Earth Pressure of the Trapdoor Problem Using Three-Dimensional Discrete Element Method

Load transformation from the yielding part of the soil to the adjacent part is known as the soil arching effect,which plays an important role in the design of various geotechnical infrastructures.Terzaghi’s trapdoor test was an importantmilestone in the development of theories on soil arching.The research on earth pressure of the trapdoor problem is presented in this paper using the three-dimensional(3D)discrete element method(DEM).Five 3D trapdoor models with different heights are established by 3DDEMsoftware PFC 3D.The variation of earth pressure on the trapdoor with the downward movement of the trapdoor,the distribution of vertical earth pressure along the horizontal direction,the distribution of vertical earth pressure along the vertical direction,the distribution of lateral earth pressure coefficient along the depth direction,the magnitude and direction of contact force chain are studied,respectively.Related research results show that the earth pressure on the trapdoor decreases rapidly after the downward movement of the trapdoor,and then reaches the minimum earth pressure.After that,the earth’s pressure will rise slightly,and whether this phenomenon occurs depends on the depth ratio.For the bottom soil,due to the stress transfer caused by the soil arching effect,the ratio of earth pressure in the loose area decreases,while the ratio of earth pressure in the stable area increases.With the trapdoor moving down,the vertical earth pressure along the depth in the stable zone is basically consistent with the initial state,which shows an approximate linear distribution.After the trapdoor moves down,the distribution of earth pressure along with the depth in the loose area changes,which is far less than the theoretical value of vertical earth pressure of its self-weight.Because of the compression of the soil on both sides,the lateral earth pressure coefficient of most areas on the central axis of the loose zone is close to the passive earth pressure coefficient Kp.The existence of a‘soil arch’can be observed intuitively from the distribution diagram of the contact force chain in the loose zone.

Generation of countless embedded trumpet-shaped chaotic attractors in two opposite directions from a new three-dimensional system with no equilibrium point

A new three-dimensional （3D） continuous autonomous system with one parameter and three quadratic terms is presented firstly in this paper. Countless embedded trumpet-shaped chaotic attractors in two opposite directions are generated from the system as time goes on. The basic dynamical behaviors of the strange chaotic system are investigated. Another more complex 3D system with the same capability of generating countless embedded trumpet-shaped chaotic attractors is also put forward.

NEW SCALAR-TYPE EQUILIBRIUM EQUATIONS OF THE GENERAL SPACE FORCE SYSTEM

Using the principle of analytical geometry, several properties of the space straight lille are proved. Based on these properties, the equilibrium of general space force system is considered and its four new scalar-type equilibrium equations are derived which are equivalent to the vector-type necessary and sufficient conditions far equilibrium.

A Geometrical Theorem about the Static Equilibrium of a Common-point-force System and its Application

A geometrical theorem for the static equilibrium of a common-point-force system has been proven by means of virtual-work principle: The equilibrium point of a common-point force system has a minimal weighted distance summation to every fixed point arbitrarily given on each force line with a weighing factor proportional to corresponding force value. Especially the mechanical simulating technique for its inverse problem has been realized by means of pulley block. The conclusions for the inverse problem derived from mechanic method are in accordance with that given by the pure mathematical method, and the self-consistence of the theorem and its inverse problem has been demonstrated. Some application examples in engineering, economy and mathematics have been discussed, especially the possible application in the research of molecular structure, has also been predicted.

Algorithms for Empirical Equations in Terms of the Cosmic Microwave Background Temperature

Previously, we presented several empirical equations using the cosmic microwave background (CMB) temperature. Next, we propose an empirical equation for the fine-structure constant. Considering the compatibility among these empirical equations, the CMB temperature (Tc) and gravitational constant (G) were calculated to be 2.726312 K and 6.673778 × 10−11 m3∙kg−1∙s−2, respectively. Every equation can be explained numerically in terms of the Compton length of an electron (λe), the Compton length of a proton (λp) and α. Furthermore, every equation can also be explained in terms of the Avogadro number and the number of electrons at 1 C. We show that every equation can be described in terms of the Planck constant. Then, the ratio of the gravitational force to the electric force can be uniquely determined with the assumption of minimum mass. In this report, we describe the algorithms used to explain these equations in detail. Thus, there are no dimension mismatch problems.

Reaction Forces on a Fixed Ladder in Static Equilibrium: Analysis and Definitive Experimental Test of the Ladder Problem

The development of a theoretical model to predict the four equilibrium forces of reaction on a simple ladder of non-adjustable length leaning against a wall has long remained an unresolved matter. The difficulty is that the problem is statically indeterminate and therefore requires complementary information to obtain a unique solution. This paper reports 1) a comprehensive theoretical analysis of the three fundamental models based on treating the ladder as a single Euler-Bernoulli beam, and 2) a detailed experimental investigation of the forces of reaction as a function of applied load and location of load. In contrast to previous untested proposals that the solution to the ladder problem lay in the axial constraint on compression or the transverse constraint on flexure, the experimental outcome of the present work showed unambiguously that 1) the ladder could be modeled the best by a pinned support at the base (on the ground) and a roller support at the top (at the wall), and 2) the only complementary relation needed to resolve the static indeterminacy is the force of friction at the wall. Measurements were also made on the impact loading of a ladder by rapid ascent and descent of a climber. The results obtained were consistent with a simple dynamical model of the ladder as a linear elastic medium subject to a pulse perturbation. The solution to the ladder problem herein presented provides a basis for theoretical extension to other types of ladders. Of particular importance, given that accidents involving ladders in the workplace comprise a significant fraction of all industrial accidents, the theoretical relations reported here can help determine whether a collapsed structure, against which a ladder was applied, met regulatory safety limits or not.

AN ATOMIC FORCE MICROSCOPY STUDY ON THE AGGREGATION OF ISOTACTIC POLY(METHYL METHACRYLATE)

Aggregation process of isotactic poly（methyl methacrylate） （i-PMMA） has been studied extensively for many years, and considerable progress has been made in both experimental and theoretical studies. They are, however, seldom sustained by real-space observations of the underlying morphology. In this paper, the aggregation process of i-PMMA in concentrated acetone solutions and the fractal structure of the resulting three-dimensional clusters were characterized on the basis of real-space AFM observations of their two-dimensional projection. It was found that spherical multiple-chain particles formed upon collapse and aggregation of the involving chains as a whole during quenching the solution to room temperature. By keeping the solution at room temperature, the initially formed particles stick together upon contact to form larger particles through reassembling very slowly. The succeeding collision of the enlarged spherical particles leads to the formation of small clusters. These newly formed small clusters grow when they meet with other clusters or single Brownian particles. This leads to the formation of large clusters with fractal dimension of 1.95 ± 0.05, which suggest a reaction-limited cluster aggregation of i-PMMA in a concentrated acetone solution. This is in accordance with the conclusion obtained by light scattering measurements.

Elemental Composition Method in Thermodynamics of Mul- tireaction Systems (I) Molar Number, Thermodynamic Properties and Partial Properties Relations

When species in the solution undergo multiple chemical reactions, the solution may be treated as a solution of all species actually present or as a hypothetical solution composed of elemental species. Based on the fundamental thermodynamic principle, the relationships of mole numbers, molar fractions, thermodynamic properties, partial molar properties, potential and fugacity between the hypothetical solution of elemental species and the equilibrated solution of actual species were derived. The hypothetical elemental solution provides a way of reducing the dimensionality of problem, simplifying the analysis and visualizing the phase behavior.

Environmental temperature effect on dimensional measurements of atomic force microscopy

Atomic force microscopy(AFM)is increasingly being used as a fundamental tool for dimensional measurements at the nanoscale in the laboratory and in industry.Since the environmental temperature is not controlled in many measurements,or is even varied on purpose,quantification of its effects on AFM dimensional measurements is needed.In this paper,the influences of the temperature in the entire environment of the AFM(excluding only the controller and computer)and that in the local environment around the tip–sample are investigated.The results show that lateral dimensional measurements are affected mainly by the entire environmental temperature.However,vertical measurements are influenced by the temperature of both the entire environment and the local environment.The effects become significant for temperatures higher than some threshold,here between 35 and 40 XC.

Study on the Characteristics and Driving Forces of Changes of the Urban Land-Use Structure in Wuhan in 1990s

On the basis of the information entropy and equilibrium degree of urban land-use spatial structure, the paper analyzes the characteristics and rules of urban land-use spatial structure changes in Wuhan in 1990s, in which the types of land-use are shrinking and urban land-use changes are disequilibria. With PCA and GRA employed, the driving forces have also been analyzed. The driving force of city welfare and social structure, the towing force of city industrial structure transition, and the pressing force of city construction and reconstruction are main momentum factors. Moreover, the latter forces are more significant.

Dimensional Variation Modeling of Aircraft Compliant Part Assembly Considering Clamping Force Change

Compliant parts are widely applied to aircraft structures.Due to the ease of deformation of compliant parts in assembly,the prediction of assembly variation is especially important for assembly quality control.A dimensional variation model considering the clamping force change in assembly is proposed based on the method of influence coefficient(MIC).First,the assembly process is decomposed into several steps including positioning,clamping,joining,and spring-back.Then,the force-displacement relationship is formulated according to the varied force conditions on the parts in each assembly step.Finally,two examples are illustrated to validate the proposed assembly variation model.The results show the impact of clamping force change is significant on the assembly variation,and the proposed model can predict the assembly variation more accurately than the referred method without clamping force correction at the over-constrained locating points of fixture.

The Role of Friction in the Static Equilibrium of a Fixed Ladder: Theoretical Analysis and Experimental Test

In a recent publication the author derived and experimentally tested several theoretical models, distinguished by different boundary conditions at the contacts with horizontal and vertical supports, that predicted the forces of reaction on a fixed (i.e. inextensible) ladder. This problem is statically indeterminate since there are 4 forces of reaction and only 3 equations of static equilibrium. The model that predicted the empirical reactions correctly used a law of static friction to complement the equations of static equilibrium. The present paper examines in greater theoretical and experimental detail the role of friction in accounting for the forces of reaction on a fixed ladder. The reported measurements confirm that forces parallel and normal to the support at the top of the ladder are linearly proportional with a constant coefficient of friction irrespective of the magnitude or location of the load, as assumed in the theoretical model. However, measurements of forces parallel and normal to the support at the base of the ladder are linearly proportional with coefficients that depend sensitively on the location (although not the magnitude) of the load. This paper accounts quantitatively for the different effects of friction at the top and base of the ladder under conditions of usual use whereby friction at the vertical support alone is insufficient to keep the ladder from sliding. A theoretical model is also proposed for the unusual circumstance in which friction at the vertical support can keep the ladder from sliding.

Reversion of Incommensurate Modulation in Cubic Lazurite: Example of Reversible Forced Equilibrium?

The sample of cubic lazurite, collected in the Baikal region, with incommensurately 3D modulated (ITM) structure has been studied by the method of high-temperature X-ray powder diffraction. At short time of annealing in high-temperature diffraction experiment the modulation recovery proceeds during cooling down the sample to room temperature. The identity of the period of both initial and recovered modulation demonstrates that the system has a structural memory. The acquired results are interpreted through comparison of thermal behavior of lazurite, sodalite and quartz structures. It is supposed that two kinetically different and thermally activated processes proceed under heating: 1) reversible framework expansion due to Si-O-Al angle increase, and 2) equalizing of periodic local distortions via the diffusion-controlled transfer of cage ions between adjacent subcells. The second process seems to be much slower than the first one, especially at lower temperatures. With increasing temperature, both processes are activated. However, the framework expands more rapidly than the cage clusters migrate, and the periodic distortions of the framework are aligned. Under lower temperatures, the framework shrinks and again accommodates to the configuration of cage cations (clusters), which may be changed at high temperature and sufficient time or may not at lower temperature, short time, unfavorable SO2 fugacity values. In the first case the modulation disappears entirely, while in the second case it arises again. The probable reason for ITM formation is the balance of counteracting energetic terms: the elastic strain energy of structure deformation and the energy of cluster ordering providing the state of forced equilibrium. The excess free energy due to structure distortion is compensated by the increment associated with the cluster ordering process. However, no significant variations in sulphur anion speciation for different degrees of modulation retention were observed by XPS S 2p. This may be due to the ordering of Na- and Ca-containing clusters rather than the clusters with different sulphur species. ITM reversion is considered as an example of reversible forced equilibrium with completely reproducible forcing factor.

THEORETICAL ANALYSIS AND EXPERIMENTAL STUDY OF CARBON NANOTUBE PROBE AND CONVENTIONAL ATOMIC FORCE MICROSCOPY PROBE ON SURFACE ROUGHNESS

In this paper, three different tips are employed, i.e., the carbon nanotube tip, monocrystalline silicon tip and silicon nitride tip. Resorting to atomic force microscope （AFM）, they are used for measuring the surface roughness of indium tin oxide （ITO） film and the immunoglobulin G （IgG） proteins within the scanning area of 10 μm×10 μm and 0.5 μm×0.5 μm, respectively. Subsequently, the scanned surface of the ITO film and IgG proteins are analyzed by using fractal dimension. The results show that the ffactal dimension measured by carbon nanotube tip is biggest with the highest frequency components and the most microscopic information. Therefore, the carbon nanotube tip is the ideal measuring tool for measuring super-smooth surface, which will play a more and more important role in the high-resolution imaging field.

An Improved Three-Dimensional Non-Equilibrium Mixing Pool Model

This paper presents an improved three-dimensional non-equilibrium mixing pool model.It is a simplified form of the original model and is more practical for applications.The simulation re-sults show that the industrial scale distillation tray columns can be described closely by the improvedmodel.The effects of model parameters,such as the number of mixing pools,the point efficiencyand flow pattern,on separation are analyzed quantitatively.

One-dimensional Mathematical Model of Numerical Simulation of Urban Heat Island

With the development of society and the acceleration of urbanization, urban heat island phenomenon is becoming increasingly prominent. In this paper, enrichment capacity of plant light energy is supplemented based on OKe model according to law of energy conservation. By contrasting each component of energy balance equation between the cities and rural areas, the causes for urban heat island are explained.

THE RESEARCH OF BLOW-UP IN 2D WEAKLY DAMPED FORCED KdV EQUATION ON THIN DOMAIN

The time estimate of the blow up of the weakly damped forced KdV equation in thin 2 D domains is given.

Three-dimensional critical slip surface locating and slope stability assessment for lava lobe of Unzen volcano

Even Unzen volcano has been declared to be in a state of relative dormancy,the latest formed lava lobe No.11 now represents a potential slope failure mass based on the latest research.This paper concentrates on the stability of the lava lobe No.11 and its possible critical sliding mass.It proposes geographic information systems (GIS) based three-dimensional (3D) slope stability analysis models.It uses a 3D locating approach to identify the 3D critical slip surface and to analyze the 3D stability of the lava lobe No.11.At the same time,the new 3D approach shows the effectiveness in selecting the range of the Monte Carlo random variables and locating the critical slip surface in different parts of the lava lobe No.11.The results are very valuable for judging the stability of the lava lobe and assigning the monitoring equipments.

VELOCITY ANALYSIS OF A SPATIALM ECHANISM USING THE PRINCIPLEOF VIRTUAL FORCES

A new method of both analysis and graphics is presented for solving the problem of velocity analysis of a spatial four-bar mechanism. Central to the method is how to use the principle of virtual forces equilibrium system connected with the principle of virtual velocity to solve the velocity analysis of a mechanism. The method is accurate in principle and much simpler than the conventional method. It can be applied to both planar and spatial mechanisms. For brevity an example of a spatial mechanism only is presented.

Theory and application of numerical simulation method of capillary force enhanced oil production

A kind of second-order implicit upwind fractional step finite difference methods are presented for the numerical simulation of coupled systems for enhanced （chemical） oil production with capillary force in the porous media. Some techniques, e.g., the calculus of variations, the energy analysis method, the commutativity of the products of difference operators, the decomposition of high-order difference operators, and the theory of a priori estimate, are introduced. An optimal order error estimate in the l2 norm is derived. The method is successfully used in the numerical simulation of the enhanced oil production in actual oilfields. The simulation results are satisfactory and interesting.