A new method for analysis of counter beams is presented in the paper. The analysis has taken into account their stiffness EI, Winkler’s space with modulus of subgrade reaction k and equality deformities of the founda...A new method for analysis of counter beams is presented in the paper. The analysis has taken into account their stiffness EI, Winkler’s space with modulus of subgrade reaction k and equality deformities of the foundation beam with the ground. The solution is found by using the numerical analysis of the Winkler’s model, with variation of different moduli of the subgrade reaction k2 outside the force zone r, while under the force P exists the modulus of the subgrade reaction k, up to the definition of minimum bending moments. The exponential function k2(r), as the geometric position of the minimum moments is approximately assumed. From the potential energy conditions of the reciprocity of displacement and reaction, the width of the zone r and the modulus of the subgrade reaction k2 are explicitly determined, introducing in the calculation initial and calculation soil displacement wsi successively. At the end of the paper, it presented numerical example in which the influence of k and k2 values on bending moments of the counter beam is analyzed. The essential idea of this paper is to decrease the quantity of the reinforcement in the foundations, beams, i.e. to obtain a cost-efficient foundation construction.展开更多
In this study,a refined numerical model for segmental lining of a shield tunnel,which contains detailed models of reinforcement and connecting bolts,is established using finite element software.The model is first vali...In this study,a refined numerical model for segmental lining of a shield tunnel,which contains detailed models of reinforcement and connecting bolts,is established using finite element software.The model is first validated by the results from a full-scale model test.Then,based on the load-structure method,this numerical model is adopted to investigate the internal force distribution and the transverse deformation characteristics of the shield tunnel when it is subject to local soil loosening.The influence of loosening position,loosening range,and loosening extent on the mechanical response is extensively studied through comprehensive numerical analyses.The results show that the main influence of local soil loosening on the ring is to disturb the force balance and change the constraint conditions,thus changing the deformation pattern and force state.After the loosening occurs,the bending moment of the ring in the loosening range increases and the axial force decreases.The vertical convergence of the ring is the largest and the equivalent stiffness of the ring is the smallest when the local soil loosened at the haunch and the loosening range a is 90°.The vertical convergence of the ring increases with increasing of the loosening extent,and the equivalent stiffness decreases linearly with increasing of the loosening extent.The results can enhance our understanding of mechanical behaviors of segmental lining associated soil loosening,and will show a possible way for detecting soil loosening based on the measured deformation and internal forces.展开更多
文摘A new method for analysis of counter beams is presented in the paper. The analysis has taken into account their stiffness EI, Winkler’s space with modulus of subgrade reaction k and equality deformities of the foundation beam with the ground. The solution is found by using the numerical analysis of the Winkler’s model, with variation of different moduli of the subgrade reaction k2 outside the force zone r, while under the force P exists the modulus of the subgrade reaction k, up to the definition of minimum bending moments. The exponential function k2(r), as the geometric position of the minimum moments is approximately assumed. From the potential energy conditions of the reciprocity of displacement and reaction, the width of the zone r and the modulus of the subgrade reaction k2 are explicitly determined, introducing in the calculation initial and calculation soil displacement wsi successively. At the end of the paper, it presented numerical example in which the influence of k and k2 values on bending moments of the counter beam is analyzed. The essential idea of this paper is to decrease the quantity of the reinforcement in the foundations, beams, i.e. to obtain a cost-efficient foundation construction.
基金the financial support provided by National Key R&D Program of China under Grant No.2018YFB2100901the National Natural Science Foundation of China under Grant Nos.51938008,52090081and China Academy of Railway Sciences Fund Project under Grand No.2019YJ181.
文摘In this study,a refined numerical model for segmental lining of a shield tunnel,which contains detailed models of reinforcement and connecting bolts,is established using finite element software.The model is first validated by the results from a full-scale model test.Then,based on the load-structure method,this numerical model is adopted to investigate the internal force distribution and the transverse deformation characteristics of the shield tunnel when it is subject to local soil loosening.The influence of loosening position,loosening range,and loosening extent on the mechanical response is extensively studied through comprehensive numerical analyses.The results show that the main influence of local soil loosening on the ring is to disturb the force balance and change the constraint conditions,thus changing the deformation pattern and force state.After the loosening occurs,the bending moment of the ring in the loosening range increases and the axial force decreases.The vertical convergence of the ring is the largest and the equivalent stiffness of the ring is the smallest when the local soil loosened at the haunch and the loosening range a is 90°.The vertical convergence of the ring increases with increasing of the loosening extent,and the equivalent stiffness decreases linearly with increasing of the loosening extent.The results can enhance our understanding of mechanical behaviors of segmental lining associated soil loosening,and will show a possible way for detecting soil loosening based on the measured deformation and internal forces.
