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.

Testing method of rock structural plane using digital drilling

The rock mass consists of rock blocks and structural planes,which can reduce its integrity and strength.Therefore,accurately obtaining the characteristics of the rock mass structural plane is a prerequisite for evaluating stability and designing supports in underground engineering.Currently,there are no effective testing methods for the characteristic parameters of the rock mass structural plane in underground engineering.The paper presents the digital drilling technology as a new testing method of rock mass structural planes.Flawed rock specimens with cracks of varying widths and angles were used to simulate the rock mass structural planes,and the multifunctional rock mass digital drilling test system was employed to carry out the digital drilling tests.The analysis focuses on the variation laws of drilling parameters,such as drilling pressure and drilling torque,affected by the characteristics of prefabricated cracks,and clarifies the degradation mechanism of rock equivalent compressive strength.Additionally,an identification model for the characteristic parameters of rock mass structural planes during drilling is established.The test results indicate that the average difference of the characteristics of prefabricated cracks identified by the equivalent compressive strength is 2.45°and 0.82 mm,respectively.The identification model while drilling is verified to be correct due to the high identification accuracy.Based on this,a method for testing the characteristic parameters of the surrounding rock structural plane while drilling is proposed.The research offers a theoretical and methodological foundation for precise in situ identification of structural planes of the surrounding rock in underground engineering.

An 8-Node Plane Hybrid Element for StructuralMechanics Problems Based on the Hellinger-Reissner Variational Principle

The finite element method (FEM) plays a valuable role in computer modeling and is beneficial to the mechanicaldesign of various structural parts. However, the elements produced by conventional FEM are easily inaccurate andunstable when applied. Therefore, developing new elements within the framework of the generalized variationalprinciple is of great significance. In this paper, an 8-node plane hybrid finite element with 15 parameters (PHQ8-15β) is developed for structural mechanics problems based on the Hellinger-Reissner variational principle.According to the design principle of Pian, 15 unknown parameters are adopted in the selection of stress modes toavoid the zero energy modes.Meanwhile, the stress functions within each element satisfy both the equilibrium andthe compatibility relations of plane stress problems. Subsequently, numerical examples are presented to illustrate theeffectiveness and robustness of the proposed finite element. Numerical results show that various common lockingbehaviors of plane elements can be overcome. The PH-Q8-15β element has excellent performance in all benchmarkproblems, especially for structures with varying cross sections. Furthermore, in bending problems, the reasonablemesh shape of the new element for curved edge structures is analyzed in detail, which can be a useful means toimprove numerical accuracy.

Dynamic damage evolution of bank slopes with serrated structural planes considering the deteriorated rock mass and frequent reservoirinduced earthquakes

To investigate the dynamic damage evolution characteristics of bank slopes with serrated structural planes,the shaking table model test and the numerical simulation were utilized.The main findings indicate that under continuous seismic loads,the deformation of the bank slope increased,particularly around the hydro-fluctuation belt,accompanying by the pore water pressure rising.The soil pressure increased and then decreased showed dynamic variation characteristics.As the undulation angle of the serrated structural planes increased(30°, 45°, and 60°),the failure modes were climbing,climbinggnawing,and gnawing respectively.The first-order natural frequency was used to calculate the damage degree(Dd)of the bank slope.During microseisms and small earthquakes,it was discovered that the evolution of Dd followed the“S”shape,which was fitted by a logic function.Additionally,the quadratic function was used to fit the Dd during moderately strong earthquakes.Through the numerical simulation,the variation characteristics of safety factors(Sf)for slopes with serrated structural planes and slopes with straight structural planes were compared.Under continuous seismic loads,the Sf of slopes with straight structural planes reduce stalely,whereas the Sf for slopes with serrated structural planes was greater than the former and the reduction rate was increasing.

Structural plane recognition from three-dimensional laser scanning points using an improved region-growing algorithm based on the robust randomized Hough transform

The staggered distribution of joints and fissures in space constitutes the weak part of any rock mass.The identification of rock mass structural planes and the extraction of characteristic parameters are the basis of rock-mass integrity evaluation,which is very important for analysis of slope stability.The laser scanning technique can be used to acquire the coordinate information pertaining to each point of the structural plane,but large amount of point cloud data,uneven density distribution,and noise point interference make the identification efficiency and accuracy of different types of structural planes limited by point cloud data analysis technology.A new point cloud identification and segmentation algorithm for rock mass structural surfaces is proposed.Based on the distribution states of the original point cloud in different neighborhoods in space,the point clouds are characterized by multi-dimensional eigenvalues and calculated by the robust randomized Hough transform(RRHT).The normal vector difference and the final eigenvalue are proposed for characteristic distinction,and the identification of rock mass structural surfaces is completed through regional growth,which strengthens the difference expression of point clouds.In addition,nearest Voxel downsampling is also introduced in the RRHT calculation,which further reduces the number of sources of neighborhood noises,thereby improving the accuracy and stability of the calculation.The advantages of the method have been verified by laboratory models.The results showed that the proposed method can better achieve the segmentation and statistics of structural planes with interfaces and sharp boundaries.The method works well in the identification of joints,fissures,and other structural planes on Mangshezhai slope in the Three Gorges Reservoir area,China.It can provide a stable and effective technique for the identification and segmentation of rock mass structural planes,which is beneficial in engineering practice.

Engineering geological classification of the structural planes for hydroelectric projects in Emeishan Basalts

The scale and characteristics of rock mass are important indexes of the rock mass structural plane classification. This paper firstly analyzes the spatial distribution characteristics, the structural plane types （original structural plane, tectonic structural plane and hypergenic structural plane） and the associated features of the Emeishan basalts and then studies the classification schemes of the built hydropower structure planes of different rock areas （the east district, the central district and the west district） in the Emeishan basalt distribution area, Southwest China. Based on the analysis and comparison of the scale and the engineering geological characteristics of the typical structure planes in the basalt hydroelectric Stations, the types of structural planes are used in the first order classification. The secondary order classification is made by considering the impact factors of rock mass quality, e.g., the state of the structural planes, infilling, joint opening, extending length, the grade of weathering and strength. The engineering geological classification for Emeishan basalt is proposed. Because there are no evidences of a large structure presenting in study area, the first-order （Ⅰ） controlling structural planes do not appear in the classification, there only appear Ⅱ, Ⅲ, Ⅳ and Ⅴ grade structural planes influencing the rock-mass quality. According to the different rock-block types in bedding fault zone, the second-grade （Ⅱ） structural planes consisted of bedding fault zone is further classified into Ⅱ1, Ⅱ2 and Ⅱ3. The third-grade （Ⅲ） structural planes constructed by intraformational faulted zones are not subdivided. According to the different characteristics of intrusion, alteration and weathering unloading structural planes, the Ⅳ grade structure plane is divided into Ⅳ1, Ⅳ2 and Ⅳ3. According to the development characteristics of joints and fractures, the V grade structure plane is divided into fracture Ⅴ1 and columnar joint Ⅴ2. In all, the structural planes are classified into four groups with nine subsets. The research proposes the engineering geological classification of the structural plane for the hydropower project in the Emishan basalts, and the result of the study has a potential application in similar regions.

Experiments and Analysis of the Hydraulic Fracture Propagation Behaviors of the Granite with Structural Planes in the Gonghe Basin

Hydraulic fracture(HF) propagation behavior is significant when building enhanced geothermal systems(EGS). HF geometry is closely related to the structural planes(SPs) in hot dry rock(HDR), such as natural fractures(NFs), quartz veins(QVs) and lithologic interfaces(LIs). However, the HF behaviors in HDR have not been well understood, especially the influence of multiple SPs on the HF geometry. To clarify this mechanism, several groups of physical simulation experiments of hydraulic fracturing were conducted to investigate the intersection relationship between the HFs and the SPs. Results show that the HF geometry shows great differences when intersecting with different SPs. In summary, the HF geometry displays four basic patterns, namely, propagation along the SPs, branching, capture, penetration/non-dilation. The fluctuation degree of the pressure-time curve and the HF complexity show a positive correlation. The cementing strength of the SP and their different mechanical properties from rock matrix influence the HF behaviors significantly. Therefore, the HF shows diverse geometries when intersecting with the NFs and LIs, while propagating along the QV when intersecting with it. For the complex networks, it is favorable for the HF to penetrate through and dilate several SPs, rather than simply cross or propagate along the SP.

Effects of external dynamic disturbances and structural plane on rock fracturing around deep underground cavern

The occurrence of disasters in deep mining engineering has been confirmed to be closely related to the external dynamic disturbances and geological discontinuities.Thus,a combined finite-element method was employed to simulate the failure process of an underground cavern,which provided insights into the failure mechanism of deep hard rock affected by factors such as the dynamic stress-wave amplitudes,disturbance direction,and dip angles of the structural plane.The crack-propagation process,stress-field distribution,displacement,velocity of failed rock,and failure zone around the circular cavern were analyzed to identify the dynamic response and failure properties of the underground structures.The simulation results indicate that the dynamic disturbance direction had less influence on the dynamic response for the constant in situ stress state,while the failure intensity and damage range around the cavern always exhibited a monotonically increasing trend with an increase in the dynamic load.The crack distribution around the circular cavern exhibited an asymmetric pattern,possibly owing to the stress-wave reflection behavior and attenuation effect along the propagation route.Geological discontinuities significantly affected the stability of nearby caverns subjected to dynamic disturbances,during which the failure intensity exhibited the pattern of an initial increase followed by a decrease with an increase in the dip angle of the structural plane.Additionally,the dynamic disturbance direction led to variations in the crack distribution for specific structural planes and stress states.These results indicate that the failure behavior should be the integrated response of the excavation unloading effect,geological conditions,and external dynamic disturbances.

Analytical and numerical solutions for shear mechanical behaviors of structural plane

The original descriptive model of shear stress and shear displacement only reflects the stress deformation characteristics of plastic structural plane.The index model was revised and piecewise index model was built to describe the stress deformation characteristics of plastic structural plane and brittle structural plane.The relation of stress and strain to the failure mode of structural plane considering the effect of its shape was investigated,and a model which could reflect the relation between undulate angle and shear strength was built.The result indicates that structural plane presents nonlinear characteristics,specifically,the value of undulate angle,as well as corresponding shear strength,becomes larger as the normal stress decreases.

Discussion of Research Related to Structural Plane of Rock Mass Slope

In this paper, firstly, the rock slope and rock mass structure are introduced. And then, two aspects of the study of the structural plane are discussed： The first aspect is method for determining mechanical parameters of structural plane; The second aspect is analysis of shear strength of structural plane.

Numerical Simulation Study on the Detection of Weak Structural Plane of Rock Slope by Using 3D Electrical Resistivity Tomography

The weak structure plane is an important factor affecting the stability of rock slope, and detecting the spatial structure of the weak structural plane is beneficial to analyze the stability of the slope and estimate the quantity of the landslide. Based on 3D electrical resistivity tomography, a model of rock slope with weak structure plane is established, and the characteristics of three-dimensional resistivity imaging of weak structure plane under different ground water conditions are simulated. The results show that the weak structural plane has a better reflection in 3D electrical resistivity tomography;the distribution of weak structural plane of 3D resistivity imaging can be roughly determined under different ground water conditions;the three-dimensional electrical resistivity tomography is feasible in the detection of weak structural plane of rock slope.

Effects of Internal Relaxation under Inplane Strain on the Structural,Electronic and Optical Properties of Perovskite BaZrO3

We present the specific ab-initio calculations that detail the variations of perovskite BaZrO3 caused by in-plane strain. Specifically, the internal relaxation, which was not captured in the widely used biaxial strain model, was included in a complementary manner to lattice relaxation. Density functional theory as well as a hybrid functional method based on a plane wave basis set was employed to calculate the lattice structure, elastic constants, electronic properties and optical properties of perovskite BaZrO3. The lattice parameter c exhibited a clear linear dependence on the imposed in-plane strain, but the Poisson＇s ratio caused by internal relaxation was smaller than the elastic deformation, indicating an ＂inelastic＂ or ＂plastic＂ relaxation manner caused by the introduction of internal relaxation. As a result, the related electronic and optical properties of perovskite BaZrO3 were also strongly affected by the in-plane strain, which revealed an effective way to adjust the properties of perovskite BaZrO3 via internal relaxation.

Determination of the Effect of Initial Inner-Core Structure on Tropical Cyclone Intensification and Track on a Beta Plane

The sensitivity of TC intensification and track to the initial inner-core structure on a β plane is investigated using a numerical model. The results show that the vortex with large inner-core winds（CVEX-EXP） experiences an earlier intensification than that with small inner-core winds（CCAVE-EXP）, but they have nearly the same intensification rate after spin-up. In the early stage, the convective cells associated with surface heat flux are mainly confined within the inner-core region in CVEXEXP, whereas the vortex in CCAVE-EXP exhibits a considerably asymmetric structure with most of the convective vortices being initiated to the northeast in the outer-core region due to the β effect. The large inner-core inertial stability in CVEX-EXP can prompt a high efficiency in the conversion from convective heating to kinetic energy. In addition, much stronger straining deformation and PBL imbalance in the inner-core region outside the primary eyewall ensue during the initial development stage in CVEX-EXP than in CCAVE-EXP, which is conducive to the rapid axisymmetrization and early intensification in CVEX-EXP. The TC track in CVEX-EXP sustains a northwestward displacement throughout the integration, whereas the TC in CCAVE-EXP undergoes a northeastward recurvature when the asymmetric structure is dominant. Due to the enhanced asymmetric convection to the northeast of the TC center in CCAVE-EXP, a pair of secondary gyres embedded within the large-scale primary β gyres forms, which modulates the ventilation flow and thus steers the TC to move northeastward.

Structural stability of intermetallic compounds of Mg-Al-Ca alloy

A first-principles plane-wave pseudopotential method based on the density functional theory was used to investigate the energetic and electronic structures of intermetallic compounds of Mg-Al-Ca alloy, such as Al2Ca, Al4Ca and Mg2Ca. The negative formation heat, the cohesive energies and Gibbs energies of these compounds were estimated from the electronic structure calculations, and their structural stability was also analyzed. The results show that Al2Ca phase has the strongest alloying ability as well as the highest structural stability, next Al4Ca, finally Mg2Ca. After comparing the density of states of Al2Ca, Al4Ca and Mg2Ca phases, it is found that the highest structural stability of Al2Ca is attributed to an increase in the bonding electron numbers in lower energy range below Fermi level, which mainly originates from the contribution of valence electron numbers of Ca(s) and Ca(p) orbits, while the lowest structural stability of Mg2Ca is resulted from the least bonding electron numbers near Fermi level.

Microstructural analysis of a subhorizontal gold-quartz vein deposit at Donalda,Abitibi greenstone belt,Canada:Implications for hydrodynamic regime and fluid-structural relationship

The Donalda gold deposit in the southern part of the Archean Abitibi greenstone belt consists mainly of a subhonzontal gold-quartz vein perpendicular to subvertical shear zones.The 0.3—0.5 m thick vein is characterized by vein-parallel banding structures indicating multiple episodes of fracture opening and mineral precipitation.Measurement of the c-axis of primary growth quartz indicates that quartz preferentially grew perpendicular to the fracture,suggesting open space filling and/or extensional nature of the fracture.Measurement of the orientations of microfractures,veinlets and fluid—inclusion planes（FIPs） crosscutting primary growth quartz indicates that the vein minerals were subject to a vertical maximum principal stress（σ_1）,which is inconsistent with the subhorizontalσ_1 inferred from the regional stress field with N—S shortening.This apparent discrepancy is explained by invoking episodic fluid pressure fluctuation between supralithostatic and hydrostatic regimes accompanied by episodic opening and closing of the sub-horizontal fracture.When fluid pressure was higher than the lithostatic value,the fracture was opened and primary growth minerals were precipitated,whereas when fluid pressure decreased toward the hydrostatic value,the hanging wall of the fracture collapsed,causing collision of protruding primary growth minerals from both sides of the fracture and resulting in formation of vein-parallel deformation bands.The columns where the two facing sides of the fracture collided were subject to higher-than-lithostatic stress due to the bridging effect and reduced support surface area,explaining the development of verticalσ_1.This hypothesis is consistent the fault-valve model,and explains the flipping ofσ_1 without having to change the regional stress field.

Far-field divergence of a vectorial plane wave diffracted by a circular aperture from the vectorial structure

Based on the vectorial structure of an electromagnetic wave, the analytical and concise expressions for the TE and TM terms of a veetorial plane wave diffracted by a circular aperture are derived in the far-field. The expressions of the energy flux distributions of the TE term, the TM term and the diffracted plane wave are also presented. The ratios of the power of the TE and TM terms to that of the diffracted plane wave are examined in the far-field. In addition, the far-field divergence angles of the TE term, the TM term and the diffracted plane wave, which are related to the energy flux distribution, are investigated. The different energy flux distributions of the TE and TM terms result in the discrepancy of their divergence angles. The influences of the linearly polarized angle and the radius of the circular aperture on the far-field divergence angles of the TE term, the TM term and the diffracted plane wave are discussed in detail. This research may promote the recognition of the optical propagation through a circular aperture.

Optimization of Honing Wheel Structure Parameters in Ultra-precision Plane Honing

Free abrasive particle machining in simple machine such as: honing, polishing can get higher surface finish mirror, but surface error, and working procedure is hard to control. Therefore, the vertical disposed ultra-precision plane honing method by ultra-particle diamond honing wheel is put forward to. The results of experiments indicate: plane-honing wheel has higher machining accuracy and machining efficiency. But at the same time the structure parameters of honing wheel effects on machining accuracy. By analyzing the relation of honing wheel structure parameters and workpiece machining accuracy, the relation of honing wheel and wear coefficient, then this paper gets honing wheel structure parameters in the condition of best accuracy coefficient and wear coefficient, and resolve the problem of choosing honing wheel structure parameters in ultra-precision plane honing at last. This paper analyses the relation of honing wheel structure parameters and workpiece machining accuracy coefficient and wear coefficient, by building relative movement math model of honing wheel and workpiece in plane honing. Through theory calculating, the result indicate: about honing machine tools for large volume manufacture, honing wheel wear is main effect factor, so honing wheel should adopt obverse triangle radial structure. About honing machining for high accuracy and low-batch quantities, machining accuracy coefficient is main factors; so honing wheel should adopt reverse triangle radial structure. Neglected the manufacturing factors of honing wheel, then we can design honing wheel with high power curve structure to meet the need of machining accuracy coefficient and honing wheel wear coefficient in higher accuracy honing.

Structural Characteristics and Mechanical Properties of Rock Mass in the Field of Tianwan Nuclear Power Plant, China

The structural characteristics and mechanical properties of the rock mass are important parts of the feasibility study on the nuclear power engineering field. In this study, by means of in situ investigation and statistics, the structural plane and joint fissure features of the rock mass were analyzed and discussed at different plots and different depth scopes in the Tianwan Nuclear Power engineering field, the rock mass integrality and its weathered degree were evaluated respectively, and especially, the unfavorable geological phenomena of strongly-weathered cystid existing in the field were studied. According to the results of indoor rock mechanical tests, in combination with drilling, the shallow seismic prospecting, sonic logging and point load tests, the statistical results of physical and mechanical indices of rocks at key plots of the field were analyzed, and the design parameters of the field were calculated. It provided scientific basis for the foundation design of the nuclear power plant.

First-principles study on structural stability of 3d transition metal alloying magnesium hydride

A first-principles plane-wave pseudopotential method based on the density functional theory was used to investigate the energy and electronic structure of magnesium hydride (MgH2) alloyed by 3d transition metal elements. Through calculations of the negative heat formation of magnesium hydride alloyed by X (X denotes 3d transition metal) element, it is found that when a little X (not including Sc) dissolves into magnesium hydride, the structural stability of alloying systems decreases, which indicates that the dehydrogenation properties of MgH2 can be improved. After comparing the densities of states(DOS) and the charge distribution of MgH2 with or without X alloying, it is found that the improvement for the dehydrogenation properties of MgH2 alloyed by X attributes to the fact that the weakened bonding between magnesium and hydrogen is caused by the stronger interactions between X (not including Cu) and hydrogen. The calculation results of the improvement for the dehydrogenation properties of MgH2-X (X=Ti, V, Mn, Fe, Co, Ni, Cu) systems are in agreement with the experimental results. Hence, the dehydrogenation properties of MgH2 are expected to be improved by addition of Cr, Zn alloying elements.

The Stress-strain Analysis for the Linearly Elastic and Power Hardening of Strength Difference Plane Structure of Bars Jointed to a Rigid-body

The plane structure of bars jointed to a rigid-body is a complex and universal structure.Some other structure of bars can be considered as its special cases. Many material have different stress-strain relation in tension and compression, generally the relation is nonlinear. In this paper,we use the constitutive model of linearly elastic and power hardening of strength difference to analyze plane structure of bars. The displacement method is used to derive the universal expression of calculating stress and strain. The nonlinear equations for computing displacements of the rigid-body has been given and general computing program has been worked out. This problem has been solved satisfactorily.