Journal of the Korean Geotechnical Society (한국지반공학회논문집)

Korean Geotechnical Society (한국지반공학회)
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Derivation of a 3D Arching Formula for Tunnel Excavation in Anisotropic Ground Conditions and Examination of Its Effects

비등방 지반에서 터널굴착을 위한 3차원 아칭식의 유도 및 그 영향 조사

  • Received : 2018.08.16
  • Accepted : 2018.12.04
  • Published : 2018.12.31
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Abstract

Terzaghi proposed a 2D formula for arching based on the assumption of a vertical sliding surface induced in the upper part due to the downward movement of a trapdoor. The formula was later expanded to consider 3D tunnel excavation conditions under inclined sliding surfaces. This study further extends the expanded formula to consider the effects of different ground properties and inclined sliding conditions in the transverse and longitudinal directions considering anisotropic ground conditions, as well as 3D tunnel excavation conditions. The 3D formula proposed in this study was examined of the induced vertical stress under various conditions (ground property, inclined sliding surface, excavation condition, surcharge pressure, earth pressure coefficient) and compared with the 2D Terzaghi formula. The examination indicated that the induced vertical stress increased as the excavation width and length increased, the inclination angle increased, the cohesion and friction angle decreased, the earth pressure coefficient decreased, and the surcharge pressure increased. Under the conditions examined, the stress was more affected at low excavation lengths and by the ground properties in the transverse direction. In addition, The comparison with the 2D Terzaghi formula showed that the induced vertical stress was lower and the difference was highly affected by the ground properties, inclined sliding conditions, and 3D tunnel excavation conditions. The proposed 3D arching formula could help to provide better understanding of complex arching phenomena in tunnel construction.

테르쟈기는 트랩도어 처짐에 기반한 상부지반의 수직활동면을 가정한 2차원 아칭식을 제안하였다. 이후 관련 식은 3차원 터널굴착조건과 경사활동면을 고려할 수 있도록 확장되었다. 본 연구에서는 3차원 터널굴착조건에서 비등방지반조건을 반영하여 터널 횡방향 및 종방향에서의 지반물성치 및 활동면의 경사각을 달리하여 고려할 수 있도록 더욱 확장된 아칭식을 유도하고 제시하였다. 제시된 식을 이용하여 다양한 조건(지반물성치, 경사활동면, 굴착조건, 상재하중, 토압계수)에서 발생되는 수직응력에 대해 조사하였고 테르쟈기의 2차원 아칭식과도 비교하였다. 조사결과, 발생 수직응력은 굴착폭 및 굴착길이, 경사각, 상재하중이 증가할수록 증가했고 점착력과 마찰각, 토압계수가 감소할수록 증가하였으며, 굴착길이가 작을 때와 횡방향 지반물성치에 의해서 더 큰 영향을 받는 것으로 나타났다. 또한 테르쟈기 2차원 아칭식과 비교하여 발생 수직응력은 더 작은 것으로 나타났고 그 차이정도는 지반물성치, 경사활동면, 3차원 터널굴착 조건에 따라 매우 큰 영향을 받는 것으로 나타났다. 제시된 3차원 아칭식은 터널굴착으로 인한 복잡한 아칭현상을 보다 잘 이해하는데 도움을 줄 수 있을 것으로 판단된다.

Keywords

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Fig. 1. Diagram illustrating the assumptions for computing pressure between two vertical sliding surfaces

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Fig. 2. Schematic of load transfer (arching) in 3D tunnel excavation conditions

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Fig. 3. Diagram illustrating assumptions for computing pressure in 3D excavation conditions with inclined sliding surfaces at angles of α1 and α2

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Fig. 4. Comparison with experimental test results

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Fig. 5. Effect of excavation width (2B) and longitudinal excavation length (2L, L=half excavation length) under varying inclination angles (α1 and α2) (H=20m, γ=18kN/m3, c1=c2=0, ϕ1=ϕ2=35°, q=0, K1=K2=1)

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Fig. 6. Effect of excavation depth (H) and longitudinal excavation length (2L, L=half excavation length) under varying inclination angles (α1 and α2) (2B=6m, γ=18kN/m3, c1=c2=0, ϕ1=ϕ2=35°, q=0, K1=K2=1)

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Fig. 7. Effect of cohesion (c) and longitudinal excavation length (2L, L=half excavation length) under varying inclination angles (α1 and α2)

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Fig. 8. Effect of friction angle (ϕ) and longitudinal excavation length (2L, L=half excavation length) under varying inclination angles (α1 and α2)

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Fig. 9. Effect of earth pressure coefficient (K) and longitudinal excavation length (2L, L=half excavation length) under varying inclination angles (α1 and α2)

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Fig. 10. Effect of surcharge pressure (q) and longitudinal excavation length (2L, L=half excavation length) under varying inclination angles (α1 and α2)

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