scholarly journals A New Unified Solution for Circular Tunnel Based on a Four-Stage Constitutive Model considering the Intermediate Principal Stress

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Liang Chen ◽  
Xianbiao Mao ◽  
Yanlong Chen ◽  
Ming Li ◽  
Yang Hao ◽  
...  
Keyword(s):  
Strain Softening ◽  
Damage Zone ◽  
Surface Displacement ◽  
Plastic Shear ◽  
Circular Tunnel ◽  
Plastic Model ◽  
Dilation Angle ◽  
Perfectly Plastic ◽  
Plastic Shear Strain ◽  
Softening Coefficient

Based on the triaxial test, the elasto-perfectly plastic strain-softening damage model (EPSDM) is proposed as a new four-stage constitutive model. Compared with traditional models, such as the elasto-brittle-plastic model (EBM), elasto-strain-softening model (ESM), elasto-perfectly plastic model (EPM), and elasto-peak plastic-brittle plastic model (EPBM), this model incorporates both the plastic bearing capacity and strain-softening characteristics of rock mass. Moreover, a new closed-form solution of the circular tunnel is presented for the stress and displacement distribution, and a plastic shear strain increment is introduced to define the critical condition where the strain-softening zone begins to occur. The new analysis solution obtained in this paper is a series of results rather than one specific solution; hence, it is suitable for a wide range of rock masses and engineering structures. The numerical simulation has been used to verify the correctness of the EPSDM. The parametric studies are also conducted to investigate the effects of supporting resistance, residual cohesion, dilation angle, strain-softening coefficient, plastic shear strain increment, and yield parameter on the result. It is shown that when the supporting resistance is fully released, both the post-peak failure radii and surface displacement could be summarized as EBM > EPBM > ESM > EPSDM > EPM; the dilation angle in the damage zone had the highest influence on the surface displacement, whereas the dilation angle in the perfectly plastic zone had the lowest influence; the strain-softening coefficient had the most significant effect on the damage zone radii; the EPSDM is recommended as the optimum model for support design and stability evaluation of the circular tunnel excavated in the perfectly plastic strain-softening rock mass.

scholarly journals A New Strain-Softening Constitutive Model for Circular Opening considering Plastic Bearing Behavior and Its Engineering Application

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Liang Chen ◽  
Xianbiao Mao ◽  
Ming Li ◽  
Wei Zhou
Keyword(s):  
Strain Softening ◽  
Damage Zone ◽  
Peak Load ◽  
Surface Displacement ◽  
Circular Opening ◽  
Tunnel Wall ◽  
Support Design ◽  
Plastic Model ◽  
Research Results ◽  
Bearing Behavior

Geomaterials generally show strain-softening characteristics after peak-load. Based on the triaxial test for sandy mudstone, a simple elastopeak plastic-strain-softening-damage model (EPSDM) was proposed. Compared with the traditional strain-softening model, EPSDM shows obvious plastic bearing characteristics before strain softening. Then, the closed-formed solution of circular opening was deduced based on the newly proposed model. A plastic shear strain increment was introduced as the extension constraint condition of peak plastic zone. The solution correctness of EPSDM was also verified by comparing with other research results. In addition, the solution based on EPSDM could degenerate for a series of results obtained by elastobrittle plastic model (EBM), elasto-strain-softening model (ESM), and elasto-perfectly plastic model (EPM) under certain conditions. Hence, it could be regarded as a unified solution. Finally, the research results denoted that when the inner pressure was fully released, the maximum postpeak failure radii and surface displacement of surrounding rock indicated the characteristics of EBM>ESM>EPSDM>EPM. Therefore, the plastic bearing behavior could effectively decrease the postpeak failure zone radii and surface displacement. The dilation coefficient noticeably influenced postpeak failure range and surface displacement, particularly the damage zone radii and tunnel wall convergence. The research results can provide very important theoretical bases for evaluating the tunnel stability and support design reliability for underground engineering.

scholarly journals Stability Analysis of Surrounding Rock in Circular Tunnels Based on Critical Support Pressure

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Hao Fan ◽  
Lianguo Wang ◽  
Kai Wang
Keyword(s):  
Principal Stress ◽  
Strain Softening ◽  
Damage Zone ◽  
Intermediate Principal Stress ◽  
Damage Variable ◽  
Support Pressure ◽  
Initial Field ◽  
Tunnel Stability ◽  
Stress Coefficient ◽  
Softening Coefficient

Accurate calculation for the critical support pressure of tunnels plays an important role in tunnel stability evaluation and support design. In this study, a mechanical model for circular tunnels is developed. Considering the intermediate principal stress and strain-softening characteristic of rock mass, the critical support pressure when the plastic zone and damage zone begin to occur is determined based on the unified strength criterion and strain-softening model. Through the example study, the critical support pressure under different intermediate principal stress coefficient is solved. Furthermore, the effect of initial field stress, softening coefficient, and maximum damage variable on the critical support pressure are also discussed. The results show that the critical support pressure and radii of plastic and damage zones all decrease with the increase of the intermediate principal stress coefficient. The larger the initial field stress, the larger the critical support pressure. The softening coefficient and maximum damage variable of rock mass has no influence on the critical support pressure when the plastic zone begins to form, but has a significant effect on the critical support pressure when the damage zone begins to form. As softening coefficient increases and maximum damage variable decreases, the critical support pressure when the damage zone which begins to form increases. Data presented in this contribution provide significant theoretical insights into evaluating tunnel stability and support system reliability.

The Improvement of Deformation Analysis for Circular Tunnel Based on Hoek-Brown Criterion in Strain-Softening Rock Mass

2017 ◽  
Vol 1142 ◽  
pp. 344-348 ◽  
Author(s):  
Jian Xin Han ◽  
Lei Wang ◽  
Bei Jiang ◽  
Chun Mei Zheng
Keyword(s):  
Rock Mass ◽  
Radial Displacement ◽  
Strain Softening ◽  
Yield Criterion ◽  
A Priori ◽  
Deformation Analysis ◽  
Support Pressure ◽  
Circular Tunnel ◽  
Perfectly Plastic ◽  
The Difference

To overcome the defect that the support pressure is required to be measured or supposed in elasto-plastic analysis in strain-softening rock mass, by the connection of the support pressure imposed on surrounding rock mass, without assuming the support pressure is known a priori, an improved model of solving plastic radius and the distribution of radial displacement around the circular tunnel is proposed. Based on Hoek-Brown yield criterion, the results obtained by strain-softening model are compared with those of elastic perfectly brittle and elastic perfectly plastic models. The examples reveal that the difference of plastic radius obtained by the three models is comparatively smaller, but the difference of radial displacement is comparatively larger. The proposed model overcomes some defects of the previous studies in deformation analysis for tunnel.

scholarly journals Elastoplastic Analysis of Circular Opening Based on a New Strain-Softening Constitutive Model and Its Engineering Application in Hydraulic Fracturing

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
T. Yang ◽  
Q. S. Ye
Keyword(s):  
Rock Mass ◽  
Constitutive Model ◽  
Hydraulic Fracturing ◽  
Bearing Capacity ◽  
Fracture Zone ◽  
Strain Softening ◽  
Circular Opening ◽  
Elastic Peak ◽  
Load Bearing ◽  
Plastic Model

Constitutive effect is extremely important for the research of the mechanical behavior of surrounding rock in hydraulic fracturing engineering. In this paper, based on the triaxial test results, a new elastic-peak plastic-softening-fracture constitutive model (EPSFM) is proposed by considering the plastic bearing behavior of the rock mass. Then, the closed-form solution of a circular opening is deduced with the nonassociated flow rule under the cavity expansion state. Meanwhile, the parameters of the load-bearing coefficient and brittles coefficient are introduced to describe the plastic bearing capacity and strain-softening degrees of rock masses. When the above two parameters take different values, the new solution of EPSFM can be transformed into a series of traditional solutions obtained based on the elastic-perfectly plastic model (EPM), elastic-brittle plastic model (EBM), elastic-strain-softening model (ESM), and elastic-peak plastic-brittle plastic model (EPBM). Therefore, it can be applied to a wider range of rock masses. In addition, the correctness of the solution is validated by comparing with the traditional solutions. The effect of constitutive relation and parameters on the mechanical response of rock mass is also discussed in detail. The research results show that the fracture zone radii of circular opening presents the characteristic of EBM > EPBM > ESM > EPSFM; otherwise, it is on the contrast for the critical hydraulic pressure at the softening-fracture zone interface; the postpeak failure radii show a linear decrease with the increase of load-bearing coefficients or a nonlinear increase with the increasing brittleness coefficient. This study indicates that the rock mass with a certain plastic bearing capacity is more difficult to be cracked by hydraulic fracturing; the higher the strain-softening degree of rock mass is, the easier it is to be cracked. From a practical point of view, it provides very important theoretical values for determining the fracture range of the borehole and providing a design value of the minimum pumping pressure in hydraulic fracturing engineering.

Automated Measurement of Near-Surface Plastic Shear Strain

2014 ◽  
Vol 3 (3) ◽  
pp. 1-16 ◽  
Author(s):  
G. Trummer ◽  
K. Six ◽  
C. Marte ◽  
A. Meierhofer ◽  
C. Sommitsch
Keyword(s):  
Shear Strain ◽  
Surface Plastic ◽  
Automated Measurement ◽  
Plastic Shear ◽  
Near Surface ◽  
Plastic Shear Strain

scholarly journals A New Unified Solution for Circular Tunnels Based on Generalized SMP Criterion considering the Strain Softening and Dilatancy

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Qifeng Guo ◽  
Jiliang Pan ◽  
Xinghui Wu ◽  
Xun Xi ◽  
Meifeng Cai
Keyword(s):  
Internal Friction ◽  
Plastic Zone ◽  
Strain Softening ◽  
Friction Angle ◽  
Surrounding Rock ◽  
Internal Friction Angle ◽  
Plastic State ◽  
Circular Tunnel ◽  
Dilatancy Angle ◽  
Elastic Plastic

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.

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

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
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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