Unsaturated nanoporomechanics

Abstract

Although some important advances in the modeling of sorption and hygrothermal deformations of nanoporous materials such as hydrated cement paste, shale, coal, and some other rocks and soils have already been made, a comprehensive nanoporomechanics theory remains elusive. Here we strive to formulate it based on Gibb's free energy of the solid-fluid system and on the recently derived Nguyen-Rahimi-Bažant (NRB) isotherm, which corrects the Brunauer-Emmett-Teller (BET) isotherm for the effect of hindered adsorbed water in filled nanopores and extends through the capillary range up to saturation. The challenge is to capture all of the basic types of relevant published experimental data, including 1) a complete sorption isotherm of hydrated cement paste (including the capillary range), 2) pore size distribution, 3) autogenous shrinkage, 4) drying shrinkage and swelling, 5) water loss or humidity change due to heating, 6) thermal expansion at various humidities, and 7) water loss of specimens caused by compression. The previous models can fit only a few data types. The present model fits all of them. It is ready for computer simulations needed to minimize the deleterious moisture effects on long-time deformations, cracking damage, and fracture in concrete infrastructure and thereby to reduce indirectly the enormous carbon footprint of concrete. Adaptations to shale, coal beds, etc., are possible.

Keywords: Biot coefficient; hindered adsorbed water; shrinkage; swelling; unsaturated poromechanics.

Fig. 1.

(A) Adsorption of new molecular layers reduces surface area exposed to vapor. (B) Stress states of different water phases where meniscus meets adsorbent wall.

Fig. 2.

Correspondence of sorption isotherm and drying shrinkage of hardened cement pastes. (A and B) Tests by (A) Baroghel-Bouny et al. (35) and (B) Sabri and Illston (36).

Fig. 3.

(A and B) Measured (37, 38) and calculated autogenous shrinkage of concrete. (C) Measured (40) and calculated swelling simultaneous with autogenous shrinkage of concrete submerged in water.

Fig. 4.

(A) Hygrothermic coefficients corresponding to NRB theory and GAB theory, compared against tests of Nilsson (41), $w/c$ = 0.4 ($♢$), $w/c$ = 0.7 ($\square$), $w/c$ = 0.7 of silica ($○$); Persson (42), $w/c$ = 0.37 ($+$), $w/c$ = 0.48 ($\times$), $w/c$ = 0.75 ($▽$); Radjy et al. (43) ($△$); and Grasley and Lange (44), $w/c$ = 0.4 ($⊲$), $w/c$ = 0.5 ($⊳$). (B) Thermal expansion coefficient according to NRB theory, compared to tests of Meyers (45) ($♢$); Mitchell (46) ($\square$); Dettling (47) ($○$); and Grasley and Lange (44), $w/c$ = 0.4 ($+$), $w/c$ = 0.5 ($\times$).

Fig. 5.

(A and B) Drying tests (A) (48) demonstrating negligible water loss caused by applied uniaxial compression 0.5$f_c^{\prime }$ and (B) confirmed here by calculations.