• Geomechanics and Engineering
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• v.13 no.2
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• pp.301-318
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• 2017

Based on the existing research results, a three-dimensional failure mechanism of tunnel face was constructed. The dynamic seismic effect was taken into account on the basis of quasi-static method, and the nonlinear Mohr-Coulomb failure criterion was introduced into the limit analysis by using the tangent technique. The collapse pressure along with the failure scope of tunnel face was obtained through nonlinear limit analysis. Results show that nonlinear coefficient and initial cohesion have a significant impact on the collapse pressure and failure zone. However, horizontal seismic coefficient and vertical seismic proportional coefficient merely affect the collapse pressure and the location of failure surface. And their influences on the volume and height of failure mechanism are not obvious. By virtue of reliability theory, the influences of horizontal and vertical seismic forces on supporting pressure were discussed. Meanwhile, safety factors and supporting pressures with respect to 3 different safety levels are also obtained, which may provide references to seismic design of tunnels.

• Geomechanics and Engineering
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• v.8 no.1
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• pp.97-111
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• 2015

The kinematical approach of limit analysis is used to estimate the three dimensional stability analysis of rock slopes with nonlinear Hoek-Brown criterion under earthquake forces. The generalized tangential technique is introduced, which makes limit analysis apply to rock slope problem possible. This technique formulates the three dimensional stability problem as a classical nonlinear programming problem. A nonlinear programming algorithm is coded to search for the least upper bound solution. To prove the validity of the present approach, static stability factors are compared with the previous solutions, using a linear failure criterion. Three dimensional seismic and static stability factors are calculated for rock slopes. Numerical results of indicate that the factors increase with the ratio of slope width and height, and are presented for practical use in rock engineering.

• Geomechanics and Engineering
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• v.15 no.6
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• pp.1183-1191
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• 2018

Reliability analysis is generally regarded as the most appropriate method when uncertainties are taken into account in slope designs. With the help of limit analysis, probability evaluation for three-dimensional rock slope stability was conducted based upon the Mote Carlo method. The nonlinear Hoek-Brown failure criterion was employed to reflect the practical strength characteristics of rock mass. A form of stability factor is used to perform reliability analysis for rock slopes. Results show that the variation of strength uncertainties has significant influence on probability of failure for rock slopes, as well as strength constants. It is found that the relationship between probability of failure and mean safety factor is independent of the magnitudes of input parameters but relative to the variability of variables. Due to the phenomenon, curves displaying this relationship can provide guidance for designers to obtain factor of safety according to required failure probability.

• Geomechanics and Engineering
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• v.16 no.6
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• pp.655-667
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• 2018

To evaluate the stability of a rock slope with one pre-exiting vertical crack, this paper performs corresponding probabilistic stability analysis. The existence of cracks is generally ignored in traditional deterministic stability analysis. However, they are widely found in either cohesive soil or rock slopes. The influence of one pre-exiting vertical crack on a rock slope is considered in this study. The safety factor, which is usually adopted to quantity the stability of slopes, is derived through the deterministic computation based on the strength reduction technique. The generalized Hoek-Brown (HB) failure criterion is adopted to characterize the failure of rock masses. Considering high nonlinearity of the limit state function as using nonlinear HB criterion, the multivariate adaptive regression splines (MARS) is used to accurately approximate the implicit limit state function of a rock slope. Then the MARS is integrated with Monte Carlo simulation to implement reliability analysis, and the influences of distribution types, level of uncertainty, and constants on the probability density functions and failure probability are discussed. It is found that distribution types of random variables have little influence on reliability results. The reliability results are affected by a combination of the uncertainty level and the constants. Finally, a reliability-based design figure is provided to evaluate the safety factor of a slope required for a target failure probability.

• Steel and Composite Structures
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• v.4 no.3
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• pp.227-246
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• 2004

This paper presents a moment-curvature method that accounts for the strength deterioration of steel at elevated temperature in estimating the response of steel beams exposed to fire. A modification to the EC4 method is proposed for a better estimation of the temperature distribution in the steel beam supporting a concrete slab. The accuracy of the proposed method is verified by comparing the results with established test results and the nonlinear finite element analysis results. The beam failure criterion based on a maximum strain of 0.02 is proposed to assess the limiting temperature as compared to the traditional criteria that rely on deflection limit or deflection rate. Extensive studies carried out on steel beams with various span lengths, load ratios, beam sizes and loading types show that the proposed failure criterion gives consistent results when compared to nonlinear finite element results.

• Geomechanics and Engineering
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• v.18 no.6
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• pp.595-603
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• 2019

A modified model combining Kriging and Monte Carlo method (MC) is proposed for probabilistic estimation of tunnel face stability in this paper. In the model, a novel uniform design is adopted to train the Kriging, instead of the existing active learning function. It has advantage of avoiding addition of new training points iteratively, and greatly saves the computational time in model training. The kinematic approach of limit analysis is employed to define the deterministic computational model of face failure, in which the Hoek-Brown failure criterion is introduced to account for the nonlinear behaviors of rock mass. The trained Kriging is used as a surrogate model to perform MC with dramatic reduction of calls to actual limit state function. The parameters in Hoek-Brown failure criterion are considered as random variables in the analysis. The failure probability is estimated by direct MC to test the accuracy and efficiency of the proposed probabilistic model. The influences of uncertainty level, correlation relationship and distribution type of random variables are further discussed using the proposed approach. In summary, the probabilistic model is an accurate and economical alternative to perform probabilistic stability analysis of tunnel face excavated in spatially random Hoek- Brown media.

• Geomechanics and Engineering
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• v.8 no.5
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• pp.741-756
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• 2015

The prediction of impending collapse of deep tunnel is one of the most difficult problems. Collapse mechanism of deep tunnel in layered soils is derived using a new curved failure mechanism within the framework of upper bound theorem, and effects of seepage forces are considered. Nonlinear failure criterion is adopted in the present analysis, and the possible collapse shape of deep tunnel in the layered soils is discussed in this paper. In the layered soils, the internal energy dissipations along velocity discontinuity are calculated, and the external work rates are produced by weight, seepage forces and supporting pressure. With upper bound theorem of limit analysis, two different curve functions are proposed for the two different soil stratums. The specific shape of collapse surface is discussed, using the proposed curve functions. Effects of nonlinear coefficient, initial cohesion, pore water pressure and unit weight on potential collapse are analyzed. According to the numerical results, with the nonlinear coefficient increase, the shape of collapse block will increase. With initial cohesion of the upper soil increase, the shape of failure block will be flat, and with the lower soil improving, the size of collapsing will be large. Furthermore, the shape of collapsing will decrease with the unit weight decrease.

• Nuclear Engineering and Technology
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• v.51 no.2
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• pp.561-572
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• 2019

In the design criterion for the nuclear power plant piping system, the limit state of the piping against an earthquake is assumed to be plastic collapse. The failure of a common piping system, however, means the leakage caused by the cracks. Therefore, for the seismic fragility analysis of a nuclear power plant, a method capable of quantitatively expressing the failure of an actual piping system is required. In this study, it was conducted to propose a quantitative failure criterion for piping system, which is required for the seismic fragility analysis of nuclear power plants against critical accidents. The in-plane cyclic loading test was conducted to propose a quantitative failure criterion for steel pipe elbows in the nuclear power plant piping system. Nonlinear analysis was conducted using a finite element model, and the results were compared with the test results to verify the effectiveness of the finite element model. The collapse load point derived from the experiment and analysis results and the damage index based on the stress-strain relationship were defined as failure criteria, and seismic fragility analysis was conducted for the piping system of the BNL (Brookhaven National Laboratory) - NRC (Nuclear Regulatory Commission) benchmark model.

• Geomechanics and Engineering
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• v.17 no.2
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• pp.181-194
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• 2019

Due to the seepage of groundwater, the resisting force of slopes decreases and the sliding force increases, resulting in significantly reduced slope stability. The instability of most natural slopes is closely related to the influence of groundwater. Therefore, it is important to study slope stability under groundwater seepage conditions. Thus, using a simplified seepage model of groundwater combined with the analysis of stresses on the slip surface, the limit equilibrium (LE) analytical solutions for two- and three-dimensional slope stability under groundwater seepage are deduced in this work. Meanwhile, the general nonlinear Mohr-Coulomb (M-C) strength criterion is adopted to describe the shear failure of a slope. By comparing the results with the traditional LE methods on slope examples, the feasibility of the proposed method is verified. In contrast to traditional LE methods, the proposed method is more suitable for analyzing slope stability under complex conditions. In addition, to facilitate the optimization of drainage design in the slope, stability charts are drawn for slopes with different groundwater tables. Furthermore, the study concluded that: (1) when the hydraulic gradient of groundwater is small, the effect on slope stability is also small for a change in the groundwater table; and (2) compared with a slope without a groundwater table, a slope with a groundwater table has a larger failure range under groundwater seepage.

• Geomechanics and Engineering
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• v.17 no.6
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• pp.515-525
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• 2019

The calculation of active earth pressure behind retaining wall is a typical three-dimensional (3D) problem with spatial effects. With the help of limit analysis, this paper firstly deduces the internal energy dissipation power equations and various external forces power equations of the 3D retaining wall under the nonlinear strength condition, such as to establish the work-energy balance equation. The pseudo-static method is used to consider the effect of earthquake on active earth pressure in horizontal state. The failure mode is a 3D curvilinear cone failure mechanism. For the different width of the retaining wall, the plane strain block is inserted in the symmetric plane. By optimizing all parameters, the maximum value of active earth pressure is calculated. In order to verify the validity of the new expressions obtained by the paper, the solutions are compared with previously published solutions. Agreement shows that the new expressions are effective. The results of different parameters are given in the forms of figures to analysis the influence caused by nonlinear strength parameters.