Nonlinear constitutive models of rock structural plane and their applications

Structural planes play an important role in controlling the stability of rock engineering,and the influence of structural planes should be considered in the design and construction process of rock engineering.In this paper,mechanical properties,constitutive theory,and numerical application of structural plane are studied by a combination method of laboratory tests,theoretical derivation,and program development.The test results reveal the change laws of various mechanical parameters under different roughness and normal stress.At the pre-peak stage,a non-stationary model of shear stiffness is established,and threedimensional empirical prediction models for initial shear stiffness and residual stage roughness are proposed.The nonlinear constitutive models are established based on elasto-plastic mechanics,and the algorithms of the models are developed based on the return mapping algorithm.According to a large number of statistical analysis results,empirical prediction models are proposed for model parameters expressed by structural plane characteristic parameters.Finally,the discrete element method(DEM)is chosen to embed the constitutive models for practical application.The running programs of the constitutive models have been compiled into the discrete element model library.The comparison results between the proposed model and the Mohr-Coulomb slip model show that the proposed model can better describe nonlinear changes at different stages,and the predicted shear strength,peak strain and shear stiffness are closer to the test results.The research results of the paper are conducive to the accurate evaluation of structural plane in rock engineering.

Study and application of monitoring plane displacement of a similarity model based on time-series images

In order to compensate for the deficiency of present methods of monitoring plane displacement in similarity model tests,such as inadequate real-time monitoring and more manual intervention,an effective monitoring method was proposed in this study,and the major steps of the monitoring method include:firstly,time-series images of the similarity model in the test were obtained by a camera,and secondly,measuring points marked as artificial targets were automatically tracked and recognized from time-series images.Finally,the real-time plane displacement field was calculated by the fixed magnification between objects and images under the specific conditions.And then the application device of the method was designed and tested.At the same time,a sub-pixel location method and a distortion error model were used to improve the measuring accuracy.The results indicate that this method may record the entire test,especially the detailed non-uniform deformation and sudden deformation.Compared with traditional methods this method has a number of advantages,such as greater measurement accuracy and reliability,less manual intervention,higher automation,strong practical properties,much more measurement information and so on.

IN-PLANE WAVE MOTION IN FINITE ELEMENT MODEL

The analysis method of lattice dynamics in classical physics is extended to study the properties of in-plane wave motion in the hybrid-mass finite element model in this paper. The dispersion equations of P and SV waves in the discrete model are first obtained by means of separating the characteristic equation of the motion equation, and then used to analyse the properties of P-and SV-homogeneous, inhomogeneous waves and other types of motion in the model. The dispersion characters, cut-off frequencies of P and SV waves, the polarization drift and appendent anisotropic property of wave motion caused by the discretization are finally discussed.

Numerical study on turbulent mixed convection in a vertical plane channel using hybrid RANS/LES and LES models

Two Delayed-Detached Eddy Simulation(DDES) models, and a Large-Eddy Simulation(LES) model are used to investigate the turbulent flows and mixed convection between a hot plate and a cold plate via the software FLUENT. The two DDES models include Production-limited DDES(PL-DDES) and Improved DDES(IDDES) models.The Wall-Adapting Local Eddy-Viscosity(WALE) model is the used LES model. The numerical computations are performed at Reynolds number Reb= 4494 and different Richardson numbers Ri = 0.025, 0.048, 0.1. The comparing data is from the Direct Numerical Simulation(DNS) at Reb= 4494 and Ri = 0.048. The comparison reveals that the two DDES models have better performance in predicting time-averaged parameters than the WALE model in the aiding flow. The best predicted time-averaged results are obtained by the PL-DDES model in the opposing flow. Furthermore, the results of different Ri obtained by the PL-DDES model agree well with the DNS data.

Modeling Walking with an Inverted Pendulum Not Constrained to the Sagittal Plane. Numerical Simulations and Asymptotic Expansions

Inverted pendulum models are commonly used to study the bio-mechanics of biped walkers. In its simplest form, the inverted pendulum consists of a point mass attached to two straight mass-less legs. Most works constrain the motion of the mass to the sagittal plane, i.e. the plane perpendicular to the ground that contains the direction toward the biped is walking. In this article, we remove this constrain to study the oscillations, the mass experiences in the direction perpendicular to the sagittal plane as the biped walks. While small, these lateral oscillations are unavoidable and of importance in the understanding of balance and stability of walkers, as well as walkers induced oscillations in pedestrian bridges.

Exploration of Water Resource and Multiple Model for Water Resource Development in Karst Areas with the Preferred Plane Theory

According to the theory of preferred plane, preferred planes (faults) alwayscontrol the distribution of bedrock fissure water and hold abundant groundwater. Thus, theexploration of fissure or karst water can be converted into searching for the watery preferred plane(WPP). In the paper, the characteristic of watery preferred planes is analyzed and a series ofsuperior indices has been set up. It is introduced that WPPs are determined by the methods ofgeological analysis, superior index and complex geophysical analysis. Meanwhile, new multiple modelfor water resource development in the water-scarce areas of karst mountainous regions are advanced.

Modeling of Plane Arrays Using a Variational Approach

The variational statement of synthesis problem is generalized in order to account the additional requirements to the synthesized radiation pattern (RP) and field distribution in the specified points of near zone. For this aim, the minimizing functional is supplemented by term providing the possibility to minimize the values of field in these points;creating the deep zeros in the RP for the certain angular coordinates is realized too. The approach foresees reduction of an explicit formula for field values in a near zone. The results of computational modeling testify the possibility to create zeros in the given RP and to minimize the values of field in a near zone of plane arrays in a great extent.

Anisotropic Plane Symmetric Two-Fluid Cosmological Model with Time-Varying G and A

We investigate a two-fluid anisotropic plane symmetric cosmological model with variable gravitational constant G（t） and cosmological term A（t）. In the two-fluid model, one fluid is chosen to be that of the radiation field modeling the cosmic microwave background and the other one a perfect fluid modeling the material content of the universe. Exact solutions of the field equations are obtained by using a special form for the average scale factor which corresponds to a specific time-varying deceleration parameter. The model obtained presents a cosmological scenario which describes an early acceleration and late-time deceleration. The gravitation constant increases with the cosmic time whereas the cosmological term decreases and asymptotically tends to zero. The physical and kinematical behaviors of the associated fluid parameters are discussed.

The use of the greater trochanter marker in the thigh segment model:Implications for hip and knee frontal and transverse plane motion

Background:The greater trochanter marker is commonly used in 3-dimensional(3D) models;however,its influence on hip and knee kinematics during gait is unclear.Understanding the influence of the greater trochanter marker is important when quantifying frontal and transverse plane hip and knee kinematics,parameters which are particularly relevant to investigate in individuals with conditions such as patellofemoral pain,knee osteoarthritis,anterior cruciate ligament(ACL) injury,and hip pain.The aim of this study was to evaluate the effect of including the greater trochanter in the construction of the thigh segment on hip and knee kinematics during gait.Methods:3D kinematics were collected in 19 healthy subjects during walking using a surface marker system.Hip and knee angles were compared across two thigh segment definitions(with and without greater trochanter) at two time points during stance:peak knee flexion(PKF) and minimum knee flexion(Min KF).Results:Hip and knee angles differed in magnitude and direction in the transverse plane at both time points.In the thigh model with the greater trochanter the hip was more externally rotated than in the thigh model without the greater trochanter(PKF:-9.34°± 5.21° vs.1.40°± 5.22°,Min KF:-5.68°± 4.24° vs.5.01°± 4.86°;p < 0.001).In the thigh model with the greater trochanter,the knee angle was more internally rotated compared to the knee angle calculated using the thigh definition without the greater trochanter(PKF:14.67°± 6.78° vs.4.33°± 4.18°,Min KF:10.54°± 6.71° vs.-0.01°± 2.69°;p < 0.001).Small but significant differences were detected in the sagittal and frontal plane angles at both time points(p < 0.001).Conclusion:Hip and knee kinematics differed across different segment definitions including or excluding the greater trochanter marker,especially in the transverse plane.Therefore when considering whether to include the greater trochanter in the thigh segment model when using a surface markers to calculate 3D kinematics for movement assessment,it is important to have a clear understanding of the effect of different marker sets and segment models in use.

Physical model test and application of 3D printing rock-like specimens to laminated rock tunnels

Weak structural plane deformation is responsible for the non-uniform large deformation disasters in layered rock tunnels,resulting in steel arch distortion and secondary lining cracking.In this study,a servo biaxial testing system was employed to conduct physical modeling tests on layered rock tunnels with bedding planes of varying dip angles.The influence of structural anisotropy in layered rocks on the micro displacement and strain field of surrounding rocks was analyzed using digital image correlation(DIC)technology.The spatiotemporal evolution of non-uniform deformation of surrounding rocks was investigated,and numerical simulation was performed to verify the experimental results.The findings indicate that the displacement and strain field of the surrounding layered rocks are all maximized at the horizontal bedding planes and decrease linearly with the increasing dip angle.The failure of the layered surrounding rock with different dip angles occurs and extends along the bedding planes.Compressive strain failure occurs after excavation under high horizontal stress.This study provides significant theoretical support for the analysis,prediction,and control of non-uniform deformation of tunnel surrounding rocks.

Review on dynamic analysis of road pavements under moving vehicles and plane strain conditions

This paper reviews works on the dynamic analysis of flexible and rigid pavements under moving vehicles on the basis of continuum-based plane strain models and linear theories.The purpose of this review is to provide in-formation about the existing works on the subject,critically discuss them and make suggestions for further research.The reviewed papers are presented on the basis of the various models for pavement-vehicle systems and the various methods for dynamically analyzing these systems.Flexible pavements are modeled by a homogeneous or layered half-plane with isotropic or anisotropic and linear elastic,viscoelastic or poroelastic material behavior.Rigid pavements are modeled by a beam or plate on a homogeneous or layered half-plane with material properties like the ones for flexible pavements.The vehicles are modeled as concentrated or distributed over a finite area loads moving with constant or time dependent speed.The above pavement-vehicle models are dynamically analyzed by analytical,analytical/numerical or purely numerical methods working in the time or frequency domain.Representative examples are presented to illustrate the models and methods of analysis,demonstrate their merits and assess the effects of the various parameters on pavement response.The paper closes with con-clusions and suggestions for further research in the area.The significance of this research effort has to do with the presentation of the existing literature on the subject in a critical and easy to understand way with the aid of representative examples and the identification of new research areas.

Computer Simulation of Compensation Method for Infrared Focal Plane Array

A major motivation for this work is to investigate a method of computer simulation for compensating fixed pattern noise of the infrared focal plane arrays. A mathematical model of the output signal of focal plane array was established; a compensating algorithm utilizing reference source was derived and simulating programs were designed. The images of compensating process verify the influence of nonuniformity of responsibility and offset on fixed pattern noise. The result show that simulating method of investigating compensation technology for focal plane arrays is feasible, the generated images and methods can be used to the study of image recognition.

Physical model test study on shear strength characteristics of slope sliding surface in Nanfen open-pit mine

A physical model for the footwall slope of Nanfen open-pit mine, China was established using a selfdeveloped deep geological engineering disaster model test system. A thermosensitive similar material,paraffin, was selected to simulate a weak structural plane in the slope to reproduce the landslide process.From an experimental perspective, the variation trend of shear strength parameters of weak structural plane and the mechanical support characteristics of NPR(negative Poisson’s ratio) anchor cable under the condition of a large landslide deformation and failure were examined. The results of this model test showed that slope failure has four distinct stages:(1) soil compaction stage,(2) crack generation stage,(3) crack propagation stage, and(4) sliding plane transfixion stage. According to the test results, the rock mechanics parameters of weak surface in the footwall slope of Nanfen open-pit mine were calculated.The cohesion is approximately 1.35×10~5 Pa, and the internal friction angle is approximately 6.33°.During slope failure, the NPR anchor cable experiences a large deformation but no damage occurs, indicating that the NPR anchor cable can be continuously monitored and reinforced during the deformation and failure of landslide. The stress characteristics of NPR anchor cables during the test are consistent with the monitoring results of Newtonian force at the landslide site, proving that NPR anchor cables are effective and reasonable in landslide monitoring and early warning.

Similarity model tests of movement and deformation of coal-rock mass below stopes

For a study of the movement and deformation of coal-rock mass and low protected seams below a stope,as well as for fracture developments and rules of evolution of permeability,we designed a plane strain model test stand to carry out model tests of similar materials in order to improve the effect of gas drainage from low protected seams and to measure the movement and deformation of coal-rock mass using a method of non-contact close-range photogrammetry.Our results show that 1) using paraffin melting to take the place of coal seam mining can satisfy the mining conditions of a protective seam;2) coal-rock mass under goafs has an upward movement after the protective seam has been mined,causing floor heaving;3) low protected seams become swollen and deformed,providing a good pressure-relief effect and causing the coal-rock mass under both sides of coal pillars to become deformed by compression and 4) the evolution of permeability of low protected seams follows the way of initial values→a slight decrease→a great increase→stability→final decrease.Simultaneously,the coefficient of air permeability increased at a decreasing rate with an increase in interlayer spacing.

A FEM-DFN model for the interaction and propagation of multi-cluster fractures during variable fluid-viscosity injection in layered shale oil reservoir

To investigate the height growth of multi-cluster fractures during variable fluid-viscosity fracturing in a layered shale oil reservoir,a two-dimensional finite element method(FEM)-discrete fracture network(DFN)model coupled with flow,stress and damage is proposed.A traction-separation law is used to describe the mixed-mode response of the damaged adhesive fractures,and the cubic law is used to describe the fluid flow within the fractures.The rock deformation is controlled by the in-situ stress,fracture cohesion and fluid pressure on the hydraulic fracture surface.The coupled finite element equations are solved by the explicit time difference method.The effects of the fracturing treatment parameters including fluid viscosity,pumping rate and cluster spacing on the geometries of multifractures are investigated.The results show that variable fluid-viscosity injection can improve the complexity of the fracture network and height of the main fractures simultaneously.The pumping rate of15 m^(3)/min,variable fluid-viscosity of 3-9-21-36-45 mPa s with a cluster spacing of 7.5 m is the ideal treatment strategy.The field application shows that the peak daily production of the application well with the optimized injection procedu re of variable fluid-viscosity fracturing is 171 tons(about 2.85 times that of the adjacent well),which is the highest daily production record of a single shale oil well in China,marking a strategic breakthrough of commercial shale oil production in the Jiyang Depression,Shengli Oilfield.The variable fluid-viscosity fracturing technique is proved to be very effective for improving shale oil production.

基于X-Plane的某巡飞弹快速原型及一体化建模

针对巡飞弹前期设计验证过程中,数学建模及气动参数分析方法研发难道大、周期长等问题,提出采用X-Plane的快速原型及一体化建模方法。分析巡飞弹的特点并总结了各类仿真方法的运行机制,分析了X-Plane的原理;通过机体建模实现了巡飞弹不依赖于数学模型及气动参数的快速原型搭建,改进了翼型及桨叶设计,实现了特殊控制(混控、伞降及折叠翼);通过软件在回路仿真方法验证了飞行器设计及控制器性能。研究成果表明:该方法能够实现各类飞行器前期快速原型设计及验证,具有研发周期短,可视化效果好等特点,对飞行器设计及控制算法研究人员均有借鉴意义。

ELASTIC-PLASTIC CRACK GROWTH ON PLANE STRAIN BIMATERIAL INTERFACE

Finite element computations are carried out to simulate plane strain crack growth on a bimaterial interface under the assumption of small scale yielding.The modified Guron constitutive equation and the element vanish technique introduced by Tvergaard et al.are used to model the final formation of an open crack.It is found from the calculation that the critical fracture toughness for crack growth is much low- er in bimaterials than that in homogeneous material.The critical fracture toughness is strongly dependent on material properties of the bimaterial pair and the mixed mode of remote loads.The interface crack grows in the more compliant(lower hardening)material or in the weaker(lower yield strength)material.In Mode-Ⅰ loading,the crack grows zigzag along the interface.

HYPERSTATIC STRUCTURE MAPPING MODEL BUILDING AND OPTIMIZING DESIGN

Hyperstatic structure plane model being built by structural mechanics is studied. Space model precisely reflected in real stress of the structure is built by finite element method （FEM） analysis commerce software. Mapping model of complex structure system is set up, with convenient calculation just as in plane model and comprehensive information as in space model. Plane model and space model are calculated under the same working condition. Plane model modular construction inner force is considered as input data; Space model modular construction inner force is considered as output data. Thus specimen is built on input data and output dam. Character and affiliation are extracted through training specimen, with the employment of nonlinear mapping capability of the artificial neural network. Mapping model with interpolation and extrpolation is gained, laying the foundation for optimum design. The steel structure of high-layer parking system （SSHLPS） is calculated as an instance. A three-layer back-propagation （BP） net including one hidden layer is constructed with nine input nodes and eight output nodes for a five-layer SSHLPS. The three-layer structure optimization result through the mapping model interpolation contrasts with integrity re-analysis, and seven layers structure through the mapping model extrpulation contrasts with integrity re-analysis. Any layer SSHLPS among 1-8 can be calculated with much accuracy. Amount of calculation can also be reduced if it is appfied into the same topological structure, with reduced distortion and assured precision.

AN SIRS EPIDEMIC MODEL

This paper considers an SIRS epidemic model that incorporates constant immigrati on rate, a general population size dependent contact rate and proportional tran sfer rate from the infective class to susceptible class.A threshold parameter σ is identified. If σ≤1, the disease free equilibrium is globally stab le. If σ>1, a unique endemic equilibrium is locally asymptotically stable. For two important special cases of mass action incidence and standard incidence, global stability of the endemic equilibrium is proved provided the threshold is larger than unity. Some previous results are extended and improved.

ANALYSIS OF THE RETURNED SIGNAL MODEL IN BISTATIC RADAR SYSTEMS

Taking the relativistic effect of high velocity moving target into account, the Doppler shift, polarization deflection, reflection coefficient and phase delay of reflected electric field are analyzed rigorously under the assumptions that incident signal to the target is a plane wave and the target is a perfect conductor plane; and their analytic expressions are obtained. The present results are of practical significance to some extent for the accurate expression of the wideband returned signal of a high velocity moving target in the bistatic radar system and for the understanding of wideband ambiguity functions.