Time-dependent deformation in geologic materials across multiple spatiotemporal scales
Keywords: Engineering.

Numerous processes in geomechanics are time- or rate-dependent. For example, the load-deformation responses of geologic materials such as soils and rocks are known to be influenced by the rate of loading. Furthermore, failure of geotechnical structures such as slopes in creeping soils can occur progressively over long periods of time even when there is no incremental applied load. Given their heterogeneous microstructure, geologic materials can also undergo time-dependent processes at different spatiotemporal scales. As an example, the expulsion of fluids from the nanopores of a shale sample can take much longer compared to the time it takes to drain the fluid through the fractures and open channels of a larger sample. Of interest in this thesis are slow processes in geomechanics, such as hydrodynamic lag or dissipation of excess fluid pressures in the pores of a geologic material, and creep, which occurs over long periods of time even in the absence of fluid flow. The contribution of this thesis is the characterization of these processes at different scales in space and time, both experimentally and mathematically, and how these processes may be connected across scales. To motivate the developments, this thesis first considers the classic 1D consolidation of soil assuming viscoplasticity in the solid deformation response and double porosity in the soil microstructure characterization. We show that with two porosity scales, namely, microporosity and macroporosity, three scales in time domain can be identified, namely, the time scale to drain the fluid through the macropores into the drainage boundary, the time scale to drain the fluid from the micropores into the macropores, and the time scale associated with the viscoplastic response of the solid skeleton. Next, we perform indentation and triaxial creep tests on organic-rich Woodford shale and show that the measured creep responses at the nanometer and millimeter scales are statistically correlated in the sense that the indentation creep tests can be used to predict the triaxial creep response. The link between the two extreme scales along with their associated time scales is facilitated by an elasto-viscoplastic constitutive model based on critical state theory. We find the creep responses at the nanometer and millimeter scales are statistically correlated in the bed-normal (BN) direction where the rock is weaker. However, the creep deformations at the two scales in the bed-parallel (BP) direction, where the rock is stronger, are significantly smaller than in the BN direction, and so, they are not as strongly correlated as the responses in the BN direction. Finally, we develop a new contact algorithm and use it to study the influence of hydrodynamic effect on the creep behavior of shale in indentation tests. The efficiency and accuracy of the algorithm is examined with the experimental data from Lawrence Berkeley National Laboratory, and coupled creep simulation has been conducted for shale with different permeability values and bedding angles. We find that hydrodynamic effect is negligible at the micrometer scale if the permeability value of bulk shale with fissures is used, but when the permeability is further reduced, significant excess pore pressure is built during the load stage. The dissipation of this pressure during the hold stage makes shale behave more viscous and creep much more, and the hydrodynamic effect decreases with a larger bedding angle.