An Analytical Solution for Stress and Displacement Field for Arbitrarily Positioned Twin-Tunnel Excavation at Great Depth

<table class="fixed-width table-group" id="tab3"><tr><td><table class="table"><colgroup><col style="width:4.79em"/><col style="width:5.08em"/><col style="width:3.41em"/><col style="width:3.39em"/><col style="width:3.37em"/><col style="width:3.37em"/><col style="width:3.41em"/><col style="width:3.42em"/></colgroup><tr><td class="thead-hr" colspan="8"><hr/></td></tr><tr class="thead"><td class="align_left" colspan="2">Distance</td><td class="align_center">2</td><td class="align_center">3</td><td class="align_center">4</td><td class="align_center">6</td><td class="align_center">10</td><td class="align_center">16</td></tr><tr><td class="thead-hr" colspan="8"><hr/></td></tr><tr><td class="align_left" rowspan="3"><span style="width: 45.7224ptpx;"><svg height="11.1467pt" id="M143" style="vertical-align:-0.3500004pt" version="1.1" viewbox="-0.0498162 -10.7967 45.7224 11.1467" width="45.7224pt" 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="M475 507C475 612 440 712 326 712C139 712 23 420 23 215C23 96 58 -12 180 -12C369 -12 475 293 475 507ZM391 522C391 486 387 448 379 394H126C155 538 222 677 310 677C386 677 391 571 391 522ZM373 346C344 193 283 22 189 22C126 22 106 114 106 196C106 243 111 293 118 346H373Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.107,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,21.37,0)"><path d="M535 290V340H323V533H265V340H52V290H265V84H323V290H535ZM535 -22V28H52V-22H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,29.001,0)"><path d="M244 635C114 635 38 519 38 422C38 317 111 240 217 240C236 240 255 244 277 256L345 292C311 140 203 39 59 15L64 -15C89 -15 150 -5 204 17C339 72 440 202 440 386C440 521 368 635 244 635ZM228 602C326 602 352 479 352 390C352 370 351 347 348 324C327 308 293 296 258 296C174 296 124 369 124 458C124 517 152 602 228 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,35.242,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,41.528,-5.741)"><path d="M339 262C339 340 273 403 193 403S48 340 48 262S113 121 193 121S339 184 339 262ZM283 262C283 210 242 168 193 168S104 210 104 262S144 356 193 356S283 314 283 262Z"></path></g></svg></span></td><td class="align_left">Ling’s</td><td class="align_center">2.569</td><td class="align_center">2.623</td><td class="align_center">2.703</td><td class="align_center">2.825</td><td class="align_center">2.927</td><td class="align_center">2.970</td></tr><tr><td class="align_left">Proposed</td><td class="align_center">2.527</td><td class="align_center">2.554</td><td class="align_center">2.673</td><td class="align_center">2.823</td><td class="align_center">2.929</td><td class="align_center">2.971</td></tr><tr><td class="align_left">Error(%)</td><td class="align_center">1.63</td><td class="align_center">2.63</td><td class="align_center">1.11</td><td class="align_center">0.07</td><td class="align_center">0.07</td><td class="align_center">0.03</td></tr><tr class="table-tr"><td colspan="8"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Circumferential stress owing to the transverse tension of unit force</div>

Mathematical Problems in Engineering

tab3

Table 3

Table 3: An Analytical Solution for Stress and Displacement Field for Arbitrarily Positioned Twin-Tunnel Excavation at Great Depth 