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

Abstract Knowledge of the spacing and size of discontinuities in a rock mass is of considerable importance for the prediction of rock behaviour. The characteristics of discontinuities can be estimated using scanline surveys but the precision of the estimates must be obtained and the bias caused by linear sampling must be eliminated before they can validly be used. Initially, an expression is presented which gives the degree of confidence that can be assigned to the measured mean discontinuity spacing. A reduced form of this expression is obtained for cases where the discontinuity spacings follow the negative exponential distribution. The precision of discontinuity frequency and RQD estimates is also explained. The distribution of trace lengths produced by the intersection of planar discontinuities with a planar rock face is used to determine the distribution of trace lengths, the distribution of semi-trace lengths and the distribution of censored semi-trace lengths intersected by a randomly located scanline. Comparison of the actual and sampled distributions demonstrates the bias introduced by scanline sampling of trace lengths. Relations between the distributions can be used to produce analytical or graphical methods of estimating mean trace length from censored measurements at exposures of limited extent.

Estimation discontinuity spacing and trace length using scanline surveys

Extraction and statistics of discontinuity orientation and trace length from typical fractured rock mass: A case study of the Xinchang underground research laboratory site, China

A model for assessing the compound risk represented by spontaneous coal combustion and methane emission in a gob

Experimental and numerical investigation on the effects of bedding plane properties on the mechanical and acoustic emission characteristics of sandy mudstone

Nuclear waste repositories have extremely stringent requirements for geological environment. However, natural fractures in rock mass can be potential channels for nuclide migration, therefore, the influence of fractures on the permeability of rock mass must be assessed. In this paper, a well research was conducted on well-exposed granite outcrops in the Xinchang site (the Chinese high-level radioactive waste repository). The high-precision three-dimensional model of a typical outcrop is built to obtain fracture information combined with field measurement, and then the three-dimensional fracture network model is generated using the relevant parameters by Monte Carlo method. To obtain more comprehensive fracture connectivity while avoiding the traditional method of searching the connectivity path in the complicated 3D fracture model taking up a lot of storage space and costing a lot of time, this paper presents an approach using MATLAB cell array instead of traditional adjacency matrix to search and store fracture network connectivity paths. In DFN model, the fracture disc with certain thickness is equivalent to three-dimensional pipe network model (EPNM) with variable diameter, and the equivalent path permeability coefficient (EPC) is proposed to objectively study the permeability characteristics of the seepage path in fractured rock mass based on that. Especially noteworthy is that some fractures in a certain strike range belong to open type, while those in another range belong to cemented closed fractures, when fresh fractures were exposed by cutting off the surface rock to a certain depth. The calculation of EPC under different conditions shows that the order of magnitude of EPC mean value is 1e−7m/s and 1e−3m/s, respectively, when fractures are cemented and not partly. On this basis, the size of the representative elementary volume (REV) of the fractured rock mass in the study area is determined to be about 25 m. By rotating the matrix in model, the spatial permeability tensor of the region (including permeability principal value and main direction) is obtained, which is within the range of borehole data. The predicted results may provide some reference for the related projects in the future.

Study on three-dimensional fracture network connectivity path of rock mass and seepage characteristics based on equivalent pipe network

The invention discloses a method for calculating and optimizing the permeability tensor of fractured rock mass based on measured structural plane parameters, which marks control points on the rock outcrop surface and takes pictures of the rock outcrop surface from different angles at the same time. The three-dimensional coordinates of the control points of the structural plane traces on the photographs are located according to the coordinates of the marked control points, and the homogeneous regions are divided according to the clustering degree of the control points on the structural plane traces. According to the coordinates of the control points of the structural plane traces, a three-dimensional model of the structural plane traces in the homogeneous region to be measured is established. According to the three-dimensional model of structural plane traces, the information of structural plane traces length, occurrence and spacing is extracted. Statistical analysis of trace length, occurrence and spacing of structural planes is carried out to determine the random distribution types and parameters obeyed by them. According to the type and parameter of random distribution, the permeability tensor of the homogeneous area to be measured is calculated. The invention improves the accuracy and efficiency of the structural plane information processing, and simultaneously improves thecalculation efficiency of the infiltration tensor and the optimal path identification in the calculation module.

Wang Xinyong

Papers

Extraction and statistics of discontinuity orientation and trace length from typical fractured rock mass: A case study of the Xinchang underground research laboratory site, China

Study on three-dimensional fracture network connectivity path of rock mass and seepage characteristics based on equivalent pipe network

A method for calculating permeability tensor of fractured rock mass based on measured structural plane parameters