The structural analysis and design methods considering joint bursting in the segment lining

조인트 버스팅을 고려한 세그먼트 라이닝 구조해석 및 설계방법

Abstract

Segment lining applied to the TBM tunnel is mainly made of concrete, and it requires sufficient structural capacity to resist loads received during the construction and also after the completion. When segment lining is design to the Limit State Design, both Ultimate Limit State (ULS) and Service Limit State (SLS) should be met for the possible load cases that covers both permanent and temporary load cases - such as load applied by TBM. When design segment lining, it is important to check structural capacity at the joints as both temporary and permanent loads are always transferred through the segment joints, and sometimes the load applied to the joint is high enough to damage the segment - so called bursting failure. According to the various design guides from UK (PAS 8810, 2016), compression stress at the joint surface can generate bursting failure of the segment. This is normally from the TBM's jacking force applied at the circumferential joint, and the lining's hoop thrust generated from the permanent loads applied at the radial joint. Therefore, precast concrete segment lining's joints shall be designed to have sufficient structural capacity to resist bursting stresses generated by the TBM's jacking force and by the hoop thrust. In this study, bursting stress at the segment joints are calculated, and the joint's structural capacity was assessed using Leonhardt (1964) and FEM analysis for three different design cases. For those three analysis cases, hoop thrust at the radial joint was calculated with the application of the most widely used limit state design codes Eurocode and AASHTO LRFD (2017). For the circumferential joints bursting design, an assumed TBM jack force was used with considering of the construction tolerance of the segments and the eccentricity of the jack's position. The analysis results show reinforcement is needed as joint bursting stresses exceeds the allowable tensile strength of concrete. This highlights that joint bursting check shall be considered as a mandatory design item in the limit state design of the segment lining.

쉴드 TBM터널에 적용되는 세그먼트 라이닝은 주로 콘크리트로 제작되며, 시공 중 및 완공 후 작용 하중에 견딜 수 있는 충분한 강도가 요구된다. 한계상태설계법에 의한 세그먼트라이닝 설계는 주로 극한하중상태(ULS) 및 사용하중상태(SLS)에 대하여 검토하며, 상시하중과 임시하중에 대하여 발생 가능한 조합을 구성하여 적용한다. 또한 TBM에 의한 시공을 고려한 한계상태 설정과 구조해석이 필요하며, 특히 세그먼트라이닝은 현장에서 조립되어 원형구조물을 완성하는 방식이기 때문에, 콘크리트표면이 접촉하는 조인트가 필수적으로 존재하며 이 조인트를 통해 상당한 크기의 압축응력이 전달되므로 조인트에 대한 구조검토가 중요하다. 일반적으로 세그먼트 라이닝의 원주방향 조인트(circumferential joint)와 반경방향 조인트(radial joint)에서의 인장응력에 대하여 FEM모델이나 이론식으로 검토한다. 영국의 설계지침(PAS 8810, 2016)에 의하면, 버스팅을 일으키는 조인트에서의 압축응력은 원주방향 조인트(circumferential joint)에 잭 추력을 가하는 경우뿐만 아니라 반경방향 조인트(radial joint)에 축력이 전달되는 경우에도 발생하므로 버스팅 응력을 검토하여 세그먼트의 인장강도와 비교하여 필요할 경우 보강을 하여야 한다. 본 연구에서는 대표적인 한계상태설계코드인 EURO CODE와 AASHTO LRFD (2017)의 하중조건을 적용하여 조인트 응력을 비교 분석하였고, FEM해석을 통하여 버스팅(bursting)을 유발하는 조인트응력을 평가하고 발생경향을 이론식과 비교 분석하였다. 분석결과, 조인트 응력이 콘크리트의 허용 인장강도를 초과하는 경우가 발생하여 보강이 필요한 것으로 검토되었다. 따라서 조인트 버스팅 검토는 세그먼트라이닝 한계상태설계 시 설계항목으로 비중 있게 고려할 필요가 있다.

Fig. 1. Illustration of segments and joints (Woo and Yoo, 2015)

Fig. 2. Bursting stresses and bursting failure of segment (ARUP, 2017)

Fig. 3. Check of joint stresses of segment lining in domestic design practice (KEPCO, 2013)

Fig. 4. Contact width reduction due to joint rotation (PAS 8810, 2016)

Fig. 5. Radial joint opening due to assumed elliptical deformation (ARUP, 2017)

Fig. 6. The stress diagram by simplified method (ARUP, 2017)

Fig. 7. The stress distribution of segment joint (ARUP, 2017)

Fig. 8. Tensile stress distribution of segment joint (Leonhardt, 1964)

Fig. 10. Details of segment joints and shape

Fig. 11. Moment diagrams of differential ram loading

Fig. 12. Joint thrust in each case

Fig. 13. Example of tensile stress diagram by Leonhardt’s method

Fig. 14. Joint tensile stress on intrados of radial joint

Fig. 15. Joint tensile stress on extrados of radial joint

Fig. 16. Joint tensile stress on circumferential joint due to the jack thrust

Fig. 17. Joint tensile force on circumferential joint in case of reinforcement

Fig. 18. Tensile stress contour diagram of SLS on Case 1 (EURO CODE)

Fig. 19. Tensile stress contour diagram of SLS on Case 2 (EURO CODE)

Fig. 20. Tensile stress contour diagram of SLS on Case 3 (EURO CODE)

Fig. 21. Tensile stress contour diagram of ULS on Case 1 (EURO CODE)

Fig. 22. Tensile stress contour diagram of ULS on Case 2 (EURO CODE)

Fig. 23. Tensile stress contour diagram of ULS on Case 3 (EURO CODE)

Fig. 9. Geometric conditions of the joint stress analysis

Table 1. Dimensions and mechanical parameters of the segment lining

Table 2. Material properties of the ground

Table 3. Segment compressive stress by jack thrust in the curved section

Table 4. Segment stress by eccentric distance (e)

Table 5. Segment stress by eccentric loading