A critical state model for sands dependent on stress and density

An elastoplastic model for sands is presented in this paper, which can describe stress–strain behaviour dependent on mean effective stress level and void ratio. The main features of the proposed model are: (a) a new state parameter, which is dependent on the initial void ratio and initial mean stress, is proposed and applied to the yield function in order to predict the plastic deformation for very loose sands; and (b) another new state parameter, which is used to determine the peak strength and describe the critical state behaviour of sands during shearing, is proposed in order to predict simply negative/positive dilatancy and the hardening/softening behaviour of medium or dense sands. In addition, the proposed model can also predict the stress–strain behaviour of sands under three-dimensional stress conditions by using a transformed stress tensor instead of ordinary stress tensor. Copyright © 2004 John Wiley & Sons, Ltd.     

On the practice of estimating fractal dimension

Coastlines epitomize deterministic fractals and fractal (Hausdorff-Besicovitch) dimensions; a divider [compass] method can be used to calculate fractal dimensions for these features. Noise models are used to develop another notion of fractals, a stochastic one. Spectral and variogram methods are used to estimate fractal dimensions for stochastic fractals. When estimating fractal dimension, the objective of the analysis must be consistent with the method chosen for fractal dimension calculation. Spectal and variogram methods yield fractal dimensions which indicate the similarity of the feature under study to noise (e.g., Brownian noise). A divider measurement method yields a fractal dimension which is a measure of complexity of shape.     

Experimental constraints on the effects of pressure and H2O on the fractional crystallization of high-Mg island arc basalt

H₂O-undersaturated melting experiments of synthesized basalt (SiO₂ = 50.7 wt.%, MgO = 8.3 wt.%, Mg# = 60) were conducted at fO₂ corresponding to NNO+1 and NNO−1 to clarify the effects of pressure (2–7 kbar) and H₂O on fractional crystallization in island arcs. H₂O content was ranged from nominally anhydrous to 4.4 wt.%. Differentiation trends, namely the liquid lines of descent, change sensitively according to pressure-H₂O relations. Tholeiitic differentiation trends are reproduced with H₂O ≤ ∼2 wt.% in primary magma. With such quantities of H₂O, fractional crystallization is controlled by olivine + plagioclase at 2 kbar. Increasing the pressure from 2 to ≥4 kbar induces early crystallization of orthopyroxene instead of olivine and therefore SiO₂ enrichment in the residual melts is suppressed. Increasing H₂O (≥ ∼2 wt.% in primary magma) stabilizes clinopyroxene relative to orthopyroxene and/or magnetite. Although the phase relations and proportions strongly depend on fO₂ and H₂O content, differentiation trends are always calc-alkaline.     

Influence of Structural Non-Stationarity of Surface Roughness on Morphological Characterization and Mechanical Deformation of Rock Joints

Summary Structural non-stationarity of surface roughness affects accurate morphological characterization as well as mechanical behaviour of rock joints at the laboratory scale using samples with a size below the stationarity threshold. In this paper, the effect of structural non-stationarity of surface roughness is investigated by studying the scale dependence of surface roughness and mechanical behaviour of rock joints. The results show that the structural non-stationarity mainly affects the accurate characterization of the surface roughness of the fracture samples. It also controls the amount and location of the contact areas during shear tests, which in turn affects the mechanical properties and asperity degradation of the samples. It is concluded that for accurate determination of the morphological and mechanical properties of rock joints at laboratory and field scales, samples with size equal to or larger than the stationarity threshold are required. Author’s address: Nader Fardin, Rock Mechanics Group, Department of Mining Engineering, Faculty of Engineering, University of Tehran, P.O. Box: 11365/4563, Tehran, Iran     

河北大庙Fe-Ti-P矿床中铁钛磷灰岩的成因: 来自磷灰石的证据

铁钛磷灰岩仅由磷灰石和铁钛氧化物组成,常赋存于岩体型斜长岩中,成因上有不混溶和分异堆晶两种不同的认识。本文从磷灰石角度讨论河北大庙铁钛磷灰岩的形成机制。大庙铁钛磷灰岩常产出于浸染状Fe—P矿体内部,有时与块状铁矿石交互出现形成韵律条带状矿石,为岩浆结晶分异的产物。铁钛磷灰岩中磷灰石呈浑圆状,含量变化于15％-34％。铁钛磷灰岩的全岩和磷灰石微量元素分析显示,磷灰石比全岩相对富集稀土元素达2．96—6．93倍,但两者的配分型式基本平行。质量平衡计算（Rocl／F）的结果表明,铁钛磷灰岩中几乎100％的稀土元素赋存于磷灰石中。综合上述特征,反映磷灰石为结晶分离的堆晶矿物,铁钛磷灰岩应为堆晶成因。因为如果磷灰石结晶于铁钛磷灰岩不混溶熔体,它的稀土元素分配系数也不会变化达2．3倍（变化于2．96—6．93）。计算出该磷灰石的母岩浆稀土元素组成,与浸染状Fe．P矿石最为相似,结合它与铁钛磷灰岩之间紧密共生的野外特征以及相似的全岩及磷灰石稀土元素配分型式,认为磷灰石最可能是在浸染状Fe．P矿浆中,经结晶分离作用形成铁钛磷灰岩。     

Fractal Determination of Coastal Types Based on GIS--A Case Study of China

The probability of fractal determination of coastal types based on GIS is preliminarily discussed with China as an example. Finally, some significant conclusions are drawn: (1) The fractal dimension of coastline of the bedrock coast is larger than that of the plain coast on the same scale map; (2) As far as the bedrock coast is concerned, the larger fractal dimension of coastline of the bedrock coast on the same scale map indicates that the bedrock coast is probably not typical; (3) As far as the plain coast is concerned, the smaller fractal dimension of coastline of the plain coast on the same scale map indicates that it is probably the silt plain coast; (4) The different substantial compositions affect the fractal dimensions of coastlines of different coastal types. In general, the coast which lies in the north of the Hangzhou Bay consists of sand mainly, its surface is flat, and it is connected with the coastal plain, its landform is broad shoal, its total change is comparatively homogenous in the tidal dynamic process, and thus, the relatively smaller fractal dimension of coastline results from this. For the bedrock coast, there is more bedrock, the coastline is comparatively smooth and straight, being affected by the faults and ocean dynamic process, which result in the larger fractal dimension.     

富钴结壳分布的分形特征

利用我国在西太平洋国际海底两个海山获得的富钴结壳资料进行分形研究后发现，富钴结壳的分布具有变维分形分布的特点，结壳丰度呈二阶累计和分形分布，结壳厚度呈多阶不定累计和分形分布，通过计算得到了它们各自的分维数，进而对两个海山的结壳资源进行了初步评价。     

Fractal Dimension and Fractals in Ocean Engineering

- This paper discusses the application of fractal dimension and fractals in ocean engineering. To handle some ocean environment problems, the existing fractal method, in which the fractal dimension is a constant, can be used. For some complicated problems in ocean engineering, this paper presents the concept of the variable dimension fractals (D = f(r)), i. e., the fractal dimension D is the function of characteristic scale r instead of a constant. By using variable dimension fractals, several deformation and stress states of offshore structures are described.     

海浪日最大波高序列的一种标度性质

应用重标度分析方法研究小麦岛海洋观测站１９６１－１９８０年二十年海浪日最大波高序列时发现，该序列并不是相互独立的，而是具有记忆性和持久性，详细的论证表明分式布朗运动模型是描述海浪日最大波高序列的一个较好的模型，同时，应用分式布朗运动模型我们找到了存在于海浪日最大波高序列中的一种标度性质－累积离差（ｔ）的统计自仿射性。     

Optimizing interpolation of shoot density data from a Posidonia oceanica seagrass bed

A case study on the optimization of Posidonia oceanica density interpolation, using a data set from a large meadow at Porto Conte Bay (NW Sardinia, Italy), is presented. Ordinary point kriging, cokriging and a weighted average based on inverse square distance were used to interpolate density data measured in 36 sampling stations. The results obtained from different methods were then compared by means of a leave‐one‐out cross‐validation procedure. The scale at which interpolation was carried out was defined on the basis of the Hausdorff dimension of the variogram. Optimizing spatial scale and data points search strategy allowed obtaining more accurate density estimates independently of the interpolation method.