1. Department of Civil Engineering, Zhejiang University City College, Hangzhou 310015, China 2. Key Laboratory of Safe Construction and Intelligent Maintenance for Urban Shield Tunnels of Zhejiang Province, Hangzhou 310015, China 3. College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China 4. Power China Huadong Engineering Co. Ltd., Hangzhou 311122, China 5. Zhejiang Institute of Communications, Hangzhou 311112, China
A calculation method of nonlinear stability ultimate bearing capacity for shield segments considering the initial ovality imperfection was proposed to study the influence of initial ovality imperfection on the ultimate bearing capacity of segment lining structure under the external confining pressure. A numerical model was established and verified by the literature experimental data. The geometric calculation theory of ovality imperfection and its value method were analyzed. By introducing the initial ovality imperfections of horizontal long axis and oblique long axis, parameter analysis was carried out to study the effects of different ovality imperfections on the nonlinear stability ultimate loading for shield segments. A method of nonlinear stability ultimate loading for segments with ovality imperfections was put forward. Analysis shows that the initial ovality imperfection has the adverse effect to nonlinear stability ultimate loading for segments and the adverse effect increases by the increase of defect amplitude. For the case of different ovality imperfections, the loading factor increases rapidly, increases gently and tends to converge with the increase of displacement. The variational trend of ultimate loading factor with different ovality imperfections of transverse long axis is summarized. Taking the soil lateral pressure coefficient 0.6 as the critical value, the variational trend experiences slow and rapid increase. Taking the soil resistance coefficient 5.0 MN/m3 as the critical value, the variational trend experiences rapid increase and slow increase. Taking the bending stiffness of the joint 50.0 MN·m/rad as the critical value, the variational trend increases rapidly and tends to be stable. For the case of different ovality imperfections, as the inclined angle increases, the ultimate loading factor improves and the absolute value for corresponding error percentage decreases. The ovality imperfection of transverse long axis is the worst adverse condition. In practical engineering, the reduction coefficient of nonlinear ultimate bearing capacity of segments with ovality imperfection could be considered as 0.85~0.90. The ultimate bearing capacity of the actual lining segment can be approximately solved according to the integral segment considering the reduction coefficient of 0.85.
Fig.16Error percentage of external confining pressure ultimate load factor-soil resistance coefficient curves for segment
Fig.17External confining pressure ultimate load factor-bending stiffness of joint curves for segment
Fig.18Error percentage of external confining pressure ultimate load factor-bending stiffness of joint curves for segment
Fig.19External confining pressure ultimate load factor-vertical displacement of top central node curves for intergral segment
Fig.20Comparison of external confining pressure ultimate load factor-elliptic imperfection amplitude curves for intergral and lining segments
Fig.21Comparison of error percentage of external confining pressure ultimate load factor-elliptic imperfection amplitude curves for intergral and lining segments
椭圆度缺陷w (‰)
α0
φ1
φ2
φ2/φ1
0
3.99
3.46
0.84~0.86
5
3.94
3.41
10
3.90
3.36
20
3.81
3.27
30
3.73
3.19
Tab.4Comparison of external confining pressure ultimate load factor and error percentage for intergral and lining segments
椭圆度缺陷w (‰)
误差百分比/%
(φ1?φ10)/φ10
φ1/φ10
(φ2?φ20)/φ20
φ2/φ20
0
0
0.935~1.000
0
0.922~1.000
5
?1.89
?1.37
10
?2.39
?2.73
20
?4.41
?5.32
30
?6.52
?7.80
Tab.4
Fig.22Comparison of external confining pressure ultimate load factor-inclination angle of major axis curves for segment
Fig.23Comparison of error percentage of external confining pressure ultimate load factor-inclination angle of major axis curves for segment
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