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In this study, we develop a coupled hydraulic fracturing model based on peridynamics, propose a contact-friction constitutive model, and establish a bond breaking criterion based on bond stress to explore hydraulic fracture propagation in jointed rock. Subsequently, we study the effects of fracturing fluid parameters (viscosity and pumping rate) on the fracture propagation behavior. Our results show that the viscosity of fracturing fluid can significantly affect the fracture morphology and propagation pattern. Fracturing fluid with higher viscosity is beneficial for the hydraulic fracture to cross natural fractures and continue to propagate in the original direction. The pumping rate mainly affects the fracture propagation speed and fracturing fluid pressure, but has limited influence on the fracture shape. Furthermore, the pumping rate has limited effect on the interaction between the hydraulic fracture and the natural fracture, but in general, lower pumping rate is conducive to the steady fracture propagation in jointed rock.

This paper presents a scale-up procedure of parameter estimation in the selection function and breakage function from single particle impact breakage to inform the predictions at the process scale of an impact pin mill. The selection and breakage functions used in population balance model (PBM) for particle breakage in the literature are briefly reviewed. Single particle breakage tests are conducted in a vertical impact tester subject to varying impact velocities. The single particle breakage results further serve to provide the database for the parameter estimation in Vogel and Peukert model (Vogel and Peukert, 2005). The estimated parameters in the particle level are upscaled in an impact pin mill using the population balance model, which is implemented in the software gPROMS (Process Systems Enterprise, UK) (gPROMS® 4.1 Release Notes, 2016). The impact milling tests were carried out in an impact pin mill UPZ100 subject to four feed rates, providing the dataset for model validation. The sensitivity analysis of the PBM parameters was conducted to help identify their leverage on the particle size distribution. The scale-up procedure by specifying the parameters from single particle level to the process level of PBM demonstrates an approach to help predict the size reduction process subject to the prevailing mechanism in an impact pin mill and other milling processes alike.

Due to the complexity of the interaction between hydraulic fractures (HFs) and natural fractures (NFs), several different interaction behaviours (arrest/cross/offset) may occur, according to hydraulic fracturing experiments. The existing analytical criteria cannot accurately describe this interaction process and predict the interaction behaviours by adopting several simple assumptions. An innovative numerical method combining strength and energy is proposed to determine the critical average stress at the most likely re-initiation position along the NF. The critical average stress for the HF crossing can be calculated by averaging the stresses around the fracture re-initiation point when the NF does not open and slip and simultaneously satisfying the energy criterion. Then, the proposed numerical method is incorporated in an extended finite element method (XFEM) scheme, in which the friction and contact of the NF are solved by a penalty function method. The numerical results suggest that the average stress can be numerically calculated and used to predict the HF crossing behaviour. The varying trends of the required maximum confining stress with respect to the coefficient of friction obtained by the proposed numerical method agree well with those predicted by the R-P and ER-P criteria. In addition, the proposed average stress method can quantitatively predict the crossing behaviour in the presence of slippage and opening after the HF terminates at the NF.

The pore structure of coal reservoirs determines the reserves of coalbed methane, and the gas permeability determines the level of the production capacity. In this study, the SEM images of coal samples were analyzed by various means. First, the grayscale threshold of binarization of the coal sample image is determined by a suitable algorithm. Comparing several different algorithms, the porosity based on Yen algorithm is closer to the results of vacuum saturation method and nuclear magnetic resonance (NMR) (8.35% vs. 7.51% vs. 8.92%). Further, the pore size distribution (PSD) of the coal sample is obtained according to discrete and continuous algorithms. By comparing the SEM results with the NMR results, it is found that the calculation results based on the continuous algorithm (CPSD) are better than the discrete algorithm (DPSD) and closer to the NMR results. For the effect of scale, we found that the image resolution has a certain influence on the minimum pore size characterized, such as sample C1: 0.29 μm ( × 1000) vs 0.58um ( × 500). At high resolution, more micro-pores are observed. Further, we predict the permeability of coal samples based on SEM images. It is found that the calculation results based on the continuous algorithm and the Hagen–Poiseuille equation are closer to the measured values (e.g., 16.97 (DPSD) vs. 0.45(CPSD) vs. 0.59 mD (Lab), sample C2, magnification of × 1000). In general, this method can effectively evaluate the pore structure characteristics and permeability of coal samples.

A novel computational methodology is proposed in this work to simulate the nonlinear hydro-mechanical process in saturated porous media containing crossing fractures. Specifically, the weak form of mechanical coupling and mass transfer equations is derived based on Biot’s theory and lubrication theory, respectively. The weak discontinuity for pressure field around T-shaped crack is described by a new junction enrichment function. The nonlinear hydro-mechanical coupled equations are obtained by Extended Finite Element Method (XFEM) discretization and solved by Newton-Raphson method. This proposed computational model is verified by comparing numerical results with analytical solution. The robustness of this numerical method is demonstrated by several examples. The effects of crack orientation, matrix stiffness, and confining stress on the equivalent permeability of fractured porous medium are investigated. Numerical results indicate that the interaction of cracks plays a critical role on the hydro-mechanical behavior of the saturated porous media containing crossing fractures.

Low-rank coal reserves account for nearly 55% of the national coal reserves in China, and it is extremely important to understand their anisotropic microstructure and coalbed methane storage and sorption characteristics. In this study, microstructures that develop parallel to and perpendicular to bedding of low-rank coals are studied through scanning electron microscopy. The micromorphology and microfracture and mineral distributions are examined. Based on fractal theory and digital image processing technology, the fractal box-counting dimensions of microfracture distributions that form parallel as well as perpendicular to the coal bedding planes are calculated, and the anisotropic fractal characteristics of these microfracture distributions are characterized. The pore-size distribution and the fractal characteristics of the microscopic pore structure are systematically examined by means of nitrogen adsorption and mercury intrusion tests. The results of the fractal box-counting dimension calculations indicate that microfractures distributed perpendicular to coal bedding are rougher and more irregular than those distributed along a bedding plane, with the former exhibiting higher space filling and methane adsorption capacity. The fractal dimension of the microscopic pore structure reveals two inflection points measuring approximately 5 and 80 nm, thereby indicating that the low-rank coal exhibits a microscopic pore structure with a three-level fractal characteristic.

Articulated design is considered an effective anti-fault measure to prevent damage to tunnel lining caused by fault movement. A new type of plastic concrete was developed for the Xianglu mountain tunnel of the water diversion project in Yunnan Province. The effectiveness of this concrete was verified by laboratory tests and numerical simulations. The mechanical characteristics of this new type of fibre plastic concrete were identified through mechanical testing. The optimal fibre volume fraction (around 0.2%) was obtained and could increase the compressive strength, splitting tensile strength, ductility and toughness without causing a significant decrease in the elastic modulus. The internal forces and plastic strain of the lining under the action of strike-slip faulting were analysed by using the finite element method. The role of fibre plastic concrete as a flexible joint material to accommodate bending and shear deformation was studied. The results showed that the plastic strain was mostly concentrated in the flexible joints, where the fibre plastic concrete with favourable ductility and toughness properties absorbed the deformation, protecting the rigid segments from complete destruction. The fibre plastic concrete maintained its considerable integrity and strength and would not suddenly droop when subjected to bending-shear and tensile-compressive loads due to the cementation between the PVA fibre and the matrix. The characteristics mentioned above would facilitate maintenance of the tunnel after an earthquake and can provide a reference for the engineering of other anti-faulting designs.

In this paper, a microscopic experimental investigation of the swelling–shrinkage behaviour of a hard clay subjected to wetting and drying (W–D) cycles is presented. Three W–D cycles with a range of relative humidity from 20 to 98% were performed on the hard clay sample through varying the temperature and the vapour pressure in an environmental scanning electron microscope (ESEM). The obtained ESEM images of the material at different hydric stages were analysed using a digital image correlation method, and full-field strains at the micrometre scale were quantified. The results show that the deformation of the material when subjected to W–D cycles is significantly heterogeneous and it is closely related to its microstructure. The different contributions of clay particles and of inclusions to swelling and shrinkage of the hard clay are revealed: the clay minerals swell, which is, however, constrained by the no-swelling inclusions; the interaction between the different phases is significant. A residual swelling is found at the end of the first W–D cycle. The residual swelling continues to accumulate during the second cycle but becomes stable for the third cycle. Further microstructural analysis shows that the irreversible swelling can be mainly attributed to the appearance and propagation of microcracks accompanied by a limited unrecoverable deformation of the clay minerals.

The stability of a fractured rock mass around a subsurface opening is critical to tunnel excavation. The traditional underground excavation analysis is based on a continuum description of randomly distributed discrete pre-existing fractures. In contrast to this, we have developed an improved hybrid finite element method (FEM) to investigate the stability of fractured rocks around an excavation by incorporating the outputs into the FEM codes. The proposed model consists of a discrete fracture network (DFN) model and cohesive zone model (CZM). The DFN model automatically generates a fracture network with a given fracture opening distribution and provides grid generation strategy to the FEM. The CZM captures material failure and intersection and surface contacts through the fracture element with different constitutive laws. As a case study, a DFN model was formulated for the underground excavation at Jinping Hydropower Station, in light of the input requirements of our model, and its deformation analysis was performed. The comparison analysis of rock deformation was made for excavation in both intact rock mass and fractured rock mass under the same boundary conditions. The numerical results show that two different modes of rock failure exist in these two rock masses and that intense deformation at the fractures intersected by the tunnel is responsible for fractured rock mass instability. The proposed approach was verified using data from field investigations. A larger displacement can be produced if the rock mass is weakened by a key block. A sensitivity analysis was carried out to investigate the effects of different model parameters on deformation variations. This study provides an insightful understanding of the deformation of fractured rock mass during tunnel excavation.

Foamed concrete has attracted increasing attention in civil engineering due to its unique properties. Permeability is one of the significant material properties that governs its long-term d...

Time-domain analyses have been widely used to investigate the seismic responses of tunnels. However, the earthquake-input mechanism which significantly influences the results, is not clearly understood, and most extant studies focused on vertically propagating waves. In this study, a series of numerical calculations were conducted to evaluate the performance of several earthquake-input methods for three typical models. The results demonstrate that the combinations of the model base and the input motion should correctly consider the interaction between the two sides of the boundary. Generally, the incident motion at the inner side of the boundary should be used with an elastic base, whereas the within motion at the boundary can be used with a rigid base. However, the rigid base is appropriate only for cases with a large impedance contrast between the two sides of the boundary and cases without outgoing waves at the boundary. Then, an earthquake-input method for the time-domain analysis of tunnels in layered ground subjected to obliquely incident P- and SV-waves was proposed. In this method, the pure incident motion at the model base is applied with an elastic base, whereas the within motions at the left boundary are applied with a rigid base. In addition, the right boundary is characterized by absorbing-elements. The closed-form solutions of the applied motions at the boundaries were presented. The proposed earthquake-input method was verified by comparing with closed-form solutions for two specific problems.

Understanding multiphase flow properties is essential for assessing and exploiting coals. These properties depend on the 3D pore space information, i.e. geometry and topology. However, determining the geometric and topological properties in coals are still challenging due to the complicated pore structures comprising several length scales. Studying pore scale structures in coals in a continuous range across over several length scales and integrating these information are necessary to increase the understanding of the role of pore structure on transport properties. Most of the current modeling methods are usually based on one or two experimental methods with limited and insufficient information. In this work, CO2 adsorption, N2 adsorption, MIP, X-ray µ-CT and FIB–SEM are used to study the pore structure characteristics of coal samples cored from the No. 9 coal seam of upper Permian Longtan formation at the Longfeng mine, China. The porosity, pore surface area, pore size distribution, connectivity and pore shapes measured by different methods are analyzed. We show that a combination of these techniques provides a richer picture of pore structure in coals. The obtained 3D pore structure can be applied to predict transport properties which are important to capture coal mine methane (CMM) and optimize field development. The results will also be helpful for the gas control in coal mines.

In-situ stress is one of the most important factors affecting the safety and stability of underground excavations. Past measurement results show that the magnitudes and directions of in- situ stresses vary substantially in different lithological formations. However, the relationship between stresses distribution and rock mechanical properties is still unclear. In this paper, the stress distribution in interbedded strong and weak layers was analytically studied based on linear elastic mechanics. Derived solutions were validated by comparison with Finite Element Method (FEM) results and field measurement results. Comparisons show that analytical results agree with the numerical results, and the maximum difference is less than 1%. The maximum difference between the analytical results and field measurements is 10.8%. Furthermore, the derived solution was used to evaluate the stress distribution in a geologically abnormal area in the Neelum-Jhelum (NJ) hydroplant project. Stress concentration state in strong layers changes as the strata change from sub-vertical to sub-horizontal, and the stress state in the sub-horizontal strata greatly favours rockburst according to the Turchaninov criterion. The change in stress concentration state might be the underlying reason for the severe rockburst in the abnormal structure area in the NJ project.

This paper addresses experimental and modeling investigations of heat transfer in sandstones subject to low-temperature conditions. At low temperature, pore liquid (e.g., water) would freeze; thus, heat is transferred not only in the form of specific heat but also in the form of latent heat. Moreover, the melting point is not constant; it depends on the pore size. Considering these characteristics, a governing equation of heat transfer with phase transition is established using the equivalent heat-capacity method. To calculate the equivalent heat capacity, the relation between ice content and temperature is assessed by the pore-size distribution curve. Heating tests (from 77 to 293 K) of sandstone samples in three saturation conditions (water-saturated, oil-saturated, and dry) are conducted and simulated using the model established. The results reveal that the temperature sensitivity of the heat capacity of dry sandstone is more pronounced in the low-temperature regime than in the high-temperature regime. The thermal conductivity of dry sandstone increases with temperature in the low-temperature regime. This is different with the case of the high-temperature regime at which the thermal conductivity decreases with temperature. The temperature evolution curve for the water-saturated sample features a plateau regime, that is, the temperature remains quasi-constant with time. The analysis demonstrates that the position and length of this temperature plateau are governed by the pore-size distribution.

The strengthening and isolation are two types of strategies to reduce seismic damages to tunnels in rock. However, few closed-form analytical solutions for their seismic responses when tunnels are subjected to SH waves have been proposed. Therefore, based on the Xianglu Mountain Tunnel in Western China, which is located in a very active seismic territory, a close-form analytical solution was presented for the scattering problem of SH waves by the strengthening layer-isolation layer-lining system using the wave-function expansion method. A parametric study was then conducted to study the effects of the isolation and strengthening layers on the dynamic responses of tunnels in rock. The results show that the isolation layer can remarkably reduce the stress in the lining, but at the same time may lead to an increase in rigid displacement; the strengthening layer can stabilize the rigid displacement and further reduce the stress in the lining, but this effect is limited by the construction technologies used in actual projects. For tunnels in high-intensity regions, the isolation layer may collaborate with the strengthening layer. Owing to the existence of the strengthening layer, a relatively large modulus and a relatively small thickness can be chosen for the isolation layer. As a result, the collaboration between the isolation and strengthening layers can not only effectively reduce the stress in the lining but also stabilize the rigid displacement.

A fully coupled extended finite element (XFEM) model is presented to investigate the effect of different well types (highly deviated and horizontal wells) on simultaneous growth of multiple fractures. The importance of the use of deviated wells is briefly described and the governing equations for multi-cluster hydraulic fracturing in a saturated porous media are stated. The weak forms of both stress equilibrium and fluid mass continuity equations are turned into a system of linear equations through XFEM-type enrichments in space and Newmark scheme in time, which are solved by Newton-Raphson iteration method. In addition, the secant method is employed to impose the pressure continuity and mass conservation conditions at the fracture-well intersections. A numerical example with considering the simultaneous propagation of four hydraulic fractures is first adopted to validate the proposed numerical model. Several examples are then employed to investigate the influence of operational parameter, deviation angle, fracture spacing, placement and number on final fracture patterns. Numerical results show that coefficient of variation in multiple fracture heights for high-angle well is lower than that for horizontal well for all fracture placements. The opposite growth directions for two neighboring fractures, partially arising from the height difference at fracture-well intersection points, can reduce the stress shadow effect, thus promoting uniform growth of multiple fractures. Those results potentially unveil the causes for higher oil and gas production rates measured after multi-cluster hydraulic fracturing along highly deviated wells.

Various investigations have been carried out on the hydro-mechanical behavior of geomaterials, but those of clayey rock are still limited. Among these existing studies, very few data are available related to the thermal effects, particularly the loading-unloading behavior of clayey rock at high temperatures. In this paper, undrained loading-unloading triaxial tests on undisturbed specimens of Boom Clay extracted from Mol, Belgium, were carried out with the aim to study (1) the influence of temperature and load path on the thermo-hydro-mechanical behavior of clayey rock, and (2) the formation mechanism of loading-unloading stress-strain hysteresis loops . The test results first revealed the stress paths–dependent stress-strain behavior of Boom Clay. The increase of initial mean effective stress p 0 ′ has a positive effect on the mechanical behavior of Boom Clay. Secondly, temperature elevation induced the strength weakening of Boom Clay even under loading-unloading conditions. Thirdly, the p 0 ′ and temperature had a bearing on the loading-unloading elastic modulus (defined as the peak-to-peak secant modulus of a hysteresis loop). Strain energy dissipation during the loading-unloading is then discussed from the perspective of thermodynamics. Finally, the study concludes that the stress-strain hysteresis loops for Boom Clay may be closely related to its high content of adsorbed water, and it may be driven by the combined effect of “friction resistance” and “viscous resistance.”

In this work, we proposed a hydraulic fracturing model for layered rock based on peridynamics and studied the mechanism of hydraulic fracturing in a layered rock mass, i.e., complex propagation behaviors at the interface such as crossing, kinking, bifurcation, and arrest. Furthermore, we explored the effects of stress difference, elastic modulus ratio, and interface dip angle on the propagation behavior of hydraulic fractures. We found that the stress difference has an important influence on the propagation of hydraulic fractures in a layered rock mass. When the hydraulic fracture design direction is perpendicular to the direction of the maximum principal stress in a layered rock mass, the fracture network will be induced.

Owing to its importance to rockslides in cold regions, the evolution of heaving pressure, which acts as a driving force for fracture propagation in freezing rocks, was studied using the extended finite element method . For the growth of a fracture, the compounds of migrating water and ice lens deliver pressure from volumetric expansion as water consolidates, which is characterized by an empirical rate law. Satisfying the fracture propagation condition at the fracture tip under a given mixture volume and fracture length can result in a critical pressure level that initiated fracture growth. First, the numerical snap-through solutions of the pressure were validated against previous experimental results. The increase in pressure seemed to be limited at the freezing stage. The realistic parameters used in the empirical law for volumetric expansion rates were determined by fitting the numerical results to the experimental results. Then, parametric studies on fracture growth speeds and pressure limits were performed. The fracture size, fracture toughness of the rock, and parameters of the empirical law had a substantial effect on the variation in heaving pressure and thin fracture aperture . When fracture growth was considered, the heaving pressure tended to decrease, and the fracture propagation speed gradually reduced to zero.

Water inrush from completely weathered granite has presented a significant challenge for tunnel construction, suggesting the urgency and importance of revealing the water inrush mechanism. In this ...

Shale swelling can cause a series of problems during the exploitation of shale gas. However, because of the complex fabric of shale, a thorough understanding of shale swelling has not been gained. In this work, an experimental multiscale approach is employed to characterize the swelling properties of a shale sample from Sichuan basin of China. Wetting/drying tests are performed by environmental scanning electron microscopy (ESEM), and deformation of the material is measured by analyzing the ESEM micrographs using digital image correlation (DIC) techniques. Investigations are conducted at three distinct scales, enabling the macroscopic behavior to be linked to the microscopic mechanisms (e.g., the role of inclusions, the behavior of clay particles). The macroscopic swelling of the tested shale is less than 2%. This limited swelling is mainly due to the presence of nonswelling inclusions as well as the low swelling capacity of the clay inside the shale. Microcracking is evidenced along both the wetting and ...

To study the influence of high temperature on the properties of foamed concrete, four densities of foamed concrete (300 kg/m 3 , 450 kg/m 3 , 600 kg/m 3 and 800 kg/m 3 ) were taken into account in a series of tests. The change laws of appearance, mass, compressive strength and elastic module at ambient temperature and after undergoing different high temperatures (200 °C, 400 °C and 600 °C) were presented. The results indicate that the appearances for all of four different densities were different. The cracks to be observed at the higher densities foamed concretes (i.e., 800 kg/m 3 and 600 kg/m 3 ). However, the pore connectivity and surface spalling phenomenon are easier to be observed at lower densities foamed concretes (i.e., 300 kg/m 3 and 450 kg/m 3 ). With temperature increasing, the density, compressive strength and elastic modulus became lower and lower for all samples, however some details are different. Furthermore, two predicting models to reflect the change laws of compressive strength and elastic modulus with different densities and temperatures are obtained and are verified by comparing the results with the experimental data and other proposed models in previous works.

This paper presents a case study of the countermeasures of water and mud inrush disasters in the Junchang Tunnel in Guangxi, China. This tunnel was constructed in a weathered granite formation, and four serious water and mud inrush disasters occurred during construction. The geological and hydrological conditions are first reviewed to understand their effects on the water and mud inrush disasters. Four potential causes of the serious water and mud inrush disasters in the Junchang Tunnel were proposed, including the poor stability of the completely weathered granite, the high groundwater level and large groundwater flow rate, insufficient pre-reinforcement of the surrounding rock and the disturbances caused by tunnel construction. Water-sealing and ground reinforcement measures were suggested before excavation to improve the stability of the surrounding rock and plug the water outflow channels, and full-face curtain grouting was considered as the first choice. Furthermore, several improvements, including the combined utilization of various grouting materials, supplementary grouting with steel pipes in collapsed boreholes and dynamically optimized grouting methods, were implemented to solve the serious water inflow and collapse problems experienced during the drilling and grouting work. A detailed curtain grouting scheme was proposed and applied in practice. A comprehensive evaluation based on inspection borehole investigations and P–Q–t analysis indicated that the curtain grouting method yielded satisfactory performance in water sealing and ground reinforcement. In addition, the groundwater level and settlement data collected in the field validated the effectiveness of the proposed countermeasures.

In this paper, the DDM numerical method is used to calculate the initiation pressure and initiation length of the circular wellbore, or the further elongated and non-elongated ‘dog-ear’ breakout wellbore under different sizes and different stress states. An analysis is made about the transfer of the fracture initiation point for the further elongated breakout wellbore and its possible impacts. The numerical results show that for small-size wellbore ((Rwσt2)/KIC2 6.4), the initiation fracture is dominated by tensile strength. There is only small difference between the initiation pressure of the ‘dog-ear’breakout wellbore and the circular wellbore. With further elongation of the ‘dog-ear’ wellbore or increase of the curvature radius around initiation point, the initiation pressure fracture along the direction of the maximum principal stress also increases in most cases. The further elongated ‘dog-ear’ wellbore causes the initiation point of the wellbore to deviate away from the direction of the maximum principal stress, and the existence of at least four initiation points tends to cause X-shaped fracture initiation around the wellbore, which may promote the further increase of the initiation pressure. The research in this paper provides a new possible version of multi-fracture initiation around wellbore and abnormally high initiation pressure during fracturing operation.

A coupled hydromechanical model based on peridynamics is proposed to simulate the hydraulic fracturing in a complex fracture network. The proposed method is validated by comparing the numerical results with the analytical and experimental solution. Then, the influence of the crustal stress distribution, the friction force acting on the natural fracture (NF) surface and the NF network on hydraulic fracture (HF) propagation are investigated. The simulation results reveal that the crustal stress ratio mainly affects the HF propagation direction. When HFs and NFs are connected, the induced stress caused by the opening of NFs deflects the propagation direction of new fractures. The friction force on NF surface is an important factor affecting the interaction between HFs and NFs.

Hydraulic fracture behaviours when a fracture reaches stratum interfaces and penetrates into adjacent layers are so complicated that they have not been well studied, particularly for three-dimensions. In this paper, cohesive zone theory (which controls the fracture propagation progress and describes the fluid characteristics when flowing within an open fracture channel and diffusing into permeable rock) is used to simulate hydraulic fracturing. Regarding the simulation method, the pore pressure nodes constraint method is introduced, and seven zero-thickness pore pressure cohesive element layers are built to simulate the initiation and propagation of hydraulic fractures by which the hydraulic fracture in a coal seam is able to propagate within stratum interfaces and even penetrate into adjacent layers. The actual propagation evolution of a crack underground could be presented as well. The hydraulic fracture morphological characteristics during the entire propagating process are analysed, and the damage evolution of the rock around the hydraulic fracture is studied based on linear damage theory. Combined with the injection pressure curve characteristics, the propagation trajectory of a ǂ-shaped hydraulic fracture is divided into seven stages, and the propagating process is described in detail for each stage. The initialization and propagation characteristics of a hydraulic fracture at different fluid injection rates are well studied.