Influence of heterogeneity on rock strength and stiffness using discrete element method and parallel bond model

The particulate discrete element method(DEM) can be employed to capture the response of rock,provided that appropriate bonding models are used to cement the particles to each other.Simulations of laboratory tests are important to establish the extent to which those models can capture realistic rock behaviors.Hitherto the focus in such comparison studies has either been on homogeneous specimens or use of two-dimensional(2D) models.In situ rock formations are often heterogeneous,thus exploring the ability of this type of models to capture heterogeneous material behavior is important to facilitate their use in design analysis.In situ stress states are basically three-dimensional(3D),and therefore it is important to develop 3D models for this purpose.This paper revisits an earlier experimental study on heterogeneous specimens,of which the relative proportions of weaker material(siltstone) and stronger,harder material(sandstone) were varied in a controlled manner.Using a 3D DEM model with the parallel bond model,virtual heterogeneous specimens were created.The overall responses in terms of variations in strength and stiffness with different percentages of weaker material(siltstone) were shown to agree with the experimental observations.There was also a good qualitative agreement in the failure patterns observed in the experiments and the simulations,suggesting that the DEM data enabled analysis of the initiation of localizations and micro fractures in the specimens.

Kekulé-based Valence Bond Model. I. The Ground-state Properties of Conjugated π-Systems

The Kekulé-based valence bond (VB) method, in which the VB model is solved using covalent Kekulé structures as basis functions, is justified in the present work. This method is demonstrated to provide satisfactory descriptions for resonance energies and bond lengths of benzenoid hydrocarbons, being in good agreement with SCF-MO and experimental results. In addition, an alternative way of discussing characters of localized substructures within a polycyclic benzenoid system is suggested based upon such simplified VB calculations. Finally, the symmetries of VB ground states for nonalternant conjugated systems are also illustrated to be obtainable through these calculations, presenting very useful information for understanding the chemical behaviors of some nonalternant conjugated molecules.

Kekulé-based Valence Bond Model. II. Diels-Alder Reactivity of Polycyclic Aromatic Hydrocarbons

The Kekulé-based valence bond (VB) method was employed to study the ground state properties of 52 polycyclic aromatic hydrocarbons. The reactivity indices defined upon our VB calculations were demonstrated to be capable of quantitatively interpreting the second order rate constants of the Diels-Alder reactions. The qualitative trends of the reactivities of many homologous series can be also explained based on the local aromaticity index defined in this work.

Theoretical Model of Transformation Superlastic Diffusion Bonding for Eutectoid Steel

Based on current theories of diffusion and creep cavity closure at high temperature, a theoretical analysis of phase transformation diffusion bonding for T8/T8 eutectoid steel is carried out. The diffusion bonding is mainly described as two-stage process: Ⅰ The interfacial cavity with shape change from diamond to cylinder.Ⅱ The radius of the cylindrical cavity are reduced and eliminated gradually. A new theoretical model is established for the process of transformation superplastic diffusion bonding (TSDB) on the basis of a theoretical model for isothermal superplastic diffusion. The model can predict the bonding quality which is affected by technological parameters, such as limit cycling temperature, the compressive stress, the numbers of thermal cycles and temperature cycling through the phase transformation in the thermal cycling and so on. Results show that the maximum temperature, the compressive stress, the numbers of thermal cycles and the rate of temperature changing speed in the thermal cycling have an important influence on TSDB process. Meanwhile, reasonable technological parameters chosen from theoretical analysis is in good agreement with those obtained from experimental results.

DEM investigation of weathered rocks using a novel bond contact model

The distinct element method（DEM） incorporated with a novel bond contact model was applied in this paper to shed light on the microscopic physical origin of macroscopic behaviors of weathered rock, and to achieve the changing laws of microscopic parameters from observed decaying properties of rocks during weathering. The changing laws of macroscopic mechanical properties of typical rocks were summarized based on the existing research achievements. Parametric simulations were then conducted to analyze the relationships between macroscopic and microscopic parameters, and to derive the changing laws of microscopic parameters for the DEM model. Equipped with the microscopic weathering laws, a series of DEM simulations of basic laboratory tests on weathered rock samples was performed in comparison with analytical solutions. The results reveal that the relationships between macroscopic and microscopic parameters of rocks against the weathering period can be successfully attained by parametric simulations. In addition, weathering has a significant impact on both stressestrain relationship and failure pattern of rocks.

Reducing the anisotropy of a Brazilian disc generated in a bonded-particle model

The Brazilian test is a widely used method for determining the tensile strength of rocks and for calibrating parameters in bondedparticle models（BPMs）. In previous studies, the Brazilian disc has typically been trimmed from a compacted rectangular specimen. The present study shows that different tensile strength values are obtained depending on the compressive loading direction. Several measures are proposed to reduce the anisotropy of the disc. The results reveal that the anisotropy of the disc is significantly influenced by the compactibility of the specimen from which it is trimmed. A new method is proposed in which the Brazilian disc is directly generated with a particle boundary, effectively reducing the anisotropy. The stiffness（particle and bond） and strength（bond） of the boundary are set at less than and greater than those of the disc assembly, respectively,which significantly decreases the stress concentration at the boundary contacts and prevents breakage of the boundary particle bonds. This leads to a significant reduction in the anisotropy of the disc and the discreteness of the tensile strength. This method is more suitable for carrying out a realistic Brazilian test for homogeneous rock-like material in the BPM.

Critical behaviours and magnetic properties of three-dimensional bond and anisotropy dilution Blume-Capel model in the presence of an applied field

This paper studies the critical behaviours and magnetic properties of three-dimensional bond and anisotropy dilution Blume-Capel model （BCM） in the presence of an applied field within the effective field theory. The trajectory of tricritical point, reentrant transitions and degenerate patterns of anisotropy are obtained both for the bond and the anisotropy dilutions. The global phase diagrams demonstrate unusually reentrant phenomena. The temperature dependences of magnetization curves undergo remarkable spin glass behaviour at low temperatures, and transform from ferromagnetism to paramagnetism at high temperature in applied fields. Temperature dependence of magnetic susceptibility curve is in qualitative agreement with experimental result.

A novel diffusion model considering curvature radius at the bonding interface in a titanium/steel explosive clad plate

This article introduces an element diffusion behavior model for a titanium/steel explosive clad plate characterized by a typical curved interface during the heat-treatment process. A series of heat-treatment experiments were conducted in the temperature range from 750℃ to 950℃, and the effects of heat-treatment parameters on the microstructural evolution and diffusion behavior were investigated by optical microscopy, scanning electron microscopy, X-ray diffraction analysis, and electron-probe microanalysis. Carbon atoms within the steel matrix were observed to diffuse toward the titanium matrix and to aggregate at the bonding interface at 850℃ or lower; in contrast, when the temperature exceeded 850℃, the mutual diffusion of Ti and Fe occurred, along with the diffusion of C atoms, resulting in the for- marion of Ti-Fe intermetallics （Fe2Ti/FeTi）. The diffusion distances of C, Ti, and Fe atoms increased with increasing heating temperature and/or holding time. On the basis of this diffusion behavior, a novel diffusion model was proposed. This model considers the effects of various factors, including the curvature radius of the curved interface, the diffusion coefficient, the heating temperature, and the holding rime. The experimental results show good agreement with the calculated values. The proposed model could clearly provide a general prediction of the elements＇ diffusion at both straight and curved interfaces.

A MULTISCALE MECHANICAL MODEL FOR MATERIALS BASED ON VIRTUAL INTERNAL BOND THEORY

Only two macroscopic parameters are needed to describe the mechanical properties of linear elastic solids, i.e. the Poisson＇s ratio and Young＇s modulus. Correspondingly, there should be two microscopic parameters to determine the mechanical properties of material if the macroscopic mechanical properties of linear elastic solids are derived from the microscopic level. Enlightened by this idea, a multiscale mechanical model for material, the virtual multi-dimensional internal bonds （VMIB） model, is proposed by incorporating a shear bond into the virtual internal bond （VIB） model. By this modification, the VMIB model associates the macro mechanical properties of material with the microscopic mechanical properties of discrete structure and the corresponding relationship between micro and macro parameters is derived. The tensor quality of the energy density function, which contains coordinate vector, is mathematically proved. From the point of view of VMIB, the macroscopic nonlinear behaviors of material could be attributed to the evolution of virtual bond distribution density induced by the imposed deformation. With this theoretical hypothesis, as an application example, a uniaxial compressive failure of brittle material is simulated. Good agreement between the experimental results and the simulated ones is found.

Integration of three-dimensional continuum model and two-dimensional bonded block model for studying the damage process in a granite pillar at the Creighton Mine,Sudbury,Canada

Bonded blockmodel(BBM)has shownpotential in replicating rockmass behavior aswell as the rockesupport interactionmechanism,but their practical application is limited totwo dimensions due to the high associated computational demand.To allow for the use of BBM in simulating three-dimensional(3D)problems,this study proposes an integrated 3D continuumetwo-dimensional(2D)discontinuum approach,in context of rock pillars.A cross-section of a granite pillar was simulated using a BBM with a load path from a calibrated mine-scale FLAC^(3D)model.Pillar support as employed in the mine was also incorporated in different stages during the simulation.Themodel was calibrated by varying the input parameters until the displacements at six locations within the pillarmatchedthosemeasuredby amulti-point borehole extensometer(MPBX)inthe field.The calibratedmodel was subsequently used to understand how the support and load path influenced the damage evolution in the pillar.The shear component of the load pathwas found to have amajor effect on the severity and extent of the damaged regions.When the support density was increased in the model,the lateral displacements along the pillar walls were significantly suppressed in a somewhat unpredictable manner.Thiswas explained by the interaction between the supports and the damaged regions at the corners,which ultimately modified the stresses along the pillar periphery.The amount of displacement reduction obtained by increasing the support density illustrates the potential of BBMto be used as a support design tool.

Universal critical properties of the Eulerian bond-cubic model

We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations, using an efficient cluster algorithm and a finite-size scaling analysis. The critical points and four critical exponents of the model are determined for several values of n. Two of the exponents are fractal dimensions, which are obtained numerically for the first time. Our results are consistent with the Coulomb gas predictions for the critical O（n） branch for n 〈 2 and the results obtained by previous transfer matrix calculations. For n = 2, we find that the thermal exponent, the magnetic exponent and the fractal dimension of the largest critical Eulerian bond component are different from those of the critical 0（2） loop model. These results confirm that the cubic anisotropy is marginal at n = 2 but irrelevant for n〈2.

Structural bonding-breakage constitutive model for natural unsaturated clayey soils

The natural clayey soils are usually structural and unsaturated,which makes their mechanical properties quite different from the remolded saturated soils.A structural constitutive model is proposed to simulate the bonding-breakage micro-mechanism.In this model,the unsaturated soil element is divided into a cementation element and a friction element according to the binary medium theory,and the stress-strain coordination for these two elements is obtained. The cementation element is regarded as elastic,whereas the friction element is regarded as elastoplastic which can be described with the Gallipoli＇s model.The theoretical formulation is verified with the comparative experiments of isotropic compressions on the saturated and unsaturated structural soils.Parametric analyses of the effects of damage variables on the model predictions are further carried out,which show that breakage deformation of natural clayey soils increases with the rising amount of initial defects.

Investigation of Highly Designable Dented Structures in HP Model with Hydrogen Bond Energy

Some highly designable protein structures have dented on the surface of their native structures, and are not full compactly folded. According to hydrophobic-polar （HP） model the most designable structures are full compactly folded. To investigate the designability of the dented structures, we introduce the hydrogen bond energy in the secondary structures by using the secondary-structure-favored HP model proposed by Ou-yang etc. The result shows that the average designability increases with the strength of the hydrogen bond. The designabilities of the structures with same dented shape increase exponentially with the number of secondary structure sites. The dented structures can have the highest designabilities for a certain value of hydrogen bond energy density.

Spectroscopic Characterization, Molecular Modeling and DFT/TD-DFT/PCM Calculations of Novel Hydrogen-Bonded Charge Transfer Complex between Chloranilic Acid and 2-Amino-4,6-Dimethylpyridine

A charge transfer hydrogen bonded complex between the electron donor (proton acceptor) 2-amino-4,6-dimethylpyridine with the electron acceptor (proton donor) chloranilic acid has been synthesized and studied experimentally and theoretically. The stability constant recorded high values indicating the high stability of the formed complex. In chloroform, ethanol, methanol and acetonitrile were found the stoichiometric ratio 1:1. The solid complex was prepared and characterized by different spectroscopy techniques. FTIR, 1H and 13C NMR studies supported the presence of proton and charge transfers in the formed complex. Complemented with experimental results, molecular modelling using the density functional theory (DFT) calculations was carried out in the gas, chloroform and methanol phases where the existence of charge and hydrogen transfers. Finally, a good consistency between experimental and theoretical calculations was found confirming that the applied basis set is the suitable one for the system under investigation.

A Study on Modifying the Calculation Model of Valid Opening Size of Heat-bonded Nonwoven Fabrics

It has been found that there are marked errors in the value of valid opening size of heat-bonded nonwoven fabrics between theoretical calculations and engineering measurements. A new modified theoretical model is advanced in this paper. The equivalent diameter of the pore of a fibre web is used to calculate the valid opening size instead of the maximum diameter of inscribed circle used, because the fibres in practical fibre webs are flexible elastomers with definite diameters and the pore of fibre web may produce deformation in screening teat and engineering usage. The results show that the theoretical calculations coincide well with the engineering measurements. This method offers a theoretical basis for computer simulation to the performance of filters of heatbonded nonwoven fabrics.

Numerical and experimental investigation on hydraulic-electric rock fragmentation of heterogeneous granite

Hydraulic-electric rock fragmentation(HERF)plays a significant role in improving the efficiency of high voltage pulse rock breaking.However,the underlying mechanism of HERF remains unclear.In this study,considering the heterogeneity of the rock,microscopic thermodynamic properties,and shockwave time domain waveforms,based on the shockwave model,digital imaging technology and the discrete element method,the cyclic loading numerical simulations of HERF is achieved by coupling electrical,thermal,and solid mechanics under different formation temperatures,confining pressure,initial peak voltage,electrode bit diameter,and loading times.Meanwhile,the HERF discharge system is conducive to the laboratory experiments with various electrical parameters and the resulting broken pits are numerically reconstructed to obtain the geometric parameters.The results show that,the completely broken area consists of powdery rock debris.In the pre-broken zone,the mineral cementation of the rock determines the transition of type CⅠcracks to type CⅡand type CⅢcracks.Furthermore,the peak pressure of the shockwave increased with initial peak voltage but decreased with electrode bit diameter,while the wave front time reduced.Moreover,increasing well depth,formation temperature and confining pressure augment and inhibit HERF,but once confining pressure surpassed the threshold of 60 MPa for 152.40,215.90,and 228.60 mm electrode bits,and 40 MPa for 309.88 mm electrode bits,HERF is promoted.Additionally,for the same kind of rock,the volume and width of the broken pit increase with higher initial peak voltage and rock fissures will promote HERF.Eventually,the electrode drill bit with a 215.90 mm diameter is more suitable for drilling pink granite.This research contributes to a better microscopic understanding of HERF and provides valuable insights for electrode bit selection,as well as the optimization of circuit parameters for HERF technology.

氯盐环境下UHPC-NC界面黏结性能试验研究

氯盐环境作为一种较为常见的化学侵蚀环境,研究其对超高性能混凝土(ultra-high performance concrete,UHPC)和普通混凝土(normal concrete,NC)界面耐久性能的影响对于UHPC加固混凝土结构和UHPC-NC组合结构的工程应用均具有重大的现实意义.基于此,通过在常规环境以及氯盐环境下的推出试验,获得了干湿循环次数(0次、25次、50次)、氯盐浸泡天数(0 d、50 d、100 d)及界面处理方式(钢丝刷刷毛、高压水射流冲毛、表面缓凝处理)对UHPC-NC界面黏结强度、界面黏结刚度及界面黏结滑移曲线的影响.结果表明:在100 d试验周期内,干湿循环及氯盐浸泡作用造成的界面黏结强度损失率不超过20%;氯盐环境作用时长的增加会导致界面黏结刚度的降低;随着界面粗糙度的增加,UHPC-NC试件的界面黏结强度以及界面黏结刚度均会增加;界面粗糙度的提高有助于界面抗氯盐侵蚀能力的提升.受到界面处理方法的影响,UHPC-NC试件经历干湿循环及氯盐浸泡后,荷载滑移曲线呈现2种不同的形式,分别对应光滑界面(钢丝刷刷毛界面)和其他界面(高压水射流冲毛界面和缓凝剂处理界面).各组试件的黏结滑移曲线在荷载到达峰值前趋于一致;荷载到达峰值后,前者存在荷载骤降段及持荷段,后者则随着滑移量的增加荷载不断降低.根据UHPC-NC黏结滑移曲线特征,提出了黏结滑移建议模型.

锚杆岩体界面载荷传递规律及锚固长度设计

为揭示巷道围岩锚固界面脱粘失效机理,量化锚杆支护设计参数,采用三线性粘结滑移模型进行理论分析,对轴向载荷作用下锚固脱粘失效全过程中,锚固段界面剪应力、锚杆轴力分布演化规律以及界面极限锚固力进行研究,根据锚固段长度不同,得到两种界面剪应力分布演化类型。研究结果表明:当锚固长度较短时,界面剪应力存在全长软化阶段;当锚固长度较长时,界面剪应力存在弹性-软化-滑移三段共存阶段。锚固粘结界面弹性段、软化段、摩擦段内的剪应力分别呈现双曲余弦函数衰减分布、余弦函数上升分布、均匀分布规律,锚杆轴力随界面剪应力分布演化呈现多种形态的衰减分布规律。根据锚固界面模型解析计算获得极限锚固力,当不考虑脱粘摩擦力时,极限锚固力随锚固长度的增加趋近于某一固定值;当考虑脱粘摩擦力时,增加锚固长度能够持续提高锚固界面安全系数。研究成果可为锚固机制分析、锚杆支护参数设计提供理论参考。

裂隙封护土遗址压力型锚固系统界面应力传递与承载性能解析方法

土遗址锚固工程中,压力型锚杆相比于全长黏结拉力型锚杆而言具有高承载力和耐易溶盐侵蚀的优势,但由于此类锚固系统传力机理尚不明确,导致其在实际工程中的应用受到严重制约.本文将遗址稳定体内锚固段分为弹性压缩段和黏结-滑移段两部分,分别基于线性弹簧和浆体/土体界面黏结-滑移强化型本构建立简化力学模型,对界面黏结-滑移全过程,即弹性阶段、弹性-强化阶段和强化阶段进行理论解析,推导了各阶段对应的位移、应变以及剪应力分布等计算公式,给出了压力型锚杆极限抗拔承载力解析解.结果表明,峰值载荷前载荷-位移曲线理论值与试验值吻合较好;弹性压缩段占比与锚固长度对载荷-位移关系的影响主要体现在弹性-强化阶段.参数敏感度分析表明,忽略弹性压缩段影响时,锚固长度与极限承载力线性相关;浆体弹性模量主要影响界面应力随载荷增加时的传递进程,对承载力影响有限;黏结-滑移模型的剪应力峰值对承载力有显著影响.该解析方法对土遗址压力型锚杆锚固系统传力过程分析具有良好适用性.

正交-响应面法在PBM细观参数标定中的应用

数值模拟作为研究岩石力学特性、再现细观裂纹演化的主要途径,已受到大量关注。现有的数值模拟参数标定方法主要为试错法及正交试验法,但二者都未能充分考虑细观参数交互作用的影响,模拟精度欠佳且宏观破坏形态与室内试验存在较大差异。因此,采用正交-响应面法相结合的数值分析方法,首先通过正交试验筛选出具有显著影响的平行黏结模型(PBM)细观参数,其次应用响应面法(RSM)研究其交互作用对模型试样宏观参量的影响规律,最后结合岩石宏观破坏形态提出一套PBM参数标定流程。结果表明:有效模量E*与刚度比k n/k s对弹性模量E影响显著;k n/k s、接触摩擦系数μ、最小颗粒半径R_(min)对泊松比ν影响显著;黏聚力c与法向黏结强度σc及其交互作用对单轴抗压强度UCS影响显著,应用响应面法计算分析得出的细观参数的模拟值与试验值误差绝对值小于7%,且二者应力应变曲线力学特征相似,宏观破坏形态相同,证明所提出的PBM细观参数标定流程具备科学性和可靠性。