Multi-domain equivalent method for prediction of elastic modulus of complex fractured rock mass

Reliable estimation of deformation and failure behaviors of fractured rock mass is important for practical engineering design.This study proposes a multi-domain equivalent method for fracture network to estimate the deformation properties of complex fractured rock mass.It comprehends both the advantages of the discrete fracture network model and the equivalent continuum model to capture the features of discontinuities explicitly while reducing computational intensity.The complex fracture network is stochastically split into a number of subfracture networks according to the domain,length or angle.An analytical solution is derived to infer theoretically the relationship between the elastic moduli of the original complex fractured rock mass and the split subfractured rock masses by introducing a correction term based on the deformation superposition principle.Numerical simulations are conducted to determine the elastic moduli of split subfractured rock masses using universal distinct element code(UDEC),while the elastic modulus of the original model is estimated based on the currently proposed analytical relationship.The results show that the estimation accuracy with the current domainbased splitting model is far superior compared to those with the other two splitting models.Thus,the estimation method of elastic modulus of complex fractured rock mass based on domain splitting mode of fracture network is identified as the multi-domain equivalent method proposed in this paper.The reliability of this method is evaluated,and its high computational efficiency is demonstrated through exemplification with regard to different geometric configurations for stochastically artificial discrete fracture network.The proposed multi-domain equivalent method constructs the theoretical framework except for the regression analysis hypothesis compared to the density-reduced model equivalent method.

Macro and meso analysis of jointed rock mass triaxial compression test by using equivalent rock mass(ERM) technique

Methods that can efficiently model the effects of rock joints on rock mass behavior can be beneficial in rock engineering. The suitability of equivalent rock mass(ERM) technique based upon particle methods is investigated. The ERM methodology is first validated by comparing calculated and experimental data of lab triaxial compression test on a set of cylindrical rock mass samples, each containing a single joint oriented in various dip angles. The simulated results are then used to study the stress-strain nonlinearity and failure mechanism as a function of the joint dip angle and confining stress. The anisotropy and size effects are also investigated by using multi-scale cubic ERM models subjected to triaxial compression test. The deformation and failure behavior are found to be influenced by joint degradation, the micro-crack formation in the intact rock, the interaction between two joints, and the interactions of micro-cracks and joints.

Impact of the equivalent center of mass separating from the sliding surface on the isolation performance of friction pendulum bearings

A new equivalent center of mass model of FPBs (friction pendulum bearings) is introduced, and based on this model, coefficient j of the equivalent center of mass separating from the sliding surface is defined. It is thought in theory that j has a significant impact on the isolation parameter of FPBs, since the equivalent post-yielding stiffness and friction coefficients are not simply determined by sliding radius and sliding friction pairs. The results of numerical simulation analysis using ABAQUS conducted on two groups of FPBs support this viewpoint. For FPBs with the same sliding radius and sliding friction pairs, the FPB modules of structural analysis software such as ETABS could only distinguish the equivalent transformation using j one by one. The seismic response data obtained in a base isolation calculation example of FPBs are very different, which reveals that j’s impact on the isolation effectiveness of FPBs cannot be ignored. The introduction of j will help improve the classical structural theory of FPBs and the weak points of structural analysis software based on this theory, which is important in achieving more accurate analyses in structural design.

An analytical solution of equivalent elastic modulus considering confining stress and its variables sensitivity analysis for fractured rock masses

The equivalent elastic modulus is a parameter for controlling the deformation behavior of fractured rock masses in the equivalent continuum approach.The confining stress,whose effect on the equivalent elastic modulus is of great importance,is the fundamental stress environment of natural rock masses.This paper employs an analytical approach to obtain the equivalent elastic modulus of fractured rock masses containing random discrete fractures(RDFs)or regular fracture sets(RFSs)while considering the confining stress.The proposed analytical solution considers not only the elastic properties of the intact rocks and fractures,but also the geometrical structure of the fractures and the confining stress.The performance of the analytical solution is verified by comparing it with the results of numerical tests obtained using the three-dimensional distinct element code(3DEC),leading to a reasonably good agreement.The analytical solution quantitatively demonstrates that the equivalent elastic modulus increases substantially with an increase in confining stress,i.e.it is characterized by stress-dependency.Further,a sensitivity analysis of the variables in the analytical solution is conducted using a global sensitivity analysis approach,i.e.the extended Fourier amplitude sensitivity test(EFAST).The variations in the sensitivity indices for different ranges and distribution types of the variables are investigated.The results provide an in-depth understanding of the influence of the variables on the equivalent elastic modulus from different perspectives.

RESEARCH ON EQUIVALENT PROCESSES OF ROCK MASS PARAMETERS WITH ANCHOR PILES

Using normal and shear rigid coefficients of intact rock and fracture plane, rigidly normal, shear equivalent rigid coefficients of fissure rock mass are conducted. On the basis of hypotheses of small displacement of rock mass, principle of superposition, irrelevance of strength parameters C and T and Coulomb theory, formulas to calculate equivalent strength parameters C and phi of equivalent continuous mass from fissured rock mass with anchor piles are given. The achievement is extremely valuable in integral stability analysis of the rock mass slope and important in promoting the research of the rock mass's constitutive relation.

Effects of fracture distribution and length scale on the equivalent continuum elastic compliance of fractured rock masses

Fracture systems have strong influence on the overall mechanical behavior of fractured rock masses dueto their relatively lower stiffness and shear strength than those of the rock matrix. Understanding theeffects of fracture geometrical distribution, such as length, spacing, persistence and orientation, isimportant for quantifying the mechanical behavior of fractured rock masses. The relation betweenfracture geometry and the mechanical characteristics of the fractured rock mass is complicated due tothe fact that the fracture geometry and mechanical behaviors of fractured rock mass are stronglydependent on the length scale. In this paper, a comprehensive study was conducted to determine theeffects of fracture distribution on the equivalent continuum elastic compliance of fractured rock massesover a wide range of fracture lengths. To account for the stochastic nature of fracture distributions, threedifferent simulation techniques involving Oda＇s elastic compliance tensor, Monte Carlo simulation （MCS）,and suitable probability density functions （PDFs） were employed to represent the elastic compliance offractured rock masses. To yield geologically realistic results, parameters for defining fracture distributionswere obtained from different geological fields. The influence of the key fracture parameters andtheir relations to the overall elastic behavior of the fractured rock mass were studied and discussed. Adetailed study was also carried out to investigate the validity of the use of a representative elementvolume （REV） in the equivalent continuum representation of fractured rock masses. A criterion was alsoproposed to determine the appropriate REV given the fracture distribution of the rock mass.

Equivalent elastic compliance tensor for rock mass with multiple persistent joint sets:Exact derivation via modified crack tensor

Discontinuities constitute an integral part of rock mass and inherently affect its anisotropic deformation behavior.This work focuses on the equivalent elastic deformation of rock mass with multiple persistent joint sets.A new method based on the space geometric and mechanical properties of the modified crack tensor is proposed,providing an analytical solution for the equivalent elastic compliance tensor of rock mass.A series of experiments validate the capability of the compliance tensor to accurately represent the deformation of rock mass with multiple persistent joint sets,based on conditions set by the basic hypothesis.The spatially varying rules of the equivalent elastic parameters of rock mass with a single joint set are analyzed to reveal the universal law of the stratified rock mass.

A Physical Interpretation of Mass-Energy Equivalence Based on the Orthogonal Collision

Einstein described the mass-energy equivalence as the most important result of special relativity. But more than a century after Einstein first derived the relationship between mass-energy equivalence (or mass-energy equation), questions left for people are how to understand that mass and energy are somehow equivalent, and how to give the dynamical process for the conversion from mass to energy (or vice versa). This paper first interprets the formula of mass-energy equivalence published by Einstein in 1905, and then gives the equivalence relationship of mass-energy transition based on the dynamics of particle orthogonal collision. As a result, the orthogonal collision of two high-energy mass particles can generate a huge mass-energy density, equivalent to the total energy of N new particles, which is a one-way dynamic process that generates new mass-energy density and new matter. This conversion of mass into energy has nothing to do with special relativity.

Density isomer of nuclear matter in an equivalent mass approach

The equation of state of symmetric nuclear matter is studied with an equivalent mass model.The equivalent mass of a nucleon has been expanded to order 4 in density.We first determine the first-order expansion coefficient in the quantum hadron dynamics,then calculate the coefficients of the second to fourth order for the given binding energy and incompressibility at the normal nuclear saturation density.It is found that there appears a density isomeric state if the incompressibility is smaller than a critical value.The model dependence of the conclusion has also been checked by varying the first-order coefficient.

Seepage simulation of high concrete-faced rockfill dams based on generalized equivalent continuum model

This research focused on the three-dimensional(3 D) seepage field simulation of a high concrete-faced rockfill dam(CFRD) under complex hydraulic conditions. A generalized equivalent continuum model of fractured rock mass was used for equivalent continuous seepage field analysis based on the improved node virtual flow method. Using a high CFRD as an example, the generalized equivalent continuum range was determined, and a finite element model was established based on the terrain and geological conditions, as well as structural face characteristics of the dam area. The equivalent seepage coefficients of different material zones or positions in the dam foundation were calculated with the Snow model or inverse analysis. Then, the 3 D seepage field in the dam area was calculated under the normal water storage conditions, and the corresponding water head distribution, seepage flow, seepage gradient, and seepage characteristics in the dam area were analyzed. The results show that the generalized equivalent continuum model can effectively simulate overall seepage patterns of the CFRD under complex hydraulic conditions and provide a reference for seepage analysis of similar CFRDs.

Gravitational radiation fields in teleparallel equivalent of general relativity and their energies

We derive two new retarded solutions in the teleparallel theory equivalent to general relativity （TEGR）. One of these solutions gives a divergent energy. Therefore, we use the regularized expression of the gravitational energymomentum tensor, which is a coordinate dependent. A detailed analysis of the loss of the mass of Bondi space-time is carried out using the flux of the gravitational energy-momentum.

Design and Evaluation of a Differential Accelerometer for Drop-Tower Equivalence Principle Test with Rotating Masses

A differential accelerometer comprising of two rotating masses made of the same material is proposed for drop tower-based free-fall testing of the spin-spin force between the rotating mass and the Earth. The measurement is performed by placing the two concentric masses of very different momenta in a vacuum drop capsule which is falling freely in the Earth＇s gravitational field. A nonzero output of the differential aeeelerometer is an indication of possible violation of new equivalence principle （NEP）. We present the conceptual design of a modified free-fall NEP experiment which can be performed at the Belting drop tower. Design and evaluation of the differential accelerometer with a hybrid electrostatic/magnetic suspension system are presented to accommodate for operation on ground and drop-tower tests. Details specific to the measurement uncertainty are discussed to yield an NEP test accuracy of 7.2×10^-9.

The Mass-Energy Equivalence Principle in Fluid Dynamics

From Lagrangian formalism as in Classical Field Theory and within the theoretical scheme of the Hamilton-Type Variational Principle, the mass-energy equivalence principle for any fluid is obtained.

隧道火灾相向射流排烟系统烟气质量流率比例系数

为探究隧道相向射流排烟系统中火灾发生时烟气的流动特性,通过FDS数值模拟研究隧道内不同上、下游风速工况下的上、下游烟气质量流率变化。基于等效风速、理论分析和数值模拟结果得到上、下游风速与烟气质量流率比例系数的关系式。结果表明:当等效风速小于临界风速时,上、下游烟气质量流率比值和烟气质量流率比例系数随等效风速增加而减小,并且等效风速与上、下游烟气质量流率比值存在线性关系;当等效风速大于临界风速时,上、下游烟气质量流率比值和烟气质量流率比例系数为0。

基于图像分析的掘进工作面粉尘颗粒检测方法

基于光散射原理测定粉尘质量浓度只能定时定点手动检测,实时性差,且只能检测出粉尘质量浓度,并不能给出粒径分布范围。目前基于图像分析的粉尘颗粒检测研究主要是针对粉尘质量浓度或粒径分布进行单方面研究,并不能实现粉尘质量浓度和粒径分布范围的同时检测。针对上述问题,提出了一种基于图像分析的掘进工作面粉尘颗粒检测方法,探究图像特征与粉尘质量浓度、粒径分布间的关系。通过粉尘样本收集及图像采集装置,采集粉尘颗粒图像并获取采集图像时的粉尘质量浓度。编写粉尘样本图像处理算法,提取图像的灰度特征、纹理特征、几何特征相关参数。对提取的图像特征与实测粉尘质量浓度进行相关性分析,选取相关性较大的图像特征作为参数建立回归数学模型。提取粉尘颗粒对象像素点个数,结合转换系数,基于几何当量等效面积径计算粉尘粒径大小及分布范围。实验结果表明:实测粉尘质量浓度与建立的图像特征多元非线性回归模型数学模型计算值间的平均相对误差为12.37%,标准实测粒径与几何当量等效面积径得到的粒径分布间的最大相对误差为8.63%,平均相对误差为6.37%,验证了基于图像特征的粉尘质量浓度回归数学模型和基于几何当量等效面积径分布数学模型的准确性。

发动机燃油泵附件的管路动力学等效设计及实现

燃油泵附件的管路空间构型复杂,在振动环境试验中直接模拟难以实现。为满足试验要求,采用系统等效缩减/扩展过程(SEREP)方法对管路进行动力学等效设计,选取管路上特定结点为主自由度,并将原管路模型缩减至主自由度模型上,得到缩减质量和刚度矩阵;对子振型矩阵采用SVD分解,使得缩减质量和刚度矩阵进一步简化,得到低阶管路模型的新缩减质量和刚度矩阵参数;提出“质量球—梁弹簧”结构模型,分别用“质量球”和“梁弹簧”来映射缩减的质量和刚度矩阵,进而确定等效设计加工参数;通过实例验证等效设计方法的可行性。结果表明:等效管路与原管路的第一阶频率误差大多在10%以内,满足工程应用要求。

基于有约束L_(1/2)范数稀疏正则化的声源识别方法

基于等效源法(equivalent source method,ESM)的近场声全息(near field acoustic holography,NAH)是一种有效的声源识别技术。然而,针对空间稀疏分布的声源识别问题,传统基于L_(2)范数以及基于L_(1)范数的ESM方法分别存在声源幅值被低估与算法稳定性差等问题。因此,提出了基于有约束L_(1/2)范数稀疏正则化的声源识别方法,该方法具有强稀疏性与强抗干扰的优势,可以解决传统方法的声源识别精度低的问题。通过数值模拟试验以及普通室内的实测实验,验证了方法的有效性。

基于任务需求和ESM分析的受控生态生保系统植物部件品种规划

针对任务周期长、距离远的长期载人深空探测,长期地外生存等任务要求建立受控生态生保系统,通过合适的植物部件利用当地资源进行空间作物生产。利用等效系统质量方法,比较了地球携带食物补给和受控生态生保系统植物部件就地生产两种补给模式的优劣。从受控生态生保系统角度讨论了主食、果蔬和蛋白质-脂肪等食物需求与植物部件设计的关系,对1~2年任务周期的深空探测飞行任务首先应配备小量蔬菜栽培装置。可以利用太阳光时,2年以上即可建立植物部件生产果蔬;15年以上方可生产粮食作物;而只能利用人工光源时,3.4年以上的深空探测任务才适合植物部件供应新鲜果蔬,而主食则需要76年以上。油料作物的空间生产在目前技术条件下不具备应用可行性。

基于联合仿真的飞机着陆机场跑道桥动载特性研究

为研究飞机着陆滑跑过程中冲击作用对机场桥梁动力响应的影响,以某拟供C类飞机使用的跑道桥为研究对象,以Boeing 737-800机型为例,首次基于有限元软件与多体动力学软件相结合的联合仿真技术建立了机-桥耦合模型,精细化模拟了飞机以不同的着陆姿态在桥梁上着陆滑跑的全过程。在验证机-桥耦合模型准确性的基础上,系统讨论了飞机着陆质量、下沉速度、俯仰角及滚转角等参数对桥梁动力响应的影响程度、影响规律,并明确了桥梁动力系数的分布范围。研究结果表明:飞机着陆冲击作用下,桥梁动力系数的主要分布区间为1.26~1.62;桥梁动力系数随着陆质量、下沉速度、滚转角增大而增大,随接地速度、俯仰角增大而减小;飞机下沉速度的影响最为显著,当下沉速度从1.00 m/s增大到3.05 m/s时,动力系数从0.98增大到1.87,增幅高达90%。跑道桥的设计需合理考虑飞机着陆滑跑过程的动载作用。

双级串联调谐质量阻尼器减振镗杆的设计与性能仿真分析

针对大长径比镗刀杆在加工大型复杂零件的孔及孔系结构中容易产生振动、加工效率低且加工质量不稳定等问题,提出了一种内置双级串联调谐质量阻尼器的新型减振镗杆,建立了减振镗杆的力学等效模型,通过求解和分析减振镗杆的振幅比,确定了减振镗杆最优的阻尼器长度及阻尼比。利用MATLAB/Simulink分别求解减振镗杆和普通镗杆的加速度响应信号,结果表明,减振镗杆的吸振性能显著提高,振动衰减时间大幅缩短。应用Workbench对两种镗杆进行模态分析和谐响应分析,得到固有频率和幅频曲线,发现减振镗杆的振幅远小于普通镗杆。本研究为减振刀具的研制与推广提供了一定的理论参考。