مرتضی جوادی اصطهباناتی

This paper investigates the effect of the method of applying pre-support in the numerical modeling of tunnel and ground interaction. Two main numerical approaches of linear pile and equivalent zone elements were considered for the modeling of pre-support in front of the advancing tunnel face. Both of these approaches were applied for one of the Tehran-Shomal Freeway as the case study of numerical modeling. The results of numerical models were compared to investigate the effect of pre-support modeling approaches. The vertical deformation of numerical models with different approaches shows a meaningful consistency; therefore, it is concluded that both of these methods of linear pile element and equivalent zone element can be applied to numerical modeling demands for other studies.

Rock mass consists of intact rocks and discontinuities such as fractures, which have a significant impact on the mechanical and hydraulic properties of the rock mass. For example, in sensitive analyzes such as tunnel stability simulation. Therefore, it is very important to determine the exact parameters of stone jointing, such as orientation and length. Using Discrete Fracture Network is one of the common methods to simulate jointed rock. Since the construction of the fracture network is done using statistical distribution functions, the uncertainty in the construction of the fracture network has always been one of the great challenges of engineers. In this study, the fracture network of of Emamzadeh Hashem tunnel was constructed by a code developed in MATLAB and 3DEC software, and the influence of statistical distribution functions on the uncertainty in the construction of the fracture network was investigated. The results indicate that a negative exponential distribution can lead to relatively large errors in constructing the fracture network, especially when used to generate the fracture dip direction.. Also, the results of the parametric study showed that the use of statistical distribution functions that have the variance of the data in their PDF (Probability Distribution Function) can increase the accuracy in the production of fracture parameters such as slope, slope direction and effect length, and To reduce the uncertainty in the production of the fracture network.

The stratified-sedimentary rock mass, as the typical host ground of coal mine tunnels, is characterized by highly non-isotropic deformation due to the very persistent discontinuity of bedding planes. This study evaluates the effect of tunnel location relative to the host ground strata on the excavation-induced displacements around a coal mine tunnel driven along the inclined coal seam. To achieve this goal, a calibrated finite element method (FEM) numerical model based on field monitoring displacements was developed for the coal mine tunnel at a depth of 300 m. This calibrated numerical model was then utilized to investigate the effect of the horizontal location of the tunnel on the induced displacement field through sensitivity analysis. Finally, the sensitivity analysis results were compared in terms of displacement components around the tunnel. The results of this study demonstrate a reasonable level of accuracy (for practical demands) of the calibrated numerical model, with an average error of about 8% for maximum displacements at measured points. The numerical models show an asymmetric spatial distribution of displacements around the tunnel due to the anisotropy of the rock mass, especially in the case of inclined layers. The arrangement of weak-strength coal and intercalary stone layers relative to the excavation line of the tunnel plays a key role in this issue. The critical state of displacements (maximum displacement in sensitivity analysis) occurs where the intersection line of the coal-intercalary stone is tangent to the tunnel excavation line. Additionally, the excavation-induced displacement decreases as the distance between the coal-intercalary stone interface and the tunnel increases, with a distance of about 1.5 m suggested for practical applications.

In this paper, the determination of equivalent elastic properties of fractured rock masses has been studied using discontinuous numerical method. For this purpose, the discontinuous media of the jointed rock mass with different jointing patterns (including one horizontal joint set, one vertical joint set, two perpendicular horizontal and vertical joint sets, and two non-orthogonal joint sets) were modeled in UDEC software and the induced strain were calculated. Then, the elastic properties of rock mass were calculated by inserting strains obtained from numerical methods into compliance matrixes. In order to verify this procedure, the results of back calculated elastic properties of rock mass from numerical models were compared with those obtained from analytical solutions. Finally, the method of back calculated elastic properties of rock mass from numerical models was applied for confining stress boundary condition (the case without analytical solutions) under different rotation angle of discontinuities and scales. The results of this study show that there is a good consistency between the back calculated elastic properties of rock mass from numerical models and analytical solution; where the relative error is about 4% to 6% for most of the cases. This consistency indicates the accuracy of back calculated elastic properties of rock mass from numerical models and this method can be applied for other cases especially those without analytical solution. Application of this method for rock mass under confining stress (the case without analytical solution) indicates that the elastic properties highly depend to rotation angle.

In this paper, the role of effective factors on the instability of tunnels and underground excavations was explored through statistical analysis. To reach this goal, the effective factors (including 25 different factors) on the tunnel instability were recognized based on the deep literature survey and expert judgment. Then, a database of previous tunnel instabilities was established based on the type of tunnels and the main factor of instabilities. The effective factors were classified into six main groups and utilized for statistical analysis based on the relative frequency of tunnel instability. The results of this paper show that the geomechanical factors, design-investigation issues, and geological-geographic conditions of the site are the main three reasons for tunnel instability, where these main factors control more than 70% of civil-utility tunnels through all case studies. In addition, the design-investigation issues and geological-geographic conditions show the lowest and highest dependency on the tunnel utility, respectively. The “weak zones”, “inadequate redesign during construction”, and “the groundwater level and conditions” are the main three effective factors in tunnel instability, where the relative frequency of instability due to these factors reaches up to 40% for most of the case studies. Based on the main effective factors of instability, the freeway and highway tunnels show the highest consistency with all other utilities for tunnels in the statistical population. Therefore, freeway and highway tunnels can be considered as the most representative of overall utilities. The outcome of this paper can be applied to risk assessment of tunnel instabilities and technical management.

One of the most important aspects of governing physical processes through rough-walled fractures is the non-linear behavior of flow. The onset of non-linear flow in rock fractures is characterized by critical Reynolds number, which is the main object of this paper. In this paper, the technical aspects of non-linear flow of crude oil through open rock fractures and critical Reynolds number were studied. These issues were studied based on the results of three-dimensional numerical simulation of the Navier-Stokes equations for crude oil flow through rough-walled fractures. The finite volume simulation of crude oil flow through three-dimensional space of rough-walled fractures was performed for a wide range of Reynolds numbers or flow rates. The results of crude oil flow simulations were analyzed based on the Forchheimer’s law. The coefficients of energy losses due to viscous and inertial dissipation mechanisms were derived from the Forchheimer’s law regression on the results. Then, the role of linear and nonlinear energy losses with viscous and inertial dissipation mechanisms was evaluated based on the relation between Reynolds and Forchheimer non-dimension numbers. Finally, the critical Reynolds number was determined for onset of non-linear flow through rough-walled fractures. The results of this study indicate that the Forchheimer’s law appropriately describes the non-linear crude oil flow through rough-walled fractures. By increasing the Reynolds number (or flow rate), the ratio of viscous energy lose from total energy losses decreases non-linearly and simultaneously, the inertial dissipation becomes the dominant mechanism of energy lose. The critical Reynolds number for crude oil is in the range of 30 to 46 for the open fractures of this study. The maximum and minimum of critical Reynolds number follow the minimum and maximum of inertial dissipation coefficient and also the gradient of Reynolds- Forchheimer curve, respectively.

Summary:

This paper reflects the role of different constitutive models on the deformations induced by tunneling in the urban area. These constitutive models were applied in finite element analysis of tunnel-induced subsidence for the case study of the Amirkabir Tunnel in Tehran. The results of this paper indicate that the numerical simulation of tunneling induced settlement with hardening soil small strain stiffness model is much more accurate than other constitutive models. 

Accurate prediction of tunneling induced settlement is one of the most important challenges encountered in urban underground projects. Generally, such predictions are usually obtained by the application of numerical simulation, where the accuracy of the results depends on several factors. The constitutive models play an indicative role in the accuracy of numerical simulation of tunneling induced settlement. This issue was studied by comparing the effect of different constitutive models on the development of ground deformations around the tunnel and the tunneling induced settlement for a case study.     

Methodology and Approaches:

Finite element analysis of tunneling induced deformations using PLAXIS software was performed for three different elastoplastic constitutive models including Mohr-Coulomb, hardening soil, and small strain hardening. The input data of numerical simulation were captured from different in-suite and laboratory tests on the host ground of the Amirkabir tunnel as a case study. Tunnel construction was modeled based on the as-built condition of the excavation stages of the T4 section of the Amirkabir tunnel. Finally, numerical results were compared and verified with monitoring results and field measurements.

Results showed that the Mohr-Coulomb model provides a lower prediction of vertical displacements comparing to two other implemented models. Furthermore, the Mohr-Coulomb model shows an unrealistic uplift of the tunnel floor after all of the excavation stages. Results illustrated that using hardening soil models, with sophisticated features including non-linearity pre-failure and high stiffness under small strain, considerably improves the prediction of displacements. It is observed that using hardening soil small strain stiffness model, the accuracy of predictions increased noticeably compared to the field measurements. A full comparison between the results from Mohr-Coulomb and Hardening Soil cases yields some important differences, which are presented in this paper.

Selecting the appropriate model size is a challenging issue in the numerical modelling of groundwater inflow into underground excavation. This issue was studied in this paper by presenting a methodology for selecting appropriate domain size for numerical modeling of groundwater inflow into tunnel that is excavated inside of semi-infinite aquifer. To reach this goal, first, a dimensionless factor, so-called normalized rate of inflow variation (NRIV), was defined in cooperation with its limit value, so-called acceptable level of variation (ALV). Then, the appropriate or suitable domain size (SDS) of numerical model was determined based on the NRIV and ALV. The applicability of suggested methodology was evaluated for the results of wide range geometrical parameter of tunnel (including different tunnel radiuses and depths) and different flow domain sizes. The results of this study indicate that the required domain size for numerical modelling of groundwater inflow into tunnel increase nonlinearly for larger and deeper tunnels. Moreover, the required domain size increases to 1.8 times by decreasing the level of ALV from 0.0005 to 0.0001, where the relative accuracy of results has only increased up to 4%. Since the larger domain size requires much computational difficulties and insignificant accuracy, the ALV in the level of 0.0005 is suggested for practical numerical modelling of groundwater inflow into tunnels.

One of the most important aspects of governing physical processes through rough-walled fractures is the non-linear behavior of flow. The main aim of this paper is to investigate the effect of non-linear flow on the hydraulic parameters and deviation from Darcy’s law. To reach this goal, the three-dimensional simulation of crude oil flow inside rough-walled fractures was performed by numerical solving the Navier-Stokes equations supplemented by the continuity equation through application of finite volume technique. The crude oil flow through three-dimensional space of rough-walled fractures was numerically simulated for a wide range of inlet velocity of flow rates. Then, the regime of flow, the deviation of crude oil flow through rough-walled open fractures from Darcy’s law, nonlinear relationship between hydraulic gradient and flow rate, and the effect of non-linear flow on the hydraulic aperture and permeability of fractures were investigated by analysis of crude oil flow simulation. The results of this study indicate that the crude oil flow through rough-walled fractures is non-linear; therefore the hydraulic parameters such as hydraulic aperture and permeability are not constant and highly depend on the flow rate of crude oil. In fact, hydraulic aperture and permeability of fractures decrease non-linearly by increment of flow rate, where these parameters show 10% and 20% of relative decrement, respectively. In addition, the results of regression analysis show that the Forchheimer’s law appropriately describes the behavior of crude oil flow through rough-walled fractures than Darcy’s law. Moreover, the accuracy of Forchheimer’s law is much more than 98%, but the relative error of Darcy’s law reaches to 27%.

In this study, modeling of groundwater inflow into underground excavations was studied based on the stochastic continuum theory. To reach this goal, the two dimensional FNETF computational code was modified based on the stochastic continuum theory and for demand of modeling of groundwater inflow into underground excavations. The accuracy of computations in this code was evaluated from the validation point of view. All geological formations show random variation (or spatial nonuniformity) in the values of the hydrogeological parameters that lead to a considerable amount of uncertainty hydrogeological models. Therefore, it is becoming essential to be able to characterize the uncertainty of groundwater processes that can be achieved through implementation of continuum theory with stochastic hydrogeology. This method can be used to estimate the most likely range of groundwater inflow into underground excavations and assess the uncertainty of estimates.
Methodology and Approaches
In this paper, the FNETF computational code was modified based on the stochastic continuum theory and then the accuracy of computations in this code was evaluated from the validation point of view. The results of numerical (by performing phase2 software) and analytical solutions for hydraulic head distribution around the circular tunnel and also the groundwater inflow rates were used to validate the accuracy of FNETF computational code. Then, the role of hydraulic properties of rock mass was investigated through parameter study. The results of this study for modification and validation of FNETF computational code show that the outputs of this code for ideal media (with near zero standard deviation of hydraulic conductivity) in terms of both hydraulic head distribution around the tunnel and the groundwater inflow rates are appropriately matched with those obtained from ideal analytical and numerical solutions. Therefore, this computational code can be successfully applied for modeling groundwater inflow into underground excavations by the application of stochastic continuum theory. The results of parameter study and sensitivity analysis also show that the maximum, minimum, and average values of groundwater inflow into tunnel decreases by increasing the standard deviation of rock mass hydraulic conductivity. Therefore, for very heterogeneous rock masses, both the analytical solution and deterministic numerical methods will overestimate (i.e. with one or more order of magnitudes) the groundwater inflow into tunnel in comparison with stochastic continuum method.

This paper investigates the crude oil flow through open and rough-walled fractures. The aim of this paper is to evaluate the effects of surface roughness and spatial arrangement of aperture segment on fluid flow phenomenon through rough-walled fractures. In addition, the validity of classic geometrical equations of cubic law correction was explored by comparing the output results of numerical simulations (in terms of permeability). To reach this goal, the crude oil flow through three-dimensional rough-walled fractures was numerically simulated by simultaneous solving of Navier-Stokes and mass conservation equations and utilizing FLUENTTM computational software. The numerical crude oil flow simulation was performed for six different three-dimensional geometrical models of fractures whit different roughness and aperture arrangements and constant porosity. The results of fluid flow simulation were analyzed with different points of view and then compared with the classic geometrical equations of cubic law correction. The results of this study show that (i) for the open fractures, the effects of roughness on the pressure lose is higher than spatial arrangement of aperture segment, (ii) due to the nonlinearity of flow, the permeability of fractures decreases by increasing the Reynolds number, and (iii) with the classic geometrical equations of cubic law correction encounter with about 5 to 35% error and the accuracy of these equations will be decrease by decrease the permeability of fractures or increase of roughness and spatial variability of aperture. These findings prove useful in proper understanding of crude oil flow in fractures, or inclusions in computational simulation of large-scale flow in fractured petroleum reservoirs.

T‌h‌i‌s p‌a‌p‌e‌r p‌r‌e‌s‌e‌n‌t‌s t‌h‌e f‌u‌n‌d‌a‌m‌e‌n‌t‌a‌l‌s o‌f g‌r‌o‌u‌n‌d‌w‌a‌t‌e‌r m‌o‌d‌e‌l‌i‌n‌g i‌n f‌r‌a‌c‌t‌u‌r‌e‌d m‌e‌d‌i‌a a‌n‌d a‌l‌s‌o t‌h‌e t‌e‌c‌h‌n‌i‌c‌a‌l d‌e‌t‌a‌i‌l‌s o‌f a d‌e‌s‌i‌r‌a‌b‌l‌e m‌o‌d‌e‌l‌i‌n‌g m‌e‌t‌h‌o‌d i‌n d‌i‌s‌c‌o‌n‌t‌i‌n‌u‌o‌u‌s r‌o‌c‌k‌s. I‌n t‌h‌i‌s p‌a‌p‌e‌r, t‌h‌e m‌o‌d‌e‌l‌i‌n‌g o‌f f‌l‌u‌i‌d f‌l‌o‌w i‌n r‌o‌c‌k m‌a‌s‌s i‌s s‌t‌u‌d‌i‌e‌d u‌s‌i‌n‌g t‌h‌e d‌i‌s‌t‌i‌n‌c‌t f‌r‌a‌c‌t‌u‌r‌e n‌e‌t‌w‌o‌r‌k (D‌F‌N) c‌o‌n‌c‌e‌p‌t. A n‌e‌w c‌o‌m‌p‌u‌t‌a‌t‌i‌o‌n‌a‌l c‌o‌d‌e, ``F‌N‌E‌T‌F'', h‌a‌s b‌e‌e‌n d‌e‌v‌e‌l‌o‌p‌e‌d f‌o‌r g‌e‌n‌e‌r‌a‌t‌i‌n‌g D‌F‌N a‌n‌d f‌l‌u‌i‌d f‌l‌o‌w a‌n‌a‌l‌y‌s‌i‌s. T‌h‌e F‌N‌E‌T‌F c‌o‌m‌p‌u‌t‌a‌t‌i‌o‌n‌a‌l c‌o‌d‌e u‌s‌e‌s a M‌o‌n‌t‌e C‌a‌r‌l‌o a‌p‌p‌r‌o‌a‌c‌h t‌o g‌e‌n‌e‌r‌a‌t‌e t‌w‌o-d‌i‌m‌e‌n‌s‌i‌o‌n‌a‌l d‌i‌s‌c‌r‌e‌t‌e f‌r‌a‌c‌t‌u‌r‌e n‌e‌t‌w‌o‌r‌k‌s, b‌a‌s‌e‌d o‌n t‌h‌e s‌t‌a‌t‌i‌s‌t‌i‌c‌s o‌f t‌h‌e g‌e‌o‌m‌e‌t‌r‌i‌c‌a‌l c‌h‌a‌r‌a‌c‌t‌e‌r‌i‌s‌t‌i‌c‌s o‌f t‌h‌e f‌r‌a‌c‌t‌u‌r‌e, i‌n t‌e‌r‌m‌s o‌f l‌o‌c‌a‌t‌i‌o‌n i‌n t‌h‌e g‌e‌n‌e‌r‌a‌t‌e‌d r‌e‌g‌i‌o‌n, o‌r‌i‌e‌n‌t‌a‌t‌i‌o‌n w‌i‌t‌h r‌e‌s‌p‌e‌c‌t t‌o t‌h‌e c‌o‌o‌r‌d‌i‌n‌a‌t‌e a‌x‌e‌s, l‌e‌n‌g‌t‌h, a‌n‌d a‌p‌e‌r‌t‌u‌r‌e. I‌n t‌h‌i‌s c‌a‌s‌e, i‌n‌d‌i‌v‌i‌d‌u‌a‌l r‌e‌a‌l‌i‌z‌a‌t‌i‌o‌n‌s o‌f h‌y‌d‌r‌a‌u‌l‌i‌c a‌t‌t‌r‌i‌b‌u‌t‌e d‌i‌s‌t‌r‌i‌b‌u‌t‌i‌o‌n, w‌h‌i‌c‌h a‌r‌e f‌o‌r‌m‌e‌d b‌y d‌i‌s‌c‌r‌e‌t‌e f‌r‌a‌c‌t‌u‌r‌e‌s, ‌r‌e ‌e‌n‌e‌r‌a‌t‌e‌d f‌r‌o‌m a s‌e‌t o‌f p‌r‌o‌b‌a‌b‌i‌l‌i‌t‌y d‌i‌s‌t‌r‌i‌b‌u‌t‌i‌o‌n‌s d‌e‌s‌c‌r‌i‌b‌i‌n‌g t‌h‌e g‌e‌o‌m‌e‌t‌r‌y o‌f t‌h‌e f‌r‌a‌c‌t‌u‌r‌e‌s. B‌e‌c‌a‌u‌s‌e t‌h‌e g‌e‌n‌e‌r‌a‌t‌e‌d f‌r‌a‌c‌t‌u‌r‌e‌s a‌r‌e f‌i‌n‌i‌t‌e, a r‌e‌l‌a‌t‌i‌v‌e‌l‌y l‌a‌r‌g‌e n‌u‌m‌b‌e‌r o‌f f‌r‌a‌c‌t‌u‌r‌e‌s i‌n t‌h‌e n‌e‌t‌w‌o‌r‌k m‌a‌y n‌o‌t b‌e p‌e‌r‌f‌e‌c‌t‌l‌y c‌o‌n‌n‌e‌c‌t‌e‌d a‌n‌d s‌o‌m‌e d‌o n‌o‌t ‌o‌n‌t‌r‌i‌b‌u‌t‌e t‌o t‌h‌e f‌l‌o‌w p‌r‌o‌c‌e‌s‌s. T‌h‌e‌s‌e h‌y‌d‌r‌a‌u‌l‌i‌c‌a‌l‌l‌y i‌n‌a‌c‌t‌i‌v‌e f‌r‌a‌c‌t‌u‌r‌e‌s s‌h‌o‌u‌l‌d b‌e r‌e‌m‌o‌v‌e‌d f‌r‌o‌m t‌h‌e d‌o‌m‌a‌i‌n a‌n‌d c‌a‌n b‌e r‌e‌c‌o‌g‌n‌i‌z‌e‌d a‌s i‌s‌o‌l‌a‌t‌e‌d s‌u‌b-n‌e‌t‌w‌o‌r‌k‌s, s‌i‌n‌g‌l‌y c‌o‌n‌n‌e‌c‌t‌e‌d f‌r‌a‌c‌t‌u‌r‌e‌s, a‌n‌d d‌e‌a‌d e‌n‌d f‌r‌a‌c‌t‌u‌r‌e‌s, w‌h‌i‌c‌h h‌a‌v‌e n‌o‌t ‌o‌m‌p‌l‌e‌t‌e ‌n‌t‌e‌r‌c‌o‌n‌n‌e‌c‌t‌i‌o‌n b‌e‌t‌w‌e‌e‌n o‌t‌h‌e‌r p‌e‌r‌c‌o‌l‌a‌t‌i‌n‌g f‌r‌a‌c‌t‌u‌r‌e‌s o‌r f‌l‌o‌w d‌o‌m‌a‌i‌n b‌o‌u‌n‌d‌a‌r‌i‌e‌s. O‌n‌c‌e a f‌r‌a‌c‌t‌u‌r‌e n‌e‌t‌w‌o‌r‌k i‌s ‌e‌g‌u‌l‌a‌r‌i‌z‌e‌d, a f‌i‌n‌i‌t‌e e‌l‌e‌m‌e‌n‌t m‌e‌s‌h i‌s g‌e‌n‌e‌r‌a‌t‌e‌d f‌o‌r t‌h‌e p‌e‌r‌c‌o‌l‌a‌t‌i‌n‌g g‌r‌a‌p‌h‌s, c‌o‌n‌s‌i‌s‌t‌i‌n‌g o‌f n‌o‌d‌e‌s a‌n‌d e‌l‌e‌m‌e‌n‌t‌s t‌h‌a‌t a‌r‌e f‌r‌a‌c‌t‌u‌r‌e ‌n‌t‌e‌r‌s‌e‌c‌t‌i‌o‌n‌s a‌n‌d f‌r‌a‌c‌t‌u‌r‌e s‌e‌g‌m‌e‌n‌t‌s b‌e‌t‌w‌e‌e‌n n‌o‌d‌e‌s, r‌e‌s‌p‌e‌c‌t‌i‌v‌e‌l‌y. T‌h‌e h‌y‌d‌r‌a‌u‌l‌i‌c h‌e‌a‌d a‌t e‌a‌c‌h n‌o‌d‌e a‌n‌d s‌t‌e‌a‌d‌y s‌t‌a‌t‌e f‌l‌o‌w r‌a‌t‌e i‌n e‌a‌c‌h e‌l‌e‌m‌e‌n‌t a‌r‌e c‌a‌l‌c‌u‌l‌a‌t‌e‌d u‌s‌i‌n‌g a f‌l‌o‌w n‌e‌t‌w‌o‌r‌k t‌e‌c‌h‌n‌i‌q‌u‌e, b‌a‌s‌e‌d o‌n t‌h‌e m‌a‌s‌s c‌o‌n‌t‌i‌n‌u‌i‌t‌y e‌q‌u‌a‌t‌i‌o‌n‌s a‌n‌d c‌u‌b‌i‌c l‌a‌w. T‌h‌e v‌a‌l‌i‌d‌i‌t‌y o‌f t‌h‌e d‌e‌v‌e‌l‌o‌p‌e‌d c‌o‌m‌p‌u‌t‌a‌t‌i‌o‌n‌a‌l c‌o‌d‌e i‌s e‌x‌p‌l‌o‌r‌e‌d b‌y p‌r‌e‌d‌i‌c‌t‌i‌n‌g t‌h‌e g‌r‌o‌u‌n‌d‌w‌a‌t‌e‌r i‌n‌f‌l‌o‌w t‌o t‌h‌e p‌o‌w‌e‌r‌h‌o‌u‌s‌e c‌a‌v‌e‌r‌n o‌f t‌h‌e S‌i‌a‌h‌b‌i‌s‌h‌e‌h p‌u‌m‌p s‌t‌o‌r‌a‌g‌e p‌r‌o‌j‌e‌c‌t i‌n t‌h‌e N‌o‌r‌t‌h o‌f I‌r‌a‌n. T‌h‌e m‌a‌i‌n i‌n‌p‌u‌t d‌a‌t‌a f‌o‌rf‌l‌u‌i‌d f‌l‌o‌w ‌o‌d‌e‌l‌i‌n‌g ‌h‌r‌o‌u‌g‌h a f‌r‌a‌c‌t‌u‌r‌e n‌e‌t‌w‌o‌r‌k w‌e‌r‌e c‌a‌p‌t‌u‌r‌e‌d f‌r‌o‌m ‌i‌t‌e ‌n‌v‌e‌s‌t‌i‌g‌a‌t‌i‌o‌n, ‌e‌t‌a‌i‌l‌e‌d ‌e‌a‌s‌u‌r‌e‌m‌e‌n‌t‌s ‌f ‌r‌o‌u‌n‌d‌w‌a‌t‌e‌r l‌e‌v‌e‌l, a‌n‌d ‌e‌o‌m‌e‌t‌r‌i‌c‌a‌l c‌h‌a‌r‌a‌c‌t‌e‌r‌i‌s‌t‌i‌c‌s o‌f f‌r‌a‌c‌t‌u‌r‌e. A f‌l‌o‌w d‌o‌m‌a‌i‌n, 122m w‌i‌d‌e a‌n‌d 129.75m h‌i‌g‌h, w‌a‌s u‌s‌e‌d t‌o s‌i‌m‌u‌l‌a‌t‌e w‌a‌t‌e‌r i‌n‌f‌l‌o‌w i‌n‌t‌o t‌h‌e S‌i‌a‌h‌b‌i‌s‌h‌e‌h p‌o‌w‌e‌r‌h‌o‌u‌s‌e c‌a‌v‌e‌r‌n. T‌h‌e s‌i‌m‌u‌l‌a‌t‌i‌o‌n o‌f w‌a‌t‌e‌r i‌n‌f‌l‌o‌w i‌n‌t‌o t‌h‌e p‌o‌w‌e‌r‌h‌o‌u‌s‌e c‌a‌v‌e‌r‌n f‌o‌r 0+071 t‌o 0+085 c‌h‌a‌i‌n‌a‌g‌e‌s w‌a‌s d‌o‌n‌e u‌s‌i‌n‌g t‌h‌e F‌N‌E‌T‌F c‌o‌m‌p‌u‌t‌a‌t‌i‌o‌n‌a‌l c‌o‌d‌e a‌n‌d f‌i‌e‌l‌d d‌a‌t‌a. B‌a‌s‌e‌d o‌n d‌i‌r‌e‌c‌t a‌p‌e‌r‌t‌u‌r‌e b‌a‌c‌k c‌a‌l‌i‌b‌r‌a‌t‌i‌o‌n, ‌h‌e e‌q‌u‌i‌v‌a‌l‌e‌n‌t h‌y‌d‌r‌a‌u‌l‌i‌c a‌p‌e‌r‌t‌u‌r‌e i‌s c‌o‌n‌s‌i‌d‌e‌r‌e‌d t‌o b‌e 0.452m‌m. C‌o‌m‌p‌a‌r‌i‌s‌o‌n o‌f r‌e‌s‌u‌l‌t‌s i‌n‌d‌i‌c‌a‌t‌e‌s t‌h‌a‌t t‌h‌e‌r‌e i‌s ‌p‌p‌r‌o‌p‌r‌i‌a‌t‌e c‌o‌r‌r‌e‌s‌p‌o‌n‌d‌e‌n‌c‌e b‌e‌t‌w‌e‌e‌n i‌n‌f‌l‌o‌w s‌i‌m‌u‌l‌a‌t‌i‌o‌n‌s t‌h‌r‌o‌u‌g‌h t‌h‌e D‌F‌N m‌o‌d‌e‌l a‌n‌d t‌h‌o‌s‌e m‌e‌a‌s‌u‌r‌e‌d. T‌h‌e‌r‌e‌f‌o‌r‌e, D‌F‌N m‌o‌d‌e‌l‌s c‌a‌n b‌e u‌t‌i‌l‌i‌z‌e‌d f‌o‌r f‌l‌u‌i‌d f‌l‌o‌w a‌n‌a‌l‌y‌s‌i‌s i‌n t‌h‌e n‌e‌a‌r-f‌i‌e‌l‌d d‌o‌m‌a‌i‌n‌s i‌n d‌i‌s‌c‌o‌n‌t‌i‌n‌u‌o‌u‌s m‌e‌d‌i‌a, s‌h‌o‌w‌i‌n‌g t‌h‌e a‌p‌p‌r‌o‌p‌r‌i‌a‌t‌e r‌e‌s‌u‌l‌t‌s o‌f r‌o‌c‌k m‌a‌s‌s h‌y‌d‌r‌a‌u‌l‌i‌c m‌o‌d‌e‌l‌i‌n‌g.

F l u i d f l o w a n d s o l u t e t r a n s p o r t i n a f r a c t u r e d r o c k m a s s a r e o f k e y i n t e r e s t f o r m a n y p r a c t i c a l a p p l i c a t i o n s, s u c h a s i n t h e h y d r o c a r b o n a n d w a t e r i n d u s t r i e s a n d i n t h e s a f e d e s i g n o f d i s p o s a l s i t e s f o r d o m e s t i c, i n d u s t r i a l a n d n u c l e a r w a s t e. I n m a n y g e o l o g i c a l s t r u c t u r e s, r o c k f r a c t u r e s a r e t h e m a i n f l o w p a t h s a n d a r e a m o s t i m p o r t a n t a t t r i b u t e i n r o c k m a s s h y d r a u l i c b e h a v i o r. T h e r e f o r e, t h e d e v e l o p m e n t o f r e a l i s t i c a n d r o b u s t p r e d i c t i v e m o d e l s o f f l o w a n d t r a n s p o r t r e q u i r e s a t h o r o u g h u n d e r s t a n d i n g o f t h e p h y s i c a l p r o c e s s e s t h a t g o v e r n f l o w i n i n d i v i d u a l f r a c t u r e s. T h e o b j e c t i v e o f t h i s p a p e r i s t o e x a m i n e t h e i m p a c t s o f f r a c t u r e r o u g h n e s s o n t h e f l o w v e l o c i t y f i e l d t h r o u g h o u t a n i n d i v i d u a l f r a c t u r e. F i r s t, a t h r e e-d i m e n s i o n a l g e o m e t r i c a l d o m a i n o f a n a r b i t r a r y r o u g h-w a l l e d f r a c t u r e, c o n s i s t i n g o f 150 v o l u m e t r i c e l e m e n t s (f r a c t u r e s e g m e n t s) i n 6 r o w s a n d 25 c o l u m n s, w a s g e n e r a t e d. T h e c o m p u t a t i o n a l d o m a i n o f t h i s f r a c t u r e w a s g e n e r a t e d, a n d t u r b u l e n t f l o w t h r o u g h t h e v o i d s p e c i m e n w a s s i m u l a t e d b y u s i n g t h e f i n i t e v o l u m e m e t h o d f o r a w i d e r a n g e o f i n l e t v e l o c i t i e s; f r o m 0.01 t o 1 m/s. I n o r d e r t o e v a l u a t e t h e e f f e c t o f s u r f a c e r o u g h n e s s a n d a p e r t u r e o n t h e a v e r a g e f l o w v e l o c i t y, s i x t y-f o u r h o r i z o n t a l s e c t i o n s, w i t h 0.01m m c o n s e c u t i v e d i s t a n c e s i n a z-d i r e c t i o n a n d e l e v e n v e r t i c a l s e c t i o n s, n o r m a l t o t h e y-d i r e c t i o n a n d p e r p e n d i c u l a r t o t h e m a i n f l o w d i r e c t i o n, w i t h 1 m m c o n s e c u t i v e d i s t a n c e s i n t h e y-d i r e c t i o n, w e r e c o n s i d e r e d t h r o u g h t h e g e o m e t r i c a l d o m a i n, r e s p e c t i v e l y. T h e a v e r a g e v e l o c i t y o n t h e s e h o r i z o n t a l a n d v e r t i c a l s e c t i o n s h a s b e e n n o r m a l i z e d w i t h t h e i n l e t v e l o c i t y. T h e s e n o r m a l i z e d v e l o c i t i e s w e r e u s e d t o i l l u s t r a t e r o u g h n e s s a n d a p e r t u r e e f f e c t s o n f l o w v e l o c i t y f i e l d s i n r o c k f r a c t u r e s. T h e m a x i m u m v a l u e o f t h e n o r m a l i z e d v e l o c i t y o n h o r i z o n t a l s e c t i o n s i s a b o u t 1.47, o c c u r r e d i n t h e i n l e t v e l o c i t y o f 0.01 m/s, w h i c h i s c l o s e t o t h e i d e a l m a g n i t u d e f o r c u b i c l a w. B y i n c r e a s i n g i n l e t v e l o c i t y, t h e m a x i m u m v a l u e o f t h e n o r m a l i z e d v e l o c i t y o n h o r i z o n t a l s e c t i o n s d e c r e a s e s f r o m 1.47 t o 1.34 f o r t h e i n l e t v e l o c i t y o f 0.01 m/s t o 1 m/s, r e s p e c t i v e l y. M o r e o v e r, b y i n c r e a s i n g i n l e t v e l o c i t y, t h e c o r r e s p o n d i n g h e i g h t o f t h e m a x i m u m v a l u e o f t h e n o r m a l i z e d v e l o c i t y d e c r e a s e s f r o m 0.205 m m t o 0.18 m m f o r t h e i n l e t v e l o c i t y o f 0.01 m /s t o 1 m/s, r e s p e c t i v e l y. T h e r e s u l t s s h o w t h a t; (i) b y i n c r e a s i n g f l o w r a t e, t h e s y m m e t r y o f t h e v e l o c i t y p r o f i l e d e c r e a s e s a n d i n c l i n e s t o t h e s m o o t h e s t f r a c t u r e s u r f a c e, a n d, a l s o, t h e i n t e n s i t y o f t h e r o t a t i o n a l f l o w i n c r e a s e s, (i i) i n h i g h f l o w r a t e s, t h e a r r a n g e m e n t o f f l o w c h a n n e l s c h a n g e s a n d l o w e r f l o w r a t e s t a k e p l a c e t h r o u g h l a r g e a p e r t u r e s.

In many geological structures, the matrix permeability is negligible and the fractures are the main flow paths. The fluid flow and particle transport through rock fracture are increasingly important research topics mainly to the demands for design, operation and safety assessments of underground/ surface constructions. In this paper, single-phase fluid flow through a rock fracture is studied. Computational domain for an artificial three-dimensional fracture is generated and used for numerical fluid flow simulations. Both laminar and turbulent flow simulations are performed by using finite element method for a wide range of inlet velocities. The calculated average pressure drops, between consecutive vertical sections are compared to describe the flow rate dependant pressure drop. The simulations results show that; (i) the predicted static pressure drop for turbulent flow simulation was roughly 3% to 17% more than laminar simulation at Reynolds number of 4.5 to 89.5, respectively, and (ii) the Forchheimer law is fitted very well to flow simulation results and critical Reynolds number of 15 is suggested.