Creep constitutive model considering nonlinear creep degradation of fractured rock

Stability analysis of underground constructions requires a model study of rock masses’ long-term performance. Creep tests under different stress conditions was conducted on intact granite and granite samples fractured at 30° and 45° angles. The experimental results indicate that the steady creep strain rates of intact and fractured rock present an exponential increase trend with the increase of stress level. A nonlinear creep model is developed based on the experimental results, in which the initial damage caused by fracture together with the damage caused by constant load have been taken into consideration. The fitting analysis results indicated that the model proposed is more accurate at identifying the full creep regions in fractured granite, especially the accelerated stage of creep deformation. The least-square fit error of the proposed creep model is significantly lower than that of Nishihara model by almost an order of magnitude. An analysis of the effects of elastic modulus, viscosity coefficient, and damage factors on fractured rock strain rate and creep strain is conducted. If no consideration is given to the effects of the damage, the proposed nonlinear creep model can degenerate into to the classical Nishihara model.

Numerical manifold method for thermo-mechanical coupling simulation of fractured rock mass

As a calculation method based on the Galerkin variation,the numerical manifold method(NMM)adopts a double covering system,which can easily deal with discontinuous deformation problems and has a high calculation accuracy.Aiming at the thermo-mechanical(TM)coupling problem of fractured rock masses,this study uses the NMM to simulate the processes of crack initiation and propagation in a rock mass under the influence of temperature field,deduces related system equations,and proposes a penalty function method to deal with boundary conditions.Numerical examples are employed to confirm the effectiveness and high accuracy of this method.By the thermal stress analysis of a thick-walled cylinder(TWC),the simulation of cracking in the TWC under heating and cooling conditions,and the simulation of thermal cracking of the SwedishÄspöPillar Stability Experiment(APSE)rock column,the thermal stress,and TM coupling are obtained.The numerical simulation results are in good agreement with the test data and other numerical results,thus verifying the effectiveness of the NMM in dealing with thermal stress and crack propagation problems of fractured rock masses.

Borehole stability in naturally fractured rocks with drilling mud intrusion and associated fracture strength weakening:A coupled DFN-DEM approach

Borehole instability in naturally fractured rocks poses significant challenges to drilling.Drilling mud invades the surrounding formations through natural fractures under the difference between the wellbore pressure(P w)and pore pressure(P p)during drilling,which may cause wellbore instability.However,the weakening of fracture strength due to mud intrusion is not considered in most existing borehole stability analyses,which may yield significant errors and misleading predictions.In addition,only limited factors were analyzed,and the fracture distribution was oversimplified.In this paper,the impacts of mud intrusion and associated fracture strength weakening on borehole stability in fractured rocks under both isotropic and anisotropic stress states are investigated using a coupled DEM(distinct element method)and DFN(discrete fracture network)method.It provides estimates of the effect of fracture strength weakening,wellbore pressure,in situ stresses,and sealing efficiency on borehole stability.The results show that mud intrusion and weakening of fracture strength can damage the borehole.This is demonstrated by the large displacement around the borehole,shear displacement on natural fractures,and the generation of fracture at shear limit.Mud intrusion reduces the shear strength of the fracture surface and leads to shear failure,which explains that the increase in mud weight may worsen borehole stability during overbalanced drilling in fractured formations.A higher in situ stress anisotropy exerts a significant influence on the mechanism of shear failure distribution around the wellbore.Moreover,the effect of sealing natural fractures on maintaining borehole stability is verified in this study,and the increase in sealing efficiency reduces the radial invasion distance of drilling mud.This study provides a directly quantitative prediction method of borehole instability in naturally fractured formations,which can consider the discrete fracture network,mud intrusion,and associated weakening of fracture strength.The information provided by the numerical approach(e.g.displacement around the borehole,shear displacement on fracture,and fracture at shear limit)is helpful for managing wellbore stability and designing wellbore-strengthening operations.

A new elastoplastic model for bolt-grouted fractured rock

Complexities in mechanical behaviours of rock masses mainly stem from inherent discontinuities,which calls for advanced bolt-grouting techniques for stability enhancement.Understanding the mechanical properties of bolt-grouted fractured rock mass(BGFR)and developing accurate prediction methods are crucial to optimize the BGFR support strategies.This paper establishes a new elastoplastic(E-P)model based on the orthotropic and the Mohr-Coulomb(M-C)plastic-yielding criteria.The elastic parameters of the model were derived through a meso-mechanical analysis of composite materials mechanics(CMM).Laboratory BGFR specimens were prepared and uniaxial compression test and variable-angle shear test considering different bolt arrangements were carried out to obtain the mechanical parameters of the specimens.Results showed that the anisotropy of BGFR mainly depends on the relative volume content of each component material in a certain direction.Moreover,the mechanical parameters deduced from the theory of composite materials which consider the short fibre effect are shown to be in good agreement with those determined by laboratory experiments,and the variation rules maintained good consistency.Last,a case study of a real tunnel project is provided to highlight the effectiveness,validity and robustness of the developed E-P model in prediction of stresses and deformations.

Identifying flow regime in the aquifer of fractured rock system in Germi Chai Basin,Iran

Considering the importance of fractured rock aquifers in the hydrogeologic process,this research aimed to analyze the flow regime,internal degree of karstification,and estimate storage volume in fractured rock aquifers of the Germi Chai Basin in northwest Iran,which is attributed to its active tectonics,erosion,and the lithological diversity.Given the geological setting,the hypothesis is that this basin is characterized by a high degree of karstification and diffuse or intermediate flow regime leading to variation in discharge flow rate.The hydrodynamic and hadrochemical analysis was conducted on 9 well distributed springs across the basin from 2019 to 2020.The maximum flow rate in most of the springs appeared in the early wet season despite their different levels of fluctuations on the monthly discharge time series.Analyzing the spring recession curve form revealed an aquifer containing multiple micro-regimes withαrecession coefficients and a degree of karstification ranging between 0.001 to 0.06 and 0.55 to 2.61,respectively.These findings indicated a dominant diffuse and intermediate flow system resulting from the development of a high density of fractures in this area.The electrical conductivity of the spring changes inversely proportional to the change in flow discharge,indicating the reasonable hydrological response of the aquifer to rainfall events.Hydrograph analysis revealed that the delay time of spring discharge after rainfall events mostly varies between 10 to 30 days.The total dynamic storage volume of the spring for a given period(2019-2020)was estimated to be approximately 1324 million cubic meters reflecting the long-term drainage potential and high perdurability of dynamic storage.Estimating the maximum and minimum ratio revealed that the springs recharging system in Germi Chai Basin comes under the slow aquifers category.This finding provides valuable insight into the hydrogeological properties of fractured rock aquifers contributing to effective water management strategy.

A method to interpret fracture aperture of rock slope using adaptive shape and unmanned aerial vehicle multi-angle nap-of-the-object photogrammetry

The aperture of natural rock fractures significantly affects the deformation and strength properties of rock masses,as well as the hydrodynamic properties of fractured rock masses.The conventional measurement methods are inadequate for collecting data on high-steep rock slopes in complex mountainous regions.This study establishes a high-resolution three-dimensional model of a rock slope using unmanned aerial vehicle(UAV)multi-angle nap-of-the-object photogrammetry to obtain edge feature points of fractures.Fracture opening morphology is characterized using coordinate projection and transformation.Fracture central axis is determined using vertical measuring lines,allowing for the interpretation of aperture of adaptive fracture shape.The feasibility and reliability of the new method are verified at a construction site of a railway in southeast Tibet,China.The study shows that the fracture aperture has a significant interval effect and size effect.The optimal sampling length for fractures is approximately 0.5e1 m,and the optimal aperture interpretation results can be achieved when the measuring line spacing is 1%of the sampling length.Tensile fractures in the study area generally have larger apertures than shear fractures,and their tendency to increase with slope height is also greater than that of shear fractures.The aperture of tensile fractures is generally positively correlated with their trace length,while the correlation between the aperture of shear fractures and their trace length appears to be weak.Fractures of different orientations exhibit certain differences in their distribution of aperture,but generally follow the forms of normal,log-normal,and gamma distributions.This study provides essential data support for rock and slope stability evaluation,which is of significant practical importance.

Study of hydro-mechanical behaviours of rough rock fracture with shear dilatancy and asperities using shear-flow model

The geometric properties of fracture surfaces significantly influence shear-seepage in rock fractures,introducing complexities to fracture modelling.The present study focuses on the hydro-mechanical behaviours of rough rock fractures during shear-seepage processes to reveal how dilatancy and fracture asperities affect these phenomena.To achieve this,an improved shear-flow model(SFM)is proposed with the incorporation of dilatancy effect and asperities.In particular,shear dilatancy is accounted for in both the elastic and plastic stages,in contrast to some existing models that only consider it in the elastic stage.Depending on the computation approaches for the peak dilatancy angle,three different versions of the SFM are derived based on Mohr-Coulomb,joint roughness coefficient-joint compressive strength(JRC-JCS),and Grasselli’s theories.Notably,this is a new attempt that utilizes Grasselli’s model in shearseepage analysis.An advanced parameter optimization method is introduced to accurately determine model parameters,addressing the issue of local optima inherent in some conventional methods.Then,model performance is evaluated against existing experimental results.The findings demonstrate that the SFM effectively reproduces the shear-seepage characteristics of rock fracture across a wide range of stress levels.Further sensitivity analysis reveals how dilatancy and asperity affect hydraulic properties.The relation between hydro-mechanical properties(dilatancy displacement and hydraulic conductivity)and asperity parameters is analysed.Several profound understandings of the shear-seepage process are obtained by exploring the phenomenon under various conditions.

Multiscale modeling of gas-induced fracturing in anisotropic clayey rocks

In the context of repositories for nuclear waste,understanding the behavior of gas migration through clayey rocks with inherent anisotropy is crucial for assessing the safety of geological disposal facilities.The primary mechanism for gas breakthrough is the opening of micro-fractures due to high gas pressure.This occurs at gas pressures lower than the combined strength of the rock and its minimum principal stress under external loading conditions.To investigate the mechanism of microscale mode-I ruptures,it is essential to incorporate a multiscale approach that includes subcritical microcracks in the modeling framework.In this contribution,we derive the model from microstructures that contain periodically distributed microcracks within a porous material.The damage evolution law is coupled with the macroscopic poroelastic system by employing the asymptotic homogenization method and considering the inherent hydro-mechanical(HM)anisotropy at the microscale.The resulting permeability change induced by fracture opening is implicitly integrated into the gas flow equation.Verification examples are presented to validate the developed model step by step.An analysis of local macroscopic response is undertaken to underscore the influence of factors such as strain rate,initial damage,and applied stress,on the gas migration process.Numerical examples of direct tension tests are used to demonstrate the model’s efficacy in describing localized failure characteristics.Finally,the simulation results for preferential gas flow reveal the robustness of the two-scale model in explicitly depicting gas-induced fracturing in anisotropic clayey rocks.The model successfully captures the common behaviors observed in laboratory experiments,such as a sudden drop in gas injection pressure,rapid build-up of downstream gas pressure,and steady-state gas flow following gas breakthrough.

3D DEM simulation of hard rock fracture in deep tunnel excavation induced by changes in principal stress magnitude and orientation

To achieve the loading of the stress path of hard rock,the spherical discrete element model(DEM)and the new flexible membrane technology were utilized to realize the transient loading of three principal stresses with arbitrary magnitudes and orientations.Furthermore,based on the deep tunnel of China Jinping Underground Laboratory II(CJPL-II),the deformation and fracture evolution characteristics of deep hard rock induced by excavation stress path were analyzed,and the mechanisms of transient loading-unloading and stress rotation-induced fractures were revealed from a mesoscopic perspective.The results indicated that the stressestrain curve exhibits different trends and degrees of sudden changes when subjected to transient changes in principal stress,accompanied by sudden changes in strain rate.Stress rotation induces spatially directional deformation,resulting in fractures of different degrees and orientations,and increasing the degree of deformation anisotropy.The correlation between the degree of induced fracture and the unloading magnitude of minimum principal stress,as well as its initial level is significant and positive.The process of mechanical response during transient unloading exhibits clear nonlinearity and directivity.After transient unloading,both the minimum principal stress and minimum principal strain rate decrease sharply and then tend to stabilize.This occurs from the edge to the interior and from the direction of the minimum principal stress to the direction of the maximum principal stress on theε1-ε3 plane.Transient unloading will induce a tensile stress wave.The ability to induce fractures due to changes in principal stress magnitude,orientation and rotation paths gradually increases.The analysis indicates a positive correlation between the abrupt change amplitude of strain rate and the maximum unloading magnitude,which is determined by the magnitude and rotation of principal stress.A high tensile strain rate is more likely to induce fractures under low minimum principal stress.

Discontinuity development patterns and the challenges for 3D discrete fracture network modeling on complicated exposed rock surfaces

Natural slopes usually display complicated exposed rock surfaces that are characterized by complex and substantial terrain undulation and ubiquitous undesirable phenomena such as vegetation cover and rockfalls.This study presents a systematic outcrop research of fracture pattern variations in a complicated rock slope,and the qualitative and quantitative study of the complex phenomena impact on threedimensional(3D)discrete fracture network(DFN)modeling.As the studies of the outcrop fracture pattern have been so far focused on local variations,thus,we put forward a statistical analysis of global variations.The entire outcrop is partitioned into several subzones,and the subzone-scale variability of fracture geometric properties is analyzed(including the orientation,the density,and the trace length).The results reveal significant variations in fracture characteristics(such as the concentrative degree,the average orientation,the density,and the trace length)among different subzones.Moreover,the density of fracture sets,which is approximately parallel to the slope surface,exhibits a notably higher value compared to other fracture sets across all subzones.To improve the accuracy of the DFN modeling,the effects of three common phenomena resulting from vegetation and rockfalls are qualitatively analyzed and the corresponding quantitative data processing solutions are proposed.Subsequently,the 3D fracture geometric parameters are determined for different areas of the high-steep rock slope in terms of the subzone dimensions.The results show significant variations in the same set of 3D fracture parameters across different regions with density differing by up to tenfold and mean trace length exhibiting differences of 3e4 times.The study results present precise geological structural information,improve modeling accuracy,and provide practical solutions for addressing complex outcrop issues.

Comprehensive assessment on dynamic roof instability under fractured rock mass conditions in the excavation disturbed zone

The damage process of fractured rock mass showed that the fracture in rocks induced roof collapse in Yangchangwan Coal Mine, China. The rock mass was particularly weak and fractured. There occurred 6 large-scale dynamical roof falls in the excavation disturbed zone （EDZ） with the collapsing volume of 216 m^3. First, the field detailed geological environment, regional seismic dynamics, and dynamic instability of roadways were generally investigated. Second, the field multiple-index monitoring measurements for detecting the deep delamination of the roof, convergence deformation, bolt-cable load, acoustic emission （AE） characteristic parameters, total AE events, AE energy-releasing rate, rock mass fracture, and damage were arranged. Finally, according to the time-space-strength relations, a quantitative assessment of the influence of rock-mass damage on the dynamic roof instability was accomplished.

A Review of Colloid Transport in Fractured Rocks

Recent recognition of colloid and colloidassociated transport of strongly sorbing contaminants in fractured rocks highlights the importance of exploring the transport behavior of colloids under conditions prevailing in the field.The rapid transport of colloids through fractured rocks-as affected by the hydraulic properties of the flow system,the properties of fracture surface and the geochemical conditionshas not been sufficiently elucidated,and predictions of colloid transport through fractures have encountered difficulties,particularly at the field scale.This article reviews the current understanding of the mechanisms and modeling of colloid transport and retention in fractured rocks.Commonly used experimental techniques and approaches for conducting colloid transport experiments at different scales,ranging from the laboratory to the field scale,are summarized and commented upon.The importance of various interactions(e.g.,dissolution,colloid deposition,generation,mobilization and deposition of filling materials within fractures) between the flowing solution and the fracture walls(in many cases,with skin or coating on the host rock at the liquid-solid interface) has been stressed.Colloid transport through fractures of high heterogeneity has not yet been well understood and modeled at the field scale.Here,we summarize the current knowledge and understanding accumulated in the last two decades in regard to colloid and colloidassociated transport through fractures.Future research needs are also discussed.

Visualization of drained rock volume(DRV) in hydraulically fractured reservoirs with and without natural fractures using complex analysis methods(CAMs)

The drainage areas(and volumes)near hydraulically fractured wells,computed and visualized in our study at high resolution,may be critically affected by the presence of natural fractures.Using a recently developed algorithm based on complex analysis methods(CAMs),the drained rock volume(DRV)is visualized for a range of synthetic constellations of natural fractures near hydraulic fractures.First,flow interference effects near a single hydraulic fracture are systematically investigated for a variety of natural fracture sets.The permeability contrast between the matrix and the natural fractures is increased stepwise in order to better understand the effect on the DRV.Next,a larger-scale model investigates flow interference for a full hydraulically fractured well with a variety of natural fracture sets.The time of flight contours(TOFCs)outlining the DRV are for all cases with natural fractures compared to a base case without any natural fractures.Discrete natural fractures,with different orientations,hydraulic conductivity,and fracture density,may shift the TOFC patterns in the reservoir region drained by the hydraulically fractured well,essentially shifting the location of the well’s drainage area.The CAM-based models provide a computationally efficient method to quantify and visualize the drainage in both naturally and hydraulically fractured reservoirs.

Determination of hydraulic conductivity of fractured rock masses:A case study for a rock cavern project in Singapore

In order to reduce the risk associated with water seepage in an underground rock cavern project inSingapore, a reliable hydro-geological model should be established based on the in situ investigationdata. The key challenging issue in the hydro-geological model building is how to integrate limitedgeological and hydro-geological data to determine the hydraulic conductivity of the fractured rockmasses. Based on the data obtained from different stages （feasibility investigation stage, constructionstage, and post-construction stage）, suitable models and methods are proposed to determine the hydraulicconductivities at different locations and depths, which will be used at other locations in thefuture. 2015 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

A discrete model for prediction of radon flux from fractured rocks

Prediction of radon flux from the fractured zone of a propagating cave mine is basically associated with uncertainty and complexity. For instance, there is restricted access to these zones for field measure- ments, and it is quite difficult to replicate the complex nature of both natural and induced fractures in these zones in laboratory studies. Hence, a technique for predicting radon flux from a fractured rock using a discrete fracture network （DFN） model is developed to address these difficulties. This model quantifies the contribution of fractures to the total radon flux, and estimates the fracture density from a measured radon flux considering the effects of advection, diffusion, as well as radon generation and decay. Radon generation and decay are classified as reaction processes. Therefore, the equation solved is termed as the advection-diffusion-reaction equation （ADRE）. Peclet number （Pe）, a conventional dimensionless parameter that indicates the ratio of mass transport by advection to diffusion, is used to classify the transport regimes. The results show that the proposed model effectively predicts radon flux from a fractured rock. An increase in fracture density for a rock sample with uniformly distributed radon generation rate can elevate radon flux significantly compared with another rock sample with an equivalent increase in radon generation rate. In addition to Pe, two other independent dimensionless parameters （derived for radon transport through fractures） significantly affect radon dimensionless flux. Findings provide insight into radon transport through fractured rocks and can be used to improve radon control measures for proactive mitigation.

Variation in hydraulic conductivity of fractured rocks at a dam foundation during operation

Characterizing the permeability variation in fractured rocks is important in various subsurface applications,but how the permeability evolves in the foundation rocks of high dams during operation remains poorly understood.This permeability change is commonly evidenced by a continuous decrease in the amount of discharge(especially for dams on sediment-laden rivers),and can be attributed to fracture clogging and/or hydromechanical coupling.In this study,the permeability evolution of fractured rocks at a high arch dam foundation during operationwas evaluated by inverse modeling based on the field timeseries data of both pore pressure and discharge.A procedure combining orthogonal design,transient flow modeling,artificial neural network,and genetic algorithm was adopted to efficiently estimate the hydraulic conductivity values in each annual cycle after initial reservoir filling.The inverse results show that the permeability of the dam foundation rocks follows an exponential decay annually during operation(i.e.K/K0=0.97e^(-0.59t)+0.03),with good agreement between field observations and numerical simulations.The significance of the obtained permeability decay function was manifested by an assessment of the long-term seepage control performance and groundwater flow behaviors at the dam site.The proposed formula is also of merit for characterizing the permeability change in riverbed rocks induced by sediment transport and deposition.

Modeling unsaturated flow in fractured rocks with scaling relationships between hydraulic parameters

Modeling unsaturated flow in fractured rocks is essential in various subsurface engineering applications,but it remains a great challenge due to the difficulties in determining the unsaturated hydraulic properties of rocks that contain various scales of fractures.It is generally accepted that the van Genuchten(VG)model can be applied to fractured rocks,provided that the hydraulic parameters could be representatively determined.In this study,scaling relationships between the VG parameters(a and n)and hydraulic conductivity(K)across 8 orders of magnitude,from 10^(-10)m/s to 10^(-2)m/s,were proposed by statistical analysis of data obtained from 1416 soil samples.The correlations were then generalized to predict the upper bounds of VG parameters for fractured rocks from the K data that could be obtained more easily under field conditions,and were validated against a limited set of data from cores,fractures and fractured rocks available in the literature.The upper bound estimates significantly narrow the ranges of VG parameters,and the representative values of a and n for fractured rocks at the field scale can then be determined with confidence by inverse modeling using groundwater observations in saturated zones.The proposed methodology was applied to saturated-unsaturated flow modeling in the right-bank slope at the Baihetan dam site with a continuum approach,showing that most of the flow behaviors in fractured rocks in this complex hydrogeological condition could be properly reproduced.The proposed method overcomes difficulties in suction measurement in fractured rocks with strong heterogeneity,and provides a feasible way for modeling of saturated-unsaturated flow in fractured rocks with acceptable engineering accuracy.

Identifying the real fracture hidden in rock microcrack zone by acoustic emission energy

Identifying the real fracture of rock hidden in acoustic emission(AE)source clusters(AE-depicted microcrack zone)remains challenging and crucial.Here we revealed the AE energy(representing dissipated energy)distribution rule in the rock microcrack zone and proposed an AE-energy-based method for identifying the real fracture.(1)A set of fracture experiments were performed on granite using wedgeloading,and the fracture process was detected and recorded by AE.The microcrack zone associated with the energy dissipation was characterized by AE sources and energy distribution,utilizing our selfdeveloped AE analysis program(RockAE).(2)The accumulated AE energy,an index representing energy dissipation,across the AE-depicted microcrack zone followed the normal distribution model(the mean and variance relate to the real fracture path and the microcrack zone width).This result implies that the nucleation and coalescence of massive cracks(i.e.,real fracture generation process)are supposed to follow a normal distribution.(3)Then,we obtained the real fracture extension path by joining the peak positions of the AE energy normal distribution curve at different cross-sections of the microcrack zone.Consequently,we distinguished between the microcrack zone and the concealed real fracture within it.The deviation was validated as slight as 1–3 mm.

Stress-dependent shear wave splitting and permeability in fractured porous rock

It is well known that shear wave propagates slower across than parallel to a fracture, and as a result, a travelling shear wave splits into two directions when it encounters a fracture. Shear wave splitting and permeability of porous rock core samples having single fracture were experimentally investigated using a high-pressure triaxial cell, which can measure seismic shear wave velocities in two directions mutually perpendicular to the sample axis in addition to the longitudinal compressive wave velocity. A single fracture was created in the samples using a modified Brazilian split test device, where the cylindrical sample edges were loaded on two diametrically opposite lines by sharp guillotines along the sample length. Based on tilt tests and fracture surface profilometry, the method of artificially induced tensile fracture in the sample was found to create repeatable fracture surfaces and morphologies. Seismic velocities of the fractured samples were determined under different levels of stress confinement and fracture shear displacement or mismatch. The effective confining stress was varied from 0.5 MPa to55 MPa, while the fractures were mismatched by 0 mm, 0.45 mm and 1 mm. The degree of matching of the fracture surfaces in the core samples was evaluated using the joint matching coefficient(JMC). Shear wave splitting, as measured by the difference in the magnitudes of shear wave velocities parallel(V_(S1))and perpendicular(V_(S2)) to the fracture, is found to be insensitive to the degree of mismatching of the fracture joint surfaces at 2 MPa, and decreased and approached zero as the effective stress was increased.Simple models for the stress-and JMC-dependent shear wave splitting and fractured rock permeability were developed based on the experimental observations. The effects of the joint wall compressive strength(JCS), JMC and stress on the stress dependency of joint aperture were discussed in terms of hydro-mechanical response. Finally, a useful relationship between fractured rock permeability and shear wave splitting was found after normalization by using JMC.

High-resolution photogrammetry to measure physical aperture of two separated rock fracture surfaces

Photogrammetry,reconstructing three-dimensional(3D)models from overlapping two-dimensional(2D)photos,finds application in rock mechanics and rock engineering to extract geometrical details of reconstructed objects,for example rock fractures.Fracture properties are important for determining the mechanical stability,permeability,strength,and shear behavior of the rock mass.Photogrammetry can be used to reconstruct detailed 3D models of two separated rock fracture surfaces to characterize fracture roughness and physical aperture,which controls the fluid flow,hydromechanical and shear behavior of the rock mass.This research aimed to determine the optimal number of scale bars required to produce high-precision 3D models of a fracture surface.A workflow has been developed to define the physical aperture of a fracture using photogrammetry.Three blocks of Kuru granite(25 cm×25 cm×10 cm)with an artificially induced fracture,were investigated.For scaling 3D models,321 markers were used as ground control points(GCPs)with predefined distances on each block.When the samples were wellmatched in their original positions,the entire block was photographed.Coordinate data of the GCPs were extracted from the 3D model of the blocks.Each half was surveyed separately and georeferenced by GCPs and merged into the same coordinate system.Two fracture surfaces were extracted from the 3D models and the vertical distance between the two surfaces was digitally calculated as physical aperture.Accuracy assessment of the photogrammetric reconstruction showed a 20-30 mm digital control distance accuracy when compared to known distances defined between markers.To attain this accuracy,the study found that at least 200 scale bars were required.Furthermore,photogrammetry was employed to measure changes in aperture under normal stresses.The results obtained from this approach were found to be in good agreement with those obtained using linear variable displacement transducers(LVDTs),with differences ranging from 1 mm to 8μm.