The shape characteristics of circular tunnel surrounding rock plastic zone in the complex stress field

According to the strain-softening characteristics of rock mass, an ideal elastic strain-softening model is developed, and the surrounding rock of tunnels is subdivided into the plastic broken zone, plastic strain-softening zone, and elastic zone. Based on the generalized spatially mobilized plane criterion, an elastic-plastic analytical solution of a circular tunnel is derived. The effects of intermediate principal stress, strain softening, and dilatancy are considered in the unified solution. The stress, displacement, and plastic zone radius of surrounding rock based on the SMP criterion are compared with those based on the Mohr–Coulomb criterion. Furthermore, the effects of parameters such as the softening modulus, dilatancy angle, and internal friction angle on the deformation and stress of tunnels are discussed. It has been found that the larger the dilatancy angle is, the larger the plastic zone displacement and the radius of the broken zone are. The larger the internal friction angle, the smaller the sizes of the plastic zone, the strain-softening zone, and the broken zone are. The deformation of surrounding rock in the broken zone is more sensitive to the internal friction angle than that in the strain-softening zone. The unified solution based on the SMP criterion provides a well understanding for the elastic-plastic state of tunnels, which can be the guidance for tunnel excavations and support designs.

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An Improved Stress and Strain Increment Approaches for Circular Tunnel in Strain-Softening Surrounding Rock Considering Seepage Force

Advances in Materials Science and Engineering ◽

10.1155/2019/2075240 ◽

2019 ◽

Vol 2019 ◽

pp. 1-17 ◽

Cited By ~ 1

Author(s):

Ling Wang ◽

Jin-feng Zou ◽

Yu-ming Sheng

Keyword(s):

Rock Mass ◽

Plastic Zone ◽

Radial Displacement ◽

Axisymmetric Problem ◽

Strain Softening ◽

Strain Increment ◽

Surrounding Rock ◽

Stress And Strain ◽

Seepage Force ◽

Circular Tunnel

Considering the effect of seepage force, a dimensionless approach was introduced to improve the stress and strain increment approach on the stresses and radial displacement around a circular tunnel excavated in a strain-softening generalized Hoek–Brown or Mohr–Coulomb rock mass. The circular tunnel can be simplified as axisymmetric problem, and the plastic zone was divided into a finite number of concentric rings which satisfy the equilibrium and compatibility equations. Increments of stresses and strains for each ring were obtained by solving the equilibrium and compatibility equations. Then, the stresses and displacements in softening zone can be calculated. The correctness and reliability of the proposed approach were performed by the existing solutions.

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Comparison of Shape Characteristics of Plastic Zone Around Circular Tunnel Under Different Strength Criteria

Journal of Mechanics ◽

10.1017/jmech.2020.45 ◽

2020 ◽

Vol 36 (6) ◽

pp. 849-856

Author(s):

H. Y. Shi ◽

Z. K. Ma ◽

Q. J. Zhu ◽

J. J. Shi ◽

Z. Q. Zhao

Keyword(s):

Plastic Zone ◽

Lateral Pressure ◽

Pressure Coefficient ◽

Strength Criterion ◽

Stress Change ◽

Circular Tunnel ◽

Strength Criteria ◽

Lateral Pressure Coefficient ◽

Low Sensitivity ◽

Shape Characteristics

ABSTRACTThe butterfly plastic zone theory based on Mohr Coulomb criterion has been widely used in coal mine production. In order to verify the universality of the theory, it is necessary to compare the distribution of plastic zone under different strength criteria. Based on the elastic-plastic mechanics, the principal stress distribution function around the circular tunnel is deduced in the paper, and the boundary and radius of the plastic zone under different strength criteria are calculated. The results show that the change laws of the plastic zone around the circular tunnel under different strength criteria has the following commonness: firstly, with the increase of the lateral pressure coefficient, the shape of the plastic zone presents the change laws of “circle ellipse butterfly”; Secondly, with the increase of the lateral pressure coefficient, the radius of the plastic zone is exponential distribution, while the characteristic value is different when the radius of the plastic zone is infinite. At same time, it shows that the butterfly plastic zone has a low sensitivity dependence on the strength criterion, no matter which strength criterion is adopted, and the butterfly plastic zone will inevitably appear in the surrounding rock mass of circular tunnel in the high deviator stress environment; The plastic zone with butterfly shape is highly sensitive to the stress change, and the small stress change may promote the expansion of the plastic zone. This result is significant for us to understand and prevent rock engineering disasters and accidents.

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Analysis of Influence of Stress Lode Angle on Stability of Roadway Surrounding Rock

Shock and Vibration ◽

10.1155/2021/6617609 ◽

2021 ◽

Vol 2021 ◽

pp. 1-17

Author(s):

Yihong Liu ◽

Hongbao Zhao ◽

Lei Wang ◽

Tao Wang ◽

Dongliang Ji ◽

...

Keyword(s):

Stress Field ◽

Plastic Zone ◽

Principal Stress ◽

Stress Gradient ◽

Surrounding Rock ◽

Stress Fields ◽

Stress Difference ◽

Distribution Law ◽

Lode Angle ◽

Formula Type

Based on the variation range of the stress lode angle, the in situ rock stress is divided into σ v -type stress field, σ H -type stress field, and σ h -type stress field. Through theoretical analysis, the principal stress difference distribution law and plastic zone distribution pattern around the roadway in different types of stress fields are obtained. Theoretical and numerical simulation calculation results show that under different stress lode angle conditions, the principal stress difference distribution of the surrounding rock of the roadway is greatly different, which has a direct effect on the shape and range of the plastic zone of the surrounding rock of the roadway. In the σ v -type stress field and the σ H -type stress field, the shape of the plastic zone of the roadway surrounding rock is mainly oval and “butterfly,” while in the σ h -type stress field, the shape of the plastic zone of the roadway surrounding rock is mainly oval. The laboratory test proves that the stress gradient has an important effect on the damage degree of the surrounding rock of the roadway. The larger the stress gradient, the higher the strength of the rock mass and the more severe the damage. The change of the stress lode angle will affect the distribution law of the stress gradient of the surrounding rock of the roadway, thus affecting the degree of fragmentation of the surrounding rock. In type σ v and type σ H stress fields, the surrounding rock of the shoulder can be regarded as a key part of the roadway. In the σ h -type stress field, the plastic zones of the surrounding rocks of the roadway are more evenly distributed, and the damage range is less affected by θ. The influence law of the stress lode angle on the stability of the roadway has been well verified by field observation, and effective support measures have been proposed.

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Mechanical Analysis of the Circular Tunnel considering the Interaction between the Ground Response Curve and Support Response Curve

Mathematical Problems in Engineering ◽

10.1155/2018/7892010 ◽

2018 ◽

Vol 2018 ◽

pp. 1-8

Author(s):

Tianming Su ◽

Hanyu Peng ◽

Hongyan Liu

Keyword(s):

Plastic Zone ◽

Radial Displacement ◽

Response Curve ◽

Mechanical Analysis ◽

Surrounding Rock ◽

Elastic Displacement ◽

Circular Tunnel ◽

Ground Response ◽

Support Structure ◽

Zone Radius

The viewpoint that the ground initial elastic displacement and the interaction between the ground response curve (GRC) and support response curve (SRC) in the surrounding rock should be considered at the same time in the mechanical analysis of the circular tunnel is proposed, and its solution method is also established. Meanwhile, in order to consider the effect of the intermediate principle stress, Drucker-Prager criterion is introduced to describe the yield property of the surrounding rock. The calculation example indicates that the final radial displacement of the tunnel circumference will increase when the ground initial elastic displacement in the surrounding rock is considered before the support structure is applied, which indicates that it is necessary to consider the ground initial elastic displacement in the surrounding rock before the support structure is applied. With increasing the support resistance force and the initial field stress, the plastic zone radius in the surrounding rock and the radial displacement of the tunnel circumference will decrease and increase, respectively, while with increasing the rock internal friction angle and cohesion, the plastic zone radius in the surrounding rock and the radial displacement of the tunnel circumference both decrease. Meanwhile, with the stress Lode parameter increasing from −1 to 1, the plastic zone radius in the surrounding rock and the radial displacement of the tunnel circumference both greatly decrease and then slightly increase. It indicates that the intermediate principle stress has some effect on the calculation results.

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Surrounding Rock Failure Characteristics and Water Inrush Mechanism of Roadway above the Aquifer in Nonuniform Stress Field

Geofluids ◽

10.1155/2021/6674616 ◽

2021 ◽

Vol 2021 ◽

pp. 1-10

Author(s):

Xiaofei Guo ◽

Yongen Li ◽

Jun Li ◽

Hongyu Liu ◽

Xianjie Ma ◽

...

Keyword(s):

Stress Field ◽

Plastic Zone ◽

Water Inrush ◽

Rock Failure ◽

Surrounding Rock ◽

Force Model ◽

Confined Water ◽

Nonuniform Stress ◽

Maximum Radius ◽

Nonuniform Stress Field

The expansion of the roadway surrounding rock failure zone may connect the floor aquifer and cause the roadway water inrush. In order to reveal the mechanism of the roadway water inrush above confined water, we established the force model of the roadway surrounding rock above confined water in nonuniform stress field and studied the shape characteristics and expansion law of the roadway surrounding rock plastic zone. The results show that the roadway surrounding rock will form three kinds of plastic zone under different lateral pressure coefficients: circular, elliptical, and butterfly; when the shape of plastic zone is circular or elliptic, the maximum radius increases linearly with the increase of regional stress; when the shape is butterfly, the maximum radius increases exponentially with the increase of stress. Under the condition of a larger bidirectional stress ratio, the surrounding rock of the roadway will show butterfly-shaped failure, and small stress change will cause malignant expansion of the plastic zone; when the plastic zone is connected with the underlying aquifer, confined water of floor will enter the rock mass from the water diversion point and eventually flood into the roadway, causing floor water inrush.

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The Nonlinear Analysis of Sensitivity of the Plastic Zone of Surrounding Rock in Underground Caverns

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.926-930.687 ◽

2014 ◽

Vol 926-930 ◽

pp. 687-692 ◽

Cited By ~ 1

Author(s):

Zhi Fang Tian ◽

Zhi Min Su ◽

Nian Hong Jiang ◽

Xue Lu ◽

Jian Bing Zhu

Keyword(s):

Analytical Solution ◽

Plastic Zone ◽

Friction Angle ◽

Calculation Model ◽

Surrounding Rock ◽

Water Tunnel ◽

Circular Tunnel ◽

Finite Element Software ◽

Underground Caverns ◽

The Relationship

As the depth and the length of the various underground cavern is increasing, the stability analysis of surrounding rock is very important. This paper first gives the analytical solution equation of the circular tunnel. About the city-gate water tunnel with no analytical solution, it can be solved by numerical method, which is based on the large finite element software ANSYS. The form of a calculation model for conveyance city-gate water tunnel was established. With the D - P criterion, it is nonlinear calculated for the computation of water conveyance tunnel. Then it is obtained that the stress characteristic and development of plastic zone characteristics of the surrounding rock of city-gate tunnel. It also gives the relationship between the development of plastic zone, plastic strain and coefficient of horizontal pressure, the internal friction angle. The last, it is analyzed the relationship between the different parameters and the plastic zone development of different parts of tunnel cavern. This result can provide technical reference for design and the tunnel construction.

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The influence of rockmass properties at the plastic zone around a circular tunnel

Bulletin of the Geological Society of Greece ◽

10.12681/bgsg.11032 ◽

2013 ◽

Vol 47 (4) ◽

pp. 1674

Author(s):

A. Antoniou ◽

I. Spyropoulos

Keyword(s):

Rock Mass ◽

Plastic Zone ◽

Hydrostatic Stress ◽

Surrounding Rock ◽

Weak Rock ◽

Geometrical Parameters ◽

Rock Mass Properties ◽

Circular Tunnel ◽

Mass Properties ◽

Weak Rock Mass

The influence of rockmass properties at the plastic zone around a circular tunnel. Tunneling in weak rock has to be carefully designed since the overestimation of weak rock mass properties or the underestimated design and behaviour of the support system can lead to increased cost or even to failure. Based on the generalized Hoek-Brown failure criterion this paper presents relation between geometrical parameters (tunnel's radius, depth, etc) and rock's mass parameters (GSI, mi, etc) with the extension of plastic zone around a circular tunnel, as well as the wall displacement of an unsupported circular tunnel. All the analyses were executed considering hydrostatic stress field and isotropic behaviour of the surrounding rock mass

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