Numerical analysis on seismic performance of underground structures in liquefiable interlayer sites from centrifuge shaking table test

When an underground structure passes through a liquefiable soil layer,the soil liquefaction may pose a significant threat to the structure.A centrifuge shaking table test was performed to research the seismic response of underground structures in liquefiable interlayer sites,and a valid numerical model was obtained through simulation model test.Finally,the calibrated numerical model was used to perform further research on the influence of various distribution characteristics of liquefiable interlayers on the seismic reaction of underground structures.The key findings are as follows.The structure faces the most unfavorable condition once a liquefiable layer is located in the middle of the underground structure.When a liquefiable layer exists in the middle of the structure,the seismic reactions of both the underground structure and model site will increase with the rise of the thickness of the liquefiable interlayer.The inter-story drift of the structure in the non-liquefiable site is much smaller than that in the liquefiable interlayer site.The inter-story drift of the structure is not only associated with the site displacement and the soil-structure stiffness ratio but also closely associated with the slippage of the soil-structure contact interface under the condition of large deformation of the site.

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.

An improved pseudo-static method for seismic resistant design of underground structures

This paper describes a commonly used pseudo-static method in seismic resistant design of the cross section of underground structures. Based on dynamic theory and the vibration characteristics of underground structures, the sources of errors when using this method are analyzed. The traditional seismic motion loading approach is replaced by a method in which a one-dimensional soil layer response stress is differentiated and then converted into seismic live loads. To validate the improved method, a comparison of analytical results is conducted for internal forces under earthquake shaking of a typical shallow embedded box-shaped subway station structure using four methods： the response displacement method, finite element response acceleration method, the finite element dynamic analysis method and the improved pseudo-static calculation method. It is shown that the improved finite element pseudo-static method proposed in this paper provides an effective tool for the seismic design of underground structures. The evaluation yields results close to those obtained by the finite element dynamic analysis method, and shows that the improved finite element pseudo-static method provides a higher degree of precision.

DYNAMIC LOAD ANALYSIS OF UNDERGROUND STRUCTURE UNDER EFFECT OF BLAST WAVE

A semi-analytical method of solving the problem of dynamic stress concentration of arbitrary underground structure under the effect of blast waves was introduced. Using the Fourier transform theory, the shock waves （in the forms of SH-waves） can be converted into frequency bands. After employing complex functions and conformal mapping, the admittance functions of various underground structures were obtained. Then, the problem of the time domain dynamic stress response of underground structure can be easily solved through the Fourier inverse transform. At last, the results and curves of the dynamic stress for the square, triangle and horseshoe cavity were presented.

Problems of durability and reinforcement measures for underground structures in China

In this paper, the bolt- and cable-supported structures mainly refer to anchored cables, anchored bolts, soil nails and other commonly used reinforcing and supporting structures in geotechnical engineering, as well as reinforced soil structures in permanent works. They are often used in combination, or formed into composite bolt-and cable-supported structures, with other traditional construction methods and relevant measures. Distinct characteristics of such structures are that they are most often invisible, exposed to more severe underground corrosive environments and with strict durability requirements. A number of serious durability problems of underground structures are discussed and major achievements and advances in China and abroad in terms of durability and reinforcement measures for underground structures are reviewed, followed by comprehensive analyses. Some suggestions for those problems are put forward.

FUNDAMENTAL OF DYNAMICAL ANALYSIS OF THE BLAST-RESISTANT UNDERGROUND STRUCTURES

In this paper, the generalized variational principle of dynamic analysis for the blast-resistant underground structures is established, and the corresponding generalized functional of elastoplastic analysis for underground structures is derived, and the generalized variational principle of nonconservative system is given, thus the fundamental of dynamical analysis for underground structures to resist blast is proposed. Finally, for the underground cylindrical structure to resist blast, dynamical calculations are made, and compared with the test results.

Analysis of Interf acial Zone Properties and Permeability of Concrete in Underground Structure

Chloride diffusion coefficient and water penetration depth of 3 types concrete were studied. The experimental results show that the concrete permeability decreases itself in the order as follow: pure portland cement concrete(CO), concrete added with fly ash(C1), concrete added with both fly ash and silica fume(C2). SEM and microhardness analyses show that the properties of interfacial zone are significantly influenced by silica fume. With the improvement of interfacial zone properties, the permeability especially the Chloride ion diffusivity of concrete significantly decreases.

Numerical investigation on seismic performance of a shallow buried underground structure with isolation devices

A design procedure for improving the seismic performance of unequal-span underground structures by installing isolation devices at the top end of columns is proposed based on the seismic failure mode of frame-type underground structures and the design concept of critical support columns.A two-dimensional finite element model(FEM)for a soil-underground structure with an unequal-span interaction system was established to shed light on the effects of a complex subway station with elastic sliding bearings(ESB)and lead rubber bearings(LRB)on seismic mitigation.It was found that the stiffness and internal force distribution of the underground structure changed remarkably with the installation of isolation devices at the top end of the columns.The constraints of the beam-column joints were significantly weakened,resulting in a decrease in the overall lateral stiffness and an increase in the structural lateral displacement.The introduction of the isolation device effectively reduces the internal force and seismic damage of the frame column;however,the tensile damage to the isolation structure,such as the roof,bottom plate,and sidewall,significantly increased compared to those of the non-isolation structure.Although the relative slip of the ESB remains within a controllable range under strong earthquake excitation as well as frame columns with stable vertical support and self-restoration functions,the LRB shows a better performance during seismic failure and better lateral displacement response of the unequal-span underground structure.The analysis results provide new ideas and references for promoting the application of seismic isolation technology in underground structures.

A comparative analysis of seismic response of shallow buried underground structure under incident P,SV and Rayleigh waves

In this study,A time-domain seismic response analysis method and a calculation model of the underground structure that can realize the input of seismic P,SV and Rayleigh waves are established,based on the viscoelastic artificial boundary elements and the boundary substructure method for seismic wave input.After verifying the calculation accuracy,a comparative study on seismic response of a shallow-buried,double-deck,double-span subway station structure under incident P,SV and Rayleigh waves is conducted.The research results show that there are certain differences in the cross-sectional internal force distribution characteristics of underground structures under different types of seismic waves.The research results show that there are certain differences in the internal force distribution characteristics of underground structures under different types of seismic waves.At the bottom of the side wall,the top and bottom of the center pillar of the underground structure,the section bending moments of the underground structure under the incidences of SV wave and Rayleigh wave are relatively close,and are significantly larger than the calculation result under the incidence of P wave.At the center of the side wall and the top floor of the structure,the peak value of the cross-sectional internal force under the incident Rayleigh wave is larger than the calculation result under SV wave.In addition,the floor of the underground structure under Rayleigh waves vibrates in both the horizontal and vertical directions,and the magnification effect in the vertical direction is more significant.Considering that the current seismic research of underground structures mainly considers the effect of body waves such as the shear waves,sufficient attention should be paid to the incidence of Rayleigh waves in the future seismic design of shallow underground structures.

Seismic performance analysis of underground structures based on random field model of soil mechanical parameters

Soils with spatial variability are the product of natural history.The mechanical properties tested by soil samples from boreholes in the same soil layer may be different.Underground structure service in surrounding soils,their seismic response is controlled by the deformation of the surrounding soils.The variability of soil mechanical parameters was not considered in the current research on the seismic response of underground structures.Therefore,a random field model was established to describe the spatial variability of surrounding soils based on the random field theory.Then the seismic response of underground structures in the random field was simulated based on the time-domain explicit global FEM analysis,and the soil mechanical parameters and earthquake intensity influencing the seismic response of surrounding soils and underground structures were studied.Numerical results presented that,the randomness of soil parameters does not change the plastic deformation mode of surrounding soils significantly.The variation coefficients of inter-story deformation of structures and lateral deformation of columns are much smaller than that of mechanical parameters,and the randomness of soil parameters has no obvious effect on the structural deformation response.

Influence of soil to structure stiffness on the accuracy of the pushover method for underground structures

The pushover method for underground structures is a seismic analysis method featured by high calculation accuracy and a simple implementation process.The method has been widely used in seismic design and other related scientific research;however,the influence of different soil-structure flexibility ratios on the accuracy of this method is still not well understood.In this study,we select the cross-section structures beneath the Daikai subway station as the research object and establish 12 finite element analysis models with different soil-structure flexibility ratios using ABAQUS.All models are computed by the dynamic time-history method or the pushover method.Furthermore,the dynamic time-history solution result is taken as the standard solution,and the precision and application of the pushover analysis method are discussed based on the parameters of peak interlayer displacement and peak internal force of the middle column section.The results show that the soil-structure flexibility ratio has a significant influence on the calculation accuracy of the pushover method,and the calculation accuracy of this method is the most ideal when the soil-structure flexibility is equal to 1.The research results can provide significant references for the seismic design of underground structures or the improvement of simplified seismic analysis methods.

Shaking table tests and numerical simulation of dynamic properties of underground structures

It is considered thai the damage of the underground structures caused by earthquakes is minor for a long time. However, the catastrophic damages induced by several recent earthquakes （e. g. Kobe earthquake in 1995 ） revealed that the study on the dynamic properties of the underground structures is indispensable. The dynamic behavior and damage mechanism of underground structure are analyzed by using shaking table tests （ both shallow-and deep-buried） and numerical simulation （3D FEM） including horizontal and vertical input motions, individually and simultaneously. From the results, the underground structure collapsed due to strong horizontal forces although vertical deformation is not negligible. The vertical excitation increases the response of structure, especially the stress and shear stress at the upper section; the soil influenced the property of soilstructure system. In the same excitation, the response in shallow-buried test is larger than deep case. Both overburden and vertical earthquake play important roles in the response of structure and those are two critical aspects in the design of the large-span underground structures, such as subway stations.

Dynamic Properties of Long Large Cross-section Underground Structures in Dynamic Seismic Analysis

Seismic safety of underground structures is one of the main concerns in underground space exploitation. As the first step for dynamic seismic response analysis, the free vibration of long large cross-section underground structures is studied in the present paper. The general free transverse vibration motion equation of long large cross-section underground structure is derived with the comprehensive consideration of internal and external damping, effects of shear, cross-sectional rotational inertia and axial force, and a twoparameter soil model. In this way, Timoshenko＇s beam theory is extended. Two limit cases of free transverse vibration of underground structures are discussed. Parameter study shows that in general wave propagation velocities in structures increase with soil elastic parameters. However the influence of Winkler＇s parameter k is significant while the effect of the second soil elastic parameter gp is insignificant. The free vibration frequency of underground structures increases with relative wave number and soil elastic parameters. Unlike the influence of soil elastic parameters on wave propagation velocities, the influence of soil elastic parameters k and gp on the vibration frequency of underground structures have the same order; therefore the influence of the second soil parameter gp on the free vibration of underground structures should not be neglected in dynamic seismic analysis of underground structures

Mechanical responses of underground carriageway structures due to construction of metro tunnels beneath the existing structure:A case study

To understand the mechanical response pattern of the existing structure and ground due to the construction of metro tunnels underneath,the finite difference method is adopted to study the torsional deformation and stress variation of the existing structure and the effect of underground carriageway structures on the surface subsidence.The curves of the maximum differential subsidence,torsion angle,and distortion of the cross-section of the existing structure show two peaks in succession during traversing of two metro tunnels beneath it.The torsion angle of the existing structure changes when the two tunnels traverse beneath it in opposite directions.The first traversing of the shield tunnel mainly induces the magnitude variation in torsional deformation of the existing structure,but the second traversing of the subsurface tunnel may cause a dynamic change in the magnitude and form of torsional deformation in the existing structure.The shielding effect can reduce the surface subsidence caused by metro tunnel excavation to a certain extent,and the development trend of subsidence becomes slower as the excavation continues.

Numerical analysis of seismic response of rectangular underground structure in coral sand

The underground structure in coral sand is threatened by earthquake.The special dynamic characteristics of coral sand were realized by finite difference program.Specifically,the stress–strain loops,shear modulus attenuation and hysteresis behaviour of coral sand were simulated using hysteresis damping.On this basis,numerical models were established to study the seismic response of the rectangular underground structure in coral sand,and the fluid–solid coupling and soil-structure interaction were considered.The results illustrate that the increasing relative density of coral sand foundation reduces the excess pore water pressure(EPWP),but amplifies the horizontal dynamic soil pressure of the coral sand-underground structure system.The increase in the permeability coefficient of coral sand reduces the EPWP accumulation,which leads to an increase of the stiffness and a decrease of the acceleration amplification of coral sand sites.

A numerical framework for underground structures in layered ground under inclined P-SV waves using stiffness matrix and domain reduction methods

A numerical framework was proposed for the seismic analysis of underground structures in layered ground under inclined P-SV waves.The free-field responses are first obtained using the stiffness matrix method based on plane-wave assumptions.Then,the domain reduction method was employed to reproduce the wavefield in the numerical model of the soil–structure system.The proposed numerical framework was verified by providing comparisons with analytical solutions for cases involving free-field responses of homogeneous ground,layered ground,and pressure-dependent heterogeneous ground,as well as for an example of a soil–structure interaction simulation.Compared with the viscous and viscous-spring boundary methods adopted in previous studies,the proposed framework exhibits the advantage of incorporating oblique incident waves in a nonlinear heterogeneous ground.Numerical results show that SV-waves are more destructive to underground structures than P-waves,and the responses of underground structures are significantly affected by the incident angles.

Practical seismic analysis of large underground structures: Theory and application

Due to the conceptual clarity and calculational simplicity, practical methods for seismic analysis have been widely used in seismic design and calculation of underground structures. All of the commonly adopted practical methods assume that the earthquake inertia force of the analysis model equals that of free-field. However, this assumption neglects the influence of underground structures on their surrounding soil layers, and may lead to significant errors in both conceptual and computational terms when the size of a structure increases. This article focuses on the practical seismic analysis of large underground structures.Theoretical derivation is demonstrated on the basis of the establishment of mechanical models of the soil-structure system and free-field, and consequently, the quantitative relation between the seismic acceleration response of the soil-structure system and that of free-field is obtained. This relation can be used to revise the earthquake inertia force applied to the analysis model so that the calculation accuracy is effectively improved. By doing so, a revised pushover analysis method, which combines the traditional pushover analysis and theoretical derivation, is proposed in order to be appropriate to seismic analysis of large underground structures. Moreover, an example of application of the proposed method is given, in which a selected large underground structure is analyzed. The results show that this revised method has higher efficiency than the traditional method thanks to the revision of the earthquake inertia force.

Pushover analysis of underground structures:Method and application

Pushover analysis is common because of its conceptual simplicity and computational attractiveness in computing seismic demand.Considering that traditional pushover analysis is restricted in underground structures due to the stark differences in the seismic response characteristics of surface structures,this paper proposes a pushover analysis method for underground structures and its application in seismic damage assessment.First,three types of force distribution are presented based on ground response analysis.Next,the target displacements and analysis models are established according to force-based and performance-based design.Then,the pushover analysis procedure for underground structures is described.Next,the applicability of pushover analysis to underground structures is verified by comparing the responses of a Chongwenmen subway station determined by the proposed procedure and by nonlinear response history analysis.In addition,two other points are made:that the inverted triangular distribution of effective earthquake acceleration is more practical than the other two distributions,and that performance-based design is more effective than force-based design.Finally,a cyclic reversal loading pattern based on one cycle of reversal loads as an earthquake event is presented and applied to the seismic damage assessment of underground structures.The results show that the proposed pushover analysis can be effectively applied to the seismic design and damage assessment of underground structures.

A flexible various-scale approach for soil-structure interaction and its application in seismic damage analysis of the underground structure of nuclear power plants

In simulations of geotechnical engineering, interface elements are versatile tools and are widely used in the modeling of the relative displacements between soils and structures. To consider the case of a local failure adjacent to a soil-structure interaction region, a partial mesh refinement should be performed. In this study, a three-dimensional(3 D) interface element with an arbitrary number of nodes is developed as a new technique to reduce the complexity and difficulty of managing the various scales between soil and structure. An asymmetric number of nodes is permissible on the two sliding surfaces. In this manner, soil and structure can be discretized independently, and the various-scale model is established conveniently and rapidly. The accuracy of the proposed method is demonstrated through numerical examples. The various-scale approach is employed in an elasto-plastic seismic damage analysis of a buried concrete drainage culvert of a nuclear power plant. The results indicate that by applying the proposed method, the number of elements decreased by 72.5%, and the computational efficiency improved by 59% with little influence on accuracy. The proposed method is powerful for local damage evolution analyses of both soil and structure and possesses great practical significance and the potential for further application, especially for nonlinear analysis of large-scale geotechnical engineering.

An end-to-end 3D seismic simulation of underground structures due to point dislocation source by using an FK-FEM hybrid approach

Based on the domain reduction idea and artificial boundary substructure method,this paper proposes an FK-FEM hybrid approach by integrating the advantages of FK and FEM(i.e.,FK can efficiently generate high-frequency three translational motion,while FEM has rich elements types and constitutive models).An advantage of this approach is that it realizes the entire process simulation from point dislocation source to underground structure.Compared with the plane wave field input method,the FK-FEM hybrid approach can reflect the spatial variability of seismic motion and the influence of source and propagation path.This approach can provide an effective solution for seismic analysis of underground structures under scenario of earthquake in regions where strong earthquakes may occur but are not recorded,especially when active faults,crustal,and soil parameters are available.Taking Daikai subway station as an example,the seismic response of the underground structure is simulated after verifying the correctness of the approach and the effects of crustal velocity structure and source parameters on the seismic response of Daikai station are discussed.In this example,the influence of velocity structure on the maximum interlayer displacement angle of underground structure is 96.5%and the change of source parameters can lead to the change of structural failure direction.