Relationship between Shear Strength and Component Content of Fault Cores

단층핵 구성물질의 함량과 전단강도 사이의 상관성 분석

Abstract

In this study, simple regression and multiple regression analyses were performed to analyze the relationship between breccia and clay content and shear strength in fault cores. The results of the simple regression analysis performed for each rock (andesitic rock, granite, and sedimentary rock) and three levels of normal stress (${\sigma}_n=54$, 108, 162 kPa), reveal that the shear strength is proportional to breccia content and inversely proportional to clay content. Furthermore, as normal stress increases, the shear strength is influenced by the change in component content, correlating more strongly with clay content than with breccia content. In the multiple regression analysis, which considers both breccia and clay content, the shear strength is found to be more sensitive to the change in breccia content than to that of clay. As a result, the most suitable regression model for each rock is proposed by comparing the coefficients of determination ($R^2$) estimated from the simple regression analysis with those from the multiple regression analysis. The proposed models show high coefficients of determination of $R^2=0.624-0.830$.

본 연구에서는 안산암질암, 화강암 및 퇴적암에서의 단층핵 시료에 대한 직접전단시험과 입도시험 결과를 이용하여 단순회귀분석과 다중회귀분석을 실시하고, 각력 및 점토 함량과 전단강도 사이의 상관성을 분석하였다. 수직응력(${\sigma}_n=54$, 108, 162 kPa) 및 암종별로 단순회귀분석을 수행한 결과, 전단강도는 각력의 함량과 비례 관계를 보이며, 점토의 함량과 반비례 관계를 보인다. 또한, 대부분의 암종에서 전단강도는 각력보다 점토와 높은 상관성을 보이며, 수직응력이 증가할수록 각력과 점토 함량의 변화에 큰 영향을 받는 것으로 분석되었다. 각력과 점토의 함량을 동시에 고려한 다중회귀분석에서 전단강도는 점토보다 각력 함량의 변화에 더 민감하게 반응하는 것으로 나타났다. 결과적으로, 단순회귀분석과 다중회귀분석으로부터 산정된 회귀모형들의 결정계수($R^2$)를 비교 분석함으로써 암종별로 가장 적합한 회귀 모형을 제안하였고, 제안된 모형들은 0.624~0.830의 높은 결정계수를 보인다.

Fig. 1. Sample equipments used to minimize disturbance of fault core during specimens preparation for the direct shear test.

Fig. 2. Representative outcrop photographs of the fault cores used in this study. (a) and (b) in andesitic rock are composed of mixed gouge and cataclasite of various colors, and the fault breccia and damage zone are partially observed. (c) and (d) of granite in Ulsan Fault are developed with low dip of reddish brown and pinkish gouge with a maximum thickness of 30 cm, and no cataclasite or breccia is observed. (e) in the Cretaceous sedimentary rock is composed of whitish gouge and greenish gray cataclasite and (f) located in Danyang is contains dark gray to black gouge due to the influence of coaly shale.

Fig. 3. Box plots for shear strength of fault cores in andesitic rock, granite, and sedimentary rock under normal stress (a) 54 kPa, (b) 108 kPa, and (c) 162 kPa. The gray boxes are IQRs (inter-quartile ranges).

Fig. 4. Photographs showing (a) a fault core specimen after the direct shear test and (b) the procedure of sieve test (using sieve No. 4 and No. 200) and soil washing test.

Fig. 5. Box plots for particle size of fault cores in andesitic rock, granite, and sedimentary rock. The gray boxes are IQRs (inter-quartile ranges).

Fig. 6. Results of simple regression analysis between the shear strength and content of breccia and clay in (a) andesitic rock, (b) granite, and (c) sedimentary rock under normal stress 54 kPa. The dotted lines are the UCI (upper confidence interval) and LCI (lower confidence interval) for 95% confidence Interval.

Fig. 7. Results of simple regression analysis between the shear strength and content of breccia and clay in (a) andesitic rock,(b) granite, and (c) sedimentary rock under normal stress 108 kPa. The dotted lines are the UCI (upper confidence interval)and LCI (lower confidence interval) for 95% confidence Interval.

Fig. 8. Results of simple regression analysis between the shear strength and content of breccia and clay in (a) andesitic rock,(b) granite, and (c) sedimentary rock under normal stress 162 kPa. The dotted lines are the UCI (upper confidence interval)and LCI (lower confidence interval) for 95% confidence Interval.

Fig. 9. Comparative analysis of coefficients of determination (R²) estimated from simple regression analysis.

Fig. 10. Comparative analysis of the regression coefficients on content of (a) breccia and (b) clay in each normal stress (σ_n=54, 108, and 162 kPa) estimated from simple regression analysis. Abbreviations of rock type are as follows: andesitic rock (AR), granite (GR), and sedimentary rock (SR).

Fig. 11. Comparative analysis of coefficients of determination (R²) estimated from simple regression analysis and multiple regression analysis. Abbreviations of rock type are as follows: andesitic rock (AR), granite (GR), and sedimentary rock (SR).

Table 1. Shear strength values of fault cores in andesitic rock, granite, and sedimentary rock under normal stress (σ_n) 54 kPa, 108 kPa, and 162 kPa. Abbreviations of rock type are as follows: andesitic rock (AR), granite (GR), and sedimentary rock (SR)

Table 2. Results of particle size analysis for fault cores in andesitic rock, granite, and sedimentary rock. Abbreviations ofrock type are as follows: andesitic rock (AR), granite (GR), and sedimentary rock (SR)

Table 3. Results of the multiple regression analysis showing the regression coefficients of the independent variables (breccia and clay) for each rock type under normal stress 54 kPa

Table 4. Results of the multiple regression analysis showing the regression coefficients of the independent variables (breccia and clay) for each rock type under normal stress 108 kPa

Table 5. Results of the multiple regression analysis showing the regression coefficients of the independent variables (breccia and clay) for each rock type under normal stress 162 kPa

Table 6. Regression equations for the shear strength of fault core estimated by simple regression analysis and multiple regression analysis