Effects of weathering depth and thickness on rock failure:Experimental approach and particle flow code simulation

This study investigated the effects of weathering depth and thickness on the failure mechanisms of rock samples through experimental and numerical methods.The first configuration involved conducting artificial weathering on limestone using the freezing and thawing(F-T)for 40 cycles.The mechanical parameters of the samples were measured at the end of the 40th cycle.In the second configuration,a series of specimens underwent salt crystallization(S-C)tests for 20 cycles.Experimental results were validated using discrete element method(DEM).Next,the weathered limestone model with dimensions of 108 mm54 mm were prepared.The weathering layers were tested at four different thicknesses(i.e.2.5 mm,5 mm,7.5 mm,and 10 mm)and three different positions(at the surface,5 mm under the rock surface,and 10 mm under the rock surface).According to the results,weathering depth and thickness have a considerable effect on the failure process.The results also showed a correlation between the values of compressive strength and failure mechanisms associated with the weathering layer.The numerical results revealed that the tension crack was the dominant factor.Additionally,with increasing weathering thickness,Young's modulus,crack initiation stress,and final strength decreased in constant weathering depth.The results also demonstrated that the failure progress of the numerical models was similar to that observed in the laboratory.

Crack mechanism of ground fissures in loess layer of Fenwei Basin, China

The Fenwei Basin, covered by loess, experiences severe ground fissure disasters. These disasters disrupt the continuity of the loess and pose significant threats to engineering construction safety along transportation routes. Nevertheless, the crack characteristics and the influence zone of ground fissures in the loess layer remain inadequately investigated. To effectively prevent and control ground fissure disasters, physical model tests and the PFC(particle flow code) numerical simulation method are used to investigate the crack mechanism of buried ground fissures in the loess layer. The results show that there are two main cracks in the layer profile, which have a Y-shape morphology. As the dip angle of the preset cracks increased from 60° to 90°, the main deformation zone at the surface gradually shifted towards the footwall. The process of crack propagation from depth to surface is divided into five stages. Additionally, the results confirm the accuracy of the width of the rupture zone d2in the footwall calculated by the cantilever beam theory. These findings can offer theoretical guidance for determining the avoidance distance of ground fissures in loess regions, as well as for implementing disaster prevention and corresponding control measures for various stages of buried ground fissure propagation.

Heterogeneities of grain boundary contact for simulation of laboratoryscale mechanical behavior of granitic rocks

From a practical point of view,grain structure heterogeneities are key parameters that control the rock response and still remains a challenge to incorporate in a quantitative manner.One of the less discussed topics in the context of the grain-based model(GBM)in the particle flow code(PFC)is the contact heterogeneities and the appropriate contact model to mimic the grain boundary behavior.Generally,the smooth joint(SJ)model and linear parallel bond(LPB)model are used to simulate the grain boundary behavior.However,the literature does not document the suitability of different models for specific problems.Another challenge in implementing GBM in PFC is that only a single bonding parameter is used at the grain boundaries.The aim of this study is to investigate the responses of a laboratory-scale specimen with SJ and LPB models,considering grain boundary heterogeneous and homogeneous contact parameters.Uniaxial and biaxial compression tests are performed to calibrate the response of Creighton granite.The stressestrain curves,volumetric dilation,inter-crack(crack in the grain boundary),and intra-crack(crack within the grain)development,and failure patterns associated with different contact models are examined.It was found that both the SJ and LPB models can reproduce the pre-peak behavior observed for a granitic rock type.However,the LPB model is unable to reproduce the post-peak behavior.Due to the large interlocking effect originating from the balls in contact and the ball size in the LPB model,local dilation is induced at the grain boundaries.This overestimates the volumetric dilation and residual shear strength.The LPB model tends to result in discontinuous inter-cracks and stress localization in the rock specimen,resulting in fine fragments at the rock surface during failure.

PFC软件在建材矿山溜井落矿方面的模拟应用探讨

利用Itasca PFC(Particle Flow Code)软件对建材矿山的矿石溜井放矿过程进行模拟,通过对溜井内矿石运动模拟具体过程的详细分析,总结了矿石在溜井内的运动规律及其对井壁的冲击位置。通过模拟,优化溜井设计,提高溜井使用的安全性,减少对井壁的冲击损伤。并对利用PFC软件进行此类模拟的优势进行了探讨。

Particle flow code simulation of intact and fissured granitic rock samples

This study presents a calibration process of three-dimensional particle flow code(PFC3D)simulation of intact and fissured granite samples.First,laboratory stressestrain response from triaxial testing of intact and fissured granite samples is recalled.Then,PFC3D is introduced,with focus on the bonded particle models(BPM).After that,we present previous studies where intact rock is simulated by means of flatjoint approaches,and how improved accuracy was gained with the help of parametric studies.Then,models of the pre-fissured rock specimens were generated,including modeled fissures in the form of“smooth joint”type contacts.Finally,triaxial testing simulations of 1 t 2 and 2 t 3 jointed rock specimens were performed.Results show that both elastic behavior and the peak strength levels are closely matched,without any additional fine tuning of micro-mechanical parameters.Concerning the postfailure behavior,models reproduce the trends of decreasing dilation with increasing confinement and plasticity.However,the dilation values simulated are larger than those observed in practice.This is attributed to the difficulty in modeling some phenomena of fissured rock behaviors,such as rock piece corner crushing with dust production and interactions between newly formed shear bands or axial splitting cracks with pre-existing joints.

Failure mechanism and stability analysis of the Zhenggang landslide in Yunnan Province of China using 3D particle flow code simulation

Based on the principle of 3D particle flow code,a numerical landslide run-out model is presented to simulate the failure process of the Zhenggang landslide(in southwestern China) under the effect of water after a rainfall.The relationship between the micro-mechanical parameters and the macro-shear strength of the grain material is determined through numerical calibrations.Then the rainfall effect is considered in numerical simulations and rain-induced sliding processes are performed,which help us to discuss the mechanism of deformation and failure of this landslide together with field observations.It shows the Zhenggang landslide would most likely be activated in Zone I and would gain momentum in Zone II.In order to prevent the potential disaster,a tailing dam is advised to be designed about 175 m downstream from the current landslide boundary of Zone II.Verified by field observations,the presented landslide model can reflect the failure mechanism after rainfall.It can also provide a method to predict the potential disaster and draft disaster prevention measures.

Numerical investigation on permeability evolution behavior of rock by an improved flow-coupling algorithm in particle flow code

Permeability is a vital property of rock mass, which is highly affected by tectonic stress and human engineering activities. A comprehensive monitoring of pore pressure and flow rate distributions inside the rock mass is very important to elucidate the permeability evolution mechanisms, which is difficult to realize in laboratory, but easy to be achieved in numerical simulations. Therefore, the particle flow code （PFC）, a discrete element method, is used to simulate permeability behaviors of rock materials in this study. Owe to the limitation of the existed solid-fluid coupling algorithm in PFC, an improved flow-coupling algorithm is presented to better reflect the preferential flow in rock fractures. The comparative analysis is conducted between original and improved algorithm when simulating rock permeability evolution during triaxial compression, showing that the improved algorithm can better describe the experimental phenomenon. Furthermore, the evolution of pore pressure and flow rate distribution during the flow process are analyzed by using the improved algorithm. It is concluded that during the steady flow process in the fractured specimen, the pore pressure and flow rate both prefer transmitting through the fractures rather than rock matrix. Based on the results, fractures are divided into the following three types： I） fractures link to both the inlet and outlet, II） fractures only link to the inlet, and III） fractures only link to the outlet. The type I fracture is always the preferential propagating path for both the pore pressure and flow rate. For type II fractures, the pore pressure increases and then becomes steady. However, the flow rate increases first and begins to decrease after the flow reaches the stop end of the fracture and finally vanishes. There is no obvious pore pressure or flow rate concentration within type III fractures.

Mechanical Behavior of Polyurethane Polymer Materials under Triaxial Cyclic Loading:A Particle Flow Code Approach

Polyurethane polymer grouting materials were studied with conventional triaxial tests via the particle flow code in two dimensions（PFC^（2D）） method, and the simulation results agreed with the experimental data. The particle flow code method can simulate the mechanical properties of the polymer. The triaxial cyclic loading tests of the polymer material under different confining pressures were carried out via PFC^（2D） to analyze its mechanical performance. The PFC^（2D） simulation results show that the value of the elastic modulus of the polymer decreases slowly at first and fluctuated within a narrow range near the value of the peak strength; the cumulative plastic strain increases slowly at first and then increases rapidly; the peak strength and elastic modulus of polymer increase with the confining pressure; the PFC^（2D） method can be used to quantitatively evaluate the damage behavior of the polymer material and estimate the fatigue life of the materials under fatigue load based on the number and the location of micro-cracks. Thus, the PFC^（2D） method is an effective tool to study polymers.

Effect of curing time on the mesoscopic parameters of cemented paste backfill simulated using the particle flow code technique

Several special mechanical properties,such as dilatancy and compressibility,of cemented paste backfill(CPB)are controlled by its internal microstructure and evolution.The mesoscopic structure changes of CPB during the development process were investigated.On the basis of the scanning electron microscopy(SEM)and mechanical test results of CPB,the particle size information of CPB was extracted,and a two-dimensional particle flow code(PFC)model of CPB was established to analyze the evolution rule of mesoscopic parameters during CPB development.The embedded FISH language in PFC was used to develop a program for establishing a PFC model on the basis of the SEM results.The mesoscopic parameters of CPB samples at different curing times,such as coordination number(C_(n)),contact force chain,and rose diagram,were obtained by recording and loading and used to analyze the intrinsic relationship between mesoscopic parameter variations and macroscopic mechanical response during CPB development.It is of considerable significance to establish the physical model of CPB using the PFC to reveal the mesoscopic structure of CPB.

PTC: Full and Drift Particle Orbit Tracing Code for α Particles in Tokamak Plasmas

Fusion born α particle confinement is one of the most important issues in burning plasmas,such as ITER and CFETR.However,it is extremely complex due to the nonequilibrium characteristics,and multiple temporal and spatial scales coupling with background plasma.A numerical code using particle orbit tracing method(PTC)has been developed to study energetic particle confinement in tokamak plasmas.Both full orbit and drift orbit solvers are implemented to analyze the Larmor radius effects on α particle confinement.The elastic collisions between alpha particles and thermal plasma are calculated by a Monte Carlo method.A triangle mesh in poloidal section is generated for electromagnetic fields expression.Benchmark between PTC and ORBIT has been accomplished for verification.For CFETR burning plasmas,PTC code is used for α particle source and slowing down process calculation in 2D equilibrium.In future work,3D field like toroidal field ripples,Alfven and magnetohydrodynamics instabilities perturbation inducing α particle transport will be analyzed.

Shear mechanical properties and energy evolution of rock-like samples containing multiple combinations of non-persistent joints

Discontinuities are often considered as important factors responsible for the instability caused by shear failure in engineering rock mass,and energy-driven instability is the root cause of rock failure.However,few studies focus on the energy evolution during the failure process using a three-dimensional(3D)numerical model.In this study,a series of laboratory direct shear tests on rock-like samples is numer-ically simulated using bonded particle models(BPMs)with multiple combinations of discontinuous in the particle flow code(PFC3D),in which the location and size of the particles conform to the uniform distribution.The effects of joint row number and inclination on the stress-strain characteristics and failure mode of rock were studied from the perspective of microcrack growth and energy evolution.The results showed that,when the number of joint rows Nr>1,the shear failure region does not change with the increase of Nr for the type B(2-columnn multiple-row at center)and the type C(2-column multiple-row at edge)as compared to the type A(1-column multiple-row at center)joint models.Notably,joints significantly increase the post-peak energy dissipation but have little effect on the proportion of energy before the peak.Friction consumes most of the energy while kinetic energy accounts for less than 1%of total energy during the shear process.Peak elastic strain energy follows the variation trend of peak shear displacement.The development and accumulation of microcracks directly affect the energy dissipation,and there is a significant linear relationship between the cumulative number of critical microcracks and the critical dissipated energy at the failure,when the dip direction of joints is opposite to the shear direction,more microcracks will be accumulated at the peak time,resulting in more energy dissipation.The results contribute to deeply understanding the shear failure process of non-persistent jointed mass.

Dynamic behavior of rock during its post failure stage in SHPB tests

In order to investigate the micro-process and inner mechanism of rock failure under impact loading, the laboratory tests were carried out on an improved split Hopkinson pressure bar （SHPB） system with synchronized measurement devices including a high-speed camera and a dynamic strain meter. The experimental results show that the specimens were in the state of good stress equilibrium during the post failure stage even when visible cracks were forming in the specimens. Rock specimens broke into strips but still could bear the external stress and keep force balance. Meanwhile, numerical tests with particle flow code （PFC） revealed that the failure process of rocks can be described by the evolution of micro-fractures. Shear cracks emerged firstly and stopped developing when the external stress was not high enough. Tensile cracks, however, emerged when the rock specimen reached its peak strength and played an important role in controlling the ultimate failure during the post failure stage.

True triaxial hydraulic fracturing test and numerical simulation of limestone

Hydraulic fracturing,as a key technology of deep energy exploitation,accelerates the rapid development of the modern petroleum industry.To study the mechanisms of hydraulic fracture propagation and rock failure mode of the vertical well hydraulic fracturing,the true triaxial hydraulic fracturing test and numerical simulation are carried out,and the influence of the principal stress difference,water injection displacement,perforation angle and natural fracture on fracture propagation is analyzed.The results show that the fracture propagation mode of limestone is mainly divided into two types:the single vertical fracture and the transverse-longitudinal crossed complex fracture.Under high displacement,the fracturing pressure is larger,and the secondary fracture is more likely to occur,while variable displacement loading is more likely to induce fracture network.Meanwhile,the amplitude of acoustic emission(AE)waveform of limestone during fracturing is between 0.01 and 0.02 mV,and the main frequency is maintained in the range of 230−300 kHz.When perforation angleθ=45°,it is easy to produce the T-type fracture that connects with the natural fracture,while X-type cracks are generated whenθ=30°.The results can be used as a reference for further study on the mechanism of limestone hydraulic fracturing.

Calibration and uniqueness analysis of microparameters for DEM cohesive granular material

The differential evolution(DE)algorithm was deployed to calibrate microparameters of the DEM cohesive granular material.4 macroparameters,namely,uniaxial compressive strength,direct tensile strength,Young’s modulus and Poisson’s ratio,can be calibrated to high accuracy.The best calibration accuracy could reach the sum of relative errors RE_(sum)<0.1%.Most calibrations can be achieved with RE_(sum)<5%within hours or RE_(sum)<1%within 2 days.Based on the calibrated results,microparameters uniqueness analysis was carried out to reveal the correlation between microparameters and the macroscopic mechanical behaviour of material:(1)microparameters effective modulus,tensile strength and normal-to-shear stiffness ratio control the elastic behaviour and stable crack growth,(2)microparameters cohesion and friction angles present a negative linear correlation that controls the axial strain and lateral strain prior to the peak stress,and(3)microparameters friction coefficient controls shear crack friction and slip mainly refers to the unstable crack behaviour.Consideration of more macroparameters to regulate the material mechanical behaviour that is dominated by shear crack and slip motion is highlighted for future study.The DE calibration method is expected to serve as an alternative method to calibrate the DEM cohesive granular material to its peak strength.

Quantitative determination of PFC3D microscopic parameters

It is important to calibrate micro-parameters for applying partied flow code(PFC)to study mechanical characteristics and failure mechanism of rock materials.Uniform design method is firstly adopted to determine the microscopic parameters of parallel-bonded particle model for three-dimensional discrete element particle flow code(PFC3D).Variation ranges of microscopic of the microscopic parameters are created by analyzing the effects of microscopic parameters on macroscopic parameters(elastic modulus E,Poisson ratio v,uniaxial compressive strengthσc,and ratio of crack initial stress to uniaxial compressive strengthσci/σc)in order to obtain the actual uniform design talbe.The calculation equations of the microscopic and macroscopic parameters of rock materials can be established by the actual uniform design table and the regression analysis and thus the PFC3D microscopic parameters can be quantitatively determined.The PFC3D simulated results of the intact and pre-cracked rock specimens under uniaxial and triaxial compressions(including the macroscopic mechanical parameters,stress−strain curves and failure process)are in good agreement with experimental results,which can prove the validity of the calculation equations of microscopic and macroscopic parameters.

Failure behavior of horseshoe-shaped tunnel in hard rock under high stress:Phenomenon and mechanisms

A particle flow code(PFC) was first applied to examining the mechanical response of a horseshoe-shaped opening in prismatic rock models under biaxial compression. Next, an improved complex variable method was proposed to derive the stress distribution around the opening. Lastly, a case study of tunnel failure caused by rock burst in Jinping Ⅱ Hydropower Station was further analyzed and discussed. The results manifest that a total of four types of cracks occur around the opening under low lateral confining stress, namely, the primary-tensile cracks on the roof-floor, sidewall cracks on the sidewalls, secondary-tensile cracks on the corners and shear cracks along the diagonals. As the confining stress increases, the tensile cracks gradually disappear whilst the spalling failure becomes severe. Overall, the failure phenomenon of the modelled tunnel agrees well with that of the practical headrace tunnel, and the crack initiation mechanisms can be clearly clarified by the analytical stress distribution.

Study on mechanical properties of soil-rock mixture of various compactness subjected to freeze-thaw cycles

The soil-rock mixture,a collection of soil particles and rock blocks,is inherently heterogeneous and anisotropic due to significant particle size and material strength differences.This study conducts triaxial tests on soil-rock mixture samples of various compactness subjected to varying freeze-thaw cycles.A mesoscopic simulation is carried out by particle flow code(PFC)to analyze the effects of freeze-thaw cycles on the mechanical properties of soil and rock particles.The results show that the mechanical properties of the soil-rock mixture under freeze-thaw cycles are greatly affected by the initial compaction.In general,when the degree of compaction is higher,the influence of freeze-thaw cycles on the soil-rock mixture is greater.The stress-strain curves of the samples with different compactness demonstrate strain-softening behavior.The freeze-thaw cycles greatly influence the failure strength of the samples with a higher degree of compaction but have little impact on the samples with a lower degree of compaction.On the microscopic level,during freeze-thaw cycles,the pore volume in the highly compacted sample is too small to accommodate the volume expansion from ice crystal formation,causing significant strength loss among the soil and rock particles and deterioration of the macroscopic properties of the soil-rock mixture.

The biaxial compression mechanical properties of crushed rock

Crushed rock subgrade, as one of the roadbed-cooling methods, has been widely used in the Qinghai-Tibet Railway. Much attention has been paid on the cooling effect of crushed rock; however, the mechanical properties of crushed rock are somehow neglected. Based on the discrete element method, biaxial compression test condition for crushed rock is com- piled in FISH language in PFC2D, and the natural shape of crushed rock is simulated with super particle ＂cluster＂. The ef- fect of particle size, crushed rock strength and confining pressure level on overall mechanical properties of the crushed rock aggregate are respectively analyzed. Results show that crushed rock of large particle size plays an essential frame- work role, which is mainly responsible for the deformation of crushed rock aggregate. The strength of gravel has a great influence on overall mechanical properties which means that strength attenuation caused by the freeze thaw cycles cannot be ignored. The stress-strain curves can be divided into two stages including shear contraction and shear expansion at different confining pressures.

Mechanism of stress distribution and failure around two different shapes of openings within fractured rock-like materials

The complexity of a rock masses structure can lead to high uncertainties and risk during underground engineering construction.Laboratory tests on fractured rock-like materials containing a tunnel were conducted,and twodimensional particle flow models were established.The principal stress and principal strain distributions surrounding the four-arc-shaped and inverted U-shaped tunnels were investigated,respectively.Numerical results indicated that the dip angle combination of preexisting fractures directly affects the principal stress,principal strain distribution and the failure characteristics around the tunnel.The larger the absolute value of the preexisting fracture inclination angle,the higher the crushing degree of compression splitting near the hance and the larger the V-shaped failure zone.With a decrease in the absolute value of the preexisting fracture inclination angle,the compressive stress concentration of the sidewall with preexisting fractures gradually increases.The types of cracks initiated around the four-arc-shaped tunnel and the inverted U-shape tunnel are different.When the fractures are almost vertical,they have a significant influence on the stress of the sidewall force of the four-arc-shaped tunnel.When the fractures are almost horizontal,they have a significant influence on the stress of the sidewall of the inverted U-shaped tunnel.The findings provide a theoretical support for the local strengthening design of the tunnel supporting structure.

An elasto-plastic constitutive model incorporating strain softening and dilatancy for interface thin-layer element and its verification

The mechanical behaviors of the interface between coarse-grained soil and concrete were investigated by simple shear tests under condition of mixed soil slurry (bentonite mixed with cement grout).For comparison,the interfaces both without slurry and with bentonite slurry were analyzed.The experimental results show that different slurries exert much influence on the strength and deformation of soil/structure interface.Under mixed soil slurry,strain softening and shear dilatation are observed,while shear dilatation appears under the small normal stress of the interface without slurry,and shear contraction is significant under the condition of the bentonite slurry.The thickness of the interface was determined by analyzing the disturbed height of the sample with both simple shear test and particle flow code (PFC).An elasto-plastic constitutive model incorporating strain softening and dilatancy for thin layer element of interface was formulated in the framework of generalized potential theory.The relation curves of shear stress and shear strain,as well as the relation curves of normal strain and shear strain,were fitted by a piecewise function composed by hyperbolic functions and resembling normal functions.The entire model parameters can be identified by tests.The new model is verified by comparing the measured data of indoor cut-off wall model tests with the predictions from finite element method (FEM).The FEM results indicate that the stress of wall calculated by using Goodman element is too large,and the maximum deviation between the test data and prediction is about 45%.While the prediction from the proposed model is close to the measured data,and the error is generally less than 10%.