Support design method for deep soft-rock tunnels in non-hydrostatic high in-situ stress field

Due to the long-term plate tectonic movements in southwestern China,the in-situ stress field in deep formations is complex.When passing through deep soft-rock mass under non-hydrostatic high in-situ stress field,tunnels will suffer serious asymmetric deformation.There is no available support design method for tunnels under such a situation in existing studies to clarify the support time and support stiffness.This study first analyzed the mechanical behavior of tunnels in non-hydrostatic in-situ stress field and derived the theoretical equations of the ground squeezing curve(GSC)and ground loosening curve(GLC).Then,based on the convergence confinement theory,the support design method of deep soft-rock tunnels under non-hydrostatic high in-situ stress field was established considering both squeezing and loosening pressures.In addition,this method can provide the clear support time and support stiffness of the second layer of initial support.The proposed design method was applied to the Wanhe tunnel of the China-Laos railway in China.Monitoring data indicated that the optimal support scheme had a good effect on controlling the tunnel deformation in non-hydrostatic high in-situ stress field.Field applications showed that the secondary lining could be constructed properly.

Arrhenius-type constitutive model and dynamic recrystallization behavior of V-5Cr-5Ti alloy during hot compression

To clarify the high temperature flow stress behavior and microstructures evolution of a V-5Cr-5Ti （mass fraction, %） alloy, the isothermal hot compression tests were conducted in the temperature range of 1423-1573 K with strain rates of 0.01, 0.1, and 1 s-1. The results show that the measured flow stress should be revised by friction and the calculated values of friction coefficient m are in the range of 0.45-0.56. Arrhenius-type constitutive equation was developed by regression analysis. The comparison between the experimental and predicted flow stress shows that the R~ and the average absolute relative error （AARE） are 0.948 and 5.44%, respectively. The measured apparent activation energy Qa is in the range of 540-890 kJ/mol. Both dis-continuous dynamic recrystallization （DDRX） and continuous dynamic recrystallization （CDRX） mechanisms are observed in the deformed alloy, but dynamic recovery （DRV） is the dominant softening mechanism up to a true strain of 1.5.

Hot deformation behavior and processing map of Cu-Ni-Si-P alloy

The high-temperature deformation behavior of Cu-Ni-Si-P alloy was investigated by using the hot compression test in the temperature range of 600-800 ℃ and strain rate of 0.01-5 s-1. The hot deformation activation energy, Q, was calculated and the hot compression constitutive equation was established. The processing maps of the alloy were constructed based on the experiment data and the forging process parameters were then optimized based on the generated maps for forging process determination. The flow behavior and the microstructural mechanism of the alloy were studied. The flow stress of the Cu-Ni-Si-P alloy increases with increasing strain rate and decreasing deformation temperature, and the dynamic recrystallization temperature of alloy is around 700 ℃. The hot deformation activation energy for dynamic recrystallization is determined as 485.6 kJ/mol. The processing maps for the alloy obtained at strains of 0.3 and 0.5 were used to predict the instability regimes occurring at the strain rate more than 1 s-1 and low temperature （〈650 ℃）. The optimum range for the alloy hot deformation processing in the safe domain obtained from the processing map is 750-800 ℃ at the strain rate of 0.01-0.1 s i The characteristic microstructures predicted from the processing map agree well with the results of microstructural observations.

Downward and upward continuation of 2-D seismic data to eliminate ocean bottom topography's effect

In order to eliminate the effect of ocean bottom topography on seismic wave field,we transformed curved（x,z）coordinate system grids into rectangular（ξ,η）coordinate system grids and derived a 2-D scalar acoustic wave equation in theξ,ηdomain.The seismic wave field collected at the sea surface was downward continued to the ocean bottom by the inverse finite difference method with the water velocity and then was reversely continued to the ocean surface by the finite difference method using the layer velocity from just below the ocean bottom in the（ξ,η）domain.Simulation calculations and practical application show that this method can not only remove the reflection travel time distortion but also correct the dynamic parameter changes caused by the ocean bottom topography.The inverted velocity after wave field continuation is much more accurate than before continuation and the image section was greatly improved compared to the original wave field.

Oscillatory Criteria for a Class of Boundary Value Problem of Nonlinear Hyperbolic Equations *L

Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments. Methods An averaging technique was used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Results and Conclusion The known results of oscillation of solutions for a class of boundary value problem of hyperbolic partial functional differential equations with discrete deviating arguments are generalized, and the oscillatory criteria of solutions for such equation with two kinds of boundary value conditions are obtained.

Conserved quantities from Lie symmetries for nonholonomic systems

This paper presents a new method to seek the conserved quantity from a Lie symmetry without using either Lagrangians or Hamiltonians for nonholonomic systems. The differential equations of motion of the systems are established. The definition of the Lie symmetrical transformations of the systems is given, which only depends upon the infinitesimal transformations of groups for the generalized coordinates. The conserved quantity is directly constructed in terms of the Lie symmetry of the systems. The condition under which the Lie symmetry can lead to the conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.

Invariant Sets and Exact Solutions to Higher-Dimensional Wave Equations

The invariant sets and exact solutions of the （1 ＋ 2）-dimensional wave equations are discussed. It is shown that there exist a class of solutions to the equations which belong to the invariant set E0 = {u ： ux = vxF（u）,uy = vyF（u） }. This approach is also developed to solve （1 ＋ N）-dimensional wave equations.

Deformation characteristics and strain-compensated constitutive equation for AA5083 aluminum alloy under hot compression

The hot deformation behavior of AA5083 aluminum alloy was studied using isothermal compression tests with a Gleeble 3500 thermal simulator at strain rate of 0.0110 s 1 and at temperature of 300500°C.The experimental results indicate that dynamic recrystallization(DRX)tends to occur at high strain rates and temperatures,and therefore the flow stress is decreased.To predict the flow behavior under different deformation conditions,a strain-compensated constitutive equation based on Arrhenius-type equation and Zener Hollomon parameters was proposed.The flow stresses obtained from the constitutive equation are consistent with the experimental results.The average absolute relative error is only 4.52%over the entire experimental range,indicating that the proposed constitutive equation exhibits high prediction precision for the hot deformation behavior of AA5083 aluminum alloy.

Grading Standards of the Coefficient of Variation in the Electronic Raw Silk Size Testing

In order to shorten the difference between the raw silk size grading standards of the world and that of China, to quicken the step of the electronic raw silk testing process, the distribution of the coefficient of variation (CV50m%) of the raw silk size in the electronic testing and the development of the new standards are studied according to the sampling and grading theory. By the theoretical deduction and the simulating experiments, the distribution of the coefficient of variation of the raw silk size is given, and the grading scheme whose quality index is the coefficient of variation(CV50m%)of the raw silk size and the grading precisions of all grades are proposed. Moreover, the rightness and the feasibility of the grading scheme are testified by the sampling and grading simulation.

Pseudo-dynamic analysis of overturning stability of retaining wall

A new method was presented to determine the safety factor of wall stability against overturning based on pseudo-dynamic approach. In this time-dependent method, the actual dynamic effect with variation of time and propagation of shear and primary wave velocities through the backfills was considered. Planar failure surface was considered behind the retaining wall. The results were compared with those obtained from Mononobe-Okabe theory. It is found that there is a higher value of safety factor by the present dynamic analysis. The effects of wall inclination, wall friction angle, soil friction angle and horizontal and vertical seismic coefficients on the overturning stability of retaining wall were investigated. The parametric study shows that both horizontal and vertical seismic accelerations have decreasing effect on the overturning stability of retaining wall.

A Dynamic Method for Quantifying Natural Warming in Urban Areas

In the study of global warming, one of the main issues is the quantification of the urbanization effect in climate records. Previous studies have contributed much to removing the impact of urbanization from surface air temperature by carefully selecting reference stations. However, due to the insufficient number of stations free from the influence of urbanization and the different criteria used to select reference stations, there are still significant controversies about the intensity of the impact of urbanization on temperature records. This study proposes a dynamic method for quantifying natural warming using information on urbanization from every station acquired from remote sensing (RS) data instead of selecting reference stations. Two different spatial scales were applied to examine the impact of urbanization, but little difference was found, indicating the stability of this method. The results showed a significant difference in original temperature data and the homogenized data-urban warming accounted for approximately 64% in the original temperature warming but only approximately 20% in the homogenized temperature records.

Evaluation of the propensity for coal spontaneous combustion based on catastrophe theory

Generally, different prevention measures should be taken according to spontaneous combustion propensities. The current methods to evaluate the propensity of coal spontaneous combustion, such as chromatographic method of oxygen adsorption, oxidation kinetics method and activation energy method, are mostly affected by human factors. Their boundaries among different classes of propensities were all established by subjective judgments. A new evaluation method using catastrophe theory is introduced. This method can accurately depict the process of coal spontaneous combustion and the evaluation index, ＂catastrophe temperature＂, be obtained based on the model. In terms of catastrophe temperature, the spontaneous combustion propensity of different coals can be sequenced. Experimental data indicate that this method is appropriate to describe the spontaneous combustion process and to evaluate the propensity of coal svontaneous combustion.

The theoretical analysis of dynamic response on cantilever beam of variable stiffness

The paper presents the theoretical analysis of a variable stiffness beam. The bending stiffness EI varies continuously along the length of the beam. Dynamic equation yields differential equation with variable co- efficients based on the model of the Euler-Bernoulli beam. Then differential equation with variable coefficients becomes that with constant coefficients by variable substitution. At last, the study obtains the solution of dy- namic equation. The cantilever beam is an object for analysis. When the flexural rigidity at free end is a constant and that at clamped end is varied, the dynamic characteristics are analyzed under several cases. The results dem- onstrate that the natural angular frequency reduces as the fiexural rigidity reduces. When the rigidity of clamped end is higher than that of free end, low-level mode contributes the larger displacement response to the total re- sponse. On the contrary, the contribution of low-level mode is lesser than that of hi^h-level mode.

Average Cycle Period in Asymmetrical Flashing Ratchet

The directed motion of a Brownian particle in a Bashing potential with various transition probabilities and waiting times in one of two states is studied. An expression for the average cycle period is proposed and the steady current J of the particle is calculated via Langevin simulation. The results show that the optimal cycle period (Tm), which takes the maximum of J, is shifted to a small value when the transition probability A from the potential on to the potential off decreases, the maximal current appears in the case of the average waiting time in the potential on being longer than in the potential off, and the direction of current depends on the ratio of the average times waiting in two states.

A DYNAMICAL INTERPRETATION OF THE WIND FIELD IN TROPICAL CYCLONES

Based on the primitive equations in polar coordinates and with the supposition that parcel velocity in tropical cyclones is in linear variation and that the distribution of surface pressure agrees with the Fujita formula, a set of equations are derived, which describe the impact of perturbations of central pressure, position of tropical cyclones, direction and velocity of movement of tropical cyclones on the wind field. It is proved that the second order approximation of the kinetic energy of tropical cyclones can be described by the equations under linear approximation. Typhoon Wipha (2007) is selected to verify the above interpretation method, and the results show that the interpretation method of the wind field could give very good results before the landfall of tropical cyclones, while making no apparent improvement after the landfall. The dynamical interpretation method in this paper is applicable to improving the forecasts of the wind field of tropical cyclones close to the coast.

Influence of Auxiliary Equation on Wave Functions for Time-Dependent Pauli Equation in Presence of Aharonov-Bohm Effect

Invariant operator method for discrete or continuous spectrum eigenvalue and unitary transformation approach are employed to study the two-dimensional time-dependent Pauli equation in presence of the Aharonov-Bohm effect （AB） and external scalar potential. For the spin particles the problem with the magnetic field is that it introduces a singularity into wave equation at the origin. A physical motivation is to replace the zero radius flux tube by one of radius R, with the additional condition that the magnetic field be confined to the surface of the tube, and then taking the limit R → 0 at the end of the computations. We point that the invariant operator must contain the step function θ（r - R）. Consequently, the problem becomes more complicated. In order to avoid this dimculty, we replace the radius R by ρ（t）R, where ρ（t） is a positive time-dependent function. Then at the end of calculations we take the limit R →0. The qualitative properties for the invariant operator spectrum are described separately for the different values of the parameter C appearing in the nonlinear auxiliary equation satisfied by p（t）, i.e., C 〉 0, C = 0, and C 〈0. Following the C＇s values the spectrum of quantum states is discrete （C 〉 0） or continuous （C ≤ 0）.

Hot compressive deformation behavior and microstructure evolution of HIPed FGH96 superalloy

Hot deformation behavior and microstructure evolution of hot isostatically pressed FGH96 P/M superalloy were studied using isothermal compression tests. The tests were performed on a Gleeble-1500 simulator in a temperature range of 1000-1150 °C and strain rate of 0.001-1.0 s-1, respectively. By regression analysis of the stress—strain data, the constitutive equation for FGH96 superalloy was developed in the form of hyperbolic sine function with hot activation energy of 693.21 kJ/mol. By investigating the deformation microstructure, it is found that partial and full dynamical recrystallization occurs in specimens deformed below and above 1100 °C, respectively, and dynamical recrystallization （DRX） happens more readily with decreasing strain rate and increasing deformation temperature. Finally, equations representing the kinetics of DRX and grain size evolution were established.

EVALUATION OF CORRECTIONS ON TURBULENT FLUXES OBTAINED BY EDDY COVARIANCE METHOD IN HIGH WINDS

This paper investigates processing of fast-response data and corrections of turbulent fluxes obtained by using eddy covariance method based on data collected at an offshore observation tower during three Cold-intrusion(CI)events in the South China Sea in 2010. This study presents the data processing procedure in detail and compares frictional velocities(u*), sensible heat fluxes(H) and latent heat fluxes(LE) yielded by using different averaging periods and different coordinate rotation methods; evaluates the sonic temperature correction for sensible heat flux and the Webb correction for latent heat flux as a function of 10 m wind speed(u10) during the CIs. The results show(1) that the different averaging periods of 30 min and 10 min cause biases of u*(H, LE) within 5%(15%, 62%). The values of u*(H,LE) averaged from 30 mins are mostly larger than those averaged from 10 mins. We suggest that the averaging period of 10 min is not sufficiently long to capture all scale eddies and recommend 30 min averaging period in calculating turbulent fluxes using eddy covariance method during CIs;(2) that the values of u*(H, LE) obtained from double rotation(DR2) and those obtained from planar fit rotation(PF) have good agreements and correlation coefficients between them are larger than 0.99. Because PF method requires unchanged environment and it is easier to apply DR2 method, we suggest DR2 coordinate rotation method in processing fast-response data; and(3) that the median values of frictional velocity(sensible heat flux and latent heat flux) binned according to 2 m s^(-1) intervals of u_(10) increase(decrease,increase) by less than 9%(4%, 10%) by Coriolis corrections(sonic temperature corrections, Webb corrections), which decreases(decreases, increases) with increasing u10 when u10 are 5-17 m s^(-1).

Lie Symmetrical Perturbation and Adiabatic Invariants of Generalized Hojman Type for Relativistic Birkhoffian Systems

For a relativistic Birkhoffian system, the Lie symmetrical perturbation and adiabatic invariants of generalized Bojman type are studied under general infinitesimal transformations. On the basis of the invariance of relativistic Birkhotfian equations under general infinitesimal transformations,Lie symmetrical transformations of the system are constructed, which only depend on the Birkhoffian variables. The exact invariants in the form of generalized Hojman conserved quantities led by the Lie symmetries of relativistic Birkhoffian system without perturbations are given. Based on the definition of higher-order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for relativistic Birkhoffian system with the action of small disturbance is investigated, and a new type of adiabatic invariants of the system is obtained. In the end of the paper, an example is given to illustrate the application of the results.

3D Dynamic Response of Layered Unsaturated Soils to Harmonic Loads

Considering compression of solid grain and pore fluids,viscous-coupling interactions and inertial force of fluids,dynamic governing equations for unsaturated soils are established by adopting an exact constitutive formula of saturation.These equations are highly versatile and completely compatible with Biot's wave equations for the special case of fully saturated soils.The governing equations in Cartesian coordinates are firstly transformed into a group of state differential equations by introducing the state vector.Then the transfer matrix for layered media are derived by means of a double Fourier transform.Using the transfer matrix followed by boundary and continuity conditions between strata,solutions of steady-state dynamic response for multi-layered unsaturated soils are obtained.Numerical examples show that the echoes generated by boundary and stratum interfaces make the displacement amplitude of the ground surface fluctuate with distance;the relative position of soft and hard strata has a significant influence on displacement.