Pore Size Distribution Influence on Suction Properties of Calcareous Stones in Cultural Heritage: Experimental Data and Model Predictions

<div>IFU procedure to reproduce porous microstructures and to calculate their sorptivity. (a) Starting point is represented by MIP tests and consequent mercury intrusion pore cumulative curve. (b) In order to reproduce this microstructure, two elementary units, based on Sierpinski carpet, and a portion of filled surface are used. After having compared experimental and IFU curves, IFU model is broken down again in the base units, and the analytical procedure is applied. (c) The calculated IFU sorptivity (<svg height="11.9316pt" id="M26" style="vertical-align:-3.2957pt" version="1.1" viewbox="-0.0498162 -8.6359 21.6258 11.9316" width="21.6258pt" 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="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,-0.0091,6.071,3.132)"><path d="M308 0V33C225 38 217 44 217 128V521C217 605 225 612 308 617V650H39V617C122 612 130 605 130 521V128C130 44 122 38 39 33V0H308Z" id="g58-71"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="348" vert-adv-y="348"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,9.238,3.132)"><path d="M502 500C497 551 492 613 491 650H43V617C122 612 130 606 130 521V129C130 45 122 38 41 33V0H319V33C227 38 217 45 217 129V305H319C411 305 413 295 427 225H461V421H427C414 357 411 348 319 348H217V580C217 609 219 612 250 612H330C401 612 423 605 439 578C452 557 458 539 467 496L502 500Z" id="g58-68"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="540" vert-adv-y="540"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,14.152,3.132)"><path d="M727 650H480V617C552 612 575 600 580 563C583 531 587 491 587 398V326C587 153 534 44 398 44C281 44 210 124 210 296V519C210 607 218 612 298 617V650H33V617C114 609 123 607 123 519V274C123 153 151 81 211 34C258 -1 314 -14 374 -14C441 -14 509 7 556 56C615 116 633 202 633 322V398C633 491 635 533 639 561C643 600 667 614 727 617V650Z" id="g58-83"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="747" vert-adv-y="747"></glyph.data></g></svg>) can be compared with the data acquired experimentally (<svg height="13.9365pt" id="M27" style="vertical-align:-5.3006pt" version="1.1" viewbox="-0.0498162 -8.6359 19.936 13.9365" width="19.936pt" 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="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,-0.0091,6.071,3.132)"><path d="M384 109C349 76 310 59 268 59C197 59 123 113 120 245C240 248 367 259 384 262C403 266 407 275 407 296C407 376 338 451 254 451H253C201 451 148 425 105 378C65 334 39 272 39 203C39 88 112 -12 235 -12C266 -12 339 5 402 84L384 109ZM230 411C285 411 319 365 319 313C319 298 313 293 294 293C236 291 180 290 125 290C141 370 185 411 230 411Z" id="g58-99"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="434" vert-adv-y="434"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,10.02,3.132)"><path d="M482 0V30C420 38 407 48 370 103L273 248C308 299 331 332 352 357C387 397 401 404 463 409V439H277V409C318 405 324 400 307 369C290 337 270 307 251 279L194 367C175 396 180 402 220 409V439H18V409C74 401 87 395 117 349L204 213C173 168 147 130 119 95C78 46 67 38 5 30V0H195V30C144 38 143 47 162 79C181 112 202 149 225 181L297 70C314 43 307 35 264 30V0H482Z" id="g58-118"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="481" vert-adv-y="481"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,14.407,3.132)"><path d="M173 382V461C125 442 68 425 25 418V390C88 382 92 382 92 317V-127C92 -191 84 -199 18 -204V-235H259V-204C180 -196 173 -192 173 -120V7C188 -1 212 -11 243 -12C375 12 495 109 495 261C495 361 427 451 316 451C303 451 283 446 266 435L173 382ZM173 345C200 365 243 388 274 388C346 388 409 329 409 222C409 111 353 40 266 40C231 40 196 56 173 79V345Z" id="g58-110"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="534" vert-adv-y="534"></glyph.data></g></svg>).</div>

Advances in Materials Science and Engineering

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Figure 2

Figure 2: Pore Size Distribution Influence on Suction Properties of Calcareous Stones in Cultural Heritage: Experimental Data and Model Predictions 