In this paper, numerical simulations are conducted to study elastic wave transport, scattering, and attenuation in a naturally fractured rock associated with length-correlated fracture normal and ...shear stiffnesses. The model represents the pattern of a real fracture outcrop in an explicit fashion based on the discrete fracture network approach and computes the dynamical interaction between waves and fractures based on the displacement discontinuity method. A broad spectrum of geologically relevant fracture stiffness values are explored to analyse the impact of fracture normal and shear stiffness components on the wavefield evolution. It is observed that when the fracture normal and shear stiffnesses are both high, the wavefield is a propagative mode dominated by a forward ballistic transport. With the reduction of fracture normal and/or shear stiffnesses, the wavefield becomes diffusive characterised by the emergence and dominance of coda waves. If the fracture stiffnesses are very low, waves become trapped entering the so-called localisation regime associated with an absence of effective transport as well as a profound attenuation. Our results show that the scattering attenuation of S waves tends to be greater than that of P waves in the propagation and diffusion regimes, but becomes similar in the localisation regime. The research findings of this paper have important implications for understanding and predicting the seismic wave attenuation behaviour in naturally fractured rocks for various geophysical applications.
•Elastic wave transport in a naturally fractured rock is numerically simulated.•Fracture stiffnesses exert a significant impact on wave scattering and attenuation.•S waves are more attenuated than P waves in the propagative and diffusive regimes.•Anderson localisation of elastic waves emerges when fracture stiffnesses are very low.
Fractures widely exist in crustal rocks and form complex networks dominating the bulk behaviour of geological media. Thus, understanding how fracture networks affect subsurface processes/phenomena is ...highly relevant to many rock engineering applications. However, the large-scale behaviour of a fractured rock mass consisting of numerous fractures and rocks cannot be predicted by simple applications of the knowledge of individual fractures and/or rocks, due to upscaling complexities involving the hierarchy of scales, heterogeneities, and physical mechanisms as well as the possible emergence of qualitatively different macroscopic properties. In other words, macroscopic phenomena in fractured rocks arise from the many-body effects (i.e. collective behaviour) of numerous interacting fractures and rocks, such that the emergent properties at the fracture system scale are much richer than those of individual components. Hence, more is different! This paper gives a discussion on the mechanism of emergence in fractured media from a combined statistical physics and rock mechanics perspective, and further presents a multiscale conceptual framework to link microscopic responses of single fractures/rocks to macroscopic behaviour of rock masses consisting of many fractures and rocks. This framework can serve as a useful tool to bridge experimentally-established constitutive relationships of fracture/rock samples at the laboratory scale to phenomenologically-observed macroscopic properties of fractured rock masses at the site scale.
Crystalline rock has been tested/selected by many countries for developing underground nuclear waste repositories at ~500 m depth to achieve geological isolation of high-level, long-lived radioactive ...waste. During the assessment period of up to one million years, large earthquakes may occur around the repository and trigger coseismic displacements along secondary fractures, jeopardising the integrity of the buffer-waste canister system. It is, therefore, of great importance to understand the coseismic behaviour of the repository site during large earthquakes. In this paper, we develop a finite element method-based seismo-mechanical model to simulate the response of fractured rocks subject to both in-situ stresses and seismic activities. The model can well capture the fracture displacement behaviour under dynamic loadings involving alternating regimes of contact loss, partial slip and total sliding. We model the earthquake-induced displacement field according to the seismic source theory in combination with a generic source time function. We apply the model to the nuclear waste repository site at Forsmark, Sweden, and analyse the coseismic responses of both single fractures and fracture networks during a potential post-glacial earthquake with a moment magnitude of Mw = 5.6. The shear dislocation of a single fracture is strongly dependent on the fracture length and dip angle, while the displacement pattern of a fracture network is dominated by its “backbone” structures. We observe that significant coseismic shear displacement occurs if the fractured rock is close to the hypocentre and located in the dilational quadrant of the primary fault due to reduced shear resistance. However, the earthquake-induced shear displacement decreases drastically with the increased distance to the hypocentre and a distance of ~700 m may be needed for a fracture up to 100 m long to not displace beyond 5 cm. If two repeated earthquakes would occur, a distance of ~1200 m may be necessary.
We propose a stochastic dynamical model to simulate slope secondary and tertiary creep phenomena. The slope secondary creep is represented by the Kesten process defined as a stochastic affine ...auto‐regressive process involving both multiplicative and additive random variables. The Kesten process can realistically capture the co‐existence of a background deformation and intermittent displacement bursts, which are together well characterized by an inverse gamma velocity distribution. The slope tertiary creep is modeled by a nonlinear stochastic dynamical equation embodying a nonlinear feedback mechanism and a nonlinear random effect, which can mimic the development of slow or catastrophic landslides. For catastrophic landslides, the probability density function of slope velocities tends to deviate from the inverse gamma distribution by populating the “dragon‐king” regime, although sometimes they may grow undetectably in the “black‐swan” regime. Our model provides a quantitative framework to understand, simulate, and interpret complex landslide displacement time series.
Plain Language Summary
Landslides that threaten life and property often exhibit complex temporal evolutions. Some landslides may creep slowly over a long period of time, while others can accelerate rapidly or even collapse catastrophically. It remains difficult to understand and/or predict their behavior. In this work, we develop a novel stochastic dynamical formulation that can realistically reproduce the displacement time series of landslides in natural systems. It can simulate the progressive deformation of a slowly creeping slope as well as mimic its rapid acceleration with/without catastrophic failure. The ever‐present fluctuations in natural systems can also be captured in this stochastic modeling framework. By conducting synthetic numerical simulations capable of resembling many of the observed essential features of real landslides, we develop quantitative insights into the mechanisms that drive their complex temporal evolutions. Recommendations for landslide hazard forecasting and mitigation are further provided.
Key Points
A slope approaching failure tends to exhibit a phase transition from secondary to tertiary creep
The stochastic Kesten process reproduces the phenomenology of intermittent bursts and inverse gamma velocity distribution of secondary creep
A nonlinear stochastic dynamical process captures the tertiary creep of a slope evolving into a slow or catastrophic landslide
Catastrophic landslides characterized by runaway slope failures remain difficult to predict. Here, we develop a physics‐based framework to prospectively assess slope failure potential. Our method ...builds upon the physics of extreme events in natural systems: the extremes so‐called “dragon‐kings” (e.g., slope tertiary creeps prior to failure) exhibit statistically different properties than other smaller‐sized events (e.g., slope secondary creeps). We develop statistical tools to detect the emergence of dragon‐kings during landslide evolution, with the secondary‐to‐tertiary creep transition quantitatively captured. We construct a phase diagram characterizing the detectability of dragon‐kings against “black‐swans” and informing on whether the slope evolves toward a catastrophic or slow landslide. We test our method on synthetic and real data sets, demonstrating how it might have been used to forecast three representative historical landslides. Our method can in principle considerably reduce the number of false alarms and identify with high confidence the presence of true hazards of catastrophic landslides.
Plain Language Summary
Catastrophic slope failures that pose great threats to life and property remain difficult to predict due to the strong variability of slope behavior. As a result, only a limited number of large rock slope failures have been so far successfully forecasted with associated risks mitigated. Here, we propose a novel predictive framework to prospectively and quantitatively detect slope failure precursors with high confidence. Our research sheds light on one of the most challenging questions in landslide prediction: Would an active landslide slowly move or catastrophically fail in the future? Our method adds a new conceptual framework and operational methodology with a significant potential to support existing early warning systems and hence reduce landslide risks.
Key Points
Tertiary creeps of catastrophic landslides accommodate dragon‐kings showing statistically different properties than secondary slope creeps
A predictive framework is developed to forecast catastrophic landslides by detecting signatures typical of the emergence of dragon‐kings
A phase diagram characterizes the detectability of dragon‐kings against black‐swans and discriminates catastrophic and slow landslides
We develop a new fully coupled thermo-hydro-mechanical (THM) model to investigate the combined effects of thermal perturbation and in-situ stress on heat transfer in two-dimensional fractured rocks. ...We quantitatively analyze the influence of geomechanical boundary constraints and initial reservoir temperature on the evolutionary behavior of fracture aperture, fluid flow and heat transfer, and further identify the underlying mechanisms dominating the coupled THM processes. The results reveal that, apart from enhancing normal opening of fractures, the transient cooling effect of thermal front may trigger shear dilations under the anisotropic in-situ stress condition. It is found that the applied in-situ stress tends to impose a strong impact on the spatial and temporal variations of fracture apertures and flow rates, and eventually affect heat transfer. The enhancement of reservoir transmissivity during transient cooling tends to be significantly overestimated if the in-situ stress effect is not incorporated, which may lead to unrealistic predictions of heat extraction performance. Our study also provides physical insights into a fundamental thermo-poroelastic behavior of fractured rocks, where fracture aperture evolution during heat extraction tends to be simultaneously governed by two mechanisms: (1) thermal expansion-induced local aperture enlargement and (2) thermal propagation-induced remote aperture variation (can either increase or decrease). The results from our study have important implications for optimizing heat extraction efficiency and managing seismic hazards during fluid injections in geothermal reservoirs.
The Gotthard Base Tunnel (GBT), constructed between 2000 and 2011, is a 57 km long and up to 2.5 km deep high-speed railway tunnel located in the Swiss Alps. Significant ground surface displacements ...reaching about 10 cm were observed during and after the tunnel construction. To gain a better understanding of the causal mechanism of such conspicuous ground deformations, we develop a three-dimensional (3D) fully-coupled hydro-mechanical model to simulate GBT-induced groundwater drainage, stress redistribution, rock mass consolidation, and fault zone deformation at the regional scale. First, we construct a geological model with topographical features, lithological units, and natural faults realistically represented. We constrain the material properties of fault zones and rock masses based on available extensive laboratory testing results and site characterisation datasets. We then simulate the tunnelling process over time, with the resulting coupled hydro-mechanical responses of faulted rock masses well captured and ground surface/subsurface displacements quantitatively analysed. The simulation results in general show a good agreement with the field monitoring data of ground surface displacement, subsurface tunnel settlement, and groundwater inflow into the tunnel. Our model indicates that ground surface displacements originate from GBT-induced water drainage and rock mass consolidation in the deep subsurface. Our results also show that the GBT construction could trigger faults to shear via drainage-induced pressure diffusion and poroelastic stressing. The research findings from our work have important implications for many groundwater drainage-related geoengineering activities such as underground excavation in alpine mountains and fluid withdrawal in subsurface reservoirs.
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•3D simulation captures tunnelling-induced groundwater flow and rock mass deformation.•The simulation explains ground subsidence in crystalline rock during deep tunnelling.•Drainage and consolidation in deep subsurface cause ground surface displacements.•Tunnelling-induced pressure diffusion and poroelastic stressing drive fault movement.
This paper studies the role of pre-existing fractures in the damage evolution around tunnel excavation in fractured rocks. The length distribution of natural fractures can be described by a power law ...model, whose exponent a defines the relative proportion of large and small fractures in the system. The larger a is, the higher proportion of small fractures is. A series of two-dimensional discrete fracture networks (DFNs) associated with different length exponent a and fracture intensity P21 is generated to represent various scenarios of distributed pre-existing fractures in the rock. The geomechanical behaviour of the fractured rock embedded with DFN geometry in response to isotropic/anisotropic in-situ stress conditions and excavation-induced perturbations is simulated using the hybrid finite-discrete element method (FEMDEM), which can capture the deformation of intact rocks, the interaction of matrix blocks, the displacement of natural fractures, and the propagation of new cracks. An excavation damaged zone (EDZ) develops around the man-made opening as a result of reactivation of pre-existing fractures and propagation of wing cracks. The simulation results show that when a is small, the system which is dominated by large fractures can remain stable after excavation given that P21 is not very high; however, intensive structurally-governed kinematic instability can occur if P21 is sufficiently high and the fracture spacing is much smaller than the tunnel size. With the increase of a, the system becomes more dominated by small fractures, and the EDZ is mainly created by the coalescence of small fractures near the tunnel boundary. The results of this study have important implications for designing stable underground openings for radioactive waste repositories as well as other engineering facilities that are intended to generate minimal damage in the host rock mass.
•Evolution of excavation damaged zone in fractured rocks is numerically simulated.•Effects of stresses and pre-existing fractures on EDZ characteristics are studied.•EDZ behaviour is affected by the relative proportion of large and small fractures.•A higher stress ratio leads to the generation of a larger EDZ in fractured rock.•Relative position of excavation to major large fractures affects EDZ properties.
The deformation and permeability of coal are largely affected by the presence and distribution of natural fractures such as cleats and bedding planes with orthogonal and abutting characteristics, ...resulting in distinct hydromechanical responses to stress loading during coal mining processes. In this research, a two-dimensional (2D) fracture network is constructed based on a real coal cleat trace data collected from the Fukang mine area, China. Realistic multi-stage stress loading is designed to sequentially mimic an initial equilibrium phase and a mining-induced perturbation phase involving an increase of axial stress and a decrease of confining stress. The geomechanical and hydrological behaviour of the fractured coal under various stress loading conditions is modelled using a finite element model, which can simulate the deformation of coal matrix, the shearing and dilatancy of coal cleats, the variation of cleat aperture induced by combined effects of closure/opening, and shear and tensile-induced damage. The influence of different excavation stress paths and directions of mining is further investigated. The simulation results illustrate correlated variations among the shear-induced cleat dilation, damage in coal matrix, and equivalent permeability of the fractured coal. Model results are compared with results of previous work based on conventional approaches in which natural fracture networks are not explicitly represented. In particular, the numerical model reproduces the evolution of equivalent permeability under the competing influence of the effective stress perpendicular to cleats and shear-induced cleat dilation and associated damage. Model results also indicate that coal mining at low stress rates is conducive to the stability of surrounding coal seams, and that coal mining in parallel to cleat directions is desirable. The research findings of this paper have important implications for efficient and safe exploitation of coal and coalbed methane resources.
The stability analysis of rock blocks on man-made excavation faces (e.g. tunnel, cavern, and slope) subject to seismic loads is an important issue in the field of rock engineering. This paper ...proposes a generalized block theory (GBT) by combining a pseudo-static method and the traditional block theory to evaluate the stability of blocky rock masses during earthquake activities. In our analysis, the basic safety factors are derived considering time-varying seismic loads to determine the stability of a rock block at each time step. Afterwards, two new parameters,
P
u
and
V
u
, are used to evaluate the seismic stability of a rock block, where
P
u
is the instability probability defined as the ratio of the time for the block becoming unstable to the total seismic loading time, and
V
u
is the probabilistic instability volume defined as
P
u
times the block volume. As for a blocky rock mass system, its probabilistic instability volume is the sum of
V
u
of all seismically unstable blocks and the instability probability is the ratio of its probabilistic instability volume and total volume of seismically unstable blocks. Through the simulation of a generic slope excavation, we observe that seismic loads significantly affect the stability and kinematics of a rock block during an earthquake. For a blocky rock mass, both
P
u
and
V
u
decay with the epicentral distance, in general following an inverse power law trend. Furthermore, it is found that the local site effect also has a strong influence on the slope stability under seismic loads.
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