Stability analysis of rock slopes subjected to seepage forces using the modified Hoek–Brown criterion

Saada, Zied; Maghous, Samir; Garnier, Denis

doi:10.1016/j.ijrmms.2012.06.010

Cited by 95 publications

(26 citation statements)

References 35 publications

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“…The fundamental kinematic inequality in limit analysis implies that the stability of an unsaturated soil slope with given height can be characterized by a safety factor as

F_{s} = \frac{D^{BCDF ‐ 3 normalD} + b \times D^{BCDF ‐ 2 normalD}}{W_{γ^{'}}^{BCDF ‐ 3 normalD} + W_{w}^{3 normalD} + b \times ((), W_{γ^{'}}^{BCDF ‐ 2 normalD} + W_{w}^{2 normalD})} .

…”

Section: Upper Bound Theorem Of Limit Analysis In Slope Stability Anamentioning

confidence: 99%

3D stability of unsaturated soil slopes with tension cracks under steady infiltrations

Wang

et al. 2019

Num Anal Meth Geomechanics

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Summary Most classical approaches for evaluating the stability of soil slopes with cracks are performed under two‐dimensional (2D) condition. Three‐dimensional (3D) effect and suction‐induced effect of unsaturated soils are generally neglected in assessing the slope stability. This paper develops a 3D limit analysis method to evaluate the stability of an unsaturated soil slope with tension cracks under steady infiltrations. The boundary‐value problem is formulated based on the 3D rotational failure mechanism by taking the effects of suction, effective unit weight, and tension crack into account. A simplified method is proposed to calculate the work rate of unsaturated soil weight. A layer‐wise summation method is developed based on the divergence theorem to calculate the internal energy dissipation rate. Detailed discussions are conducted to investigate the effects of suction and Poisson's ratio on the stability of unsaturated soil slopes. Examples are given to illustrate the 3D effect, the suction‐induced effect as well as the effects of infiltration and water in cracks on the slope stability.

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“…The fundamental kinematic inequality in limit analysis implies that the stability of an unsaturated soil slope with given height can be characterized by a safety factor as

F_{s} = \frac{D^{BCDF ‐ 3 normalD} + b \times D^{BCDF ‐ 2 normalD}}{W_{γ^{'}}^{BCDF ‐ 3 normalD} + W_{w}^{3 normalD} + b \times ((), W_{γ^{'}}^{BCDF ‐ 2 normalD} + W_{w}^{2 normalD})} .

…”

Section: Upper Bound Theorem Of Limit Analysis In Slope Stability Anamentioning

confidence: 99%

3D stability of unsaturated soil slopes with tension cracks under steady infiltrations

Wang

et al. 2019

Num Anal Meth Geomechanics

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“…In each quadrilateral element, seepage forces are input as applied external forces at the nodal points in the direction opposite to the hydraulic gradient (Lee et al, ; Lee et al, ; Saada et al, ; Shin et al, ). It follows mathematically (Goodman, ) that the seepage forces at each node are

f_{s} = - γ_{w} \int_{Ω} {[boldN]}^{T} ({}, \begin{array}{c} \frac{\partial H}{\partial x} \\ \frac{\partial H}{\partial z} \end{array}) dΩ = - γ_{w} \int_{Ω} {[boldN]}^{T} ({}, \begin{array}{c} \frac{\partial h}{\partial x} \\ 1 + \frac{\partial h}{\partial z} \end{array}) dΩ

where γ w is the unit weight of the water.…”

Section: Mechanical and Hydrological Modelsmentioning

confidence: 99%

Fusion of Hydraulic Tomography and Displacement Back Analysis for Underground Cavern Stability Investigation

Gao

Yeh

et al. 2018

Water Resources Research

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This paper first elucidates the importance of hydraulic heterogeneity of a rock mass on the design of an underground water‐sealed storage cavern. It then introduces an information fusion approach that integrates hydraulic tomography, displacement back analysis, and a stochastic successive linear estimator to map spatially varying hydraulic conductivity (Ks), Young's modulus (E′), cohesion (c′), and internal friction angle (ϕ′). This algorithm yields statistically unbiased estimate of the Ks, E′, c′, and ϕ′ fields and their uncertainty due to insufficient samples of their heterogeneity. Afterward, this uncertainty is translated into the probability of failure distribution around the cavern for the risk assessment. Results show that heterogeneity of Ks plays an important role in the deformation and failure of the cavern. They also show that the proposed approach can reveal more detailed parameter distributions than kriging approach, based on a large number of samples of the parameters before excavations. Further, the predicted probability of failure distribution based on the proposed approach can effectively reflect the actual failure locations.

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“…The distribution of excess pore pressure which is derived from the study of Saada et al [38] can be written as…”

Section: Calculation Of External Workmentioning

confidence: 99%

Functional Catastrophe Analysis of Collapse Mechanism for Shallow Tunnels with Considering Settlement

Zhang

Xiao

2016

Mathematical Problems in Engineering

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Limit analysis is a practical and meaningful method to predict the stability of geomechanical properties. This work investigates the pore water effect on new collapse mechanisms and possible collapsing block shapes of shallow tunnels with considering the effects of surface settlement. The analysis is performed within the framework of upper bound theorem. Furthermore, the NL nonlinear failure criterion is used to examine the influence of different factors on the collapsing shape and the minimum supporting pressure in shallow tunnels. Analytical solutions derived by functional catastrophe theory for the two different shape curves which describe the distinct characteristics of falling blocks up and down the water level are obtained by virtual work equations under the variational principle. By considering that the mechanical properties of soil are not affected by the presence of underground water, the strength parameters in NL failure criterion can be taken to be the same under and above the water table. According to the numerical results in this work, the influences on the size of collapsing block different parameters have are presented in the tables and the upper bounds on the loads required to resist collapse are derived and illustrated in the form of supporting forces graphs that account for the variation of the embedded depth and other factors.

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Stability analysis of rock slopes subjected to seepage forces using the modified Hoek–Brown criterion

Cited by 95 publications

References 35 publications

3D stability of unsaturated soil slopes with tension cracks under steady infiltrations

3D stability of unsaturated soil slopes with tension cracks under steady infiltrations

Fusion of Hydraulic Tomography and Displacement Back Analysis for Underground Cavern Stability Investigation

Functional Catastrophe Analysis of Collapse Mechanism for Shallow Tunnels with Considering Settlement

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