Modelling the performance of immersed tunnel via considering variation of subsoil property

Wang, Yanning; Zhou, Huanzhu; Min, Xinhao

doi:10.1016/j.oceaneng.2022.113114

Cited by 9 publications

(2 citation statements)

References 26 publications

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“…According to the study of Wang et al., 28 the equivalent compression coefficient of the Vlasov foundation ( k e ) and the equivalent shear coefficient of the Vlasov foundation ( t e ) can be expressed as follows:

\begin{equation}{k_{\mathrm{e}}} = \frac{{D{E_{\mathrm{s}}}}}{{(1 - v_{\mathrm{s}}^{\mathrm{2}})(1 - \frac{{v_{\mathrm{s}}^{\mathrm{2}}}}{{{{(1 - {v_{\mathrm{s}}})}^2}}})}}\int\limits_{0}^{H}{{{{\left( {\frac{{{\mathrm{d}}h(z)}}{{{\mathrm{d}}z}}} \right)}^2}{\mathrm{d}}z}}\end{equation}

\begin{equation}{t_{\mathrm{e}}} = \frac{{D{E_{\mathrm{s}}}}}{{4(1 - v_{\mathrm{s}}^{\mathrm{2}})(1 - \frac{{{v_{\mathrm{s}}}}}{{1 - {v_{\mathrm{s}}}}})}}\int\limits_{0}^{H}{{h{{(z)}^2}{\mathrm{d}}z}}\end{equation}

where h ( z ) = 1‐ z / H , is a linear function in displacement along the z ‐axis; v s is the Poisson's ratio of the soil; E s is Elastic modulus of the soil; H is thickness of the elastic layer of the Vlasov foundation, which is generally taken as 2.5 D .…”

Section: Formulationmentioning

confidence: 99%

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Analytical prediction for longitudinal deformation of shield tunnel subjected to ground surface surcharge considering the stiffness reduction

Cao,

Liang,

Kang

et al. 2023

Num Anal Meth Geomechanics

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This paper presents an improved longitudinal beam‐spring model on the Vlasov foundation for estimating the longitudinal deformation of the shield tunnel when subjected to the ground surface surcharge. This model incorporates an improved subgrade modulus and treats each segmental ring as a Timoshenko short beam, with each circumferential joint modeled by two mechanical springs. It can accurately reflect the discontinuous deformation, and capture the dislocation and opening deformation of shield tunnels. Two‐stage analysis methodology is adopted to consider soil and tunnel interaction. The feasibility of this model is verified by comparing it with two well‐documented field monitoring cases. The computed results are also compared with those based on other analytical models. The results show that the Timoshenko continuous beam overestimates the dislocation deformation, while underestimates the opening deformation. In addition, the settlement curve exhibits neither smooth nor differentiable features. Finally, this paper also conducted some parameter analysis to examine the impact on tunnel deformation, encompassing dimensions of ground surface surcharge, the dual‐area loading, and the joint reinforcement. This approach provides valuable insights into how the deformation characteristics of shield tunnels are influenced by ground surface surcharge.

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\begin{equation}{k_{\mathrm{e}}} = \frac{{D{E_{\mathrm{s}}}}}{{(1 - v_{\mathrm{s}}^{\mathrm{2}})(1 - \frac{{v_{\mathrm{s}}^{\mathrm{2}}}}{{{{(1 - {v_{\mathrm{s}}})}^2}}})}}\int\limits_{0}^{H}{{{{\left( {\frac{{{\mathrm{d}}h(z)}}{{{\mathrm{d}}z}}} \right)}^2}{\mathrm{d}}z}}\end{equation}

\begin{equation}{t_{\mathrm{e}}} = \frac{{D{E_{\mathrm{s}}}}}{{4(1 - v_{\mathrm{s}}^{\mathrm{2}})(1 - \frac{{{v_{\mathrm{s}}}}}{{1 - {v_{\mathrm{s}}}}})}}\int\limits_{0}^{H}{{h{{(z)}^2}{\mathrm{d}}z}}\end{equation}

Section: Formulationmentioning

confidence: 99%

“…According to the study of Wang et al, 28 the equivalent compression coefficient of the Vlasov foundation (k e ) and the equivalent shear coefficient of the Vlasov foundation (t e ) can be expressed as follows:…”

Section: Coefficient Of Subgrade Modulusmentioning

confidence: 99%