Displacements under linearly distributed pressures by extended Mindlin’s equations

Sun, Huasheng; Gan, Lei; Ng, Charles Wang Wai; Zheng, Qiang

doi:10.1016/j.compgeo.2013.01.009

Cited by 7 publications

(7 citation statements)

References 9 publications

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“…The complex geotechnical formation can be treated as an elastic half space [ 24 – 27 ];…”

Section: Methodsmentioning

confidence: 99%

“…Analytical elasticity solutions provide an efficient means of performing a first approximate analysis in foundation engineering. Engineering practice has proven that a homogeneous elastic semi-infinite medium can be used to model rock and soil to meet the general engineering requirements [ 25 – 27 ]. In this paper, the Mindlin solution is used to study the deformation in shield tunneling [ 28 , 29 ].…”

Section: Methodsmentioning

confidence: 99%

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Numerical prediction of the optimal shield tunneling strategy for tunnel construction in karst regions

Liu

Ming

et al. 2021

PLoS ONE

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Shield tunneling in karst areas poses significant challenges, as vibration caused by the shield machine can disturb the stability of the karst caves, ultimately resulting in the collapse of a tunnel. In the present study, a numerical model involving an iteration process was developed based on the Mindlin solution scheme to identify the optimal shield tunneling speed for minimizing the disturbance to karst cave stability. The developed model was then implemented to investigate an underground tunnel constructed in a karst region with different shield tunneling strategies. By using the variation in the energy density of a karst cave as a performance index, the model predicts that when approaching the affected zone of a karst carve (e.g., approximately 5 m from the carve), the shield tunneling machine should be controlled within a certain speed (i.e., < 30 mm/min). Once the shield tunneling machine moves into the affected zone of the cave, the speed of the machine needs to be decelerated to 11 mm/min, and the speed of 30 mm/min can be restored when the shield machine moves out of the affected zone. This finding demonstrates that the developed model could potentially be used to identify the optimal shield tunneling speed to minimize the disturbance to karst cave stability and ensure the safety of tunnel construction in karst regions.

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“…The complex geotechnical formation can be treated as an elastic half space [ 24 – 27 ];…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Numerical prediction of the optimal shield tunneling strategy for tunnel construction in karst regions

Liu

Ming

et al. 2021

PLoS ONE

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show abstract

“…For the purpose of presenting the derived stress solutions in a compact form, the following notations are assumed the same as those used for deriving the displacements under linearly distributed loading over a rectangular area by Sun et al (2013).…”

Section: Coordinate System and Notationsmentioning

confidence: 99%

“…Many solutions have been proposed for stress in the fields of soil and rock mechanics (Poulos and Davis 1974). Among them, the solutions for loading over a rectangular area in a homogeneous, isotropic, elastic half-space are the most frequently applied ones in foundation engineering analysis (Skopek 1961;Giroud 1970;Griffiths 1984; Sharma and Venkatappa Rao 1984; Vitone and Valsangkar 1986;Li 1991; Rossa and Auvinet 1992; De Jaeger 1994;Align 2000Align , 2001Sun et al 2013). These solutions are commonly expressed in the form of graphs and tables.…”

Section: Introductionmentioning

confidence: 99%

Vertical stress under vertical pressure by extended Mindlin's equation

Lei

Sun

et al. 2016

JGS Special Publication

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Analytical elasticity solutions provide an efficient means of performing a first approximate analysis in foundation engineering. One of the well-known basic solutions is Mindlin's solution to the stress and displacement induced by a point load at an embedment depth in a half-space. This solution is more superior but less widely used than Boussinesq's solution for a point load at only the boundary of half-space. To promote the applications of Mindlin's solution, its vertical stress equation is integrated to obtain an explicit formula for calculating vertical stresses at any arbitrary point. The stresses are induced by uniformly and triangularly distributed vertical pressure, which is exerted over a rectangular area in the interior of a homogeneous, isotropic, elastic half-space. It shows that the vertical stress decreases as the embedment depth of loaded area increases.

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“…In terms of mechanical effect factors, Mindlin's solution is one of the well-known solutions to calculate the stress and displacement caused by a point load at an embedment depth in an elastic half-space [29]. Based on Mindlin's solution, many modified analytical solutions are proposed [30][31][32][33]. For instance, Verruijt et al derived a theoretical solution for the deformations of an elastic half-plane with a circular cavity, which is often used in tunnel excavation.…”

Section: Introductionmentioning

confidence: 99%

Quantitative Analysis of Soil Displacement Induced by Ground Loss and Shield Machine Mechanical Effect in Metro Tunnel Construction

et al. 2019

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In order to relieve the increasing ground traffic pressure in the process of urbanization in China, it is inevitable to build more metro lines. However, the stratum movement caused by tunneling affects the safety of adjacent underground structures and aboveground buildings. Therefore, how to evaluate and control the stratum movement is a prominent problem. In this paper, based on the engineering project of an interval tunnel between Shizishan Station and Chuanshi Station in Chengdu Metro Line 7, China, the action mechanism of stratum movement induced by shield tunneling is analyzed, and the effect factors are divided into two categories: ground loss factors and mechanical factors. Combining the advantages of Loganathan method and mirror source-sink method, a new solution of three-dimensional displacement induced by ground loss is proposed. Based on the elastic half-space Mindlin model, the displacement at any point induced by four mechanical effect factors is deduced. Finally, the total displacement is verified by field monitoring data and quantitative analyzed in various parts.

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Displacements under linearly distributed pressures by extended Mindlin’s equations

Cited by 7 publications

References 9 publications

Numerical prediction of the optimal shield tunneling strategy for tunnel construction in karst regions

Numerical prediction of the optimal shield tunneling strategy for tunnel construction in karst regions

Vertical stress under vertical pressure by extended Mindlin's equation

Quantitative Analysis of Soil Displacement Induced by Ground Loss and Shield Machine Mechanical Effect in Metro Tunnel Construction

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