Journal of the Korea Academia-Industrial cooperation Society (한국산학기술학회논문지)

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Comparison of Two Methods for Analyzing Stress-Strain Behavior of Soil Beam

지반보의 응력-변형률 거동에 대한 해석법 비교

  • Lee, Seung-Hyun (Division of Architecture, Architectural Engineering and Civil Engineering, Sunmoon University) ;
  • Han, Jin-Tae (Korea Institute of Construction Technology)
  • 이승현 (선문대학교 건축사회환경공학부) ;
  • 한진태 (한국건설기술연구원)
  • Received : 2018.08.28
  • Accepted : 2018.12.07
  • Published : 2018.12.31
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Abstract

To analyze the behavior of a soil beam under pore water pressure, the results of analytical solutions and finite element analysis (FEM) were compared quantitatively. In contrast to the results of the analytical solution, the horizontal stress obtained from the FEM did not show a symmetrical distribution. On the other hand, the horizontal stress became closer to symmetrical distribution as the number of elements of the soil beam were increased. A comparison of the horizontal stresses from the analytic solution with those obtained from Gaussian points of FEM showed that the magnitude of the tensile stress from the FEM using 3 elements was 6% of the maximum value of the analytical solution and the compressive stress from the FEM using the same elements was 37% of the maximum value of the analytical solution. The magnitude of the tensile stress from the FEM using 6 elements was 61% of the maximum value of the analytical solution and the magnitude of the compressive stress from the FEM using the elements was 83% of the maximum value of the analytical solution. Vertical stresses, which were obtained from the analytical solution, showed a continuous distribution with the depth of the soil beam, whereas the vertical stresses from the FEM showed a discrete distribution corresponding to each element. The results also showed that the average value of the vertical stresses of each element was close to that of the pore water pressure. A comparison of the vertical displacements computed at the near vertical center line of the soil beam from the FEM with those of the analytical solution showed that the magnitude of the vertical displacement from FEM using 3 elements was 35% of the value of the analytical solution and the magnitude of the vertical displacement from FEM using 6 elements was 57% of the value of the analytical solution.

간극수압을 받는 지반보의 응력-변형률 거동 분석을 위해 해석해와 유한요소해석결과를 정량적으로 상호 비교해 보았다. 유한요소해석을 통해 얻은 수평응력은 해석해에 의한 결과와는 달리 지반보의 수평축에 대하여 대칭성을 보이지 않았으나 요소의 개수가 증가함에 따라 대칭에 가까운 형태를 보였다. 해석해에 의한 수평응력을 유한요소의 가우스점에 대하여 얻은 수평응력과 비교해 볼 때 3개의 요소를 고려한 유한요소해석을 통해 얻은 인장응력의 값은 해석해에 의한 최대 인장응력값의 6% 였고 압축응력의 값은 해석해에 의한 최대값의 37% 였다. 6개의 요소를 고려한 유한요소해석을 통해 얻은 인장응력의 값은 해석해를 통해 얻은 최대값의 61% 였고 압축응력의 값은 해석해를 통해 얻은 최대값의 83% 였다. 지반보 내에 발생되는 연직응력은 해석해에 의할 경우 보의 깊이에 따라 연속적인 분포양상을 보인다. 유한요소해석에 의한 연직응력은 유한요소를 구성하는 요소에 따라 이산적인 분포를 보이는데 요소내의 4개의 가우스점에 대하여 얻은 평균 연직응력은 지반보에 작용하는 간극수압의 크기에 가까운 값을 보였다. 지반보의 중앙 근처에서의 연직변위량을 비교해 볼 때 3개의 요소로 구성된 지반보에 대한 유한요소해석을 통해 얻은 값은 해석해에 의한 값의 35% 였으며 6개의 요소로 구성된 지반보에 대한 유한요소해석을 통해 얻은 값은 해석해에 의한 값의 57% 였다.

Keywords

SHGSCZ_2018_v19n12_294_f0001.png 이미지

Fig. 1. Soil beam under pore water pressure

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Fig. 2. Natural coordinates and Gauss points

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Fig. 3. Soil beam for anlaysis

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Fig. 5. Comparison of horizontal stresses

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Fig. 6. Distribution of vertical stress with depth of soilbeam

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Fig. 7. Comparison of vertical displacements

Table 1. Properties of the soil beam

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Fig. 4. Two types of elements for FEM

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