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.

Study on the tunnel shape and soil-lining interaction influencing the lining behavior under seismic loading

The response of tunnels subjected to seismic loading is a complex mechanism and depends not only on the seismic nature but also on tunnel structure and surrounding soil properties.The individual behavior of circular,rectangular,and sub-rectangular tunnels subjected to seismic loadings has already been studied in the literature.In the present research,two case scenarios of circular,rectangular tunnels and four sub-rectangular shaped tunnels,with similar cross-section areas,were adopted to perform a comprehensive numerical investigation.The purpose of the study was to determine the mechanical behavior of tunnels of different shapes,depending upon seismic conditions.Analyses were performed by considering the influence of soil-lining interaction,soil parameters,and lining thickness,as well as lining rigidity.Computations were performed for no-slip and full-slip conditions.The results indicate that the tunnel shape design is of great importance when regarding the mechanical behavior of the surrounding soil.This concerns no-slip as well as full-slip soil-lining interaction,especially when the lining is subjected to seismic loading.Moreover,it is shown that changes in incremental bending moments for circular,rectangular and sub-rectangular tunnels that depend upon the soil-lining interaction conditions differ significantly.

STABILITY ANALYSIS OF TWO-DIMENSIONAL LANDSLIDES SUBJECTED TO SEISMIC LOADS

In the past, the pseudo-static method used to be the most common for evaluating the stability of landslides under seismic loads, in which static forces acting on the center of gravity of a sliding body are used to consider the effects of earthquake. However, seismic loads of rock and soil differ from time and location to time and location. Obviously, it is irrational for the pseudo-static approach to be applied to solving dynamic problems. In this paper, a displacement- pseudo-dynamic model is proposed to assess seismic stability of landslides, in which the sinusoidal- cosinusoidal wave is applied to simulating earthquake displacement, and an ＂amplification factor＂ of peak seismic displacement is referred to as the amplification of seismic wave when it propagates from the bottom to the top of the landslide. The effects of physico-mechanical behaviors of a sliding body on seismic stability of soil slopes are taken into account as well as inertia forces and damping forces. The sensitivity analyses on the permanent displacement and the dynamic factor of safety of landslides are studied in detail. Moreover, a large-scale Tangjiashan landslide that occurred in Wenchuan earthquake is investigated to verify the robustness and precision of the present method. It is found that the results from the present method is in good agreement with those from the previous method.

Generalized response displacement methods for seismic analysis of underground structures with complex cross section

The response displacement method(RDM)is recommended for the seismic analysis of underground structures in the transverse direction for many codes,including bases for design of structures-seismic actions for designing geotechnical works(ISO 23469)and code for seismic design of urban rail transit structures(GB 50909-2014).However,there are some obvious limitations in the application of RDM.Springs and the shear stress of the soil could be approximately evaluated for the structures having a simple cross section,such as rectangular and circular structures.It is necessary to propose simplified seismic analysis methods for structures with complex cross sections.This paper refers to the idea of RDM and proposes three generalized response displacement methods(GRDM).In GRDM1,a part of the soil surrounding a structure is selected to generate a generalized underground structure with a rectangular cross section,and the same analysis model as RDM is applied to analyze the responses of the structure.In GRDM2,a hollow soil model without a generalized structure is used to compute the equivalent load caused by the relative displacement of the soil,and the soil-structure interaction model is applied to calculate the responses of the structure.In GRDM3,a continuous soil model is applied to compute the equivalent load caused by the relative displacement and shear stress of the soil,and the soil-structure interaction model is applied to analyze the responses of the structure,which is the same as the model used in GRDM2.The time-history analysis method(THAM)is used to evaluate the accuracy of the proposed simplified methods.Results show that the error of GRDM1 is about 20%,while the error is only 5%for GRDM2 and GRDM3.Among the three proposed methods,GRDM3 has obvious advantages regarding calculation efficiency and accuracy.Therefore,it is recommended to use GRDM3 for the seismic response analysis of underground structures that have conventional simple or complex cross sections.

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.

Topology optimization of shear wall structures under seismic loading

A topology optimization formulation is developed to find the stiffest structure with desirable material distribution subjected to seismic loads. Finite element models of the structures are generated and the optimality criteria method is modified using a simple penalty approach and introducing fictitious strain energy to simultaneously consider both material volume and displacement constraints. Different types of shear walls with/without opening are investigated. Additionally, the effects of shear wall-frame interaction for single and coupled shear walls are studied. Gravity and seismic loads are applied to the shear walls so that the definitions provide a practical approach for locating the critical parts of these structures. The results suggest new viewpoints for architectural and structural engineering for placement of openings.

The Effect of Core Eccentricity on the Structural Behavior of Concrete Tall Buildings

The main purpose of this paper is to investigate the effect of core eccentricity on the structural behavior of concrete tall buildings.Concrete buildings of 55 floors with plan dimensions 48.0×48.0 m2 were investigated.Three cases of main core locations are studied:centric(A),eccentric by one sixth(B)and one third(C)of building width.The three-dimensional finite element method has been used in conducting structural analysis through ETABS software.Gravity and lateral(wind and seismic)loadings are applied to all building cases.It has been concluded that the core location is the prime parameter governing the structural behavior of tall buildings.Although the first two cases(A,B)have acceptable and similar structural behaviors conforming to code limits,in the third case(C),the building behavior came beyond code limits.The author introduced remedial action by adding two secondary cores in the opposite direction of the main core(C-R)to restore the building behavior to the code limits.The results of this action were satisfactory.

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.

Contribution of tuned liquid column gas dampers to the performance of offshore wind turbines under wind, wave, and seismic excitations

The main intention of the present study is to reduce wind, wave, and seismic induced vibrations of jacket- type offshore wind turbines （JOWTs） through a newly developed vibration absorber, called tuned liquid column gas damper （TLCGD）. Using a Simulink-based model, an analytical model is developed to simulate global behavior of JOWTs under different dynamic excitations. The study is followed by a parametric study to explore efficiency of the TLCGD in terms of nacelle acceleration reduction under wind, wave, and earthquake loads. Study results indicate that optimum frequency of the TLCGD is rather insensitive to excitation type. In addition, while the gain in vibration control from TLCGDs with higher mass ratios is generally more pronounced, heavy TLCGDs are more sensitive to their tuned frequency such that ill-regulated TLCGD with high mass ratio can lead to destructive results. It is revealed that a well regulated TLCGD has noticeable contribution to the dynamic response of the JOWT under any excitation.

Earth slope reliability analysis under seismic loadings using neural network

A new method was proposed to cope with the earth slope reliability problem under seismic loadings. The algorithm integrates the concepts of artificial neural network, the first order second moment reliability method and the deterministic stability analysis method of earth slope. The performance function and its derivatives in slope stability analysis under seismic loadings were approximated by a trained multi-layer feed-forward neural network with differentiable transfer functions. The statistical moments calculated from the performance function values and the corresponding gradients using neural network were then used in the first order second moment method for the calculation of the reliability index in slope safety analysis. Two earth slope examples were presented for illustrating the applicability of the proposed approach. The new method is effective in slope reliability analysis. And it has potential application to other reliability problems of complicated engineering structure with a considerably large number of random variables.

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.

Complex of general seismic zoning maps OSR-2017 of Uzbekistan

The quantitative assessment of seismic hazard of Uzbekistan has been examined,and new maps of seismic zoning has been developed.Quasihomogeneous seismological areas and seism-generating zones are considered as seismic sources,based on the analysis of seismotectonic data.The seismological parametrization of seismic sources has been carried out,including determination of parameters of earthquake’s reoccurrence for different power levels,seismic potential and a predominant type motion in the source of occurring earthquakes.The reoccurrence parameters of seismic sources were both determined by directly from Gutenberg-Richter dependence law and using summation and distribution methods.Setting were conducted separately for a sample of strong(M≥5)and weak(M<5)earthquakes.The seismic potential Mmax of seismic active zones was determined by seismological and seismotectonic methods.The predominant type of movement in the faulting for each seismic source is reverse fault.Regional regularities of seismic intensity attenuation with distance of different power levels are determined.The seismic hazard is expressed in points of a macro seismic scale,in velocities and accelerations of ground motions,and it is characterized by calculated seismic intensity with the set probability(P=0.9,P=0.95,P=0.98 and P=0.99)not exceed within 50 years in the constructed maps.In seismic zoning map,the seismic intensity was in average soil conditions.The developed complex of maps considers a number of uncertainties of the input parameters in relation to both incompleteness of initial seismological and seismotectonic data,as well the probabilistic nature of seismic process and seismic intensity.The factors of uncertainty of the input parameters are taken into account by constructing a logic tree.The constructed maps of the general seismic zoning are intended for imple menting antiseismic actions in Uzbekistan.

Comparative Analysis of High-Rise Reinforced Concrete Structures According to International Seismic Design Codes

The field of earthquake engineering and seismology is of great importance to structural engineers around the world. The location, size and consequences of an earthquake are variable depending on several conditions. Surface conditions, boundary/fault type, distance from the boundary and hypocenter are all elements that dictate the outcome of a seismic event. The paper presents a comparison of seismic provisions of two seismic design codes--EC8 （Eurocode 8） and IBC （International Building Code） 2006, to a high-rise reinforced concrete building. The building is irregular and composes of 20 floors. The equivalent lateral force analysis was performed using the well-known structure program--ETABS （Extended 3D Analysis of Building Systems）. Based on the analysis results （inter-storey index, global damage index, storey displacement, inter-storey drift ratio and base shear）, EC8 was found to be conservative when compared with IBC 2006. The conclusion is that for the design and analysis of high-rise reinforced concrete buildings with certain irregularity, EC8 provisions were considered to be conservative.

Seismic Response of a Structure under Various Subsoi Models

Three types of the soil-structure interaction are used for structure analysis loaded by seismic effects. An example of the real RC building is used to demonstrate differences in the dynamic response results in the calculation of internal forces and displacements. Variant three options of the soil models were used as a building supporting structure. In the case of soil model A, the soil was modelled by using of equivalent stiffness values, stemming from the theory of a rigid circular disc on an elastic homogeneous half-space. Non-uniformly modelled vertical stiffness of the soil according to the Boussinesq model was used for model B. Both models A and B are characterised by the ＂averaged＂ soil model on the bases of spring constants. Model C was used for the soil better corresponding to its actual composition by the Winkler-Pasternak theory. Model C, where the actual layered soil is considered, is modelled more accurately than for the ＂averaged＂ soil of models A and B. The dynamic response of models operating with ＂averaged＂ values of rigid and soft soil layers is markedly shifted to the conservative smaller values of internal forces. The building response tbr model C in dynamic displacements is significantly higher than for the both models A and B.

Seismic Performance Assessment of Reinforced Concrete Box Culverts under Near and Far Fault Seismic Ground Motion Records

Studying the critical response characteristics of reinforced concrete box culverts with diverse geometrical configurations under seismic excitations is a necessary step to develop a reasonable design method. In this work, numerical analysis and assessment of reinforced concrete box culverts for seismic loading in addition to standard static loading from dead and live loads is conducted, aiming to highlight the critical difference in the seismic performances between two and three cell box culverts under near and far-fault ground motion. The results show how and where the seismic loading alters the responses of seismic loading of the models including the effect on safety and failure. The geometrical configurations of the culvert combined with the loading scenarios also significantly influence the magnitude and distribution of the seismic responses. The findings of this work shed light on the critical role of the geometrical configurations and shaking event in the seismic responses of reinforced concrete box culverts and this procedure can be applied as seismic assessment method to any culvert shape, size, and material.

Kriging metamodels for the dynamic response of high-rise buildings with outrigger systems and fragility estimates for seismic and wind loads

This paper proposes kriging metamodels for the dynamic response of high-rise buildings with outrigger systems subject to seismic and wind loads.Three types of outrigger systems are considered.Three-dimensional(3D)finite element models of high-rise buildings with outrigger systems are developed using ANSYS.Data generated from the finite element models are used to develop the proposed kriging metamodels.A sensitivity analysis is then carried out to determine the most sensitive input parameters in kriging metamodels to gain insights and suggest possible future developments.The proposed kriging metamodels are used to develop fragility estimates for high-rise buildings with three types of outrigger systems under seismic and wind loads.

Reliability analysis of reinforced concrete columns under combined seismic and blast loads

It is possible for certain building structures to encounter both the seismic load and blast load during their service life.With the development of the economy and the increase of security demand,the need for design of building structures against multi-hazard is becoming more and more obvious.Therefore,the damage analysis of building structures under the combined action of multiple hazards has become a very urgent requirement for disaster prevention and reduction.In this paper,the refined finite element model of reinforced concrete(RC)columns is established by using the explicit dynamic analysis software LS-DYNA.Combined with the Monte Carlo method,the damage law of RC columns under the combined action of random single earthquake or explosion disaster and multi-hazard is studied,and the damage groups are distinguished according to the damage index.Based on the support vector machine(SVM)algorithm,the dividing line between different damage degree groups is determined,and a rapid method for determining the damage degree of RC columns under the combined seismic and blast loads is proposed.Finally,suggestions for the design of RC column against multi-disaster are put forward.

Pseudo-static stability analysis of rock slopes reinforced by passive bolts using the generalized Hoek-Brown criterion

The stability analysis of passive bolt-reinforced rock slopes under seismic loads is investigated within the framework of the kinematic approach of limit analysis theory.A pseudo-static method is adopted to account for the inertial forces induced in the rock mass by seismic events.The strength properties of the rock material are described by a modified Hoek-Brown strength criterion,whereas the passive bolts are modeled as bar-like inclusions that exhibit only resistance to tensile-compressive forces.Taking advantage of the ability to compute closed-form expressions for the support functions associated with the modified Hoek-Brown strength criterion,a rotational failure mechanism is implemented to derive rigorous lower bound estimates for the amount of reinforcement strength to prevent slope failure.The approach is then applied to investigating the effects of relevant geometry,strength and loading parameters in light of a preliminary parametric study.The accuracy of the approach is assessed by comparison of the lower bound estimates with finite element limit analysis solutions,thus emphasizing the ability of the approach to properly predict the stability conditions and to capture the essential features of deformation localization pattern.Finally,the extension of the approach to account for slipping at the interface between reinforcements and surrounding rock mass is outlined.

Ground vibration analysis under combined seismic and high-speed train loads

The rise of high-speed railway induces an increased probability of serious derailment accidents of operating high-speed trains during earthquakes.A two-and-half-dimensional finite element model(2.5D FEM)was developed to investigate the ground vibration under combined seismic and high-speed train loads.Numerical examples were demonstrated and the proposed method was turned out to provide an effective means for estimating ground vibration caused by high-speed train load during earthquakes.The dynamic ground displacement caused by combined seismic and high-speed train loads increases with the increase of the train speed,and decreases with the increase of the stiffness of ground soil.Compared with the seismic load alone,the coupling effect of the seismic and high-speed train loads results in the low-frequency amplification of ground vibration.The moving train load dominants the medium–high frequency contents of the ground vibration induced by combined loads.It is observed that the coupling effects are significant as the train speed is higher than a critical speed.The critical train speed increases with the increase of the ground stiffness and the intensity of the input earthquake motion.

A comprehensive review on coupling vibrations of train-bridge systems under external excitations

In recent years,high-speed railways in China have developed very rapidly,and the number and span of the railway bridges are keeping increasing.Meanwhile,frequent extreme disasters,such as strong winds,earthquakes and floods,pose a significant threat to the safety of the train–bridge systems.Therefore,it is of paramount importance to evaluate the safety and comfort of trains when crossing a bridge under external excitations.In these aspects,there is abundant research but lacks a literature review.Therefore,this paper provides a comprehensive state-of-the-art review of research works on train–bridge systems under external excitations,which includes crosswinds,waves,collision loads and seismic loads.The characteristics of external excitations,the models of the train–bridge systems under external excitations,and the representative research results are summarized and analyzed.Finally,some suggestions for further research of the coupling vibration of train–bridge system under external excitations are presented.