Influence of Pier Size on its Failure Mode under Near-Fault Vertical Earthquake

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td class="align_left">Height of piers/m</td><td class="align_center">Ratio of longitudinal natural frequencies <svg height="12.5794pt" id="M19" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 39.6248 12.5794" width="39.6248pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,2.179,0)"><path d="M615 290C615 392 563 448 529 448C511 448 491 441 484 434L483 425C518 400 546 349 546 273C546 158 504 46 417 46C381 46 356 77 356 142C356 184 380 293 392 334L387 340L307 323C305 288 296 228 287 188C265 94 221 52 180 52C144 52 112 89 112 171C112 278 164 372 241 430L226 454C106 394 23 288 23 155C23 40 79 -12 139 -12C184 -12 245 32 285 85C292 31 322 -12 376 -12C423 -12 470 18 501 45C570 104 615 184 615 290Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.148,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.095,0)"><path d="M368 703H309L44 -163H104L368 703Z"></path></g><g transform="matrix(.013,0,0,-0.013,22.635,0)"><path d="M615 290C615 392 563 448 529 448C511 448 491 441 484 434L483 425C518 400 546 349 546 273C546 158 504 46 417 46C381 46 356 77 356 142C356 184 380 293 392 334L387 340L307 323C305 288 296 228 287 188C265 94 221 52 180 52C144 52 112 89 112 171C112 278 164 372 241 430L226 454C106 394 23 288 23 155C23 40 79 -12 139 -12C184 -12 245 32 285 85C292 31 322 -12 376 -12C423 -12 470 18 501 45C570 104 615 184 615 290Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,30.604,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,35.036,3.132)"><path d="M397 380C406 395 404 411 396 425S369 451 350 451C302 451 239 372 192 294H189L199 338C214 407 207 451 180 451C152 451 83 405 30 345L48 318C87 354 117 372 125 372S135 362 127 324L55 -5L61 -12C87 -5 117 3 139 5C154 87 168 162 179 207C198 250 240 310 260 332C281 355 297 366 307 366C321 366 333 360 347 346C351 342 360 342 369 348C379 355 389 366 397 380Z"></path></g></svg></td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td class="align_left">7</td><td class="align_center">1.01</td></tr><tr><td class="align_left">10</td><td class="align_center">1.05</td></tr><tr><td class="align_left">13</td><td class="align_center">1.14</td></tr><tr><td class="align_left">16</td><td class="align_center">1.32</td></tr><tr><td class="align_left">19</td><td class="align_center">1.57</td></tr><tr><td class="align_left">22</td><td class="align_center">1.84</td></tr><tr><td class="align_left">25</td><td class="align_center">2.09</td></tr><tr><td class="align_left">28</td><td class="align_center">2.28</td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>The Ratio of longitudinal frequencies before and after pier separation at different heights.</div>

Mathematical Problems in Engineering

tab1

Table 1

Table 1: Influence of Pier Size on its Failure Mode under Near-Fault Vertical Earthquake 