利用四元数的运算法则推导球面三角公式

基于四元数的运算法则，引入向量的共轭和逆概念及2个向量之间的另一种乘法运算--格拉斯曼乘积。结果表明，球面上大圆弧对应的四元数为球心指向大圆弧终点的单位向量与球心指向大圆弧始点的单位向量逆的格拉斯曼乘积；球面角对应的四元数为终大圆弧（指向顶点）平面法向的单位向量与始大圆弧（背向顶点）平面法向的单位向量逆的格拉斯曼乘积。利用四元数运算法则可方便地推导球面三角形边或角正弦和余弦公式及第一和第二五元素公式。     

Data assimilation using the particle filter for identifying the elasto‐plastic material properties of geomaterials

A computational method, incorporating the finite element model (FEM) into data assimilation using the particle filter, is presented for identifying elasto‐plastic material properties based on sequential measurements under the known changing traction boundary conditions to overcome some difficulties in identifying the parameters for elasto‐plastic problems from which the existing inverse analysis strategies have suffered. A soil–water coupled problem, which uses the elasto‐plastic constitutive model, is dealt with as the geotechnical application. Measured data on the settlement and the pore pressure are obtained from a synthetic FEM computation as the forward problem under the known parameters to be identified for both the element tests and the ground behavior during the embankment construction sequence. Parameter identification for elasto‐plastic problems, such as soil behavior, should be made by considering the measurements of deformation and/or pore pressure step by step from the initial stage of construction and throughout the deformation history under the changing traction boundary conditions because of the embankment or the excavation because the ground behavior is highly dependent on the loading history. Thus, it appears that sequential data assimilation techniques, such as the particle filter, are the preferable tools that can provide estimates of the state variables, that is, deformation, pore pressure, and unknown parameters, for the constitutive model in geotechnical practice. The present paper discusses the priority of the particle filter in its application to initial/boundary value problems for elasto‐plastic materials and demonstrates a couple of numerical examples. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical analysis of the hydrofracturing behaviour of heterogeneous glutenite considering hydro‐mechanical coupling effects based on bonded particle models

The heterogeneity of tight reservoirs significantly influences hydrofracturing behaviours, such as crack morphology, type, initiation, propagation, and distribution. The accurate characterisation of the influencing mechanisms has become a pivotal issue in enhancing the fracturing stimulation of tight reservoirs, as well as in the prediction of tight oil and gas production. In this study, the hydrofracturing behaviours of heterogeneous glutenites and their influencing mechanisms were numerically investigated based on bonded particle models (BPMs). The geometry and mechanical properties of the natural glutenites were obtained using microfocus computed tomography (CT) and triaxial tests and were used to construct heterogeneous BPMs. The hydrofracturing behaviours of the heterogeneous BPMs under various in‐situ stresses were analysed with hydro‐mechanical coupling effects considered and compared with those of homogeneous BPMs under the same conditions. The numerical results show that gravels in heterogeneous glutenites inhibit crack propagation. The shear cracks that appear in the initial stage of crack development subsequently propagate and distribute around the injection hole, and there are fewer hydraulic shear cracks than tensile cracks. The crack morphologies of BPMs are found to be consistent with the experimental forms. The numerical simulation provides a way to understand the mechanisms that govern the hydrofracturing crack types and propagation of heterogeneous reservoirs.     

Automatic calibration of HEC‐HMS using single‐objective and multi‐objective PSO algorithms

This study presents single‐objective and multi‐objective particle swarm optimization (PSO) algorithms for automatic calibration of Hydrologic Engineering Center‐ Hydrologic Modeling Systems rainfall‐runoff model of Tamar Sub‐basin of Gorganroud River Basin in north of Iran. Three flood events were used for calibration and one for verification. Four performance criteria (objective functions) were considered in multi‐objective calibration where different combinations of objective functions were examined. For comparison purposes, a fuzzy set‐based approach was used to determine the best compromise solutions from the Pareto fronts obtained by multi‐objective PSO. The candidate parameter sets determined from different single‐objective and multi‐objective calibration scenarios were tested against the fourth event in the verification stage, where the initial abstraction parameters were recalibrated. A step‐by‐step screening procedure was used in this stage while evaluating and comparing the candidate parameter sets, which resulted in a few promising sets that performed well with respect to at least three of four performance criteria. The promising sets were all from the multi‐objective calibration scenarios which revealed the outperformance of the multi‐objective calibration on the single‐objective one. However, the results indicated that an increase of the number of objective functions did not necessarily lead to a better performance as the results of bi‐objective function calibration with a proper combination of objective functions performed as satisfactorily as those of triple‐objective function calibration. This is important because handling multi‐objective optimization with an increased number of objective functions is challenging especially from a computational point of view. Copyright © 2012 John Wiley & Sons, Ltd.     

Constitutive modeling of dense gravelly soils subjected to cyclic loading

A constitutive model for dense gravelly soils was developed to reproduce their responses under cyclic loadings. Its application aims at nonlinear dynamic analyses of earth structures involving gravelly soils, such as rockfill dams and railroad ballasts. The framework of generalized plasticity was modified to incorporate the concept of stress distance for better simulation of unloading and reloading responses. It was then combined with the theory of critical state soil mechanics to develop the constitutive model. The model has the following important features: unified simulation of particle breakage through translating critical state line, smooth transition from unloading to reloading in the stress space, and proper modeling of cyclic hysteresis, cyclic densification, and cyclic hardening of dense gravelly soils. Most of the model parameters can be obtained through simple calculation using conventional triaxial test results, and their calibration process was discussed. The model was used to simulate the cyclic responses of three gravelly soils with satisfactory accuracy. Copyright © 2014 John Wiley & Sons, Ltd.     

尾砂胶结充填体蠕变模型及在FLAC3D 二次开发中的实验研究

关于岩石蠕变特性的研究已有诸多成果,但对胶结充填体的蠕变特性还缺乏系统地研究。在室内充填体单轴蠕变试验的基础上,利用Hoek-Kelvin模型表征充填体的蠕变特性,运用粒子群优化算法,对选用的蠕变模型的参数进行辨识,并研究各蠕变参数对应力水平的敏感程度。研究结果表明,在不同分级应力水平加载下,弹性模量EH和黏滞系数η变化较小,而参数EK对应力水平变化较敏感。利用FLAC3D软件二次开发所建立的蠕变模型,用开发的模型进行分级加载蠕变的数值模拟,计算结果与试验数据吻合。     

横流中多孔射流流动特性实验研究

横流中多孔射流的流动特性是揭示其输移扩散机理的基础。利用粒子图像测速技术PIV测量了横向流动条件下单孔、两孔和四孔射流的速度场,对射流主体范围内、射流的迎流面和各个射流之间的流场进行了研究。实验研究表明,多个射流中的第1个射流迎流面卷吸强度明显大于单个射流情况;两个射流之间的区域可分为两个部分,上游部分水体被卷吸进入上一个射流,下游部分水体被卷吸进入下一个射流;后面射流迎流面的横向流速明显低于第1个射流迎流面的横向流速,揭示了导致后面射流弯曲的横向有效流速沿程发展变化过程;揭示了横向有效流速的沿程变化规律。     

Inter‐instrument comparison of particle‐size analysers

This paper presents a methodological framework for inter‐instrument comparison of different particle‐size analysers. The framework consists of: (i) quantifying the difference between complete particle‐size distributions; (ii) identifying the best regression model for homogenizing data sets of particle‐size distributions measured by different instruments; (iii) quantifying the precision of a range of particle‐size analysers; and (iv) identifying the most appropriate instrument for analysing a given set of samples. The log‐ratio transform is applied to particle‐size distributions throughout this study to avoid the pitfalls of analysing percentage‐frequency data in ‘closed‐space’. A Normalized Distance statistic is used to quantify the difference between particle‐size distributions and assess the performance of log‐ratio regression models. Forty‐six different regression models are applied to sediment samples measured by both sieve‐pipette and laser analysis. Interactive quadratic regression models offer the best means of homogenizing data sets of particle‐size distributions measured by different instruments into a comparable format. However, quadratic interactive log‐ratio regression models require a large number of training samples (n > 80) to achieve optimal performance compared to linear regression models (n = 50). The precision of ten particle‐size analysis instruments was assessed using a data set of ten replicate measurements made of four previously published silty sediment samples. Instrument precision is quantified as the median Normalized Difference measured between the ten replicate measurements made for each sediment sample. The Differentiation Power statistic is introduced to assess the ability of each instrument to detect differences between the four sediment samples. Differentiation Power scores show that instruments based on laser diffraction principles are able to differentiate most effectively between the samples of silty sediment at a 95% confidence level. Instruments applying the principles of sedimentation offer the next most precise approach.     

青岛市环胶州湾各河流输沙特征分析

通过对青岛市环胶州湾各河流上的水文站历年含沙量、输沙量资料分析计算,推求出各河流的入海输沙量,并对输沙特征进行分析评价,最后得出以下以下结论:(1)从空间分布来看,胶州湾河流输沙主要来自胶州湾西北部和东北部。(2)河流属中沙河流。河道上游多年平均含沙量和输沙模数均大于河道中下游。(3)输沙量年际变化较大,最大年输沙量是最小年输沙量的518.7倍,且年降水量较大时,年入海水量也较大,年输沙量也较大。(4)河流悬移质颗粒特征为河流从源头到河口,泥沙粒径是不断减小。     

能谱仪PPA分析方法的实验研究: 以山西大同新生代玄武岩样品为例

以山西大同新生代玄武岩样品为例, 利用Quanta 200扫描电镜、GENESIS能谱仪对能谱仪PPA分析方法进行了实验研究, 该方法为粒度和物相自动分析方法.笔者首次把能谱仪PPA分析方法应用到地质学领域的岩石光薄片研究中, 快速得出了一系列不同物相的形态学数据及化学成分分析结果: 物相种类、每一种物相的颗粒数、每一个颗粒的平均直径、面积、周长、圆度、长宽比及化学成分等, 并得出了不同物相在该视域所占的面积百分比及每种物相颗粒的平均直径, 克服了传统光薄片粒度分析方法的所有缺点, 为矿物学、岩石学及矿床学研究提供了一套非常有意义的数据.