Seismically induced racking of tunnel linings

An analytical procedure is presented for evaluating the racking deformation of rectangular and circular tunnel linings caused by soil–structure interaction during a seismic event. The procedure, as applied to rectangular linings, is supplementary to that previously published by Penzien and Wu (Earthquake Engineering and Structural Dynamics, 1998; 27 :283–300) for circular linings. Copyright © 2000 John Wiley & Sons, Ltd.     

不滑移状态下深埋圆形隧道地震响应研究

地下结构的地震响应主要取决于由地震波传播产生的土体变形与土结相互作用。剪切波传播过程中将会引起隧道衬砌的椭圆化变形,进而降低衬砌有效承载力。剪切波作用下的深埋圆形隧道可认为处于均质的纯剪状态,基于相对刚度法的拟静力解析解可充分考虑土结相互作用对隧道结构内力的影响。基于此,本文将通过有限元数值分析获得的自由场地地基变形引入不滑移状态下深埋圆形隧道内力求解公式,并结合二维和三维数值模拟途径,将动力分析结果与解析解结果进行对比分析,以评价各种解析方法的适用性和数值途径的可靠性。     

Bridge–embankment interaction under transverse ground excitation

Seismic performance and dynamic response of bridge–embankments during strong or moderate ground excitations are investigated through finite element (FE) modelling and detailed dynamic analysis. Previous research studies have established that bridge–embankments exhibit increasingly flexible performance under high‐shear deformation levels and that soil displacements at bridge abutment supports may be significant particularly in the transverse direction. The 2D equation of motion is solved for the embankment, in order to evaluate the dynamic characteristics and to describe explicitly the seismic performance and dynamic response under transverse excitations accounting for soil nonlinearities, soil–structure interaction and imposed boundary conditions (BCs). Using the proposed model, equivalent elastic analysis was performed so as to evaluate the dynamic response of approach embankments while accounting for soil–structure interaction. The analytical procedures were applied in the case of a well‐documented bridge with monolithic supports (Painter Street Overcrossing, PSO) which had been instrumented and embankment participation was identified from its response records after the 1971 San Fernando earthquake. The dynamic characteristics and dynamic response of the PSO embankments were evaluated for alternative BCs accounting for soil–structure interaction. Explicit expressions for the evaluation of the critical embankment length L_c are provided in order to quantify soil contribution to the overall bridge system under strong intensity ground excitations. The dynamic response of the entire bridge system (deck–abutments–embankments) was also evaluated through simplified models that considered soil–structure interaction. Results obtained from this analysis are correlated with those of detailed 3D FE models and field data with good agreement. Copyright © 2007 John Wiley & Sons, Ltd.     

Three-dimensional dynamic soil–structure interaction analysis in the time domain

A new numerical procedure is proposed for the analysis of three-dimensional dynamic soil–structure interaction in the time domain. In this study, the soil is modelled as a linear elastic solid, however, the methods developed can be adapted to include the effects of soil non-linearities and hysteretic damping in the soil. A substructure method, in which the unbounded soil is modelled by the scaled boundary finite-element method, is used and the structure is modelled by 8–21 variable-number-node three-dimensional isoparametric or subparametric hexahedral curvilinear elements. Approximations in both time and space, which lead to efficient schemes for calculation of the acceleration unit-impulse response matrix, are proposed for the scaled boundary finite-element method resulting in significant reduction in computational effort with little loss of accuracy. The approximations also lead to a very efficient scheme for evaluation of convolution integrals in the calculation of soil–structure interaction forces. The approximations proposed in this paper are also applicable to the boundary element method. These approximations result in an improvement over current methods. A three-dimensional Dynamic Soil–Structure Interaction Analysis program (DSSIA-3D) is developed, and seismic excitations (S-waves, P-waves, and surface waves) and externally applied transient loadings can be considered in analysis. The computer program developed can be used in the analysis of three-dimensional dynamic soil–structure interaction as well as in the analysis of wave scattering and diffraction by three-dimensional surface irregularities. The scattering and diffraction of seismic waves (P-, S-, and Rayleigh waves) by various three-dimensional surface irregularities are studied in detail, and the numerical results obtained are in good agreement with those given by other authors. Numerical studies show that the new procedure is suitable and very efficient for problems which involve low frequencies of interest for earthquake engineering. Copyright © 1999 John Wiley & Sons Ltd     

Steady-state harmonic response of a rigid plate bearing on a liquid-saturated poroelastic halfspace

Soil–structure interaction problems are typically modelled by assuming subgrade behaviour to be either elastic or viscoelastic. Herein, compliance functions that may be used to solve soil–structure interaction problems are evaluated by treating the subgrade as a liquid-saturated poroelastic material whose behaviour is governed by Biot's theory. The compliances are evaluated for the harmonic rocking and vertical motions of rigid permeable and impermeable plates bearing on a poroelastic halfspace. Comparisons are made with elastic solutions which assume the subgrade to be either completely drained or undrained. Also, solid and fluid contact stresses are reported for the poroelastic case and compared to the solid contact stresses for the elastic cases.     

Dynamic response of an eccentrically lined circular tunnel in poroelastic soil under seismic excitation

An exact analysis for two-dimensional dynamic interaction of monochromatic progressive plane compressional and shear seismic waves with a permeable circular tunnel lining of circumferentially varying wall thickness buried in a boundless porous elastic fluid-saturated formation is presented. The novel features of Biot dynamic theory of poroelasticity in conjunction with the translational addition theorems for cylindrical wave functions, along with the appropriate wave field expansions and the pertinent boundary conditions are employed to develop a closed-form solution in form of infinite series. The analytical results are illustrated with numerical examples in which an air-filled and water-saturated permeable tunnel lining of variable wall thickness, embedded within water-saturated surrounding formations of distinct frame properties (soft, stiff, and stiff viscoelastic soil), is insonified by fast compressional or shear waves at selected angles of incidence. The effects of liner eccentricity, interface permeability, formation material type, incident wave frequency, and angle of incidence on the hoop stress amplitude are evaluated and discussed for representative values of the parameters characterizing the system. Limiting cases are considered and good agreements with the solutions available in the literature are obtained.     

Quantifying the effects of plant litter in the topsoil on the soil detachment process by overland flow in typical grasslands of the Loess Plateau,China

Plant litter can be incorporated into topsoil by a natural process, affecting the soil erosion process. This is a widespread phenomenon in erosion-prone areas. This study was conducted to investigate the effect of litter incorporation on the process of soil detachment on the Loess Plateau, China. Four common plant litters (Bothriochloa ischaemum L. Keng., Artemisia sacrorum Ledeb., Setaria viridis L. Beauv., and Artemisia capillaris Thunb.) were collected, then incorporated into the silt loam soil at five rates (0.1, 0.4, 0.7, 1.0, and 1.3 kg m⁻²) on the basis of our field investigation. Twenty litter–soil treatments and one bare soil control were prepared. After 50 days of natural stabilization, 30 soil samples of each treatment were collected. We used a flume test to scour the soil samples under six flow shear stress conditions (5.66, 8.31, 12.21, 15.55, 19.15, and 22.11 Pa). The results showed that the different incorporated litter masses and morphological characteristics, such as litter tissue density (ranging from 0.52 to 0.68 g cm⁻³), length density (2.34 to 91.00 km m⁻³), surface area density (LSAD; 27.9 to 674.2 m² m⁻³), and volume ratio (0.003 to 0.050 m³ m⁻³), caused varied soil detachment capacities (0.043 to 4.580 kg·m⁻²·s⁻¹), rill erodibilities (0.051 to 0.237 s m⁻¹), and critical shear stresses (2.02 to 6.83 Pa). The plant litter incorporated within the soil reduced the soil detachment capacities by 38%–59%, lowered the rill erodibilities by 32%–46%, and increased the critical shear stresses by 98%–193% compared with the bare soil control. The soil containing B. ischaemum (L.) Keng. litter was more resistant to erosion. By comparing different parameters, we found that the contact area between the litter and soil was the main factor affecting the soil detachment process. The soil erosion resistance increased with the increasing contact area between the soil and litter. Furthermore, the litter incorporation effect on rill erodibility can be comprehensively reflected by LSAD (R² = .93; Nash–Sutcliffe efficiency = 0.79), which could be used to adjust the rill erodibility parameter in physical process-based soil erosion models.     

Kinematic soil–structure interaction for long-span cable-supported bridges

A general procedure is presented to study the dynamic soil–structure interaction effects on the response of long-span suspension and cable-stayed bridges subjected to spatially varying ground motion at the supporting foundations. The foundation system is represented by multiple embedded cassion foundations and the frequency-dependent impedance matrix for the multiple foundations system takes into account also the cross-interaction among adjacent foundations through the soil. To illustrate the potential implementation of the analysis, a numerical example is presented in which the dynamic response of the Vincent–Thomas suspension bridge (Los Angeles, CA) subjected to the 1987 Whittier earthquake is investigated. Although both kinematic and inertial effects are included in the general procedure, only the kinematic effects of the soil–structure interaction are considered in the analysis of the test case. The results show the importance of the kinematic soil–foundation interaction on the structural response. These effects are related to the type, i.e. SH-, SV-, P- or Rayleigh waves and to the inclination of the seismic wave excitation. Moreover, rocking components of the foundation motion are emphasized by the embedment of the foundation system and greatly alter the structural response.     

饱和土体-地下综合管廊结构地震响应分析

将土体视为固-液两相介质,基于饱和土体有效应力原理,建立饱和土体-地下综合管廊结构体系相互作用动力模型:在地应力平衡的静力状态下采用Duncan-Chang非线性弹性本构模型,在地震波作用的动力状态下采用Davidenkov非线性黏弹性本构模型;考虑饱和土体黏弹性动力人工边界条件,将地震动作用转化为作用在人工边界节点上的动力荷载。模型考察不同地震波时程、地震波加速度峰值、入射角度、孔隙率以及地应力场的影响,得出如下结论:(1)地震波的卓越周期与场地卓越周期相近时引起结构上的变形最大;随着地震波加速度峰值的增大结构变形增大;随着地震波入射角度的增加结构变形增大,地震波斜入射情况下产生的行波效应使得结构变形最大。(2)土体材料的孔隙水压力是影响地震中结构变形的主要因素之一。(3)将土体材料考虑为单相介质时结构上的变形要比考虑为固-液两相介质时大得多,直接将饱和土体场地中得到的地震波等效荷载施加到单相土介质-结构动力相互作用模型上,能够得到与完全基于有效应力法一致的结果。     

Circular tunnels in sand: dynamic response and efficiency of seismic analysis methods at extreme lining flexibilities

The paper discusses the seismic response of circular tunnels in dry sand and investigates the efficiency of current seismic analysis methods at extreme lining flexibilities. Initially, a dynamic centrifuge test on a flexible circular model tunnel, embedded in dry sand, is analyzed by means of rigorous full dynamic analysis of the coupled soil–tunnel system, applying various non-linear soil and soil–tunnel interface models. The numerical results are compared to the experimental ones, aiming to better understand the recorded response and calibrate the numerical models. Then a series of numerical analyses are conducted using the validated numerical model, in order to investigate the effect of the tunnel lining rigidity on the dynamic response of the soil–tunnel system. In parallel, the accuracy of currently used simplified analysis methods is evaluated, by comparing their predictions with the results of the a priori more accurate and well validated numerical models. The comparative analyses allow us to highlight and discuss several crucial aspects of the soil-tunnel system seismic response, including (1) the post-earthquake residual values of the lining forces, which are amplified with the increase of the flexibility of the tunnel and (2) the importance of the soil-tunnel interface conditions. It is finally concluded that simplified analysis methods may provide a reasonable framework for the analysis at a preliminary stage, under certain conditions.     

Generalized method for non-linear seismic response analysis of a three dimensional soil–structure interaction system

Previous achievements using the dynamic non-linear analysis of an interaction system are reviewed briefly, after which a three dimensional (3D) model of the stress redistribution of soil based on the Mohr–Coulomb failure law is presented to evaluate the unbalanced tensor at every iteration in the load transfer method. A 3D, full non-linear analysis was used to examine the validity and accuracy of results obtained by 2D analysis by combining the model of redistributed stresses proposed here with the joint element model. Based on the numerical solution reported here, we concluded that both the 3D and 2D models of stress redistribution work well and reflect the yielding pattern of soil during excitation, but the former is more realistic. The failure area in the structural zone obtained by 3D analysis is slightly larger but similar to that obtained by 2D analysis. The ratio of maximum strain to yield strain and non-linear time ratio, β_s, for the soil elements in the structural zone are also a little larger. In contrast, the maximum separation values for the joint elements are much smaller and the separation pattern for the x-side wall interface is the reverse of that found by 2D analysis. These values, however, affect only responses in the short period range and the regions close to the interface. In general, the tendencies shown by 2D analysis for the effects of non-linear behaviour on structural responses are confirmed for the parameters investigated.     

Excavation of subglacial bedrock channels by seasonal meltwater flow

Subglacial water flow drives the excavation of a variety of bedrock channels including tunnel valleys and inner gorges. Subglacial floods of various magnitudes – events occurring once per year or less frequently with discharges larger than a few hundred cubic metres per second – are often invoked to explain the erosive power of subglacial water flow. In this study we examine whether subglacial floods are necessary to carve bedrock channels, or if more frequent melt season events (e.g. daily production of meltwater) can explain the formation of substantial bedrock channels over a glacial cycle. We use a one‐dimensional numerical model of bedrock erosion by subglacial meltwater, where water flows through interacting distributed and channelized drainage systems. The shear stresses produced drive bedrock erosion by bed‐ and suspended‐load abrasion. We show that seasonal meltwater discharge can incise an incipient bedrock channel a few tens of centimetres deep and several metres wide, assuming abrasion is the only mechanism of erosion, a particle size of D=256 mm and a prescribed sediment supply per unit width. Using the same sediment characteristics, flood flows yield wider but significantly shallower bedrock channels than seasonal meltwater flows. Furthermore, the smaller the shear stresses produced by a flood, the deeper the bedrock channel. Shear stresses produced by seasonal meltwater are sufficient to readily transport boulders as bedload. Larger flows produce greater shear stresses and the sediment is carried in suspension, which produces fewer contacts with the bed and less erosion. We demonstrate that seasonal meltwater discharge can excavate bedrock volumes commensurate with channels several tens of metres to a few hundred metres wide and several tens of metres deep over several thousand years. Such simulated channels are commensurate with published observations of tunnel valleys and inner gorges. Copyright © 2018 John Wiley & Sons, Ltd.     

A time‐domain seismic SSI analysis method for inelastic bridge structures through the use of a frequency‐dependent lumped parameter model

It is highlighted in the past that the soil–structure interaction phenomenon can produce a significant alteration on the response of a bridge structure. A variety of approaches has been developed in the past, which is capable of tackling the soil–structure interaction problem from different perspectives. The popular approach of a discretized truncated finite element model of the soil domain is not always a numerically viable solution, especially for computationally demanding simulations such as the probabilistic fragility analysis of a bridge structure or the real time hybrid simulation. This paper aims to develop a complete modeling procedure that is capable of coping with the soil–structure interaction problem of inelastic bridge structures through the use of a frequency dependent lumped parameter assembly. The proposed procedure encounters accuracy and global stability issues observed on past methods while maintaining the broad applicability of the method by any commercial FEM software. A case study of an overpass bridge structure under earthquake excitations is illustrated in order to verify the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Evaluation of seismic performance of pile‐supported models in liquefiable soils

The seismic performance of four pile‐supported models is studied for two conditions: (i) transient to full liquefaction condition, i.e. the phase when excess pore pressure gradually increases during the shaking; (ii) full liquefaction condition, i.e. defined as the state where the seismically induced excess pore pressure equalises to the overburden stress. The paper describes two complementary analyses consisting of an experimental investigation, carried out at normal gravity on a shaking table, and a simplified numerical analysis, whereby the soil–structure interaction (SSI) is modelled through non‐linear Winkler springs (commonly known as p–y curves). The effects of liquefaction on the SSI are taken into account by reducing strength and stiffness of the non‐liquefied p–y curves by a factor widely known as p‐multiplier and by using a new set of p–y curves. The seismic performance of each of the four models is evaluated by considering two different criteria: (i) strength criterion expressed in terms of bending moment envelopes along the piles; (ii) damage criterion expressed in terms of maximum global displacement. Comparison between experimental results and numerical predictions shows that the proposed p–y curves have the advantage of better predicting the redistribution of bending moments at deeper elevations as the soil liquefies. Furthermore, the proposed method predicts with reasonable accuracy the displacement demand exhibited by the models at the full liquefaction condition. However, disparities between computed and experimental maximum bending moments (in both transient and full liquefaction conditions) and displacement demands (during transient to liquefaction condition) highlight the need for further studies. Copyright © 2016 The Authors Earthquake Engineering & Structural Dynamics Published by John Wiley & Sons Ltd.     

Free‐vibration analysis of a three‐dimensional soil–structure system

A procedure which involves a non‐linear eigenvalue problem and is based on the substructure method is proposed for the free‐vibration analysis of a soil–structure system. In this procedure, the structure is modelled by the standard finite element method, while the unbounded soil is modelled by the scaled boundary finite element method. The fundamental frequency, and the corresponding radiation damping ratio as well as the modal shape are obtained by using inverse iteration. The free vibration of a dam–foundation system, a hemispherical cavity and a hemispherical deposit are analysed in detail. The numerical results are compared with available results and are also verified by the Fourier transform of the impulsive response calculated in the time domain by the three‐dimensional soil–structure–wave interaction analysis procedure proposed in our previous paper. The fundamental frequency obtained by the present procedure is very close to that obtained by Touhei and Ohmachi, but the damping ratio and the imaginary part of modal shape are significantly different due to the different definition of damping ratio. This study shows that although the classical mode‐superposition method is not applicable to a soil–structure system due to the frequency dependence of the radiation damping, it is still of interest in earthquake engineering to evaluate the fundamental frequency and the corresponding radiation damping ratio of the soil–structure system. Copyright © 2001 John Wiley & Sons, Ltd.     

A simple model for structural control including soil–structure interaction effects

A simple model for the seismic response of a one-storey structure subjected to active control in the presence of soil–structure interaction effects is presented. The approach is based on the successive use of equivalent 1-DOF oscillators which account for the effects of control and soil–structure interaction. Simple expressions for these oscillators based on exact analytical solutions of the control equations and approximate solutions of the interaction equations are presented. The study includes an evaluation of the effects of soil–structure interaction on the seismic response of actively controlled structures in which the control gains have been determined with and without inclusion of soil–structure interaction effects. A simple procedure to include the interaction effects on the control gains is also presented. © 1998 John Wiley & Sons, Ltd.     

地裂缝环境下马蹄形地铁隧道与土体相互作用的研究

以穿越地裂缝带的西安地铁2号线为研究背景,通过数值模拟对地裂缝作用下马蹄形地铁隧道与土体相互作用的机理进行了研究。研究结果表明：随着上、下盘位错量的增加,地裂缝处受影响的土体范围逐渐增大,土体的竖向位移也逐渐变大;上盘下降过程中,下盘隧道顶部沉降变形最大,上盘隧道顶部沉降变形最小;隧道的变形区域出现在预设地裂缝两侧,并且随着竖向位错的增大而增大,当错距d=100mm时,地裂缝处的隧道结构发生破坏。隧道的最大主应力位于结构出现裂缝和受剪切破坏的区域,随着位错量的增加,隧道的最大主应力变化剧烈。地裂缝处,隧道结构上部靠下盘区域受拉,靠上盘区域受压,隧道结构下部靠下盘区域受压,靠上盘区域受拉。在实际工程中,地铁隧道穿越地裂缝时,宜采用分段式隧道结构。     

Seismic response of underground utility tunnels: shaking table testing and FEM analysis

Underground utility tunnels are widely used in urban areas throughout the world for lifeline networks due to their easy maintenance and environmental protection capabilities. However, knowledge about their seismic performance is still quite limited and seismic design procedures are not included in current design codes. This paper describes a series of shaking table tests the authors performed on a scaled utility tunnel model to explore its performance under earthquake excitation. Details of the experimental setup are first presented focusing on aspects such as the design of the soil container, scaled structural model, sensor array arrangement and test procedure. The main observations from the test program, including structural response, soil response, soil-structure interaction and earth pressure, are summarized and discussed. Further, a finite element model (FEM) of the test utility tunnel is established where the nonlinear soil properties are modeled by the Drucker-Prager constitutive model; the master-slave surface mechanism is employed to simulate the soil-structure dynamic interaction; and the confining effect of the laminar shear box to soil is considered by proper boundary modeling. The results from the numerical model are compared with experiment measurements in terms of displacement, acceleration and amplification factor of the structural model and the soil. The comparison shows that the numerical results match the experimental measurements quite well. The validated numerical model can be adopted for further analysis.     

Numerical modeling for wave–seabed–pipe interaction in a non-homogeneous porous seabed

An evaluation of the wave-induced pore pressures and effective stresses has been recognized by marine geotechnical engineers as an important factor in the design of marine pipelines. Most previous investigations for such a problem have considered the pipeline as a rigid material. Thus, the internal stresses within the pipeline have not been examined in the wave–seabed–pipe interaction problem. In this paper, we consider the pipeline itself to be an elastic material, and link the analysis of the pipeline with the wave–seabed interaction problem. Based on the numerical model presented, the effects of pipe geometry and variable soil characteristics on the wave-induced pore pressure and internal stresses will be discussed in detail. It is found that the internal normal stresses in the angular direction (σ_pθ) and shear stress (τ_p) within the pipe are much larger than the amplitude of wave pressure at the surface of the seabed.     

Seismic soil–structure interaction in multi‐span bridges: Application to a railway bridge

The effects of soil‐structure interaction on the seismic response of multi‐span bridges are investigated by means of a modelling strategy based on the domain decomposition technique. First, the analysis methodology is presented: kinematic interaction analysis is performed in the frequency domain by means of a procedure accounting for radiation damping, soil–pile and pile‐to‐pile interaction; the seismic response of the superstructure is evaluated in the time domain by means of user‐friendly finite element programs introducing suitable lumped parameter models take into account the frequency‐dependent impedances of the soil–foundation system. Second, a real multi‐span railway bridge longitudinally restrained at one abutment is analyzed. The input motion is represented by two sets of real accelerograms: one consistent with the Italian seismic code and the other constituted by five records characterized by different frequency contents. The seismic response of the compliant‐base model is compared with that obtained from a fixed‐base model. Pile stress resultants due to kinematic and inertial interactions are also evaluated. The application demonstrates the importance of performing a comprehensive analysis of the soil–foundation–structure system in the design process, in order to capture the effects of soil‐structure interaction in each structural element that may be beneficial or detrimental. Copyright © 2011 John Wiley & Sons, Ltd.