Three-dimensional Fracture Network Model Research Articles

A model of cement grout flow in a fracture network system

Understanding the mechanism of cement grout flow in fractured rocks is essential for controlling seepage in the construction of hydraulic projects. However, simulating grouting in fractured rocks is complex due to random fracture distribution and non-Newtonian grout flow. This study proposes a numerical model for simulating cement grout flow, considering the hydro-mechanical coupled process in a three-dimensional fracture network system based on the unified pipe-network method. A pipe-network equivalence method is used to derive equivalent pipes for the process of grouting displacement, and the flow field can be solved in unified pipe networks. The hydro-mechanical coupled process is achieved by incorporating an analytical solution for the stress distribution of the center borehole model on an infinitely large plane and a constitutive model for the estimation of the fracture aperture. The time-varying property of the cement grout flow is also considered in the simulation of grouting. The reliability of the numerical model is verified by comparing with analytical solutions for grout flow in a water-saturated fracture. Grouting experiments in fracture networks are also performed to demonstrate the applicability of the proposed method. The influence of various factors on the propagation of cement grout is further investigated in three-dimensional fracture network models.

Comprehensive identification of statistical homogeneity of fractured rock masses for a candidate HLW repository site, China

Determining the statistically homogeneous regions is important for engineering geological modeling and promoting systematic research on regional rock mass characteristics and rock engineering designs. This study proposes a comprehensive framework considering multiple discontinuity geometry parameters (e.g., orientation, trace length, density, and cluster characteristics.) to distinguish statistical homogeneity of fractured rock masses. First, based on the equal-area plot method (Schmidt net), the quantitative judgment ability of the Miller method for determining the similarity between two discontinuity orientation populations was improved by optimizing block network division scheme and blank area merging principle. Then, considering the distribution characteristics of discontinuity in rock mass space and the variation features of discontinuity at different geographical locations, a three-dimensional fracture network model, established using the discontinuity geometry parameters obtained from field investigation, was combined with the fractal dimension method (called the network fractal dimension method; NFD) to further evaluate the statistical homogeneity of fractured rock mass. The proposed approaches were subsequently applied to the identification of the statistical homogeneity of several typical granite fracture outcrops in the Beishan area, which is a candidate site for high-level radioactive waste (HLW) repository of China. The case study reveals that the optimized Miller method is more flexible and applicable than the conventional orientation-based methods, especially in dealing with the complex situation of the coexistence of gentle dip angle and steep dip angle as well as clustering characteristics of discontinuity. The NFD method was used to unify the influence of the main discontinuity characteristic parameters for a logical and unbiased evaluation of the statistical homogeneity. The comprehensive framework developed herein integrates the advantages of the two methods and reduces the interference of subjective evaluation. Therefore, it can be employed to efficiently determine the statistical homogeneity of rock masses at different locations at a large scale without concern over the deviation caused by different directions and size of the compared areas.

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

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.

Determination of the geometrical REV based on fracture connectivity: a case study of an underground excavation at the Songta dam site, China

This paper presents a technique for estimating the geometrical representative elementary volume (REV) of a fractured rock mass based on fracture connectivity. A three-dimensional fracture network model, of dimensions 78 m × 50 m × 50 m, was generated and validated for a granite rock mass using joint data collected from an exploration tunnel at the Songta dam site in southwest China. Two hundred and forty cubic specimens with edge lengths ranging from 1 to 20 m were sampled from the model, and connectivity parameters of each specimen, including the number of intersections per unit volume (C 1) and the intersection length per unit volume (L 1), were calculated. The REV was determined using the connectivity parameters and a series of statistical tests. The results demonstrate that both the C 1- and L 1-based REVs are equal to 11 m × 11 m × 11 m. In this work, the volumetric fracture intensity (P32) was also used to calculate the REV for comparison. The REV obtained by P32 is 9 m × 9 m × 9 m, which is smaller than that calculated by C 1 and L 1. Finally, the geometrical REV for the rock mass by integrating C 1, L 1, and P32 is 11 m × 11 m × 11 m.

Determination of the hydraulic conductivity components using a three-dimensional fracture network model in volcanic rock

Accurate prediction of the pathways as well as the leakage rates of contaminated material from the underground storage facilities is one of the important tasks to protect the environment from the impact of such facilities. In particular, predicting the pathway and travel time for any radioactive nuclides escaping from an underground nuclear waste repository to the biosphere is one of the most critical factors for the performance assessment of the repository. Radioactive nuclides released from a repository are dissolved by groundwater in saturated rock mass. In the case of crystalline rock, it is normally assumed that the rock matrix is impermeable and groundwater flow is only allowable through fractures. Thus, the generation of an actual fracture network is essential for the accurate prediction of the flow path and travel time of groundwater. In order to predict the groundwater flow path more accurately, the anisotropic hydraulic conductivity should be considered. It takes, however, time and efforts to determine the anisotropic hydraulic conductivities of a site from in situ tests. In this study, a method to calculate the anisotropic hydraulic conductivities from the fracture network realized based on the in situ condition was suggested. The following two steps were suggested to realize the three-dimensional fracture network representing in situ conditions. The fracture network can be generated by using the stereographic net of the fracture data obtained from the borehole logging and the surface survey. Through this fracture network generated, an effective hydraulic conductivity tensor corresponding to the in situ hydraulic conductivities could be determined.

Modelling groundwater flow in the Sellafield area

Abstract This paper presents a snapshot of how numerical modelling of groundwater is being used in the interpretation of hydrogeological data for the proposed Sellafield radioactive waste repository. The main objective of the modelling at the present stage of the investigation is to help develop a conceptual understanding of the site hydrogeology, by testing whether particular concepts are quantitatively feasible and whether they are able to explain observations. Models have been constructed with differing levels of detail: they each contribute to building a consistent conceptual model of the behaviour of the site as a whole, but they do not individually provide such an integrated conceptual model. They are presented here to illustrate the approach to developing the conceptual understanding, and to illustrate the range of quantitative approaches being applied to different aspects of the site hydrogeology. Four groups of models are described in outline, incorporating variously porous medium and fracture flow, complex geology, anisotropic formations, and dense solutes from more than one source. These are modelled in two and three dimensions. A two-dimensional areal model reproduces head variation observed in shallow wells penetrating the Sherwood Sandstone Group, identifying recharge and discharge areas, and constraining the hydraulic conductivity of the sandstone. Vertical section models through the geological sequence, incorporating one or two sources of dense saline water were able to reproduce qualitatively the main features observed in deep boreholes, in terms of pressure and salinity. The two-source model produces the better match to the salinity distribution. A three-dimensional model, using simplified geology, was able to demonstrate the interaction of salinity and geology, and demonstrate how pressures and salinity may evolve with time. Three-dimensional fracture network models of the Borrowdale Volcanic Group show head variability with depth similar to that observed in some deep boreholes. A number of fracture concepts and parameter distributions are compatible with the data. The modelling work presented shows progress towards a numerically consistent conceptual hydrogeological model of the Sellafield region that can accommodate the site characterization data, and further work is under way to continue this progress.

Three-dimensional fracture network models from laboratory-scale rock samples

Three-dimensional fracture network models from laboratory-scale rock samples

Three-dimensional fracture network models from laboratory-scale rock samples

Three-dimensional fracture network models from laboratory-scale rock samples

Application of a three-dimensional fracture network model to a hot-dry-rock reservoir : Lanyon, G W; Kingdon, R D; Herbert, A W Proc 33rd US Symposium on Rock Mechanics, Santa Fe, 3–5 June 1992P561–570. Publ Rotterdam: A A Balkema, 1992

Application of a three-dimensional fracture network model to a hot-dry-rock reservoir : Lanyon, G W; Kingdon, R D; Herbert, A W Proc 33rd US Symposium on Rock Mechanics, Santa Fe, 3–5 June 1992P561–570. Publ Rotterdam: A A Balkema, 1992