scholarly journals A New Unified Solution for Circular Opening considering Different Strength Criteria and the Postpeak Elastic Strain Form

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Xuyang Shi ◽  
Wei Zhou ◽  
Liang Chen ◽  
Qingxiang Cai ◽  
Ming Li ◽  
...  
Keyword(s):  
Rock Mass ◽  
Plastic Zone ◽  
Elastic Strain ◽  
Surrounding Rock ◽  
The Self ◽  
External Boundary ◽  
Circular Opening ◽  
Strength Criteria ◽  
Criterion Equation ◽  
Zone Radius

The strength criterion is an extremely important basis for evaluating the stability of surrounding rock and optimizing the support pressure design. In this paper, nine different strength criteria are summarized and simplified based on the reasonable assumption. Then, a new unified criterion equation is established, which includes all strength theories proposed by this paper. Meanwhile, a new unified closed-form solution for circular opening based on the newly proposed unified criterion equation is deduced with the infinite and finite external boundary combining with the nonassociative flow rule under plane strain conditions. In the plastic zone, four different elastic strain assumptions are applied to solving the plastic zone deformation considering the effect of rock mass damage. The solution’s validity is also verified by comparison with the traditional solution. Finally, the influences of strength criteria, dilation coefficient, elastic strain form of plastic zone, and rock mass damage on the mechanical response of surrounding rock are discussed in detail. The research result shows that TR and VM criteria give the largest plastic zone radius, followed by IDP, MC, and MDP criteria, and seem to underestimate the self-strength of rock mass; The CDP criterion gives the smallest plastic zone radius and may overestimate the self-strength of rock mass; UST0.5, GSMP, GMC, and GLD criteria that reasonably consider the effect of internal principal stresses give an intermediate range and can be strongly recommended for evaluating the mechanics and deformation behavior of surrounding rock; as the dilation coefficient gradually increases, the dimensionless surface displacement presents the nonlinear increase characteristics; the deformation of plastic zone and the ground response curve, which are closely related to the strength criteria, are also greatly influenced by the elastic strain assumption in the plastic zone and rock mass damage degree. The assumption that the elastic strain satisfies Hook’s law (Case 3) may be more reasonable compared with the continuous elastic strain (Case 1) and thick-walled cylinders (Case 2) assumptions; in addition, the Young’s modulus power function damage model seems to give more reasonable solution for the deformation of plastic zone and is suggested to be a preferred method for solving plastic displacement. The research results can provide very important theoretical bases for evaluating the tunnel stability and support design reliability of different lithology rock masses in underground engineering.

scholarly journals Analytical Solution of a Circular Opening considering Nonuniform Pressure and Its Engineering Application

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Peng Wu ◽  
Yanlong Chen ◽  
Liang Chen ◽  
Xianbiao Mao ◽  
Wei Zhang
Keyword(s):  
Analytical Solution ◽  
Plastic Zone ◽  
Young’S Modulus ◽  
Lateral Pressure ◽  
Young's Modulus ◽  
Pressure Coefficient ◽  
Surrounding Rock ◽  
Engineering Practice ◽  
Circular Opening ◽  
Lateral Pressure Coefficient

Based on the Mohr–Coulomb criterion, a new analytical solution of a circular opening under nonuniform pressure was presented, which considered rock dilatancy effect and elastic-brittle-plastic failure characteristics. In the plastic zone, the attenuation of Young’s modulus was considered using a radius-dependent model (RDM), and solution of the radius and radial displacement of plastic zone was obtained. The results show that many factors have important impact on the response of the surrounding rock, including lateral pressure coefficient, dilation coefficient, buried depth, and Young’s modulus attenuation. Under nonuniform pressure condition, the distribution of plastic zone and deformation around the opening show obvious nonuniform characteristic: with the increasing of lateral pressure coefficient, the range of plastic zone and deformation decrease gradually at side, while they increase at roof and floor, and the location of the maximum value of support and surrounding rock response curve transfers from side to roof. Based on the analytical results and engineering practice, an optimization method of support design was proposed for the circular opening under nonuniform pressure.

scholarly journals Displacement Solution of Salt Cavern with Shear Dilatation Behavior Based on Hoek-Brown Strength Criterion

2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Huabin Zhang ◽  
Qingqing Zhang ◽  
Laigui Wang
Keyword(s):  
Plastic Zone ◽  
Elastic Strain ◽  
Large Strain ◽  
Structural Characteristics ◽  
Strength Criterion ◽  
Surrounding Rock ◽  
Salt Formation ◽  
Salt Cavern ◽  
The Stability ◽  
Influence Degree

In this study, an analytical solution of stress, strain, and displacement, in the elastic and plastic zone is proposed. The solution is derived on the basis of ideal elastoplastic mechanical model of spherical salt cavern with shear dilatation behavior, by adopting Hoek-Brown (H-B) criterion. The solution obtains not only in small and large strain stage but also in creep stage. The proposed solution is validated, by comparison of the obtained results with numerical results in FLAC3D. The results indicate that the result obtained adopting the H-B criterion is closer to that one obtained adopting the Mohr-Coulomb (M-C). The H-B criterion is more applicable for the salt cavern construction as it considers the structural characteristics of the rock salt formation. The displacement difference obtained by two different methods decreases with the increase of GSI or running pressure, but it increases with the enlarged angle of dilation. The influence of different assumptions of elastic strain of plastic zone on displacements is more significant under large strain conditions. The influence of the angle of dilation on displacements is more obvious when the elastic strain of plastic zone is given to stationary values, and the influence degree increases with the enlarged angle of dilation. Under the same conditions, the creep displacement decreases with the increase of GSI, and both the creep displacement and the effect degree enhance with the enlarged dilation angle. The proposed solutions can be used in the stability analysis of surrounding rock in the construction and operation of salt cavern storage.

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.

scholarly journals Research on the Reasonable Strengthening Time and Stability of Excavation Unloading Surrounding Rock of High-Stress Rock Mass

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Wensong Xu ◽  
Wentao Xu ◽  
Yunhai Cheng
Keyword(s):  
Rock Mass ◽  
Plastic Zone ◽  
Failure Process ◽  
High Stress ◽  
Stable State ◽  
Surrounding Rock ◽  
Triaxial Tests ◽  
Uniaxial Compression Test ◽  
True Triaxial ◽  
True Triaxial Tests

This study is aimed at better understanding the deformation and failure mechanism of surrounding rock during excavation unloading of a high-stress rock mass and determining the reasonable reinforcement time for the surrounding rock. To fulfill this aim, true triaxial tests were carried out on different loading and unloading paths during the unilateral unloading of a high-stress rock mass. The variational condition for minimization of plastic complementary energy is obtained, the optimal reinforcement time is determined, and the range of the plastic zone in the surrounding rock reinforced by anchor mesh-cable-grouting is compared and analyzed. The results are as follows: (1) Based on the Mohr-Coulomb yield criterion and the deformation reinforcement theory of surrounding rock, the stable state with the minimum reinforcement force is obtained. (2) After the true triaxial tests on the unilateral unloading of the third principal stress were carried out under different confining pressures, loading continued to be performed. Compared with rock failure without confining pressure, in the conventional uniaxial compression test, the failure of samples is dominated by composite splitting-shear failure; the unilateral unloading stress-concentration failure is a progressive failure process of splitting into plates followed by cutting into blocks and then the ejection of blocks and pieces. (3) The relationship between the time steps of the surrounding rock stability and the excavation distance is obtained. The supporting time can be divided into four stages: presupport stage, bolt reinforcement stage, anchor cable reinforcement stage, and grouting reinforcement stage. (4) In the range of within 5 m behind the tunneling face, the plastic zone of the surrounding rock with support is reduced by 7 m as compared with that with no support. In the range of over 5 m behind the tunneling face, the plastic zone of the roadway floor with support is reduced by 2.6 m as compared with that without support, and the deformation is reduced by 90%. These results can serve as a reference for controlling the behavior of surrounding rock during excavation unloading of high-stress rock masses.

A Study on Stability of Expressway Tunnel Surrounding Rock Containing Weak Intercalated Rock

2010 ◽  
Vol 168-170 ◽  
pp. 2543-2547
Author(s):  
Da Kun Shi ◽  
Yang Song Zhang
Keyword(s):  
Rock Mass ◽  
Plastic Zone ◽  
Surrounding Rock ◽  
Constitutive Law ◽  
Numerical Tests ◽  
Stability Of Surrounding Rock ◽  
Strain Type ◽  
Deformation Stress ◽  
Plain Strain ◽  
The Stability

Weak intercalated rock plays an important role in the stability of engineering rock mass. It controls the mechanism of deformation and breakage of rocks. Systematic numerical tests have been carried out to study the stability of surrounding rock mass with different distributions of weak intercalated rock has been analyzed by the FEM software ABAQUS. All of the numerical modelings are plain-strain type with elasto-plastic constitutive law and Drucker-Prager failure criterion. Some quantificational results about the influence of weak intercalated rock are summarized, especially the influence on the deformation, stress of surrounding rocks and plastic zone. Because of weak intercalated rock, the stress of surrounding rock appears the character of discontinuity. In addition, the distribution of plastic zone is also affected. When weak intercalated rocks exist in vault, spandrel and bottom, the situation of surrounding rock is comparatively unfavorable. These results have a certain role in guiding significance to the site selection and layout, the majorization of supporting system and the construction of tunnel of the same kind.

Numerical Analysis of Damage for Y-Shape Tunnel

2011 ◽  
Vol 368-373 ◽  
pp. 2517-2520
Author(s):  
Da Ming Lin ◽  
Yan Jun Shang ◽  
Guo He Li ◽  
Yuan Chun Sun
Keyword(s):  
Numerical Simulation ◽  
Rock Mass ◽  
Numerical Analysis ◽  
Plastic Zone ◽  
Comprehensive Analysis ◽  
Surrounding Rock ◽  
Tunnel Construction ◽  
Deformation And Failure ◽  
Single Beam ◽  
Flac 3D

There are many effective researches about tunnel at home and abroad, because the complexity of design and construction for Y-shape tunnel, in public there is no research about it yet, with the background of nanliang-tunnel which merge two single-beam into a two-lane tunnel as Y-shape. This paper obtains the rock mass mechanics parameters on the basis of nonlinear Hoek-Brown criterion first, and has a numerical simulation according the tunnel construction with FLAC-3D. we arrange many monitor sections in this model and discuss the law of deformation and failure in different section, at last have a comprehensive analysis of displacement, stress, plastic zone of different sites which caused by tunnel construction and discover that: with the distance of two single tunnels decreased, the interaction caused by the merging increase together with the compressive stress, tensile stress. The displacements of surrounding rock increase corresponding, the amplitude of variation is up to 44.8%, After the two-lane tunnel is 15m long, the stress and displacements redistribution of surrounding rock become stable.

Stability Analysis of Highway Tunnel through Mined-Out Area during Excavation Process

2013 ◽  
Vol 838-841 ◽  
pp. 1352-1358 ◽  
Author(s):  
Zhi Hao Yang ◽  
Ge Cui ◽  
Ya Peng Fu ◽  
Yong Fang ◽  
Bin Yang
Keyword(s):  
Rock Mass ◽  
Plastic Zone ◽  
Axial Force ◽  
Construction Safety ◽  
Surrounding Rock ◽  
Two Dimensional ◽  
Highway Tunnel ◽  
Excavation Process ◽  
Caving Zone ◽  
Pass Through

Tianpingzhai Tunnel on Dazhou-Wanzhou Expressway passes through the mined-out area, the spatial position of the goaf changes constantly comparing to the tunnel during excavation, and broken rock mass of the caving zone is most likely to collapse, which affects construction safety in return. Two dimensional computation models were built by using finite differential software FLAC to simulate excavation process when the coal-mined area is right above or below the tunnel. In 2D models, goaf strata were regarded as horizontal, and buried depth and coal thickness were limited to 300 meters and 0.5 meter respectively. The displacement around the tunnel, forces of primary lining, axial force of bolts and plastic zone of surrounding rock have been analyzed under these circumstances that the distances between tunnel and goaf are 1m, 6m and 12m. According to the results, when the distance between goaf and tunnel is less than 12 meters,underlying goaf has greater impact on the displacement around the tunnel and average axial force of bolts than overlying goaf, as well as the size of plastic zone of surrounding rock. Its strongly suggested to avoid underlying goaf if the tunnel have to pass through the mined-out area.

scholarly journals Study on the Effect of Isotropic Initial Stress on the Anchoring Performance of Self-Expanding Bolts

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Jie Liu ◽  
Hongya Li ◽  
Yunzhou Li ◽  
Yunan Yang ◽  
Tao Sun ◽  
...  
Keyword(s):  
Rock Mass ◽  
Energy Consumption ◽  
Surrounding Rock ◽  
Interface Stress ◽  
The Self ◽  
Additional Stress ◽  
Confining Stress ◽  
Internal Interface ◽  
Pull Out ◽  
Anchoring System

In order to study the anchoring performance of a new type of self-expanding, high-strength, precompression anchoring technology with a large amount of expansion agent (ω ≥ 5) cement slurry as anchoring solids under confined surrounding rock conditions, a rock mass anchoring device and methods that simulate in situ stress are developed, and real-time monitoring of expansion stress and anchor pull-out tests are carried out. The results show that the internal interface stress has a loss effect over time, and the stress loss value shows a linear increase trend with the dosage, but the loss rate shows a linear decreasing relationship with the dosage. This paper defines the coordinated additional stress and obtains its temporal and spatial evolution law in the rock mass. It is pointed out that there is a lag time difference between the peak of internal interface stress and the peak of coordinated additional stress, explaining its mechanical mechanism from the perspective of stress transfer. The strong restraint of the sealing section of the anchor hole causes the anchor solid to form a “shuttle-shaped” microexpanded head with thin ends and a middle drum under the expansion stress. During the drawing process, the microexpanded head is “stuck” in the anchor hole and moves upward to form the unique “load platform effect” of the anchoring system. And the mechanical mechanism diagram of this effect is obtained. It is pointed out that this effect can greatly improve the ductility of the anchoring system and the ultimate energy consumption value of damage. A prediction model for the ultimate pull-out force of self-expanding bolts is established. It is pointed out that the initial confining stress value has an exponential effect on the ultimate pull-out force. It shows that the surrounding rock with strong confinement constraints can greatly increase the ultimate pull-out resistance of the bolt. The self-expanding strengthening coefficient λ and the surrounding rock stress influence coefficient k are introduced, the bolt interface mechanics formula and energy equation of the self-expanding anchor system are established, and the feasibility of the formula is verified by the calculation example. It is concluded that the ultimate pull-out resistance of the anchorage with ω = 30 is increased by 3.38 times compared with the ordinary anchorage under the initial confining stress condition of 0.7 MPa, the prepeak displacement of the bolt is increased by 2.08 times, and the prepeak energy consumption of the anchoring system is increased by 7.34 times. The cost only increased by 0.023% based on the literature example.

scholarly journals Excavation Sequence and Surrounding Rock Mass Stability of Large-Scale Underground Engineering with 8 Tunnels

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Zhiqiang Zhang ◽  
Mingming He ◽  
Fangfang Chen ◽  
Ning Li
Keyword(s):  
Rock Mass ◽  
Plastic Zone ◽  
Large Scale ◽  
Mutual Influence ◽  
Surface Displacement ◽  
Surrounding Rock ◽  
In Situ Monitoring ◽  
Hydroelectric Power ◽  
Tunnel Face ◽  
Axial Forces

In some large-scale hydroelectric power projects, there are more than 3 tunnels that are too close to each other to eliminate the mutual influence during the excavation period, especially for large-scale tunnel groups. In this paper, aimed at analyzing the Bukun hydropower station consisting of 8 tunnels in Malaysia, the displacement, stress, and plastic zone of the surrounding rock mass are analyzed to study the effect of the excavation sequence on the stability of the surrounding rock mass for large-scale tunnel groups. On the one hand, the in situ monitoring of the surface displacement of the rock mass surrounding the tunnel using extensometers is performed to obtain the deformation characteristics on the excavation limit under the typical excavation sequence. On the other hand, a series of elastic-plastic 3D numerical experiments are carried out to explore the displacement characteristics, stability of the large-scale tunnel groups, and safety of the initial supporting system. The results show that the tendencies of the displacement increase corresponding to the tunnel face movement are similar for the three excavation sequences. The displacement under initial excavation sequence 2 (IES2) is the smallest among the three sequences; the area of the plastic zone under IES2 is the smallest among them; and the stresses in the shotcrete layer and axial forces in the rock bolt under the three excavation sequences are within the safety limitation. Initial excavation sequence 2 is an optimized excavation sequence, in which tunnels #1 and #5 are excavated first; after an advance of 3 times the diameter of the tunnel, tunnels #3 and #7 are excavated; tunnels #2 and #6 are excavated after an advance of 3 times diameters; and tunnels #4 and #8 are excavated after an advance of 3 times diameters.

scholarly journals The Principle of Invariant Stress of the Surrounding Rock of the Hole under the Condition of Equal Pressure in the Deep Rock Mass

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Xiangye Wu ◽  
Jingya Wang ◽  
Jingang Li ◽  
Jianwei Li ◽  
Tao Xu ◽  
...  
Keyword(s):  
Rock Mass ◽  
Plastic Zone ◽  
Surrounding Rock ◽  
Small Scale ◽  
Depth Range ◽  
Central Idea ◽  
Deep Rock Mass ◽  
Study Results ◽  
Deep Rock ◽  
Stress Influence

Based on the hydrostatic pressure theory of initial stress state of rock mass, combined with Saint-Venant’s principle central idea, the principle of invariant stress of surrounding rock mass of the hole under the condition of equal pressure in deep rock mass is put forward. Numerical simulation is used to study the properties of surrounding rock and section shape of different holes, the depth of the plastic zone, the range of stress influence, and the relationship between them. The study results showed the following. (1) In the current mining depth range, it is difficult to reach the limit of 5 times the hole radius under the condition of invariant pressure of deep rock mass, and it has a significant impact on the near field and relatively small impact on the far field, reflecting the localization effect of the stress influence range. (2) The increase of stress influence range mainly moves outward with the increase of plastic zone range, and its growth slope is low and tends to be horizontal, and the increase amount is negligible. (3) When the failure range of the plastic zone of the hole is small, the influence range of the stress does not change itself, which reflects the stress invariability of the small-scale failure of the surrounding rock of the hole. The research results verify the principle of stress invariability of the surrounding rock of the hole under the condition of equal pressure of the deep rock mass, which is consistent with Saint-Venant’s central idea.

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