Difference solutions for responses of foundation-beams with arbitrary boundary conditions considering spatial soil variability and its applications

Wang, Zuxian; Shi, Chenghua; Gong, Chenjie; Cao, Chengyong; Peng, Zhu; Sun, Yan

doi:10.1016/j.compgeo.2022.105002

Cited by 17 publications

(6 citation statements)

References 37 publications

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“…A comparison of tunnel deflection and bending moment is shown in Figure5. The P-T model aligns well with the finite difference decomposition of the V-T model as proposed in reference[12], in terms of both numerical values and trends. However, the W-T model does not account for continuity between the soil layers,…”

supporting

confidence: 77%

“…5. Comparison of results obtained by semi-analytical solution and the finite difference method: a) deflection diagram; b) bending moment diagram.The semi-analytical solution presented in this study suggests that when beam section A is constant and the Timoshenko beam consists of a homogeneous material, it degenerates to the computational case outlined in the reference[12]. Similarly, the P-T model degenerates to the W-T model when the shear modulus of the Pasternak foundation layer is zero.…”

mentioning

confidence: 79%

“…3.1 Comparison with existing studies on difference decomposition Wang et al proposed a calculation method for the Timoshenko beam model on a Vlasov foundation [12]. This method, featuring arbitrary boundary conditions, employs translational and rotational constraint springs to solve the bending moment and deflection curve of the shield tunnel under load 150 P kPa = within 100 m 2 of the ground surface.…”

Section: ( ) ( )mentioning

confidence: 99%

“…To address the effect of shear stiffness in beam structures and enhance the constructive equation, scholars have proposed nonlinear beam theories [10]. The Timoshenko beam theory, which introduces a shear correction coefficient to account for shear deformation and rotational inertia, is widely applied in practical engineering models [12]. Much of the preceding work has centered on the mechanical analysis of normal section beams.…”

Section: Introductionmentioning

confidence: 99%

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Variable-Section Functional Gradient Beams on Pasternak Foundations: An Enhanced Interaction Theory for Construction Applications

Ling

Huang

et al. 2023

Preprint

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Functional gradient materials are ubiquitous in construction projects. Enhancing the theory of interaction between variable-section functional gradient beams (FGBs) and soil holds significant implications for engineering applications. Based on the variational principle and the transfer matrix method, this paper formulates semi-analytical solutions for displacement and internal force in the Timoshenko beam model (P-T model). The model features variable-section axial functional gradients on a Pasternak foundation. It accounts for the shear effects in the FGB structure and the soil's continuity and shear strength influences. Next, the semi-analytical solution is compared with finite difference decomposition results from existing studies. The comparison validates the proposed computational theory's precision and accuracy. The P-T model can degenerate to the Winkler-Timoshenko model (W-T model) when the foundation's shear layer stiffness is zero. Examining the displacement and internal force change when the beam stiffness varies along the axial direction reveals that an asymmetrical stiffness distribution on both sides of the midspan increases the displacement in the midsection. Moreover, when the beam stiffness gradient follows a Gaussian distribution along the axial direction, displacement sharply increases at the boundary position. Finally, the proposed method is incorporated with the Mindlin stress solution to assess the impact of construction on a tunnel existing within a foundation pit project in Shenzhen. We compare theoretical calculations, monitoring data, and numerical simulation results. The results show considerable agreement across the three methods. The tunnel's overall deflection follows an "M" shape, and the calculation using the variable-section FGB predicts the existing tunnel's deformation trend more accurately. This method reduces the calculation error from 35% to 8.3% in comparison to the traditional normal section beam.

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supporting

confidence: 77%

mentioning

confidence: 79%

Section: ( ) ( )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Variable-Section Functional Gradient Beams on Pasternak Foundations: An Enhanced Interaction Theory for Construction Applications

Ling

Huang

et al. 2023

Preprint

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“…The results showed that the Euler-Bernoulli model underestimates deformation but overestimates internal forces of tunnels. Wang et al 16 derived a difference solution under arbitrary distributed loads, by simplifying the tunnel as a Timoshenko beam model. This model took the spatial soil variability and arbitrary elastic boundary conditions into consideration.…”

Section: Introductionmentioning

confidence: 99%

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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Analytical Method for Predicting Tunnel Deformation Caused by Overlying Excavation Considering the Dewatering

Li,

Wang,

Luo

et al. 2024

Num Anal Meth Geomechanics

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Predicting the tunnel deformation caused by overlying excavation is a crucial catch in current rail transit construction. Most theoretical studies overlook the effect of dewatering on tunnel response. This study utilized Mindlin's stress solution and an improved incremental method to calculate the additional load resulting from excavation. The load increment due to dewatering was determined based on the effective stress principle and a modified Dupuit infiltration curve. Treating the tunnel as a series of segment rings on a Vlazov foundation, the energy variance method and a collaborative deformation model were employed to develop a tunnel deformation prediction model. The proposed model's validity was confirmed by examining two traceable cases. Based on this, further discussion addressed the impact of dewatering depth, tunnel burial depth, tunnel‐pit relative distance, and intersection angle on existing tunnel deformation. Finally, combining the proposed model with multiple regression analysis, a semi‐empirical method was established to determine the tunnel's maximum vertical displacement. The study found that dewatering extends the tunnel force range, and the tunnel subsidence was positively correlated with groundwater level drop depth. The increase in the tunnel burial depth and distance from the excavation center led to a longer soil unloading transfer path, resulting in reduced disturbance to the tunnel. A smaller intersection angle between the excavation's short edge and the tunnel led to less disturbance of the underlying tunnel, which should be avoided in practical engineering. The developed semi‐empirical formulae have sufficient engineering accuracy, guiding the reinforcement of the underlying tunnel.

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Difference solutions for responses of foundation-beams with arbitrary boundary conditions considering spatial soil variability and its applications

Cited by 17 publications

References 37 publications

Variable-Section Functional Gradient Beams on Pasternak Foundations: An Enhanced Interaction Theory for Construction Applications

Variable-Section Functional Gradient Beams on Pasternak Foundations: An Enhanced Interaction Theory for Construction Applications

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

Analytical Method for Predicting Tunnel Deformation Caused by Overlying Excavation Considering the Dewatering

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