Prediction of the Required Supporting Pressure for a Shallow Tunnel in Layered Rock Strata Based on 2D and 3D Upper Bound Limit Analysis

<div>The required supporting pressure under varying coefficient <span class="nowrap"><svg height="14.6294pt" id="M163" style="vertical-align:-5.34107pt" version="1.1" viewbox="-0.0498162 -9.28833 15.1585 14.6294" width="15.1585pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 2 107 8C115 62 130 128 142 180C153 193 179 220 204 241C231 170 259 106 288 54C317 0 336 -12 358 -12C381 -12 423 2 477 80L460 100C434 74 408 54 398 54C385 54 374 65 351 107C326 154 282 241 263 299C296 332 351 377 403 377C424 377 436 372 445 368C449 366 456 368 462 375C472 386 480 402 480 416Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.474,3.132)"><path d="M558 454L532 470C512 451 497 442 465 442C421 442 376 450 318 450C146 450 24 313 24 164C24 46 91 -12 183 -12C317 -12 439 105 439 247C439 306 428 346 382 385L383 389C414 384 450 379 485 379C517 379 539 412 558 454ZM357 273C357 191 313 28 205 28C149 28 111 79 111 160C111 266 175 396 280 396C298 396 328 386 341 357C353 331 357 315 357 273Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,11.306,5.233)"><path d="M391 403C391 426 353 454 306 454C250 454 180 419 133 378C71 324 25 229 25 151C25 44 73 -12 148 -12C214 -12 303 36 368 102L350 133C324 102 250 54 194 54C151 54 114 82 114 168C114 232 133 291 155 330C170 356 197 399 245 399C278 399 305 383 328 353C335 344 348 342 361 349C383 361 391 384 391 403Z"></path></g></svg>.</span></div>

Advances in Civil Engineering

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Figure 10

Figure 10: Prediction of the Required Supporting Pressure for a Shallow Tunnel in Layered Rock Strata Based on 2D and 3D Upper Bound Limit Analysis 