The use of computer animation techniques in the teaching of stereographic projection

A suite of 10 programs, written for the BBC Model B, uses computer animation techniques to aid in the teaching of the principles of stereographic projection. The representation of the net remains static in the background whilst plotting and rotation occur on a foreground plane. This mimics the actual operations that are required using a net and tracing paper. Plotting of planes, lines, intersection and rotation problems are covered by this package. The methods of computer animation are reviewed.     

赤平投影图的数学解析

先对赤平投影成图原理进行分析,在此基础上对投影图作了数学解析,得出构图要素(线、面)在投影图上的等量关系和组合规律,使得用计算机语言来精确表达成为可能,以便于编程求解线与面问题。另外,文中还对其计算机语言表达的相关问题进行了探索,提出了在实现编程求解过程中值得注意的一些问题。     

Pedagogy of stereographic projection

Three sorts of problem are encountered by students learning stereographic projection. Lack of familiarity with compass directions and with the specification of planar and linear orientations is the most fundamental problem. The second problem is one of poor visualisation which prohibits the correct understanding of the principles and practice of projection, although students can sometimes perform remarkably well on certain exercises without this understanding. A third problem is a lack of interest or appreciation of the usefulness of the technique. A solution to the first problem is to provide a thorough grounding in compass directions, and concepts of strike, dip, dip direction, plunge and plunge bearing immediately before teaching stereographic projection. Visual aids, such as a transparent hemisphere to represent half of the projection sphere, and a large stereonet, are helpful for visualisation. Estimation and sketching exercises help to develop an understanding of the geometry of projection. Computer-aided teaching and plotting is recommended after an introduction to manual techniques. Interest can be stimulated through the use of exercises based on real geological maps.     

Modified perspective cylindrical map projection

Some of the famous cylindrical projections are defined by a geometric process that is based on the perspective. This process can be imagined as a semitransparent sphere wrapped by a tube, secant, or tangent, with the same center; then all features of the sphere surface are projected onto the tube surface by light rays from a source in the equatorial plane. Just by changing the light source’s position and tube’s diameter, different maps can result. In every cylindrical perspective projections, distortions are functions of latitude only, thus, the value of distortion is fixed along a parallel (or a small circle). Therefore, distortion isograms are parallels (or small circles), symmetrical in relation of the equator. Consequently, it is suitable for territories having narrow band shape, extended by the equator (or an oblique equator). The proposed projection in this paper introduces another possible adjustment in cylindrical projections, in which axis of cylinder does not pass through the center of the sphere. This may satisfy case, where territories have a closed curve shape. By comparing the distribution of distortions in other famous perspective cylindrical projections (Lambert, stereographic, and central), with that in the proposed modified perspective cylindrical projection, it was found that distribution of area distortion in the proposed projection can be considered better than others. Therefore, in relation to area representation, the modified perspective cylindrical projection can be considered suitable for mapping regions, having shape close to an ellipse.     

某水电站引水洞进口侧山体边坡块体识别

某水电站进口侧山体边坡岩体为完整性较差的中--薄层状灰岩,岩体中主要发育3 条断层、1 组岩脉和4 组优势节理,严重影响了该山体边坡的稳定性。根据结构面分布,采取块体理论搜索边坡上的关键块体,通过赤平投影法找出边坡上所有的非空裂隙锥,将这些非空裂隙锥与临空面组合,从而获得所有可动块体; 利用矢量法计算不同运动形式下块体JP 编号、净滑力即可获得关键块体。结果表明: 该水电站引水洞进口侧山体边坡有4 块关键块体( JP 编号为00010111、00110111、10110111、 10111011) ,为该边坡稳定性的进一步研究提供了基础。     

Fuzzified kinematic analysis of discontinuity-controlled rock slope instabilities

In this study, it is aimed to bring a different approach to kinematic analyses of discontinuity-controlled rock slope instabilities. For this purpose, the data of a detailed discontinuity survey carried out in Ankara, the capital city of Turkey, were updated and reevaluated. Serious discontinuity-controlled instability events were observed in the andesites covering large areas with dense population in the city. Instead of analyzing the effects of the planes belonging only to the major discontinuity sets on the stereographic projection net, all discontinuities were taken into consideration, and kinematic analyses were carried out for planar, wedge, and toppling type failures on pixel basis of the Digital Elevation Model (DEM) of the study area. By doing so, it could be possible to compensate for the deficiency created by neglecting the planes in the lower concentration zones of the stereographic projection. A computer program named FUDIKA (Fuzzified Digital Kinematic Analyses) was written to perform modular kinematic analyses and fuzzy operations, having four modules and operating in three stages. First, Potential Instability Index (PII) was introduced to define instability potential of the rock slopes based on the number of possible instability events for each failure type. Next, the PII values were normalized and fuzzified to obtain PII map of the area. It was seen that when tested on previously occurred instabilities in the area, the PII values obtained through the methodology proposed in the study showed quite a high performance.     

Structural orientation files: creation,modification and storage using a bbc microcomputer

Field orientation and universal-stage data are easily stored as computer data files. A stereographic projection package has been developed to create and modify such data files and allow their use in conjunction with plotting and contouring routines. The first of these programs, the filing system, is discussed.     

Structural data extraction from stereographic or equal area projections using image processing

Structural orientation data from the field are commonly represented on stereographic or equal area projections, and the raw data are usually not accessible to other workers for integration into larger datasets or comparative study. We have developed a technique for retrieving raw planar structural data from the above projection types using image analysis techniques. The principle involves two steps: (i) conversion of the foliation pole plots in the image into Cartesian coordinates, and (ii) inversion of the data soobtained into a geographic reference frame. The process involves either scanning of the target projection, or cropping of the projection figure from a pdf file using image processing software, followed by tracing of the data points and generation of an image file that can be subsequently input into a MATLAB supported program, “StrucExtract”. The results from the program are displayed in the form of dips and dip directions. The program has been tested with synthetic and natural examples, and may be invaluable for retrieval of structural data from older structural literature.     

SMR and Kinematic analysis for slope instability along Bodi-Bodimettu ghat section,Tamil Nadu

This study evaluates slope stability of 19km stretch Bodimettu ghat section, Theni,Tamil Nadu. The study involves 107.8km to 117.5km stretch by dividing it into two zones - Kaththuparai and Bodimettu slope. These two sections are considered for slope stability studies. In this study, analysis of the rock slope stability was performed using Modified SMR technique. Hoek and Bray (1981) analysis have been used for rock cut slopes. 12 rock slopes were identified in Kaththuparai section and four slopes in Bodimettu section. The detailed field investigations were carried out to collect data required for RMR and SMR calculation and SMR was calculated for each section. As per Hoek and Bray (1981) stereographic projection methods, FOS was calculated. In this study, sections R1 and R2 fulfill wedge conditions and R1, R2, R5, R7, R9, R10, R11, R12, R13, R14 and R16 are suitable for planar and stereographic analysis. The details are furnished in this paper. The planar analysis shows that, FOS for the sections R2/J2, R5, R9, R10, and R11/J3 was < 1, and stereographic projection study shows that sections R2, R5, R7, R9, R10, R11/J3 and R13 are present in unstable zone.     

极射赤平投影在定向钻进轨迹设计计算中的应用

赤平投影是将物体三维空间的几何要素(线、面)反映在投影平面上进行处理的方法。将极射赤平投影方法应用到定向钻进轴线的设计计算中,将空间问题转化为平面问题,再利用球面三角形有关公式进行计算,即可得到一系列的特征参数计算公式。研究表明,采用极射赤平投影和球面三角形解析几何相结合的设计计算方法,是一种既简便又快捷的定向钻进轨迹设计方法。      

Study on Three-dimensional Visualization for Rock Structure

The visualization of rock structure is a very useful and important technique in many aspects in geological and geotechnical engineering such as investigating and evaluating the stability of a high rock slope. The conventional method used to visualize rock structure is limited to plotting the orientation of individual discontinuities by using the Schmidt stereographic net. The present paper shows a new technique to visualize the three-dimensional structure of rock masses. The fitting function for three-dimensional rock structure was established based on data gathered from field survey. Two fitting methods by which the discontinuous points gathered from a plane and discrete points from field survey were fitted respectively are suggested. The technique to visualize the three-dimensional structure of rock masses includes many aspects such as projection transformation, blanking and mutual cutting, are investigated. Based on the visualizing technique, the rock structure at the site of Xilupdu dam which is being built in Southwest of China was investigated.     

九台地区岩质边坡稳定性及运动过程评价方法探讨

文章对九台地区岩质边坡的稳定性及运动过程进行了评价方法的探讨,通过岩质边坡的发育特征,分析了边坡失稳的原因,通过赤平投影图与离散元数值模拟对边坡的稳定性进行了分析,并对边坡崩塌的范围进行了预测,为边坡的稳定性计算提供借鉴参考.     

裂隙化岩体中圆形断面调压井围岩稳定性分析

块体理论是适用于裂隙化岩体变形失稳分析的有效方法。运用块体理论赤平投影法研究某水电站超大型调压井围岩随机块体的稳定性,将圆形断面调压井开挖临空面抽象简化为八个方位的边墙加以研究,分析了井周各部位可能的关键块体及其运动形式,计算了关键块体的净滑力。分析结果对工程施工具有可靠的现实指导作用,为锚固设计和永久衬砌设计提供了依据,可供类似工程参考。     

Characteristics and remediation of a landslide complex triggered by the 2008 Wenchuan, China earthquake-case from Yingxiu near the earthquake epicenter

During the 2008 Wenchuan earthquake, the river valley from Yingxiu to Wenchuan experienced numerous landslides and became a prominent area of landslide complexes. The present large landslide complex near the earthquake epicenter consisted of Laohuzui slide 1, Laohuzui slide 2 and Douyaping slide. The scale, geology, morphology, sliding process, and failure mechanism of the landslide complex are analyzed by means of field investigation, aerial photograph and stereographic projection technique. Characteristics of these three slides including seismic response of slope, landslide debris, damage and potential failure are discussed: the convex slope and the upslope of fractured granitic rock at high altitude are highly prone to landsliding under earthquake; the high source altitude and long travel path determine grain sizes and the deposit angle of the slide debris; the landslide complex completely buries the G213 roadway and dams up the Minjiang River in these sections; after the earthquake, rainfall, aftershocks and river erosion may retrigger new failures, such as retrogressive slide of weathered fractured rock, colluvial landslide, debris flow, embankment failure and rockfall. The following are presented as suggested remedial measures to protect the roadway and stabilize the slope: the removing and trenching, protective concrete/rock blocks against erosion, retaining structure, rockfall stopping wall, rockfall restraining net, rock bolt, and the planting of vegetation.     

河北丰宁窄岭金矿古岩体的剪切变形与成矿

河北丰宁窄岭金矿伴随剪切带早期活动侵入的斑状花岗石（γ＾１２）闪长岩（δ）等古岩体，由于剪切带的进一步演化，形成了一套独特的剪切变形糜棱岩，其中斑状花岗岩经剪切变形产生的糜棱岩化花岗岩，眼球状、条带状和微细粒支状花岗质糜棱片麻岩系列尤为典型。而伴随古岩体剪切变形所出现的面型，裂隙型碱交代作用，则是窄岭金矿最科聚集成矿的重要条件。     

基于极射赤平投影的岩质边坡稳定性评价和防治措施

岩质边坡破坏主要由结构切割形成的楔形体失稳造成.通过对无锡滨湖区-露天采矿形成的岩质边坡稳定性的评价,介绍利用极射赤平投影法评价岩质边坡稳定性和提出不稳定岩质边坡防治措施的基本原理和方法.     

An improved Monte Carlo simulation method for discontinuity orientations based on Fisher distribution and its program implementation

Fisher distribution is the most commonly used probability density function for discontinuity orientations. Based on Fisher distribution, Monte Carlo simulation method for discontinuity orientations was reviewed and improved. Those orientations extending beyond the edge of an upper hemisphere projection (OEBEUHP) often have an important influence on both the mean orientation and Fisher constant K, thus affecting simulation results. The detailed algorithms for identifying and adjusting those OEBEUHP were developed in this paper. Based on the improved method, a program for generating discontinuity orientations and plotting their stereographic projection maps, named as MCSDO, was developed. Due to the aforementioned adjustment, the generated orientations by MCSDO are close to the original discontinuity orientations, which were mapped in field, and satisfactory. Only the original orientations and target number of generated orientations need to be input. By running the program we can directly obtain the follows: orientations of generated discontinuities, mean orientations of both original and generated discontinuities, Fisher constant K of both original and generated discontinuities, and stereographic projection maps of both original and generated discontinuities. MCSDO is a freeware designed for researchers and practicing engineers, and can be easily mastered with a little computer knowledge.     

延庆县南天门崩塌灾害的治理研究

本文采用了赤平投影的方法,对延庆县南天门崩塌灾害的稳定性进行分析评价,提出采用危岩清理、$5/S防护网等综合治理措施进行治理。实际情况表明,治理措施对防治崩塌灾害是切实有效的。     

裂隙化硬岩洞室围岩失稳分析方法

根据岩体的力学介质分类和块体理论及赤平投影,结合工程实例,推导了滑动方向的计算公式,研究了裂隙化岩体地下采空区围岩的稳定性分析方法。利用该方法分析了华北某大型地下采空区围岩的稳定性,展示了该模型的实用性。