Fuzzy Plastic Constitutive Model and Its Application to Subgrade

<table class="table-group" id="tab5"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left">Position (m)</td><td class="align_center"><svg height="12.7178pt" id="M154" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 23.744 12.7178" width="23.744pt" 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="M538 96L524 119C492 88 454 63 446 63C439 63 434 70 440 101C463 223 491 341 518 448H508L433 422L401 276C355 192 240 56 188 56C163 56 154 89 163 133C184 233 207 338 235 443L230 448L152 424L58 17C40 -60 23 -143 23 -185C23 -241 42 -261 63 -261C92 -261 117 -241 125 -227L124 -221C109 -209 89 -165 89 -103C89 -55 96 -13 105 26H107C121 -3 134 -12 151 -12C172 -12 194 -5 221 16C279 61 330 124 384 194H386C381 159 377 141 368 105C343 3 363 -12 383 -12C416 -12 486 35 538 96Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.216,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.714,0)"><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"></path></g><g transform="matrix(.013,0,0,-0.013,19.061,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg> (%)</td><td class="align_center">Fuzzy results (<svg height="6.1673pt" id="M155" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 7.51131 6.1673" width="7.51131pt" 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="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z"></path></g></svg>  = 1.85)</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left">0</td><td class="align_center">100</td><td class="align_center">1320</td></tr><tr><td class="align_left">−5</td><td class="align_center">20</td><td class="align_center">210</td></tr><tr><td class="align_left">−10</td><td class="align_center">11</td><td class="align_center">167</td></tr><tr><td class="align_left">−15</td><td class="align_center">6</td><td class="align_center">87</td></tr><tr><td class="align_left">−20</td><td class="align_center">1.5</td><td class="align_center">17</td></tr><tr><td class="align_left">−25</td><td class="align_center">0.2</td><td class="align_center">5</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Shear stress at different depths and <i>t</i> = 4/8 (kPa).</div>

Advances in Civil Engineering

tab5

Table 5

Table 5: Fuzzy Plastic Constitutive Model and Its Application to Subgrade 