Functional Catastrophe Analysis of Collapse Mechanism for Shallow Tunnels with Considering Settlement

Limit analysis is a practical and meaningful method to predict the stability of geomechanical properties. This work investigates the pore water effect on new collapse mechanisms and possible collapsing block shapes of shallow tunnels with considering the effects of surface settlement. The analysis is performed within the framework of upper bound theorem. Furthermore, the NL nonlinear failure criterion is used to examine the influence of different factors on the collapsing shape and the minimum supporting pressure in shallow tunnels. Analytical solutions derived by functional catastrophe theory for the two different shape curves which describe the distinct characteristics of falling blocks up and down the water level are obtained by virtual work equations under the variational principle. By considering that the mechanical properties of soil are not affected by the presence of underground water, the strength parameters in NL failure criterion can be taken to be the same under and above the water table. According to the numerical results in this work, the influences on the size of collapsing block different parameters have are presented in the tables and the upper bounds on the loads required to resist collapse are derived and illustrated in the form of supporting forces graphs that account for the variation of the embedded depth and other factors.

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Limit Analysis of Collapse Mechanisms for Tunnel Roofs Subjected to Pore Water Pressure: A Numerical Approach

Advances in Civil Engineering ◽

10.1155/2021/3591670 ◽

2021 ◽

Vol 2021 ◽

pp. 1-14

Author(s):

Jing-jing Liu ◽

Tie-lin Chen ◽

Chang-ling Xie ◽

Jian-hua Tian ◽

Yu-xin Wei

Keyword(s):

Pore Water ◽

Limit Analysis ◽

Pore Water Pressure ◽

Water Pressure ◽

Numerical Approach ◽

Collapse Mechanism ◽

Upper Bound Theorem ◽

Collapse Mechanisms ◽

Support Force ◽

Function Expression

The collapse mechanism of a circular unlined tunnel roof subjected to the pore water pressure under plane strain conditions is investigated in this article. First, the model of calculating the function expression of the detaching surface for the collapsing block is formed in the framework of the upper bound theorem of limit analysis and the extremum principle. The analytical solution of the pore water pressure around the tunnel in a two-dimensional steady seepage field is employed in the equations of the model. Then, the numerical approach based on the Runge–Kutta algorithm and traversal search method is proposed to solve the complex equations. The obtained expression of the detaching surface for the collapsing block provides the shape of the collapsing block and a theoretical basis for designing the support force for tunnels. The proposed limit analysis method and numerical approach are verified by comparing with existing theoretical solutions and the numerical simulation result, and they are suitable for deep, shallow tunnels and layered strata. Moreover, the effects of different parameters on the collapse mechanism are investigated, and qualitative results are provided.

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Three-dimensional collapse mechanism and failure probability analysis of deep-buried tunnel based on the upper bound theorem of limit analysis and Hoek-Brown failure criterion

Arabian Journal of Geosciences ◽

10.1007/s12517-021-09392-2 ◽

2022 ◽

Vol 15 (2) ◽

Author(s):

Dexin Lei ◽

Lingli Xie ◽

Li Wu

Keyword(s):

Failure Probability ◽

Upper Bound ◽

Limit Analysis ◽

Failure Criterion ◽

Three Dimensional ◽

Probability Analysis ◽

Collapse Mechanism ◽

Upper Bound Theorem ◽

Bound Theorem

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Hydro-Mechanical Coupled Analysis of the Stability of Surrounding Rock Mass of Underground Water-Sealed Oil Storage

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.405-408.402 ◽

2013 ◽

Vol 405-408 ◽

pp. 402-405 ◽

Cited By ~ 1

Author(s):

Yun Jie Zhang ◽

Tao Xu ◽

Qiang Xu ◽

Lin Bu

Keyword(s):

Rock Mass ◽

Underground Water ◽

Surrounding Rock ◽

Comsol Multiphysics ◽

Coupled Analysis ◽

Coupling Theory ◽

Oil Storage ◽

Stability Of Surrounding Rock ◽

Straight Wall ◽

The Stability

Based on the fluid-solid coupling theory, we study the stability of surrounding rock mass around underground oil storage in Huangdao, Shandong province, analyze the stress of the surrounding rock mass around three chambers and the displacement change of several key monitoring points after excavation and evaluate the stability of surrounding rock mass using COMSOL Multiphysics software. Research results show that the stress at both sides of the straight wall of cavern increases, especially obvious stress concentration forms at the corners of the cavern, and the surrounding rock mass moves towards the cavern after excavation. The stress and displacement of the surrounding rock mass will increase accordingly after setting the water curtains, but the change does not have a substantive impact on the stability of surrounding rock mass.

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Functional catastrophe analysis of collapse mechanisms for deep tunnels based on the Hoek-Brown failure criterion

Journal of Zhejiang University SCIENCE A ◽

10.1631/jzus.a1400014 ◽

2014 ◽

Vol 15 (9) ◽

pp. 723-731 ◽

Cited By ~ 12

Author(s):

Cheng-ping Zhang ◽

Kai-hang Han ◽

Qian Fang ◽

Ding-li Zhang

Keyword(s):

Failure Criterion ◽

Collapse Mechanisms

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Brief communication: The influence of mica-rich rocks on the shear strength of ice-filled discontinuities

The Cryosphere ◽

10.5194/tc-14-1849-2020 ◽

2020 ◽

Vol 14 (6) ◽

pp. 1849-1855

Author(s):

Philipp Mamot ◽

Samuel Weber ◽

Maximilian Lanz ◽

Michael Krautblatter

Keyword(s):

Shear Strength ◽

Failure Criterion ◽

Rock Slopes ◽

Surface Charges ◽

Permafrost Rock ◽

Rock Types ◽

Negative Surface ◽

The Stability ◽

Stress Dependent ◽

Dependent Failure

Abstract. A temperature- and stress-dependent failure criterion for ice-filled rock (limestone) joints was proposed in 2018 as an essential tool to assess and model the stability of degrading permafrost rock slopes. To test the applicability to other rock types, we conducted laboratory tests with mica schist and gneiss, which provide the maximum expected deviation of lithological effects on the shear strength due to strong negative surface charges affecting the rock–ice interface. Retesting 120 samples at temperatures from −10 to −0.5 ∘C and normal stress of 100 to 400 kPa, we show that even for controversial rocks the failure criterion stays unaltered, suggesting that the failure criterion is transferable to mostly all rock types.

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Collapse mechanism of shallow tunnel based on nonlinear Hoek–Brown failure criterion

Tunnelling and Underground Space Technology ◽

10.1016/j.tust.2011.05.008 ◽

2011 ◽

Vol 26 (6) ◽

pp. 686-691 ◽

Cited By ~ 89

Author(s):

X.L. Yang ◽

F. Huang

Keyword(s):

Failure Criterion ◽

Collapse Mechanism ◽

Shallow Tunnel

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Influence of Anisotropy and Nonhomogeneity on Stability Analysis of Fissured Slopes Subjected to Seismic Action

Mathematical Problems in Engineering ◽

10.1155/2020/6582787 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13

Author(s):

Zhidan Liu ◽

Jingwu Zhang ◽

Weiping Chen ◽

Di Wu

Keyword(s):

Upper Bound ◽

Mathematical Optimization ◽

Optimization Procedure ◽

Seismic Action ◽

Anisotropy Coefficient ◽

Upper Bound Theorem ◽

Bound Theorem ◽

Software Codes ◽

The Stability ◽

The Impact

Based on the upper bound theorem of limit analysis, this paper presents a procedure for assessment of the influence of the soil anisotropy and nonhomogeneity on the stability of fissured slopes subjected to seismic action. By means of a mathematical optimization procedure written in Matlab software codes, the stability factors NS and λcφ are derived with respect to the best upper bound solutions. A series of stability charts are obtained in this paper, and then the critical locations of cracks are determined for cracks of known depth. The results demonstrate a significant influence of the soil anisotropy and nonhomogeneity on the stability of the fissured slopes and the location distribution of the cracks. In addition, the procedures for getting the factor of safety are put forward. It is shown that a decrease in the nonhomogeneity coefficient n0 and an increase in the anisotropy coefficient k could lead to the fissured slopes becoming unsafe. Finally, this article also illustrates the variation in the safety factor of fissured slopes under the impact of three factors (Kh, H1/H, and λ).

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Plastic Collapse of a Thin Annular Disk Subject to Thermomechanical Loading

Journal of Applied Mechanics ◽

10.1115/1.4023478 ◽

2013 ◽

Vol 80 (5) ◽

Author(s):

Sergei Alexandrov ◽

Elena Lyamina ◽

Yeau-Ren Jeng

Keyword(s):

Analytic Solution ◽

Hydrostatic Stress ◽

Yield Criterion ◽

The Other ◽

Collapse Mechanism ◽

Plastic Collapse ◽

Thermomechanical Loading ◽

Annular Disk ◽

Collapse Mechanisms ◽

Inner Radius

A semi-analytic solution for plastic collapse of a thin annular disk subject to thermomechanical loading is presented. It is assumed that the yield criterion depends on the hydrostatic stress. A distinguished feature of the boundary value problem considered is that there are two loading parameters. One of these parameters is temperature and the other is pressure over the inner radius of the disk. The general qualitative structure of the solution at plastic collapse is discussed in detail. It is shown that two different plastic collapse mechanisms are possible. One of these mechanisms is characterized by strain localization at the inner radius of the disk. The entire disk becomes plastic according to the other plastic collapse mechanism. In addition, two special regimes of plastic collapse are identified. According to one of these regimes, plastic collapse occurs when the entire disk is elastic, except its inner radius. According to the other regime, the entire disk becomes plastic at the same values of the loading parameters at which plastic yielding starts to develop.

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Seismic Vulnerability of Ancient Churches: I. Damage Assessment and Emergency Planning

Earthquake Spectra ◽

10.1193/1.1737735 ◽

2004 ◽

Vol 20 (2) ◽

pp. 377-394 ◽

Cited By ~ 85

Author(s):

Sergio Lagomarsino ◽

Stefano Podestà

Keyword(s):

Damage Assessment ◽

Seismic Behavior ◽

Seismic Vulnerability ◽

Collapse Mechanism ◽

Damage Level ◽

Bell Tower ◽

Collapse Mechanisms ◽

Damage Grades ◽

Definition Of ◽

The Church

This paper describes a new methodology used to assess seismic damage in the churches of Umbria and the Marches, which is based on 18 indicators, each representative of a possible collapse mechanism for a macroelement. The subdivision of the church into macroelements consists of the identification of architectonic elements in which the seismic behavior is almost independent from the rest of the structure (façade, apse, dome, bell tower, etc.). For each macroelement, by considering its typology and connection to the rest of the church, it is possible to identify the damage modes and the collapse mechanisms. During inspection operations, the surveyors must indicate: (a) the actual macroelements; (b) the damage level; and (c) the vulnerability of the church to that mechanism, related to some specific details of construction. From these data a damage score is defined, which is a number from 0 to 1, obtained as a normalized mean of the damage grades in each mechanism. The analysis of the collected data (more than 1,000 churches in Umbria) allows the definition of the correlation between macroseismic intensity and damage.

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