A main aspect of wellbore stability analysis is the selection of an appropriate rock failure criterion. The most commonly used criterion for brittle failure of rocks is the Mohr-Coulomb criterion. This criterion involves only the maximum and minimum principal stresses, a, and sigma(3), and therefore assumes that the intermediate stress 92 has no influence on rock strength. As the Mohr-Coulomb criterion ignores the strengthening effect of the intermediate stress, it is expected to be too conservative in estimating the critical mud weight required to maintain wellbore stability. Recently, Al-Ajmi and Zimmerman [Relationship between the parameters of the Mogi and Coulomb failure criterion. Int J Rock Mech Min Sci 2005;42(3):431-39.] developed the Mogi-Coulomb failure criterion, and showed that it is reasonably accurate in modelling polyaxial failure data from a variety of rocks. We then develop a model for the stability of vertical boreholes, using linear elasticity theory to calculate the stresses, and the fully-polyaxial Mogi-Coulomb criterion to predict failure. Our model leads to easily computed expressions for the critical mud weight required to maintain wellbore stability.
We have shown that linear Mogi criterion does a good job in representing rock failureunder polyaxial stress states. When σ2 = σ3 the linear version of Mogi's triaxial failurecriterion reduces exactly to the Coulomb criterion. Hence, the linear Mogi criterion can be thought of as a natural extension of the Coulomb criterion into three dimensions (i.e., polyaxial stress space). As Mohr's extension of the Coulomb criterion into three dimensions is often referred to as the Mohr-Coulomb criterion, we propose that the linear version of the Mogi criterion be known as the "Mogi-Coulomb" failure criterion. The classical Coulomb failure criterion can therefore be thought of as a special case, which applies only when σ2 = σ3 of the more general linear Mogi failure criterion. Furthermore, we found that the numerical values of the parameters that appear in the Mogi-Coulombcriterion can be estimated from conventional triaxial test data. Thus, this polyaxial failurecriterion can be applied even in the absence of polyaxial (true triaxial) data. This offers a great advantage, as most laboratories are equipped to conduct only traditional σ2 = σ3tests. Finally, we showed that if the linear form of the Mogi criterion is used, the parameters that appear in it can be unambiguously related to the traditional parameters appearing in the Coulomb failure law. The lack of such a relationship for the parameters appearing in the power-law Mogi criterion has been cited in [8] as a major drawback to the use of that model.
A 1-m-thick pillar was subject to coupled excavation- and thermal-induced stresses to induce brittle rock mass yielding. The yielding strength of the heterogeneous and fractured rock mass consisting of Aspo diorite was evaluated at eighteen discrete locations using data from the displacement, acoustic emission, and thermal monitoring systems. The average rock mass yielding strength was determined to be 0.59 of the uniaxial compressive strength. The onset of dilation in uniaxial laboratory tests, determined from strain gauge data, was found to occur at approximately 0.45 of the uniaxial compressive strength. It was shown that that the onset of acoustic emission events in situ also occurred when the tangential stress exceeded 0.43 of the uniaxial compressive strength. For sites with absence of in situ data it is recommended that this lower-bound value determined from laboratory data may be used for assessing the in situ rock mass yielding strength. Visual observation and displacement monitoring showed that extent of rock mass yielding is sensitive to small changes in the tangential stress magnitudes. It was determined using three-dimensional modelling that changes in the tangential stress magnitude of approximately 1 MPa was sufficient to cause yielding of the pillar to propagate in what appeared to be intact rock. Observations suggest that without this small stress change yielding of the rock mass would not occur. In other words, there appeared to be a well defined boundary, and if the stresses reached this boundary yielding was observed. However, if stresses were only slightly below this boundary yielding or time-dependant processes were not observed over the monitoring period used in the experiment.
This paper is the second dealing with measurement-related uncertainties of overcoring data undertaken at the Aspo Hard Rock Laboratory and focuses on the biaxial test data from CSIRO HI overcore samples. The first paper dealt with measurement-related uncertainties in connection with the overcoring phase [1]. The uncertainties identified in connection to biaxial tests of CSIRO HI overcore samples include too large applied pressures and poor sampling frequency. At the Aspo HRL, the results yield that most overcore samples fractured during biaxial testing, meaning that a significant part, 56%, of available strain gauge combinations were removed from calculations of the elastic parameters. Remaining strain gauge combinations indicate average values of 62 +/- 5 GPa for Young's modulus and 0.25 +/- 0.01 for Poisson's ratio, which are considerably lower than previously published values [2-5], and are in good agreement with results from biaxial tests on Borre Probe overcore samples [6-10]. The stress calculations were obtained from re-analyzed elastic parameters and strains, and show primarily a reduction in stress magnitudes. Overall, the stress field obtained with different stress measurement methods and its variation with depth is now quite well resolved. The overcoring data suggest that the principal stresses are inclined with a vertical component dipping about 65 degrees from the horizontal over the investigated rock volume (140-420 m depth). This is interpreted as a result of influence from the sub-vertical NE-2 Fracture Zone that divides the stress data into two stress domains [11], although it may also be an artefact because the sigma(2)- and sigma(3)-magnitudes are of the same order of magnitude.
The Integrated Stress Determination Method (ISDM) is a powerful tool for estimating the regional stress tensor from in-situ measurements of local stress tensors using a wide variety of stress measuring techniques. This study presents new developments of the ISDM: The stress field may be described with up to 12 model parameters; and is applicable to data from CSIR- and CSIRO HI-type of overcoring devices, hydraulic fracturing, hydraulic tests of pre-existing fractures (HTPF), as well as to combined data sets. Furthermore, in combined data sets, the hydraulic fracturing and/or HTPF data may be used to constrain the average elastic parameters, Young's modulus and Poisson's ratio. The new ISDM developments were applied to the extensive and recently re-analysed rock stress data at the Aspo Hard Rock Laboratory. The results reveal a good fit of the re-analysed data. Overall, the re-analysis indicates that the stress field at Aspo HRL is relatively well constrained and consistent with depth. The NE-2 Fracture Zone influences the stresses, and dividing the regional stress field into a NW and a SE stress domain. When the hydraulic fracturing data were used to constrain the average elastic parameters, Young's modulus, E, and Poisson's ratio, v, quite similar results were obtained (E = 50.8 GPa and v = 0.33) compared with results from biaxial tests of overcore samples (E = 61.6 MPa and v = 0.26).
The Punch-Through Shear (PTS) test was introduced as a method to determine the ModeII fracture toughness of rock material (Backers et al., 2002). Its unique feature is the ability to apply a confining pressure independent of the Mode II (shear) loading. This contribution reports new data on Mode II fracture toughness', KIIC, dependency on confining pressure, loading rate, sample size, and cyclic loading for six different rocktypes. Samples are subjected to different confining pressures up to 70 MPa. KIICincreases with increasing confining pressure and tends to reach a constant value at confining pressures higher than 20-35 MPa. Evidence for 'pure' Mode II fracturetoughness at high confining pressures is reported. Variation of loading rate over five orders of magnitude (10-8 - 10-3 m/s) does not change KIIC. The influence of sample size on coarser grained rocks is verified. Cyclic loading illustrates change of stiffness of the system as fracture propagation takes place. It is concluded that the PTS- test is a suitable future method for KIICtermination.
Permeability of fractured rocks is investigated considering the correlation between distributed fracture aperture and trace length, based on a newly developed correlation equation. The influence of the second moment of the lognormal distribution of apertures on the existence of representative elementary volume (REV), and the possibility of equivalent permeability tensor of the fractured rock mass, is examined by simulating flow through a large number of stochastic discrete fracture network (DFN) models of varying sizes and varying fracture properties.
The REV size of the DFN models increases with the increase of the second moment of the lognormal distribution, for both the correlated and uncorrelated cases. The variation of overall permeability between different stochastic realizations is an order of magnitude larger when the aperture and length are correlated than when they are uncorrelated. The mean square error of the directional permeability increases with increasing value of the second moment of the lognormal distribution function, and good fitting to an ellipsis of permeability tensor can only be reached with very large sizes of DFN models, compared with the case of constant fracture aperture, regardless of fracture trace length.
The effect of stress on permeability and fluid flow patterns in fractured rock masses is studied when distributed fracture aperture is correlated with fracture trace length, using a discrete element method (DEM). The basic assumptions are that the rock matrix is impermeable and linearly elastic, and that the fluid flows only in fractures. A new nonlinear algorithm is developed for prediction of normal stress-normal displacement behavior of fractures based on the Bandis model and the correlation between aperture and length. The results show that when small stress ratios (K = horizontal/vertical stress) are applied at the model boundaries, the overall permeability of the fracture network is generally decreased. However, contribution from a few large fractures of higher hydraulic conductivity prevents drastic reduction of the overall permeability, compared with models that assume uniform fracture apertures. With large values of the stress ratio, both the overall permeability and flow patterns are controlled by a combination of highly conductive larger fractures and fractures with shear slipping and dilation, with much increased overall permeability and shear-induced flow channeling. With increasing stress ratios, it becomes more and more difficult to establish an equivalent permeability tensor and representative elementary volume (REV) of a fractured rock, compared with the unstressed model. These results show significant difference between correlated and non-correlated aperture and fracture length distributions, and highlight more significant scale and stress dependence of hydro-mechanical behavior of fractures rocks when geometric parameters of rock fractures are correlated.
This paper provides an overview of an international research collaboration for advancing the understanding and modeling of coupled thermo-hydro-mechanical-chemical (THMC) processes in geological systems. The creation of the international DECOVALEX Project, now running for over 25 years, was initially motivated by the recognition that prediction of these coupled effects is an essential part of the performance and safety assessment of geologic disposal systems for radioactive waste and spent nuclear fuel. Later it was realized that these processes also play a critical role in other subsurface engineering activities, such as storage of CO2, exploration of enhanced geothermal systems, and unconventional oil and gas production through hydraulic fracturing. Research teams from radioactive waste management organizations, national research institutes, regulatory agencies, universities, as well as industry and consulting groups have participated in the DECOVALEX Project, providing a wide range of perspectives and solutions to these complex problems. Analysis and comparative modeling of state-of-the-art field and laboratory experiments has been at the core of the collaborative work, with an increasing focus on characterizing uncertainty and blind prediction of experimental results. Over these 25 years, many of the major advances in this field of research have been made through DECOVALEX, as evidenced by three books, seven journal special issues, and a good number of seminal papers that have emerged from the DECOVALEX modeling work. Examples of specific research advances will be presented in this paper to illustrate the significant impact of DECOVALEX on the current state-of-the-art of understanding and modeling coupled THMC processes. These examples range from the modeling of large-scale in situ heater tests representing mock-ups of nuclear waste disposal tunnels, to studies of fluid flow and chemical-mechanical coupling in heterogeneous fractures, and to the numerical analysis of controlled-injection meso-scale fault slip experiments.
According to Eurocode 7, two accepted approaches for managing uncertainty in tunnel design are reliability based methods and the observational method. Reliability-based methods account for uncertainty by acknowledging the random variation of the input parameters; the observational method does this by verifying the expected behavior from an initial design during the course of construction. However, in the framework of the observational method, as defined in Eurocode 7, no guidance is given on the selection of suitable parameters for observation and how they can be linked to the limits of acceptable behavior and, at a sufficiently early stage, the decision for implementing contingency actions. Furthermore, no guidance is given on how to verify that the structure fulfills society's required safety level. In this paper, we present a design procedure for shotcrete-supported rock tunnels that combines reliability-based methods with the observational method. The design procedure applies a deformation-based limit state function for the shotcrete support that is based on the convergence confinement method. We suggest how the requirements in the observational method, as defined in Eurocode 7, may be satisfied for this application. In particular, we focus on the structural reliability aspects. The structural reliability of the preliminary design is assessed with Monte Carlo simulations by calculating the expected deformations of the tunnel. The appropriateness of the preliminary design is then verified by observing the actual deformations during the course of construction. The observed deformations are used to predict the future behavior of the tunnel and to update the assessed probability of unsatisfactory behavior. If the defined deformation-based alarm limit regarding the structural reliability is exceeded, predefined contingency actions are put into operation. The procedure is illustrated with a shotcrete-lined circular rock tunnel and practical aspects in satisfying the reliability requirements with the observational method are discussed.
This paper presents some laboratory tests performed on the bentonite used as buffer material in the engineered barrier experiment in Kamaishi mine in Japan and a collective effort of four research groups to characterise the coupled thermo-hydro-mechanical behaviour of the bentonite by comparing numerical calculations with the laboratory test results. Each research group used finite element programs with constitutive models capable to simulate both liquid and vapour flux of water, heat transfer, volume change, swelling pressure and mechanical deformation. Numerical calibrations were performed against results obtained from three types of laboratory tests: water infiltration tests, thermal gradient tests and swelling pressure tests. Parameter values, which could not be directly measured in laboratory tests, were obtained with these calculations.
It is important for rock engineering design to be able to validate numerical simulations, i.e. to check that they adequately represent the rock reality. In this paper, the capability and validity of four numerical models is assessed through the simulation of an apparently simple case: the complete process of microstructural breakdown during the uniaxial compressive failure of intact crystalline rock. In addition to comparing the capabilities of the four models, the results generated by each model were compared with the experimentally determined complete stress-strain curves for the Swedish Avro granite for different porewater conditions. In this way, it has been possible to audit the models' adequacy for this particular simulation task. It was found that although the models had common features, they were each idiosyncratically different and required considerable expertise to match the actual stress-strain curves (which did not monotonically increase in axial strain)-indicating that, for more complex simulations, both adequate modelling and appropriate validation are not going to be an easy task. The work was conducted within the framework of the international 2004-2007 DEmonstration of COupled models and their VALidation against EXperiments with emphasis on Thermo Hydro Mechanic and Chemical aspects (DECOVALEX-THMC) phase on coupled modelling extended to include chemical effects and with application to the excavation damaged zone (EDZ) in crystalline rock.
A number of studies related to past and on-going deep repository performance assessments have identified glaciation/ deglaciation as major future events in the next few hundred thousand years capable of causing significant impact on the long term performance of the repository system. Benchmark Test 3 (BMT3) of the international DECOVALEX III project has been designed to provide an illustrative example that explores the mechanical and hydraulic response of a fractured crystalline rock mass to a period of glaciation. The primary purpose of this numerical study is to investigate whether transient events associated with a glacial cycle could significantly influence the performance of a deep geological repository in a crystalline Shield setting. A conceptual site-scale (tens of kilometres) hydro-mechanical (HM) model was assembled based primarily on site-specific litho-structural, hydrogeological and geomechanical data from the Whiteshell Research Area in the Canadian Shield, with simplification and generalization. Continental glaciological modelling of the Laurentide ice sheet through the last glacial cycle lasting approximately 100,000 years suggests that this site was glaciated at about 60 ka and between about 22.5 and 11 ka before present with maximum ice sheet thickness reaching 2500 m and maximum basal water pressure head reaching 2000m. The ice-sheet/drainage model was scaled down to generate spatially and temporally variable hydraulic and mechanical glaciated surface boundary conditions for site-scale subsurface HM modelling and permafrost modelling. Under extreme periglacial conditions permafrost was able to develop down to the assumed 500-m repository horizon. Two- and three-dimensional coupled HM finite-element simulations indicate: during ice-sheet advance there is rapid rise in hydraulic head, high transient hydraulic gradients and high groundwater velocities 2-3 orders of magnitude higher than under nonglacial conditions; surface water recharges deeper than under nonglacial conditions; upon ice-sheet retreat, the gradients reverse; fracture zone network geometry, interconnectivity and hydraulic properties significantly influence flow domain response; residual elevated heads are preserved for 10,000s in the low-diffusivity rock; and no hydraulic jacking or shear failure occurs at depth. It was found that transient coupled modelling is necessary to capture the essence of glacial effects on Performance Assessment. Model dimensionality also significantly affects simulated results.
Triaxial compression tests with measurements of permeability were performed on core granite samples taken at 450-550 m depth from the Beishan area in Gansu Province, a potential site for China's high-level radioactive waste (HLW) disposal. Corresponding to the distinct features in the stress-strain behaviors, the permeability of the Beishan granite was found to evolve with a clear permeability decrease in the initial microcrack closure region, a constant permeability value in the elastic region and a dramatic permeability increase in the crack growth region. The permeability increases by up to and over two orders of magnitude as deviatoric stress increases up to sample failure; but at a given deviatoric stress, the permeability reduces remarkably with the increase of confining pressure. An empirical upper bound permeability model was presented by relating the mechanisms involved in the microstructure alteration to the permeability change, and the experimental results were well simulated by the proposed model. Combined with field geological characterization and numerical simulation, the implications of the experimental results for China's HLW disposal were discussed.
Geological disposal of the spent nuclear fuel often uses the concept of multiple barrier systems. In order to predict the performance of these barriers, mathematical models have been developed, verified and validated against analytical solutions, laboratory tests and field experiments within the international DECOVALEX III project. These models in general consider the full coupling of thermal (T), hydraulic (H) and mechanical (M) processes that would prevail in the geological media around the repository. For Bench Mark Test no. 1 (BMTI) of the DECOVALEX III project, seven multinational research teams studied the implications of coupled THM processes on the safety of a hypothetical nuclear waste repository at the near-field and are presented in three accompanying papers in this issue. This paper is the first of the three companion papers, which provides the conceptualization and characterization of the BMT1 as well as some general conclusions based on the findings of the numerical studies. It also shows the process of building confidence in the mathematical models by calibration with a reference T-H-M experiment with realistic rock mass conditions and bentonite properties and measured outputs of thermal, hydraulic and mechanical variables.
The grouting results for a tunnel at a depth of 450 min crystalline rock at Aspo HRL were studied. The aims were to investigate whether the methodology used resulted in a successful grouting design and producing a sufficiently dry tunnel, and whether grout penetration and inflow into the finished tunnel corresponded to the predictions. An analysis was made of data from an original cored borehole, drilled before the tunnel was constructed and mapped thoroughly with regard to fractures and transmissivities. The predicted inflow into the tunnel was calculated and found to be four times higher than the measured inflow. The latter was 51/min a long the 70 m tunnel, considered to be a good result at the current depth. New cored control boreholes were drilled along a section of the tunnel. The inflow positions and quantities in these holes, and the positions of grout found in the corresponding cores, were compared with the data from the original borehole. It was found that at the predicted positions of larger fractures, grout was observed and there was no inflow, showing that these had been successfully sealed. At the predicted positions of small fractures, no grout was visible in the cores, and small inflows showed that the grout had not sealed these fractures. The results indicated that cement-based grout successfully sealed fractures down to a hydraulic aperture of about 50 mm but not below 30 mm. This concurs with the initial design aimed at sealing fractures larger than 50 mm.
The effect of fracture geometry on bentonite erosion for a generic repository site in crystalline host rock environment was investigated by means of 2-d numerical simulations. Fracture geometry was varied systematically using random aperture normal distributions with a mean aperture of 1 mm and standard deviations between 0 and 0.7 mm, respectively. Moreover, two aperture correlation lengths (0.2 m and 2 m) were applied. Based on the synthetic fracture aperture fields generated the cubic law in conjunction with the Darcy equation is used to simulate fracture flow fields for mean flow velocities in the fracture between 1 x 10(-5) m/s and 1 x 10(-7) m/s. These flow fields are used in a two-way coupling approach to bentonite erosion simulations. The results of the study clearly show the influence of variable fracture aperture on bentonite erosion behaviour and erosion rates (kg/a). Increasing fracture aperture standard deviation leads to increasing heterogeneous flow velocity distributions governing the erosion behaviour and erosion rates. Calculated steady state erosion rates are in the range of similar to 0.25 kg/a down to similar to 0.014 kg/a. The highest erosion rate is calculated for the highest mean flow velocity in conjunction with the highest standard deviation. The effect of aperture heterogeneity diminishes for the lowest flow velocities. In summary, the results show the effect of fracture heterogeneity on bentonite erosion, especially for high to medium mean flow velocities combined with high to medium fracture heterogeneity under the model boundary conditions and model capabilities and limitations considered. An increase of up to g heterogeneous flow velocity distributions governing the erosion behaviour and erosion rates. Calculated steady state erosion rates are in the range of similar to 83% in erosion rate compared to the constant aperture case highlights the need to consider fracture aperture heterogeneity and its effect on the bentonite erosion in the assessment of the safety and evolution of a high-level nuclear waste repository.
In this paper. coupled thermo-hydro-mechanical (THM) issues relating to nuclear waste repository design and performance are reviewed. Concise statements. that were developed from DECOVALEX discussions, on the current state-of-knowledge are presented. Section 1 describes the THM background and the interface with performance assessment (PA). The role of THM issues in the overall repository design context is amplified in Section 2, which includes a review of the processes in terms of repository excavation. operation and post-closure stages. It is important to understand the overall context, the detailed THM issues, the associated modelling and how these issues will be resolved in the wider framework. Also, because uncoupled and coupled numerical codes have been used fur this subject, there is discussion in Section 3 on the nature of the codes and how the content of the codes can be audited. To what extent does a particular code capture the essence of the problem in hand? Consideration is also given to the associated question of code selection and the future of numerical codes. The state-of-knowledge statements are presented in Section 4 under 11 headings which follow the repository design sequence. The overview conclusion is that A predictive THM capability is required to support repository design because precedent practice information is insufficient. Many aspects of THM processes and modelling are now well understood and there is a variety of numerical codes available to provide solutions for different host rock and repository conditions. However, modelling all the THM mechanisms in space and time is extremely complex and simplifications will have to be made - if only because it is not possible to obtain all the necessary detailed supporting information. Therefor, an important step is to clarify the THM modelling requirement within the PA context. This will help to indicate the complexity of THM modelling required and hence the models. mechanisms, type of computing, supporting data, laboratory and in situ testing, etc, required. An associated transparent and open audit trail should be developed. We also include comments from reviewers and highlight four outstanding issues which are currently being studied in the DECOVALEX III programme.
This paper provides advice on how to incorporate thermo-hydro-mechanical (THM) coupled processes into performance and safety assessments and design studies for radioactive waste disposal in geological formations. The advice is based on work conducted for the EU research project BENCHPAR: "Benchmark Tests and Guidance on Coupled Processes for Performance Assessment of Nuclear Waste Repositories". In Section 1, there is an explanation of why numerical analyses incorporating THM mechanisms are required for radioactive waste studies and background material on the subject is provided. Then, the THM processes and their interactions are explained in Section 2. Three case examples of THM numerical analysis are presented in Section 3 to illustrate the type of work that can be conducted to study the near-field, upscaling, and the far-field. The importance and priority of the THM couplings are summarized in Section 4. Recommended soft and hard auditing procedures are presented in Section 5. We place special emphasis on the fact that the most important step in numerical modelling is not executing the calculations per se, but the earlier conceptualization of the problem regarding the dominant processes, the material properties and parameters, the engineering perturbations, and their mathematical presentations. The associated modelling component of addressing the uncertainties and estimating their influence on the results is also important. Thus, the specific models and codes should be studied first to evaluate the harmony between the nature of the problem and the nature of the codes. The tactical use of particular numerical techniques will then be based on a sound strategic foundation. An associated listing of bullet point recommendations and issues for future directions for this THM subject area is given in Section 6.
The purpose of this review paper is to present the techniques. advances. problems and likely future developments in numerical modelling for rock mechanics. Such modelling is essential for studying the fundamental processes occurring in rocks and for rock engineering design. The review begins by explaining the special nature of rock masses and the consequential difficulties when attempting to model their inherent characteristics of discontinuousness. anisotropy, inhomogencity and inelasticity. The rock engineering design backdrop to the review is also presented. The different types of numerical models are outlined in Section 2. together with a discussion on how, to obtain the necessary parameters for the models. There is also discussion on the value that is obtained from the modelling. especially the enhanced understanding of those mechanisms initiated by engineering perturbations. In Section 3, the largest section. states-of-the-art and advances associated with the main methods are presented in detail. In many cases. for the model to adequately represent the rock reality. it is necessary to incorporate couplings between the thermal. hydraulic and mechanical processes. The physical processes and the equations characterizing the coupled behaviour are included in Section 4. with an illustrative example and discussion on the likely future development of coupled models. Finally. in Section 5. the advances and outstanding issues in the subject are listed and in Section 6 there are specific recommendations concerning quality control. enhancing confidence in the models, and the potential future developments.
The coupled hydro-mechanical behaviour of rock fractures plays an important role in design, performance and safety assessments of rock engineering projects. However, due to the complexity in the mathematical representation of the fracture surface geometry and its effects on the stress-flow behaviour of the fractures, and the limitations in the test conditions in laboratories, significant lack of knowledge still exists in testing and modelling approaches regarding rock fractures. Based on a general review of the roughness characterization and shear-flow testing of rock fractures, this paper presents the definition of the stationarity threshold of roughness, and a combined experimental-numerical approach for simulating rock fracture testing conditions for more general fluid flow behaviour of the rock fractures. The conclusions are that fracture roughness characterization must be conducted and represented in three-dimensions and the more general fluid flow behaviour cannot be observed with conventional parallel shear-flow tests or compressionradial flow tests. Numerical simulations are needed to reveal more general behaviour of stress-flow processes of rock fractures with boundary and loading conditions that are difficult or impractical in laboratory tests.
The purpose of this CivilZone review paper is to present the techniques, advances, problems and likely future development directions in numerical modelling for rock mechanics and rock engineering. Such modelling is essential for Studying the fundamental processes occurring in rock,, for assessing the anticipated and actual performance of structures built on and in rock masses, and C hence for Supporting rock engineering design. We begin by providing the rock engineering design backdrop to the review in Section 1. The states-of-the-art of different types of numerical methods are outlined in Section 2, with focus on representations of fractures in the rock mass. In Section 3, the numerical methods for incorporating couplings between the thermal, hydraulic and mechanical processes are described. In Section 4, inverse solution techniques are summarized. Finally, in Section 5, we list the issues of special difficulty and importance in the subject. In the reference Est, 'significant' references are asterisked and 'very significant' references are doubly asterisked.
It is widely recognized that the mechanical parameters for unfilled and rough rock joints, such as the peak shear strength, can vary with scale. However, due to contradictory results concerning the extent and nature of the scale effect reported in the literature, it is still a debated subject. A conceptual model developed by Johansson and Stille 2014 suggests how roughness and matedness at different scales influences the peak shear strength for fresh, rough and unweathered joint. However, the model's ability to predict how the roughness and matedness affects the peak shear strength at different scales was not verified. The aim of this paper is to investigate the ability of the conceptual model to estimate the peak shear strength at different degrees of matedness and scales. A series of direct shear test were carried out at two different scales and two different degrees of matedness. The peak shear strength from the tests was compared to the peak shear strength calculated with the conceptual model. The results showed that the model can predict the peak shear strength for both the perfectly mated and the unmated joints. No scale effect was observed in the shear tests, which is in line with the predictions using the model. The influence of matedness in combination with scale might explain some of the contradictory findings regarding the scale effect.
Several criteria have been proposed over the years in order to predict the peak shear strength of rock joints.The most widely used criterion is the JRC-JCS criterion by Barton. It says that changes in the peak shear strength originate from surface roughness, joint wall compressive strength and normal stress. A limitation with this criterion is that the contribution from roughness could be overestimated for natural and mismatched joints if the joint roughness coefficient, JRC, is estimated based on the direct profiling method. To account for this effect, Zhao introduced the joint matching coefficient, JMC, which accounts for the matedness of the joint. In addition to this, it is known that the scale of the sheared joint could affect the peak shear strength. However, no criterion exists that describes how roughness, matedness and scale interact. In this paper, a conceptual model is proposed. The model is based on adhesion and fractal theory, measurements of surface roughness and the anticipated variation of the number and size of the contact points. The model proposes how the compressive strength and the roughness of the joint surface together with the matedness of the joint interact in order to form the shear strength of the joint under constant normal load conditions. The model also suggests an explanation for the scale effect of rock joints with respect to the surface roughness.
The study on fluid flow and transport processes of rock fractures in most practical applications involves two fundamental issues: the validity of Reynolds equation for fluid flow (as most often assumed) and the effects of shear displacements on the magnitudes and anisotropy of the fluid flow velocity field. The reason for such concerns is that the impact of the surface roughness of rock fractures is still an unresolved challenging issue. The later has been systematically investigated with results showing that shear displacement plays a dominant role on evolutions of fluid velocity fields, for both magnitudes and anisotropy, but the former has not received examinations in details due to the numerical complexities involving solution of the Navier-Stokes (NS) equations and the representations of fracture geometry during shear. The objective of this paper aims to solve this problem through a FEM modeling effort. Applying the COMSOL Multiphysics code (FEM) and assuming a 2D problem, we consider the coupled hydromechanical effect of fracture geometry change due to shear on fluid flow (velocity patterns) and particle transport (streamline/velocity dispersion), using measured topographical data of natural rock fracture surfaces. The fluid flow in the vertical 2D cross-sections of single rock fractures was simulated by solving both the Navier-Stokes and the Reynolds equation, and the particle transport was predicted by the streamline particle tracking method with calculated flow velocity fields (vectors) from the flow simulations, obtaining results such as flow velocity profiles, total flow rates, particle travel time, breakthrough curves and the Peclet number, Pe, respectively. The results obtained using NS and Reynolds equations were compared to illustrate the degree of the validity of the Reynolds equation for general applications in practice since the later is mush more computationally efficient for solving large-scale problems. The flow simulation results show that both the total flow rate and the flow velocity fields in a rough rock fracture predicted by the NS equation were quite different from those predicted by the Reynolds equation. The results show that a roughly 5-10% overestimation on the flow rate is produced when the Reynolds equation is used, and the ideal parabolic velocity profiles defined by the local cubic law, when Reynolds equation is used, is no longer valid, especially when the roughness feature of the fracture surfaces changes with shear. These deviations of flow rate and flow velocity profiles across the fracture aperture have a significant impact on the particle transport behavior and the associated properties, such as the travel time and Peclet number. The deviations increase with increasing flow velocity and become more significant when fracture aperture geometry changes with shear.
The effects of rotary shear displacements on fluid flow rates and patterns under shear-flow test conditions were numerically investigated in this paper. A pair of digitized surfaces of a concrete fracture replica of size 250 x 250mm was numerically manipulated to simulate the translational and rotary shearing processes of the sample, which provided the evolution of the aperture distributions during shearing and was used to determine the evolution of the fracture transmissivity field. The translational shear test has bidirectional (x and y) hydraulic head boundary conditions and shearing in the x-direction with 1mm shear displacement interval up to 20mm. The rotary shear test has a 0.5° rotation interval up to 90°. The results of flow simulations show that with increasing rotary shear, the flow rate increases but its pattern becomes rapidly isotropic. For bi-directional translational flow, the flow rate increases with shear but significant channelling, anisotropy and heterogeneity developed with shear displacement. The above flow simulations illustrated the more realistic flow patterns under general fracture deformation modes of translation and rotation, and provided insights for the design of more flexible and complementary laboratory coupled stressflow tests.
Fluid flow anisotropy in a single rock fracture during a shear process is an important issue in rock mechanics and is investigated in this paper using FEM modelling, considering evolutions of aperture and transmissivity with shear displacement history. The distributions of fracture aperture during shearing with large shear displacements were obtained by numerically manipulating relative translational movements between two digitalized surfaces of a rock fracture replica, with changing sample sizes. The scale dependence of the fluid behaviour and properties were also investigated using a fractal approach. The results show that the fracture aperture increases anisotropically during shear with a more pronounced increase in the direction perpendicular to the shear displacement, causing significant fluid flow channelling effect, as also observed by other researchers. This finding may have important impacts on the interpretation of the results of coupled hydro-mechanical experiments for measurements of hydraulic properties of rock fractures because the hydraulic properties are usually calculated from flow test results along the shear directions while ignoring the more significant anisotropic flow perpendicular to the shear direction. This finding indicates that the coupled stress-flow tests of rough rock fractures should be conducted in true three-dimensions if possible. Significant change in fracture aperture/ transmissivity in the out-of-plane direction should be properly evaluated if two-dimensional tests are conducted. Results obtained from numerical simulations also show that fluid flow through a single rough fracture changes with increasing sample size and shear displacements, indicating that representative hydro-mechanical properties of the fractures in the field can only be more reliably determined using samples of large enough sizes beyond the stationarity threshold and tested with larger shear displacements.
Fluid flow and tracer transport in a single rock fracture during shear is investigated using the finite element method (FEM) and streamline particle tracking, considering evolutions of aperture and transmissivity with shear displacement histories under different normal stresses, based on laboratory tests. The distributions of fracture aperture and its evolution during shear were calculated from the initial aperture fields, based on the laser-scanned surface roughness of feature replicas of rock fracture specimens, and shear dilations measured during the coupled shear-flow tests in laboratory. The coupled shear-flow tests were performed under two levels of constant normal loading (CNL). A special algorithm for treating the contact areas as zero-aperture elements was used to produce more accurate flow field simulations using FEM. The simulation results agreed well with the flow rate data obtained from the laboratory tests, showing complex histories of fracture aperture and tortuous flow channels with changing normal stresses and increasing shear displacements for the flow parallel with the shear direction. A greater increase was observed for flow in the direction perpendicular to the shear direction, due to the significant flow channels created by the shearing process. From the obtained flow velocity fields, particle transport was predicted using a streamline particle tracking method with the flow velocity fields (vectors) taken from the flow simulations, yielding particle travel times, breakthrough curves, and the Peclet number, Pe. The transport behavior in the fracture is also anisotropic, and advective transport is greater in the direction parallel with the shear direction. The effect of normal stress on the particle transport is significant, and dispersion becomes larger with increasing normal stress.
In recent years, geological disposal of radioactive wastes is considered to be the most promising option, which requires the understanding of the coupled mechanical, hydraulic and thermal properties of the host rock masses and rock fractures. The hydro-mechanical behavior and properties of rock fractures are usually determined by laboratory experiments on fracture specimens that serve as the basic building block of the constitutive models of fractured rock masses. Laboratory testing of rock fractures involve a number of technical issues that may have significant impacts on the reliability and applicability of the testing results, chief among them are the quantitative estimation of the evolutions of hydraulic transmissivity fields of fractures during shear under different normal constraint conditions, and the sealing techniques when fluid flow during shear is involved. In this study, a new shear-flow testing apparatus with specially designed fluid sealing techniques for rock fractures were developed, under constant normal load (CNL) or constant normal stiffness (CNS) constraint. The topographical data of all fracture specimens were measured before testing to constitute the geometrical models for simulating the change of mechanical aperture distributions during shearing. A number of shear-flow coupling tests were carried out on three kinds of rock fracture specimens to evaluate the influence of morphological properties of rock fractures on their hydro-mechanical behaviour. Some empirical relations were proposed to evaluate the effects of contact area and surface roughness on the behavior of fluid flow through rock fractures.
The influences of surface roughness and shear processes on fluid flow and solute transport through three-dimensional (3D) crossed rock fractures, a vital element of fracture networks, were systematically investigated. Surfaces of tensile fractures created by splitting granite and sandstone samples along its two orthogonal central axes were optically scanned to generate rough-walled crossed fracture models. Shearing processes on the models were realized by assigning experimentally measured normal and shear displacements to one fracture while fixing the other. Fluid flow and solute transport through the models were numerically simulated taking into account different combinations of inlets and outlets, in which distilled water and solution are injected into the two inlets, respectively. The results show that compared to the parallel-plate model, the rough-walled crossed fracture model exhibits obvious flow channelization and fluid redistribution at the intersection, significantly promoting the mixing. The shear process affects the mixing at the intersection as it induces dilation and geometric change of the intersection. Increasing shear displacement can either enhance or reduce the mixing depending on combinations of the inlets and outlets, and the mixing ratio is controlled by the aperture difference between two outlet branches and the surface roughness. Effects of surface roughness, shear displacement and shear-induced dilation on the mixing ratio are quantified, upscaling of which can be potentially useful for field-scale characterization of solute transport in fractured systems.
This study focuses on rock damage potentially developing in the near-field of a planned underground nuclear waste repository at the Forsmark site (Sweden). In hard, crystalline rocks, mechanical damage in the form of spalling may be induced during construction by overstressing of the excavation periphery. During operation, thermal damage may develop due to additional thermo-elastic stresses forming in response to the increasing rock temperatures induced by the heat-emitting spent nuclear fuel. Prediction of damage occurrence, location, and extent is critical for an effective repository design and long-term safety assessment as it may negatively affect the long-term isolation properties of the host rock. In this paper, the response of underground structures was studied using a novel 3D coupled thermo-mechanical simulator based on the finite-discrete element method (FDEM). It is the first numerical study to date that explicitly captures both mechanical and thermal fracturing processes while using the latest repository design and site-specific geomechanical input data. A sensitivity study is performed to investigate different combinations of rock mechanical properties, in-situ stresses, and deposition tunnel geometry on the host rock behaviour. Rock mass deconfinement is shown to promote the development of tensile damage in the tunnel sidewalls and floor with fracture surfaces growing parallel to the excavation boundaries. The negative effects deriving from the adoption of a relatively narrower tunnel cross-section and from an increase of horizontal in-situ stresses are highlighted. Thermo-mechanical analyses capture the rock mass behaviour following an increase of borehole surface temperature to 100 °C. Numerical results indicate that the temperature evolution is affected by the shape of the underground cavities and their distance from the heated boreholes. The coupled thermal expansion of the rock induces additional stresses which, in turn, promotes further damage. Despite this increase, however, the total amount of induced rock damage at final conditions remains relatively low.
An evaluation of the importance of the thermo-hydro-mechanical couplings (THM) on the performance assessment of a deep underground radioactive waste repository has been made as a part of the international DECOVALEX III project. It is a numerical study that simulates a generic repository configuration in the near field in a continuous and homogeneous hard rock. A periodic repository configuration comprises a single vertical borehole, containing a canister surrounded by an over-pack and a bentonite layer, and the backfilled upper portion of the gallery. The thermo-hydro-mechanical evolution of the whole configuration is simulated over a period of 100 years. The importance of the rock mass's intrinsic permeability has been investigated through scoping calculations with three values: 10(-17), 10(-18) and 10(-19) m(2). Comparison of the results predicted by fully coupled THM analysis as well as partially coupled TH, TM and HM analyses, in terms of several predefined indicators of importance for performance assessment, enables us to identify the effects of the different combinations of couplings, which play a crucial role with respect to safety issues. The results demonstrate that temperature is hardly affected by the couplings. In contrast, the influence of the couplings on the mechanical stresses is considerable.
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.
A numerical investigation is conducted on the impacts of the thermal loading history on the evolution of mechanical response and permeability field of a fractured rock mass containing a hypothetical nuclear waste repository. The geological data are extracted from the site investigation results at Sellafield, England. A combined methodology of discrete and continuum approaches is presented. The results of a series of simulations based on the DFN-DEM (discrete fracture network-distinct element method) approach provide the mechanical and hydraulic properties of fractured rock masses, and their stress-dependencies. These properties are calculated on a representative scale that depends on fracture network characteristics and constitutive models of intact rock and fractures. In the present study, data indicate that the large scale domain can be divided into four regions with different property sets corresponding to the depth. The results derived by the DFN-DEM approach are then passed on to a large-scale analysis of the far-field problem for the equivalent continuum analysis. The large-scale far-field analysis is conducted using a FEM code, ROCMAS for coupled thermo-mechanical process. The results show that the thermal stresses of fractured rock masses vary significantly with mechanical properties determined at the representative scale. Vertical heaving and horizontal tensile displacement are observed above the repository. Observed stress and displacement fields also shows significant dependency on how the mechanical properties are characterized. The permeability changes induced by the thermal loading show that it generally decreases close to the repository. However, change of permeability is small, i.e., a factor of two, and thermally induced dilation of fracture was not observed. Note that the repository excavation effects were not considered in the study. The work presented in this paper is the result of efforts on a benchmark test (BMT2) within the international co-operative projects DECOVALEX III and BENCHPAR.
A thermo-hydro-mechanical experiment was conducted in a fractured granitic ruck mass at the Kamaishi Mine in Japan. The experiment consists of the excavation of a cylindrical test pit on the floor of an experimental drift. The test pit was then lilted with bentonite with an embedded heater. During the excavation of the test pit, the hydromechanical response of the surrounding rock was monitored. This paper presents the efforts of four research teams to numerically simulate the hydro-mechanical response of the rock mass during excavation. While the total inflow rate to the test pit, the flow distribution on the pit walls and the displacements in the rock mass away From the pit could be reasonably predicted, the pore pressure in individual boreholes, and the expansion behaviour of the pit were less successfully simulated. The reasons for these discrepancies are discussed in the paper.
We investigate the ultrasonic transport properties of such an idealised fracture whose 100 µm aperture is about 0.02 the wavelength, and filled with various fluids flowing under external forcing. As the artificial fracture is made of two solid and parallel walls separated by a thin fluid layer, we use the thin fluid layer concept to study the compressional (P-) wavefield transmitted across and reflected off the fracture, with no mode-conversion considered. We demonstrate that air and various fluids (water, grouts of varied w/c – water to cement ratio) can be distinguished when injected into the fracture, both at atmospheric pressure or under over-pressure as done in real grouting cases in the field. Then, using an analytical solution, we verify our experimental data and predict the results that can be obtained with a different fracture aperture. Our results illustrate that replicating such ultrasonic measurements both in space and time would allow successfully monitoring the grout propagation within an artificial fracture.
This paper presents the general governing equations for coupled thermohydromechanical (THM) processes in saturated and unsaturated geologic formations and reviews four finite element codes fur modeling of such system. Three of the codes are developed for the special purpose of analyzing coupled THM processes in unsaturated porous and fractured geological media, and the fourth is a commercial code that has been used in its standard version, with a few adaptations for this specialized problem. The basic assumptions and fundamental equations for coupled THM processes in unsaturated porous fractured rock are presented. and formulations of the four finite element models are compared.
Four computer codes were applied for a prediction of coupled thermo-hydro-mechanical responses during an in situ heater experiment which simulates a nuclear waste deposition hole with a waste over-pack and bentonite buffer, surrounded by fractured rock. The elevated temperature in the heater surroundings, which was maintained at 100 C for 8.5 months, generated substantial heat-driven moisture flow and swelling in the clay buffer, and thermal expansion of the surrounding fractured rock. Predicted system responses - including temperature. moisture content, fluid pressure, stress and displacement - were compared to measurements at 70 sensors located both in the clay buffer and the near-field rock. An overall good agreement between modeling and measured results indicates that most thermo-hydro-mechanical responses are fairly well represented by the coupled numerical models. Uncertainties occur for modeling of hydromechanical behavior of the swelling clay buffer at low saturation, modeling of near-field heterogeneous mechanical behavior of the low-stressed fractured reek, and modeling of the rock-buffer interface.
As a part of the international DECOVALEX III project, and the European BENCHPAR project, the impact of thermal-hydrological-mechanical (THM) couplings on the performance of a bentonite-back-filled nuclear waste repository in near-field crystalline rocks is evaluated in a Bench-Mark Test problem (BMT1) and the results are presented in a series of three companion papers in this issue. This is the third paper with focuses on the effects of THM processes at a repository located in a sparsely fractured rock. Several independent coupled THM analyses presented in this paper show that THM couplings have the most significant impact on the mechanical stress evolution, which is important for repository design, construction and post-closure monitoring considerations. The results show that the stress evolution in the bentonite-back-filled excavations and the surrounding rock depends on the post-closure evolution of both fields of temperature and fluid pressure. It is further shown that the time required to full resaturation may play an important role for the mechanical integrity of the repository drifts. In this sense, the presence of hydraulically conducting fractures in the near-field rock might actually improve the mechanical performance of the repository. Hydraulically conducting fractures in the near-field rocks enhances the water supply to the buffers/back-fills, which promotes a more timely process of resaturation and development of swelling pressures in the back-fill, thus provides timely confining stress and support to the rock walls. In one particular case simulated in this study, it was shown that failure in the drift walls could be prevented if the compressive stresses in back-fill were fully developed within 50 yr, which is when thermally induced rock strain begins to create high differential (failure-prone) stresses in the near-field rocks. Published by Elsevier Ltd.