147.402 149.814 77.023 E /μ-GM /μ 45.452 71.475 105.994 123.325 74.326 E /μ-HM /μ 55.430 71.312 102.677 119.048 74.095

5B*2B

E /μ-AM /μ 104.727 124.811 131.662 124.978 56.273 E /μ-GM /μ 39.290 62.436 86.302 92.289 53.307 E /μ-HM /μ 52.055 65.159 89.128 92.308 53.064

5B*5B

E /μ-AM /μ 104.269 120.813 128.735 126.868 62.638 E /μ-GM /μ 37.821 58.700 89.260 102.398 61.567 E /μ-HM /μ 54.185 69.120 101.058 111.232 63.359

10B*1B

E /μ-AM /μ 105.296 126.989 156.807 167.915 99.074 E /μ-GM /μ 44.640 73.021 120.490 143.372 95.082 E /μ-HM /μ 56.015 76.826 123.049 147.519 95.173

10B*2B

E /μ-AM /μ 105.373 125.264 146.808 153.736 86.701 E /μ-GM /μ 41.364 68.479 110.973 130.172 82.719 E /μ-HM /μ 54.418 73.133 116.915 136.557 83.516

10B*5B

E /μ-AM /μ 105.030 122.962 146.216 159.274 94.118 E /μ-GM /μ 39.614 64.971 110.791 136.529 91.507 E /μ-HM /μ 54.873 74.289 119.278 146.160 94.376 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

143

表 B. 5 等向性

3 單位基礎寬下楊氏模數與不同範圍之數學平均總相差值 (1B，2B，V = 1 )

 = 1  = 2  = 5  = 10  = 100 V = 1

1B*1B

E /μ-AM /μ 272.962 321.668 338.192 340.942 138.877 E /μ-GM /μ 109.827 160.387 233.549 277.931 136.225 E /μ-HM /μ 111.089 129.130 189.115 239.241 134.088

1B*2B

E /μ-AM /μ 272.675 313.799 307.519 315.701 102.460 E /μ-GM /μ 83.418 119.953 170.533 212.858 97.108 E /μ-HM /μ 100.232 108.215 130.747 164.881 94.187

1B*5B

E /μ-AM /μ 274.187 313.477 322.952 300.517 112.080 E /μ-GM /μ 73.262 104.441 157.026 179.422 102.198 E /μ-HM /μ 105.318 113.238 136.198 152.086 97.243

2B*1B

E /μ-AM /μ 270.518 308.904 311.000 310.174 127.533 E /μ-GM /μ 78.623 112.534 173.362 220.083 123.226 E /μ-HM /μ 101.543 111.282 140.087 181.895 120.579

2B*2B

E /μ-AM /μ 271.169 308.605 293.742 291.033 87.784 E /μ-GM /μ 64.947 87.215 123.382 158.843 79.079 E /μ-HM /μ 103.102 105.912

107.798 119.723

76.383

2B*5B

E /μ-AM /μ 271.862 312.321 313.672 279.980 103.231 E /μ-GM /μ

63.524 84.229

123.197 146.696 93.572 E /μ-HM /μ 108.416 117.103 130.205 141.962 89.204 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

144

表 B. 6 等向性

3 單位基礎寬下楊氏模數與不同範圍之數學平均總相差值 (5B，10B，V = 1 )

 = 1  = 2  = 5  = 10  = 100 V = 1

5B*1B

E /μ-AM /μ 267.570 312.786 318.959 299.802 137.083 E /μ-GM /μ 72.231 103.765 155.642 182.536 126.976 E /μ-HM /μ 108.690 114.251 144.523 166.128 124.126

5B*2B

E /μ-AM /μ 270.472 312.293 300.479 289.102 105.290 E /μ-GM /μ 66.140 90.351 121.762 147.245 89.071 E /μ-HM /μ 108.631 116.975 136.207 143.608 87.829

5B*5B

E /μ-AM /μ 272.077 313.421 312.244 273.177 117.280 E /μ-GM /μ 65.804 88.157 120.815 144.949 102.906 E /μ-HM /μ 110.668 125.107 154.470 177.334 105.377

10B*1B

E /μ-AM /μ 264.786 311.769 328.380 324.426 172.881 E /μ-GM /μ 68.613 104.489 167.768 205.855 159.158 E /μ-HM /μ 112.540 122.575 171.047 212.411 165.251

10B*2B

E /μ-AM /μ 268.610 311.333 316.379 313.443 152.033 E /μ-GM /μ 66.189 95.380 150.199 186.752 137.669 E /μ-HM /μ 112.317 125.778 164.722 202.390 146.086

10B*5B

E /μ-AM /μ 270.304 309.884 322.674 308.264 171.260 E /μ-GM /μ 66.717 92.473 145.918 191.673 154.278 E /μ-HM /μ 112.617 131.110 173.882 220.467 163.492 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

145

表 B. 7 等向性

3 單位基礎寬下楊氏模數與不同範圍之數學平均 P-value (1B，2B，V = 0.1)

 = 1  = 2  = 5  = 10  = 100 V = 0.1

1B*1B

E /μ&AM /μ 9.3E-29 1.6E-25 2.7E-15 1.5E-05 8.5E-01 E /μ&GM /μ 1.5E-20 7.0E-19 1.4E-13 4.4E-05 8.5E-01 E /μ&HM /μ 1.2E-27 8.8E-17 8.3E-12 9.9E-05 8.2E-01

1B*2B

E /μ&AM /μ 1.0E-25 5.0E-14 5.6E-11 1.1E-03 9.5E-01 E /μ&GM /μ 5.0E-14 4.9E-09 2.0E-08 1.6E-03 9.5E-01 E /μ&HM /μ 3.5E-14 7.1E-14 8.7E-10 2.2E-04 9.3E-01

1B*5B

E /μ&AM /μ 1.4E-13 2.7E-07 6.6E-04 5.2E-02 1.0E+00 E /μ&GM /μ 1.6E-02 2.4E-02 1.3E-01 1.9E-01 1.0E+00 E /μ&HM /μ 1.5E-04 5.8E-03 2.8E-02 2.4E-02 1.0E+00

2B*1B

E /μ&AM /μ 1.8E-22 1.9E-15 1.0E-10 5.4E-05 8.5E-01 E /μ&GM /μ 3.6E-10 1.0E-10 2.0E-08 2.6E-04 8.5E-01 E /μ&HM /μ 1.3E-16 5.6E-11 4.5E-07 7.9E-04 8.8E-01

2B*2B

E /μ&AM /μ 3.9E-15 2.6E-08 2.1E-07 2.1E-02 9.5E-01 E /μ&GM /μ 1.2E-04 1.8E-04 6.6E-05 3.6E-02 9.7E-01 E /μ&HM /μ 6.6E-05 9.5E-07 5.4E-05 1.6E-02 9.8E-01

2B*5B

E /μ&AM /μ 1.6E-18 2.8E-09 1.2E-02 1.8E-01 9.9E-01 E /μ&GM /μ 3.6E-03 4.1E-02 6.0E-01 7.5E-01 1.0E+00 E /μ&HM /μ 1.5E-08 1.1E-03 1.0E-01 2.3E-01 9.9E-01 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

146

表 B. 8 等向性

3 單位基礎寬下楊氏模數與不同範圍之數學平均 P-value (5B，10B，V = 0.1)

 = 1  = 2  = 5  = 10  = 100 V = 0.1

5B*1B

E /μ&AM /μ 1.0E-13 2.1E-09 3.6E-02 2.4E-02 9.8E-01 E /μ&GM /μ

1.2E-01

2.6E-03 3.3E-01 1.8E-01 9.9E-01 E /μ&HM /μ 9.9E-05 7.9E-04 8.4E-02 4.3E-01 9.8E-01

5B*2B

E /μ&AM /μ 4.7E-23 1.7E-07 5.9E-02 2.8E-02 1.0E+00 E /μ&GM /μ 6.6E-05

1.9E-01 9.1E-01

3.1E-01 1.0E+00 E /μ&HM /μ 4.5E-08 9.5E-04 7.5E-02

9.5E-01

1.0E+00

5B*5B

E /μ&AM /μ 1.1E-45 1.6E-25 6.5E-10 2.6E-04 9.7E-01 E /μ&GM /μ 5.9E-17 3.1E-12 7.8E-06 2.8E-02 9.8E-01 E /μ&HM /μ 2.7E-21 1.9E-16 2.5E-06 3.6E-02 9.1E-01

10B*1B

E /μ&AM /μ 1.8E-22 4.1E-13 3.6E-05 3.8E-04 8.8E-01 E /μ&GM /μ 1.5E-04 1.5E-04 1.4E-02 1.6E-02 9.5E-01 E /μ&HM /μ 1.6E-09 6.2E-06 3.8E-04 1.9E-01 8.8E-01

10B*2B

E /μ&AM /μ 4.0E-38 1.5E-20 2.1E-09 6.2E-06 7.9E-01 E /μ&GM /μ 2.9E-13 3.7E-09 4.4E-05 1.5E-04 7.2E-01 E /μ&HM /μ 4.0E-17 8.1E-13 3.6E-05 1.1E-02 5.3E-01

10B*5B

E /μ&AM /μ 7.0E-67 8.1E-42 4.2E-21 1.6E-12 3.9E-01 E /μ&GM /μ 8.4E-31 7.1E-22 8.2E-15 6.5E-09 2.3E-01 E /μ&HM /μ 1.3E-36 9.3E-29 8.2E-15 9.5E-07 1.8E-01 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

147

表 B. 9 等向性

3 單位基礎寬下楊氏模數與不同範圍之數學平均 P-value (1B，2B，V = 0.5)

 = 1  = 2  = 5  = 10  = 100 V = 0.5

1B*1B

E /μ&AM /μ 4.6E-127 1.6E-61 3.8E-26 6.0E-12 6.0E-01 E /μ&GM /μ 1.8E-40 5.3E-27 2.7E-15 4.5E-08 6.8E-01 E /μ&HM /μ 7.9E-49 2.4E-36 1.0E-10 4.4E-05 7.9E-01

1B*2B

E /μ&AM /μ 2.9E-152 7.4E-66 4.3E-25 5.6E-11 4.9E-01 E /μ&GM /μ 1.2E-29 4.2E-21 7.7E-11 9.7E-06 7.2E-01 E /μ&HM /μ 4.3E-52 2.6E-28 1.9E-10 7.8E-06 8.5E-01

1B*5B

E /μ&AM /μ 1.6E-200 5.3E-87 1.1E-24 2.6E-10 7.2E-01 E /μ&GM /μ

1.9E-16

1.2E-09 1.3E-03 4.6E-02 9.5E-01 E /μ&HM /μ 1.1E-70 1.1E-24 4.5E-08 1.3E-03 9.3E-01

2B*1B

E /μ&AM /μ 2.2E-155 7.0E-67 1.6E-25 1.6E-12 6.8E-01 E /μ&GM /μ 2.0E-29 1.2E-17 1.2E-09 1.5E-06 7.9E-01 E /μ&HM /μ 1.5E-60 7.1E-28 2.6E-08 9.5E-04 9.1E-01

2B*2B

E /μ&AM /μ 2.1E-189 1.3E-81 6.2E-26 1.6E-09 5.3E-01 E /μ&GM /μ 1.7E-21 4.1E-13 9.8E-08 6.6E-04 7.9E-01 E /μ&HM /μ 3.4E-66 7.4E-23 2.7E-07 2.2E-04 9.9E-01

2B*5B

E /μ&AM /μ 2.0E-253 2.4E-109 5.6E-29 1.6E-12 6.0E-01 E /μ&GM /μ 4.7E-23 1.2E-09

4.3E-03 8.4E-02

9.8E-01 E /μ&HM /μ 6.0E-93 4.1E-30 1.4E-10 2.6E-03 9.5E-01 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

148

表 B. 10 等向性

3 單位基礎寬下楊氏模數與不同範圍之數學平均 P-value (5B，10B，V = 0.5)

 = 1  = 2  = 5  = 10  = 100 V = 0.5

5B*1B

E /μ&AM /μ 6.1E-220 1.3E-101 5.6E-29 4.8E-10 6.8E-01 E /μ&GM /μ 3.0E-19

1.6E-09

4.6E-04 1.1E-02 9.3E-01 E /μ&HM /μ 3.4E-66 3.0E-23 9.5E-07 6.6E-04 9.9E-01

5B*2B

E /μ&AM /μ 3.7E-262 2.4E-131 2.3E-34 1.7E-14 5.7E-01 E /μ&GM /μ 1.9E-23 3.6E-18 5.5E-04 3.6E-02 9.3E-01 E /μ&HM /μ 5.8E-89 3.3E-29 2.8E-09 9.1E-03 9.5E-01

5B*5B

E /μ&AM /μ 1.01E-317 6.0E-177 4.0E-49 1.7E-21 4.6E-01 E /μ&GM /μ 4.0E-49 3.7E-33 3.7E-09 5.5E-04 9.7E-01 E /μ&HM /μ 1.2E-137 3.6E-63 1.0E-20 9.5E-07 6.4E-01

10B*1B

E /μ&AM /μ 6.8E-276 2.9E-133 5.8E-48 5.9E-17 4.6E-01 E /μ&GM /μ 8.7E-27 5.9E-17 3.7E-09 4.3E-03 8.2E-01 E /μ&HM /μ 9.4E-90 1.3E-36 1.2E-14 4.5E-07 8.2E-01

10B*2B

E /μ&AM /μ 2.68E-310 3.1E-169 6.5E-54 1.8E-22 2.3E-01 E /μ&GM /μ 1.5E-44 3.3E-29 8.3E-12 1.9E-05 5.7E-01 E /μ&HM /μ 5.2E-121 2.6E-53 4.5E-22 1.4E-10 6.8E-01

10B*5B

E /μ&AM /μ 0.0E+00 3.1E-216 1.3E-81 1.3E-37 1.3E-01 E /μ&GM /μ 1.1E-75 1.7E-51 1.2E-23 2.2E-11 5.3E-01 E /μ&HM /μ 1.0E-174 6.1E-91 1.5E-41 8.8E-17 2.6E-01 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

149

表 B. 11 等向性

3 單位基礎寬下楊氏模數與不同範圍之數學平均 P-value (1B，2B，V = 1)

 = 1  = 2  = 5  = 10  = 100 V = 1

1B*1B

E /μ&AM /μ 2.6E-224 6.5E-130 2.8E-41 1.2E-17 4.6E-01 E /μ&GM /μ 2.0E-49 7.5E-37 5.4E-18 1.9E-10 6.0E-01 E /μ&HM /μ 5.8E-89 2.3E-42 5.7E-15 1.5E-05 6.8E-01

1B*2B

E /μ&AM /μ 4.4E-280 4.6E-167 3.4E-51 1.3E-19 6.0E-01 E /μ&GM /μ 1.5E-44 8.4E-31 2.2E-11 2.5E-06 8.2E-01 E /μ&HM /μ 2.6E-113 4.0E-49 7.1E-14 1.5E-05 8.5E-01

1B*5B

E /μ&AM /μ 0.0E+00 8.2E-234 5.7E-75 1.6E-28 3.1E-01 E /μ&GM /μ 5.3E-50 2.9E-24 2.0E-08 9.9E-05 9.5E-01 E /μ&HM /μ 1.4E-159 3.4E-66 5.4E-18 4.9E-06 9.5E-01

2B*1B

E /μ&AM /μ 2.6E-284 2.0E-156 5.8E-46 7.0E-19 4.3E-01 E /μ&GM /μ 2.8E-44 1.7E-31 2.2E-12 4.5E-07 6.4E-01 E /μ&HM /μ 3.2E-110 4.4E-56 1.9E-16 2.3E-05 8.5E-01

2B*2B

E /μ&AM /μ 0.0E+00 1.1E-204 1.3E-53 1.1E-24 4.3E-01 E /μ&GM /μ 1.2E-38

1.2E-23

5.8E-08 1.9E-05 8.2E-01 E /μ&HM /μ 3.8E-138 1.4E-59 8.1E-18 1.9E-05 9.5E-01

2B*5B

E /μ&AM /μ 0.0E+00 8.7E-281 6.0E-93 2.9E-31 1.8E-01 E /μ&GM /μ 3.2E-60 2.0E-29 2.1E-09 1.5E-04 8.2E-01 E /μ&HM /μ 1.1E-204 3.7E-94 4.6E-24 1.2E-06 9.8E-01 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

150

表 B. 12 等向性

3 單位基礎寬下楊氏模數與不同範圍之數學平均 P-value (5B，10B，V = 1)

 = 1  = 2  = 5  = 10  = 100 V = 1

5B*1B

E /μ&AM /μ 0.0E+00 3.6E-233 3.2E-67 4.1E-30 1.9E-01 E /μ&GM /μ

1.3E-37

3.2E-27 5.8E-08

9.5E-04

6.0E-01 E /μ&HM /μ 1.4E-159 3.0E-59 1.6E-18 4.5E-07 9.7E-01

5B*2B

E /μ&AM /μ 0.0E+00 1.7E-281 1.9E-85 3.7E-39 2.6E-01 E /μ&GM /μ 2.1E-56 2.9E-31

7.6E-08

4.9E-06 8.2E-01 E /μ&HM /μ 9.6E-199 1.3E-86 1.0E-25 7.4E-07 9.5E-01

5B*5B

E /μ&AM /μ 0.0E+00 0.0E+00 9.4E-134 3.2E-54 7.5E-02 E /μ&GM /μ 7.5E-98 3.2E-54 1.9E-16 1.3E-07 6.8E-01 E /μ&HM /μ 8.4E-261 3.6E-137 5.2E-41 1.4E-13 6.0E-01

10B*1B

E /μ&AM /μ 0.0E+00 2.9E-289 9.9E-107 6.8E-51 1.6E-02 E /μ&GM /μ 1.3E-53 1.4E-30 1.6E-11 4.5E-08 6.0E-01 E /μ&HM /μ 1.3E-215 3.3E-96 1.2E-33 3.5E-14 3.6E-01

10B*2B

E /μ&AM /μ 0.0E+00 0.0E+00 7.9E-132 6.7E-60 3.2E-02 E /μ&GM /μ 7.8E-86 1.5E-41 7.0E-19 2.0E-08 4.9E-01 E /μ&HM /μ 3.7E-262 1.5E-127 2.8E-44 1.6E-18 1.8E-01

10B*5B

E /μ&AM /μ 0.0E+00 0.0E+00 7.2E-181 2.2E-79 3.6E-03 E /μ&GM /μ 1.7E-128 6.9E-74 2.4E-35 5.9E-17 3.9E-01 E /μ&HM /μ 1.3E-306 1.1E-183 1.5E-67 1.9E-32 5.9E-02 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

151

表 B. 13 等向性

3 單位基礎寬下楊氏模數除不同範圍之數學平均之期望值與變異系數 (1B，2B，V = 0.1)

 = 1  = 2  = 5  = 10  = 100

V = 0.1

1B*1B

E / AM 0.996 0.021 0.995 0.030 0.996 0.040 0.998 0.041 1.000 0.021 E / GM 1.000 0.021 0.998 0.030 0.999 0.040 0.999 0.041 1.000 0.021 E / HM 1.003 0.021 1.001 0.030 1.001 0.040 1.001 0.041 1.000 0.021

1B*2B

E / AM 0.995 0.014 0.996 0.022 0.996 0.031 0.998 0.030 1.000 0.014 E / GM 0.999 0.014 1.000 0.022 0.999 0.031 1.000 0.030 1.000 0.014 E / HM 1.002 0.014 1.004 0.022 1.002 0.031 1.002 0.031 1.000 0.014

1B*5B

E / AM 0.995 0.011 0.995 0.019 0.996 0.031 0.998 0.032 0.999 0.018 E / GM 0.999 0.011 0.999 0.019 1.000 0.031 1.000 0.032 1.000 0.018 E / HM 1.002 0.011 1.003 0.019 1.003 0.031 1.003 0.033 1.001 0.018

2B*1B

E / AM 0.996 0.013 0.994 0.020 0.995 0.031 0.997 0.034 1.000 0.020 E / GM 0.999 0.013 0.998 0.020 0.998 0.031 0.999 0.034 1.000 0.020 E / HM 1.003 0.013 1.002 0.020 1.001 0.031 1.001 0.034 1.000 0.020

2B*2B

E / AM 0.995 0.009 0.996 0.014 0.995 0.021 0.996 0.022 0.999 0.012 E / GM 0.998 0.009 1.000 0.014 0.998 0.021 0.999 0.022 1.000 0.012 E / HM 1.002 0.009 1.004 0.014 1.001 0.021 1.001 0.022 1.000 0.012

2B*5B

E / AM 0.995 0.009 0.994 0.015 0.995 0.025 0.997 0.027 0.999 0.016 E / GM 0.999 0.009 0.998 0.015 0.999 0.025 1.000 0.027 1.000 0.016 E / HM 1.002 0.009 1.003 0.015 1.003 0.025 1.003 0.027 1.000 0.016 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

152

表 B. 14 等向性

3 單位基礎寬下楊氏模數除不同範圍之數學平均之期望值與變異系數 (5B，10B，V = 0.1)

 = 1  = 2  = 5  = 10  = 100

V = 0.1

5B*1B

E / AM 0.995 0.011 0.994 0.019 0.996 0.029 0.994 0.033 0.999 0.021 E / GM 0.999 0.011 0.998 0.019 1.000 0.029 0.997 0.033 1.000 0.021 E / HM 1.003 0.011 1.002 0.019 1.004 0.029 1.000 0.033 1.000 0.021

5B*2B

E / AM 0.995 0.010 0.995 0.015 0.995 0.024 0.994 0.026 0.999 0.014 E / GM 0.999 0.010 0.999 0.015 0.999 0.024 0.998 0.026 1.000 0.014 E / HM 1.002 0.010 1.003 0.015 1.003 0.024 1.001 0.026 1.000 0.014

5B*5B

E / AM 0.995 0.010 0.994 0.016 0.995 0.027 0.995 0.030 0.999 0.017 E / GM 0.999 0.010 0.999 0.016 0.999 0.027 0.999 0.030 1.000 0.017 E / HM 1.002 0.010 1.003 0.016 1.004 0.027 1.003 0.030 1.001 0.017

10B*1B

E / AM 0.995 0.011 0.994 0.019 0.995 0.033 0.994 0.042 1.000 0.027 E / GM 0.999 0.011 0.998 0.019 0.999 0.033 0.998 0.042 1.001 0.027 E / HM 1.002 0.011 1.003 0.019 1.004 0.033 1.002 0.042 1.002 0.027

10B*2B

E / AM 0.995 0.011 0.995 0.017 0.995 0.031 0.994 0.038 1.000 0.023 E / GM 0.999 0.011 0.999 0.017 0.999 0.031 0.998 0.038 1.001 0.023 E / HM 1.002 0.011 1.003 0.017 1.003 0.031 1.002 0.038 1.002 0.023

10B*5B

E / AM 0.995 0.011 0.994 0.018 0.995 0.032 0.994 0.039 0.999 0.025 E / GM 0.999 0.011 0.999 0.018 1.000 0.032 0.998 0.039 1.001 0.025 E / HM 1.002 0.011 1.003 0.018 1.004 0.032 1.003 0.039 1.002 0.025 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

153

表 B. 15 等向性

3 單位基礎寬下楊氏模數除不同範圍之數學平均之期望值與變異系數 (1B，2B，V = 0.5)

 = 1  = 2  = 5  = 10  = 100

V = 0.5

1B*1B

E / AM 0.903 0.093 0.909 0.148 0.925 0.195 0.949 0.196 0.991 0.099 E / GM 0.976 0.091 0.979 0.146 0.974 0.193 0.981 0.194 0.994 0.099 E / HM 1.054 0.093 1.054 0.148 1.026 0.193 1.015 0.193 0.998 0.099

1B*2B

E / AM 0.898 0.067 0.894 0.107 0.910 0.148 0.938 0.155 0.987 0.070 E / GM 0.973 0.065 0.972 0.104 0.971 0.145 0.981 0.152 0.993 0.069 E / HM 1.055 0.065 1.057 0.107 1.038 0.146 1.027 0.153 0.998 0.069

1B*5B

E / AM 0.898 0.056 0.889 0.094 0.903 0.145 0.925 0.158 0.987 0.081 E / GM 0.976 0.055 0.974 0.092 0.981 0.144 0.989 0.158 0.998 0.081 E / HM 1.061 0.055 1.067 0.094 1.067 0.149 1.057 0.165 1.010 0.083

2B*1B

E / AM 0.899 0.064 0.895 0.099 0.908 0.149 0.935 0.162 0.988 0.091 E / GM 0.975 0.061 0.973 0.095 0.969 0.144 0.977 0.159 0.993 0.091 E / HM 1.058 0.063 1.058 0.097 1.035 0.144 1.023 0.158 0.999 0.091

2B*2B

E / AM 0.896 0.044 0.886 0.069 0.897 0.105 0.923 0.112 0.985 0.058 E / GM 0.974 0.041 0.968 0.064 0.967 0.099 0.975 0.108 0.992 0.058 E / HM 1.058 0.042 1.059 0.065 1.044 0.101 1.031 0.109 1.000 0.058

2B*5B

E / AM 0.895 0.044 0.884 0.070 0.893 0.117 0.914 0.131 0.985 0.071 E / GM 0.974 0.043 0.971 0.069 0.977 0.116 0.984 0.131 0.998 0.071 E / HM 1.060 0.043 1.066 0.070 1.068 0.120 1.059 0.138 1.012 0.073 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

154

表 B. 16 等向性

3 單位基礎寬下楊氏模數除不同範圍之數學平均之期望值與變異系數 (5B，10B，V = 0.5)

 = 1  = 2  = 5  = 10  = 100

V = 0.5

5B*1B

E / AM 0.895 0.059 0.883 0.096 0.893 0.146 0.917 0.166 0.982 0.095 E / GM 0.973 0.058 0.967 0.093 0.972 0.142 0.981 0.164 0.994 0.095 E / HM 1.059 0.058 1.059 0.095 1.060 0.146 1.051 0.170 1.006 0.096

5B*2B

E / AM 0.893 0.049 0.878 0.081 0.889 0.119 0.905 0.126 0.980 0.069 E / GM 0.973 0.048 0.964 0.079 0.973 0.116 0.974 0.122 0.993 0.068 E / HM 1.059 0.048 1.059 0.079 1.066 0.120 1.050 0.126 1.007 0.069

5B*5B

E / AM 0.893 0.048 0.880 0.078 0.886 0.126 0.903 0.144 0.979 0.081 E / GM 0.973 0.047 0.968 0.078 0.977 0.124 0.982 0.142 0.999 0.081 E / HM 1.060 0.047 1.066 0.078 1.077 0.126 1.070 0.146 1.018 0.082

10B*1B

E / AM 0.894 0.058 0.883 0.099 0.888 0.168 0.913 0.201 0.976 0.127 E / GM 0.973 0.057 0.969 0.098 0.976 0.168 0.992 0.201 0.997 0.126 E / HM 1.059 0.057 1.064 0.099 1.074 0.172 1.080 0.208 1.017 0.127

10B*2B

E / AM 0.893 0.052 0.880 0.091 0.887 0.153 0.904 0.182 0.974 0.111 E / GM 0.972 0.052 0.968 0.091 0.978 0.154 0.986 0.182 0.995 0.110 E / HM 1.059 0.052 1.065 0.091 1.079 0.157 1.077 0.188 1.018 0.111

10B*5B

E / AM 0.892 0.050 0.880 0.087 0.885 0.154 0.899 0.190 0.973 0.121 E / GM 0.973 0.050 0.969 0.087 0.979 0.154 0.987 0.190 1.000 0.120 E / HM 1.060 0.050 1.068 0.087 1.084 0.155 1.085 0.195 1.028 0.122 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

155

表 B. 17 等向性

3 單位基礎寬下楊氏模數除不同範圍之數學平均之期望值與變異系數 (1B，2B，V = 1)

 = 1  = 2  = 5  = 10  = 100

V = 1

1B*1B

E / AM 0.737 0.182 0.740 0.262 0.809 0.325 0.859 0.341 0.984 0.174 E / GM 0.936 0.170 0.931 0.241 0.948 0.315 0.949 0.335 0.995 0.174 E / HM 1.191 0.181 1.181 0.245 1.114 0.321 1.051 0.336 1.006 0.175

1B*2B

E / AM 0.719 0.129 0.708 0.196 0.769 0.266 0.809 0.269 0.972 0.122 E / GM 0.924 0.116 0.916 0.177 0.936 0.250 0.928 0.253 0.988 0.121 E / HM 1.190 0.120 1.190 0.185 1.147 0.263 1.071 0.258 1.005 0.122

1B*5B

E / AM 0.709 0.107 0.689 0.170 0.717 0.266 0.767 0.284 0.954 0.144 E / GM 0.921 0.099 0.913 0.162 0.924 0.255 0.939 0.281 0.988 0.144 E / HM 1.196 0.102 1.212 0.175 1.199 0.275 1.157 0.310 1.024 0.149

2B*1B

E / AM 0.719 0.117 0.710 0.188 0.770 0.265 0.819 0.282 0.974 0.158 E / GM 0.926 0.107 0.921 0.163 0.936 0.243 0.938 0.273 0.991 0.158 E / HM 1.194 0.117 1.200 0.172 1.146 0.248 1.080 0.282 1.009 0.159

2B*2B

E / AM 0.711 0.084 0.692 0.137 0.737 0.199 0.780 0.209 0.962 0.101 E / GM 0.922 0.074 0.912 0.116 0.927 0.174 0.921 0.186 0.984 0.099 E / HM 1.195 0.081 1.206 0.124 1.173 0.187 1.095 0.193 1.008 0.100

2B*5B

E / AM 0.708 0.084 0.680 0.132 0.698 0.214 0.751 0.239 0.945 0.130 E / GM 0.921 0.078 0.909 0.122 0.916 0.203 0.936 0.233 0.985 0.128 E / HM 1.199 0.080 1.218 0.130 1.209 0.220 1.174 0.258 1.027 0.133 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

156

表 B. 18 等向性

3 單位基礎寬下楊氏模數除不同範圍之數學平均之期望值與變異系數 (5B，10B，V = 1)

 = 1  = 2  = 5  = 10  = 100

V = 1

5B*1B

E / AM 0.715 0.109 0.688 0.167 0.730 0.275 0.774 0.293 0.955 0.174 E / GM 0.928 0.103 0.911 0.155 0.940 0.257 0.948 0.279 0.990 0.172 E / HM 1.204 0.108 1.210 0.166 1.225 0.283 1.173 0.303 1.027 0.175

5B*2B

E / AM 0.709 0.089 0.680 0.140 0.709 0.214 0.748 0.246 0.943 0.125 E / GM 0.922 0.086 0.909 0.133 0.932 0.203 0.933 0.228 0.983 0.121 E / HM 1.201 0.089 1.216 0.139 1.232 0.228 1.176 0.252 1.026 0.125

5B*5B

E / AM 0.706 0.090 0.675 0.139 0.685 0.216 0.732 0.256 0.928 0.143 E / GM 0.921 0.087 0.909 0.135 0.922 0.209 0.945 0.244 0.984 0.139 E / HM 1.202 0.088 1.226 0.140 1.249 0.222 1.230 0.262 1.044 0.144

10B*1B

E / AM 0.714 0.103 0.683 0.171 0.708 0.300 0.756 0.367 0.939 0.232 E / GM 0.929 0.100 0.914 0.165 0.945 0.292 0.978 0.372 1.001 0.231 E / HM 1.208 0.103 1.225 0.172 1.271 0.312 1.284 0.426 1.070 0.246

10B*2B

E / AM 0.709 0.094 0.679 0.154 0.696 0.268 0.738 0.335 0.929 0.201 E / GM 0.924 0.092 0.913 0.151 0.938 0.267 0.966 0.336 0.995 0.199 E / HM 1.205 0.095 1.229 0.157 1.270 0.286 1.280 0.380 1.070 0.215

10B*5B

E / AM 0.708 0.094 0.677 0.152 0.678 0.259 0.729 0.338 0.917 0.215 E / GM 0.923 0.093 0.914 0.150 0.928 0.257 0.971 0.340 0.998 0.212 E / HM 1.205 0.093 1.235 0.153 1.275 0.266 1.304 0.365 1.089 0.225 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

157

158

159

表 B. 19 異向性

3 單位基礎寬下楊氏模數與不同範圍之數學平均總相差值 (V = 0.1)

 = 1  = 2  = 5  = 10  = 100 V = 0.1

1B*1B

E /μ-AM /μ 26.961 34.425 36.799 33.433 15.025 E /μ-GM /μ 26.472 34.036 36.625 33.349 15.028 E /μ-HM /μ 26.256 33.828 36.489 33.286 15.031

1B*2B

E /μ-AM /μ 16.178 18.905 22.180 20.547 8.845 E /μ-GM /μ 15.305 18.274 21.895 20.299 8.851 E /μ-HM /μ 15.016 18.105 21.797 20.120 8.861

1B*5B

E /μ-AM /μ 14.675 19.096 23.181 21.993 11.546 E /μ-GM /μ 13.685 18.313 22.959 21.886 11.517 E /μ-HM /μ

13.477 17.955 22.917 21.900

11.492 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

160

表 B. 20 異向性

3 單位基礎寬下楊氏模數與不同範圍之數學平均總相差值 (V = 0.5、1)

 = 1  = 2  = 5  = 10  = 100 V = 0.5

1B*1B

E /μ-AM /μ 167.563 180.389 194.861 172.589 75.623 E /μ-GM /μ 126.784 150.425 176.589 164.474 75.435 E /μ-HM /μ 109.566 135.691 163.906 158.222 75.256

1B*2B

E /μ-AM /μ 145.404 146.573 144.355 121.905 43.525 E /μ-GM /μ 83.701 96.521 110.966 103.891 42.752 E /μ-HM /μ 62.325 79.100 94.486 95.186 42.388

1B*5B

E /μ-AM /μ 139.984 147.061 131.071 112.267 56.234 E /μ-GM /μ 68.676 84.446 96.784 95.913 55.452 E /μ-HM /μ

56.798 71.913 91.992 95.568

54.899

V = 1

1B*1B

E /μ-AM /μ 385.581 400.567 373.094 305.396 127.138 E /μ-GM /μ 222.232 262.542 300.509 275.033 126.149 E /μ-HM /μ 150.431 193.990 254.157 254.808 125.512

1B*2B

E /μ-AM /μ 358.945 372.329 325.303 272.466 79.702 E /μ-GM /μ 153.201 183.940 196.145 198.350 74.985 E /μ-HM /μ 79.179 109.010 131.995 152.816 71.816

1B*5B

E /μ-AM /μ 359.472 368.168 308.389 266.950 95.628 E /μ-GM /μ 131.090 136.797 142.581 156.078 90.990 E /μ-HM /μ

75.110 96.947 117.287 137.691

88.545 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

161

表 B. 21 異向性

3 單位基礎寬下楊氏模數與不同範圍之數學平均 P-value (V = 0.1)

 = 1  = 2  = 5  = 10  = 100 V = 0.1

1B*1B

E /μ&AM /μ 1.7E-14 1.4E-10 6.2E-06 5.5E-04 9.9E-01 E /μ&GM /μ 6.0E-12 3.7E-09 2.3E-05 7.9E-04 9.9E-01 E /μ&HM /μ 1.2E-09 1.6E-09 6.6E-05 9.5E-04 9.9E-01

1B*2B

E /μ&AM /μ 1.3E-07 3.8E-04 5.8E-03 3.2E-02 1.0E+00 E /μ&GM /μ 1.5E-04 2.2E-03 2.4E-02 4.6E-02 1.0E+00 E /μ&HM /μ 6.8E-03 5.0E-03 5.9E-02 8.4E-02 1.0E+00

1B*5B

E /μ&AM /μ 6.5E-09 3.6E-05 2.8E-02 2.1E-01 9.1E-01 E /μ&GM /μ 3.1E-03 6.8E-03 2.3E-01 5.3E-01 9.5E-01 E /μ&HM /μ

8.4E-02 1.2E-01 2.6E-01 5.7E-01

9.9E-01 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

162

表 B. 22 異向性

3 單位基礎寬下楊氏模數與不同範圍之數學平均 P-value (V = 0.5、1)

 = 1  = 2  = 5  = 10  = 100 V = 0.5

1B*1B

E /μ&AM /μ 4.0E-49 1.2E-33 1.9E-15 4.5E-08 8.5E-01 E /μ&GM /μ 7.4E-24 1.7E-21 5.6E-11 6.2E-06 9.1E-01 E /μ&HM /μ 2.8E-09 1.9E-10 1.3E-07 1.8E-04 9.3E-01

1B*2B

E /μ&AM /μ 1.3E-58 6.5E-33 2.4E-14 3.1E-06 9.3E-01 E /μ&GM /μ 1.8E-17 4.3E-12 9.5E-07 9.5E-04 9.5E-01 E /μ&HM /μ 9.5E-04 3.2E-04 3.1E-03 1.2E-01 9.9E-01

1B*5B

E /μ&AM /μ 2.9E-78 5.6E-58 8.8E-17 2.1E-07 4.6E-01 E /μ&GM /μ 3.6E-18 5.7E-15 3.6E-05 7.5E-02 7.5E-01 E /μ&HM /μ

7.8E-06 4.3E-03 3.2E-02 2.8E-01

9.9E-01

V = 1

1B*1B

E /μ&AM /μ 6.7E-109 1.6E-73 4.3E-25 8.7E-09 7.9E-01 E /μ&GM /μ 1.6E-46 7.6E-36 2.4E-14 3.9E-06 8.2E-01 E /μ&HM /μ 1.1E-12 8.3E-12 1.3E-07 4.6E-04 9.1E-01

1B*2B

E /μ&AM /μ 9.5E-152 1.1E-84 6.9E-30 8.3E-12 7.5E-01 E /μ&GM /μ 8.1E-42 2.0E-27 2.9E-13 2.3E-05 9.8E-01 E /μ&HM /μ 9.5E-07 1.1E-03 5.0E-03 4.6E-02 1.0E+00

1B*5B

E /μ&AM /μ 4.1E-210 7.9E-132 2.0E-49 1.0E-20 3.6E-01 E /μ&GM /μ 6.5E-54 2.3E-26 7.7E-11 1.2E-04 9.3E-01 E /μ&HM /μ

8.7E-09 2.1E-09 5.0E-03 2.1E-01

9.9E-01 註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

163

表 B. 23 異向性

3 單位基礎寬下楊氏模數除不同範圍之數學平均之期望值與變異系數 (V = 0.1)

 = 1  = 2  = 5  = 10  = 100

V = 0.1

1B*1B

E / AM 0.994 0.033 0.996 0.043 0.997 0.046 0.997 0.041 1.000 0.019 E / GM 0.997 0.033 0.999 0.043 0.999 0.046 0.998 0.041 1.001 0.019 E / HM 1.000 0.033 1.001 0.043 1.000 0.046 0.999 0.041 1.001 0.019

1B*2B

E / AM 0.993 0.019 0.995 0.023 0.996 0.028 0.996 0.025 1.000 0.011 E / GM 0.997 0.019 0.998 0.023 0.998 0.027 0.998 0.025 1.000 0.011 E / HM 1.000 0.019 1.002 0.023 1.000 0.028 0.999 0.025 1.001 0.011

1B*5B

E / AM 0.993 0.017 0.992 0.023 0.994 0.029 0.997 0.027 0.999 0.014 E / GM 0.997 0.017 0.996 0.023 0.998 0.029 1.000 0.027 0.999 0.014 E / HM

1.001 0.017 1.000 0.023 1.001 0.029 1.002 0.027 0.999 0.014

註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

164

表 B. 24 異向性

3 單位基礎寬下楊氏模數除不同範圍之數學平均之期望值與變異系數(V = 0.5、1)

 = 1  = 2  = 5  = 10  = 100

V = 0.5

1B*1B

E / AM 0.886 0.161 0.904 0.191 0.933 0.213 0.950 0.199 0.995 0.093 E / GM 0.943 0.153 0.953 0.186 0.962 0.210 0.967 0.198 0.996 0.093 E / HM 1.005 0.155 1.007 0.188 0.992 0.209 0.985 0.198 0.998 0.093

1B*2B

E / AM 0.868 0.102 0.880 0.126 0.906 0.141 0.935 0.127 0.992 0.054 E / GM 0.938 0.091 0.945 0.115 0.952 0.131 0.966 0.124 0.996 0.054 E / HM 1.015 0.093 1.017 0.118 1.002 0.128 0.999 0.124 1.000 0.054

1B*5B

E / AM 0.861 0.087 0.857 0.115 0.885 0.138 0.918 0.133 0.985 0.069 E / GM 0.942 0.079 0.937 0.105 0.956 0.130 0.972 0.129 0.995 0.069 E / HM

1.031 0.079 1.026 0.105 1.033 0.133 1.032 0.136 1.005 0.070

V = 1

1B*1B

E / AM 0.693 0.317 0.722 0.344 0.831 0.371 0.909 0.329 0.988 0.155 E / GM 0.838 0.277 0.846 0.316 0.909 0.355 0.956 0.324 0.993 0.155 E / HM 1.028 0.283 1.001 0.324 1.000 0.351 1.007 0.324 0.998 0.155

1B*2B

E / AM 0.652 0.211 0.678 0.252 0.751 0.265 0.824 0.238 0.977 0.095 E / GM 0.827 0.161 0.837 0.209 0.867 0.225 0.901 0.219 0.989 0.092 E / HM 1.063 0.177 1.045 0.218 1.011 0.219 0.990 0.213 1.000 0.090

1B*5B

E / AM 0.629 0.184 0.643 0.232 0.700 0.254 0.760 0.250 0.955 0.115 E / GM 0.825 0.149 0.839 0.190 0.870 0.221 0.899 0.227 0.983 0.114 E / HM

1.088 0.149 1.106 0.199 1.091 0.237 1.076 0.254 1.012 0.118

註：AM 代表算數平均(Arithmetic average); GM 代表幾何平均(Geometric average);

HM 代表倒數平均(Harmonic average)

165

圖 B. 11 等向性 7.5 單位基礎寬下楊氏模數與不同範圍之數學平均比較( 1B，  = 2，V=0.5 )

在文檔中在簡單應力狀態下探討具有空間變異性土壤的整體彈性模數 (頁 124-200)