We investigate the stress-dependent permeability issue in fractured rock masses considering the effects of nonlinear normal deformation and shear dilation of fractures using a two-dimensional distinct element method program, UDEC, based on a realistic discrete fracture network realization. A series of “numerical” experiments were conducted to calculate changes in the permeability of simulated fractured rock masses under various loading conditions. Numerical experiments were conducted in two ways: (1) increasing the overall stresses with a fixed ratio of horizontal to vertical stresses components; and (2) increasing the differential stresses (i.e., the difference between the horizontal and vertical stresses) while keeping the magnitude of vertical stress constant. These numerical experiments show that the permeability of fractured rocks decreases with increased stress magnitudes when the stress ratio is not large enough to cause shear dilation of fractures, whereas permeability increases with increased stress when the stress ratio is large enough. Permeability changes at low stress levels are more sensitive than at high stress levels due to the nonlinear fracture normal stress-displacement relation. Significant stress-induced channeling is observed as the shear dilation causes the concentration of fluid flow along connected shear fractures. Anisotropy of permeability emerges with the increase of differential stresses, and this anisotropy can become more prominent with the influence of shear dilation and localized flow paths. A set of empirical equations in closed-form, accounting for both normal closure and shear dilation of the fractures, is proposed to model the stress-dependent permeability. These equations prove to be in good agreement with the results obtained from our numerical experiments.
Rocks with shear fractures or faults widely exist in nature such as oil/gas reservoirs, and hot dry rocks, etc. In this work, the fractal scaling law for length distribution of fractures and the relationship among the fractal dimension for fracture length distribution, fracture area porosity and the ratio of the maximum length to the minimum length of fractures are proposed. Then, a fractal model for permeability for fractured rocks is derived based on the fractal geometry theory and the famous cubic law for laminar flow in fractures. It is found that the analytical expression for permeability of fractured rocks is a function of the fractal dimension for fracture area, area porosity , fracture density , the maximum fracture length , aperture , the facture azimuth and facture dip angle . Furthermore, a novel analytical expression for the fracture density is also proposed based on the fractal geometry theory for porous media. The validity of the fractal model is verified by comparing the model predictions with the available numerical simulations.
Instabilities in rock structures involve coupled mechanisms related to both deformations along existing discontinuities and brittle fracture of intact rock. Conventional kinematic and limit equilibrium techniques used to study rock slope stability suffer from oversimplifications. Mass strength degradation and progressive failure mechanisms in rock bridges cannot be ignored and must be considered to predict the overall slope behaviour. A 3D numerical model based on the discrete element method has been developed to overcome these limitations. Pre-existing discontinuities as a Discrete Fracture network (DFN) can be initially plugged into a set of discrete elements combined with the use of a modified contact logic which provides an explicit representation of joints. Both fracturing of intact material and yielding within discontinuities can therefore be reproduced, depending on the loading conditions and material strength. Simulations of referenced experimental tests are presented here to show the capabilities of the model in tackling the failure mechanisms of intact rock in the presence of pre-existing discrete fractures, with an emphasis on the initiation and propagation processes. This model proves to be a promising tool in understanding and predicting instabilities that could lead to the failure of fractured rock slopes. ► Discrete Element Model with a Discrete Fracture Network. ► Progressive failure mechanisms in rock bridges. ► Calibration of the model for fractured rocks. ► Wing cracks simulation in 3D. ► Slope stability of fractured rock mass.
Seismic wave propagation through fractured rocks is greatly influenced by their fracture system and fluid content. In this paper, we derive expressions for the anisotropic frequency-dependent elastic constants. These depend on the relativemobilities of the saturating fluids and the coupled impact of 'squirt' and 'patch' effects, which have typically been considered independently, on anisotropic seismic wave propagation. The effect of relative permeability is pronounced; fluid mobility can be lower in partially saturated rocks compared to the fully saturated case, and this can lead to a stiffening which dominates compressibility effects. This can result in unexpected non-monotonic relationships between moduli and water saturation, complicating attempts to invert saturation from seismic data. We use our model to explain laboratory measurements of seismic anisotropy in partially saturated fractured rocks, concluding that both squirt and patch mechanisms are significant.
This paper presents the results of a shear slip experiment in hot rock and its simulation and analysis using 3D coupled thermo-poromechanical model with the aim of assessing the role of pore pressure and temperature change on shear slip in granitic rock. The test is carried out in a triaxial system at representative reservoir pressure and temperature using right circular cylindrical specimens of Westerly granite with a 30° precut and ground surface. After the pore pressure and temperature were stabilized, the differential stress and absolute pore pressure were systematically varied to produce different effective stress states to evaluate the shearing response of the saw-cut fracture. The key objective of the experiment is to test the cooling effect on the fracture slip. The experimental results were then analyzed using a newly developed 3D thermo-poromechanical finite element model which uses traditional 4 node tetrahedron elements for intact rock deformation and transport processes. Zero thickness contact interface element is employed to capture the closure and slip on the fracture surface. The stick/slip state of fracture is determined by the Mohr-Coulomb criterion. Simulation results show that the convective cooling effects on rock/fracture surface promote deformation and slip of the fracture. The cold fluid cools the surrounding rock material and results in normal stress reduction that causes portions of the fracture surface to undergo stick/slip state changes, and induces irreversible slip. The experimental work along with modeling provides a physics-based understanding of the role of coupled processes on shear stimulation phenomenon.
The influence of in-situ stresses on flow processes in fractured rock is investigated using a novel modelling approach. The combined finite-discrete element method (FEMDEM) is used to model the deformation of a fractured rock mass. The fracture wall displacements and aperture changes are modelled in response to uniaxial and biaxial stress states. The resultant changes in flow properties of the rock mass are investigated using the Complex Systems Modelling Platform (CSMP++). CSMP++ is used to model single-phase flow through fractures with variable aperture and a permeable rock matrix. The study is based on a geological outcrop mapping of a low density fracture pattern that includes the realism of intersections, bends and segmented features. By applying far-field (boundary) stresses to a square region, geologically important phenomena are modelled including fracture-dependent stress heterogeneity, the re-activation of pre-existing fractures (i.e. opening, closing and shearing), the propagation of new fractures and the development of fault zones. Flow anisotropy is investigated under various applied stresses and matrix permeabilities. In-situ stress conditions that encourage a closing of fractures together with a more pervasive matrix-dominated flow are identified. These are compared with conditions supporting more localised flow where fractures are prone to dilatational shearing and can be more easily exploited by fluids. The natural fracture geometries modelled in this work are not perfectly straight, promoting fracture segments that dilate as they shear. We have demonstrated the introduction of several realistic processes that have an influence on natural systems: fractures can propagate with wing cracks; there is the potential for new fractures to connect with existing fractures, thus increasing the connectivity and flow; blocks can rotate when bounded by fractures, bent fractures lead to locally different aperture development; highly heterogeneous stress distributions emerge naturally. Results presented in this work provide a mechanically rigorous demonstration that a change in the stress state can cause reactivation of pre-existing fractures and channelling of flow in critically stressed fractures. ► We model fractures and new fracturing with the Finite-Discrete Element Method. ► A natural network including bent fractures is deformed under biaxial stresses. ► Fracture walls displace, apertures change, dilational jogs open under shearing. ► Fracture and matrix flow is modelled with the Complex Systems Modelling Platform. ► Fracture reactivation and flow channelling occurs in critically stressed fractures.
This paper is focused on analysis of the damage process in rock that contains some pre-existing fractures. The methodology employs an enhanced embedded discontinuity approach, which is extended here to account for the presence of multiple sets of joints. The approach can be easily implemented in standard FE codes and the results are virtually independent of mesh size/alignment. This is in view of incorporation of a ‘characteristic dimension’ which explicitly depends on discretization of the domain. It is demonstrated that the approach is capable of predicting complex fracture modes associated with formation and propagation of new cracks within the region that contains the pre-existing flaws.
Although the upstream translation of waterfalls is often thought to occur by undercutting of resistant strata, collapse, and headwall retreat (e.g., Niagara Falls), many propagating waterfalls maintain a vertical face in the absence of undercutting. To explain this observation, we propose that bedrock-fracture geometry exerts a fundamental control on knickpoint morphology and evolution such that vertical waterfalls can persist during retreat due to toppling in bedrock with near horizontal and vertical sets of joints (e.g., columnar basalt). At a waterfall, rock columns are affected by shear and drag from the overflowing water, buoyancy from the plunge pool at the foot of the waterfall, and gravity. We used a torque balance to determine the stability of a rock column and any individual blocks that comprise the column. Results indicate that rotational failure should occur about the base of a headwall (and therefore preserve its form during upstream propagation) where columns are tilted in the downstream direction or slightly tilted in the upstream direction, depending on the plunge-pool depth. Flume experiments were performed to test the model, and the model provides a good prediction of the flow necessary to induce toppling and the morphology of the headwall. Waterfall-induced toppling explains the morphology of canyon headwalls in the volcanic terrain of the northwestern United States, where catastrophic paleofloods (e.g., Bonneville Flood) have carved steep amphitheater-headed canyons in columnar basalt. This model may also explain similar land-forms elsewhere on Earth and Mars, and it can be used to predict the minimum flow discharge needed to create these features.
The effective viscoelastic properties of a rock mass embedding many sets of planar fractures are estimated. The rock matrix is modeled by a standard Zener rheological model, while the linear elastic or a linear non ageing viscoelastic laws is considered to relate the opening displacement of a fracture and the stresses acting on its surfaces. The correspondence principle is considered to transform the problem in hand to an equivalent elastic problem in Laplace-Carson (LC) space. Then, closed form solutions to the creep parameters in time space are derived. For the case of elastic fractures, we show that the presence of the fractures modifies the instantaneous and long term compliances of viscoelastic fractured rocks by the same way as it does for the case of elastic fractured rocks. However, they do not affect the variations versus time of the creep parameters. Unlike the case of elastic fractures, viscoelastic fractures modify the variations versus time of the creep parameters. However for all the situations, we observe that the effective creep properties of a fractured medium made of a Zener solid matrix and Zener fractures can be explicitly expressed by an effective Generalized Maxwell rheology of which the rheological parameters are functions of the viscoelastic parameters of the matrix and the fractures.
A fractal model that represents the geometric characteristics of rock fracture networks is proposed to link the fractal characteristics with the equivalent permeability of the fracture networks. The fracture networks are generated using the Monte Carlo method and have a power law size distribution. The fractal dimension is utilized to represent the tortuosity of the fluid flow, and another fractal dimension is utilized to represent the geometric distribution of fractures in the networks. The results indicate that the equivalent permeability of a fracture network can be significantly influenced by the tortuosity of the fluid flow, the aperture of the fractures and a random number used to generate the fractal length distribution of the fractures in the network. The correlation of fracture number and fracture length agrees well with the results of previous studies, and the calculated fractal dimensions are consistent with their theoretical values, which confirms the reliability of the proposed fractal length distribution and the stochastically generated fracture network models. The optimal hydraulic path can be identified in the longer fractures along the fluid flow direction. Using the proposed fractal model, a mathematical expression between the equivalent permeability and the fractal dimension is proposed for models with large values of . The differences in the calculated flow volumes between the models that consider and those that do not consider the influence of fluid flow tortuosity are as high as 17.64–19.51%, which emphasizes that the effects of tortuosity should not be neglected and should be included in the fractal model to accurately estimate the hydraulic behavior of fracture networks.