Journal of the Korean GEO-environmental Society (한국지반환경공학회 논문집)

Korean Geo-Environmental Society (한국지반환경공학회)
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Study on the Estimation of Duncan & Chang Model Parameters-initial Tangent Modulus and Ultimate Deviator Stress for Compacted Weathered Soil

다짐 풍화토의 Duncan & Chang 모델 매개변수-초기접선계수와 극한축차응력 산정에 관한 연구

  • Yoo, Kunsun (Department of Civil Engineering, Halla University)
  • Received : 2018.10.10
  • Accepted : 2018.11.27
  • Published : 2018.12.01
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Abstract

Duncan & Chang(1970) proposed the Duncan-Chang model that a linear relation of transformed stress-strain plots was reconstituted from a nonlinear relation of stress-strain curve of triaxial compression test using hyperbolic theory so as to estimate an initial tangent modulus and ultimate deviator stress for the soil specimen. Although the transformed stress-strain plots show a linear relationship theoretically, they actually show a nonlinearity at both low and high values of strain of the test. This phenomenon indicates that the stress-strain curve is not a complete form of a hyperbola. So, if linear regression analyses for the transformed stress-strain plot are performed over a full range of strain of a test, error in the estimation of their linear equations is unavoidable depending on ranges of strain with non-linearity. In order to reduce such an error, a modified regression analysis method is proposed in this study, in which linear regression analyses for transformed stress-strain plots are performed over the entire range of strain except the range the non-linearity is shown around starting and ending of the test, and then the initial tangent modulus and ultimate deviator stresses are calculated. Isotropically consolidated-drained triaxial compression tests were performed on compacted weathered soil with a modified Proctor density to obtain their model parameters. The modified regression analyses for transformed stress-strain plots were performed and analyzed results are compared with results estimated by 2 points method (Duncan et al., 1980). As a result of analyses, initial tangent moduli are about 4.0% higher and ultimate deviator stresses are about 2.9% lower than those values estimated by Duncan's 2 points method.

Duncan & Chang(1970)는 던컨-창 모델을 제안하면서 흙시료의 초기 접선계수와 극한 축차응력을 구하기 위하여 쌍곡선이론을 사용하여 삼축압축시험의 응력-변형률의 비선형관계를 변환된 변형률/축차응력-변형률의 선형관계로 재구성하였다. 그러나 변환된 응력-변형률 관계는 이론적으로 선형관계를 나타내지만, 실제로는 시험이 시작되는 변형률이 작은 구간과 시료가 파괴에 이르는 변형률이 큰 구간에서는 비선형관계를 보인다. 이러한 현상은 삼축압축시험의 응력-변형률 곡선이 완전한 쌍곡선 형태가 아님을 나타낸다. 따라서 변환된 응력-변형률 곡선의 전 구간에 대하여 선형 회귀분석을 실시하여 직선의 식을 구하게 되면, 비선형관계를 나타내는 구간의 범위에 따라 선형관계식의 산정에 편차가 발생하게 된다. 이러한 편차를 줄이기 위하여 본 연구에서는 변환응력-변형률 관계에서 비선형을 나타내는 초반과 종반 구간을 제외한 구간에 대하여 선형회귀분석을 실시함으로써 초기접선계수와 극한 축차응력을 산정하는 수정회귀분석법을 제안하였다. 수정회귀분석법을 검증하기 위하여, 풍화토의 다짐시료에 대하여 압밀-배수 삼축압축시험을 실시하였다. 삼축압축시험의 응력-변형률 곡선으로부터 구한 변환응력-변형률 관계에 대해서 수정회귀분석을 실시하여 Duncan et al.(1980)이 제안한 2점법으로 구한 결과와 비교하였다. 분석결과 수정회기분석법에 비해 Duncan의 2점법으로 산정한 초기 접선계수는 4.0% 크게, 그리고 극한 축차응력은 2.9% 작게 평가되었다.

Keywords

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Fig. 1. Hyperbolic stress-strain curve

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Fig. 2. Transformed hyperbolic stress-strain curve

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Fig. 3. Comparison between actual stress strain curve and hyperbolic model

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Fig. 4. Deviator stress - axial strain plot for 5 Sites

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Fig. 5. Stress-strain plot and transformed stress-strain plot for Site-A

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Fig. 6. Comparison between measured plot and calculated result due to regression analysis of A-D range for Site-A

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Fig. 7. Stress-strain plot and transformed stress-strain plot for Site-C

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Fig. 8. Comparison between measured plot and calculated result due to regression analysis of A-D range for Site-C

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Fig. 9. Comparison of original regression analysis line and modified regression analysis line of transformed stress-strain plot for Site-A and Site-C

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Fig. 10. Comparison of Ei and (σ1 - σ3)ult of original regression analysis and modified regression analysis for 5 Sites

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Fig. 11. Stress-strain curve calculated with original regression analysis line and modified regression analysis line for Site-A

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Fig. 12. Stress-strain curve calculated with original regression analysis line and modified regression analysis line for Site-C

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Fig. 13. Finding representative two points so as to determine the equation of modified regression analysis line ($\overline{A'D'}$) for Site-A and Site-C

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Fig. 14. Estimation of parameter a and b using 2 points method for Site-A and Site-C

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Fig. 15. Measured and calculated stress-strain curves for drained triaxial tests on compacted weathered soils at 5 Sites

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Fig. 16. Comparison of Ei and (σ1 - σ3)ult between Duncan et al.(1980) and modified regression analysis for 5 Sites

Table 1. Summary of physical properties and modified proctor test

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Table 2. Duncan-Chang model parameters calculated within range of AD for 5 Sites

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Table 3. Duncan-Chang model parameters calculated within range of BC for 5 Sites

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Table 4. Stress level, $\frac{{\sigma}_1-{\sigma}_3}{({\sigma}_1-{\sigma}_3)_f}$ of two points on stress-strain curve for 5 Sites

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Table 5. Comparison of Ei and (σ1 - σ3)ult of Duncan et al.(1980) and Modified regression analysis

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