Stresses and Displacements around a Cylindrical Cavity in Soft Rock

Reed, M. B.

doi:10.1093/imamat/36.3.223

Cited by 34 publications

(23 citation statements)

References 5 publications

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“…Radial displacement of tunnel wall is 0.017238 m, radius of plastic zone is 5.5616 m. Fig. 6 shows the comparisons of solutions which proposed by Park and Kim [24], Ogawa and Lo [25] and Reed [26]. Radius of plastic zone in this study is the same as Park, Kim and Ogawa, Lo, which approach to 0.0550 m. But the value given by Reed is slightly small, which is 0.046974 m. All results show that the radial displacement reduces with the increase of distance form tunnel axis, and it will slow while reaching to elastic zone.…”

Section: Examples and Comparison Of Solutionsmentioning

confidence: 98%

Analytical and Reliability Study of the Tunnel with Rockbolts in Rock Masses

Meng¹,

Zhao²,

Zhu³

et al. 2018

Period. Polytech. Civil Eng.

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IntroductionRockbolts have been widely used to reinforce the surrounding rock mass in tunnel engineering. A proper design of rockbolts, which depends on the full understanding of the mechanism and effectiveness of rockbolts, is very important to reinforcement, stabilization and safety construction of rock tunnel [1][2][3]. Meanwhile, there are lots of uncertainties in rock tunnel. Uncertainties are critical to design and safety construction due to the complexity of rock mass [4]. Reliability analysis is a widely developed method to determine the uncertainty in engineering system [5]. The stresses and displacements around tunnel is an important problem considering the uncertainty in tunnel engineering.Various analytical, experimental, and numerical methods have been developed to analyze and understand the mechanism of rockbolts in tunnel based on different assumptions and conditions. Analytical models are able to define the stresses and the deformations and have been widely used due to the computational simplicity [6,7]. Hoek and Brown (1980) had presented analytical solutions of tunnel with rockbolts [8]. Brown et al (1983) proposed an analytical solution based on elastic-brittle-plastic material behavior and Hoek-Brown yield criterion [9]. Li and Stillborg (1999) developed three analytical models for rockbolts based on the mechanical coupling at the various interface of the rockbolts, the grout medium and the rock mass

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Section: Examples and Comparison Of Solutionsmentioning

confidence: 98%

Analytical and Reliability Study of the Tunnel with Rockbolts in Rock Masses

Meng¹,

Zhao²,

Zhu³

et al. 2018

Period. Polytech. Civil Eng.

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“…By assuming the plastic zone as the thicklywalled cylinder, which is subjected to the inner stress (p i −p o ) at r=a and the outer stress (p y −p o ) at r=R [3,5,14], the elastic strains can be written as…”

Section: Unified Solutions For Stresses and Displacementsmentioning

confidence: 99%

Unified solutions for stresses and displacements around circular tunnels using the Unified Strength Theory

Changguang

Jun-hai

2010

Sci. China Technol. Sci.

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The unified solutions are presented for stresses and displacements around a circular tunnel subjected to a hydrostatic stress field. The rock mass is assumed to be elastic-brittle-plastic and governed by the Unified Strength Theory. The displacements are obtained accounting for three different definitions for elastic strains and different Young's modulus in the plastic zone. The unified solutions obtained in this paper are especially versatile in reflecting the intermediate principal stress effect to different extents for different materials. The conventional solutions, based on the Mohr-Coulomb failure criterion and the Generalized Twin Shear Stress yield criterion, are special cases of the present unified solutions. The new unified solutions can compare with those computed by the latest generalized Hoek-Brown failure criterion. The results obtained demonstrate the importance of the intermediate principal stress influence for the stresses and displacements analysis. The effects of different definitions for elastic strains and different Young's modulus in the plastic zone on the displacements are significant. Unified Strength Theory, intermediate principal stress, different definitions for elastic strains, different Young's modulus Citation:Zhang C G, Wang J F, Zhao J H. Unified solutions for stresses and displacements around circular tunnels using the Unified Strength Theory. Sci

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“…Later, more studies were done in this area (e.g., Reed [2]; Ogawa and Lo [3]; Gates [4]; Sharan [5,6]; Park and Kim [7]; Yuan and Chen [8]; Jiang et al [9]; Yu [10]). However, most of those solutions are based on the common elasto-perfectly-plastic and elasto-brittle-plastic models, because those solutions can be easily obtained using simple mathematical methods.…”

Section: Introductionmentioning

confidence: 99%

Analytical Strain-softening Solutions of a spherical cavity

Zhang

Quan

et al. 2018

Lat. Am. j. solids struct.

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This paper deals with a spherical cavity excavated in infinite homogeneous and isotropic strain-softening rock mass subjected to a hydrostatic initial Displacements and stresses distributions are two of the most important information for underground engineering, for that it can provide a theoretical foundation for geotechnical engineering optimism design and stability evaluation. In past few years, many scholars have developed series of (semi-)analytical and numerical solutions for circular openings and spherical cavities. . However, most of those solutions are based on the common elasto-perfectly-plastic and elasto-brittle-plastic models, because those solutions can be easily obtained using simple mathematical methods. However, most of the geotechnical materials display strain-softening behavior in the post-failure region. Therefore, the normally used elasto-perfectly plastic model and elasto-brittleplastic model can't well represent the actual failure process. Brown et al. were the earliest ones to analyze the stresses and displacements of circular openings excavated in the strain-softening rock mass. But, the assumption of constant elastic strain in the plastic region, which should obey the generalized Hooke's law, leads to a poor accuracy of the results. And Wang points out that Brown et al.'s solution is difficult to predict the plastic radius [11]. Carranza-Torres and Fairhurst's solution for H-B rock mass, which is based on the so-called self-similarity of H-B criterion, is theoretically rigorous. But, it seems rather complicated for practical use and is applicable only to the As we see, all of the solutions for strain-softening rock mass are based on semi-analytical and numerical method, no analytical solutions are available. Additionally, most of the indoor and field tests show that material properties of rock mass change during the failure process, not only strength parameters but also elastic parameters, i.e. Yong's modulus and Poisson's ratio. This is the so-called elasto-plastic coupling effect. Generally speaking, the effect of Young's modulus is analyzed in two ways. One is the pressure-dependent Young's modulus model (PDM) [26][27], the progressive failure process may be more significant. However, the two models can hardly be solved with analytical method. Considering the different tensile and compressive Young's modulus, Luo et al. obtained the closed-form solutions of spherical cavities in elastobrittle-plastic rock mass [28]. The difficulty of analytical methods for strain-softening rock mass is the coupling effect between softening index and material properties. In view of this, the Multi-step Brittle-Plastic model (MBPM) is proposed to solve the stress, strain, and displacement in the post-failure region for the spherical cavity. Moreover, the deterioration process of elastic parameters and strength parameters are also considered.

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Stresses and Displacements around a Cylindrical Cavity in Soft Rock

Cited by 34 publications

References 5 publications

Analytical and Reliability Study of the Tunnel with Rockbolts in Rock Masses

Analytical and Reliability Study of the Tunnel with Rockbolts in Rock Masses

Unified solutions for stresses and displacements around circular tunnels using the Unified Strength Theory

Analytical Strain-softening Solutions of a spherical cavity

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