Efficient slope reliability analysis under soil spatial variability using maximum entropy distribution with fractional moments

Spatial variability of soil properties imposes a challenge for practical analysis and design in geotechnical engineering.The latter is particularly true for slope stability assessment,where the effects of uncertainty are synthesized in the so-called probability of failure.This probability quantifies the reliability of a slope and its numerical calculation is usually quite involved from a numerical viewpoint.In view of this issue,this paper proposes an approach for failure probability assessment based on Latinized partially stratified sampling and maximum entropy distribution with fractional moments.The spatial variability of geotechnical properties is represented by means of random fields and the Karhunen-Loève expansion.Then,failure probabilities are estimated employing maximum entropy distribution with fractional moments.The application of the proposed approach is examined with two examples:a case study of an undrained slope and a case study of a slope with cross-correlated random fields of strength parameters under a drained slope.The results show that the proposed approach has excellent accuracy and high efficiency,and it can be applied straightforwardly to similar geotechnical engineering problems.

Coseismic deformation and fault slip distribution of the 2023 M_(W)7.8 and M_(W)7.6 earthquakes in Türkiye

On February 6,2023,a devastating earthquake with a moment magnitude of M_(W)7.8 struck the town of Pazarcik in south-central Türkiye,followed by another powerful earthquake with a moment magnitude of M_(W)7.6 that struck the nearby city of Elbistan 9 h later.To study the characteristics of surface deformation caused by this event and the influence of fault rupture,this study calculated the static coseismic deformation of 56 stations and dynamic displacement waveforms of 15 stations using data from the Turkish national fixed global navigation satellite system(GNSS)network.A maximum static coseismic displacement of 0.38 m for the M_(W)7.8 Kahramanmaras earthquake was observed at station ANTE,36 km from the epicenter,and a maximum dynamic coseismic displacement of 4.4 m for the M_(W)7.6 Elbistan earthquake was observed at station EKZ1,5 km from the epicenter.The rupture-slip distributions of the two earthquakes were inverted using GNSS coseismic deformation as a constraint.The results showed that the Kahramanmaras earthquake rupture segment was distinct and exposed on the ground,resulting in significant rupture slip along the Amanos and Pazarcik fault segments of the East Anatolian Fault.The maximum slip in the Pazarcik fault segment was 10.7 m,and rupture occurred at depths of 0–15 km.In the Cardak fault region,the Elbistan earthquake caused significant ruptures at depths of 0–12 km,with the largest amount of slip reaching 11.6 m.The Coulomb stress change caused by the Kahramanmaras earthquake rupture along the Cardak fault segment was approximately 2 bars,and the area of increased Coulomb stress corresponded to the subsequent rupture region of the M_(W)7.6 earthquake.Thus,it is likely that the M_(W)7.8 earthquake triggered or promoted the M_(W)7.6 earthquake.Based on the cumulative stress impact of the M_(W)7.8 and M_(W)7.6 events,the southwestern segment of the East Anatolian Fault,specifically the Amanos fault segment,experienced a Coulomb rupture stress change exceeding 2 bars,warranting further attention to assess its future seismic hazard risk.

Effects of different irrigation methods on micro-environments and root distribution in winter wheat fields

The irrigation method used in winter wheat fields affects micro-environment factors, such as relative humidity（RH） within canopy, soil temperature, topsoil bulk density, soil matric potential, and soil nutrients, and these changes may affect plant root growth.An experiment was carried out to explore the effects of irrigation method on micro-environments and root distribution in a winter wheat field in the 2007–2008 and 2008–2009 growing seasons.The results showed that border irrigation（BI）, sprinkler irrigation（SI）, and surface drip irrigation（SDI） had no significant effects on soil temperature.Topsoil bulk density, RH within the canopy, soil available N distribution, and soil matric potential were significantly affected by the three treatments.The change in soil matric potential was the key reason for the altered root profile distribution patterns.Additionally, more fine roots were produced in the BI treatment when soil water content was low and topsoil bulk density was high.Root growth was most stimulated in the top soil layers and inhibited in the deep layers in the SDI treatment, followed by SI and BI, which was due to the different water application frequencies.As a result, the root profile distribution differed, depending on the irrigation method used.The root distribution pattern changes could be described by the power level variation in the exponential function.A good knowledge of root distribution patterns is important when attempting to model water and nutrient movements and when studying soil-plant interactions.

Numerical simulation of 80 ℃ temperature field distribution of thick plate multi-pass welding with SYSWELD

The PPG PITT-CHAR XP flame retardant system has been used by COOEC to preventing the thermal softening of steel in the high temperature,whose degradation temperature is 80 ℃.To prevent damage to PPG PITT-CHAR XP fire retardant paint from excessive heat during welding,it is necessary to get accurately reserved area near the welding joints prior to welding. For the foregoing reasons,the 80 ℃ temperature field distribution of thick plate multi-pass welding was analyzed with SYSWELD.The influence of welding groove form and time interval on welding temperature field was also analyzed. Results showed that the range of 80 ℃ welding temperature field increased with the increasing of weld layers at first and then it inclined to stable value. Interpass time setting was crucial to control the range of 80 ℃ welding temperature field. It was also found that double V groove had better thermal diffusivity than double-bevel groove.And double-bevel groove was better than single V groove.

ANALYTIC EXPRESSION OF MAGNETIC FIELD DISTRIBUTION OF RECTANGULAR PERMANENT MAGNETS

From the molecular current viewpoint,an analytic expression exactly describing magnetic field distribution of rectangular permanent magnets magnetized sufficiently in one direction was derived from the Biot-Savart's law. This expression is useful not only for the case of one rectangular permanent magnet bulk,but also for that of several rectangular permanent magnet bulks. By using this expression,the relations between magnetic field distribution and the size of rectangular permanent magnets as well as the magnitude of magnetic field and the distance from the point in the space to the top (or bottom) surface of rectangular permanent magnets were discussed in detail. All the calculating results are consistent with experimental ones. For transverse magnetic field which is a main magnetic field of rectangular permanent magnets,in order to describe its distribution,two quantities,one is the uniformity in magnitude and the other is the uniformity in distribution of magnetic field,were defined. Furthermore,the relations between them and the geometric size of the magnet as well as the distance from the surface of permanent magnets were investigated by these formulas. The numerical results show that the geometric size and the distance have a visible influence on the uniformity in magnitude and the uniformity in distribution of the magnetic field.

Optimization by Estimation of Distribution with DEUM Framework Based on Markov Random Fields

This paper presents a Markov random field （MRP） approach to estimating and sampling the probability distribution in populations of solutions. The approach is used to define a class of algorithms under the general heading distribution estimation using Markov random fields （DEUM）. DEUM is a subclass of estimation of distribution algorithms （EDAs） where interaction between solution variables is represented as an undirected graph and the joint probability of a solution is factorized as a Gibbs distribution derived from the structure of the graph. The focus of this paper will be on describing the three main characteristics of DEUM framework, which distinguishes it from the traditional EDA. They are： 1） use of MRF models, 2） fitness modeling approach to estimating the parameter of the model and 3） Monte Carlo approach to sampling from the model.

Ultrasonic Scattered Field Distribution of One and Two Cylindrical Solids with Phased Array Technique

The scattered fields of plane waves in a solid from a cylinder or sphere are critical in determining its acoustic characteristics as well as in engineering applications. This paper investigates the scattered field distributions of different incident waves created by elastic cylinders embedded in an elastic isotropic medium. Scattered waves, including longitudinal and transverse waves both inside and outside the cylinder, are described with specific modalities under an incident plane wave. A model with a scatterer embedded in a structural steel matrix and filled with aluminum is developed for comparison with the theoretical solution. The frequency of the plane wave ranged from 235 kHz to 2348 kHz, which corresponds to scaling factors from 0.5 to 5. Scattered field distributions in matrix materials blocked by an elastic cylindrical solid have been obtained by simulation or calculated using existing parameters. The simulation results are in good agreement with the theoretical solution, which supports the correctness of the simulation analysis. Furthermore, ultrasonic phased arrays are used to study scattered fields by changing the characteristics of the incident wave. On this foundation, a partial preliminary study of the scattered field distribution of double cylinders in a solid has been carried out, and the scattered field distribution at a given distance has been found to exhibit particular behaviors at different moments. Further studies on directivities and scattered fields are expected to improve the quantification of scattered images in isotropic solid materials by the phased array technique.

Analysis of the impact on the gravity field determination from the data with the ununiform noise distribution using block-diagonal least squares method

The block-diagonal least squares method, which theoretically has specific requirements for the observation data and the spatial distribution of its precision, plays an important role in ultra-high degree gravity field determination. On the basis of block-diagonal least squares method, three data processing strategies are employed to determine the gravity field models using three kinds of simulated global grid data with different noise spatial distri- bution in this paper. The numerical results show that when we employed the weight matrix corresponding to the noise of the observation data, the model computed by the least squares using the full normal matrix has much higher precision than the one estimated only using the block part of the normal matrix. The model computed by the block-diagonal least squares method without the weight matrix has slightly lower precision than the model computed using the rigorous least squares with the weight matrix. The result offers valuable reference to the using of block-diagonal least squares method in ultra-high gravity model determination.

Seepage field distribution and water inflow laws of tunnels in water-rich regions

Currently,the water inrush hazards during tunnel construction,the water leakage during tunnel operation,and the accompanying disturbances to the ecological environment have become the main problems that affect the structural safety of tunnels in water-rich regions.In this paper,a tunnel seepage model testing system was used to conduct experiments of the grouting circle and primary support with different permeability coefficients.The influences of the supporting structures on the water inflow laws and the distribution of the water pressure in the tunnel were analyzed.With the decrease in the permeability coefficient of the grouting circle or the primary support,the inflow rate of water into the tunnel showed a non-linear decreasing trend.In comparison,the water inflow reduction effect of grouting circle was much better than that of primary support.With the increase of the permeability coefficient of the grouting ring,the water pressure behind the primary lining increases gradually,while the water pressure behind the grouting ring decreases.Thus,the grouting of surrounding rock during the construction of water-rich tunnel can effectively weaken the hydraulic connection,reduce the influence range of seepage,and significantly reduce the decline of groundwater.Meanwhile,the seepage tests at different hydrostatic heads and hydrodynamic heads during tunnel operation period were also conducted.As the hydrostatic head decreased,the water pressure at each characteristic point decreased approximately linearly,and the water inflow rate also had a gradual downward trend.Under the action of hydrodynamic head,the water pressure had an obvious lagging effect,which was not conducive to the stability of the supporting structures,and it could be mitigated by actively regulating the drainage rate.Compared with the hydrostatic head,the hydrodynamic head could change the real-time rate of water inflow to the tunnel and broke the dynamic balance between the water pressure and water inflow rate,thereby affecting the stress state on the supporting structures.

Distribution of Electrical Field Energy for Conversion of Methane to C_2 Hydrocarbons via Dissymmetrical Electric Field Enhanced Plasma

Direct conversion of methane into C2 hydrocarbons through alternating current electric field enhanced plasma was studied under room temperature, atmospheric pressure and low power conditions. The distribution of electrical field intensity and distribution of energy were calculated with software that was developed by us according to the charge simulation method. The results indicated that the energy of tip of electrode was 0.36 J/mm^3 and it was higher than the methane dissociation energy （0.0553 J/mm^3）. The methane located at this area can be activated easily. The higher-energy particles produced by dissociation collided with molecules around them and initiated consecutive reactions between free radicals and molecules. The method was proved to be valided and could be taken as a basis for the electrical field study concerned.

Formation and distribution characteristics of Proterozoic–Lower Paleozoic marine giant oil and gas fields worldwide

There are rich oil and gas resources in marine carbonate strata worldwide.Although most of the oil and gas reserves discovered so far are mainly distributed in Mesozoic,Cenozoic,and upper Paleozoic strata,oil and gas exploration in the Proterozoic–Lower Paleozoic（PLP）strata—the oldest marine strata—has been very limited.To more clearly understand the oil and gas formation conditions and distributions in the PLP marine carbonate strata,we analyzed and characterized the petroleum geological conditions,oil and gas reservoir types,and their distributions in thirteen giant oil and gas fields worldwide.This study reveals the main factors controlling their formation and distribution.Our analyses show that the source rocks for these giant oil and gas fields are mainly shale with a great abundance of type I–II organic matter and a high thermal evolution extent.The reservoirs are mainly gas reservoirs,and the reservoir rocks are dominated by dolomite.The reservoir types are mainly karst and reef–shoal bodies with well-developed dissolved pores and cavities,intercrystalline pores,and fractures.These reservoirs arehighly heterogeneous.The burial depth of the reservoirs is highly variable and somewhat negatively correlated to the porosity.The cap rocks are mainly thick evaporites and shales,with the thickness of the cap rocks positively correlated to the oil and gas reserves.The development of high-quality evaporite cap rock is highly favorable for oil and gas preservation.We identified four hydrocarbon generation models,and that the major source rocks have undergone a long period of burial and thermal evolution and are characterized by early and long periods of hydrocarbon generation.These giant oil and gas fields have diverse types of reservoirs and are mainly distributed in paleo-uplifts,slope zones,and platform margin reef-shoal bodies.The main factors that control their formation and distribution were identified,enabling the prediction of new favorable areas for oil and gas exploration.

GENERALIZED OPERATORS AND OPERATOR-VALUED DISTRIBUTIONS IN QUANTUM FIELD THEORY

The relation between generalized operators and operator-valued distributions is discussed so that these two viewpoints can be used alternatively to explain quantum fields.

Analysis of the far spatial coherent suppressed single peak field distribution of a rectangular wave-guide laser

A theory of the far spatial coherent-suppressed single-peak field distribution of a rectangular wave-guide CO2 laser is presented. The theoretical analysis shows that a rectangular wave-guide laser can have an output intensity distribution in far field similar to that produced from a wave-guide array laser, which is in agreement with the experimental result. A single-peak mode output is obtained within 5 metres. The experimental far-field spread angle in the bigger-Fresnel number direction is 0.63 mrad, compared to the calculated one, 0.6 mrad, and when the length of the laser resonator is changed, a double-peak or multi-peak in far-field distribution of the laser is obtained.

Velocity distribution of the flow field in the cyclonic zone of cyclone-static micro-bubble flotation column

Laboratory experiments have been conducted to study the flow field in a cyclone static micro-bubble flotation column. The method of Particle Image Velocimetry (PIV) was used. The flow field velocity distribution in both cross section and longitudinal section within cyclonic zone was studied for different circulating volumes. The cross sectional vortex was also analyzed. The results show that in cross section as the circulating volume increases from 0.187 to 0.350 m 3 /h, the flow velocity ranges from 0 to 0.68 m/s. The flow field is mainly a non-vortex potential flow that forms a free vortex without outside energy input. In the cyclonic region the vortex deviates from the center of the flotation column because a single tangential opening introduces circulating fluid into the column. The tangential component of the velocity plays a defining role in the cross section. In the longitudinal section the velocity ranges from 0 to 0.08 m/s. The flow velocity increases as does the circulating volume. Advantageous mineral separation conditions arise from the combined effects of cyclonic flow in cross and longitudinal section.

Effect of magnetic field distribution on ECR ion source discharge

An electron cyclotron resonance ion source model that uses a coaxial antenna to inject the RF power was simulated, and the corresponding hydrogen plasma densities of the ion source were calculated at different magnetic field distributions via a fluid model. The results show that most of the microwave power is absorbed around the resonance surface near the antenna when the plasma density is below the cutoff density of 7.4 × 10^(16) m^(-3) for 2.45 GHz microwaves, and the simulation results also show that the plasma density is strongly influenced by the position and shape of the resonance surface, where a larger resonance surface would improve the plasma density.

Reconstruction of Current Density Distribution in Weld Area During Resistance Spot Welding of Aluminum Alloy Based on Magnetic Field

Magnetic flux density around the weld area was used to reconstruct the current density distribution during resistance spot welding(RSW) of aluminum alloy according to inverse problem theory. A current-magnetic field model was established and the conjugate gradient method was used to solve this model. The results showed that the current density was low at the center of nugget while high on the edge of nugget. Moreover, the welding time of 30ms—60 ms is a key period for nucleation. The current density distribution can reflect whether the weld nugget is formed or splashed, therefore it has the potential to monitor the weld quality of RSW.

Distribution characteristics of intensity and phase vortices of speckle fields produced by N-pinhole random screens

We analyze the distribution properties of phase and phase vortices in a speckle field generated by N-pinhole random screens, and find that the phase vortex distributions show similarity and clustering in local regions. The phase patterns have a lot of sets composed of two phase vortices with opposite signs or four phase vortices which are positive and negative vortices alternately. Cases are also found where two adjacent phase vortices have the same topological charges. The density of phase vortices becomes larger with the increase of the radius of circumference and the number of pinholes on screen.Then, the relative positions of phase vortices can be adjusted by changing the radius of circumference and the number of pinholes.

Influence of non-uniform electric field distribution on the atmospheric pressure air dielectric barrier discharge

The dielectric barrier discharge(DBD)in air at atmospheric pressure is not suitable for industrial applications due to its randomly distributed discharge filaments.In this paper,the influence of the electric field distribution on the uniformity of DBD is theoretically analyzed and experimentally verified.It is found that a certain degree of uneven electric field distributions can control the development of electron avalanches and regulate their transition to streamers in the gap.The discharge phenomena and electrical characteristics prove that an enhanced Townsend discharge can be formed in atmospheric-pressure air with a curved-plate electrode.The spectral analysis further confirms that the gas temperature of the plasma produced by the curved-plate electrode is close to room temperature,which is beneficial for industrial applications.This paper presents the relationship between the electron avalanche transition and the formation of a uniform DBD,which can provide some references for the development and applications of the DBD in the future.

Electric field distribution and effective nonlinear AC and DC responses of graded cylindrical composites

The perturbation method is used to study the localization of electric field distribution and the effective nonlinear response of graded composites under an external alternating-current（AC） and direct-current（DC） electric field E app = E 0（1 ＋ sin ωt）.The dielectric profile of the cylindrical inclusions is modeled by function ε i（r） = C k r k（r ≤ a）,where r is the radius of the cylindrical inclusion,and C k,k,a are parameters.In the dilute limit,the local potentials and the effective nonlinear responses at all harmonics are derived.Meanwhile,the general effective nonlinear responses are also derived and compared with the effective nonlinear responses at harmonics under the AC and DC external field.It is found that the effective nonlinear AC and DC responses at harmonics can be calculated by those of the general effective nonlinear of the graded composites under the external DC electric field.Moreover,the obtained local electrical fields show that the electrical field distribution in the cylindrical inclusions is controllable,and the maximum of the electric field inside the cylinder is at its center.

Electron beam modeling and analyses of the electric field distribution and space charge effect

In electron beam technology, one of the critical focuses of research and development efforts is on improving the measurement of electron beam parameters. The parameters are closely related to the generation, emission, operation environment, and role of the electron beam and the corresponding medium. In this study, a field calculation method is proposed, and the electric field intensity distribution on the electron beam’s cross-section is analyzed. The characteristics of beam diffusion caused by the space charge effect are investigated in simulation, and the obtained data are compared with the experiment. The simulation demonstrated that the cross-sectional electric field distribution is primarily affected by the electron beam current, current density distribution, and electron beam propagation speed.