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-Bazant (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.
ABSTRACT
While hydraulic fracturing technology, aka fracking (or fraccing, frac), has become highly developed and astonishingly successful, a consistent formulation of the associated fracture mechanics that would not conflict with some observations is still unavailable. It is attempted here. Classical fracture mechanics, as well as current commercial software, predict vertical cracks to propagate without branching from the perforations of the horizontal well casing, which are typically spaced at 10 m or more. However, to explain the gas production rate at the wellhead, the crack spacing would have to be only about 0.1 m, which would increase the overall gas permeability of shale mass about 10,000×. This permeability increase has generally been attributed to a preexisting system of orthogonal natural cracks, whose spacing is about 0.1 m. However, their average age is about 100 million years, and a recent analysis indicated that these cracks must have been completely closed by secondary creep of shale in less than a million years. Here it is considered that the tectonic events that produced the natural cracks in shale must have also created weak layers with nanocracking or microcracking damage. It is numerically demonstrated that seepage forces and a greatly enhanced permeability along the weak layers, with a greatly increased transverse Biot coefficient, must cause the fracking to engender lateral branching and the opening of hydraulic cracks along the weak layers, even if these cracks are initially almost closed. A finite element crack band model, based on a recently developed anisotropic spherocylindrical microplane constitutive law, demonstrates these findings [Rahimi-Aghdam S, et al. (2018) arXiv:1212.11023].
