Preparation of TiC powders by carbothermal reduction method in vacuum

The preparation of fine TiC powders by carbothermal reduction of TiO2 in vacuum was investigated by XRD,SEM,XRF and laser particle sizer.Thermodynamic analysis indicates that it is easy to prepare TiC in vacuum and the formation sequence of products are Ti4O7（Magneli phase）,Ti3O5,Ti2O3,TiCxO1-x and TiC with the increase of reaction temperature.Experimental results demonstrate that TiC powders with single phase are obtained with molar ratio of TiO2 to C ranging from 1：3.2 to 1：6 at 1 550 ℃ for 4 h when the system pressure is 50 Pa,and TiC1.0 is gained when the molar ratio of TiO2 to C is 1：4 and 1：5.In addition,fine TiC1.0 powders（D50 equals 3.04 μm） with single phase and low impurities are obtained when the molar ratio of TiO2 to C is 1：4.SEM observation shows that uniform shape,low agglomeration,and loose structure are observed on the surface of block product.

Preparation of V-Ti-Fe master alloys by metallothermic reduction method

V-Ti-Fe master alloys were prepared by metaUothermic reduction method, and the influences of the mass ratio of V205 to TiO2, Al and Al-Mg alloy addition amounts on the metal recovery rates and alloy compositions were investigated. The results show that appropriate technological parameters are： the mass ratio of V205 to TiO2 is 0.5：1, Al addition represents 95% of the theoretical value, and the Al-Mg alloy addition amount is one third that of the Al addition. The results from energy spectrum analysis show that V and Fe distribute uniformly in the prepared alloy, while the segregation for Ti, i.e. Ti-rich phase is detected. A spray refming process was carried out to reduce the impurity contents of Al and O in the prepared alloys. The Al content drops from 4.27% to 1.86%, and the O content drops from 2.10% to 0.91% after the refining process.

Preparation of Cu nanoparticles with ascorbic acid by aqueous solution reduction method

Cu nanoparticles were prepared by reducing Cu2＋ ions with ascorbic acid through aqueous solution reduction method. The effects of solution pH and average size of Cu2O particles on the preparation of Cu nanoparticles were investigated. Cu particles were prepared at pH 3, 5 or 7, with the smallest Cu particles obtained at pH 7. However, Cu particles could not be prepared at pH 9 or 11. The average size of Cu2O particles can affect that of Cu particles. Larger Cu2O particles result in larger Cu particles. In addition, experiments were conducted to explore the reaction process by measuring the X-ray diffraction （XRD） patterns of specimens collected at different time points during the reaction. It was found that Cu（OH）2 was initially formed as a precursor, followed by the formation of Cu2O, which was finally reduced to Cu particles.

A new double reduction method for slope stability analysis

The core of strength reduction method(SRM) involves finding a critical strength curve that happens to make the slope globally fail and a definition of factor of safety(FOS). A new double reduction method, including a detailed calculation procedure and a definition of FOS for slope stability was developed based on the understanding of SRM. When constructing the new definition of FOS, efforts were made to make sure that it has concise physical meanings and fully reflects the shear strength of the slope. Two examples, slopes A and B with the slope angles of 63° and 34° respectively, were given to verify the method presented. It is found that, for these two slopes, the FOSs from original strength reduction method are respectively 1.5% and 38% higher than those from double reduction method. It is also found that the double reduction method predicts a deeper potential slide line and a larger slide mass. These results show that on one hand, the double reduction method is comparative to the traditional methods and is reasonable, and on the other hand, the original strength reduction method may overestimate the safety of a slope. The method presented is advised to be considered as an additional option in the practical slope stability evaluations although more useful experience is required.

Effects of reaction parameters on preparation of Cu nanoparticles via aqueous solution reduction method with NaBH_4

The preparation of Cu nanoparticles by the aqueous solution reduction method was investigated. The effects of different reaction parameters on the preparation of Cu nanoparticles were studied. The optimum conditions for preparing well-dispersed nanoparticles were found as follows: 0.4 mol/L NaBH4 was added into solution containing 0.2 mol/L Cu2+, 1.0% gelatin dispersant in mass fraction, and 1.2 mol/L NH3?H2O at pH 12 and 313 K. In addition, a series of experiments were performed to discover the reaction process. NH3?H2O was found to be able to modulate the reaction process. At pH=10, Cu2+ was transformed to Cu(NH3)42+ as precursor after the addition of NH3?H2O, and then Cu(NH3)42+ was reduced by NaBH4 solution. At pH=12, Cu2+ was transformed to Cu(OH)2 as precursor after the addition of NH3?H2O, and Cu(OH)2 was then reduced by NaBH4 solution.

A strength reduction method based on double reduction parameters and its application

In the traditional strength reduction method,the cohesion and the friction angle adopt the same reduction parameter,resulting in equivalent proportional reduction.This method does not consider the different effects of the cohesion and friction angle on the stability of the same slope and is defective to some extent.Regarding this defect,a strength reduction method based on double reduction parameters,which adopts different reduction parameters,is proposed.The core of the double-parameter reduction method is the matching reduction principle of the slope with different angles.This principle is represented by the ratio of the reduction parameter of the cohesion to that of the friction angle,described as η.With the increase in the slopeangle,ηincreases; in particular,when the slope angle is 45°,tηis 1.0.Through the matching reduction principle,different safety margin factors can be calculated for the cohesion and friction angle.In combination with these two safety margin factors,a formula for calculating the overall safety factor of the slope is proposed,reflecting the different contributions of the cohesion and friction angle to the slope stability.Finally,it is shown that the strength reduction method based on double reduction parameters acquires a larger safety factor than the classic limit equilibrium method,but the calculation results are very close to those obtained by the limit equilibrium method.

ELASTIC MODULUS REDUCTION METHOD FOR LIMIT LOAD EVALUATION OF FRAME STRUCTURES

A new strategy for elastic modulus adjustment is proposed based on the element bearing ratio （EBR）,and the elastic modulus reduction method （EMRM） is proposed for limit load evaluation of frame structures. The EBR is defined employing the generalized yield criterion,and the reference EBR is determined by introducing the extrema and the degree of uniformity of EBR in the structure. The elastic modulus in the element with an EBR greater than the reference one is reduced based on the linear elastic finite element analysis and the equilibrium of strain energy. The lower-bound of limit-loads of frame structures are analyzed and the numerical example demonstrates the flexibility,accuracy and effciency of the proposed method.

Limit analysis of vertical anti-pulling screw pile group under inclined loading on 3D elastic-plastic finite element strength reduction method

Based on the functional theory, catastrophe theory, simultaneity principle and the idea of strength reduction method （SRM）, the bearing capacity functional anti SRM of pile group foundation were established, and the criteria of ultimate load and the concept of safety storage coefficient （Css） were advanced. The inclined ultimate loads by the static loading test, load increment method （LIM） and SRM are compared. Theoretically, the ultimate load of piles does not change with the loading levels when it is calculated by SRM. When the one strength reduction parameter is applied in the calculation boundary, there are calculating errors because the bearing capacity action of soils happened in the finite zone. The inclined 10adings are 108, 132 and 144 kN, and SSC are 1.07, 0.94 and 0.79, respectively, so the calculation values of ultimate loads are about 115.56, 124.08 and 113.76 kN, respectively. The error between calculations and observation values is less than 6%. But .the error between calculations of LIM and observations is 20%. Because of the effect of inclined loading, the push-rotation phenomenon of screw pile group appears. Under this testing, the ultimate bearing capacity of piles is mostly determined by the horizontal ultimate bearing capacity, and the effect of the vertical component of inclined load should also be considered.

Strength reduction method for slope based on a ubiquitous-joint criterion and its application

In order to expand the application of strength reduction methods with the ubiquitous-joint criterion, the corresponding program is compiled using FLAC3D software. A procedure for strength reduction in the ubiquitous-joint criterion is proposed to study the safety factor of slopes as well as the relationships of the bedding plane inclination angle β and the safety factor F. The results show that： 1） for the bedding rock slope, the various failure modes cause different variations of the safety factor F; 2） a bed- ding rock slope can be divided into two types by the angle between the bedding plane inclination and slope surface inclination a; when a_〈45~, the bedding slope can be strictly defined as the subsequent bedding rock slope; when 45°〈α〈90°, the bedding slope is defined as an oblique bedding slope; 3） for bedding rock slopes, the safety factor increases with an increase in a; for inverse bed- ding slopes, when the bedding plane inclination angle fl is small, the safety factor F of the slope increases at first, then decreases with an increase in a; when β is large, the safety factor F increases with an increase in α.

Slope analysis based on local strength reduction method and variable-modulus elasto-plastic model

Employing an ideal elasto-plastic model,the typically used strength reduction method reduced the strength of all soil elements of a slope.Therefore,this method was called the global strength reduction method(GSRM).However,the deformation field obtained by GSRM could not reflect the real deformation of a slope when the slope became unstable.For most slopes,failure occurs once the strength of some regional soil is sufficiently weakened; thus,the local strength reduction method(LSRM)was proposed to analyze slope stability.In contrast with GSRM,LSRM only reduces the strength of local soil,while the strength of other soil remains unchanged.Therefore,deformation by LSRM is more reasonable than that by GSRM.In addition,the accuracy of the slope's deformation depends on the constitutive model to a large degree,and the variable-modulus elasto-plastic model was thus adopted.This constitutive model was an improvement of the Duncan–Chang model,which modified soil's deformation modulus according to stress level,and it thus better reflected the plastic feature of soil.Most importantly,the parameters of the variable-modulus elasto-plastic model could be determined through in-situ tests,and parameters determination by plate loading test and pressuremeter test were introduced.Therefore,it is easy to put this model into practice.Finally,LSRM and the variable-modulus elasto-plastic model were used to analyze Egongdai ancient landslide.Safety factor,deformation field,and optimal reinforcement measures for Egongdai ancient landslide were obtained based on the proposed method.

Routh Order Reduction Method of Relativistic Birkhoffian Systems

Routh order reduction method of the relativistic Birkhoffian equations is studied. For a relativistic Birkhoffian system, the cyclic integrals can be found by using the perfect differential method. Through these cyclic integrals, the order of the system can be reduced. If the relativistic Birkhoffian system has a cyclic integral, then the Birkhoffian equations can be reduced at least by two degrees and the Birkhoffian form can be kept. The relations among the relativistic Birkhoffian mechanics, the relativistic Hamiltonian mechanics, and the relativistic Lagrangian mechanics are discussed, and the Routh order reduction method of the relativistic Lagrangian system is obtained. And an example is given to illustrate the application of the result.

Application of strength reduction method to dynamic anti-sliding stability analysis of high gravity dam with complex dam foundation

Considering that there are some limitations in analyzing the anti-sliding seismic stability of dam-foundation systems with the traditional pseudo-static method and response spectrum method, the dynamic strength reduction method was used to study the deep anti-sliding stability of a high gravity dam with a complex dam foundation in response to strong earthquake-induced ground action. Based on static anti-sliding stability analysis of the dam foundation undertaken by decreasing the shear strength parameters of the rock mass in equal proportion, the seismic time history analysis was carried out. The proposed instability criterion for the dynamic strength reduction method was that the peak values of dynamic displacements and plastic strain energy change suddenly with the increase of the strength reduction factor. The elasto-plastic behavior of the dam foundation was idealized using the Drucker-Prager yield criterion based on the associated flow rule assumption. The result of elasto-plastic time history analysis of an overflow dam monolith based on the dynamic strength reduction method was compared with that of the dynamic linear elastic analysis, and the reliability of elasto-plastic time history analysis was confirmed. The results also show that the safety factors of the dam-foundation system in the static and dynamic cases are 3.25 and 3.0, respectively, and that the F2 fault has a significant influence on the anti-sliding stability of the high gravity dam. It is also concluded that the proposed instability criterion for the dynamic strength reduction method is feasible.

Preparation of Cu nanoparticles with NaBH_4 by aqueous reduction method

Cu nanoparticles were prepared by reducing Cu2＋ ions with NaBH4 in alkaline solution. The effects of NaBH4 concentration and dripping rate on the formation of Cu nanoparticles were studied. The optimum conditions are found to be 0.2 mol/L Cu2＋, solution with pH=12, temperature of 313 K and 1% gelatin as dispersant, to which 0.4 mol/L NaBH4 is added at a dripping rate of 50 mL/min. NH3-H2O is found to be the optimal complexant to form the Cu precursor. A series experiments were conducted to study the reaction process at different time points.

Evaluation of the possible slip surface of a highly heterogeneous rock slope using dynamic reduction method

A new method, the dynamic reduction method(DRM) combined with the strain-softening method, was applied to evaluate the possible slip surface of a highly heterogeneous rock slope of the Dagangshan hydropower station in Southwest China.In DRM, only the strength of the failure elements is reduced and the softening reduction factor K is adopted to calculate the strength parameters. The simulation results calculated by DRM show that the further slip surface on the right slope of the Dagangshan hydropower station is limited in the middle part of the slope, while both SRM(strength reduction method) and LEM(limit equilibrium method) predict a failure surface which extends upper and longer. The observations and analysis from the three recorded sliding events indicate that the failure mode predicted by DRM is more likely the scenario.The results in this study illustrate that for highly heterogeneous slopes with geological discontinuities in different length scales, the proposed DRM can provide a reliable prediction of the location of the slip surface.

A case study of multi-seam coal mine entry stability analysis with strength reduction method

In this paper,the advantage of using numerical models with the strength reduction method(SRM) to evaluate entry stability in complex multiple-seam conditions is demonstrated.A coal mine under variable topography from the Central Appalachian region is used as a case study.At this mine,unexpected roof conditions were encountered during development below previously mined panels.Stress mapping and observation of ground conditions were used to quantify the success of entry support systems in three room-and-pillar panels.Numerical model analyses were initially conducted to estimate the stresses induced by the multiple-seam mining at the locations of the affected entries.The SRM was used to quantify the stability factor of the supported roof of the entries at selected locations.The SRM-calculated stability factors were compared with observations made during the site visits,and the results demonstrate that the SRM adequately identifies the unexpected roof conditions in this complex case.It is concluded that the SRM can be used to effectively evaluate the likely success of roof supports and the stability condition of entries in coal mines.

Static output feedback stabilization for second-order singular systems using model reduction methods

In this paper,the static output feedback stabilization for large-scale unstable second-order singular systems is investigated.First,the upper bound of all unstable eigenvalues of second-order singular systems is derived.Then,by using the argument principle,a computable stability criterion is proposed to check the stability of secondorder singular systems.Furthermore,by applying model reduction methods to original systems,a static output feedback design algorithm for stabilizing second-order singular systems is presented.A simulation example is provided to illustrate the effectiveness of the design algorithm.

The Preparation of Nano Silver by Chemical Reduction Method

A silver nanostructures prepared by using chemical reduction method. The silver nanoparticles were prepared with diameters of about (20 nm). Numerous techniques had been used to study the optical, structural like the UV-Vis absorption spectrometer, Ttransmission Electron Microscopy (TEM), Field-Emission Scanning Electron microscope (FESEM), and X-ray diffraction (XRD). The practical results exhibited the absorption spectrum of the prepared nanoparticles at (357 nm), it was found that there is a relationship between the positions of the optical absorption peak and the size of the silver nanoparticles. The analysis of TEM results showed the presence of nanoparticles in the range (20 nm). The analyzing of XRD results explained the crystal structure for silver nanoparticles. It is found a cubic unit cell have a lattice constants (a = 4.0855 Å), with the Miller indices were (111), (002), (002), and (113).

A New Criterion for Defining Inhomogeneous Slope Failure Using the Strength Reduction Method

A new variational method treating the system as a whole with rigorous mathematical and physical derivation was presented in this paper.Combined with classical and engineering examples,variational energy expressions of slopes were derived.In addition,the calculation programs were written in the FISH language set in FLAC3D(fast Lagrangian analysis of continua in three dimensions)software.Factors of safety(FOSs)of the models were determined by the variational method based on the strength reduction method(SRM)and then compared with other criteria or methods.The result showed that the variational method reflected the process of slope plasticity and failure uniformly and was feasible to analyze the stability of inhomogeneous slopes.The method was applicable to both two-dimensional and three-dimensional heterogeneous slopes.The small error with other criteria or methods also showed the accuracy of this method.This method unified other criteria,avoided the artificial error of other criteria,and provided a logical derivation for the instability of heterogeneous slope.This method considered the system as a whole and avoided the shortcomings of the general method of one-sided instability analysis.The proposed method is of great significance as it considers the coupling effect of stress and strain of materials and gives the mechanical basis for the instability of complex slopes.

Approximate direct reduction method:infinite series reductions to the perturbed mKdV equation

The approximate direct reduction method is applied to the perturbed mKdV equation with weak fourth order dispersion and weak dissipation. The similarity reduction solutions of different orders conform to formal coherence, accounting for infinite series reduction solutions to the original equation and general formulas of similarity reduction equations. Painleve Ⅱ type equations, hyperbolic secant and Jacobi elliptic function solutions are obtained for zeroorder similarity reduction equations. Higher order similarity reduction equations are linear variable coefficient ordinary differential equations.

State space solution to 3D multilayered elastic soils based on order reduction method

Starting with the governing equations in terms of displacements of 3D elastic media, the solutions to displacement components and their first derivatives are obtained by the application of a double Fourier transform and an order reduction method based on the Cayley-Hamilton theorem. Combining the solutions and the constitutive equations which connect the displacements and stresses, the transfer matrix of a single soil layer is acquired. Then, the state space solution to multilayered elastic soils is further obtained by introducing the boundary conditions and continuity conditions between adjacent soil layers. The numerical analysis based on the present theory is carried out, and the vertical displacements of multilayered foundation with a weak and a hard underlying stratums are compared and discussed.