KR101549540B1 - Apparatus and method for estimating fault of shear strength - Google Patents

Abstract

The present invention relates to a method for estimating shear strength of a fault rock, which comprises the following steps: converting the shear strength of an acquired fault rock specimen into database; setting a model for the shear strength; finding an intercept for a dependent variable and a coefficient for each independent variable by means of the weight ratio by particle sizes, a normal stress, and the shear strength; and determining an equation of the shear strength. According to the present invention, it is possible to calculate the shear strength of the fault rock by substituting only the weight ratio by the particle sizes of the fault rock into the equation of the shear strength, thereby minimizing a manual labor.

Description

[0001] APPARATUS AND METHOD FOR ESTIMATING FAULT OF SHEAR STRENGTH [0002]

The present invention relates to a method of estimating the shear strength of a single-layer arm, and more particularly, to a method of estimating a shear strength of a single-layer arm using a weight ratio of a single layer arm sample to a shear strength.

Recently, due to the increase of construction of linear tunnels and linear tunnels, geologic factors unfavorable to excavation such as faults, folds, and water spots are found in the construction section, resulting in large and small scale collapse and rehabilitation. Tunnel uplift in the fault zone is one of the main reasons that the unfavorable geologic conditions are not reflected in the design due to insufficiency of geological survey and the poor prediction of the excavated surface through geological and geological survey during construction. As such, the fault layer that appears during the tunnel construction is an important factor that determines the strength of the ground with difficulty in predicting the direction, size, and strength. In the case of 4 or 5 grade rocks for the purpose of changing the design pattern during construction, it is not classified in detail in the existing rock classification such as RMR (Rock Mass Rating), and it leads to reinforcement and inhibits economical construction. Geological hazards are one of the factors that impede the stability and economical efficiency of tunnels due to the difficulty of surveying and classifying the rocks by field engineers. In order to solve these problems, geometrical characteristics and strength characteristics of the geological structure should be clarified. However, studies on the engineering properties of fault or fault rocks have been limited to studies on fault structures and permeability (Caine et al., 1996; Evans et al., 1997; Rawling et al., 2001; Mizoguchi et al., 2008) In this study, the strength characteristics of the faults were investigated by using numerical analysis or empirical application (Dalgic, 2003; Giochi et al., 2003; Sausgruber and Brandner, 2003; Kun and Onargan, 2013). There are few studies conducted indoors to obtain the dynamic constants of faults (Sulem et al., 2004; Kim et al., 2010).

In the central part of the fault layer, unconsolidated material containing mainly non-sandy clay and chain (or angular) is distributed (Fig. 1). These materials are characterized by a low degree of circularity and sphericity and an inhomogeneous distribution, but they also have similar basic behavior to soil. Therefore, a study on the strength characteristics of soil containing coarse material is as follows. Varadarajan et al. (2003) conducted a triaxial compression test of granular material after classifying rockfill materials of 0.075 mm to 80 mm into 10 particle sizes. As the particle size increases, the shear strength decreases as the particle size increases during the triaxial compression test, and when the same material is used, the larger the particle size of the sample, the higher the shear strength Results were obtained. Lee et al. (2009) studied the behavior of shear behavior of forest aggregates made by crushing parent rocks in a rock mass using a large direct shear tester, with changes in maximum particle size, soaking condition, density, uniformity factor, and crushing rate. The shear strength of the specimens was higher than that of the specimens. The shear strength of specimens was higher than that of specimens. Teuten (2012) conducted a ring shear test to analyze the correlation between grain size distributions and friction angles. Samples were classified into sand, fine - grained particles and clay, and the relationship between each content and shear rate was examined. The results of the study on the content of grain size showed that the higher the content of clay, the lower the friction angle and the higher the sand content, the more the friction angle increased. The shear rate of clay samples increased with increasing shear rate, whereas the shear rate of specimens with clay samples tended to increase with increasing shear rate.

The fault zone has a target structure internally and consists of the most central fault gouge zone, a cataclastic zone surrounding the non-zone and a thick zone of damage on the outer zone (Fig. 1 (a) ), Chester et al., 1993). The fault core is called a fault core by connecting a fault zone with a fracture zone. Depending on the position and shape of the fault zone and fracture zone, symmetric fault core, asymmetric fault core, Anastomosing fault core, and multiple fault core (Fig. 1, Chang and Choo, 1998). When a fault occurs by a single fault action, it is calculated as a simple model as shown in Fig. 1 (a) and (b), but when the faults are operated more than twice, 1 (c), (d)).

However, in order to measure the shear strength of such a single-layered arm, classification of single-layered arm samples and various shear strength tests are all manually performed. As a result, the strength and rock classification of the fault zone are applied empirically in many construction sites.

Korean Registered Patent No. 10-0636000 (Published on October 18, 2006) Korean Registered Patent No. 10-0638792 (Published on October 30, 2006)

[1] ASTM D422-63, 2007, Standard test method for particlesize analysis of soils, Annual Book of ASTM standard, 04.08. [2] ASTM D2487-06, 2006, Standard practice for classification of soils for engineering purposes (Unified Soil Classification System, USCS), Annual Book of ASTM standard, 04.08. [3] ASTM D3080-98, 1998, Standard test method for direct shear test of soils under consolidated drained conditions, Annual Book of ASTM standard, 04.08. [4] Caine, J. S., Evans, J. P., and Forster, C. B., 1996, Fault zone architecture and permeability structure, The Geological Society of America, 24 (11), 1025-1028. [5] Chang, T. W. and Choo, C. O., 1998, Formation processes of fault gouges and their K-ares along the Dongnae Fault, The Journal of Engineering Geology, 8 (2), 175-188. (in Korean with English abstract) [6] Chester, F. H., Evans, J. P., and Biegel, R. L., 1993, Internal structure and weakening mechanisms of the San Andreas Fault, J. Geophys. Res., 98, 77, 1-786. [7] Dalgic, S., 2003, Tunneling in fault zones, Tuzla tunnel, Turkey, Tunneling and Underground Space Technology, 18, 453-465. [8] Evans, J. P., Forster, C. B., and Goddard, J. V., 1997, Permeability of fault-related rocks, and implications for hydraulic structures of fault zones, Journal of Structural Geology, 19 (11), 1393-1404. [9] Gudmundsson, A., 2004, Effects of Young's modulus on fault displacement, C.R. Geoscience, 336, 85-92. [10] Hu, C., Cai, Y., Liu, M, and Wang, Z., 2013, Aftershocks due to property variations in the fault zone: A mechanical model, Tectonophysics, 588, 179-188. [11] Iio, Y., 1997, Frictional coefficient on faults in a seismogenic region inferred from earthquake mechanism solutions, Journal of Geophysical Research, 12 (B3), 5403-5412. [12] Kim, B. C., Jung, H. G. and Seo, Y. S., 2010, Effect of fault distribution on ground settlements, Korea Society of Engineering Geology Conference, 8-9, April 2010, Gyengju Korea. (in Korean) [13] KS F 2302, 2002, Test method for particle size distribution of soils. (in Korean) [14] KS F 2309, 2009, Standard test method for amount of material in passing standard sieve 0.075 mm in soils. (in Korean) [15] KS F 2343, 2007, Tseting method for direct shear test of soils under consolidated drained conditions. (in Korean) [16] Kun, M. and Onargan, T., 2013, Influence of the fault zone in shallow tunneling: A case study of Izmir Metro Tunnel, Tunneling and Underground Space Technology, 33, 34-45. [17] Lee, DS, Kim, KY, Hong, SY, Oh, GD and Jeong, SS, 2009, Characteristics of Shear Behavior for Coarse Grained Materials Based on Large Scale Direct Shear Test (III) Korean Geotechnical Society, 25 (4), 39-54. (in Korean with English abstract) [18] Mizoguchi, K., Hirose, T., Shimamoto, T., and Fukuyama, E., 2008, Internal structure and permeability of the Nojima fault, Southwestern Japan, Journal of Structural Geology, 30, 513-524. [19] Oh, HS, Shin, WS, Kim, JH, Hwang, IS, Hur, J., Shin, HS, Oh, JE, Huh, of heavy metals in river and lake sediments, Korean Geo-Environmental Society, 11 (5), 15-23. (in Korean with English abstract) [20] Rawling, G. C., Goodwin, L. B., and Wilson, J. L., 2001, Internal architecture, permeability structure, and hydrologic significance of contrasting fault-zone types, 29, 43-46. [21] Riedmiiller, G., Brosch, F. J., Air Conditioning, K., and Medley, E. W., 2001, Engineering geological characterization of brittle faults and classification of fault rocks, Felsbau 19 (4), 13-19. [22] Sausgruber, T., and Brandner, R., 2003, The relevance of brittle fault zones in tunnel construction - lower Inn Valley Feeder Line North of the Brenner Tunnel, Tyrol, Austria, Mitt. der ㅦ sterr. Geol. Ges., 94, 157-172. [23] Sulem, J., Vardoulakis, I., Ouffoukh, H., Boulon, M., and Hans, J., 2004, Experimental characterization of the thermo-poro-mechanical properties of the Aegion Fault gouge, C.R. Geoscience, 336, 455-466. [24] Teuten, J. M., 2012, Shear characteristics of soils with varying silt / clay fractions, Civil and Environmental Engineering Student Conference, 25-26, June 2012, Imperial College London. [25] Varadarajan, A., Sharma, K. G., Venkatachalam, K., and Gupta, A. K., 2003. Testing and modeling two rockfill materials, Journal of Geotechnical and Geoenvironmental Eng., ASCE, 129 (3), 206-218.

SUMMARY OF THE INVENTION The present invention has been made in order to solve the problems of the prior art described above, and it is an object of the present invention to provide a data base for a monolayer arm having a weight ratio, a vertical stress and a shear strength, The present invention also provides a method for estimating the shear strength of a single-layer arm, which can easily calculate the shear strength by calculating an optimal shear strength diagram using multiple regression analysis and substituting the weight ratios of the single-layer arms with the shear strength schemes.

In order to achieve the above object, a method of estimating the shear strength of a single-layer arm according to the present invention is a method of estimating a shear strength of a single-layer arm using the shear strength diagram obtained from the data of the weight ratio, vertical stress, And estimates the degree of the error. At this time, the shear strength scheme is preferably obtained through multiple regression analysis.

In order to achieve the above object, a method of estimating shear strength of a single-layer arm according to the present invention is a method for estimating shear strength of a single-layer arm, A database; Setting a shear strength model in which the shear strength is a dependent variable and the weight ratio of the grain size and the vertical stress are independent variables; Obtaining a slice of the dependent variable and a coefficient for each independent variable using the weight ratio, the normal stress and the shear strength according to the particle size; And determining the shear strength scheme by applying the slice and the coefficient to the shear strength model.

At this time, the intercept and the coefficient can be obtained by using multiple regression analysis.

The particle size of the single-layered rock samples may be divided into gravel, sand, and silt / clay.

The shear strength diagram is preferably defined by the following equation when the vertical stress is divided into one variable.

(여기서,

는 각 입도의 무게비,

는 수직응력,

는 다중회귀분석을 통해 얻은 계수를 각각 나타낸다.)

(here,

The weight ratio of each particle size,

Lt; / RTI >

Represent the coefficients obtained by multiple regression analysis, respectively.)

The shear strength diagram is preferably defined by the following equation when the normal stress is divided into a dummy variable.

(여기서,

은 각 입도의 무게비,

는 수직응력,

는 다중회귀분석을 통해 얻은 계수,

는 수직응력

일 때의 가변수,

는 다중회귀분석을 통해 얻은 계수를 각각 나타내고,

,

은 자연수이다.)

(here,

The weight ratio of each particle size,

Lt; / RTI >

Is the coefficient obtained through multiple regression analysis,

Lt; / RTI >

A variable number when

Represents the coefficient obtained through multiple regression analysis,

,

Is a natural number.)

As described above, according to the method of estimating the shear strength of a single-layer arm according to the present invention, since the shear strength of the single-layer arm can be obtained by substituting the weight ratio of the single- The speed of obtaining the shear strength can be remarkably improved.

Fig. 1 is a view showing the classification of a single-stratum nucleus in a fault layer.
Figs. 2 and 3 are examples of single-layer and single-layer arcs produced from outdoor outcrops.
Fig. 4 shows a sample preparation process of the direct shear test.
5 is a view showing a sieve analysis process.
Figure 6 shows the correlation between the vertical stress and shear strength, gravel, sand, and silt / clay weight ratios in multivariate scatterplots.
Fig. 7 shows the scattering degree and the determination coefficient of the measured value and the estimated value of each model.
8 is a flowchart of a method for estimating the shear strength of a single-layer arm of the present invention.

The present invention analyzes the correlation between the weight ratio and the shear strength of a single layer material using multiple regression analysis and obtains a shear strength diagram using the weight ratio, normal stress and shear strength of the single layer arm obtained through the analysis. Therefore, in order to identify the factors affecting the shear strength of the single-stranded core, which is classified as a risk factor in the construction of underground structures, the present invention acquires a total of 109 samples from nine faults and performs shear test and particle size analysis. In the multiple regression analysis, the correlation between the shear strength and the weight ratio of the monolayer material is analyzed using 97 test data, and then the applicability is examined with 12 data that are not used for the regression analysis.

Hereinafter, a method for estimating the shear strength of a single-layer arm according to the present invention will be described in detail with reference to the accompanying drawings.

Geologic and outdoor weathering of sampling faults

The monolayer cancer used in the present invention is classified into 13 kinds of samples in 9 regions in total. In each fault, samples of Buddhism are taken into consideration, such as the types of monolithic rocks such as single-layer beads and crushing rocks, [Table 1] shows the location, type, and information of the sample and faults.

Sample No. 1 was taken from a location near the Danyang public playground in Danyang-eup, Chungcheongbuk-do and sampled from the slope incised for road extension work. This area is a sedimentary layer corresponding to the Mesozoic Jurassic, and the coal stratum of the purchase is arranged along the fault or stratum. The sampled part is a single layer of clay in a monolayer, and its width is about 70 cm.

No.2, No.10, No.11 The outcrops of the samples are located within the site of the Magok General Industrial Complex in Maegok-dong, Ulsan Metropolitan City. The No.2 sample corresponds to the Ulsan Formation of the Cretaceous Cretaceous, and is a monolayer material of mudstone and shale origin. In the case of No. 10 and No. 11 samples, it is a single layer material from the Mesozoic Cretaceous granitic origin and is exposed to the fresh condition in the outdoors with a width of about 30 cm (FIG. 2 (a)). This monolayer is developed as a low - angle superficial layer with a reversible and superior motion sensation. The fault plane has a N52 ° E / 20 ° NW orientation, and the directionality of the single stratigraphy developed on the surface is observed at 12/086 (Fig. 2 (b)).

No.3 to No.8 samples are located in the northern part of Yangsan Fault, and they are distributed in Pohang City and Yeongdeok County in Gyeongsangbuk Province in the administrative district. Samples of No.3 to No5 were collected at Bokyeongsa Seongil Park in Songra-myeon, Buk-gu, Pohang. It is a boundary between the andesite and andesite tuff and red shale of the Mesozoic Cretaceous period, exposed in the stream flowing from the northwest to the east. This area is where the massive fault passes, and the width of the single layer core is about 1 m. The single - bed fracture zone, which is a parent rock of andesite and andesite tuff, is observed as if it captured the single - layer fracture zone, which is greenish and the red shale is the parent rock. The monolayer is an inverted stratum of superior incense sense and the fault plane has a directionality of N10 ° E / 84 ° NW (Fig. 3).

Samples of No. 6 were collected from the outcrops located on the roads of Yangseongri in Namjeong-myeon, Youngdeok-gun, and correspond to volcanic rocks of the Cretaceous period. The monolayer observed in the northern part is a non-inverted layer showing the directionality of N10 ° W / 88 ° SW. The samples are produced in the form of a mixture of single clay and single layer persimmon.

Samples No. 7 and No. 8 were taken from the slope cut-out site for the extension of the No. 7 country at Gangguk-myeon, Yeongdeok-gun. These outcrops correspond to the Mesozoic strata, and shale and sandstone of purple color are distributed. The monolayer shows an orientation of N50 ° E / 60 ° SE and shows a moving sense of the inverse component of the inverse component. No. 7 sample was taken from a portion where the single-layered clay of the single-layer core portion predominated, and No. 8 sample was taken from a portion containing a relatively large amount of single-

The No. 9 sample was collected from the river outcrop in the Yangsan Fault located in Samnam-myeon, Ulsan City. It is a sedimentary layer of the Mesozoic Cretaceous, and sandstone and shale are alternating. The shale layer shows delamination. The width of the fault observed on the outcrop is about 1 m, and it develops parallel to the bedding surface (N30 ° E / 88 ° NW).

The No.12 sample was taken from a slope located on the entrance road of the head company located in Habuk-myeon, Yangsan-si, Gyeongsangnam-do. It is located within the fault mass, and the observed carcinoma is Ansan porphyry of the Cretaceous period. The fault plane has a vertical N40 ° E direction, and the joint is developed in parallel with it.

No.13 The sample was taken from the outskirts of the entrance fault located in the outer eastern part of Gyeongju city, Gyeongbuk province. Single-layered clay and monolithic marginal zone are well developed, and sedimentary rocks of the Cretaceous period are thermodynamically transformed into Hornpelse. The fault plane has a directionality of N02 ° E / 86 ° SE, and has a sense of good-directional mobile stationary layer.

Room test

In the present invention, a direct shear test and particle size analysis are carried out using a Buddhist sample collected from a monolayer non-sand bed and a fracture bed. Monolithic rocks are characterized by a high proportion of clay, and the fact that they contain angular forces that are very poor in roundness and sphericity. Therefore, the standardized test method of the soil is basically followed by particle size distribution analysis as a sample after the shear test to obtain the test result reflecting the characteristics of the fault layer sample.

Direct shear test

The direct shear test of single layer materials is to be carried out in accordance with the soil shear test under the drainage conditions specified in ASTM D 3080-98 and KS F 2343 Test Methods. The shear tester is the first precision model JI-620 and the horizontal force is 2.5 kN. The shear test box uses two types of 60 mm diameter and 80 mm diameter as shown in [Table 2]. The vertical load at the time of the test is increased by the same weight by using a weight of 1,414 g.

Fig. 4 shows a sample preparation process of the direct shear test. The specimens are fully saturated for 6 to 8 hours and the shear rate is tested at 1 mm / min for 0.5 to 2% / min of sample diameter, which is the speed range suggested by ASTM. At least one test shall be carried out per normal stress in all specimens.

This makes it possible to database the shear strength corresponding to the normal stress.

Particle size analysis

After the direct shear test is completed, samples are taken for each shear box, dried and analyzed for particle size. For single layer materials, clay minerals are generally contained in a large amount, and drying is generally performed at 60 ° C or less to prevent deterioration of minerals. Therefore, in this analysis, it is dried at a set temperature of 40 ° C considering the temperature difference between the dryer internal temperature sensor and the sample position.

The test method for particle size analysis (KS F 2302) is divided into sieve analysis and hydrometric analysis according to the kind of soil. In the case of granulated soil, general sieve analysis test is carried out. Although the single layer material to be treated in the present invention is a mixture of granulation and fine granules, a sieve analysis method (KS F 2309-95, ASTM D422-63) is used in accordance with the classification purpose. Riedmiiller et al. (2001) classify the coarse-grains and fine-grains as 0.063 mm in the classification of crushed rocks. In the present invention, gravel (4.75 mm or more), sand (4.75 to 0.075 mm), silt and clay (0.075 mm or less) such as USCS (ASTM 2487-06) and Japanese Industrial Standards (JIS) And the analysis is carried out.

Unlike ordinary soil, a high content of clay in a single layer material is not separated and remains as a lump, so it is difficult to test it in a dry state. Therefore, the soil washing test method (KSF 2309) is applied together with the conventional sieve analysis method to filter the clay. To explain the sieve analysis process, the total dry weight of the sample is measured before the sieve analysis, and the sample is saturated and the soil is washed until the water is clean on the sieve. In this process, the particles filtered at # 10 (greater than 4.75 mm) and # 200 (0.075 to 4.75 mm) are collected separately and dried again. When the particles are removed from the dry weight of the whole sample, mm) can be obtained (Fig. 5). The weight of each of the obtained granules is divided by the weight of the whole soil to calculate the weight ratio to each of the gravel, sand and silt / clay.

The disadvantage of this method is that gravel and sand-sized particles can be recovered after the sieve analysis, but the clay-sized particles washed away in water are not recoverable. However, the wet sieving method (Oh et al., 2010) is disadvantageous in filtering the gravel and sand particles and takes a lot of time because of the hydrometallurgical analysis method or the wet sieving method in which the sample is placed in a 63 μm mesh and immersed in water to separate the fine grain particles. In the present invention, since the silt and the clay are analyzed in one category, the modified type sieve analysis method using the soil washing method is applied.

Thus, the weight ratios corresponding to the vertical stresses and the shear strengths, which have been databaseed through the direct shear test, can be stored in a database.

Analysis of Correlation between Weight Ratio and Shear Strength by Particle Size

The strength characteristics of monolayer rocks are determined by various variables such as content of constituent materials such as angular force and substrate, kind of parent rock, and expansion property of clay. In addition, even in the samples taken from the same fault zone, there is no sample having the same constituent material ratio, so that the dispersion of the strength is remarkably different from that of rock and soil. In the present invention, in order to reveal the strength characteristics of the single layer arm, the correlation between the weight ratio and the shear strength of the constituent materials was analyzed using 97 shear tests and particle size analysis results, and the remaining 12 results were used The applicability will be examined.

Multivariate scatter plot

FIG. 6 shows the correlation between the vertical stress, shear strength, gravel, sand, and silt / clay weight ratio derived from the direct shear test and the particle size analysis as a multivariate scatterplot. The relationship between shear strength according to normal stresses shows that the higher the vertical stress, the wider the distribution of shear strength. This means that the higher the normal stress is, the more the effect is due to the heterogeneity of the constituent materials. In the scattering of particle size and shear strength, the shear strength of the sand increases with increasing the weight ratio of the gravel, but the tendency is not clear in sand and silt / clay tend to be inversely proportional. Comparing the weight ratios of the constituent materials, gravel and silt / clay, sand and silt / clay are inversely proportional, but gravel and sand do not show a clear tendency. The above results are judged to be the result of the test reflecting the characteristics of the monolayer cancer in which the kinds and contents of constituent materials are heterogeneous.

Multiple regression analysis

The above scattering analysis is a 1: 1 correlation analysis between variables, and it is difficult to find a correlation when a plurality of variables are simultaneously influenced. Therefore, we conduct multiple regression analysis that can simultaneously consider the variables (gravel, sand, silt / clay, vertical stress) that affect the shear strength of single layer materials.

Multiple regression analysis is similar to the general simple regression model, but when two or more independent variables are used, the effect of each independent variable on the dependent variable can be modeled. In the present invention, the analysis is performed by dividing into three types according to a method of handling vertical stress.

1. When the vertical stress is divided into one variable (Model 1, 2)

The general form of the multiple regression model is (Equation 1).

--- (식 1)

--- (1)

는 종속변수,

는 독립변수,

는 독립변수가 변하지 않더라도 일반적으로 반응계수가 갖는 값(절편),

는 각 독립변수들이 반응계수에 미치는 영향으로서, 본 발명에서는

는 전단강도,

은 자갈의 무게비,

는 모래의 무게비,

는 실트/점토의 무게비,

는 수직응력을 독립변수를 각각 의미한다.Here, in statistics

Is dependent variable,

Is an independent variable,

Is the value (intercept) of the reaction coefficient generally, even if the independent variable does not change,

Is the effect of each independent variable on the response coefficient,

Shear strength,

The weight ratio of the gravel,

The weight ratio of sand,

The weight ratio of silt / clay,

The vertical stress is independent variable.

Model 1 is independent of gravel and model 2 is composed of sand and silt / clay. It can be concluded that if two of the three variables are explained together, the other variables are also explained as the independent variables that have a mutual influence of 100% of the sum of gravel, sand and silt / clay.

Therefore, applying all possible multiple regressions with three variables and vertical stress variables as independent variables showed that model 2 with sand and silt / clay together and model 1 with only gravel were significant [Table 3].

는 95% 이상 신뢰수준을 의미한다.
here,

Means a confidence level of 95% or more.

2. Vertical stress divided by dummy variable (Models 3 and 4)

In the multiple regression analysis, six normal stresses applied in the shear test are set as categories and analyzed.

로써 수직응력이 30 kPa인 경우에 나머지 수직응력에 대한

는 0으로 고정된다. 이를 식으로 나타내면 (식 2)와 같다.The normal stresses are

And the vertical stress is 30 kPa.

Is fixed to zero. This can be expressed as (Equation 2).

--- (식 2)

--- (Equation 2)

인 경우가 회귀식의 기본적인 기준이 되며,

은 범주로써 분석은 되나 각 요소의 p-value (Pr)가 0.05 이상으로 통계적으로 신뢰하기 어려운 수치로 나타난다. 그러나 수직응력이 증가할수록 요소(factor)들의 계수(Estimate)가 선형적으로 증가하는 관계로 나타나므로 모델 1, 2처럼 수직응력을 하나의 변수가 아닌 가변수로 취급하여도 통계적으로 문제가 없다고 판단된다.
When the vertical stress is taken as a variable number

Is the basic criterion of the regression equation,

, But the p-value (Pr) of each element is 0.05 or more, which is statistically unreliable. However, as the vertical stress increases linearly with the coefficients of the factors, it is not statistically significant even if the vertical stress is treated as a variable instead of a single variable as in Models 1 and 2 do.

3. Vertical stresses are grouped into four categories (Models 5 and 6)

(Equation 3) simplifies the regression equation by grouping the variable numbers specified in the category in (Equation 2).

--- (식 3)

--- (Equation 3)

의 경우 유의미한 통계수치가 나오지 않아 상관계수의 신뢰성이 매우 낮다. 이러한 현상은 가변수 데이터의 편차 폭이 크거나 데이터의 개수가 너무 적기 때문에 발생하는 문제이다. 본 발명에서 다중회기분석에 사용된

의 데이터 개수는 8개로 다른 수직 응력 조건의 데이터들 중 가장 적다. 또한

의 경우는 데이터 개수가 25개로 많은 수를 차지하고 있지만, 전단강도가 최저 11.95 kPa, 최고 74.11 kPa, 평균 42.06 kPa으로 분포 범위가 넓게 나타나며 평균에서 최고와 최저의 편차 또한 크다. 반면

은 최저 25.87 kPa, 최고 71.77 kPa, 평균 47.26 kPa로서 평균에서 최고와 최저의 편차가

에 비해 상대적으로 작기 때문에

과

을 그룹화하여 데이터의 개수와 편차폭에 대한 문제를 완화시키도록 모델 5와 6을 작성한다.In Models 3 and 4, six stress conditions were treated as variable numbers, and each correlation coefficient was analyzed. However,

The reliability of the correlation coefficient is very low. This phenomenon occurs because the variation width of the variable number of data is large or the number of data is too small. In the present invention,

The number of data is 8, which is the smallest among data of other normal stress conditions. Also

, The number of data is 25, which is a large number. However, the distribution range is wide with a shear strength of 11.95 kPa, a maximum of 74.11 kPa, and an average of 42.06 kPa. On the other hand

Was the lowest of 25.87 kPa, the highest was 71.77 kPa, and the average was 47.26 kPa.

Is relatively small compared to

and

To create models 5 and 6 to mitigate the problem of the number and width of data.

Table 3 shows the multiple regression analysis results for Models 1 to 6, and Table 4 summarizes the multiple regression equations for each model.

범위를 포함한다. 이는 본 실시예에서 제시한 다중회귀분석 이외의 통계기법을 이용할 경우에 발생될 수 있는 범위를 고려한 것이다.
Here, the constant applied to the multiple regression equation for each model is

Range. This takes into consideration the range that can be generated when statistical techniques other than the multiple regression analysis described in the present embodiment are used.

The plot of Q-Q plot for the normal distribution of data, which is the basic assumption of the multiple regression analysis, and the distribution of residuals are shown graphically, and the density plot graph confirming the assumption of normality for the error shows significant results but is omitted.

값이 높게 나타난다.Compared to the model considering gravel (No. 1, No. 3, No. 5), the model considering sand and silt / clay (No. 2, No. 4, No. 6)

The value is high.

Because the sum of gravel, sand, and silt / clay is 100%, these two factors are more accurate than the model considering only one of these three variables. For example, if the weight ratio of sand and silt / clay is known, the weight ratio of the gravel is fixed, but if the weight ratio of the gravel is known, the accuracy of the model is inferior because the individual weight ratio of sand and silt / clay is not known.

Applicability of Regression Analysis Model

To examine the applicability of the six regression models, we apply the indoor test results of the 12 data collected from the different layers to the regression model, which is different from the 97 data used in the regression analysis. Table 5 shows the shear strength test values and calculated values for each model.

) 를 도출한다. 회귀식은 추정값과 측정값이 유사할수록 y = x 직선에 가깝게 점시되며 적합성이 우수하다고 할 수 있다. 결정계수를 계산하기 위해서 (식 4)와 (식 5)를 이용한다.In order to examine the fitness of the regression equation, the measured value and the estimated value are plotted on the x-axis and the y-axis, respectively.

). The regression equation shows that the similarity between the estimated value and the measured value is closer to y = x, and the fitness is better. (4) and (5) are used to calculate the coefficient of determination.

--- (식 4)

--- (Equation 4)

--- (식 5)

--- (Equation 5)

는 측정값,

는 평균값,

는 추정값이다. 결정계수는 (식 5)와 같이 각 변동들과 상호관계에 있으므로 (식 4)에서 구한 SSR/SST를 이용하여 계산한다. 각 모델의 측정값과 추정값의 산포도와 결정계수

를 도시하면 도 7과 같다. 이 때,

은 피어슨 상관계수를 의미한다.Here, SSR is the regression variation, SSE is the error variation, and SST is the total variation, and the square sum of the differences is defined in order to measure the fitness with the regression line by the statistic.

Lt; / RTI >

Is an average value,

Is the estimated value. Since the decision coefficient is correlated with each variation as shown in Eq. (5), it is calculated using SSR / SST obtained from Eq. (4). The distribution of the measured and estimated values of each model and the coefficient of determination

As shown in FIG. At this time,

Is the Pearson correlation coefficient.

로 가장 높게 나타나며, 대부분의 모델이 0.6~0.7 사이에 분포한다. 또한 측정값이 80 kPa 이하에서는 y = x 그래프에 가깝게 분포하면서 높은 상관성을 보여주고 있다. 이는 단순히 적용성 검토에 활용한 데이터의 수가 적기 때문에 나타난 결과일 수도 있지만, 높은 수직응력하에서는 단층암의 쇄편의 영향도가 증가하기 때문에 편차가 반영된 것이 원인일 수도 있다. 이에, 본 발명에서는 단층쇄편의 원마도, 시료 내 분포도, 팽창성 점토광물의 함량 등이 전단강도를 구하는 변수로 이용할 수 있을 것이다.
7, the correlation between the shear strength measured by the actual test of Model 3 and the shear strength obtained by the regression equation

, And most models are distributed between 0.6 and 0.7. Also, when the measured value is less than 80 kPa, it is closely related to the y = x graph and shows high correlation. This may be the result of a small number of data used for applicability review, but it may be due to the fact that the effect of the single-stranded armature is increased under high vertical stresses. Accordingly, in the present invention, the circularity of the single-layer chain, the distribution in the sample, and the content of the expandable clay mineral may be used as variables for obtaining the shear strength.

The above procedure is summarized in FIG.

S1: The database of the weight ratio of the sampled single-layered rock samples and the shear strength corresponding to the normal stresses of the sampled single-layer rock samples are collected.

S2: Set the shear strength model with the shear strength as a dependent variable and the weight ratio and vertical stress as independent variables.

S3: Determine the intercepts of the dependent variables and the coefficients by the independent variables using the weight ratio, vertical stress and shear strength.

S4: Shear strength and modulus are applied to shear strength model to determine shear strength.

conclusion

In the present invention, particle size analysis and direct shear test were carried out using the Buddhist sample collected from the single-layer nucleus, and multiple regression analysis was performed using the result, and the weight ratio of the size of the chain and the matrix included in the single layer arm And the influence of the Gravel, sand, silt / clay, and normal stress were selected as the variables affecting the shear strength in multiple regression analysis. Six regression models to reflect these variables were analyzed and the fitness of each model was analyzed. Model 2 and 4, which consider the vertical stresses individually and the sand / clay / silt weight ratio, were high in the fit for each model.

이상을 보이며, 모델 1과 3이

이상으로 높게 나타났다. 이 결과는 모델별 적합도와 상이한 결과이지만, 적용성 검증용 데이터 수가 한정적이고, 각 모델별 적합도에서도 큰 차이가 없기 때문에 분석결과의 신뢰도를 떨어뜨리지는 않는 것으로 판단한다.In order to examine the applicability of the multiple regression model, we used 12 separate test data that were not used in regression analysis and analyzed the correlation between the measured values and the calculated values by model. As a result,

, And models 1 and 3

Respectively. This result is different from the model-specific fitness, but it is judged that the reliability of the analysis results is not deteriorated because the number of data for applicability verification is limited and there is no big difference in the fitness of each model.

Applicability analysis shows that the measured and calculated values are relatively close to the line y = x under low normal stresses below 80 kPa.

As a result of the present invention, considering the influence factors of the shear strength in the future and increasing the number of the samples to increase the suitability of the model, the methodology of determining the dynamic properties of the fault blocks which were dependent on the experience or numerical analysis in designing the geotechnical structures It is expected to be able to become.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the invention.

Claims (16)

A database of the weight ratio of the sampled single layer rock samples to the weight ratio and the shear strength corresponding to the normal stress of the sampled single layer rock samples;
Setting a shear strength model in which the shear strength is a dependent variable and the weight ratio of the grain size and the vertical stress are independent variables;
Obtaining a slice of the dependent variable and a coefficient for each independent variable using the weight ratio, the normal stress and the shear strength according to the particle size; And
Applying the slice and modulus to the shear strength model to determine a shear strength scheme,
The shear steel scheme,
A method for estimating a shear strength of a single-layer arm defined by the following equation when the normal stress is divided into one variable.

--- Expression
here,

The weight ratio of each particle size,

Lt; / RTI >

Are the coefficients obtained through multiple regression analysis, respectively.
A database of the weight ratio of the sampled single layer rock samples to the weight ratio and the shear strength corresponding to the normal stress of the sampled single layer rock samples;
Setting a shear strength model in which the shear strength is a dependent variable and the weight ratio of the grain size and the vertical stress are independent variables;
Obtaining a slice of the dependent variable and a coefficient for each independent variable using the weight ratio, the normal stress and the shear strength according to the particle size; And
Applying the slice and modulus to the shear strength model to determine a shear strength scheme,
The shear steel scheme,
A method for estimating a shear strength of a single-layer arm as defined by the following equation when the vertical stress is divided into a variable number.

--- Expression
here,

The weight ratio of each particle size,

Lt; / RTI >

Is the coefficient obtained through multiple regression analysis,

Lt; / RTI >

A variable number when

Represents the coefficient obtained through multiple regression analysis,

,

Is a natural number.
A database of the weight ratio of the sampled single layer rock samples to the weight ratio and the shear strength corresponding to the normal stress of the sampled single layer rock samples;
Setting a shear strength model in which the shear strength is a dependent variable and the weight ratio of the grain size and the vertical stress are independent variables;
Obtaining a slice of the dependent variable and a coefficient for each independent variable using the weight ratio, the normal stress and the shear strength according to the particle size; And
Applying the slice and modulus to the shear strength model to determine a shear strength scheme,
The shear strength scheme is a method for estimating the shear strength of a single layer arm as follows.

here,

The weight ratio of the gravel,

Respectively.
A database of the weight ratio of the sampled single layer rock samples to the weight ratio and the shear strength corresponding to the normal stress of the sampled single layer rock samples;
Setting a shear strength model in which the shear strength is a dependent variable and the weight ratio of the grain size and the vertical stress are independent variables;
Obtaining a slice of the dependent variable and a coefficient for each independent variable using the weight ratio, the normal stress and the shear strength according to the particle size; And
Applying the slice and modulus to the shear strength model to determine a shear strength scheme,
The shear strength scheme is a method for estimating the shear strength of a single layer arm as follows.

here,

The ratio of sand to weight,

Silver silt / clay weight ratio,

Respectively.
A database of the weight ratio of the sampled single layer rock samples to the weight ratio and the shear strength corresponding to the normal stress of the sampled single layer rock samples;
Setting a shear strength model in which the shear strength is a dependent variable and the weight ratio of the grain size and the vertical stress are independent variables;
Obtaining a slice of the dependent variable and a coefficient for each independent variable using the weight ratio, the normal stress and the shear strength according to the particle size; And
Applying the slice and modulus to the shear strength model to determine a shear strength scheme,
The shear strength scheme is a method for estimating the shear strength of a single layer arm as follows.

here,

The weight ratio of the gravel,

Lt; / RTI >

The

Respectively.
A database of the weight ratio of the sampled single layer rock samples to the weight ratio and the shear strength corresponding to the normal stress of the sampled single layer rock samples;
Setting a shear strength model in which the shear strength is a dependent variable and the weight ratio of the grain size and the vertical stress are independent variables;
Obtaining a slice of the dependent variable and a coefficient for each independent variable using the weight ratio, the normal stress and the shear strength according to the particle size; And
Applying the slice and modulus to the shear strength model to determine a shear strength scheme,
The shear strength scheme is a method for estimating the shear strength of a single layer arm as follows.

here,

The ratio of sand to weight,

Silver silt / clay weight ratio,

Lt; / RTI >

The

Respectively.
A database of the weight ratio of the sampled single layer rock samples to the weight ratio and the shear strength corresponding to the normal stress of the sampled single layer rock samples;
Setting a shear strength model in which the shear strength is a dependent variable and the weight ratio of the grain size and the vertical stress are independent variables;
Obtaining a slice of the dependent variable and a coefficient for each independent variable using the weight ratio, the normal stress and the shear strength according to the particle size; And
Applying the slice and modulus to the shear strength model to determine a shear strength scheme,
The shear strength scheme is a method for estimating the shear strength of a single layer arm as follows.

here,

The weight ratio of the gravel,

Lt; / RTI >

The

Respectively.
A database of the weight ratio of the sampled single layer rock samples to the weight ratio and the shear strength corresponding to the normal stress of the sampled single layer rock samples;
Setting a shear strength model in which the shear strength is a dependent variable and the weight ratio of the grain size and the vertical stress are independent variables;
Obtaining a slice of the dependent variable and a coefficient for each independent variable using the weight ratio, the normal stress and the shear strength according to the particle size; And
Applying the slice and modulus to the shear strength model to determine a shear strength scheme,
The shear strength scheme is a method for estimating the shear strength of a single layer arm as follows.

here,

The ratio of sand to weight,

Silver silt / clay weight ratio,

Lt; / RTI >

The

Respectively.
9. The method according to any one of claims 1 to 8,
The method for estimating the shear strength of a single layer arm using the multiple regression analysis.
9. The method according to any one of claims 1 to 8,
Wherein the particle size of the monolayer cancer sample is classified into gravel, sand and silt / clay.
9. The method according to any one of claims 3 to 8,
The constants indicated in the shear steel diagram are for the constant

A method for estimating the shear strength of a single - layer arm including a range.
9. The method according to any one of claims 1 to 8,
Further comprising the step of verifying the shear strength scheme.
13. The method of claim 12,
Wherein verifying the shear steel scheme comprises:
A Method for Estimating Shear Strength of Faulted Rocks Using Pearson Correlation Coefficient. delete delete delete

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