Seismic Soil-Tunnels Interaction Via Bem Part II. Numerical Results (original) (raw)

Seismic Response Analysis Of Lined Tunnels InPoroelastic Soil Medium

WIT Transactions on the Built Environment, 1970

The problem of harmonic wave diffraction by tunnels in an infinite poroelastic saturated soil obeying Biot's theory is studied numerically under conditions of plane strain and the effect of poroelasticity on the response is assessed through some parametric studies. The method is based on the theory of Mei and Foda, which considers the total field to be approximated by the superposition of an elastodynamic problem with modified elastic constants and mass density for the whole domain and a diffusion problem for the pore fluid pressure confined to a boundary layer at free boundaries. Both problems are solved numerically by the boundary element method (BEM) in the frequency domain. Results dealing with the response of a circular tunnel with and without an elastic concrete liner in an infinite poroelastic medium to incident harmonic P waves are provided and compared against analytical ones as well as to those corresponding to linear elastic soil behavior.

A 2.5D-Fourier-BEM model for vibrations in a tunnel running through layered anisotropic soil

Engineering Analysis with Boundary Elements, 2012

A boundary element model of a tunnel running through horizontally layered soil with anisotropic material properties is presented. Since there is no analytical fundamental solution for wave propagation inside a layered orthotropic medium in 3D, the fundamental displacements and stresses have to be calculated numerically. In our model this is done in the Fourier domain with respect to space and time. The assumption of a straight tunnel with infinite extension in the x direction makes it possible to decouple the system for every wave number k x , leading to a 2.5D-problem, which is suited for parallel computation. The special form of the fundamental solution, resulting from our Fourier ansatz, and the fact, that the calculation of the boundary integral equation is performed in the Fourier domain, enhances the stability and efficiency of the numerical calculations.

Seismic response of buried metro tunnels by a hybrid FDM-BEM approach

Bulletin of Earthquake Engineering, 2014

In this work, we present a 2D elastodynamic model for the seismic response of subway tunnels embedded in a laterally inhomogeneous, multilayered geological region overlying the half-plane. To this end, a finite difference-boundary element methodology (FDM-BEM) is developed, with the latter method embedded in the former so as to capture near-site field effects. More specifically, the FDM is used for simulating in-plane elastic wave propagation from the underlying bedrock through the overlying soil deposits to the surface. A 'box' area is then defined within the original FDM mesh and contains lined tunnels. The 'box' is modeled by the BEM and its upper boundary coincides with the free surface of the geological deposit. This way, seismically-induced motions are imparted from the FDM mesh to the 'box' perimeter, so that the BEM may now be used to efficiently model the near-site layers which contain the tunnels. Verification studies are then successfully conducted for upward moving Gabor pulses, using the FDM alone, the present hybrid FDM-BEM and a hybrid FDM-finite element method formulation. Given that the FDM is defined in the time domain and the BEM in the frequency domain, the fast Fourier transform is used for linking these two constituent parts of the hybrid approach. This methodology is finally applied to a north-south geological cross-section of Thessaloniki, Greece, which contains two Metro tunnels placed directly below an important Roman-era monument known as the Arch of

Numerical modelling in seismic analysis of tunnels regarding soil-structure interaction

Facta universitatis - series: Architecture and Civil Engineering, 2013

The paper is related to the most significant aspects of numerical simulations in seismic analysis of tunnels, highlighting the soil-structure interaction phenomenon. The modelling of a problem and analysis of relevant influences may be completed by an application of software packages based on the finite element method. In order to define a reliable and efficient numerical model, that should simultaneously put together both the criteria of simplicity and realistic presentation of a physical problem, analyses should start from the most simple modelling techniques (theory of elasticity, replacing the soil medium with elastic springs, pseudo-static analysis), with the final goal to accomplish a more complex and realistic model (theory of elasto-plasticity, finite element method, full dynamic analysis).

A Numerical Study of Seismic Response of Shallow Square Tunnels in Two Layered Ground

2019

In this study, the seismic behavior of a shallow tunnel with square cross section is investigated in a two layered and elastic heterogeneous environment using numerical method. To do so, FLAC finite difference software was used. Behavioral model of the ground and tunnel structure was assumed linear elastic. Dynamic load was applied to the model for 0.2 seconds from the bottom in form of a square pulse with maximum acceleration of 1 m/s 2. The interface between the two layers was considered at three different levels of crest, middle, and bottom of the tunnel. The stiffness of the two upper and lower layers was considered to be varied from 10 MPa to 1000 MPa. Deformation of cross section of the tunnel due to dynamic load propagation, as well as the values of axial force and bending moment created in the tunnel structure, were examined in the three states mentioned above. The results of analyses show that heterogeneity of the environment, its stratification, and positioning of the interface of the two layers with respect to tunnel height and the stiffness ratio of the two layers have significant effects on the value of bending moment, axial force, and distortion of tunnel cross-section.

Advanced numerical modelling of the transverse behaviour of tunnels under seismic loading

In this paper, a two-dimensional finite element model is employed to simulate the transverse behaviour of a shallow circular tunnel in a typical soft clay deposit subjected to earthquake loading. To investigate the effect of the constitutive assumption on dynamic soil-tunnel interaction, an advanced kinematic-hardening multi-surface model and its reduced single surface version are calibrated against real laboratory data, including undrained triaxial and resonant column tests. The results of the simulations obtained applying two different input motions at bedrock level are interpreted in terms of maximum accelerations induced at different depths in the soil deposit and corresponding distribution of tunnel lining forces. The constitutive hypothesis adopted in the modelling proves to play a significant role on the seismic induced lining loads. 1 INTRODUCTION In recent years there have been many documented failures of geotechnical structures due to earthquake events with huge consequences in terms of fatalities and financial costs. These failures are associated with significant deformation of the soil deposits which can cause major damage to buildings and infrastructure facilities. Despite the response of tunnels to seismic actions has been usually considered relatively safe as compared to that of surface geotechnical structures, several examples of damage to underground structures caused by earthquake events can be found in the literature [e.g. 1-3]. In particular, ovaling and racking of the lining, together with the shallow depth of the structure and the poor geological conditions of the surrounding deposit, are reported to be the most critical sources of damage [4]. The seismic design of tunnels has been addressed in the past by a number of researchers which have proposed solutions based on analytical or numerical analysis. Current analytical design methods rely on elasticity solutions to calculate the dynamic lining forces a tunnel experiences during an earthquake event and generally ignore the inertial effects. The Soil-Structure Interaction (SSI) approach has, instead, the ability to consider relatively complex conditions in terms of heterogeneity of soil strata, non regularity of tunnel geometry, pre-existence of surface and sub-surface structures, ground water flow. In such cases, the analysis of SSI can take advantage of the use of numerical two-dimensional (2D) and three

Investigation of acoustic waves behavior of an underground tunnel in a multilayer soil

Scientific Reports

Understanding the acoustic behavior of buried tunnels is valuable for locating them and monitoring their structure health. This research focuses on the acoustic behavior of buried tunnels in multilayer soil structures. The reflected and transmitted acoustic wave pressure variations are investigated exclusively for a multilayer soil buried tunnel. The tunnel system's 3D finite element model is presented, which contains the tunnel lining, surrounding soil, and the air inside the tunnel and at the ground surface. A free air explosion is used as the acoustic wave source. The reflected and transmitted waves' pressure values are measured to evaluate the effects of mechanical characteristics of soil layers, tunnel buried depths, and lining concrete types on the acoustic wave behavior of the tunnel. In addition, a utility line is introduced to the system in different positions related to the main tunnel to investigate its effect on the main tunnel’s acoustic wave behavior. The resul...

Freefield vibrations due to dynamic loading on a tunnel embedded in a stratified medium

Journal of Sound and Vibration - J SOUND VIB, 2005

An efficient and modular numerical prediction model is developed to predict vibration and re-radiated noise in adjacent buildings from excitation due to metro trains in tunnels for both newly built and existing situations. The three-dimensional dynamic tunnel–soil interaction problem is solved with a subdomain formulation, using a finite element formulation for the tunnel and a boundary element method for the soil. The periodicity of the tunnel and the soil in the longitudinal direction is exploited using the Floquet transform, limiting the discretization effort to a single bounded reference cell. It is demonstrated in the paper how the boundary element method can efficiently be extended to deal with periodic media, reusing the available three-dimensional Green's tensors for layered media. The efficiency of the method is demonstrated with a numerical example, where the case of harmonic and transient point loading on the invert of a shallow cut-and-cover masonry tunnel in Paris ...

Elastic wave fields in a half-plane with free-surface relief, tunnels and multiple buried inclusions

Acta Mechanica, 2013

In this work, we study the elastic wave fields that develop in an isotropic half-plane which contains different types of heterogeneities such as free-surface relief, unlined and lined tunnels, as well as multiple buried inclusions. The half-plane is swept by traveling harmonic waves, namely pressure waves, vertically polarized shear waves and Rayleigh waves, as well as by waves emanating from an embedded source. The computational tool used is the direct boundary element method (BEM) with sub-structuring capabilities. Following development and numerical implementation of the BEM, two stages of work are performed, namely a detailed verification study followed by extensive parametric investigations. These last numerical simulations help determine the dependence of the elastic waves that develop along the surface of the half-plane, as well as of the dynamic stress concentration factors in the different types of buried inclusions, to the following key factors: geometry of the free-surface relief, geometry, depth of burial and separation distance of the inclusions, wavelength to inclusion diameter ratio and dynamic interaction phenomena between the multiple heterogeneities. In closing, the potential of the enhanced BEM formulation to treat dynamic soil-structureinteraction problems with the kind of complexity expected in realistic engineering applications is discussed.

Fundamental solutions in modeling of vibrations radiated from tunnels with 2.5D - BEM

Proceedings of the ICA congress, 2019

In this work, we analyze a method to model vibrations within horizontally layered orthotropic soil. After taking the Fourier transform with respect to both horizontal variables x and y, the fundamental solution of the wave propagation has a simple structure in the wavenumber (k x , k y)-domain. Inside a single layer, the fundamental solution can be represented by a superposition of six waves with complex wavenumbers. Their corresponding coefficients are computed by solving a linear system obtained by imposing a boundary condition at the surface, continuity conditions at the interfaces between the layers, and a radiation condition at infinity. We study stabilizing strategies for the evaluation of the fundamental solution.