Elastic solutions for stresses in a transversely isotropic half‐space subjected to three‐dimensional buried parabolic rectangular loads

In many areas of engineering practice, applied loads are not uniformly distributed but often concentrated towards the centre of a foundation. Thus, loads are more realistically depicted as distributed as linearly varying or as parabola of revolution. Solutions for stresses in a transversely isotropic half‐space caused by concave and convex parabolic loads that act on a rectangle have not been derived. This work proposes analytical solutions for stresses in a transversely isotropic half‐space, induced by three‐dimensional, buried, linearly varying/uniform/parabolic rectangular loads. Load types include an upwardly and a downwardly linearly varying load, a uniform load, a concave and a convex parabolic load, all distributed over a rectangular area. These solutions are obtained by integrating the point load solutions in a Cartesian co‐ordinate system for a transversely isotropic half‐space. The buried depth, the dimensions of the loaded area, the type and degree of material anisotropy and the loading type for transversely isotropic half‐spaces influence the proposed solutions. An illustrative example is presented to elucidate the effect of the dimensions of the loaded area, the type and degree of rock anisotropy, and the type of loading on the vertical stress in the isotropic/transversely isotropic rocks subjected to a linearly varying/uniform/parabolic rectangular load. Copyright © 2002 John Wiley & Sons, Ltd.     

Stability of the periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions

The periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions are well known (Kurcheeva, 1973). Here the stability of these solutions are examined by applying Poncaré's characteristic equation for periodic solutions. It is found that the isoperiodic solutions are stable and all other solutions are unstable.     

Restricted Three-Body Problem: An Approximation of its General Solution – Part One – the Manifold of Symmetric Periodic Solutions

This paper gives the results of a programme attempting to exploit ‘la seule bréche’ (Poincaré, 1892, p. 82) of non-integrable systems, namely to develop an approximate general solution for the three out of its four component-solutions of the planar restricted three-body problem. This is accomplished by computing a large number of families of ‘solutions précieuses’ (periodic solutions) covering densely the space of initial conditions of this problem. More specifically, we calculated numerically and only for μ = 0.4, all families of symmetric periodic solutions (1st component of the general solution) existing in the domain D:(x ₀ ∊ [−2,2],C ∊ [−2,5]) of the (x ₀, C) space and consisting of symmetric solutions re-entering after 1 up to 50 revolutions (see graph in Fig. 4). Then we tested the parts of the domain D that is void of such families and established that they belong to the category of escape motions (2nd component of the general solution). The approximation of the 3rd component (asymmetric solutions) we shall present in a future publication. The 4th component of the general solution of the problem, namely the one consisting of the bounded non-periodic solutions, is considered as approximated by those of the 1st or the 2nd component on account of the `Last Geometric Theorem of Poincaré' (Birkhoff, 1913). The results obtained provoked interest to repeat the same work inside the larger closed domain D:(x ₀ ∊ [−6,2], C ∊ [−5,5]) and the results are presented in Fig. 15. A test run of the programme developed led to reproduction of the results presented by Hénon (1965) with better accuracy and many additional families not included in the sited paper. Pointer directions construed from the main body of results led to the definition of useful concepts of the basic family of order n, n = 1, 2,… and the completeness criterion of the solution inside a compact sub-domain of the (x ₀, C) space. The same results inspired the ‘partition theorem’, which conjectures the possibility of partitioning an initial conditions domain D into a finite set of sub-domains D i that fulfill the completeness criterion and allow complete approximation of the general solution of this problem by computing a relatively small number of family curves. The numerical results of this project include a large number of families that were computed in detail covering their natural termination, the morphology, and stability of their member solutions. Zooming into sub-domains of D permitted clear presentation of the families of symmetric solutions contained in them. Such zooming was made for various values of the parameter N, which defines the re-entrance revolutions number, which was selected to be from 50 to 500. The areas generating escape solutions have being investigated. In Appendix A we present families of symmetric solutions terminating at asymptotic solutions, and in Appendix B the morphology of large period symmetric solutions though examples of orbits that re-enter after from 8 to 500 revolutions. The paper concludes that approximations of the general solution of the planar restricted problem is possible and presents such approximations, only for some sub-domains that fulfill the completeness criterion, on the basis of sufficiently large number of families.     

Non-Existence of New Meromorphic First Integrals in the Planar Three-Body Problem

We consider the planar three-body problem and prove that, apart from some exceptional cases, there is no additional first integral meromorphic with respect to positions, mutual distances and momenta.     

圆盘固相萃取富集-气相色谱法测定地表水中有机氯和有机磷农药

采用环境友好的圆盘固相萃取新技术富集水体中有机氯农药和有机磷农药,分别用微池电子捕获检测器(μECD)和火焰光度检测器(FPD)气相色谱法检测,实现了水中有机氯和有机磷农药残留物的测定。结果表明,16种有机氯农药的平均回收率为64.7%~102%,精密度(RSD,n=6)为2.9%~15%;13种有机磷农药的平均回收率为65.9%~104%,精密度(RSD,n=6)为1.7%~17%。方法快速、灵敏、低污染,可用于水体中多种有机氯农药和有机磷农药的残留分析。     

The double solid reactant method: II. An application to the shallow groundwaters of the Porto Plain,Vulcano Island (Italy)

This paper presents an example of application of the double solid reactant method (DSRM) of Accornero and Marini (Environmental Geology, 2007a), an effective way for modeling the fate of several dissolved trace elements during water–rock interaction. The EQ3/6 software package was used for simulating the irreversible water–rock mass transfer accompanying the generation of the groundwaters of the Porto Plain shallow aquifer, starting from a degassed diluted crateric steam condensate. Reaction path modeling was performed in reaction progress mode and under closed-system conditions. The simulations assumed: (1) bulk dissolution (i.e., without any constraint on the kinetics of dissolution/precipitation reactions) of a single solid phase, a leucite-latitic glass, and (2) precipitation of amorphous silica, barite, alunite, jarosite, anhydrite, kaolinite, a solid mixture of smectites, fluorite, a solid mixture of hydroxides, illite-K, a solid mixture of saponites, a solid mixture of trigonal carbonates and a solid mixture of orthorhombic carbonates. Analytical concentrations of major chemical elements and several trace elements (Cr, Mn, Fe, Ni, Cu, Zn, As, Sr and Ba) in groundwaters were satisfactorily reproduced. In addition to these simulations, similar runs for a rhyolite, a latite and a trachyte permitted to calculate major oxide contents for the authigenic paragenesis which are comparable, to a first approximation, with the corresponding data measured for local altered rocks belonging to the silicic, advanced argillic and intermediate argillic alteration facies. The important role played by both the solid mixture of trigonal carbonates as sequestrator of Mn, Zn, Cu and Ni and the solid mixture of orthorhombic carbonates as scavenger of Sr and Ba is emphasized.

Shear strength characterization of municipal solid waste at the Suzhou landfill, China

The current practice of slope stability analysis for a municipal solid waste (MSW) landfill usually overlooks the dependence of waste properties on the fill age or embedment depth. Changes in shear strength of MSW as a function of fill age were investigated by performing field and laboratory studies on the Suzhou landfill in China. The field study included sampling from five boreholes advanced to the bottom of the landfill, cone penetration tests and monitoring of pore fluid pressures. Twenty-six borehole samples representative of different fill ages (0 to 13 years) were used to perform drained triaxial compression tests. The field and laboratory study showed that the waste body in the landfill can be sub-divided into several strata corresponding to different ranges of fill age. Each of the waste strata has individual composition and shear strength characteristics. The triaxial test results showed that the MSW samples exhibited a strain-hardening and contractive behavior. As the fill age of the waste increased from 1.7 years to 11 years, the cohesion mobilized at a strain level of 10% was found to decrease from 23.3 kPa to 0 kPa, and the mobilized friction angle at the same strain level increasing from 9.9° to 26°. For a confinement stress level greater than 50 kPa, the shear strength of the recently-placed MSW seemed to be lower than that of the older MSW. This behavior was consistent with the cone penetration test results. The field measurement of pore pressures revealed a perched leachate mound above an intermediate cover of soils and a substantial leachate mound near the bottom of the landfill. The measurements of shear strength properties and pore pressures were utilized to assess the slope stability of the Suzhou landfill.     

Characteristic analysis on oxygen isotopic tracer in the East China Sea and waters to east of the Ryūkyū-guntō

Samples of O isotopic tracer were mlleMed at Sections P₃,P₂₅,P_cM-t/2-E and P_CM-1/2.w in both the Fast China Sea and the area to the east of the Ryūkyū-gunto during October-November,1991.Analytical results of the δ¹⁸O are as follows: (1) In the Kuroshio area,the δ¹⁸O isolines are almost parallel to the 200 m isobath.The value of δ¹⁸O is negative and reaches minimum mt the main axis of the Kuroshio,and increases on both sides.(2) In the Taiwan Warm Current (TWC) area there is a high δ¹⁸O tongue extending to the northeast.(3) In the area near the coast,the distribution of δ¹⁸O isoline shows that the Changjiang River runoff diffuses seaward and the land-ocean isotopic effect from the nearshore to the offshore.(4) The values of δ¹⁸O are from -1.0×10^-3 to -0.5×10^-3 in the shelf.(5) There is a low mre of δ¹⁸O value(<-1.6×10^-3) at the 600 m layer in the Kuroshio area,which is quite in accord with the existence of a low salinity mre (S G 34.30) between the 600 and 800 m layers in the same area.Finally,the mrrelations of the δ¹⁸O with the salinity and temperature,the upwelling and so on are discussed.     

黄河利津水文站不同粒径悬浮颗粒物中有机碳含量的研究

估算不同粒径TSS中POC的入海日通量,对黄河利津水文站悬浮颗粒物(total suspended solid,TSS)样品,采用基于stokes原理的沉降法分为Ⅴ级,对分级后的样品测其有机碳(particulate organic carbon,POC)含量和粒度组成。在此基础上,用多元线性回归法对数据进一步处理,准确得到样品中不同粒径TSS中POC的含量。研究表明,黄河口淡水端水体TSS,<8μm的粘土和极细粉砂、8~16μm的细粉砂中,POC的含量为0.600%和0.400%左右;16~32μm的中粉砂中,POC的含量不足0.200%;而32~63μm的粗粉砂和>63μm砂中POC含量仅为0.050%和0.004%左右,80%以上的POC主要集中在<16μm的TSS中,而<32μm的TSS承载了95%以上的POC。