Reliability Analysis for Bypass Seepage Stability of Complex Reinforced Earth-Rockfill Dam with High-Order Practical Stochastic Response Surface Method

<table class="table-group" id="tab7"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left">Method</td><td class="align_center">Failure probability (<span class="nowrap"><svg height="11.9413pt" id="M197" style="vertical-align:-0.3499002pt" version="1.1" viewbox="-0.0498162 -11.5914 30.8134 11.9413" width="30.8134pt" 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="M528 54L331 254L528 455L492 493L294 291L96 493L60 455L257 254L60 54L96 16L294 217L492 16L528 54Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.631,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,13.871,0)"><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,-0.0091,20.158,-5.741)"><path d="M556 236V289H56V236H556Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,25.718,-5.741)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"></path></g></svg>)</span></td><td class="align_center">Number of calling functions</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left">Hermite SRSM (<i>m</i> = 5)</td><td class="align_center">3.3661</td><td class="align_center">13</td></tr><tr><td class="align_left">High-order practical SRSM</td><td class="align_center">3.3405</td><td class="align_center">17</td></tr><tr><td class="align_left">Gavin–Yau SRSM</td><td class="align_center">3.2466</td><td class="align_center">43</td></tr><tr><td class="align_left">NESSUS—MCS</td><td class="align_center">3.2833</td><td class="align_center">10<sup>6</sup></td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Comparison of calculation result of example two.</div>

Mathematical Problems in Engineering

tab7

Table 7

Table 7: Reliability Analysis for Bypass Seepage Stability of Complex Reinforced Earth-Rockfill Dam with High-Order Practical Stochastic Response Surface Method 

Table 7 | Reliability Analysis for Bypass Seepage Stability of Complex Reinforced Earth-Rockfill Dam with High-Order Practical Stochastic Response Surface Method 