Research PaperThe influence of stress anisotropy and stress shadow on frost cracking in rock
Introduction
In underground geological media and constructions, rock freezing below water freezing temperature may cause water–ice expansion strain and crack propagation (frost cracking), which will impact the facilities underground and/or on the ground (Matsuoka and Murton, 2010, Krautblatter et al., 2013). Storing liquefied natural gas (LNG) underground is an example of an underground facility exposed to freezing (Park et al., 2010). In order to minimize the volume of the LNG for efficient transportation and storage, LNG needs to be kept at low temperature, which causes the surrounding rock to be frozen. A safe storage of LNG requires comprehensive understanding the coupled thermo-hydro-mechanical (THM) processes in the pre-stressed underground involving temperature distribution, deformation behavior, and cracking as well as their impact on the safety of underground structures. Additionally, the instability of rock slopes (Luo et al., 2015, Xu et al., 2020) also frequently influenced by the freeze–thaw process (Muceku et al., 2016). When ice forms in rock pores and cracks, the crack initiates and propagates because of freezing-induced water–ice expansion and associated frost pressure (Huang et al., 2018). Currently, two theories are widely used to investigate the mechanism of frost cracking in rocks as well as for frost heaving in soils. They are volumetric expansion theory (Davidson and Nye, 1985) and ice segregation theory (Murton, 1996). The volumetric expansion theory suggests that 9% volumetric expansion of ice in pores and cracks leads to the damage of rocks (Embleton and King, 1969, Matsuoka and Sakai, 1999). According to the volumetric expansion theory, at least 91% initial water saturation is necessary for producing enough frost heaving pressure to trigger cracking (Hallet et al., 2010). However, this volumetric expansion theory cannot be applied in unsaturated or open systems for considering potential freeze damage. By contrast, the ice segregation theory (Murton, 1996) was proposed and it suggests that ice lenses grow because water migrates from the unfrozen regions towards the frozen fringe (Murton et al., 2006), which leads to cracking. Actually, the volumetric expansion and ice segregation dominate under different conditions. For rocks with low permeability, frost cracking happens most likely due to volumetric expansion (Huang et al., 2018). For rocks with high permeability and in an environment with sufficient hydraulic and temperature gradients, the occurrence of frost cracking is dominated by ice segregation (Wilen and Dash, 1995, Zhu et al., 2000, Powers and Helmuth, 2008).
Many experimental and analytical approaches have been developed for the freeze–thaw damage in geological media. Davidson and Nye (1985) measured the ice pressure through prefabricating a slot in a low-permeability transparent material. Walder and Hallet (1985) investigated the water migration at sub-freezing temperature by a mathematical model considering the coupling of water migration and fracture mechanics. Tharp (1987) analyzed the conditions for frost cracking by considering different crack geometries and proposed a minimum crack length for propagation. Akagawa and Fukuda (2010) proposed an empirical equation describing the relationship between the segregation freezing temperature and frost heaving pressure. Vlahou and Worster (2010) presented an idealized model with a spherical cavity in rock and quantified ice growth and pressure considering water migration. Duca et al. (2015) designed a laboratory experiment on a cube of gneiss to investigate the water migration and ice crystallization. Jia et al. (2017) investigated the mechanism of frost cracking in fractured low-permeability granite, finding that freezing direction and duration play important roles on cracking. Huang et al. (2019) investigated the damage of rocks with pre-existing cracks after freeze–thaw experiments.
Some numerical methods have been developed to investigate the freeze–thaw damage process, which simultaneously consider the thermo-hydro-mechanical (THM) coupling processes and water–ice phase transition in rock. Liu and Yu (2011) investigated the influence of freezing temperature on the content of ice, heat transfer coefficient and heat capacity. Kang et al. (2013) used finite-difference method to model the cooling process of underground gas storage under freeze–thaw conditions. Huang et al. (2018) developed a fully coupled THM model based on COMSOL, to model freezing-induced rock deformation.
In this work, the TOUGH-FEMM simulator is extended to analyze the freezing-induced three-dimensional (3D) cracking in rocks. Then the influence of the stress anisotropy and stress shadow on frost cracking is investigated numerically and experimentally. The hybrid finite element-meshfree method (FEMM) for fracturing has previously been coupled with TOUGH2 multiphase fluid flow simulator successfully to simulate hydraulic fracturing (Tang et al., 2019) and thermal cracking (Tao et al., 2020). Additionally, a set of experiments have been carried out to investigate the influence of the stress anisotropy and stress shadow on the path of frost cracking, which are then simulated by TOUGH-FEMM.
Section snippets
TOUGH-FEMM for the 3D non-planar frost cracking modelling
In TOUGH-FEMM, the heat transfer and fluid flow above and below freezing temperatures are analyzed using TOUGH2, while the mechanical deformation and cracking are simulated using FEMM. TOUGH2 is an established software, which has been linked to various geomechanics codes to model fluid flow and geomechanical processes in porous and fractured geological media (Rutqvist, 2017). The FEMM (Liu et al., 2018) is developed to model the mechanical deformation, fracturing and fragmentation of geological
Governing equations
TOUGH2 is used for solving fluid flow and heat transfer with considering water/ice phase change in this work (Pruess et al., 1999). Herein, we present the governing equations of mass conservation and the balance of thermal energy in general conservation form:
As TOUGH2 is based on the integral finite difference method, by integrating the above equation on a representative element volume, the principle of conservation of mass and conservation of thermal energy that can be uniformly
Equilibrium equation for rock deformation
Consider a solid body crossed by a crack surface where the displacement is discontinuous. The strong form of the equilibrium equation is:where is the Cauchy stress tensor and is the body force. The boundary condition on the fracture surface is:where n is the unit normal vector of fracture surface; n+ and n− represent two sides of the crack surface, respectively; is the frost expansion pressure acting on the fracture surface.
The Cauchy stress tensor is
Validation of TOUGH-FEMM for frost expansion of water saturated sandstone
The TOUGH-FEMM based model is validated by a previous experimental study on freezing of a saturated sandstone sample presented in Neaupane et al. (1999). In their experiment, a rock specimen 30 × 45 × 15 cm was prepared with a borehole of 4.6 cm diameter in the center. The sandstone specimen had a porosity of 13% and was fully saturated before the experiment. Then, brine was circulated in the hole to impose a cooling temperature of −20 °C for 72 h to freeze the rock. In order to simulate the
Experiments under uniaxial stress
In order to investigate the frost cracking under anisotropy stress, an experimental equipment has been constructed that includes a high-low temperature cycling chamber and a high-pressure cell, as shown in Fig. 10a and b. The analogue rock specimens containing a pre-existing crack (see Fig. 10c) were prepared according to the previous research (Huang et al., 2019). The specimen consists of cement, quartz sand, water, silica fume, defoamer, water reducer and the mass ratio is
The propagation and interaction of two cracks under freeze–thaw conditions
In previous reference (Li et al., 2020); the propagation and interaction of multiple pre-existing cracks under freeze–thaw loading have been investigated experimentally. In these experiments, there are two pre-existing cracks in analogue rock specimens, and the uniaxial stress is not considered. Other experimental processes, including sample preparation and freeze–thaw loading, are same with the experiments presented in Section 6.1.1.
The geometry of the samples is shown in Fig. 18. The
Conclusions
This work investigates the influence of stress anisotropy and stress shadow on frost cracking in rocks experimentally and numerically. The TOUGH-FEMM simulator is developed to consider the water–ice phase transition and simulate non-planar frost cracking. The following contributions can be drawn:
- 1.
The TOUGH2 is extended to consider the effect of water–ice phase transition on heat transfer and fluid flow. The unfrozen water saturation is related to freezing temperature, and the relative
CRediT authorship contribution statement
Siji Tao: Methodology, Software, Writing - original draft. Xuhai Tang: Supervision, Methodology, Software, Writing - review & editing. Jonny Rutqvist: Software, Writing - review & editing. Quansheng Liu: Software, Conceptualization. Mengsu Hu: Investigation, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors thanks the support of the National Key Research and Development Program of China No. 2017YFC1501300. Support for the LBNL authors was provided by the U.S. Department of Energy under contract No. DE-AC02-05CH11231 to the Lawrence Berkeley National Laboratory.
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