Focal mechanism of earthquakes in the Kamchatka-Commander region and heterogeneities of the active seismic zone

Summary Focal mechanisms of 74 shallow and 16 intermediate earthquakes (1964–1970) in the Kamchatka-Commander region are discussed. Regional stress systems and the nature of faulting are analyzed. Complex stress fields in the Kamchatka-Commander region and variable aftershock processes of strong Kamchatka earthquakes show the existence of heterogeneities of the active seismic zone in the Region.     

区间系统与区间优化模型——理论与应用

区间系统与区间优化模型是一种应用广泛的描述不确定性问题的数学模型.本文综述区间系统与区间优化模型在理论与应用方面的研究进展.特别地,本文将介绍区间线性系统的解和可解性问题、区间线性优化模型的最优解和最优性问题以及区间二次优化模型的最优解和最优性问题,最后简单概述它们的各种应用实例.     

Transient solution for a plane‐strain fracture driven by a shear‐thinning,power‐law fluid

This paper analyses the problem of a fluid‐driven fracture propagating in an impermeable, linear elastic rock with finite toughness. The fracture is driven by injection of an incompressible viscous fluid with power‐law rheology. The relation between the fracture opening and the internal fluid pressure and the fracture propagation in mobile equilibrium are described by equations of linear elastic fracture mechanics (LEFM), and the flow of fluid inside the fracture is governed by the lubrication theory. It is shown that for shear‐thinning fracturing fluids, the fracture propagation regime evolves in time from the toughness‐ to the viscosity‐dominated regime. In the former, dissipation in the viscous fluid flow is negligible compared to the dissipation in extending the fracture in the rock, and in the later, the opposite holds. Corresponding self‐similar asymptotic solutions are given by the zero‐viscosity and zero‐toughness (J. Numer. Anal. Meth. Geomech. 2002; 26 :579–604) solutions, respectively. A transient solution in terms of the crack length, the fracture opening, and the net fluid pressure, which describes the fracture evolution from the early‐time (toughness‐dominated) to the large‐time (viscosity‐dominated) asymptote is presented and some of the implications for the practical range of parameters are discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

Lateral stress caused by horizontal and vertical surcharge strip loads on a cross‐anisotropic backfill

This study derives analytical solutions for estimating the lateral stress caused by horizontal and vertical surcharge strip loads resting on a cross‐anisotropic backfill. The following loading types are employed in this work: point load, line load, uniform strip load, upward linear‐varying strip load, upward nonlinear‐varying strip load, downward linear‐varying strip load and downward nonlinear‐varying strip load. The cross‐anisotropic planes are assumed to be parallel to the horizontal surface of the backfill. The solutions proposed herein have never been mentioned in previous literature, but can be derived by integrating the point load solution in a Cartesian co‐ordinate system for a cross‐anisotropic medium. The calculations by the presented solutions are quick and accurate since they are concise and systematized. Additionally, the proposed calculations demonstrate that the type and degree of material anisotropy and the horizontal/vertical loading types decisively influence the lateral stress. This investigation presents examples of the proposed horizontal and vertical strip loads acting on the surface of the isotropic and cross‐anisotropic backfills to elucidate their effects on the stress. The analytical results reveal that the stress distributions accounting for soil anisotropy and loading types are quite different from those computed from the available isotropic solutions. Restated, the derived solutions, as well as realistically simulating the actual surcharge loading circumstances, provide a good reference for the design of retaining structures for the backfill materials are cross‐anisotropic. Copyright © 2005 John Wiley & Sons, Ltd.     

On matrix diffusion: formulations, solution methods and qualitative effects

 Matrix diffusion has become widely recognized as an important transport mechanism. Unfortunately, accounting for matrix diffusion complicates solute-transport simulations. This problem has led to simplified formulations, partly motivated by the solution method. As a result, some confusion has been generated about how to properly pose the problem. One of the objectives of this work is to find some unity among existing formulations and solution methods. In doing so, some asymptotic properties of matrix diffusion are derived. Specifically, early-time behavior (short tests) depends only on φ _m ² R _m D _m  / L _m ², whereas late-time behavior (long tracer tests) depends only on φ _m R _m , and not on matrix diffusion coefficient or block size and shape. The latter is always true for mean arrival time. These properties help in: (a) analyzing the qualitative behavior of matrix diffusion; (b) explaining one paradox of solute transport through fractured rocks (the apparent dependence of porosity on travel time); (c) discriminating between matrix diffusion and other problems (such as kinetic sorption or heterogeneity); and (d) describing identifiability problems and ways to overcome them. Received, October 1997 · Revised, November 1997 · Accepted, December 1997     

中心裂纹巴西圆盘压缩载荷下T应力研究

为了研究中心裂纹巴西圆盘试件在压缩载荷作用下T应力的解析计算方法,通过权函数法推导出集中载荷作用下T应力的显式表达式,进而得到分布载荷作用下的T应力表达式。与边界配位法进行对比,所得公式优点在于任意相对裂纹长度和任意加载角下的T应力值都能较容易的精确得到。进一步分析表明,分布载荷与集中载荷作用下T应力的偏差随着载荷分布角的增加而增加。集中载荷作用下,相对裂纹长度固定时,T应力随着加载角的增大而增大。中心裂纹巴西圆盘纯I型与纯II型断裂试验时,大多数情况下的T应力都为负值。T应力值对中心裂纹巴西圆盘测定断裂韧度试验有影响,想要通过使T应力为0来消除这种影响是很难达到目的的。     

A finite strain solution for the elastoplastic ground response curve in tunnelling: rocks with non‐linear failure envelopes

This paper generalizes the finite strain Coulomb solution of Vrakas and Anagnostou (Int J Numer Anal Meth Geomech 2014; 38(11): 1131–1148) for the classic tunnel mechanics problem of the ground response curve to elastoplastic grounds satisfying a non‐linear Mohr's failure criterion. A linear (Coulomb‐type) plastic potential function is used, leading to a non‐associated flow law, and edge plastic flow is considered in the plastic zone. The solution for a general non‐linear Mohr's failure criterion is semi‐analytical in that it requires the evaluation of definite integrals. In the special case of the Hoek–Brown criterion, however, these integrals are calculated analytically, resulting in a rigorous closed‐form series solution. The applicability of the derived solution is illustrated through the example of the Yacambú‐Quibor tunnel, where very large deformations were observed when crossing of weak graphitic phyllites. Copyright © 2016 John Wiley & Sons, Ltd.     

Second-Order Solutions for Random Interfacial Waves Under Steady Uniform Currents

1.Introduction Owingtothesimilaritiesbetweenthesurfacewaveandtheinterfacialwave,itisnaturaltoapply themethodsdevelopedforsurfacewavestothestudyofinterfacialwavesasreviewedbyUmeyama (1998;2000).Recently,Song(2004)derivedsecond ordersolutionsforrandominterfacialwavesat aconstantdepthinatwo layerfluidsystemwitharigidlidusinganexpansiontechnique,analogousto thatusedbyLonguet Higgins(1963)andSharmaandDean(1979),tostudyrandomsurfacewaves. Inthispaper,Song’sresultsareextendedtoamoregeneralcaseoft…     

Evaluation of foam conditioning effect on groundwater inflow at tunnel cutting face

This paper presents an analytical evaluation on the influence of foam conditioning on groundwater inflow at shield tunnel cutting face by the force-equilibrium principle. Three key variables are highlighted, namely, the maximum foam infiltration distance, the critical infiltration distance, and the hydraulic conductivity of foam-conditioned soil or rock fissure. To capture the variation of water level induced by foam injection, a dynamic water-level equation is considered in the force-equilibrium principle. The proposed analytical equations are employed to analyze a water inflow case during shield tunneling in a weathered mylonite fault. The results indicate that the hydraulic conductivity of foam-conditioned mylonite and the infiltration distance decrease with an increase of shear stress of foam fluid. A three-dimensional finite element model is employed to validate the analytical solutions. The comparison between the observed and calculated results confirms that the proposed method can predict groundwater inflow in foam-conditioned soils.     

Comparative analysis between analytical approximations and numerical solutions describing recession flow in unconfined hillslope aquifers

Recession flow of aquifers from a hillslope can be described by the non-linear Boussinesq equation. Under strong assumptions and for specific conceptual formulations, different authors derived analytical approximations or linearized versions to this partial differential equation. A comparative analysis between some analytical approximations of the Boussinesq equation and the numerical solution of the recession flow of an unconfined homogeneous aquifer (horizontal, inclined and concave aquifer floor) was carried out. The objective was to define the range where the analytical solutions approximate the numerical solution. The latter was considered in this study as the reference method, because it requires fewer assumptions. From the considered analytical approximations, exponential decay relationships were found to be mainly valid for fine domain materials when horizontal, mild slopes (less than 2%) and concave aquifer floors were considered, but failed to reproduce coarse aquifer numerical model outflows, in contrast to the quadratic decay relationship, which better reproduce outflows in such domains. On the basis of the comparative analysis, it has been found that recession flows obtained with the considered analytical approximations yield similar values only for certain ranges of aquifer properties and geometries.

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Résumé L’écoulement de décrue dans les aquifères de versant peut être décrit par l’équation non-linéaire de Boussinesq. En considérant d’importantes hypothèses et des formulations conceptuelles spécifiques, différents auteurs ont dérivé des approximations analytiques ou des versions linéarisées de cette équation partielle différentielle. Une analyse comparative entre des approximations analytiques de l’équation de Boussinesq et une solution numérique de la décrue d’un aquifère homogène libre (limite inférieure de l’aquifère horizontale, inclinée et concave) a été effectuée. L’objectif était de définir la plage pour laquelle les solutions analytiques approchent la solution numérique. Cette dernière a été considérée dans cette étude comme la méthode de référence car elle demande moins d’hypothèses. Parmi les approximations analytiques considérées, les relations de décroissance exponentielle se sont avérées être principalement valides pour des matériaux fins lorsque des couches aquifères horizontales, concaves et de pentes douces (moins de 2%) étaient considérées; en revanche, celles-ci n’ont pas réussi à reproduire les écoulements sortants d’un modèle numérique pour un aquifère à matériaux grossiers, contrairement à la relation de décroissance quadratique qui reproduit mieux les écoulements sortants dans de tels milieux. Sur la base de l’analyse comparative, il s’est avéré que les écoulements en décrue obtenus avec les approximations analytiques considérées présentent des valeurs similaires seulement pour certains critères géométriques et propriétés de l’aquifère.

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Resumen Puede describirse el flujo de recesión de acuíferos de una ladera mediante la ecuación no-lineal de Boussinesq. Bajo fuertes supuestos y para formulaciones conceptuales específicas, distintos autores han derivado aproximaciones analíticas o versiones lineales para esta ecuación parcial diferencial. Se realizó un análisis comparativo entre algunas aproximaciones analíticas de la ecuación de Boussinesq y la solución numérica del flujo de recesión de un acuífero homogéneo no confinado (piso de acuífero cóncavo, inclinado, y horizontal). El objetivo consistió en definir el rango donde las soluciones analíticas aproximan la solución numérica. En este estudio se consideró la solución numérica como el método de referencia debido a que requiere menores supuestos. De las aproximaciones analíticas consideradas se encontró que las relaciones de desintegración exponencial eran principalmente válidas para materiales de ámbitos finos donde se consideraron pisos de acuíferos horizontal, pendientes medianas (menores a 2%) y cóncavos pero fallaron en reproducir flujos de salida de modelos numéricos de ámbito grueso, en contraste con la relación de desintegración cuadrática la cual reproduce mejor los flujos de salida en tales ámbitos. En base al análisis comparativo se encontró que los flujos de recesión obtenidos con las aproximaciones analíticas consideradas aportaron valores similares solo para ciertos rangos de propiedades y geometrías de acuíferos.