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. 2025 Jan 7;15:1040. doi: 10.1038/s41598-025-85327-1

Table 4.

Results of the orthogonal experiment and the range analysis.

Experimental number Factor Circular pipe section Rectangular pipe section
Pipe-soil frictional resistance/N
A Empty B C F1c F2c F3c Inline graphic F1r F2r F3r Inline graphic
1 1 1 1 1 353 394 369 372 365 351 388 368
2 1 2 2 2 398 395 371 388 385 417 371 391
3 1 3 3 3 407 411 424 414 409 426 404 413
4 2 1 2 3 317 338 338 331 428 397 417 414
5 2 2 3 1 322 342 350 338 386 420 427 411
6 2 3 1 2 322 301 298 307 434 425 422 427
7 3 1 3 2 309 326 322 319 300 322 329 317
8 3 2 1 3 292 327 299 306 308 298 321 309
9 3 3 2 1 288 279 294 287 301 315 308 308
K 1 1174 1022 985 997

Shape: Circular pipe section

Order of factors (primary to secondary): A > B > C

Optimal scheme: A3B1C1
K 2 976 1032 1006 1014
K 3 912 1008 1071 1051
k 1 391.33 340.67 328.33 332.33
k 2 325.33 344 335.33 338
k 3 304 336 357 350.33
R 87.33 8 28.67 18
K 1 1162 1089 1094 1077

Shape: Rectangular pipe section

Order of factors (primary to secondary): A > B > C

Optimal scheme: A3B1C1
K 2 1252 1111 1113 1135
K 3 934 1148 1141 1136
k 1 387.33 363 364.67 359
k 2 417.33 370.33 371 378.33
k 3 311.33 382.67 380.33 378.67
R 106 19.67 15.67 19.67