Littlewood-Paley characterizations of anisotropic Hardy-Lorentz spaces

Let p ∈(0, 1], q ∈(0, ∞] and A be a general expansive matrix on R~n. Let H_A~(p,q )(R~n) be the anisotropic Hardy-Lorentz spaces associated with A defined via the nontangential grand maximal function. In this article, the authors characterize H_A~(p,q )(R~n) in terms of the Lusin-area function, the Littlewood-Paley g-function or the Littlewood-Paley g~*_λ-function via first establishing an anisotropic Fefferman-Stein vector-valued inequality in the Lorentz space L_(p,q)(R~n). All these characterizations are new even for the classical isotropic Hardy-Lorentz spaces on R~n. Moreover, the range of λ in the g~*_λ-function characterization of H_A~(p,q )(R~n) coincides with the best known one in the classical Hardy space H~p(R~n) or in the anisotropic Hardy space H_A~p (R~n).     

考虑地震力方向的倾倒式危岩可靠度分析

侧向卸荷作用导致高陡边坡发育大量危岩体,危岩体在降雨、地震作用下易发生失稳破坏,判断其失稳的概率对危岩防治具有重要意义.该文以倾倒式危岩体为例,建立了考虑地震力作用方向下最危险方向的物理力学模型,利用函数极值理论建立了最危险地震力作用方向的表达式,结合可靠度理论建立了倾倒式危岩体可靠度指标、失稳概率表达式及判断标准.通过对重庆南川金佛山危岩体案例的分析表明:工况1的最危险地震力作用方向与水平方向的偏转角θ在5°范围内,工况2的最危险地震力作用方向与水平方向的偏转角θ在10°左右;危岩体最危险作用方向不是一个固定角,其值与危岩体形态、裂隙水作用力大小、岩腔深度等有关.当主控结构面裂隙长度较小时,最危险地震力作用方向与水平夹角很小,随主控结构面裂隙长度增大,最危险地震力作用方向与水平夹角显著增大;危岩体失稳概率随主控结构面裂隙长度增加而增大,工况2较工况1增大幅度更明显.该研究成果对危岩的防灾减灾具有重要意义.     

隧道围岩压力监测的非线性回归分析研究

隧道围岩压力的变化是导致公路隧道岩块错动、掉块、甚至塌方的重要因素。结合田心隧道工程,将一种可以把压力转变成光纤Bragg光栅波长移位的FBG土压力传感器应用于隧道围岩压力的监测;将40支土压力传感器安装在20个代表性断面中。采用非线性回归分析统计方法对隧道的量测数据进行分析,比较了监测数据的处理分析方法,选取最优的非线性回归分析模型。监测数据与回归拟合数据分析表明,非线性回归分析预测方法不仅可以反映隧道围岩变形和压力变化过程,还能根据其变化趋势进行结构异常判断。     

Multiple positive fixed points for the sum of expansive mappings and k‐set contractions

In this work, we are concerned with the existence of multiple positive fixed points for the sum of an expansive mapping with constant h > 1 and a k‐set contraction when 0 ≤ k < h ? 1. In particular, the case of the sum of an expansive mapping with constant h > 1 and an e‐concave operator and an e‐convex operator is considered. Two examples of application illustrate some of the theoretical results.     

Numerical study of failure behaviour of pre-cracked rock specimens under conventional triaxial compression

Macroscopic pre-existing flaws play an important role in evaluating the strength and the failure modes of a heterogeneous rock mass. Crack initiation, propagation and coalescence from macroscopic pre-existing flaws are considered in a 3-D numerical model (RFPA3D) to investigate their effects on the underlying failure modes of rock. A feature of the code RFPA3D is that it can numerically simulate the evolution of cracks in three-dimensional space, as well as the heterogeneity of the rock mass. Three types of flaw geometries were evaluated numerically against experimental results: Type A for intact specimen, and Types B and C for flawed cylindrical specimens with different macroscopic pre-existing flaws, respectively. The effect of confining pressure on the fracture evolution was also considered. Numerical results showed that both the ligament angle and the flaw angle of two pre-existing cracks can affect the uniaxial compressive strength of the specimen and the mechanism of fracture evolution. In addition, both the uniaxial compressive strength and the accumulated acoustic emission increase with increasing heterogeneity.     

Particle flow study on strength and meso-mechanism of Brazilian splitting test for jointed rock mass

A discrete element method （DEM） called particle flow code （PFC2D） was used to construct a model for Brazilian disc splitting test in the present study. Based on the experimental results of intact Brazilian disc of rock-like material, a set of micro-parameters in PFC2D that reflected the macro-mechanical behavior of rock-like materials were obtained. And then PFC2D was used to simulate Brazilian splitting test for jointed rock mass specimens and specimen containing a central straight notch. The effect of joint angle and notch angle on the tensile strength and failure mode of jointed rock specimens was detailed analyzed. In order to reveal the meso-mechanical mechanism of crack coalescence, displacement trend lines were applied to analyze the displacement evolution during the crack initiation and propagation. The investigated conclusions can be described as follows. （1） The tensile strength of jointed rock mass disc specimen is dependent to the joint angle. As the joint angle increases, the tensile strength of jointed rock specimen takes on a nonlinear variance. （2） The tensile strength of jointed rock mass disc specimen containing a central straight notch distributes as a function of both joint angle and notch angle. （3） Three major failure modes, i.e., pure tensile failure, shear failure and mixed tension and shear failure mode are observed in jointed rock mass disc specimens under Brazilian test. （4） The notch angle roles on crack initiation and and joint angle play important propagation characteristics of jointed rock mass disc specimen containing a central straight notch under Brazilian test.     

干湿循环效应对风化砂改良膨胀土膨胀力影响的研究

本文将0、10%、20%、30%、40%、50%的风化砂掺入膨胀土中,分别进行0、1、2、3、4、5次干湿循环,对干湿循环之后的试样进行膨胀力测试;研究了不同掺量风化砂改良膨胀土膨胀力的大小及增长时程随着干湿循环次数的变化规律,分析了干湿循环作用一定次数后,风化砂掺量对试样表面的剥落程度及裂隙发育的影响。实验结果表明:干湿循环效应对风化砂改良膨胀土的膨胀力影响较为显著,且膨胀力与干湿循环次数间的关系可以用三次方函数很好地进行描述;在风化砂掺量一定时,经过2~3次干湿循环时膨胀力降低幅度最大,且随着风化砂掺量的增加,这一降低幅度在逐渐减少,干湿循环4~5后膨胀力趋于稳定;当风化砂掺量相同时,随着干湿循环次数的增加,膨胀力达到稳定所需要的时间逐渐减少,而膨胀力的增长速度先增大后减小;干湿循环5次后,试样表面的裂隙发育已基本达到稳定,裂隙数量随着风化砂掺量的增加而逐渐减少;当风化砂掺量为30%时,试样周边基本上不存在剥落现象。     

地下坑道对其临界震塌爆距处钻地武器爆炸载荷的动力响应

利用非线性显式动力有限元程序,采用多物质流固耦合计算方法,就GBU-28钻地弹在地下坑道临界震塌爆距处爆炸时,对地下直墙拱坑道的动力响应进行数值模拟。根据围岩动力稳定性和混凝土动态强度判据,结合模拟结果,分析衬砌结构与围岩的相互作用。钻地弹在直墙圆拱断面的坑道临界震塌爆距处爆炸时:围岩处于临界破坏状态,但混凝土衬砌结构处于稳定状态;拱顶的应力峰值明显,且柱状装药情况下,爆炸近区的应力较集团装药情况下的大;拱肩位置出现应力集中;围岩与衬砌结构特征位置处的相互作用载荷与对应质点的振动速度相互耦合,基本成对应的关系。     

87Sr/86Sr in Saxon Mineral and Spa Waters

Abstract

Understanding and preserving the genesis of natural mineral and spa waters is a matter of keen interest. Under a complex analysis programme, ⁸⁷Sr/⁸⁶Sr ratios (as well as other isotopes) were measured in such waters at various sites in Saxony, producing values ranging between 0.708 and 0.731. The strontium isotope ratio was found to be closely linked to the flow patterns and variations in the chemical composition of water. The ⁸⁷Sr/⁸⁶Sr ratio can thus be used as an indicator to characterize groundwater-rock interaction and hence the variation of flow paths. It is especially useful for differentiating waters in a lithologically heterogeneous aquifer system. However, it has to be applied together with other methods and different samples from the same area should be compared.     

Experimental study of uranium isotope fractionation of rock material from two aquifers

This paper presents results of a study carried out in order to estimate the uranium isotope fractionation ²³⁴U/²³⁸U in groundwater from laboratory experiments. Matrix rock from borcholes in a Triassic sandstone aquifer and a Pleistocene sand aquifer was leached with 1 N HCl, 0.1 N HCl and deionized water.

Additionally, the uranium isotope composition of the bulk rock (index “R”) and several groundwater samples of corresponding horizons were analysed. The results indicate the relation between the portion of leached uranium (index “L”) and the observed activity ratio ²³⁴U/²³⁸U (AU)

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If this relation can be confirmed by further investigations new possibilities of using uranium isotopes in hydrogeology would be made available

Die Arbeit stellt Ergebnisse einer Studie vor, die zur Abschützung der Uranium-Isotopenfraktionierung ²³⁴U/²³⁸U im Grundwasser aus Laborexperimenten durchgeführt wurde. Matrixgestein von Bohrlöchern in einem Triassischen Sandstein-Grundwasserleiter und einem aus pleislozänen Sanden bestehenden Grundwasserleiter wurde mit 1 N HCl, 0,1 HCl und entionisiertem Wasser gelaugt. Auβerdem wurden die Uranium-Isotopenzusammensetzung des Gesteins (Index “R”) und einige Grundwasserproben zugehöriger Horizonte analysiert. Die Ergebnisse zeigen cine Beziehung zwischen dem Anteil des gelaugten Uraniums (Index “L”) und dem Aktivitätsverhältnis ²³⁴U/²³⁸U (AU)

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Wenn diese Relation durch weitere Untersuchungen bestäligt werden kann, eröffnen sich neue Möglichtkeiten für die Nutzung der Uraniumisotope in der Hydrogeologie.