This paper proposes a longitudinal vulnerability-based analysis method to evaluate the impact of foundation pit excavation on shield tunnels,accounting for geological uncertainties.First,the shield tunnel is modeled a...This paper proposes a longitudinal vulnerability-based analysis method to evaluate the impact of foundation pit excavation on shield tunnels,accounting for geological uncertainties.First,the shield tunnel is modeled as an Euler Bernoulli beam resting on the Pasternak foundation incorporating variability in subgrade parameters along the tunnel’s length.A random analysis method using random field theory is introduced to evaluate the tunnel’s longitudinal responses to excavation.Next,a risk assessment index system is established.The normalized relative depth between the excavation and the shield tunnel is used as a risk index,while the maximum longitudinal deformation,the maximum circumferential opening,and the maximum longitudinal bending moment serve as performance indicators.Based on these,a method for analyzing the longitudinal fragility of shield tunnels under excavation-induced disturbances is proposed.Finally,the technique is applied to a case study involving a foundation pit excavation above a shield tunnel,which is the primary application scenario of this method.Vulnerability curves for different performance indicators are derived,and the effects of tunnel stiffness and subgrade stiffness on the tunnel vulnerability are explored.The results reveal significant differences in vulnerability curves depending on the performance index used.Compared to the maximum circumferential opening and the maximum longitudinal bending moment,selecting the maximum longitudinal deformation as the control index better ensures the tunnel’s usability and safety under excavation disturbances.The longitudinal vulnerability of the shield tunnel nonlinearly decreases with the increase of the tunnel stiffness and subgrade stiffness,and the subgrade stiffness has a more pronounced effect.Parametric analyses suggest that actively reinforcing the substratum is more effective on reducing the risk of tunnel failure due to adjacent excavations than passive reinforcement of the tunnel structure.展开更多
Free vibration analysis of non-homogeneous orthotropic plates resting on a Pasternak type of elastic foundation is investigated. A set of admissible orthogonal polynomials are generated with Gram-Schmidt orthogonaliza...Free vibration analysis of non-homogeneous orthotropic plates resting on a Pasternak type of elastic foundation is investigated. A set of admissible orthogonal polynomials are generated with Gram-Schmidt orthogonalization procedure and adopted in the Rayleigh-Ritz method. Accuracy and applicability of the method are examined by comparison of the results for different boundary conditions and material types with those available in literature. It is found that this method has good accuracy regardless of type of boundary condition and yields very accurate results even with low number of terms of orthogonal polynomials for the first mode of vibration. For higher modes of vibration, higher terms of orthogonal polynomials should be used. The effects of foundation parameter, density and non-homogeneity parameters on natural frequency are examined. It is concluded that natural frequency of plates are more sensitive to shearing layer coefficient rather than Winkler coefficient and density parameter has weakening effect on natural frequency.展开更多
基金Project(52178402) supported by the National Natural Science Foundation of China。
文摘This paper proposes a longitudinal vulnerability-based analysis method to evaluate the impact of foundation pit excavation on shield tunnels,accounting for geological uncertainties.First,the shield tunnel is modeled as an Euler Bernoulli beam resting on the Pasternak foundation incorporating variability in subgrade parameters along the tunnel’s length.A random analysis method using random field theory is introduced to evaluate the tunnel’s longitudinal responses to excavation.Next,a risk assessment index system is established.The normalized relative depth between the excavation and the shield tunnel is used as a risk index,while the maximum longitudinal deformation,the maximum circumferential opening,and the maximum longitudinal bending moment serve as performance indicators.Based on these,a method for analyzing the longitudinal fragility of shield tunnels under excavation-induced disturbances is proposed.Finally,the technique is applied to a case study involving a foundation pit excavation above a shield tunnel,which is the primary application scenario of this method.Vulnerability curves for different performance indicators are derived,and the effects of tunnel stiffness and subgrade stiffness on the tunnel vulnerability are explored.The results reveal significant differences in vulnerability curves depending on the performance index used.Compared to the maximum circumferential opening and the maximum longitudinal bending moment,selecting the maximum longitudinal deformation as the control index better ensures the tunnel’s usability and safety under excavation disturbances.The longitudinal vulnerability of the shield tunnel nonlinearly decreases with the increase of the tunnel stiffness and subgrade stiffness,and the subgrade stiffness has a more pronounced effect.Parametric analyses suggest that actively reinforcing the substratum is more effective on reducing the risk of tunnel failure due to adjacent excavations than passive reinforcement of the tunnel structure.
文摘Free vibration analysis of non-homogeneous orthotropic plates resting on a Pasternak type of elastic foundation is investigated. A set of admissible orthogonal polynomials are generated with Gram-Schmidt orthogonalization procedure and adopted in the Rayleigh-Ritz method. Accuracy and applicability of the method are examined by comparison of the results for different boundary conditions and material types with those available in literature. It is found that this method has good accuracy regardless of type of boundary condition and yields very accurate results even with low number of terms of orthogonal polynomials for the first mode of vibration. For higher modes of vibration, higher terms of orthogonal polynomials should be used. The effects of foundation parameter, density and non-homogeneity parameters on natural frequency are examined. It is concluded that natural frequency of plates are more sensitive to shearing layer coefficient rather than Winkler coefficient and density parameter has weakening effect on natural frequency.
