Mixed empirical-numerical method for investigating tunnelling effects on structures

doi:10.1016/j.tust.2017.12.008

Tunnelling and Underground Space Technology

Volume 73, March 2018, Pages 92-104

https://doi.org/10.1016/j.tust.2017.12.008 Get rights and content

Abstract

The assessment of potential for building damage due to ground displacements caused by tunnelling is a global issue being faced by engineers. There is a two-way interaction between tunnelling and existing buildings; tunnel construction affects a building by inducing displacements in the soil underlying its foundation, and buildings influence tunnelling induced displacements via their weight and stiffness. Numerical analyses are widely used to investigate tunnelling and its impact on structures, however numerically predicted ground displacements are generally wider and shallower than those observed in practice. This paper presents a two-stage mixed empirical-numerical technique to estimate the effect of building stiffness on ground displacements due to tunnelling. In the first stage, greenfield soil displacements are applied to the soil model and the nodal reaction forces are recorded. In the second stage, the effect of tunnelling on a structure is evaluated by applying the recorded nodal reactions to an undeformed mesh. Results from conventional numerical analyses of the problem are compared against those obtained using the mixed empirical-numerical approach. Results demonstrate the importance of imposing realistic inputs of greenfield displacements when evaluating structural response to tunnelling.

Introduction

As cities grow and urban infrastructure systems expand, the need for tunnels increases. Tunnel construction inevitably leads to the potential for ground displacements and damage to existing buildings and infrastructure. This paper focuses on the problem of how to evaluate tunnelling-induced movements within buildings. There have been many investigations of the effect of tunnelling on buildings. These studies include the influence of ground movements induced by tunnelling on both surface and subsurface structures. The interaction between a newly constructed tunnel and an existing building is a two-way relationship. The constructed tunnel affects the building by creating displacements in the soil underlying its foundation, and the existence of the building influences resulting soil movements. The effect of structural stiffness (Mair and Taylor, 1997, Franzius et al., 2006, Dimmock and Mair, 2008, Maleki et al., 2011, Farrell et al., 2014, Franza and DeJong, 2017) and building weight (Franzius et al., 2004, Giardina et al., 2015, Bilotta et al., 2017) have been shown to have an effect on the resulting ground movements.

Researchers have proposed several approaches to account for the effect of building stiffness in tunnel-structure interaction problems. Potts and Addenbrooke (1997) proposed a method based on the relative stiffness of a building compared to the underlying soil. They used 2D finite element (FE) analyses and considered several influential parameters of both the soil and the structure, such as material elastic moduli, building length, and cross sectional moment of inertia. This approach was extended by Franzius et al. (2006) who investigated the effect of structural stiffness on ground displacements in a 3D environment. The relative stiffness method was further examined by researchers and new approaches have been proposed, some of which included the effect of building weight (Goh and Mair, 2014, Mair, 2013, Giardina et al., 2015).

In the analysis of Potts and Addenbrooke (1997) and Franzius et al. (2006), the effect of tunnelling on ground displacements was simulated within the FE model. The numerical simulation of a tunnel is an effective method for estimating tunnelling effects on buildings, however, FE methods generally predict a wider and shallower greenfield settlement trough than observed in practice (Mair et al., 1982, Augarde, 1997, Franzius et al., 2005, Franzius et al., 2006, Jurecic et al., 2013). This issue can be overcome by the use of sophisticated soil constitutive models (Addenbrooke et al., 1997), however the input parameters for these models are generally not readily available. A wider/shallower input of greenfield displacements can affect the results of a soil-structure interaction analysis in two ways. First, for a given settlement trough shape, a smaller maximum settlement produces less distortions and therefore less damage to a building. Second, the width of the settlement trough can alter the response of the building; a building affected along its entire length will show less resistance to deformation compared to the same building subjected to ground displacements along part of its length. This feature, which relates to the effective end-fixity of the building, can be demonstrated using a beam analogy (Haji et al., 2018). A relatively long building extending further outside the ground displacement zone can be thought of like a beam with a relatively stiff support that constrains the rotation of the beam (similar to a fixed ended beam), whereas a shorter building behaves like a beam with a more flexible support that allows a degree of rotation (similar to a simply supported beam).

The aim of this paper is to describe the use of a two-stage mixed empirical-numerical (E-N) method to estimate the effect of the stiffness of a weightless building on ground displacements caused by tunnelling. In this method, realistic greenfield ground displacements, obtained from empirical or analytical relationships, are used as an input in a numerical analysis in order to determine the nodal reaction forces within the numerical mesh required to obtain the greenfield displacements (stage 1). The tunnel-building interaction is then solved in stage 2 by including the building within the model and applying the greenfield nodal reaction forces to the mesh. The applied numerical analysis adopts simple linear elastic constitutive soil behaviour; the effects of building weight on the tunnelling-induced response is therefore not considered in the analysis.

The paper begins with an overview of the relative stiffness approach, followed by a description of the adopted numerical analyses, including ‘conventional’ numerical analyses (in which the tunnelling process is simulated) and mixed E-N analyses. The purpose of the ‘conventional’ numerical analysis is to provide results for comparison which might be obtained by a practising engineer considering this problem, using reasonably standard numerical modelling methods. Results from the two numerical analyses are compared and the importance of having an accurate input of greenfield displacements in evaluating structural distortions is demonstrated.

Section snippets

Relative stiffness approach

Potts and Addenbrooke (1997) estimated the stiffness effect of a weightless structure on tunnelling induced ground movements in London clay. Based on 2D numerical analyses, they represented the building as an elastic beam and proposed two relationships to estimate the relative bending and axial stiffness of the soil and the structure: $ρ^{*} = \frac{E_{b} I_{b}}{E_{s} {(L_{bldg} / 2)}^{4}}; α^{*} = \frac{E_{b} A_{b}}{E_{s} (L_{bldg} / 2)}$ where $ρ^{*}$ is the relative bending stiffness, $α^{*}$ is the relative axial stiffness, $E_{b}$ and $E_{s}$ are the elastic moduli of the

Mixed empirical-numerical approach (mixed E-N)

To address the issues related to poor prediction of tunnelling induced settlement trough shape using numerical methods, yet still take advantage of the capabilities of numerical modelling for soil-structure interaction analysis, several authors have incorporated an empirical or analytical greenfield input into numerical analyses. Selby (1999) applied tunnelling induced ground surface movements to a finite element numerical model using Gaussian equations to estimate tunnelling effects on

Finite element software and material properties

The ABAQUS finite element software (SIMULIA, 2012) was used for both the conventional and mixed E-N analyses. All soil and building parts were created using 3D 8-node linear brick, solid elements (C3D8R) with reduced integration to relieve shear lock. The system was considered as a 2D problem; the effect of tunnel advancement was not included and the building was considered as a beam.

For the conventional numerical analysis, the soil was modelled as an elasto-plastic material with a Mohr-Coulomb

Conventional numerical model

In the conventional numerical analyses, a 4.65 m diameter tunnel was modelled within a soil domain $43 D_{t}$ long and $10 D_{t}$ deep, as illustrated in Fig. 4. A unit length mesh was used in the direction of the tunnel axis. Two tunnel depths were considered, with $C / D_{t}$  = 2.4 and 4.4, as well as three relative tunnel-building eccentricities, $e / L_{bldg} = 0.0, 0.5$ and 0.75. A 60 m long building (also 1 m wide in direction of tunnel axis) was attached to the soil surface using a tie constraint (does not allow

Greenfield input

In addition to predicting a wide settlement trough, conventional numerical methods are also not able to replicate the complex distribution of soil volume loss that occurs above a tunnel in a drained granular soil, where shear strains can lead to contraction or dilation of the soil. The amount of contraction/dilation of the soil, which depends on its relative density, the depth of the tunnel, and the magnitude of tunnel volume loss, ultimately leads to a change in the shape of the settlement

Comparison of mixed E-N with numerical results

Results presented in this section are based on three cases of tunnel location: $e / L_{bldg}$  = 0, 0.5 and 0.75. Results relate to cases with $C / D_{t}$  = 2.4 with $V_{ls, surf}$  = 1.55% or $C / D_{t}$  = 4.4 with $V_{ls, surf}$  = 2.77%.

Conclusions

A mixed empirical-numerical (mixed E-N) method to predict the response of buildings to realistic inputs of tunnelling induced ground movements was presented in the paper. A modified semi-analytical method was used to obtain the greenfield displacements in the paper, however any input could be incorporated into the methodology. The input greenfield displacements were based on centrifuge test data and included both horizontal and vertical displacements. The mixed E-N method allows the application

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In the presence of an existing structure, the free-field ground movement is partially or totally transmitted to the building which may result in a structural or functional damage. Different methods (analytical, numerical, experimental, etc.) have been developed to predict the building deflection in response to the ground movements [4–14,49–52]. With the exception of empirical methods that are based on observations of real existing structures, these methods do not consider a specific study of a particular case but they are generally applied to simplified structures, such as elastic 2D beams, in order to assess the global trend of ground movements induced phenomena.
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Mixed empirical-numerical method for investigating tunnelling effects on structures

Abstract

Introduction

Section snippets

Relative stiffness approach

Mixed empirical-numerical approach (mixed E-N)

Finite element software and material properties

Conventional numerical model

Greenfield input

Comparison of mixed E-N with numerical results

Conclusions

Tunnel. Undergr. Space Technol.

Tunnel. Undergr. Space Technol.

Tunnel. Undergr. Space Technol.

Soils Found.

Tunnel. Undergr. Space Technol.

Soils Found.

Tunnel. Undergr. Space Technol.

Tunnel. Undergr. Space Technol.

Tunnel. Undergr. Space Technol.

The influence of pre-failure soil stiffness on the numerical analysis of tunnel construction

Geotechnique

Foundation Analysis and Design

Semi-analytical prediction of ground movements due to shallow tunnels in sand

Proceedings of the XVI ECSMGE - Geotechnical Engineering for Infrastructure and Development

The influence of soil anisotropy and k0 on ground surface movements resulting from tunnel excavation

Géotechnique

The influence of building weight on tunnelling-induced ground and building deformation

Soils Found.

The response of surface structures to tunnel construction

Proc. ICE-Geotech. Eng.