Elastoplastic Modelling of an In Situ Concrete Spalling Experiment Using the Ottosen Failure Criterion

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr class="thead"><td class="align_left">Stress interpretation</td><td class="align_center"><svg height="11.6726pt" id="M19" style="vertical-align:-5.52901pt" version="1.1" viewbox="-0.0498162 -6.14359 17.6041 11.6726" width="17.6041pt" 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="M548 455L523 469C505 448 490 439 461 439C416 439 374 447 316 447C144 447 23 310 23 161C23 47 89 -12 179 -12C312 -12 429 106 429 244C429 303 419 344 368 386L371 388C404 383 440 378 474 378C507 378 530 411 548 455ZM350 274C350 191 308 25 198 25C144 25 108 75 108 157C108 264 170 395 276 395C296 395 320 384 333 360C347 334 350 316 350 274Z" id="g113-240"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="565" vert-adv-y="565"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.76,3.132)"><path d="M563 395C563 428 543 451 519 451C500 451 480 438 472 423C468 415 465 403 470 394C477 381 482 368 482 347C482 272 386 136 342 74H340C334 163 323 257 312 337C302 410 290 451 257 451C214 451 160 385 127 338L145 310C169 341 203 373 209 373C219 373 225 369 232 325C249 215 269 62 271 -15C220 -80 135 -165 18 -231L26 -257L142 -230C254 -105 279 -74 342 13C394 85 484 211 526 286C553 334 563 365 563 395Z" id="g50-122"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,11.601,3.132)"><path d="M563 395C563 428 543 451 519 451C500 451 480 438 472 423C468 415 465 403 470 394C477 381 482 368 482 347C482 272 386 136 342 74H340C334 163 323 257 312 337C302 410 290 451 257 451C214 451 160 385 127 338L145 310C169 341 203 373 209 373C219 373 225 369 232 325C249 215 269 62 271 -15C220 -80 135 -165 18 -231L26 -257L142 -230C254 -105 279 -74 342 13C394 85 484 211 526 286C553 334 563 365 563 395Z" id="g50-122"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g></svg> [MPa]</td><td class="align_center">Dip direction [°]</td><td class="align_center"><svg height="9.4347pt" id="M20" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -6.14359 17.7777 9.4347" width="17.7777pt" 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="M548 455L523 469C505 448 490 439 461 439C416 439 374 447 316 447C144 447 23 310 23 161C23 47 89 -12 179 -12C312 -12 429 106 429 244C429 303 419 344 368 386L371 388C404 383 440 378 474 378C507 378 530 411 548 455ZM350 274C350 191 308 25 198 25C144 25 108 75 108 157C108 264 170 395 276 395C296 395 320 384 333 360C347 334 350 316 350 274Z" id="g113-240"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="565" vert-adv-y="565"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.76,3.132)"><path d="M545 403C545 425 527 451 498 451C448 451 400 404 312 286L290 341C262 412 246 451 219 451C182 451 138 404 92 345L112 323C152 368 169 378 181 378C192 378 201 359 216 321L257 214C184 115 142 69 113 69C102 69 93 73 88 79S78 89 68 89C47 89 24 61 24 40C24 8 49 -12 75 -12C125 -12 175 31 271 175L312 64C330 15 357 -12 382 -12C421 -12 475 35 515 98L496 121C466 88 439 62 420 62C402 62 384 92 363 147L325 247C349 280 374 309 397 333C422 361 446 381 462 381C471 381 481 374 488 366C493 360 499 357 505 357C521 357 545 380 545 403Z" id="g50-121"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="569" vert-adv-y="569"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,11.938,3.132)"><path d="M545 403C545 425 527 451 498 451C448 451 400 404 312 286L290 341C262 412 246 451 219 451C182 451 138 404 92 345L112 323C152 368 169 378 181 378C192 378 201 359 216 321L257 214C184 115 142 69 113 69C102 69 93 73 88 79S78 89 68 89C47 89 24 61 24 40C24 8 49 -12 75 -12C125 -12 175 31 271 175L312 64C330 15 357 -12 382 -12C421 -12 475 35 515 98L496 121C466 88 439 62 420 62C402 62 384 92 363 147L325 247C349 280 374 309 397 333C422 361 446 381 462 381C471 381 481 374 488 366C493 360 499 357 505 357C521 357 545 380 545 403Z" id="g50-121"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="569" vert-adv-y="569"></glyph.data></g></svg> [MPa]</td><td class="align_center">Dip direction [°]</td><td class="align_center"><svg height="9.52604pt" id="M21" style="vertical-align:-3.38245pt" version="1.1" viewbox="-0.0498162 -6.14359 16.6085 9.52604" width="16.6085pt" 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="M548 455L523 469C505 448 490 439 461 439C416 439 374 447 316 447C144 447 23 310 23 161C23 47 89 -12 179 -12C312 -12 429 106 429 244C429 303 419 344 368 386L371 388C404 383 440 378 474 378C507 378 530 411 548 455ZM350 274C350 191 308 25 198 25C144 25 108 75 108 157C108 264 170 395 276 395C296 395 320 384 333 360C347 334 350 316 350 274Z" id="g113-240"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="565" vert-adv-y="565"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.76,3.132)"><path d="M481 445L456 468C426 437 403 427 388 427C372 427 356 428 302 438C256 447 221 451 187 451C159 451 130 428 105 384C93 363 80 340 65 305L96 290C122 342 149 381 193 381C216 381 267 377 294 374S346 372 365 376L75 105C37 70 24 35 24 16C24 2 30 -5 35 -8C42 -8 46 -6 48 -2C58 14 75 35 90 41C102 46 116 46 147 32C200 8 267 -21 298 -21C347 -21 390 12 448 126L420 151C369 77 338 56 311 56C287 56 249 68 212 81C180 92 149 100 127 98C212 172 353 308 413 372L481 445Z" id="g50-123"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="505" vert-adv-y="505"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,11.356,3.132)"><path d="M481 445L456 468C426 437 403 427 388 427C372 427 356 428 302 438C256 447 221 451 187 451C159 451 130 428 105 384C93 363 80 340 65 305L96 290C122 342 149 381 193 381C216 381 267 377 294 374S346 372 365 376L75 105C37 70 24 35 24 16C24 2 30 -5 35 -8C42 -8 46 -6 48 -2C58 14 75 35 90 41C102 46 116 46 147 32C200 8 267 -21 298 -21C347 -21 390 12 448 126L420 151C369 77 338 56 311 56C287 56 249 68 212 81C180 92 149 100 127 98C212 172 353 308 413 372L481 445Z" id="g50-123"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="505" vert-adv-y="505"></glyph.data></g></svg> [MPa]</td></tr><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr><td class="align_left">EDZ and VT1 −3 m</td><td class="align_center">25.1</td><td class="align_center">166</td><td class="align_center">21.5</td><td class="align_center">256</td><td class="align_center">4.0</td></tr><tr><td class="align_left">ONK-EH3 −3 m</td><td class="align_center">23.0</td><td class="align_center">120</td><td class="align_center">15.0</td><td class="align_center">210</td><td class="align_center">3.0</td></tr><tr class="table-tr"><td colspan="6"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

The in-plane stresses below the tunnel at experiment hole location.

Journal of Engineering

tab2

Table 2

Table 2: Elastoplastic Modelling of an In Situ Concrete Spalling Experiment Using the Ottosen Failure Criterion 