Effect of Block Size and Joint Geometry on Jointed Rock Hydraulics and REV

The effect of joint geometry parameters and the size of jointed rock block on the hydraulic properties of jointed rock, including the equivalent continuum behavior, was investigated through numerical experimentation. The chance to reach equivalent continuum behavior for a rock mass having a certain joint configuration increases with the increase of block size. The REV (representative elementary volume) size to show hydraulic equivalent continuum behavior for a jointed rock system was found to depend on the orientation of the joint sets; the REV size seems to decrease with increasing joint density and joint size. The REV does not seem to exist for some rock masses having joint systems with low relative orientation angles (systems with two joint sets) and low densities. The average block permeability (K0) value at the REV size for a joint system increases with increase in joint size and joint density. The equivalent continuum behavior of a joint system can be expressed with respect to a cut-off value for the first invariant of fracture tensor (F0). The block size corresponding to the aforementioned cut-off F0 (between 10 and 30 for the joint systems investigated in this study) can be considered to provide the REV size for a given joint configuration. A threshold value for F0 (a joint network having two perpendicular joint sets produced 2.75) can be used to find the chance for a given joint network to have nonzero block permeability. A strong power functional relation seems to exist between the directional permeability and the fracture tensor component for the connected joint configuration when rock blocks contain minor discontinuities.     

Crossed-Wire Laser Microwelding of Pt-10 Pct Ir to 316 Low-Carbon Vacuum Melted Stainless Steel: Part I. Mechanism of Joint Formation

The excellent biocompatibility and corrosion properties of Pt alloys and 316 low-carbon vacuum melted (LVM) stainless steel (SS) make them attractive for biomedical applications. With the increasing complexity of medical devices and in order to lower costs, the challenge of joining dissimilar materials arises. In this study, laser microwelding (LMW) of crossed Pt-10 pct Ir to 316 LVM SS wires was performed and the weldability of these materials was determined. The joint geometry, joining mechanism, joint breaking force (JBF), and fracture modes were investigated using optical microscopy, scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDX), and microtensile testing. It was shown that the mechanisms of joint formation transitioned from (1) brazing, (2) a combination of brazing and fusion welding, and (3) fusion welding with increasing pulsed laser energy. The joints demonstrated various tensile failure modes including (1) interfacial failure below a peak power of 0.24 kW, (2) partial interfacial failure that propagated into the Pt-Ir wire, (3) failure in the Pt-Ir wire, and (4) failure in the SS wire due to porosity and severe undercutting caused by overwelding. During this study, the optimal laser peak power range was identified to produce joints with good joint geometry and 90 pct of the tensile strength of the Pt-10 pct Ir wire.     

Deformation and failure of brazed joints—macroscopic considerations

Experimental data are presented on the influence of component yield strength and joint geometry on the mechanical behavior of transverse brazed joints. The systems studied were various iron alloys brazed with dilute silver alloys. From these data a model is developed for the deformation and ductile failure of brazed joints. In thick and thin joints, macroscopic plastic instability and hydrostatic tension respectively are the major causes of void growth and ductile fracture. Strain hardening in the braze metal is found to be an important factor in delaying fracture in both cases. Increases in the braze metal yield strength are accompanied by increases in the tensile strength of a brazed joint if the yield strength of the base metal exceeds the fracture strength of the joint. The loss of stress triaxiality which accompanies base metal yielding severely limits joint strength.     

Interface Behavior and Lap Shear Properties of the 7075-T6 Al FSLW Joint Using a Tip-Threaded Pin

For the purpose of reducing the hook and increasing the effective sheet thickness of the friction stir lap welding joint, a tip-threaded pin was used to weld 3 mm-thick 7075-T6 aluminum alloy in this work. Material flow behavior, joint formation mechanism and lap shear properties of the lap joints were mainly discussed. Results showed that when using the tip-threaded pin, lap joint with nearly aequilate stir zone (SZ) along thickness and rather flat hooks were obtained. When using high rotating speeds, the width of the lower SZ exceeded that of the middle SZ. A void, which resulted from the material loss near the lap interface, was observed at the same time. With increasing the rotating speed, the lap shear failure load of the joint initially increased and then decreased, while the fracture mode changed from tensile fracture to shear fracture mode. The maximum failure load of 17661 N was attained for the joint without void at 850 rpm.     

N型组合节理类岩体单轴压缩破坏试验

针对实际工程中平行与交叉裂隙组合呈N字形裂隙岩体的稳定性问题,以N型组合节理为研究对象,开展了N型节理类岩体试件超声波检测试验和单轴静载试验,结合断裂力学理论,分析其强度特征、破坏特征和超声波波速衰减规律。结果表明：（1）N型组合节理类岩体的裂纹类型依次有翼型裂纹和次生倾斜裂纹,其扩展路径最终均趋向于主应力方向,不同于单节理下的裂纹发展规律;（2）当主节理倾角一定时,主次节理夹角和节理条数对试件的物理性能有一定的影响。各组合节理试件的波速衰减率范围在0.9%～9.6%之间,且15°和90°夹角节理试件的波速衰减最快,而60°夹角节理试件的衰减最慢;（3）组合节理类岩体的本构关系、峰值强度和破坏特征均表现出非线性特征。峰值强度分布规律基本服从M型分布,不同于单节理下的U型分布,其中15°、30°、45°、75°和90°夹角试件,以及完整试件呈准脆性破坏,其他夹角试件呈脆性破坏。     

Characteristics of Welding Crack Defects and Failure Mode in Resistance Spot Welding of DP780 Steel

The mechanical properties of welded joints in resistance spot welding of DP780 steel were tested,and three dif-ferent types of welding cracks in welded joints were investigated by optical microscopy,scanning electron microscopy and electron back-scattered diffraction.Finally,the failure mode of the welded joints in shear tensile test was dis-cussed.It is found the shear tensile strength of welded joints can be greatly improved by adding preheating current or tempering current.The surface crack in welded joint is intergranular fracture,while the inner crack in welded joint is transgranular fracture,and the surface crack on the edge of the electrode imprint can be improved by adding prehea-ting current or tempering current.The traditional failure mode criterion advised by American Welding Society is no longer suitable for DP780 spot welds and the critical nugget size suggested by Pouranvari is overestimated.     

Practical Equivalent Continuum Model for Simulation of Jointed Rock Mass Using FLAC3D

A simple practical equivalent continuum numerical model for simulating the behavior of jointed rock mass has been extended to three-dimensional using FLAC3D. This model estimates the properties of jointed rock mass from the properties of intact rock and a joint factor (Jf), which is the integration of the properties of joints to take care of the effects of frequency, orientation, and strength of joint. A new FISH function has been written in FLAC3D specifically for modeling jointed rocks using the Duncan and Chang hyperbolic model. This model has been validated first with simple element tests at different confining pressures for different rocks with different joint configurations. Explicit modeling of the joints has also been done in element tests and results obtained compare well with the results of equivalent continuum model and also with experimental results. Further, this has been applied for a case study of a large underground power house cavern in the Himalayas. The analysis has been done under various stages of excavation, assigning a null model available in FLAC3D for simulating the excavation.     

Lateral Load Capacity of Drilled Shafts in Jointed Rock

Large vertical (axial) and lateral loads often act on the heads of drilled shafts in jointed rock. In current design practice, the p-y curve method used in design of laterally loaded drilled shafts in soil is often also used for shafts in jointed rock. The p-y curve method treats the soil as a continuum, which is not appropriate in jointed rock, particularly when failure occurs due to sliding on joints. A new discontinuum model was developed to determine the lateral load capacity of drilled shafts or piers in a jointed rock mass with two and three joint sets. It consists two parts: a kinematic and a kinetic analysis. In the kinematic analysis, Goodman and Shi’s block theory is expanded to analyze the removability of a combination of blocks laterally loaded by a pier. Based on the expanded theory, a method was developed to select removable combinations of blocks using easily constructed two-dimensional diagrams. In the kinetic analysis, each kinematically selected removable combination of blocks is examined with the limit equilibrium approach to determine the ultimate lateral load capacity. Although the procedure is similar to slope stability analysis, it is more complicated with the addition of a lateral force and the vertical load exerted by the pier. Simple analytical relations were developed to solve for the ultimate lateral load capacity.     

预制裂隙花岗岩的强度特征与破坏模式试验

为了探究单轴压缩条件下裂隙岩石的强度特性、裂纹起裂规律及破坏模式, 采用水刀切割技术预制裂隙花岗岩试件, 利用GAW2000刚性试验机对单裂隙花岗岩试样进行单轴压缩试验.试验结果表明: 与完整试样相比, 裂隙岩石试样单轴抗压强度明显降低, 降低幅度与预制裂隙和外荷载方向的夹角β密切相关, β=75°时, 强度最低, 降幅达到84.5%, 基于最大畸变能准则计算了裂隙花岗岩的峰值抗压强度与裂隙倾角的关系, 试验结果与数值解吻合; 裂隙的存在改变了岩石的破坏模式, 裂纹起裂角随裂隙倾角的增加而单调增大, 岩石试样的破坏模式由剪切破坏为主转变为张拉破坏占主导.真实裂隙岩石试样的力学性质及裂纹起裂特征更准确地揭示了单裂隙花岗岩的强度变化规律和破坏模式, 为岩土工程设计和巷道裂隙围岩体的支护提供科学依据.      

基于裂纹扩展模型的脆性岩石破裂特征及力学性能研究

为了探究初始微裂纹参数分布对岩石破裂特征及力学性能的影响,进一步系统地了解脆性岩石破裂演化过程,依据线弹性断裂力学理论,建立了非均质性二维细观弹性损伤模型,并运用FLAC^2D数值分析软件,数值模拟研究了单轴压缩条件下不同形态岩石试样的破裂过程。研究结果表明,当初始微裂纹长度和角度服从不同的随机分布时,岩石材料表现出不同的破裂特征,其中初始微裂纹长度和角度均服从正态分布时,岩石破裂区域较完整;初始微裂纹长度或角度服从均匀分布和指数分布时,岩石破裂区域较分散;初始微裂纹角度对于解释脆性岩石单轴抗压试验时岩石试样出现剪切破坏和劈裂破坏的原因具有一定的指导意义,且当初始微裂纹角度均值ɑ=45°时,模型具有最小的峰值强度和轴向最大应变。模型还模拟了脆性岩石单轴抗压试验、巴西劈裂试验和断裂韧度试验的演化过程,模拟结果与试验结果具有较高的一致性。     

Mechanical strength of thermally aged Sn-3.5Ag/Ni-P solder joints

This work presents an investigation on the influence of the solder/under bump metallization (UBM) interfacial reaction to the tensile strength and fracture behavior of Sn-3.5Ag/Ni-P solder joints under different thermal aging conditions. The tensile strength of Sn-3.5Ag/Ni-P solder joints decreases with aging temperature and duration. Four types of failure modes have been identified. The failure modes shift from the bulk solder failure mode in the as-soldered condition toward the interfacial failure modes. Kirkendall voids do not appear to affect the tensile strength of the joint. The volume change of Ni-P phase transformation during the thermal aging process generates high tensile stress inside the Ni-P layer; this stress causes mudflat cracks on the remaining Ni-P coating and also leads to its delamination from the underlying Ni substrate. In general, interfacial reaction and the subsequent growth of Ni₃Sn₄ intermetallic compound (IMC) layer during solid-state reaction are the main reasons for the decrease of tensile strength of the solder joints. The current study finds there is an empirical linear relation between the solder joint strength and the Ni₃Sn₄ intermetallic compound (IMC) thickness. Therefore, the IMC thickness may be used as an indication of the joint strength.     

Numerical Implementation of Anisotropic Continuum Model for Rock Masses

In this technical note, rock mass has been regarded as an equivalent anisotropic continuum. Constitutive relationships for the rock masses have been derived. The approach aims to capture the overall behavior of the rock mass based on the constitutive characteristics of intact rock and rock joints including their orientation, spacing, roughness (waviness), number of joint sets, block size, and normal and shear stiffness, etc. This model has been applied to analyze a tunnel using a software package developed for the purpose, with satisfactory results.     

Characterization of Strength and Deformation of Jointed Rock Mass Based on Statistical Analysis

This paper deals with the statistical analysis of the uniaxial compressive strength and of the elastic modulus of jointed rock masses under different confining pressures. Properties of the rock masses with different joint fabric, with and without gouge have been considered in the analysis. A large amount of experimental data of jointed rock masses from the literature has been compiled and used for this statistical analysis. The uniaxial compressive strength of a rock mass has been represented in a nondimensional form as the ratio of the compressive strength of the jointed rock to the intact rock. In the case of the elastic modulus, the ratio of elastic modulus of jointed rock to that of intact rock at different confining pressures is used in the analysis. The effect of the joints in the rock mass is taken into account by a joint factor. The joint factor is defined as a function of joint frequency, joint orientation, and joint strength. Several empirical relationships between the strength and deformation properties of jointed rock and the joint factor have been arrived at via statistical analysis of the experimental data. A comparative study of these relationships is presented. The effect of confining pressure on the elastic modulus of the jointed rock mass is also considered in the analysis. These empirical relationships are incorporated in a nonlinear FEM code to carryout the equivalent continuum analysis of jointed rock masses. The method presented in this paper recognizes that the jointed rock mass will act both as an elastic material and a discontinuous mass. The results obtained by the model with equivalent properties of the jointed rock mass predict fairly well the behavior of jointed rock mass.     

巴西圆盘劈裂二维及三维数值模拟研究

为揭示巴西圆盘起裂模式的变化规律及其破裂演化过程,运用连续介质弹塑性分析开展巴西圆盘劈裂二维及三维数值模拟研究。通过开展二维模拟研究,探究压拉比及加载角对试样起裂破坏模式的影响;通过三维模拟研究,探究圆盘试样三维破裂面的形成及扩展过程。二维数值模拟结果表明,接触加载角及压拉比越大,巴西圆盘试样越容易发生中心起裂;端部起裂由剪切破坏引起,而劈裂裂纹进一步扩展则由张拉破坏驱动。三维数值模拟结果表明,初始起裂点位于三维圆盘端面,随加载角增大其逐渐向端面圆心移动;当圆盘发生端面中心起裂时,三维破裂面以弧形边界向试样内部发散扩展。无论圆盘试样发生中心起裂还是端部起裂,由于三维效应巴西劈裂试验可能都会低估岩石的抗拉强度。      

Comparison between Models of Rock Discontinuity Strength and Deformation

One important component in the design of tunnels in urban areas is a correct assessment of the interaction between the underground excavation with other structures in the vicinity. In this sense a correct stress-strain response by the model representing the rock mass behavior is essential. The shear and normal displacement of rock discontinuities and their shear and normal stiffness control the distribution of stress and displacement within a discontinuous rock mass. In conditions where an equivalent continuum based approach is not applicable, the joint material model should be able to describe important mechanisms such as asperity sliding and shearing, post-peak behavior, asperity deformation, and the effect of soft infilling. The distinct element code UDEC was used to simulate the direct shear tests on a natural joint profile, and the prediction of two existing models of discontinuity strength and deformation were then compared with a new soil-infilled joint model and with experimental data for clean and soil-infilled rock joints. A numerical modeling of a cavern excavated in a jointed medium is also presented to illustrate the response of different models. The proposed soil-infilled joint model described more comprehensively the occurrence of dilation and compression with lateral displacements and also better represented the double peak shearing in relation to the adopted squeezing mechanism that could not be captured by the two existing models.     

Numerical Studies of Estimation of Fracture Parameters for Mismatched Welded Joints with HAZ Cracks

An idealized tri-material assumption is established to describe the constitutive relationship of mismatched welded joints by considering the influence of heat affected zone(HAZ).The fracture parameters Jand C*are estimated for mismatched welded joints with HAZ cracks by finite element analysis with ABAQUS.A middle crack tension(M(T))specimen is utilized in the analysis for different material properties and geometries of the weldment.The influence of mechanical property and geometry on the fracture parameters Jand C*of the specimen is discussed for the welded joints with HAZ crack.The results suggest that the HAZ property is a significant factor in the estimation of Jand C*for the mismatched welded joint with HAZ crack.     

New Approach for Modeling the Contribution of NSM FRP Strips for Shear Strengthening of RC Beams

This paper presents the main features of an analytical model recently developed to predict the near-surface mounted (NSM) fiber-reinforced polymer (FRP) strips shear strength contribution to a reinforced concrete (RC) beam throughout the beam’s loading process. It assumes that the possible failure modes that can affect the ultimate behavior of an NSM FRP strip comprise: loss of bond (debonding); concrete semiconical tensile fracture; mixed shallow-semicone-plus-debonding; and strip tensile fracture. That model was developed by fulfilling equilibrium, kinematic compatibility, and constitutive law of both the adhered materials and the bond between them. The debonding process of an NSM FRP strip to concrete was interpreted and closed-form equations were derived after proposing a new local bond stress-slip relationship. The model proposed also addressed complex phenomena such as the interaction between the force transferred to the surrounding concrete through bond stresses and concrete fracture as well as the interaction among adjacent strips. The main features of the proposed modeling strategy are shown along with the main underlying physical-mechanical concepts and assumptions. Using recent experimental data, the predictive performance of the model is assessed. The model is also applied to single out the influence of relevant parameters on the NSM technique effectiveness for the shear strengthening of RC beams.     

Homogenization of Masonry Using Numerical Simulations

Homogenization is one of the most important steps in the numerical analysis of masonry structures where the continuum method is used. In the present study, equivalent elastic properties, strength envelope, and different failure patterns of masonry material are homogenized by numerically simulating responses of a representative volume element (RVE) under different stress conditions. The RVE is modeled with distinctive consideration of the material properties of mortar and brick. In the numerical simulation, various displacement boundaries are applied on the RVE surfaces to derive the stress-strain relation under different conditions. The equivalent overall material properties of the RVE are averaged by integrating the stresses and strains over the entire area. Failure of masonry is defined by three different modes, namely, tensile failure of mortar (Mode I), shear failure of mortar or combined shear failure of brick and mortar (Mode II), and compressive failure of brick (Mode III). The homogenized elastic properties and failure model can be used to analyze large-scale masonry structures.     

一种块体–颗粒–杆件的耦合方法及其在隧道支护模拟中的应用

为了模拟隧道开挖过程中边帮的失稳垮塌过程以及锚杆对隧道的支护过程,提出了一种基于罚弹簧的块体–颗粒–杆件的耦合方法.该耦合方法基于连续–非连续的数值模拟方法(CDEM),采用离散颗粒簇表征隧道周边松动圈以内的破碎岩体,采用块体单元表征松动圈以外的完整岩体,采用杆件单元描述锚杆及锚索等杆系类支护结构,采用插值耦合的方式实现杆件单元与离散颗粒及块体单元间力与位移的传递,从而实现高应力环境下隧道开挖失稳过程的模拟及支护效果的评价.颗粒与块体之间采用1根法向线性弹簧及2根切向线性弹簧进行耦合,法向弹簧引入拉伸断裂本构,切向弹簧引入Mohr–Coulomb脆性断裂本构.杆件与颗粒及杆件与块体之间的耦合模式基本一致,包含1根沿着杆件轴向的罚弹簧S_gn及1根垂直于杆件轴向的罚弹簧S_gs,S_gn主要用于描述杆件与围岩之间的拉拔效应及推压效应,S_gs则主要用于描述杆件与围岩之间的侧向挤压效应.圆形盾构隧道弹性场分析、预应力锚杆加固矩形巷道模拟、全长连接锚杆对岩块的锚固作用分析、以及碎裂岩体中的隧道开挖支护效果分析等案...     

Development of New Peak Shear-Strength Criterion for Anisotropic Rock Joints

The roughness of a natural rock joint was measured in different directions using a laser profilometer. Two stationary roughness parameters and a nonstationary roughness parameter (all fractal based) were used to quantify anisotropic roughness. A plaster of Paris based model material was used to make model material replicas of the natural rock joint. Direct shear tests were performed at five different normal stresses, in each of the directions that were used for the roughness measurements, to measure the anisotropic peak shear strength of the model joint. Required observations and experiments were conducted to estimate (1) the asperity shear area as a proportion of the total surface area of the joint, for each tested joint; (2) the basic friction angle of the model material; and (3) the joint compressive strength. Tests were also conducted to develop a peak shear-strength criterion for the intact model material. Part of the direct shear test data was used to develop a new peak shear-strength criterion for joints including the aforementioned parameters. The other part of the data was used for model validation.