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Rock and Soil Mechanics

Analytical solution

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Full-Text Articles in Civil and Environmental Engineering

Simplified Analytical Solution For Horizontal Seismic Response Of Single Piles To Vertically Incident S Waves, Chang-Jie Zheng, Yi-Qin Cui, Chen Wu, Tong Luo, Lu-Bao Luan Apr 2023

Simplified Analytical Solution For Horizontal Seismic Response Of Single Piles To Vertically Incident S Waves, Chang-Jie Zheng, Yi-Qin Cui, Chen Wu, Tong Luo, Lu-Bao Luan

Rock and Soil Mechanics

Based on the continuous medium model and the pile-soil interaction, the horizontal seismic response of a single pile subjected to vertically propagating S waves was investigated by regarding the single pile as a one-dimensional linearly elastic beam. The time-harmonic displacement of bedrock was introduced as the vertically propagating S waves, and the horizontal dynamic impedance function of the soil was derived by the governing equations of the plane strain model. Analytical solutions for the seismic response of the single pile subjected to vertically propagating S waves were obtained by subsuming soil impedance into the governing equation of the single pile …


Analytical Method To Estimate The Influence Of Foundation Pit Excavation Adjacent To The Station (Working Shaft) On The Underlying Shield Tunnel, Zu-Xian Wang, Cheng-Hua Shi, Chen-Jie Gong, Cheng-Yong Cao, Jian-Wen Liu, Zhu Peng Oct 2022

Analytical Method To Estimate The Influence Of Foundation Pit Excavation Adjacent To The Station (Working Shaft) On The Underlying Shield Tunnel, Zu-Xian Wang, Cheng-Hua Shi, Chen-Jie Gong, Cheng-Yong Cao, Jian-Wen Liu, Zhu Peng

Rock and Soil Mechanics

The shield tunnel is typically simplified as an infinite beam with two free ends in existing analytical models, which are used to calculate the longitudinal deformation of the underlying shield tunnel induced by the excavation of a foundation pit. However, the applicability of those analytical models is limited due to the simplification. The current study is aimed at estimating analytically the longitudinal deformation of the underlying shield tunnel induced by the excavation of a foundation pit adjacent to the station (working shaft). The constraint on the shield tunnel generated by the joint between the station (working shaft) and the tunnel …


Analytical Solution Of The Long-Term Service Performance Of Tunnel Considering Surrounding Rock Rheology And Lining Deterioration Characteristics, Chang Liu, Ding-Li Zhang, Su-Lei Zhang, Qian Fang, Huang-Cheng Fang Jan 2022

Analytical Solution Of The Long-Term Service Performance Of Tunnel Considering Surrounding Rock Rheology And Lining Deterioration Characteristics, Chang Liu, Ding-Li Zhang, Su-Lei Zhang, Qian Fang, Huang-Cheng Fang

Rock and Soil Mechanics

Deterioration of lining is a common phenomenon in tunnel engineering that threatens the safety of operating tunnel. For tunnel lining deterioration in rheological rock mass, an analytical model is established which the rheology effect of surrounding rock and deterioration of lining are considered. The surrounding rock displacement and support pressure of tunnel during its service life are obtained. And then the correctness of analytical model is verified by numerical simulation. Subsequently, the sensitivity analyses of deterioration coefficient of lining, thickness of lining, support time, and rheological properties of surrounding rock are carried out by the proposed analytical model. Finally, the …


Analytical Solution Of Additional Response Of Shield Tunnel Under Asymmetric Jack Thrust, Zu-Xian Wang, Cheng-Hua Shi, Jian-Wen Liu Dec 2021

Analytical Solution Of Additional Response Of Shield Tunnel Under Asymmetric Jack Thrust, Zu-Xian Wang, Cheng-Hua Shi, Jian-Wen Liu

Rock and Soil Mechanics

When shield is driving along a curve alignment or during deviation correction, the asymmetrical thrust will generate an additional bending moment at the head of the tunnel, which will cause construction problems such as longitudinal deformation of the tunnel and dislocation between rings. Based on the theory of elastic foundation beam, the shield tunnel is simplified as a Timoshenko beam in Winkler foundation, an analytical model for evaluating the additional response of the shield tunnel induced the asymmetric thrust is established, and the analytical solutions of longitudinal deformation and internal force of shield tunnel are deduced. Then the correctness and …


Analytical Solution To Consolidation Of Unsaturated Soil By Vertical Drains With Continuous Permeable Boundary, Ai-Fang Qin, Liang-Hua Jiang, Wei-Fang Xu, Guo-Xiong Mei Sep 2021

Analytical Solution To Consolidation Of Unsaturated Soil By Vertical Drains With Continuous Permeable Boundary, Ai-Fang Qin, Liang-Hua Jiang, Wei-Fang Xu, Guo-Xiong Mei

Rock and Soil Mechanics

In this paper, based on the axisymmetric consolidation theory of unsaturated soil and equal-strain assumption, an analytical solution using the homogenization of boundary conditions and eigenfunction method is proposed to three-dimensional consolidation of unsaturated soil enhanced by vertical drains under instantaneous loading, in which the continuous permeable boundary conditions are properly introduced. Then, the proposed solution is verified by the special cases of double drainage boundary conditions. Finally, the solution is analyzed using examples and the results show that the proposed solution can be used to simulate the arbitrary distribution of permeability of the top and bottom boundary by setting …