Multistage Warning Indicators of Concrete Dam under Influences of Random Factors

<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" rowspan="2">Data series</td><td class="align_center" colspan="2">Parameter values</td></tr><tr class="thead"><td class="align_center"><span style="width: 7.34167ptpx;"><svg height="9.39034pt" id="M233" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 7.34167 9.39034" width="7.34167pt" 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" id="g113-234"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="555" vert-adv-y="555"></glyph.data></g></svg></span></td><td class="align_center"><span style="width: 12.4186ptpx;"><svg height="11.7978pt" id="M234" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.5914 12.4186 11.7978" width="12.4186pt" 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" 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410C277 542 256 679 256 809C256 861 268 908 363 920V950C295 950 197 933 197 793C197 667 208 520 208 391C208 349 204 294 87 287V254C204 246 208 192 208 150C208 26 197 -118 197 -257S295 -410 363 -410Z" id="g119-135"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="438" vert-adv-y="438"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,5.715,0)"><path d="M449 634C442 637 425 643 405 650C376 660 341 666 307 666C181 666 98 590 98 485C98 400 170 343 215 310L246 288C307 243 343 204 343 147C343 67 291 18 219 18C104 18 61 124 51 202L23 199C28 124 27 71 27 47C47 22 122 -16 204 -16C324 -16 428 60 428 174C428 256 379 309 307 360L276 382C223 419 179 455 179 516C179 576 221 632 293 632C379 632 410 564 418 487L448 490C446 536 446 592 449 634Z" id="g113-84"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="472" vert-adv-y="472"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,11.852,-5.741)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z" id="g50-49"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,11.786,3.784)"><path d="M781 91L765 118C733 86 702 70 693 70C686 70 685 77 692 106L738 297C772 439 736 451 712 451S675 445 647 431C605 410 526 356 452 257H450L459 294C491 426 459 451 429 451C403 451 386 445 361 431C312 404 239 343 170 253H168L188 333C208 411 205 451 175 451C148 451 85 417 24 346L39 318C57 338 100 374 112 374C120 374 122 372 115 339C91 226 62 112 28 -6L37 -12C59 -4 87 3 114 6C125 68 142 127 154 168C184 227 316 383 372 383C397 383 396 366 381 289C362 192 338 92 312 -6L317 -12C339 -5 367 3 396 6L434 170C468 234 598 383 650 383C668 383 676 369 664 319L609 90C593 23 600 -12 629 -12C654 -12 722 23 781 91Z" id="g50-110"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="805" vert-adv-y="805"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,18.445,3.784)"><path d="M400 606C400 634 383 656 353 656C316 656 294 620 294 593C294 564 317 545 343 545C375 545 400 573 400 606ZM366 351C379 413 381 451 356 451C323 451 251 408 183 341L199 313C223 335 267 365 277 365C285 365 284 354 277 312C245 132 222 27 193 -100C182 -148 160 -188 131 -188C113 -188 90 -178 75 -170C64 -164 55 -168 48 -175C38 -185 24 -203 24 -222S48 -257 71 -257C89 -257 131 -241 186 -192C243 -141 286 -46 310 74L366 351Z" id="g50-107"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="430" vert-adv-y="430"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,22.898,2.0537e-005)"><path d="M351 254V287C234 294 230 349 230 391C230 520 241 667 241 793C241 933 143 950 75 950V920C170 908 182 861 182 809C182 679 161 542 161 410C161 346 185 288 249 273V269C186 252 161 195 161 130C161 -5 182 -189 182 -264C182 -319 170 -368 75 -380V-410C143 -410 241 -396 241 -257S230 26 230 150C230 192 234 246 351 254Z" id="g119-136"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="438" vert-adv-y="438"></glyph.data></g></svg></span></td><td class="align_center">0.488355</td><td class="align_center">0.0129</td></tr><tr><td class="align_left"><span style="width: 28.736ptpx;"><svg height="18.6667pt" id="M236" style="vertical-align:-6.1814pt" version="1.1" viewbox="-0.0498162 -12.4853 28.736 18.6667" width="28.736pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,2.0537e-005)"><path d="M363 -410V-380C268 -368 256 -319 256 -264C256 -189 277 -5 277 130C277 195 252 252 189 269V273C253 288 277 346 277 410C277 542 256 679 256 809C256 861 268 908 363 920V950C295 950 197 933 197 793C197 667 208 520 208 391C208 349 204 294 87 287V254C204 246 208 192 208 150C208 26 197 -118 197 -257S295 -410 363 -410Z" id="g119-135"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="438" vert-adv-y="438"></glyph.data></g><g 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451 712 451S675 445 647 431C605 410 526 356 452 257H450L459 294C491 426 459 451 429 451C403 451 386 445 361 431C312 404 239 343 170 253H168L188 333C208 411 205 451 175 451C148 451 85 417 24 346L39 318C57 338 100 374 112 374C120 374 122 372 115 339C91 226 62 112 28 -6L37 -12C59 -4 87 3 114 6C125 68 142 127 154 168C184 227 316 383 372 383C397 383 396 366 381 289C362 192 338 92 312 -6L317 -12C339 -5 367 3 396 6L434 170C468 234 598 383 650 383C668 383 676 369 664 319L609 90C593 23 600 -12 629 -12C654 -12 722 23 781 91Z" id="g50-110"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="805" vert-adv-y="805"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,18.445,3.784)"><path d="M400 606C400 634 383 656 353 656C316 656 294 620 294 593C294 564 317 545 343 545C375 545 400 573 400 606ZM366 351C379 413 381 451 356 451C323 451 251 408 183 341L199 313C223 335 267 365 277 365C285 365 284 354 277 312C245 132 222 27 193 -100C182 -148 160 -188 131 -188C113 -188 90 -178 75 -170C64 -164 55 -168 48 -175C38 -185 24 -203 24 -222S48 -257 71 -257C89 -257 131 -241 186 -192C243 -141 286 -46 310 74L366 351Z" id="g50-107"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="430" vert-adv-y="430"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,22.898,2.0537e-005)"><path d="M351 254V287C234 294 230 349 230 391C230 520 241 667 241 793C241 933 143 950 75 950V920C170 908 182 861 182 809C182 679 161 542 161 410C161 346 185 288 249 273V269C186 252 161 195 161 130C161 -5 182 -189 182 -264C182 -319 170 -368 75 -380V-410C143 -410 241 -396 241 -257S230 26 230 150C230 192 234 246 351 254Z" id="g119-136"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="438" vert-adv-y="438"></glyph.data></g></svg></span></td><td class="align_center">0.490627</td><td class="align_center">0.0151</td></tr><tr><td class="align_left"><span style="width: 30.7586ptpx;"><svg height="18.6667pt" id="M237" style="vertical-align:-6.1814pt" version="1.1" viewbox="-0.0498162 -12.4853 30.7586 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424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z" id="g113-83"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="627" vert-adv-y="627"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,13.867,-5.741)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z" id="g50-49"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,13.801,3.784)"><path d="M781 91L765 118C733 86 702 70 693 70C686 70 685 77 692 106L738 297C772 439 736 451 712 451S675 445 647 431C605 410 526 356 452 257H450L459 294C491 426 459 451 429 451C403 451 386 445 361 431C312 404 239 343 170 253H168L188 333C208 411 205 451 175 451C148 451 85 417 24 346L39 318C57 338 100 374 112 374C120 374 122 372 115 339C91 226 62 112 28 -6L37 -12C59 -4 87 3 114 6C125 68 142 127 154 168C184 227 316 383 372 383C397 383 396 366 381 289C362 192 338 92 312 -6L317 -12C339 -5 367 3 396 6L434 170C468 234 598 383 650 383C668 383 676 369 664 319L609 90C593 23 600 -12 629 -12C654 -12 722 23 781 91Z" id="g50-110"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="805" vert-adv-y="805"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,20.46,3.784)"><path d="M400 606C400 634 383 656 353 656C316 656 294 620 294 593C294 564 317 545 343 545C375 545 400 573 400 606ZM366 351C379 413 381 451 356 451C323 451 251 408 183 341L199 313C223 335 267 365 277 365C285 365 284 354 277 312C245 132 222 27 193 -100C182 -148 160 -188 131 -188C113 -188 90 -178 75 -170C64 -164 55 -168 48 -175C38 -185 24 -203 24 -222S48 -257 71 -257C89 -257 131 -241 186 -192C243 -141 286 -46 310 74L366 351Z" id="g50-107"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="430" vert-adv-y="430"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,24.913,2.0537e-005)"><path d="M351 254V287C234 294 230 349 230 391C230 520 241 667 241 793C241 933 143 950 75 950V920C170 908 182 861 182 809C182 679 161 542 161 410C161 346 185 288 249 273V269C186 252 161 195 161 130C161 -5 182 -189 182 -264C182 -319 170 -368 75 -380V-410C143 -410 241 -396 241 -257S230 26 230 150C230 192 234 246 351 254Z" id="g119-136"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="438" vert-adv-y="438"></glyph.data></g></svg></span></td><td class="align_center">−0.50210</td><td class="align_center">0.0249</td></tr><tr><td class="align_left"><span style="width: 30.7586ptpx;"><svg height="18.6667pt" id="M238" style="vertical-align:-6.1814pt" version="1.1" viewbox="-0.0498162 -12.4853 30.7586 18.6667" width="30.7586pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,2.0537e-005)"><path d="M363 -410V-380C268 -368 256 -319 256 -264C256 -189 277 -5 277 130C277 195 252 252 189 269V273C253 288 277 346 277 410C277 542 256 679 256 809C256 861 268 908 363 920V950C295 950 197 933 197 793C197 667 208 520 208 391C208 349 204 294 87 287V254C204 246 208 192 208 150C208 26 197 -118 197 -257S295 -410 363 -410Z" id="g119-135"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="438" vert-adv-y="438"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,5.715,0)"><path d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z" id="g113-83"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="627" vert-adv-y="627"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,13.867,-5.741)"><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" id="g50-50"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,13.801,3.784)"><path d="M781 91L765 118C733 86 702 70 693 70C686 70 685 77 692 106L738 297C772 439 736 451 712 451S675 445 647 431C605 410 526 356 452 257H450L459 294C491 426 459 451 429 451C403 451 386 445 361 431C312 404 239 343 170 253H168L188 333C208 411 205 451 175 451C148 451 85 417 24 346L39 318C57 338 100 374 112 374C120 374 122 372 115 339C91 226 62 112 28 -6L37 -12C59 -4 87 3 114 6C125 68 142 127 154 168C184 227 316 383 372 383C397 383 396 366 381 289C362 192 338 92 312 -6L317 -12C339 -5 367 3 396 6L434 170C468 234 598 383 650 383C668 383 676 369 664 319L609 90C593 23 600 -12 629 -12C654 -12 722 23 781 91Z" id="g50-110"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="805" vert-adv-y="805"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,20.46,3.784)"><path d="M400 606C400 634 383 656 353 656C316 656 294 620 294 593C294 564 317 545 343 545C375 545 400 573 400 606ZM366 351C379 413 381 451 356 451C323 451 251 408 183 341L199 313C223 335 267 365 277 365C285 365 284 354 277 312C245 132 222 27 193 -100C182 -148 160 -188 131 -188C113 -188 90 -178 75 -170C64 -164 55 -168 48 -175C38 -185 24 -203 24 -222S48 -257 71 -257C89 -257 131 -241 186 -192C243 -141 286 -46 310 74L366 351Z" id="g50-107"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="430" vert-adv-y="430"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,24.913,2.0537e-005)"><path d="M351 254V287C234 294 230 349 230 391C230 520 241 667 241 793C241 933 143 950 75 950V920C170 908 182 861 182 809C182 679 161 542 161 410C161 346 185 288 249 273V269C186 252 161 195 161 130C161 -5 182 -189 182 -264C182 -319 170 -368 75 -380V-410C143 -410 241 -396 241 -257S230 26 230 150C230 192 234 246 351 254Z" id="g119-136"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="438" vert-adv-y="438"></glyph.data></g></svg></span></td><td class="align_center">−0.49674</td><td class="align_center">0.0245</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Parameter values of the probability density function.

Mathematical Problems in Engineering

tab7

Table 7

Table 7: Multistage Warning Indicators of Concrete Dam under Influences of Random Factors 