Probabilistic analysis of tunnel face seismic stability in layered rock masses using Polynomial Chaos Kriging metamodel

Face stability is an essential issue in tunnel design and construction.Layered rock masses are typical and ubiquitous;uncertainties in rock properties always exist.In view of this,a comprehensive method,which combines the Upper bound Limit analysis of Tunnel face stability,the Polynomial Chaos Kriging,the Monte-Carlo Simulation and Analysis of Covariance method(ULT-PCK-MA),is proposed to investigate the seismic stability of tunnel faces.A two-dimensional analytical model of ULT is developed to evaluate the virtual support force based on the upper bound limit analysis.An efficient probabilistic analysis method PCK-MA based on the adaptive Polynomial Chaos Kriging metamodel is then implemented to investigate the parameter uncertainty effects.Ten input parameters,including geological strength indices,uniaxial compressive strengths and constants for three rock formations,and the horizontal seismic coefficients,are treated as random variables.The effects of these parameter uncertainties on the failure probability and sensitivity indices are discussed.In addition,the effects of weak layer position,the middle layer thickness and quality,the tunnel diameter,the parameters correlation,and the seismic loadings are investigated,respectively.The results show that the layer distributions significantly influence the tunnel face probabilistic stability,particularly when the weak rock is present in the bottom layer.The efficiency of the proposed ULT-PCK-MA is validated,which is expected to facilitate the engineering design and construction.

The effect of seismic action on stability of saline soil subgrade in cold region based on isothermal stratification method

With the change of seasons, the shear strength of saline soil subgrade filler will change with the change of external temperature, which will aggravate the adverse effects of seismic on the subgrade. To explore the influence of seismic action on the stability of saline soil subgrade under the influence of temperature on the strength of saline soil subgrade filler, this paper first carried out saline soil shear tests at different temperatures to obtain the influence of temperature on the shear strength of saline soil. Then, the temperature field of the saline soil subgrade was simulated, and then based on the subgrade isothermal stratification model and FLAC3D, the displacement and acceleration amplification effects of seismic action on the shady slope, sunny slope and subgrade of saline soil subgrade in different months were analyzed. The following conclusions were finally drawn: under the action of seismic, In the process of the change of subgrade temperature of Qarhan-Golmud Expressway between 7.7°C and 27°C, the change of saline soil cohesion is the main factor affecting the stability of subgrade slope, and the maximum and minimum values of subgrade surface settlement appear in September and June of each year,respectively. In August, the differences of settlement between the shady slope and the sunny slope shoulder of the subgrade were the largest, and the acceleration of the shady slope and the sunny slope and the inside of the subgrade changed most significantly in the vertical direction. Special attention should be paid to the seismic early warning in the above key months;In the range from both sides of the shoulder to the centerline of the roadbed,the acceleration amplification effect starts to increase significantly from about 3m from the centerline of the roadbed to the centerline, so it is necessary to pay attention to the seismic design of this range.

Improved Prediction of Slope Stability under Static and Dynamic Conditions Using Tree-BasedModels

Slope stability prediction plays a significant role in landslide disaster prevention and mitigation.This paper’s reduced error pruning(REP)tree and random tree(RT)models are developed for slope stability evaluation and meeting the high precision and rapidity requirements in slope engineering.The data set of this study includes five parameters,namely slope height,slope angle,cohesion,internal friction angle,and peak ground acceleration.The available data is split into two categories:training(75%)and test(25%)sets.The output of the RT and REP tree models is evaluated using performance measures including accuracy(Acc),Matthews correlation coefficient(Mcc),precision(Prec),recall(Rec),and F-score.The applications of the aforementionedmethods for predicting slope stability are compared to one another and recently established soft computing models in the literature.The analysis of the Acc together with Mcc,and F-score for the slope stability in the test set demonstrates that the RT achieved a better prediction performance with(Acc=97.1429%,Mcc=0.935,F-score for stable class=0.979 and for unstable case F-score=0.935)succeeded by the REP tree model with(Acc=95.4286%,Mcc=0.896,F-score stable class=0.967 and for unstable class F-score=0.923)for the slope stability dataset The analysis of performance measures for the slope stability dataset reveals that the RT model attains comparatively better and reliable results and thus should be encouraged in further research.

Slope stability analysis under seismic load by vector sum analysis method

The vibration characteristics and dynamic responses of rock and soil under seismic load can be estimated with dynamic finite element method （DFEM）. Combining with the DFEM, the vector sum analysis method （VSAM） is employed in seismic stability analysis of a slope in this paper. Different from other conventional methods, the VSAM is proposed based on the vector characteristic of force and current stress state of the slope. The dynamic stress state of the slope at any moment under seismic load can he obtained by the DFEM, thus the factor of safety of the slope at any moment during earthquake can be easily obtained with the VSAM in consideration of the DFEM. Then, the global stability of the slope can be estimated on the basis of time-history curve of factor of safety and reliability theory. The VSAM is applied to a homogeneous slope under seismic load. The factor of safety of the slope is 1.30 under gravity only and the dynamic factor of safety under seismic load is 1.21. The calculating results show that the dynamic characteristics and stability state of the slope with input ground motion can be actually analyzed. It is believed that the VSAM is a feasible and practical approach to estimate the dynamic stability of slopes under seismic load.

Effects of vertical seismic acceleration on 3D slope stability

The conventional pseudo-static approach often neglects the effect of the vertical＇ seismic acceleration on the stability of a slope, but some analyses under plane-strain （2D） conditions show a significant effect on the slope stability. The purpose of this study is to investigate the effect of the vertical acceleration on the safety of three-dimensional （3D） slopes. In the strict framework of limit analysis, a 3D kinematically admissible rotational failure mechanism is adopted here for 3D homogeneous slopes in frictional/cohesive soils. A set of stability charts is presented in a wide range of parameters for 3D slopes under combined horizontal and vertical seismic loading conditions. Accounting for the effects of the vertical seismic acceleration, the difference in safety factors for 3D slopes can exceed 10%, which will significantly overestimate the safety of the 3D slopes.

Seismic stability assessment of an arch dam-foundation system

A seismic stability assessment of arch dam-foundation systems is presented using a comprehensive approach,in which the main factors that significantly influence the seismic response of an arch dam-foundation system are considered.A large scale finite element model with over 1 million degrees of freedom is constructed for the Baihetan arch dam(289 m high),which is under construction in the Southwest of China.In particular,the complicated geological conditions with faults intersecting interlayer shear weakness zones at the dam base and the dam abutment resisting force body is modeled in the analysis.Three performance indices are adopted to assess the seismic stability of the arch dam.The results demonstrate that the opening of the joints of the Baihetan arch dam is small and the water stop installed between the joints would not be torn during a design earthquake.The yielding formed in the interface between the dam and foundation does not reach the grouting curtain that would remain in an elastic state after an earthquake.The yielding zones occurring on the upper portion of the dam faces extend 1/8 thickness of block section into the dam body and thus cantilever blocks need not be concerned with sliding stability.The faults and interlayer shear weakness zones in the near field foundation exhibit severe yielding,and a potential sliding surface is penetrated.Although the factor of safety against sliding of the surface fluctuates with a decreased trend during an earthquake,the minimum instantaneous value reaches 1.02 and is still larger than 1.0.Therefore,a conclusion is drawn that the Baihetan arch dam-foundation system will remain stable under the design earthquake.

Limit analysis for the seismic stability of three-dimensional rock slopes using the generalized Hoek-Brown criterion

The parameters that influence slope stability and their criteria of failure are fairly understood but over-conservative design approaches are often preferred,which can result in excessive overburden removal that may jeopardize profitability in the context of open pit mining.Numerical methods such as finite element and discrete element modelling are instrumental to identify specific zones of stability,but they remain approximate and do not pinpoint the critical factors that influence stability without extensive parametric studies.A large number of degrees of freedom and input parameters may make the outcome of numerical modelling insufficient compared to analytical solutions.Existing analytical approaches have not tackled the stability of slopes using non-linear plasticity criteria and threedimensional failure mechanisms.This paper bridges this gap by using the yield design theory and the Hoek-Brown criterion.Moreover,the proposed model includes the effect of seismic forces,which are not always taken into account in slope stability analyses.The results are presented in the form of rigorous mathematical expressions and stability charts involving the loading conditions and the rock mass properties emanating from the plasticity criterion.

Pseudo-dynamic analysis of seismic stability of reinforced slopes considering non-associated flow rule

The required reinforcement force to prevent instability and the yield acceleration of reinforced slopes are computed under seismic loading by applying the kinematic approach of limit analysis in conjunction with the pseudo-dynamic method for a wide range of soil cohesion, friction angle, dilation angle and horizontal and vertical seismic coefficients. Each parameter threatening the stability of the slope enhances the magnitude of the required reinforcement force and vice versa. Moreover, the yield acceleration increases with the increase in soil shear strength parameters but decreases with the increase in the slope angle. The comparison of the present work with some of the available solutions in the literatures shows a reasonable agreement.

Seismic stability of jointed rock slopes under obliquely incident earthquake waves

Seismic stability of slopes has been traditionally analyzed with vertically propagated earthquake waves.However,for rock slopes,the earthquake waves might approach the outcrop still with a evidently oblique direction.To investigate the impact of obliquely incident earthquake excitations,the input method for SV and P waves with arbitrary incident angles is conducted,respectively,by adopting the equivalent nodal force method together with a viscous-spring boundary.Then,the input method is introduced within the framework of ABAQUS software and verified by a numerical example.Both SV and P waves input are considered herein for a 2 D jointed rock slope.For the jointed rock mass,the jointed material model in ABAQUS software is employed to simulate its behavior as a continuum.Results of the study show that the earthquake incident angles have significance on the seismic stability of jointed rock slopes.The larger the incident angle,the greater the risk of slope instability.Furthermore,the stability of the jointed rock slopes also is affected by wave types of earthquakes heavily.P waves induce weaker responses and SV waves are shown to be more critical.

Seismic stability of reinforced soil walls under bearing capacity failure by pseudo-dynamic method

In order to evaluate the seismic stability of reinforced soil walls against bearing capacity failure,the seismic safety factor of reinforced soil walls was determined by using pseudo-dynamic method,and calculated by considering different parameters,such as horizontal and vertical seismic acceleration coefficients,ratio of reinforcement length to wall height,back fill friction angle,foundation soil friction angle,soil reinforcement interface friction angle and surcharge.The parametric study shows that the seismic safety factor increases by 24-fold when the foundation soil friction angle varies from 25°to 45°,and increases by 2-fold when the soil reinforcement interface friction angle varies from 0 to 30°.That is to say,the bigger values the foundation soil and/or soil reinforcement interface friction angles have,the safer the reinforced soil walls become in the seismic design.The results were also compared with those obtained from pseudo-static method.It is found that there is a higher value of the safety factor by the present work.

Probabilistic seismic stability of three-dimensional slopes by pseudo-dynamic approach

Probabilistic analysis is a rational approach for engineering design because it provides more insight than traditional deterministic analysis. Probabilistic evaluation on seismic stability of three dimensional (3D) slopes is studied in this paper. The slope safety factor is computed by combining the kinematic approach of limit analysis using a three-dimensional rotational failure mechanism with the pseudo-dynamic approach. The variability of input parameters, including six pseudo-dynamic parameters and two soil shear strength parameters, are taken into account by means of Monte-Carlo Simulations (MCS) method. The influences of pseudo-dynamic input variables on the computed failure probabilities are investigated and discussed. It is shown that the obtained failure probabilities increase with the pseudo-dynamic input variables and the pseudo-dynamic approach gives more conservative failure probability estimates compared with the pseudo-static approach.

Comparison of seismic stability for slopes with tensile strength cut-off and cracks

The strength of geomaterials is typically predicted by the Mohr-Coulomb yield criterion in slope stability analysis.The tensile strength of soils in this yield criterion,which is an extrapolation of the triaxial compression test results,is usually overestimated.Generally,the influences of tensile stresses in slopes are evaluated by two approaches:1)introducing cracks to eliminate the tensile stresses in slopes,and 2)truncating the strength envelope to reduce the tensile strength of the soils.However,comparative analyses of the two approaches have not been fully implemented,especially under dynamic conditions.In this study,three slope failure mechanisms corresponding to the predictions of slope stability by the mentioned two approaches subjected to seismic loadings are systematically evaluated.The stability factor considering the pre-existing crack,crack formation,and tension cut-off are compared one another.The most unfavorable crack locations corresponding to the different mechanisms are evaluated.The influence of tensile strength on the factor of safety of slopes is estimated as well.Further,the critical acceleration and the permanent displacement of slopes with pre-existing crack,and tension cut-off are derived in the framework of the kinematic theorem of limit analysis.The vertical effects of seismic coefficient on critical acceleration and permanent displacement are discussed.Conclusions can be drawn that the consideration of tension zone effects can sharply reduce the stability factor of slopes,especially for steep slopes and large horizontal seismic loads;different from the static condition,the slope with pre-existing crack is not always the most vulnerable to collapse,the tension cut-off mechanism in steep slopes may predict the lowest stability factor.In addition,the calculation shows that an evidently increase in the slope displacement is induced by the increasing downward vertical loads,while a decrease occurs if the vertical loads are upward.

Applying real time seismic monitoring technology for slope stability assessment—An Indian opencast coal mine perspective

This paper outlines the results obtained from real time microseismic monitoring of an opencast coal mine in South India.The objective of the study is to investigate the stress changes within the rockmass along the slope due to underground mine development operation and their impact on the stability of the highwall slope.The installed microseismic systems recorded the seismic triggerings down toà2 moment magnitude.In general,most of the events recorded during the monitoring period are weak in seismic energy.The study adopts a simple and more reliable tool to characterize the seismically active zone for assessing the stability of the highwall in real time.The impact of underground working on the slope is studied on the basis of the seismic event impact contours and seismic clusters.During the monitoring period,it is observed that the intensity of the overall microseismic activity along the slope due to the mine development operations did not cause any adverse impact on the highwall stability.

System reliability analysis of seismic pseudo-static stability of rock wedge based on nonlinear Barton–Bandis criterion

Based on the nonlinear Barton–Bandis(B–B)failure criterion,this study considers the system reliability of rock wedge stability under the pseudo-static seismic load.The failure probability(Pf)of the system is calculated based on the Monte−Carlo method when considering parameter correlation and variability.Parameter analysis and sensitivity analysis are carried out to explore the influence of parameters on reliability.The relationships among the failure probability,safety factor(Fs),and variation coefficient are explored,and then stability probability curves of the rock wedge under the pseudo-static seismic load are drawn.The results show that the parameter correlation of the B–B failure criterion has a significant influence on the failure probability,but correlation increases system reliability or decreases system reliability affected by other parameters.Under the pseudo-static seismic action,sliding on both planes is the main failure mode of wedge system.In addition,the parameters with relatively high sensitivity are two angles related to the joint dip.When the coefficient of variation is consistent,the probability of system failure is a function of the safety factor.

Stochastic seismic slope stability assessment using polynomial chaos expansions combined with relevance vector machine

This paper presents probabilistic assessment of seismically-induced slope displacements considering uncertainties of seismic ground motions and soil properties.A stochastic ground motion model representing both the temporal and spectral non-stationarity of earthquake shakings and a three-dimensional rotational failure mechanism are integrated to assess Newmark-type slope displacements.A new probabilistic approach that incorporates machine learning in metamodeling technique is proposed,by combining relevance vector machine with polynomial chaos expansions(RVM-PCE).Compared with other PCE methods,the proposed RVM-PCE is shown to be more effective in estimating failure probabilities.The sensitivity and relative influence of each random input parameter to the slope displacements are discussed.Finally,the fragility curves for slope displacements are established for sitespecific soil conditions and earthquake hazard levels.The results indicate that the slope displacement is more sensitive to the intensities and strong shaking durations of seismic ground motions than the frequency contents,and a critical Arias intensity that leads to the maximum annual failure probabilities can be identified by the proposed approach.

Seismic stability analysis of concrete gravity dams with penetrated cracks

The seismic stability of a cracked dam was examined in this study. Geometric nonlinearity and large deformations, as well as the contact condition at the crack site, were taken into consideration. The location of penetrated cracks was first identified using the concrete plastic-damage model based on the nonlinear finite element method （FEM）. Then, the hard contact algorithm was used to simulate the crack interaction in the normal direction, and the Coloumb friction model was used to simulate the crack interaction in the tangential direction. After verification of numerical models through a case study, the seismic stability of the Koyna Dam with two types of penetrated cracks is discussed in detail with different seismic peak accelerations, and the collapse processes of the cracked dam are also presented. The results show that the stability of the dam with two types of penetrated cracks can be ensured in an earthquake with a magnitude of the original Koyna earthquake, and the cracked dam has a large earthquake-resistant margin. The failure processes of the cracked dam in strong earthquakes can be divided into two stages： the sliding stage and the overturning stage. The sliding stage ends near the peak acceleration, and the top block slides a long distance along the crack before the collapse occurs. The maximum sliding displacement of the top block will decrease with an increasing friction coefficient at the crack site.

Probabilistic Analysis for Seismic Stability of Beach Earth Embankment

The current safety factor method for evaluating earth embankment stability is not very rational since the assessment of slope stability is really an uncertainty problem. In order to consider the random property of this problem, the probabilistic analysis is introduced herein. Finally, the stability of a real beach earth embankment is analysed by means of the suggested probabilitic approach. It may be seen that the results of analysis can represent the numerical assessment of the degree of seismic stability.

Fuzzy Probabilistic Analysis of Seismic Stability of Coastal Embankment

The stability of slope is affected by a number of factors, some of which have not only random property but also fuzzy characteristic. Therefore, the analysis of slope stability is really an uncertain problem. The customary safety factor does not in reality reflect stability scientifically, quantitatively and practically. In order to obtain more practical results, the slope stability is treated as a fuzzy random event for the evaluation of its fuzzy probability. Finally, the seismic stability of an existing coastal embankment is analyzed by means of the suggested fuzzy probabilistic method. It may be seen that the results of analysis can more fully represent the numerical assessment of the degree of slope seismic stability.

Seismic stability evaluation of embankment slope based on catastrophe theory

An evaluation method for the seismic stability of embankment slope was presented based on catastrophe theory. Seven control factors, including internal frictional angle, cohesion force, slope height, slope angle, surface gradients, peak acceleration, and distance to fault were selected for analysis of multi-level objective decomposition. According to the normalization formula and the fuzzy subject function produced by combination of catastrophe theory and fuzzy math, a recursive calculation was carried out to obtain a catastrophic affiliated functional value, which can be used to evaluate the seismic stability of embankment slope. Fifteen samples were used to verify the effectiveness of this method. The results show that compared with the traditional quantitative method, the catastrophe progression owns higher accuracy and good application potential in predicting the seismic stability of embankment slope.

Seismic stability analysis of slopes with pre-existing slip surfaces

In analyzing seismic stability of a slope with upper bound limit analysis method, the slip surface is often assumed as a log-spiral or plane slip surface. However, due to the presence of a weak layer and unfavorable geological structural surface or a bedrock interface with overlying soft strata, the preexisting slip surface of the slope may be irregular and composed of a series of planes rather than strictly logspiral or plane shape. A computational model is developed for analyzing the seismic stability of slopes with pre-existing slip surfaces. This model is based on the upper bound limit analysis method and can consider the effect of anchor bolts. The soil or rock is deemed to follow the Mohr-Coulomb yield criterion. The slope is divided into multiple block elements along the slip surface. According to the displacement compatibility and the associated flow rule, a kinematic velocity field of the slope can be obtained computationally. The proposed model allows not only calculation of the rate of external work owing to the combined effect of self-weight and seismic loading, but also that of the energy dissipation rate caused by the slip surface, interfaces of block elements and anchorage effect of the anchors. Considering a direct relationship between the rate of external work and the energy dissipation rate, the expressions of yield acceleration and permanent displacement of anchored slopes can be derived. Finally, the validity of this proposed model is illustrated by analysis on three typical slopes. The results showed that the proposed model is more easily formulated and does not need to solve complex equations or time consuming iterations compared with previous methods based on the conditions of force equilibrium.