Yüzey pürüzlülüğünün sayısal tanımı ve süreksizliğin kesme dayanımına etkisi

Quantification of surface roughness and its effect on the shear strength of a discontinuity

Özet

Bu çalışmada, süreksizliklerin yüzey pürüzlülüğünün sayısal olarak tanımlanması amaçlanmıştır. Yüzeylerin sayısallaştırılması için tamamen bilgisayar kontrollü yeni bir yüzey tarama cihazı ile kesme dayanımlarının belirlenmesi için yeni bir laboratuvar doğrudan (direkt) kesme deney cihazı özel olarak geliştirilmiştir. Doğal süreksizlik örneklerinin yüzeyleri sayısallaştırılarak 2-boyutlu veri setleri elde edilmiştir. Bu örnekler $sigma_n$=300 kPa sabit normal gerilme altında kesilerek en büyük kesme dayanımları ($tau_ p$) bulunmuştur. 2-boyutlu veri setlerine, güç spektrum yoğunluğu analizi ile üçgen prizma yüzey alanı yöntemleri uygulanmış ve yüzeyler için fraktal boyutlar ($D_{psd}$ ve $D_{tpsam}$) iki farklı yöntemle hesaplanmıştır. Kesme deneylerindeki değme alanlarının önceden hesaplanması için yeni bir yaklaşım geliştirilmiş ve 2-boyutlu veri setlerine uygulanmıştır. Böylece literatürde daha önce de tanımlanmış olan ve bir süreksizlik yüzeyi üzerinde kesme yönündeki geometriyi tanımlayan parametreler; “maksimum olası değme alanı $(A_0)$, toplam potansiyel değme alanı $(A_0)$, en büyük görünür eğim açısı ($theta_max$), şekil parametresi (C) ve yüzeydeki açısallığın değişimini tanımlayan $theta_max/C $ oranı” bu yeni yaklaşım ile de hesaplanmıştır. Yeni bir parametre olarak, $A_0/C$ oranı tanımlanmıştır. $D_{tpsam}$ değerleri ile yöne bağlı C, $theta_ max/C$, $A_0/C $ değerleri arasında önemli ilişkiler bulunmuştur. $theta_max/C $ ve $A_0/C $ oranları arasında yüksek korelasyon izlenmiştir. $D_{tpsam}$, C, $theta_max/C $ ve $A_0/C $ değerleri ile en büyük kesme dayanımı oranları ($tau_ p/ sigma_n$) arasında önemli ilişkiler elde edilmiştir. $D_{psd}$ değerleri ile diğer yüzey parametreleri ve $tau_ p/ sigma_n$ oranları arasında önemli bir ilişki gözlenmemiştir. $tau_ p/ sigma_n$ oranı ile en iyi ilişkiyi $A_0/C $ oranı sunmuştur.

Abstract

In this study, quantification of surface roughness is aimed. Samples taken from the discontinuities of a volcanic tuff outcrop were selected as a material. A new computer-controlled surface scanning device has been specially developed for this study in order to digitize discontinuity surfaces. Depending on a specified sampling interval, elevations in each coordinates on a discontinuity surface are automatically measured and recorded by this device. Also, a new direct shear test device has been specially developed for this study in order to define frictional properties of discontinuities. Upper and lower surfaces of all samples were scanned with a sampling interval of 1mm in the horizontal axes by using the developed scanning device. Thus, 2-D data sets with the size of 65x65 were obtained for these surfaces. After that, all samples were sheared at the laboratory under the constant normal stress ($sigma_n$) level of 300 kPa by using the developed direct shear test device. So, maximum shear strengths ($tau_ p$) of the samples were obtained. Fractal geometry concept was used for quantitative definition of the surface roughness. Note that higher values of fractal dimensions correspond to rougher surfaces in the fractal theory. Two different fractal methods were chosen. These are “power spectral density analysis” suitable for self-affine 2-D data sets and “triangular prism surface area method” suitable for self-similar 2-D data sets. These two methods were applied to the 2-D surface data sets obtained by digitizing process. Fractal dimensions ($D_{psd}$ and $D_{tpsam}$) with two different methods were calculated. A new approach has been developed which enables calculating of contact areas occurring in shearing process depending on the specified shear direction. Algorithm of this method is based on the main algorithm of triangular prism surface area method which is used to calculate fractal dimensions of surfaces. This new approach was applied to the 2-D data sets obtained by a digitizing process. So, surface parameters, previously defined in the literature, were calculated in this study with this new approach. These parameters define the surface geometry in a specified shear direction on a discontinuity surface. These are maximum possible contact area $(A_0)$, total potential contact area $(A_0)$, maximum apparent dip angle ($theta_max$), shape parameter (C) and the ratio $theta_max/C $ describing angularity of the surface in the shear direction. The shape parameter (C) and the ratio $theta_max/C $ is directly related to surface roughness. Higher values of shape parameter (C) correspond to smoother surfaces while higher values of the ratio $theta_max/C $ correspond to rougher surfaces in a specified direction on a surface. Additionally, the ratio $A_0/C $ as a new direction-depended parameter has been defined. The notations given previously for these parameters were used in this study without any change to keep the literature same. All of these parameters were calculated in the shear direction. The values of the parameters C, $theta_max/C $ and $A_0/C $ calculated in the shear direction for upper and lower parts of all samples were compared with the fractal dimensions ($D_{psd}$ and $D_{tpsam}$) which characterize roughness of whole surface. Good agreements were obtained between Dtpsam and the parameters C, $theta_max/C $ and $A_0/C $ . $D_{tpsam}$) was found to be proportional to the ratios $theta_max/C $ and $A_0/C $ . Also, a high correlation between the ratios $theta_max/C $ and $A_0/C $ was obtained and these two parameters are proportional to each other. On the other hand no correlation was found between $D_{psd}$ and the parameters C, $theta_max/C $ and $A_0/C $. Additionally, calculated values of both fractal dimensions ($D_{psd}$ and $D_{tpsam}$) and the parameters C, $theta_max/C $ and $A_0/C $ for both sides of the discontinuity samples were compared to maximum shear strengths of these samples obtained from laboratory shear tests. Maximum shear strength ratios $tau_ p/ sigma_n$ were used in these comparisons. It was found that $D_{tpsam}$ and the parameters C, $theta_max/C $ and $A_0/C $ show good correlations with the maximum shear strength ratios $tau_ p/ sigma_n$. $D_{tpsam}$ , $theta_max/C $ and $A_0/C $ were found to be proportional to the ratio $tau_ p/ sigma_n$. The best agreement was observed between the ratio $A_0/C $ and the ratio $tau_ p/ sigma_n$. But no correlation was found between $D_{psd}$ and the ratio $tau_ p/ sigma_n$. $D_{tpsam}$ is a useful tool to describe the geometry of whole surface. The developed new approach is successful for calculation of directional surface parameters. The parameters $theta_max/C $, $A_0/C $ and C are also useful for characterization of direction-depended surface geometry. The data acquired by the developed surface scanning device are reliable.