Evaluation of hydrodynamic dispersion parameters in fractured rocks

A numerical procedure to determine the equivalent hydrodynamic dispersion coefficients and Péclet number(Pe) of a fractured rock is presented using random walk particle tracking method.The geometrical effects of fracture system on hydrodynamic dispersion are studied.The results obtained from the proposed method agree well with those of empirical models,which are the scale-dependent hydrodynamic dispersion coefficients in an asymptotic or exponential form.A variance case is added to investigate the influence of longitudinal hydrodynamic dispersion in individual fractures on the macro-hydrodynamic dispersion at the fracture network scale,and its influence is demonstrated with a verification example.In addition,we investigate the influences of directional flow and stress conditions on the behavior of hydrodynamic dispersion in fracture networks.The results show that the magnitudes of the hydrodynamic dispersion coefficients are relatively smaller when the flow direction is parallel to the dip directions of fracture sets.Compressive stresses significantly reduce hydrodynamic dispersion.However,the remaining questions are:(1) whether the deformed fracture network under high stress conditions may make the scale-dependent hydrodynamic dispersion coefficients have asymptotic or exponential forms,and(2) what the conditions for existence of a well-defined equivalent hydrodynamic dispersion tensor are.They need to be further investigated.     

Anisotropy of strength and deformability of fractured rocks

Anisotropy of the strength and deformation behaviors of fractured rock masses is a crucial issue for design and stability assessments of rock engineering structures, due mainly to the non-uniform and non- regular geometries of the fracture systems. However, no adequate efforts have been made to study this issue due to the current practical impossibility of laboratory tests with samples of large volumes con- taining many fractures, and the difficulty for controlling reliable initial and boundary conditions for large-scale in situ tests. Therefore, a reliable numerical predicting approach for evaluating anisotropy of fractured rock masses is needed. The objective of this study is to systematically investigate anisotropy of strength and deformability of fractured rocks, which has not been conducted in the past, using a nu- merical modeling method. A series of realistic two-dimensional （2D） discrete fracture network （DFN） models were established based on site investigation data, which were then loaded in different directions, using the code UDEC of discrete element method （DEM）, with changing confining pressures. Numerical results show that strength envelopes and elastic deformability parameters of tested numerical models are significantly anisotropic, and vary with changing axial loading and confining pressures. The results indicate that for design and safety assessments of rock engineering projects, the directional variations of strength and deformability of the fractured rock mass concerned must be treated properly with respect to the directions of in situ stresses. Traditional practice for simply positioning axial orientation of tunnels in association with principal stress directions only may not be adequate for safety requirements. Outstanding issues of the present study and su~zestions for future study are also oresented.     

流固化学耦合作用下裂隙岩体渗透特性研究进展

从物理试验和数学模型研究两方面介绍和总结了近10多年来渗流–应力–化学溶蚀耦合作用下裂隙岩体渗透特性的研究现状。目前无论是物理试验还是数学模型研究,都还是主要利用宏观均匀化的方法来研究裂隙岩体渗透特性变化规律、及其与各影响因素（如应力、温度、渗透流体酸碱度、溶质浓度等）之间的宏观关系,但这种宏观均匀化方法还存在很多不足：如难以表述由于溶蚀作用岩石孔隙结构的细观变化,也难以表述渗流通道的形成和发展过程等。因此认为进一步深入开展以下3方面的研究将更有利于揭示复杂地质环境下裂隙岩体渗透特性机理：控制和量测技术一流的耦合渗流试验设备的开发以及现代无损探测技术引入（实现细观的实时的观察图像和数据）、数字岩芯技术的开发、建立微观－细观－宏观不同尺度的多物理化学场耦合的数学模型与分析方法。     

Numerical evaluation of strength and deformability of fractured rocks

Knowledge of the strength and deformability of fractured rocks is important for design, construction and stability evaluation of slopes, foundations and underground excavations in civil and mining engineering. However, laboratory tests of intact rock samples cannot provide information about the strength and deformation behaviors of fractured rock masses that include many fractures of varying sizes, orientations and locations. On the other hand, large-scale in situ tests of fractured rock masses are economically costly and often not practical in reality at present. Therefore, numerical modeling becomes necessary. Numerical predicting using discrete element methods(DEM) is a suitable approach for such modeling because of their advantages of explicit representations of both fractures system geometry and their constitutive behaviors of fractures, besides that of intact rock matrix. In this study, to generically determine the compressive strength of fractured rock masses, a series of numerical experiments were performed on two-dimensional discrete fracture network models based on the realistic geometrical and mechanical data of fracture systems from feld mapping. We used the UDEC code and a numerical servo-controlled program for controlling the progressive compressive loading process to avoid sudden violent failure of the models. The two loading conditions applied are similar to the standard laboratory testing for intact rock samples in order to check possible differences caused by such loading conditions. Numerical results show that the strength of fractured rocks increases with the increasing confning pressure, and that deformation behavior of fractured rocks follows elasto-plastic model with a trend of strain hardening. The stresses and strains obtained from these numerical experiments were used to ft the well-known Mohr-Coulomb(MC) and Hoek-Brown(H-B) failure criteria, represented by equivalent material properties defning these two criteria. The results show that both criteria can provide fair estimates of the co     

Probabilistic simulations of TBM tunnelling in highly fractured and faulted rocks

Despite the potential excellent performance of TBMs in favourable ground conditions, the presence of fault zones or heavily jointed rocks represents important geological hazards encountered during tunnel excavation. The effects of these challenging environments on the final tunnel construction time and costs can be investigated through a specific computer code: the Decision Aids for Tunnelling (DAT). In this framework the DAT simulate the tunnel excavation in several geological profiles, where changing ground scenarios are described in terms of different “fault zone” classes (from highly fractured rocks, to faulted and crushed material). For each class a certain reduction of the TBM advance rate is specified based on real data analyses. Although the great uncertainty, the results give a reliable estimation of the effect of degrading rock mass conditions on the tunnelling performance. Finally, a real case-study has been simulated by DAT in order to validate the use of the “fault zone” classes (and the relative advance rate reductions) in the estimation of the final time of tunnel construction. The predicted time values prove to be very close to the ones recorded on the field, confirming the importance of a more detailed and comprehensive characterisation of difficult ground conditions such as fault and highly fractured zones.     

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 measurements, 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.     

Block system construction for three-dimensional discrete element models of fractured rocks

Realistic computer models of fracture-block systems have significant impacts on the performance of DEM models of fractured rocks, especially for near-field coupled hydro-mechanical problems. In this paper, the basic components of an algorithm for establishing geometry of block systems of fractured rocks for discrete element methods are presented. The algorithm is based on the basic principles of combinatorial topology. It uses a boundary chain operator for block tracing, using fracture intersection data, and the Euler–Poincáre formula of polyhedra for ensuring the correctness of the tracing operations. Effort was made to simplify the presentation of the theory and techniques without introducing too many concepts and principles of combinatorial topology. The main advantage of this new algorithm is that its capability to deal with any complex geometry of natural rock fracture systems of finite sizes and arbitrary shapes, therefore it is able to represent more realistically the fracture system connectivity and block system formation for coupled hydro-mechanical analyses using DEM models. The disadvantage of using infinitely large fractures for block system generation, which tends to overestimate the fracture connectivity, can therefore be avoided.     

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 (α 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 α 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.     

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.     

The relationships between post-failure state and compression strength of sudetic fractured rocks

The behaviour of the Sudetic crystalline rocks in a pre- and a post-critical state of stress is the topic of this work. The pre-and post-critical failure energy ratio has been discussed, and the regression lines of residual strength of fractured rocks has been detrmined, based on which the residual strength (R_rez) and the standard compression strength (R_e) relationship was empirically determined as R_rez=0.18R_c+5.6;     

考虑多尺度结构的贯通节理岩体损伤摩擦耦合模型

基于贯通节理岩体结构的多尺度特征,采用两步均匀化方法,给出了节理岩体在复杂荷载作用下的自由焓表达式,建立了节理岩体损伤摩擦耦合本构模型。模型可同时考虑岩块损伤扩展、微裂纹滑移剪胀、法向刚度恢复,节理面多阶凸起体滑移磨损、剪胀演化以及节理与岩块相互作用等特征,较好地反映岩体内部微裂纹、节理等不同尺度微结构变化对其力学特性的影响。采用Lac du Bonnet花岗岩三轴压缩试验、花岗岩节理剪切试验以及不同节理倾角与不同围压下Martinsburg板岩三轴压缩强度试验等成果对模型进行了验证,模型预测值与实测值相当吻合,论证了模型的准确性。     

Groundwater flow through fractured rocks and seepage control in geotechnical engineering: Theories and practices

Groundwater flow through fractured rocks has been recognized as an important issue in many geotechnical engineering practices. Several key aspects of fundamental mechanisms, numerical modeling and engineering applications of flow in fractured rocks are discussed. First, the microscopic mechanisms of fluid flow in fractured rocks, especially under the complex conditions of non-Darcian flow, multiphase flow, rock dissolution, and particle transport, have been revealed through a combined effort of visualized experiments and theoretical analysis. Then, laboratory and field methods of characterizing hydraulic properties (e.g. intrinsic permeability, inertial permeability, and unsaturated flow parameters) of fractured rocks in different flow regimes have been proposed. Subsequently, high-performance numerical simulation approaches for large-scale modeling of groundwater flow in fractured rocks and aquifers have been developed. Numerical procedures for optimization design of seepage control systems in various settings have also been proposed. Mechanisms of coupled hydro-mechanical processes and control of flow-induced deformation have been discussed. Finally, three case studies are presented to illustrate the applications of the improved theoretical understanding, characterization methods, modeling approaches, and seepage and deformation control strategies to geotechnical engineering projects.     

Effects of local rock heterogeneities on the hydromechanics of fractured rocks using a digital-image-based technique

A digital-image-based (DIB) finite element approach is developed based on the numerical code rock failure process analysis (RFPA) to characterize micro-scale rock heterogeneity, and to understand the impact of micro-scale rock heterogeneity on the macro-scale hydromechanical response of rocks. The DIB technique incorporates small-scale spatial variability of initial deformation modulus, strength and permeability directly into a coupled hydromechanical model. Variability in Young's modulus, strength, and permeability is applied by a property map defined from the pixel-scale of a digital image. In the RFPA, mechanical deformation is followed, including the accumulation of damage applied in individual elements, which modifies modulus, strength, and permeability with the intensity of damage. The RFPA simulates progressive failure in fractured rocks, representing both the growth of existing fractures and the formation of new fractures, without having to identify crack tips and their interaction explicitly. In this DIB simulation approach, image voxels are used to give equivalent mechanical and flow properties. These property maps are ported to the model capable of solving directly for the evolving deformation, and fluid flow fields. The model is validated through comparisons of the simulated results with phenomenological observations documented in previous studies. The validated model is then applied to investigate the hydromechanical response of fractured rock characterized by digital image. The model is able to reproduce the spatial evolution of damage in the sample, the coalescence of existing cracks, and the formation of new cracks.     

Quantifying fractured rock hydraulic heterogeneity and groundwater inflow prediction in underground excavations: the heterogeneity index

This paper presents an approach to quantify the degree of heterogeneity of a fracture network starting from the information that is collected for a geomechanical classification of rock masses. Six synthetic experiments have been used to prove the existence of a correspondence between the variability in fracture properties and in the direction and magnitude of flow. Statistical analyses conducted using fracture data collected at a tunnel crossing the north-western Italian Alps have also shown that variability in fracture characteristics is indeed related to the magnitude of inflows. These findings have proved that it is reasonable to estimate the degree of heterogeneity of a fracture network by combining the variance of those fracture characteristics that regulate both flow and the geomechanical behavior of a rock mass. An index comprising a combination of variances of fracture parameters at different scales is presented. Its dependence on scale showed that the heterogeneity of fractured rock increases with scale up to a certain scale and then gradually decreases at large scales.     

Thermal response testing of a fractured hard rock aquifer with and without induced groundwater flow

This study quantifies experimentally the influence of groundwater on the thermal conductivity measurements via thermal response tests (TRT) in a fractured hard rock with low matrix permeability. An artificial groundwater flow towards a nearby well was induced by groundwater extraction and a TRT performed simultaneously. The results were compared with a TRT performed 24?days later in the same well without groundwater extraction. The effect of the groundwater flow is shown indirectly by the enhanced effective thermal conductivity and directly through the comparison of temperature profiles before and 4?h after both TRTs. Simulations in FEFLOW show that a groundwater flow velocity of 130–1,300?m?d^?1 through one open horizontal fracture of small volume increases the effective thermal conductivity by 11?% in the studied system.