Improved analytical solutions for the response of underground excavations in rock masses satisfying the generalized Hoek–Brown failure criterion

Rojat, Fabrice; Labiouse, V.; Mestat, Philippe

doi:10.1016/j.ijrmms.2015.08.002

Cited by 16 publications

(13 citation statements)

References 17 publications

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“…The only assumption made was that the out‐of‐plane stress remains the intermediate principal stress throughout unloading. Rojat et al extended these solutions by considering the corner flow in the plastic zone, while also presenting a closed‐form solution for the case of associated plasticity. As will be shown in the following, however, the error introduced by neglecting corner flow is very small.…”

Section: Special Case: Hoek–brown Criterionmentioning

confidence: 99%

“…where σ ci denotes the uniaxial compressive strength of the intact rock, and m , s and n are dimensionless constants. Following Londe and Carranza‐Torres , Rojat et al introduced the following stress normalization:

\overset{σ}{true} = \frac{σ}{m^{\frac{n}{1 - n}} σ_{ci}} + \frac{s}{m^{\frac{1}{1 - n}}},

…”

Section: Special Case: Hoek–brown Criterionmentioning

confidence: 99%

“…The corresponding critical radial stresses σ ρ 1 and σ ρ 2 satisfy the following relations (after Eqs. and , for example ):

{\overset{true¯}{σ}}_{ρ 1}^{n} + 2 ((),, {\overset{true¯}{σ}}_{ρ 1} - {\overset{true¯}{σ}}_{0}) = 0,

((),, 1 - ν) {\overset{true¯}{σ}}_{ρ 2}^{n} + ((),, 1 - 2 ν) ((),, {\overset{true¯}{σ}}_{ρ 2} - {\overset{true¯}{σ}}_{0}) = 0,

…”

Section: Special Case: Hoek–brown Criterionmentioning

confidence: 99%

“…which in the special case of n = 0.5 give (e.g. )

{\overset{true¯}{σ}}_{ρ 1} = {(\frac{\sqrt{1 + 16 {\overset{true¯}{σ}}_{0}} - 1}{4})}^{2},

{\overset{true¯}{σ}}_{ρ 2} = {[\frac{\sqrt{{(1 - ν)}^{2} + 4 {(1 - 2 ν)}^{2} {\overset{true¯}{σ}}_{0}} - 1 + ν}{2 ((),, 1 - 2 ν)}]}^{2},

…”

Section: Special Case: Hoek–brown Criterionmentioning

confidence: 99%

“…All of the existing analytical solutions for the ground response curve (GRC; ) in grounds with non‐linear failure envelopes are based on small strain theory (see ), that is, they assume that deformations are so small that the tunnel geometry remains practically unchanged during unloading. However, this is not true when large convergences take place, commonly in tunnels through weak rocks under a high overburden .…”

Section: Introductionmentioning

confidence: 99%

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A finite strain solution for the elastoplastic ground response curve in tunnelling: rocks with non‐linear failure envelopes

Vrakas

2016

Num Anal Meth Geomechanics

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Summary This paper generalizes the finite strain Coulomb solution of Vrakas and Anagnostou (Int J Numer Anal Meth Geomech 2014; 38(11): 1131–1148) for the classic tunnel mechanics problem of the ground response curve to elastoplastic grounds satisfying a non‐linear Mohr's failure criterion. A linear (Coulomb‐type) plastic potential function is used, leading to a non‐associated flow law, and edge plastic flow is considered in the plastic zone. The solution for a general non‐linear Mohr's failure criterion is semi‐analytical in that it requires the evaluation of definite integrals. In the special case of the Hoek–Brown criterion, however, these integrals are calculated analytically, resulting in a rigorous closed‐form series solution. The applicability of the derived solution is illustrated through the example of the Yacambú‐Quibor tunnel, where very large deformations were observed when crossing of weak graphitic phyllites. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Special Case: Hoek–brown Criterionmentioning

confidence: 99%

\overset{σ}{true} = \frac{σ}{m^{\frac{n}{1 - n}} σ_{ci}} + \frac{s}{m^{\frac{1}{1 - n}}},

…”

Section: Special Case: Hoek–brown Criterionmentioning

confidence: 99%

“…The corresponding critical radial stresses σ ρ 1 and σ ρ 2 satisfy the following relations (after Eqs. and , for example ):

{\overset{true¯}{σ}}_{ρ 1}^{n} + 2 ((),, {\overset{true¯}{σ}}_{ρ 1} - {\overset{true¯}{σ}}_{0}) = 0,

((),, 1 - ν) {\overset{true¯}{σ}}_{ρ 2}^{n} + ((),, 1 - 2 ν) ((),, {\overset{true¯}{σ}}_{ρ 2} - {\overset{true¯}{σ}}_{0}) = 0,

…”

Section: Special Case: Hoek–brown Criterionmentioning

confidence: 99%

“…which in the special case of n = 0.5 give (e.g. )

{\overset{true¯}{σ}}_{ρ 1} = {(\frac{\sqrt{1 + 16 {\overset{true¯}{σ}}_{0}} - 1}{4})}^{2},

{\overset{true¯}{σ}}_{ρ 2} = {[\frac{\sqrt{{(1 - ν)}^{2} + 4 {(1 - 2 ν)}^{2} {\overset{true¯}{σ}}_{0}} - 1 + ν}{2 ((),, 1 - 2 ν)}]}^{2},

…”

Section: Special Case: Hoek–brown Criterionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A finite strain solution for the elastoplastic ground response curve in tunnelling: rocks with non‐linear failure envelopes

Vrakas

2016

Num Anal Meth Geomechanics

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Probabilistic analysis of three‐dimensional tunnel face stability in soft rock masses using Hoek–Brown failure criterion

Zhang

et al. 2020

Num Anal Meth Geomechanics

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SummaryThis paper investigates tunnel face stability in soft rock masses via coupled limit and reliability analyses. Specifically, a 3D face collapse mechanism was first constructed. Then the Hoek–Brown failure criterion was introduced into the limit analysis via the tangential technique. Taking the variability of rock mass parameters and loads into consideration, a reliability model was established. The collapse pressure and failure range of tunnel faces were determined. In addition, the required factor of safety (FS) and supporting pressure under three safety levels were obtained, and the corresponding safety level graphs for support design were presented. Comparison of the obtained results with previous work demonstrates the rationality of the 3D collapse mechanism and the validity of the results. A decrease in the geological strength index, Hoek–Brown parameter mi, and uniaxial compressive strength or an increase in the disturbance factor results in a nonlinear increase of the collapse pressure and an enlargement of the failure zone. Such changes also lead to a nonlinear increase of the required support pressure under a certain safety level. By contrast, the FS does not exhibit any obvious change when these parameters vary. Therefore, when a rock mass is of poor quality or heavily disturbed, the advance support should be enlarged from upper front to right above the tunnel face. Moreover, as the safety level increases, both the required FS and supporting pressure of the tunnel face increase nonlinearly at a higher rate.

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Empirical and Numerical Evaluation of a Cut Slope Near Rishikesh, India

Pandey

Kainthola

Singh

2022

Lecture Notes in Civil Engineering

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Improved analytical solutions for the response of underground excavations in rock masses satisfying the generalized Hoek–Brown failure criterion

Cited by 16 publications

References 17 publications

A finite strain solution for the elastoplastic ground response curve in tunnelling: rocks with non‐linear failure envelopes

A finite strain solution for the elastoplastic ground response curve in tunnelling: rocks with non‐linear failure envelopes

Probabilistic analysis of three‐dimensional tunnel face stability in soft rock masses using Hoek–Brown failure criterion

Empirical and Numerical Evaluation of a Cut Slope Near Rishikesh, India

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