International Journal of Rock Mechanics and Mining Sciences
Coupled analysis of flow, stress and damage (FSD) in rock failure
Introduction
Among the problems that are faced by rock and civil engineers, there is none more challenging than the characterisation of fluid flow though fracturing rocks, especially those which are highly stressed. In mining and civil engineering projects, the re-distribution of the stress field during the excavation of tunnels and underground chambers leads to the formation of new fractures. This damage can cause dramatic changes in the permeability of the rock masses. Consequently, the rate of water flowing into the tunnels and chambers will increase [1], [2], [3], [4], [5], [6], [7], [8]. Moreover, stress-induced changes in flow properties can affect the performance of underground chambers for the storage of nuclear waste [5]. For instance, the stresses in the rock immediately around the waste canisters can induce crack initiation and growth, and potentially create a highly permeable damage zone around the canisters. On a larger scale, the combination of thermal and mechanical stresses around the emplacement drifts can cause certain flow paths to be enhanced, which will result in significant changes in the far-field flow field.
Within rock and civil engineering structures, general issues concerning fluid flow cannot be resolved in any practical manner prior to investigating the fracturing behaviour of rocks under hydraulic loading and the original nature of the fracture networks themselves. Comparable difficulties arise when carrying out constructions in rock masses under the strong influence of groundwater. Similar, if not greater, difficulties have commanded our attention recently in regard to the safety of buildings in the vicinity of slopes under hydraulic loading. Predicting the behaviour of fluid flow through fractured and fracturing rocks, especially in highly stressed rocks, is a formidable task.
Of course, fracturing rocks under hydraulic loading exhibit a unique feature: the flow and transport behaviour within developing fractures are dramatically different from those in rocks with existing fractures under the same loading. In fact, the contrasts in hydraulic conductivity between fractured rocks and fracturing rocks can be extreme and localised. The permeability of rocks with existing fractures does not change, but it can change dramatically due to damage evolution in fracturing rocks. Thus, when examining the hydraulic behaviour of rocks, we must determine the influence of damage on the variation of permeability as well as the original nature of the existing fractures in rocks.
Another major problem in characterising the hydraulic behaviour of rocks concerns the irregular flow paths that depend on the mechanical heterogeneity of the rocks. In working with heterogeneous rocks, a key factor is to determine the specific data that are needed to ascertain the effect of heterogeneity on the complicated flow paths in fracturing rocks.
Given the complexity of the problems, one of the most promising approaches is to develop numerical methods for analyses. Rutqvist [9], [10] reviewed the large number of computer codes for flow-stress or flow-strain (FS) coupling analysis that were developed in recent years. Noorishad [11] developed one of the first programmes for flow analysis in rock masses that fracture due to the coupled effects of fluid forces and loadings. Witherpoon et al. [12] developed a finite element programme that involved the coupled action of flow forces, body forces and boundary loads. Gale [13] developed a numerical model that took into account the behaviour of deformable fractures that can close or open under the action of fluid forces. Such coupled thermo-hydro-mechanical numerical models were first made available in the early 1980s [14], and the formulations were based on Biot's theory of consolidation. Tham [15] developed solutions for confined and unconfined flow in porous media using higher order elements. Time-space elements were also used to solve transient flow problems under various boundary conditions [16], [17], [18]. Furthermore, a finite strip solution [19], [20] was developed for the consolidation analysis of layered soils. For flow in fractured rocks, the dual-porosity model was used in the groundwater flow analysis of a hydropower station in China [21]. In view of the randomness in the distributions and geometries of fractures in rock masses, a stochastic approach was used to predict the depth of penetration of grout [22].
However, few of these methods took into account the effects of the extension of existing fractures, the initiation of new fractures, and the coupled effects of flow, stresses and damage (FSD) on the extension of existing/new fractures and the permeability of the rocks. To improve the performance and upgrade the safety of engineering projects, it is necessary to accurately predict the behaviour of fluid flow in fractured and fracturing rocks, and particularly the effects that arise from the damage to the rocks (that is, the initiation, development and coalescence of fractures). To this end, a coupled finite-element strategy is developed, in which the problem is formulated in the context of the theories of fluid-saturated porous media and damage mechanics. The theory of fluid-saturated porous media can be derived from the classical phenomenological approach of Biot [23] using the effective stress concept of Terzaghi. The theory of damage mechanics that is applied in this strategy is based on the elastic damage model [24].
To solve the coupled flow-damage problems, a numerical method is needed to directly simulate fracture initiation, propagation and coalescence in stressed rocks. Fortunately, many numerical techniques, such as the finite element, boundary element, finite difference and discrete element methods, have been developed to simulate the damage behaviour of rocks or rock masses. Recognising the dominant roles played by heterogeneity and fractures in the deformation and collapse behaviour of rock structures, Li and Zimmermann [25] simulated fracture propagation using a laminate model. They introduced an additional set of lamina, which was orientated according to the maximum principal stress at the onset of fracturing, and associated it with a softening stress–strain law. Van Mier [27] used the lattice model [26] to simulate concrete and sandstone laboratory scale specimens. Cundall [28], [29] developed the distinct element model to simulate the failure of rocks. Tang [24] developed a rock failure process analysis code (RFPA) that was based on the FEM. In this model, the properties of the rocks were defined spatially by Weibull's function. By varying the coefficients of the function, rocks were simulated with different degrees of heterogeneity.
The objective of this paper is to present a flow-stress-damage (FSD) coupling model of saturated rocks by taking into account the growth of existing fractures and the formation of new fractures. This FSD model can be used to trace the development of fractures and the associated fluid flow, and to simulate the overall response of rock masses arising from the fracture process under hydraulic and boundary loadings.
Section snippets
Model for flow-stress-damage (FSD) coupling analysis
This section proceeds as follows: Section 2.1 gives the experimental results of flow-stress-damage (FSD) coupling, Section 2.2 describes the coupled flow-stress relationship, and Section 2.3 describes the coupling effects of permeability and damage.
Examples to validate the model, and discussion
In this section, we numerically simulate a rock failure and the associated fluid flow using the flow coupled RFPA2D code (F-RFPA2D). Moreover, a parametric study is carried out to investigate the effect of heterogeneity on fluid flow and the failure mode.
Conclusions
Numerous researchers have carried out investigations to gain a better understanding of the factors that control the behaviour of fluid flow in rocks or rock masses. Such intensive studies of fluid flow in fractured rocks are useful as initial approaches to many problems, but their usefulness is limited when one examines the failure process of rocks to understand the evolution of fluid flow behaviour. It has been found experimentally that failure induces dramatic changes in permeability.
Acknowledgements
The study that is presented in this paper was supported by grants from the China National Key Fundamental Research “973 Programme” (No. G1998040700) and the China National Natural Science Foundation (No. 49974009, No. 50134040 and No. 50174013). It was also partially supported by the Department of Civil Engineering at the University of Hong Kong. Thanks are given to Dr. Q.Y. Feng, who kindly provided help in conducting the experiments in the Laboratory of Rock Mechanics, China University of
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