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2026 Vol.28, Issue 1 Preview Page

Research Paper

Stability analysis of circular shaft based on inclination and discontinuity dip

수직구 경사도와 불연속면 경사에 따른 안정성 분석

Soojeong Kim1
,
Hyuksang Jung2*
,
Jinsuck Kim3
,
Jaekook Lee4
김 수정1
,
정 혁상2*
,
김 진석3
,
이 재국4
1A Graduate Student in the Master’s Program, Dept. of Facility Safety Engineering, Dongyang University
2Professor, Dept. of Facility Safety Engineering, Dongyang University
3Director, Technology Research Institute, Sungpoong Construction Co.
4Vice President, Saman Corp.
1비회원, 동양대학교 시설안전공학과 석사과정
2정회원, 동양대학교 시설안전공학과 교수
3정회원, ㈜성풍건설 기술연구소장
4정회원, ㈜삼안 부사장
*Corresponding Author
31 January 2026. pp. 21-40
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Abstract

The stability of circular vertical shafts, while benefiting from stress arching, is highly susceptible to shear-driven kinematic failure in rock masses containing predominant discontinuities. Conventional continuum methods, such as FEM, inherently fail to accurately predict these structurally-controlled movements due to their inability to explicitly model large-strain block interaction and separation. This study overcomes this limitation by employing the Three-Dimensional Distinct Element Method (3DEC) to quantitatively assess stability, focusing on the combined effects of shaft inclination (θs), representing construction tolerance, and discontinuity dip angle (θd), representing geological structure. A systematic parametric analysis was conducted, varying θs (0° to 15°), θd (30° to 60°), and joint shear stiffness (Ks from 0.5 to 50.0 MPa/mm). The results demonstrated that the maximum horizontal displacement in the discontinuous model was approximately 44% higher than in the intact rock model, providing clear quantitative evidence that stability is governed predominantly by the structural properties of the joints rather than the rock matrix strength. Critically, the peak displacement (1.50 mm) was identified not at the maximum analyzed tolerance, but at a minor shaft inclination of θs = 5° (θd = 60° for Against Dip), establishing the novel finding of a Critical Geometric Misalignment Condition within standard construction limits. Displacement sensitivity reached its peak when the angular difference between the shaft axis and the discontinuity plane approached 45°, which is attributed to the geometric characteristics of stress redistribution and the reduction of the arching effect in circular openings. Furthermore, the Ks analysis confirmed a Stiffness Saturation phenomenon, indicating that stability control shifts from elastic stiffness to the joint’s residual shear strength above a certain threshold. Rock bolt analysis verified an asymmetric increase in axial forces under misalignment. These findings strongly suggest that Differential Support Systems (e.g., increased rockbolt length to 6.0 m and 20% increase in shotcrete thickness) must be deployed in kinematically vulnerable shaft sections identified by the established 5° misalignment criterion.

Keywords
Shaft stability
Discontinuity
Inclination
Three-Dimensional Distinct Element Method (3DEC)
Kinematic failure

원형 수직구는 주변 응력 아칭(Stress Arching) 효과로 구조적 안정성이 높게 평가되나, 절리 및 단층과 같은 우세 불연속면(Predominant Discontinuities)의 존재로 인해 전단 구동형 운동학적 파괴(Kinematic Failure)에 근본적으로 취약하다는 문제점이 있다. 기존의 유한요소법(FEM) 등의 연속체 해석 기법은 암반 블록 간의 명시적인 상호작용 및 대변위를 모사할 수 없어 이러한 구조적 불안정성을 정확히 예측하는 데 그 한계가 명확하므로 본 연구에서는 이러한 방법론적 한계를 극복하고자 3차원 개별요소법(Three-Dimensional Distinct Element Method, 3DEC)을 적용하여, 시공 오차를 대변하는 수직구 경사도(θs)와 지질 구조를 대변하는 불연속면 경사각(θd)의 복합적 영향을 정량적으로 평가했으며, 체계적인 매개변수 분석은 θs (0–15°), θd (30–60°), 절리면 전단 강성(Ks: 0.5부터 50.0 MPa/mm까지)을 포함하여 시행하였다. 해석 결과, 불연속성 모델의 최대 수평 변위는 무결암 모델 대비 약 44% 증가율을 기록하였으며, 이는 수직구 안정성이 암반 매질 강도보다는 불연속면의 구조적 활동성에 의해 지배됨을 명확히 입증한 것이다. 특히, 최대 변위(1.50 mm)는 극한 오차 조건(15°)이 아닌, 일반 시공 허용 오차 내인 θs = 5° 조건(θd = 60°, Against Dip)에서 관찰되어, 임계 기하학적 부정합 조건이 미세한 경사 불량에서도 형성될 수 있다는 것을 규명하였다. 변위 민감도는 수직구축과 불연속면 간의 각도 차이가 약 45°에 근접할 때 최대치를 기록하며, 이는 원형 단면의 응력 재분배 특성에 기인한 기하학적 취약성을 의미한다. Ks 분석에서는 강성이 일정 수준 이상에서 변위가 포화되는 강성 포화(Stiffness Saturation) 현상이 확인되었으며, 이는 지반 거동이 탄성 강성보다 절리면의 잔류 전단 강도에 의해 주로 제어됨을 시사한다. 록볼트 축력은 기하학적 부정합 조건에서 비대칭적으로 증가했으며, 이 5° 경사 기준을 활용하여 운동학적으로 취약한 구간에 대한 정교한 리스크 맵핑과 구체화된 차등 지보 시스템(Differential Support System) 적용의 필요성을 제안하고자 한다.

키워드
수직구 안정성
불연속면
경사도
3차원 개별 요소법(3DEC)
운동학적 파괴
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Information
  • Publisher :Korean Tunneling and Underground Space Association
  • Publisher(Ko) :한국터널지하공간학회
  • Journal Title :Journal of Korean Tunnelling and Underground Space Association
  • Journal Title(Ko) :한국터널지하공간학회 논문집
  • Volume : 28
  • No :1
  • Pages :21-40
  • Received Date : 2025-12-19
  • Revised Date : 2026-01-12
  • Accepted Date : 2026-01-12
  • DOI :https://doi.org/10.9711/KTAJ.2026.28.1.021
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