A Prediction Model for Concrete Cracks due to Chloride-Induced Corrosion

<div>Elastic mechanics analysis of concrete differentials. <svg height="12.7373pt" id="M34" style="vertical-align:-3.429399pt" version="1.1" viewbox="-0.0498162 -9.3079 14.0226 12.7373" width="14.0226pt" 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="M517 51L485 54C448 58 441 63 441 115V712C404 700 337 684 285 678V653C357 648 362 645 362 580V437C339 446 309 449 295 449C159 449 38 340 38 201C38 61 143 -12 223 -12C234 -12 261 -6 301 17L362 53V-12C420 9 495 22 517 26V51ZM362 85C338 67 301 51 266 51C201 51 128 109 128 228C128 373 212 411 259 411C296 411 338 395 362 360V85Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.89,0)"><path d="M516 277C516 378 460 448 376 448C335 448 288 434 240 401C158 345 127 277 107 159C53 -161 38 -221 23 -247L28 -261C43 -260 95 -250 114 -226C122 -216 129 -199 146 -75C152 -29 157 0 164 31C182 9 206 -12 237 -12C267 -12 325 8 376 46C451 102 516 179 516 277ZM432 259C432 134 366 40 259 40C236 40 204 48 171 76L195 203C219 327 253 400 326 400C398 400 432 336 432 259Z"></path></g></svg>—distance between two cylinders of a thick-walled cylinder; <svg height="12.7373pt" id="M35" style="vertical-align:-3.429399pt" version="1.1" viewbox="-0.0498162 -9.3079 14.5837 12.7373" width="14.5837pt" 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="M517 51L485 54C448 58 441 63 441 115V712C404 700 337 684 285 678V653C357 648 362 645 362 580V437C339 446 309 449 295 449C159 449 38 340 38 201C38 61 143 -12 223 -12C234 -12 261 -6 301 17L362 53V-12C420 9 495 22 517 26V51ZM362 85C338 67 301 51 266 51C201 51 128 109 128 228C128 373 212 411 259 411C296 411 338 395 362 360V85Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.89,0)"><path d="M559 271C559 395 493 448 433 448C370 448 304 394 275 297C259 245 235 121 219 37C157 54 113 110 113 201C113 310 180 386 276 429L265 457C131 410 23 326 23 186C23 83 86 5 211 -10C180 -159 167 -220 158 -252L165 -261C198 -255 236 -246 251 -218L287 -5C421 9 559 119 559 271ZM484 273C484 144 400 40 293 33L352 331C364 389 382 406 405 406C431 406 484 370 484 273Z"></path></g></svg>—angle cut between two radial planes; <svg height="11.6726pt" id="M36" style="vertical-align:-5.52901pt" version="1.1" viewbox="-0.0498162 -6.14359 14.3223 11.6726" width="14.3223pt" 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"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.76,3.132)"><path d="M569 272C569 396 502 451 440 451C377 451 308 398 280 296C262 229 239 121 223 41C163 58 116 110 116 203C116 313 187 386 283 428L269 460C133 413 24 332 24 189C24 85 87 3 215 -10C187 -153 174 -212 164 -249L173 -257C208 -253 245 -243 260 -214L295 -5C427 6 569 118 569 272ZM493 270C493 139 401 42 302 37L357 327C369 388 390 405 412 405C438 405 493 369 493 270Z"></path></g></svg>—circular normal stress; <svg height="11.4899pt" id="M37" style="vertical-align:-5.52899pt" version="1.1" viewbox="-0.0498162 -5.96091 18.0059 11.4899" width="18.0059pt" 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="M471 456L444 459C426 433 414 430 388 430C324 430 270 434 216 434C103 434 51 374 23 338L43 317C96 366 146 380 221 375L154 109C149 86 147 68 147 52C147 4 168 -12 197 -12C240 -12 291 25 334 71L320 96C295 75 268 58 252 58C238 58 227 79 238 138C251 211 272 296 292 372C310 372 332 368 350 368C391 368 421 369 434 371C444 388 455 413 471 456Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.434,3.132)"><path d="M525 275C525 381 464 451 380 451C338 451 289 439 241 405C158 347 127 277 106 152C51 -168 37 -216 24 -242L28 -257C42 -256 92 -247 117 -222C126 -213 134 -193 150 -69L166 32C184 10 211 -12 245 -12C276 -12 332 8 384 46C458 100 525 176 525 275ZM436 260C436 131 366 41 267 41C246 41 208 51 175 82C181 125 187 162 195 200C220 322 257 400 328 400C398 400 436 338 436 260Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.432,3.132)"><path d="M569 272C569 396 502 451 440 451C377 451 308 398 280 296C262 229 239 121 223 41C163 58 116 110 116 203C116 313 187 386 283 428L269 460C133 413 24 332 24 189C24 85 87 3 215 -10C187 -153 174 -212 164 -249L173 -257C208 -253 245 -243 260 -214L295 -5C427 6 569 118 569 272ZM493 270C493 139 401 42 302 37L357 327C369 388 390 405 412 405C438 405 493 369 493 270Z"></path></g></svg>—shear stress of the cylinder.</div>

Advances in Materials Science and Engineering

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Figure 3

Figure 3: A Prediction Model for Concrete Cracks due to Chloride-Induced Corrosion 