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

Changguang, Zhang; Jun-hai, Zhao

doi:10.1007/s11431-010-3224-0

Cited by 23 publications

(10 citation statements)

References 13 publications

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“…Based on the elasticity theory, the solution of a thick-walled cylinder under hydrostatic pressure can be easily obtained. e stresses and displacement for the elastic zone can be expressed as [18,23]…”

Section: Stresses and Displacement Of Elastic Zonementioning

confidence: 99%

“…e EBM applies only to the poor-quality rock mass, while ESM is suitable for average-quality rock mass and EPM for high-quality rock mass [10][11][12][13][14][15]. In addition, EPBM is suitable for the brittle rock masses with a certain plastic bearing capacity [16][17][18]. In fact, many strainsoftening rock masses also show a certain plastic bearing behavior after load peak.…”

Section: Introductionmentioning

confidence: 99%

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

Tai

2018

Advances in Civil Engineering

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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.

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Section: Stresses and Displacement Of Elastic Zonementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Tai

2018

Advances in Civil Engineering

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“…One major drawback of this procedure is that an aluminum pigment used as substrate isn't stable under the conditions required for the precipitation, as it dissolves in both acidic and basic media [22] . Therefore, it must be encapsulated in a protective shell, normally SiO 2 , prior to the desired metal oxide coating [7,23–26] . This additional layer renders the process more difficult and is disadvantageous from a coloristic point of view, as it causes the hiding power to decrease due to the higher pigment thickness [27,28] .…”

Section: Introductionmentioning

confidence: 99%

Environmentally Benign Solution‐Based Procedure for the Fabrication of Metal Oxide Coatings on Metallic Pigments

Bies

Hoffmann

Stöter³

et al. 2020

ChemistryOpen

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Aluminum pigments were coated with Fe2O3 and CuO by solution‐based thermal decomposition of the urea nitrate compounds hexakisureairon(III)nitrate and tetrakisureacopper(II)nitrate. The deposition process was optimized to obtain homogeneously coated aluminum pigments. The growth of the surface coatings was controlled by investigation with scanning electron microscopy, energy dispersive X‐ray spectroscopy and static light scattering as well as infrared, X‐ray diffraction and thermogravimetric analysis. The iron precursor showed an incomplete decomposition in solution, incorporating traces of urea molecules inside the coatings while the copper precursor showed complete dissociation accompanied by in situ formation of amine complexes. The amount of organic residues resulting from ligand fragments in the final oxide coatings could be reduced to 22 % for the iron oxide and 12 % for the copper oxide by further temperature treatment in solution (259 °C). Colorimetric investigations of the obtained pigments revealed an excellent hiding power, outperforming the pigments used in current state‐of‐the‐art formulations.

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“…On the condition that the rock elastoplastic model is adopted to study the plastic zone in the surrounding rock, it is assumed that the strength of the surrounding rock can be fully activated to reduce the support workload when the intermediate principal stress is taken into account. And many researchers [13][14][15][16][17] have conducted lots of works on it. Meanwhile, the shape of the tunnel section, the time of support applied, and the external stress field also have much influence on the displacement and stress in the surrounding rock.…”

Section: Introductionmentioning

confidence: 99%

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

TianMing

Peng

Liu

2018

Mathematical Problems in Engineering

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

Cited by 23 publications

References 13 publications

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

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

Environmentally Benign Solution‐Based Procedure for the Fabrication of Metal Oxide Coatings on Metallic Pigments

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

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