Numerical simulation on the seismic performance of retrofitted masonry walls based on the combined finite-discrete element method

Due to the long construction life,improper design methods,brittle material properties and poor construction techniques,most existing masonry structures do not perform well during earthquakes.The retrofitting method using an external steel-meshed mortar layer is widely used to retrofit existing masonry buildings.Assessing the seismic performance of masonry walls reinforced by an external steel-meshed mortar layer reasonably and effectively is a difficult subject in the research field of masonry structures.Based on the combined finite-discrete elements method,the numerical models of retrofitted brick walls with four different masonry mortar strengths by an external mortar layer are established.The shear strength of mortar and the contact between the retrofitted mortar layer and the brick blocks are discussed in detail.The failure patterns and load-displacement curves of the retrofitted brick walls were obtained by applying low cycle reciprocating loads to the numerical model,and the bearing capacity and the failure mechanism of the retrofitted walls were obtained by comparing the failure patterns,ultimate bearing capacity,deformability and other aspects with the tests.This study provides a basis for improving the seismic strengthening design method of masonry structures and helps to better assess the seismic performance of masonry structures after retrofitting.

Characterizing the influence of stress-induced microcracks on the laboratory strength and fracture development in brittle rocks using a finite-discrete element method-micro discrete fracture network FDEM-μDFN approach

Heterogeneity is an inherent component of rock and may be present in different forms including mineralheterogeneity, geometrical heterogeneity, weak grain boundaries and micro-defects. Microcracks areusually observed in crystalline rocks in two forms： natural and stress-induced; the amount of stressinducedmicrocracking increases with depth and in-situ stress. Laboratory results indicate that thephysical properties of rocks such as strength, deformability, P-wave velocity and permeability areinfluenced by increase in microcrack intensity. In this study, the finite-discrete element method （FDEM）is used to model microcrack heterogeneity by introducing into a model sample sets of microcracks usingthe proposed micro discrete fracture network （mDFN） approach. The characteristics of the microcracksrequired to create mDFN models are obtained through image analyses of thin sections of Lac du Bonnetgranite adopted from published literature. A suite of two-dimensional laboratory tests including uniaxial,triaxial compression and Brazilian tests is simulated and the results are compared with laboratory data.The FDEM-mDFN models indicate that micro-heterogeneity has a profound influence on both the mechanicalbehavior and resultant fracture pattern. An increase in the microcrack intensity leads to areduction in the strength of the sample and changes the character of the rock strength envelope. Spallingand axial splitting dominate the failure mode at low confinement while shear failure is the dominantfailure mode at high confinement. Numerical results from simulated compression tests show thatmicrocracking reduces the cohesive component of strength alone, and the frictional strength componentremains unaffected. Results from simulated Brazilian tests show that the tensile strength is influenced bythe presence of microcracks, with a reduction in tensile strength as microcrack intensity increases. Theimportance of microcrack heterogeneity in reproducing a bi-linear or S-shape failure envelope and itseffects on the mechanisms leading to spalling damage near an underground opening are also discussed.

Assessment of strain bursting in deep tunnelling by using the finite-discrete element method

Rockbursting in deep tunnelling is a complex phenomenon posing significant challenges both at the design and construction stages of an underground excavation within hard rock masses and under high in situ stresses. While local experience, field monitoring, and informed data-rich analysis are some of the tools commonly used to manage the hazards and the associated risks, advanced numerical techniques based on discontinuum modelling have also shown potential in assisting in the assessment of rockbursting. In this study, the hybrid finite-discrete element method(FDEM) is employed to investigate the failure and fracturing processes, and the mechanisms of energy storage and rapid release resulting in bursting, as well as to assess its utility as part of the design process of underground excavations.Following the calibration of the numerical model to simulate a deep excavation in a hard, massive rock mass, discrete fracture network(DFN) geometries are integrated into the model in order to examine the impact of rock structure on rockbursting under high in situ stresses. The obtained analysis results not only highlight the importance of explicitly simulating pre-existing joints within the model, as they affect the mobilised failure mechanisms and the intensity of strain bursting phenomena, but also show how the employed joint network geometry, the field stress conditions, and their interaction influence the extent and depth of the excavation induced damage. Furthermore, a rigorous analysis of the mass and velocity of the ejected rock blocks and comparison of the obtained data with well-established semi-empirical approaches demonstrate the potential of the method to provide realistic estimates of the kinetic energy released during bursting for determining the energy support demand.

Space decomposition based parallelization solutions for the combined finiteediscrete element method in 2D

The combined finiteediscrete element method （FDEM） belongs to a family of methods of computationalmechanics of discontinua. The method is suitable for problems of discontinua, where particles aredeformable and can fracture or fragment. The applications of FDEM have spread over a number of disciplinesincluding rock mechanics, where problems like mining, mineral processing or rock blasting canbe solved by employing FDEM. In this work, a novel approach for the parallelization of two-dimensional（2D） FDEM aiming at clusters and desktop computers is developed. Dynamic domain decompositionbased parallelization solvers covering all aspects of FDEM have been developed. These have beenimplemented into the open source Y2D software package and have been tested on a PC cluster. Theoverall performance and scalability of the parallel code have been studied using numerical examples. Theresults obtained confirm the suitability of the parallel implementation for solving large scale problems. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Numerical simulation of hydraulic fracturing and associated microseismicity using finite-discrete element method

Hydraulic fracturing （HF） technique has been extensively used for the exploitation of unconventional oiland gas reservoirs. HF enhances the connectivity of less permeable oil and gas-bearing rock formationsby fluid injection, which creates an interconnected fracture network and increases the hydrocarbonproduction. Meanwhile, microseismic （MS） monitoring is one of the most effective approaches to evaluatesuch stimulation process. In this paper, the combined finite-discrete element method （FDEM） isadopted to numerically simulate HF and associated MS. Several post-processing tools, includingfrequency-magnitude distribution （b-value）, fractal dimension （D-value）, and seismic events clustering,are utilized to interpret numerical results. A non-parametric clustering algorithm designed specificallyfor FDEM is used to reduce the mesh dependency and extract more realistic seismic information.Simulation results indicated that at the local scale, the HF process tends to propagate following the rockmass discontinuities; while at the reservoir scale, it tends to develop in the direction parallel to themaximum in-situ stress. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

岩石类材料直接拉伸破坏的FDEM数值模拟

有限元-离散元耦合算法(FDEM)在岩石裂纹扩展模拟中广泛应用,尤其在直接拉伸模拟中用于参数校核。然而,模拟结果通常受到拉伸速率和网格尺寸的影响。本文首先阐述FDEM基本原理;然后,建立直接拉伸数值计算模型,探究拉伸速率、网格尺寸及高径比对破坏模式和力学参数的影响;最后,给出直接拉伸模拟中建议采用的拉伸速率和网格尺寸。研究结果表明:随着拉伸速率增加,试样抗拉强度、破坏程度和峰值应变率增加,而平均弹性模量减小;在较低拉伸速率下(v≤0.01 m/s),试样仅产生1条主拉伸裂缝;当拉伸速率较高时,有分支裂缝出现在主拉伸裂缝上侧。网格尺寸对抗拉强度、峰值应变率和平均弹性模量的影响较小,但对破坏模式和破坏程度的影响较显著。随着高径比增加,试样的抗拉强度、破坏程度和峰值应变率增大,但平均弹性模量呈相反趋势,并且高径比对破坏程度的影响较为显著。建议在直接拉伸模拟中使用0.01 m/s的拉伸速率,并将网格尺寸限制在1.5 mm以内。

GPGPU-parallelised hybrid finite-discrete element modelling of rock chipping and fragmentation process in mechanical cutting

Mechanical cutting provides one of the most flexible and environmentally friendly excavation methods.It has attracted numerous efforts to model the rock chipping and fragmentation process,especially using the explicit finite element method(FEM) and bonded particle model(BPM),in order to improve cutting efficiency.This study investigates the application of a general-purpose graphic-processing-unit parallelised hybrid finite-discrete element method(FDEM) which enjoys the advantages of both explicit FEM and BPM,in modelling the rock chipping and fragmentation process in the rock scratch test of mechanical rock cutting.The input parameters of FDEM are determined through a calibration procedure of modelling conventional Brazilian tensile and uniaxial compressive tests of limestone,A series of scratch tests with various cutting velocities,cutter rake angles and cutting depths is then modelled using FDEM with calibrated input parameters.A few cycles of cutter/rock interactions,including their engagement and detachment process,are modelled for each case,which is conducted for the first time to the best knowledge of the authors,thanks to the general purpose graphic processing units(GPGPU) parallelisation.The failure mechanism,cutting force,chipping morphology and effect of various factors on them are discussed on the basis of the modelled results.Finally,it is concluded that GPGPU-parallelised FDEM provides a powerful tool to further study rock cutting and improve cutting efficiencies since it can explicitly capture different fracture mechanisms contributing to the rock chipping as well as chip formation and the separation process in mechanical cutting.Moreover,it is concluded that chipping is mostly owed to the mix-mode Ⅰ-Ⅱ fracture in all cases although mode Ⅱ cracks and mode Ⅰ cracks are the dominant failures in rock cutting with shallow and deep cutting depths,respectively.The chip morphology is found to be a function of cutter velocdty,cutting depth and cutter rake angle.

Anisotropic shearing mechanism of Kangding slate:Experimental investigation and numerical analysis

The shear mechanical behavior is regarded as an essential factor affecting the stability of the surrounding rocks in underground engineering.The shear strength and failure mechanisms of layered rock are significantly affected by the foliation angles.Direct shear tests were conducted on cubic slate samples with foliation angles of 0°,30°,45°,60°,and 90°.The effect of foliation angles on failure patterns,acoustic emission(AE)characteristics,and shear strength parameters was analyzed.Based on AE characteristics,the slate failure process could be divided into four stages:quiet period,step-like increasing period,dramatic increasing period,and remission period.A new empirical expression of cohesion for layered rock was proposed,which was compared with linear and sinusoidal cohesion expressions based on the results made by this paper and previous experiments.The comparative analysis demonstrated that the new expression has better prediction ability than other expressions.The proposed empirical equation was used for direct shear simulations with the combined finite-discrete element method(FDEM),and it was found to align well with the experimental results.Considering both computational efficiency and accuracy,it was recommended to use a shear rate of 0.01 m/s for FDEM to carry out direct shear simulations.To balance the relationship between the number of elements and the simulation results in the direct shear simulations,the recommended element size is 1 mm.

Assessing fracturing mechanisms and evolution of excavation damaged zone of tunnels in interlocked rock masses at high stresses using a finitediscrete element approach

Deep underground excavations within hard rocks can result in damage to the surrounding rock mass mostly due to redistribution of stresses.Especially within rock masses with non-persistent joints,the role of the pre-existing joints in the damage evolution around the underground opening is of critical importance as they govern the fracturing mechanisms and influence the brittle responses of these hard rock masses under highly anisotropic in situ stresses.In this study,the main focus is the impact of joint network geometry,joint strength and applied field stresses on the rock mass behaviours and the evolution of excavation induced damage due to the loss of confinement as a tunnel face advances.Analysis of such a phenomenon was conducted using the finite-discrete element method (FDEM).The numerical model is initially calibrated in order to match the behaviour of the fracture-free,massive Lac du Bonnet granite during the excavation of the Underground Research Laboratory (URL) Test Tunnel,Canada.The influence of the pre-existing joints on the rock mass response during excavation is investigated by integrating discrete fracture networks (DFNs) of various characteristics into the numerical models under varying in situ stresses.The numerical results obtained highlight the significance of the pre-existing joints on the reduction of in situ rock mass strength and its capacity for extension with both factors controlling the brittle response of the material.Furthermore,the impact of spatial distribution of natural joints on the stability of an underground excavation is discussed,as well as the potentially minor influence of joint strength on the stress induced damage within joint systems of a non-persistent nature under specific conditions.Additionally,the in situ stress-joint network interaction is examined,revealing the complex fracturing mechanisms that may lead to uncontrolled fracture propagation that compromises the overall stability of an underground excavation.

Fracture development around deep underground excavations: Insights from FDEM modelling

Over the past twenty years, there has been a growing interest in the development of numerical modelsthat can realistically capture the progressive failure of rock masses. In particular, the investigation ofdamage development around underground excavations represents a key issue in several rock engineeringapplications, including tunnelling, mining, drilling, hydroelectric power generation, and the deepgeological disposal of nuclear waste. The goal of this paper is to show the effectiveness of a hybrid finitediscreteelement method （FDEM） code to simulate the fracturing mechanisms associated with theexcavation of underground openings in brittle rock formations. A brief review of the current state-of-theartmodelling approaches is initially provided, including the description of selecting continuum- anddiscontinuum-based techniques. Then, the influence of a number of factors, including mechanical and insitu stress anisotropy, as well as excavation geometry, on the simulated damage is analysed for threedifferent geomechanical scenarios. Firstly, the fracture nucleation and growth process under isotropicrock mass conditions is simulated for a circular shaft. Secondly, the influence of mechanical anisotropy onthe development of an excavation damaged zone （EDZ） around a tunnel excavated in a layered rockformation is considered. Finally, the interaction mechanisms between two large caverns of an undergroundhydroelectric power station are investigated, with particular emphasis on the rock mass responsesensitivity to the pillar width and excavation sequence. Overall, the numerical results indicate that FDEMsimulations can provide unique geomechanical insights in cases where an explicit consideration offracture and fragmentation processes is of paramount importance. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

New approaches to quantify progressive damage and associated dynamic rock mass blockiness

In the past decade, numerical modelling has been increasingly used for simulating the mechanical behaviour of naturally fractured rock masses. In this paper, we introduce new algorithms for spatial and temporal analyses of newly generated fractures and blocks using an integrated discrete fracture network (DFN)-finite-discrete element method (FDEM) (DFN-FDEM) modelling approach. A fracture line calculator and analysis technique (i.e. discrete element method (DEM) fracture analysis, DEMFA) calculates the geometrical aspects of induced fractures using a dilation criterion. The resultant two-dimensional (2D) blocks are then identified and characterised using a graph structure. Block tracking trees allow track of newly generated blocks across timesteps and to analyse progressive breakage of these blocks into smaller blocks. Fracture statistics (number and total length of initial and induced fractures) are then related to the block forming processes to investigate damage evolution. The combination of various proposed methodologies together across various stages of modelling processes provides new insights to investigate the dependency of structure's resistance on the initial fracture configuration.

A review of discrete modeling techniques for fracturing processes in discontinuous rock masses

The goal of this review paper is to provide a summary of selected discrete element and hybrid finitediscrete element modeling techniques that have emerged in the field of rock mechanics as simulation tools for fracturing processes in rocks and rock masses. The fundamental principles of each computer code are illustrated with particular emphasis on the approach specifically adopted to simulate fracture nucleation and propagation and to account for the presence of rock mass discontinuities. This description is accompanied by a brief review of application studies focusing on laboratory-scale models of rock failure processes and on the simulation of damage development around underground excavations.

Numerical Simulation of Interaction Between Laminar Flow and Elastic Sheet

A numerical simulation of the interaction between laminar flow with low Reynolds number and a highly flexible elastic sheet is presented. The mathematical model for the simulation includes a three-dimensional finitevolume based fluid solver for incompressible viscous flow and a combined finite-discrete element method for the three-dimensional deformation of solid. An immersed boundary method is used to couple the simulation of fluid and solid. It is implemented through a set of immersed boundary points scattered on the solid surface. These points provide a deformable solid wall boundary for the fluid by adding body force to Navier-Stokes equations. The force from the fluid is also obtained for each point and then applied on the boundary nodes of the solid. The vortex-induced vibration of the highly flexible elastic sheet is simulated with the established mathematical model. The simulated results for both swing pattern and oscillation frequency of the elastic sheet in low Reynolds number flow agree well with experimental data.

基于3D打印和FDEM算法的层状岩体力学特性研究

为探究层状岩体的强度和变形破坏特征随层理倾角和试样尺寸等因素的变化规律,利用粉末黏结成型3D打印技术制作涵盖多种倾角和尺寸的层理试样,并开展单轴压缩和巴西劈裂试验,利用有限元-离散元耦合算法(FDEM)对室内试验结果进行验证。研究结果表明:(1)抗压强度、弹性模量和变形模量随层理倾角呈“U”型变化,倾角90°试样的测试结果明显大于其他角度的;抗拉强度与层理倾角呈负相关关系,倾角0°试样的抗拉强度明显小于均质试样。(2)单轴压缩试样呈现张拉主导型(0°和90°)和剪切主导型破坏(5°和67.5°);随着层理倾角的逐渐增大,试样逐渐由延性破坏过渡到脆性破坏;巴西劈裂试样均呈现张拉破坏,裂隙走向呈直线型(0°和90°)和弧线型(45°)。(3)随着试样尺寸的逐渐增大,抗压强度逐渐趋于稳定,峰值应变逐渐减小并稳定在0.005左右;抗拉强度随试样尺寸呈倒“U”型变化,弹性模量和变形模量随试样尺寸在2.1 GPa附近波动,三者均未呈现稳定趋势。

北山花岗岩细观非均质性对单轴压缩力学特性影响的FDEM数值研究

为了研究细观非均质性对北山花岗岩中微裂纹萌生、扩展和贯通等破裂过程的影响,基于有限元/离散元耦合方法(FDEM)和数字图像处理技术(DIP),结合矿物晶体模型(GBM),分别构建3类北山花岗岩细观结构表征模型:聚类均布模型、Voronoi颗粒模型和聚类镶嵌模型。基于3类模型开展了单轴压缩试验研究,探究细观非均质性对北山花岗岩力学特性、声发射(AE)特征以及颗粒尺度裂纹扩展规律的影响。研究结果表明:3类模型均能捕获从微破裂损伤至宏观破裂的演化过程,即首先以晶间张拉裂纹为主,随后产生穿晶断裂,转变为以晶内裂纹为主,张拉破坏占主导地位;细观结构表征方式对模拟岩石的特征应力(启裂应力和损伤应力)控制效应非常显著;Voronoi颗粒模型和聚类镶嵌模型的AE特征与室内试验更为吻合;硬矿物含量的增大,会导致单轴抗压强度、特征应力和弹性模量增大,而泊松比反之;颗粒尺寸的增大,会导致单轴抗压强度和损伤应力明显减小;特征应力与刚度非均质性因子呈负相关。