Harşit Vadisi-kürtün Barajı Aks Yeri Kayaçlarında Çatlak Yüzeylerindeki Pürüzlülüğün Sayısal Tanımı

Abstract

Bu çalışmada; çatlak düzlemi yüzey pürüzlülüğünün, stabilite analizlerinde kullanılan mekanik parametrelerden içsel sürtünme açısı (())) ve kohezyon (c) üzerine olan etkisinin ortaya konmasına ve farklı yüzey geometrilerine sahip çatlak düzlemlerinin pürüzlülük derecelerinin birbirleriyle nicel olarak kıyaslanmasına imkan verecek, sayısal değerlerin tanımlanması amaçlanmıştır. Bu amaca yönelik olarak, çatlak yüzeyleri üzerinde farklı koordinat noktalarındaki yükselti değerlerinin ölçümü ve haritalanması ve bu ölçümlerden elde edilen veriler yardımıyla pürüzlülüğün sayısal- olarak ifadesi hedeflenmiştir. Pürüzlülüğün ölçümü ve haritalanması için özel bir kontrol ünitesi ve yazılım ile bilgisayar tarafından kontrol edilen bir yüzey tarama aleti geliştirilmiştir. Bu alet sayesinde, araştırmada kullanılan numune yüzeylerine ait yükselti değerleri yatay düzlemde x ve y doğrultularında 1 mm'lik, düşey doğrultuda (z) ise 1/10 mm'lik örnekleme hassasiyeti ile ölçülmüş ve bu ölçümler sırasında elde edilen değerler her numune için farklı isimler altında oluşturulan veri dosyalarına kaydedilmiştir. Farklı numuneler için yüzey pürüzlülüğünün sayısal ifadesine yönelik olarak çatlak yüzey pürüzlülüğünün fraktal boyut (D) ile karakterize edilmesi metod olarak seçilmiş, fraktal boyut hesabında ise spektral analiz yöntemi kullanılmıştır. Yüzey tarama aleti ile çatlak yüzeyi üzerinde uzaklık ortamında ölçülmüş verilere 2-boyutlu ayrık fourier transformu uygulanmış ve uzaklık ortamında ölçülmüş bu veriler dalgasayısı (k) ortamına aktarılmıştır. Böylece her bir numune için yüzey güç spektrumu grafikleri [log S(k) - log k] elde edilmiş ve bu grafiklerdeki nokta dağılımlarını en iyi karakterize eden lineer doğruların eğim (m) değerleri hesaplanılmştır.Bu çalışmada aşağıdaki sonuçlar elde edilmiştir: Güç spektrumu grafiklerinde; düşük dalga sayılarında yüksek, yüksek dalga sayılarında ise düşük enerji yoğunlukları görülmektedir. Ancak bu ilişkiyi karakterize eden noktalar oldukça saçılmış bir görünüm sunmakta ve bu durum özellikle yüksek dalga sayılarında görülmektedir. Yüzey fraktal boyutu (D) nin 2

Due to natural events or surface excavations conducted by human beings, primary state of stresses is disturbed and thus, the differences in the direction, location and intensity of natural stresses result in the formation of secondary stress conditions. Under the secondary stress conditions, natural and / or man-made slopes can face the risk of losing their stability and this results in various kind of mass movements. Block and wedge sliding are planar sliding movements which are observed in rock slopes. In the stability analyses of rock blocks and wedges, it is assumed that the movement occurs in accordance with COULOMB (1773) failure criterion. This criterion is based on shear failure which occurs on a plane. Shear stress (t) resulting in failure is defined as a function of mechanical parameters of the plane such as cohesion (c), internal friction angle (<|>), and the normal stress (a") affecting the plane. In researches on rock mechanics, the effects of joint surface roughness on cohesion, friction angle of a joint and thus on the shear strength are studied in both the laboratory as well as in the field teste. In such observations, it is particularly aimed to define the surface roughness of the joint planes. In researches aiming to define the surface roughness of the joint planes, usually one or several surface profiles are obtained parallel to directions where sliding movements are expected and the definition of surface roughness are obtained in the light of the geometry of those profiles. Nevertheless, when it is considered that geometry's of the profiles are different in most cases even though they are obtained parallel to each other, it should be concluded that the surface roughness of the joint planes should be defined in 3-dimensional analyses rather than profiles. In this study, it is aimed to define the surface roughness of the joint planes quantitatively, and for this reason, measurement and mapping of roughness and mathematical definition of it by using data obtained through these measurements are the main objectives of this research. In the first introductory chapter of this research, the definition of the problem is presented. In the following chapter the geology of the Kürtün Dam site in the Harşit Valley where the samples on which the roughness measuremets and definitions were made is introduced. In the third chapter, planner sliding movements that are observed in rock slopes are discussed. In addition, stereographic projection method that is used in their stability analyses is explained. In the forth chapter, previous studies available xiv in the literature related to quantitative and qualitative definition of roughness of joint planes are presented in detail. The fifth and sixth chapters form the essential parts of this research. They are as follows : i) introduction of computer-controlled surface scannig device that was developed for the purpose of measurement and mapping of surface roughness of joint planes (Chapter 5). ii) detailed presentation of the fractal geometry concept and fractal dimension calculation methods which are chosen as a method to define roughness quantitatively (Chapter 6). A computer-controlled surface scanning device to carry out the measurements and mapping of roughness was designed, developed and manufactured specially for this research (Figure 1). COMPUTER-CONTROLLED STEP MOTORS 1 Movement along x-direction 2 Movement along y-direction 3 Movement along z-direction Figure 1 : View of the surface scanning device from different angles. This device illustrated in Figure 1 is a computer-controlled instrument, using a specially designed software. The connection between the device and the computer is obtained by a specially manufactured control unit (Figure 2). By using this device, height values on a joint plane are measured in a resolution of 1/10 mm in vertical axis. XV SG1 SURFACE SCANWG DEVICE SOI CONTROL UMT Figure 2: The block diagram of measurement system Roughness of the sample surfaces which were supplied from the Kürtün Dam site in the Harşit Valley was measured with sample interval of 1 mm (A=l mm ) and the data obtained were recorded automatically into the data files on the computer. Those data files were processed by the help of a software called SURFER which is used widely in earth science and thus the contour maps and the block diagrams of the sample surfaces were obtained (App. 4a, b). The contour map and the block diagram of the sample K2 is shown in Figure 3. In order to the define surface roughness quantitatively for the different samples, fractal dimension concept was chosen as a method. So, the first time this concept was tried to be applied to characterization of surface roughness in rock mechanics discipline in our country. Spectral analysis method was used in the calculation of fractal dimension. At the first stage of the calculation, data measured on the sample surfaces was gridded in size 32 mm x 32 mm by using of a software called MKGRD. Two dimensional discrete fourier transform was applied to these data in the form of square grids and thus these spatial data were transformed into the wavenumber (k) space. At this stage, a software called FAST2 was used. To obtain energy density ( or power) as a function of the wavenumber logaritmatically, another software called FRACDIM2 was applied. At the following stage, surface power spectrum graphs, [log S(k) - log k], were drawn by using software GRAPHER. In addition, linear lines characterizing the best point distribution on the graphs were fitted and the slopes of these lines were calculated. The power spectrum graph for the sample K2 is shown in Figure 4. Also, graphs for the all samples used in this study are presented in Appendix 4.c When the point distributions on the power spectrum graphs are observed, the higher energy densities (power) at the lower wavenumbers and the lower energy densities at the higher wavenumbers are shown. However, the points characterizing this relationship present heavily scattered view and this situation is certainly seem at high XVI wavenumber values. In a case where the points are scattered so much, it can be discussed how valid the definition of the point ditributions on the graphs with a single z(mm) 5^ Figure 3: For the sample K2 a) contour map b) block diagram linear line is. As a matter of fact, slope values (m) of the linear lines fitted the point distributions on the graphs vary between -4.41 and -3.49 (-4.41^ m <-3.49). When it is considered that surface fractal dimension (D) should have the values varying between 2 and 3