The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.

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VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship

Effects of water content on fracture and mechanical behavior of sandstone with a low clay mineral content

Water saturation effects on dynamic fracture behavior of sandstone

Effect of high temperature on physical and mechanical properties of Jalore granite

Fracture networks play a more significant role in conducting fluid flow and solute transport in fractured rock masses, comparing with that of the rock matrix. Accurate estimation of the permeability of fracture networks would help researchers and engineers better assess the performance of projects associated with fluid flow in fractured rock masses. This study provides a review of previous works that have focused on the estimation of equivalent permeability of two-dimensional (2-D) discrete fracture networks (DFNs) considering the influences of geometric properties of fractured rock masses. Mathematical expressions for the effects of nine important parameters that significantly impact on the equivalent permeability of DFNs are summarized, including (1) fracture-length distribution, (2) aperture distribution, (3) fracture surface roughness, (4) fracture dead-end, (5) number of intersections, (6) hydraulic gradient, (7) boundary stress, (8) anisotropy, and (9) scale. Recent developments of 3-D fracture networks are briefly reviewed to underline the importance of utilizing 3-D models in future research.

Review: Mathematical expressions for estimating equivalent permeability of rock fracture networks

Fracture and mechanical properties of the water saturated sedimentary rocks have been experimentally investigated in the present paper. Three types of sandstones and one type of shale were saturated in water for different periods of time. They were then tested for their index geomechanical properties such as Brazilian tensile strength (BTS), Young’s modulus (YM), P-wave velocity and all pure and mixed-mode fracture toughness (FT). FT was measured using semicircular bend specimens in a three-point bend set-up. All the geomechanical and fracture properties of the saturated rocks were compared together to investigate their interrelations. Further, statistical methods were employed to measure the statistical significance of such relationships. Next, three types of fracture criteria were compared with the present experimental results. Results show that degree of saturation has significant effect on both the strength and fracture properties of sedimentary rock. A general decrease in the mechanical and fracture toughness was noticed with increasing saturation levels. But, t-test confirmed that FT, BTS, P-wave velocity and YM are strongly dependent on each other and linear relationships exist across all the saturation values. Calculation of the ‘degradation degree’ (DD) appeared to be a difficult task for all types of sedimentary rocks. While in sandstone, both the BTS and mode-I FT overestimated the DD calculated by YM method, in shale BTS was found to give a closure value.

Effect of Water Saturation on the Fracture and Mechanical Properties of Sedimentary Rocks

The effect of heat treatment and the layer orientation on the tensile properties of granitic gneiss were studied under the unconfined stress condition. The tensile strength of the samples was studied using a Brazilian configuration, and the geochemical and microstructural properties were studied using the X-ray diffraction technique as well as scanning electron microscopy (SEM), respectively. The fracture pattern and the geometrical analyses were performed using the digital photographs. The results show that both the heat treatment and layer orientation have strong control on the tensile strength, force-parallel and layer-parallel strains, and on the tensile fracture geometry. A general decrease in the tensile strength of the rock was documented with the increasing heat treatment. Although, in the heat-treated samples, X-ray diffraction study do not reveal any major change in the mineral composition, but the SEM shows the development of several micro-cracks in the grains. In the samples with different layer orientation, along with the changes in the tensile strength and layer-parallel to force-parallel strain ratio, the layer activation under shear stress is also noticed. Here, the ratio between the tensile to shear stress, acting along the layers is thought to be the major controlling factor of the tensile properties of rocks, which has many applications in mining, civil constructions, and waste disposal work.

Effect of Heat Treatment and Layer Orientation on the Tensile Strength of a Crystalline Rock Under Brazilian Test Condition

For the effect of thermal treatment on the mode-I fracture toughness (FT), three crystalline rocks (two basalts and one tonalite) were experimentally investigated. Semi-circular bend specimens of the rocks were prepared following the method suggested by the International Society for Rock Mechanics (ISRM) and were treated at various temperatures ranging from room temperature (25 °C) to 600 °C. Mode-I FT was correlated with tensile strength (TS), ultrasonic velocities, and Young's modulus (YM). Additionally, petrographic and X-ray diffraction analyses were carried out to find the chemical changes resulting from the heat treatment. Further, scanning electron microscopy (SEM) was conducted to observe the micro structural changes when subjected to high temperatures. These experiments demonstrate that heat treatment has a strong negative impact on the FT and mechanical properties of the rocks. From room temperature to 600 °C, mode-I FT values of massive basalt, giant plagioclase basalt, and tonalite were reduced by nearly 52%, 68%, and 64%, respectively. Also, at all temperature levels, FT and mechanical properties are found to be exponentially correlated. However, the exact nature of the relationship mainly depends on rock type. Besides, TS was found to be a better indicator of degradation degree than the mode-I FT. SEM images show that micro crack density and structural disintegration of the mineral grains increase with temperature. These physical changes confirm the observed reduction in the stiffness of heat-treated crystalline rocks.

Correlating mode-I fracture toughness and mechanical properties of heat-treated crystalline rocks

Carbon dioxide sequestration is considered to be an efficient method of curbing the release of carbon dioxide emissions into the atmosphere and to mitigating corresponding effects on climate change. In this regard, basaltic rocks are among the potential repositories due to their ability to trap carbon dioxide in form of carbonate minerals. A series of laboratory-scale saturation experiments was conducted on three types of basalts that were collected from different horizons of the Deccan Volcanic Province (DVP), India. The basalt cores were treated in a saturation chamber for different exposure periods under low-pressure and room-temperature conditions. A set of key mechanical, physical, and chemical properties of the pre- and post-treated samples were analyzed to identify saturation-related changes. The results show that exposure of the basalts to carbon dioxide has a strong effect on their strength. However, the extent of the effect is different for different types of basalts and is strongly controlled by the exposure time, the mineralogical composition, and rock texture. X-ray diffraction and scanning electron microscopy (SEM) show that saturation leads to dissolution of the mafic minerals, and precipitation of new carbonate minerals in the cracks and vesicles of the host rock. These changes in the mineralogical content and the development of micro-cracks in the samples are interpreted as being the primary factors that affect the loss of integrity in the rock.

Effect of carbon dioxide sequestration on the mechanical properties of Deccan basalt

Fracture toughness of the rock is an essential parameter for designing large-scale civil engineering, mining and reservoir geomechanics projects. This parameter represents a material’s resistance against the propagation of fracture. Therefore, study of fracture properties has drawn a wide attention from the rock mechanics and rock engineering communities. Several standards have been suggested by ISRM to experimentally calculate the fracture toughness of the rocks (Ouchterlony 1988; Fowell 1995; Zhou et al. 2012; Kuruppu et al. 2014). However, it is a difficult parameter to obtain than the index geomechanical properties due to difficulties in sample preparation, fragility of soft rocks, complex instrumental requirement and premature sample failure. Therefore, several efforts have been made in past to derive the fracture toughness from the geomechanical properties of the rocks. Several researchers have shown that mode-I fracture toughness can be correlated with the strength properties of the rocks such as uniaxial compressive strength and tensile strength (Whittaker et al. 1992; Zhang et al. 1998; Chang et al. 2002; Zhang 2002; Guha Roy et al. 2016). Similarly, several approximate relationships were obtained between the fracture toughness and ultrasonic velocities (both P-wave and S-wave), densities and point load index of the rocks (Bearman 1991; Zhixi et al. 1997; Brown and Reddish 1997; Chang et al. 2002). In addition to these studies, the mechanical and fracture properties of different soils have also been investigated by several researchers (Haberfield and Johnston 1989; Harison et al. 1994; Wang et al. 2007). But, these results were not incorporated in the present analysis, and it was kept limited to the rocks only. The fracture toughness and geomechanical properties were collected from the following references: Heuze (1983), Whittaker et al. (1992) and references therein, Brown and Reddish (1997), Zhixi et al. (1997), Nordlund et al. (1999), Zhang et al. (1998), Haimson and Chang (2000), Khan and Al-Shayea (2000), Al-Shayea et al. (2000), Yu (2001), Chang et al. (2002), Backers et al. (2003), Funatsu et al. (2004), Kahraman and Altindag (2004), Nasseri et al. (2005, 2007), Qiu-hua et al. (2007), Cho et al. (2007), Nasseri et al. (2009), Ayman (2010), Nara et al. (2012), Siren (2012), Kwasniewski et al. (2012), Yin et al. (2012), Kataoka et al. (2015), and Mahanta et al. (2016). Some properties were calculated based on the other available & Debanjan Guha Roy geo.debanjan@gmail.com

Debanjan Guha Roy

Papers

Effect of Water Saturation on the Fracture and Mechanical Properties of Sedimentary Rocks

Effect of Heat Treatment and Layer Orientation on the Tensile Strength of a Crystalline Rock Under Brazilian Test Condition

Correlating mode-I fracture toughness and mechanical properties of heat-treated crystalline rocks

Effect of carbon dioxide sequestration on the mechanical properties of Deccan basalt

Correlating the Mechanical and Physical Properties with Mode-I Fracture Toughness of Rocks