Theoretical Analysis on Stress and Deformation of Overburden Key Stratum in Solid Filling Coal Mining Based on the Multilayer Winkler Foundation Beam Model

<div>Vertical stress distribution of the key stratum #1 at top, middle, and bottom under various (a–c) <span class="nowrap"><svg height="11.8174pt" id="M130" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 18.1704 11.8174" width="18.1704pt" 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="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.943,3.132)"><path d="M517 0V26C453 32 447 37 447 100V450C395 439 339 437 259 437H180V471C180 551 194 602 213 628C225 647 246 664 275 664C322 664 356 632 379 605C387 596 396 596 408 604C417 609 425 619 430 628C434 639 434 651 425 664C414 680 379 710 319 712C281 708 235 690 194 658C140 614 120 563 112 538C106 517 101 491 101 460V437H53L25 408L29 397H101V100C101 38 93 33 30 26V0H250V26C187 32 180 38 180 100V397H316C365 397 368 390 368 345V100C368 37 361 31 305 26V0H517Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.857,3.132)"><path d="M238 0V26C174 32 166 38 166 104V712C132 700 70 683 18 677V653C81 647 87 645 87 577V104C87 38 78 32 15 26V0H238Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,15.205,3.132)"><path d="M238 0V26C174 32 166 38 166 104V712C132 700 70 683 18 677V653C81 647 87 645 87 577V104C87 38 78 32 15 26V0H238Z"></path></g></svg>,</span> (d–f) <span class="nowrap"><svg height="9.49473pt" id="M131" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.83278 9.49473" width="6.83278pt" 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="M499 88L487 113C459 86 422 65 413 65C403 65 403 74 409 98L461 318C487 426 460 448 431 448C408 448 383 441 352 424C305 398 223 344 157 257H155L243 674C249 702 249 712 240 712C227 712 170 680 87 673L82 648H117C155 648 162 644 150 590L23 -4L30 -12C55 -4 81 3 105 8C113 53 131 150 143 187C199 281 323 387 372 387C390 387 393 369 380 311L328 86C313 19 319 -12 347 -12C379 -12 442 24 499 88Z"></path></g></svg>,</span> and (g–i) <span class="nowrap"><svg height="12.5794pt" id="M132" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 10.7458 12.5794" width="10.7458pt" 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="M499 88L487 113C459 86 422 65 413 65C403 65 403 74 409 98L461 318C487 426 460 448 431 448C408 448 383 441 352 424C305 398 223 344 157 257H155L243 674C249 702 249 712 240 712C227 712 170 680 87 673L82 648H117C155 648 162 644 150 590L23 -4L30 -12C55 -4 81 3 105 8C113 53 131 150 143 187C199 281 323 387 372 387C390 387 393 369 380 311L328 86C313 19 319 -12 347 -12C379 -12 442 24 499 88Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.643,3.132)"><path d="M357 391C357 416 325 451 270 451C241 451 179 431 146 400C109 365 97 334 97 307C97 248 143 213 196 180C250 146 261 123 261 101C261 75 237 40 190 40C153 40 110 72 86 109C81 116 68 119 55 112C37 102 24 87 24 66C24 30 85 -12 137 -12C229 -12 331 62 331 140C331 189 304 218 236 260C197 284 164 309 164 346C164 381 194 400 220 400C259 400 282 380 304 350C310 342 321 339 330 344C347 353 357 372 357 391Z"></path></g></svg>.</span></div>

Geofluids

fig12

Figure 12

Figure 12: Theoretical Analysis on Stress and Deformation of Overburden Key Stratum in Solid Filling Coal Mining Based on the Multilayer Winkler Foundation Beam Model 

Figure 12 | Theoretical Analysis on Stress and Deformation of Overburden Key Stratum in Solid Filling Coal Mining Based on the Multilayer Winkler Foundation Beam Model 