Numerical analyses of soil-foundation-building interaction due totunnelling

M. Boonpichetvong, H. Netzel & J.G. RotsDepartment of Building Mechanics, Faculty of Architecture, Delft University of Technology,Delft, the Netherlands

ABSTRACT: Numerical modelling of soil-foundation-building response due to tunnelling is presented in thispaper.An overview of parametric studies for the future development of an improved damage classification systemis given. The adopted numerical models allow for all possible inelastic factors in soil, soil-structure interfaceand buildings. It is demonstrated that the implementation of the soil-structure interface model in the numericalanalyses is essential for the determination of strain transmitted from the soil to the buildings.

1 INTRODUCTION

From the past experiences, ground movements asso-ciated with tunnelling activities may endanger safetyand serviceability of surrounding buildings. Reliableprediction of cracking in the surrounding structuresis indeed essential to assess the risk of tunnellingprojects. With the aid of numerical tools like the FiniteElement Method (FEM), engineers can predict build-ing and soil response of this soil-structure interactionproblem and necessary mitigating measures can bedesigned.

At Delft University of Technology, the researchproject entitled “computational modelling of tun-nelling induced settlement damage to masonry build-ings” is established on the numerical modelling aspect(Boonpichetvong & Rots 2002, Boonpichetvonget al. 2003). Attention points are both computationalmechanics (i.e. development and improvement ofexisting models in DIANA) and computational mod-elling (i.e. application of the improved models to thesoil-structure interaction problem). The final aims areto understand the behaviour of cracking in buildingsdue to the tunnelling activity and to distribute theknowledge to the design community.

Presently at the final stage of the research, a seriesof detailed numerical analyses has been carried out tostudy the influence of each interacting parameter onbuilding response due to tunnelling for both shallowand deep foundation systems (Figure 1). These para-metric studies include an investigation of the influenceof different building geometries and locations, dif-ferent soil types and different fracture properties ofbuilding materials on the induced settlement damage.The numerical results serve as inputs for a compan-ion project to interpret the FEM outputs of cracking

Figure 1. Influence of tunnelling on buildings with shallowand pile foundations.

patterns, crack-width and crack distribution and torelate these findings to the development of a damageclassification system (Netzel 2004).

In this paper, an overview of such parametric studiesis summarized. The emphasis is given to considerationof all possible nonlinear factors in the numerical anal-yses i.e. cracking of building materials, slipping andgap opening of soil-structure interface, and nonlin-ear soil behaviour. Our scope presented in this paperis restricted to the building response with shallowfoundation.

2 THE PARAMETRIC STUDY

2.1 Background

Soil-structure interaction responses due to tunnellingwere largely investigated in the past e.g. the worksby Addenbrooke (1995), Liu (1997). The crack modeladopted in their studies is either a no-tension crackmodel or a conventional Tresca elastoplasticity model.The features of so-called tensile softening, whichplay an important role in post-cracking behaviour, are

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missing in their numerical analyses (Boonpichetvong &Rots 2004a). The characterisation of tensile-softeningin crack models has proven to give a good correlationbetween numerical results and various fracture exper-iments available e.g. Rots (1988). So far, the properinclusion of fracture mechanics to predict the crackingdamage in this large-scale fracture problem appears tobe a challenging issue.

Another major restriction is the characterisation ofthe soil-structure interface. In those works, the build-ing models are rigidly tied with the ground models.This implies an enforcement of continuity along theboundary between the building and the soil domains.Inevitably, ground strains are transferred to the build-ing model without a possibility to capture a gapopening and a shear sliding along the soilstructureinterface. The behaviour of soil-structure interac-tion can be improved if interface elements with aproper interface characterisation are inserted along theground-structure boundary.

In this paper, the second restriction is elaborated toelucidate the influence of soil-structure interface onthe coupled response.

2.2 Computational model

In the studies, 2D and 3D finite element models havebeen developed for different purposes. The properstress distribution from above-ground structures tounderlying soil thus the realistic soilstructure inter-action can only be captured by 3D computationalanalyses (Figure 2). However, due to excessive compu-tational expense required in 3D analyses, the parame-tric studies are primarily focused on the 2D numericalmodelling. This is justified by the fact that the under-standing of 3D response can be related to the sim-plified 2D response. Therefore, only for the specialcorrelation of 2D numerical results to 3D numericalresults, 3D numerical analyses are then performed.Herein, only 2D analyses are discussed for the restof the paper.

2.2.1 Greenfield model2D plane strain analyses with plane strain 8-nodedquadrilateral elements for soil continuum are takento characterise 2D greenfield ground movements.The modified Mohr-Coulomb soil is adopted for thesandy ground response.The nonlinear properties of theground are assumed to be isotropic, homogeneous andnormally consolidated (OCR = 1) in each stratum.Thestiffness of soil is stress-dependent accounting for theinitial situation and stress path of soil. The four val-ues of soil’s triaxial loading stiffness E50,ref = 5, 10,50 and 100 MPa are selected in the parametric studies.The ground model’s geometry is 44 m deep and 100 mwide with tunnel diameter of 9.5 m located at the depthof 22 m from ground surface (Figure 3).

Figure 2. (a) An example of 3D coupled soil-structuremodelling and (b) the 3D effect of soil stress distribution.

Figure 3. Finite element model of greenfield analy-ses revealing soil localisation due to tunnelling at thedepth of 22 m.

The greenfield model allows for the study of theeffect of the variation of tunnel depth and soil stiff-ness on the trough characteristics in both saggingand hogging zones. The settlement and transverse soilmovements at both the ground surface and subsurfacehalf-tunnel depth are recorded for further correlationwith the findings from coupled analyses.

The simplified contraction model is used to simu-late the tunnelling process. It is emphasized, that theauthors are aware of the restrictions in determiningabsolute settlements with the contraction model (amodel including tail void process and grout processgives more realistic results). The main objective of thenumerical soil-structure interaction parametric studiesis however to judge the interaction of the building withthe soil and not to predict the absolute soil and buildingsettlement accurately. Different greenfield settlementprofiles are therefore described in terms of relative dif-ferential settlements (angular distortion and deflectionratio) at the location of the influenced building. The

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resulting response of the building is then used to quan-tify the soil-structure interaction for different degreesof relative greenfield distortion.

2.2.2 Coupled modelFor the 2D coupled analyses, in addition to theexisting plane strain soil elements, plane stress8-noded quadrilateral elements representing unrein-forced masonry are generated. Quadratic interfaceelements are inserted between the underlying groundand the wall. The inclusion of the interface elementsallows for the investigation of stress, strain and back-check in the assumption of contact condition betweenthe underlying ground and the wall.

In the analyses, after a successful initialization ofthe in situ initial stress in the soil, the dead load ofthe masonry and the live load along each floor areactivated creating the initial situation of building. Theline load on the roof level is 7 kN/m and the loading onthe other floor levels is 10.5 kN/m.These loads includethe deadweight of the floor and roof constructions and50% of the mobile load, which is applicable for a mas-sive common bearing wall carrying floor loads fromtwo house units, which is a typical situation for the his-torical Dutch houses in urban surrounding. Next, theinduced settlements have been incremented by con-trolling the percentage of volume loss in the coupledanalyses.

Both façade and massive bearing walls are studied.The wall geometries chosen cover the wall length var-ied from length (L) = 10 to 40 m with aspect ratios(L/H) = 0.5, 1 and 3 (for example, see Figure 4). Thethickness of the masonry wall unit is assumed to be300 mm throughout the wall height.

To predict the settlement damage for the masonrywall, a decomposed-strain fixed smeared crack model(Rots 1988) is chosen. The fixed crack model is pre-ferred over the rotating crack model as it renders theproper cracking response in case of nonproportionalloadings (Boonpichetvong & Rots 2004b). Masonryis known to possess anisotropic properties due tothe nature of arrangement of brick units and jointarrangement. However due to the scarce reliable test-ing data, the masonry is simplified to be isotropicin the present study. The tensiles-oftening propertiesof the reference masonry are assumed as follows.Young’s modulus and Poisson’s ratio are taken as6000 N/mm2 and 0.2 respectively. Fracture propertiesof the reference masonry are chosen with a tensilestrength = 0.3 N/mm2, fracture energy = 0.05 N/mmwith a linear softening diagram. Mass density ofmasonry is 2000 kg/m3.

2.3 Characterisation of soil-structure interface

The interaction between soil and structure is modelledby inserting interface elements along the boundary

Figure 4. Massive wall mesh and load scheme for L/H = 3,L = 20 m, H = 6.5 m.

Figure 5. Characterisation of soil-structure interfaceelements.

of the soil and the wall in the finite element model.These interface elements control the horizontal andvertical stresses transferred between soil and structure.Two conditions regarding the transfer of horizontalmovement of soil-structure interfaces are consideredrepresenting the likely extreme scenarios i.e. rough andsmooth interface nature.

The interface element relates the stresses acting onthe interface to the relative displacement of the twosides of the interface as shown in Figure 5a. In princi-ple, the behaviour of the geo-material interface can bemodelled by Coulomb friction (full line in Figure 5b).In this study, the cohesion c is taken as zero. Thisimplies a zero tensile strength of the stress-relative dis-placement relation in the normal direction of interface(dashed line in Figure 5b). A gap is assumed to openonce such tension cut-off criterion is violated. Thenormal compressive behaviour is assumed to be in theelastic regime (Figure 5c). This normal direction rela-tion is the same for both the rough and the smooth inter-face. The yield function of tangential traction τ acrossthe interface is controlled by the magnitude of nor-mal traction σ , cohesion c and angle of friction ϕ i.e.√

τ 2 + tan ϕ − c = 0 as elastoplastic behaviour with-out stress hardening (Figure 5d). For the elastic regimebelow the yield limit, the shear relative displacement�ut is related to shear traction via τ = kt × �ut.

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For the rough interface, the normal and tangent stiff-ness of the soil-structure interface (kn and kt), are takenas 1 N/mm3 as the average number observed in soil lab-oratory findings. In fact, this interface stiffness servesas a penalty value to suppress the initial elastic defor-mation in the interface elements. From the presentexperience, higher values of interface stiffness mustbe avoided to prevent the problem of stress oscilla-tion. For the smooth interface, a very low value of ktis adopted here to neglect any shear transfer from theunderlying ground to the above ground structures.

3 SOIL-STRUCTURE INTERACTIONDUE TO TUNNELLING

As a benefit of the coupled analysis, useful informationon the relation of model parameters allows for insightof the resisting mechanism, crack initiation, and thefinal resulting damage of masonry building response.Considering all inelastic factors in the numerical ana-lyses i.e. the cracking of the masonry, the slippingand gap opening of the soil-structure interface, andthe nonlinear soil behaviour enables a complete viewof the tunnelling induced soilstructure response (forinstance, see Figure 6). The key features derived fromthe coupled response are a) the influence of the build-ing weight and stiffness on the ground movement andb) the role of the soil-structure interface in transmittingthe ground distortion and strain to the structures.

3.1 Changes of surface ground movement

The building weight affects the soil stress path his-tory e.g. over-consolidation ratio and thus the groundresponse induced by the subsequent tunnelling pro-cess. This feature can be unveiled only by the fullycoupled analysis. It is found that the building stiff-ness plays an important role in modifying the shapeand magnitude of the surface ground movements(Figure 7).

3.2 Influence of soil-structure interface onwall response

By establishing a relation among the ground response(differential ground settlement, ground angular distor-tion, ground deflection ratio) and the building response(building distortion, induced damage) for the furtherdevelopment of engineering design rules, it is foundthat the structural distortions are strongly influencedby the properties of the soil-structure interface. Inaddition, the relation between ground and buildingdistortions is revealed to depend on the ratio of soiland building stiffness which agrees with the recentexperiment findings by Son & Cording (2005).

The relation between the building and ground dis-tortions is determined by comparing the greenfield

Figure 6. Consideration of all inelastic factors in the numer-ical analyses i.e. cracking of building materials, slippingand gapopening of soil-structure interface, and nonlinear soilbehaviour.

Figure 7. Changes of the final ground surface movementpattern due to the coupled soil-structure interaction, for awall dimensioned L = 40 m, H = 6.5 m with rough interface.

surface settlement troughs that yield the surfaceground slope of 1/450, 1/200 and 1/80 at the pointof inflection, with the wall responses at the corre-sponding volume loss by the coupled analyses. Forexample, the development of greenfield surface set-tlement troughs corresponding to the specified surfaceground slopes for stiff soil with triaxial loading stiff-ness E50,ref = 50 MPa is as shown in Figure 8. Figure 10depicts the corresponding development of traction and

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Figure 8. Greenfield surface settlement troughs of soil withE50,ref = 50 MPa and different surface ground slopes at pointof inflection, i.e. at 1/450 (volume loss 1), 1/200 (volume loss2) and 1/80 (volume loss 3).

Figure 9. Finite element model of the discussed wall sizedL = 20 m, H = 6.5 m in the sagging situation.

relative displacement along the soil-structure interfacefor a wall sized L = 20 m, H = 6.5 m with rough inter-face and no live load. The wall is located in the saggingzone above the tunnel centreline. The finite elementmodel of the discussed wall is as shown in Figure 9.It is observed that the normal and tangential tractionsalong the soil-structure interface undergo significantchanges developed at the different values of volumeloss. Particularly, the normal pressure underneath thewall is redistributed from the central part to the edge

Figure 10. Changes in traction and relative displacementalong the soil-structure interface, for a wall dimensionedL = 20 m, H = 6.5 m with rough interface but no live load.

of the wall.The tangential response suggests that shearmobilisation of the interface is reached and highertangential slip develops with higher volume loss.

With an additional surcharge of the live load tothe same wall, the allowable shear traction increasesdue to the higher confinement along the soil-structureinterface. This additional restraint results in less tan-gential slip along the soil-structure interface at thesame volume loss (Figure 11). The final induced walldistortions for such two cases are given in Figure 12.For a comparison, the response of the wall with smoothinterface and no live load is also enclosed and discov-ered to be the most vulnerable case for the stress andstrain in the wall. All these findings emphasise the

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Figure 11. Changes in traction and relative displacementalong the soil-structure interface, for a wall dimensionedL = 20 m, H = 6.5 m with rough interface and live load.

necessity to include the soilstructure interface modelin the numerical analyses for a proper determination ofthe strain transmitted from the ground to the structures.A detailed description of all parametric studies andinterpretations is given in Boonpichetvong & Netzel(2005).

4 CONCLUSION

In this contribution, parametric studies undertaken forthe future development of a damage classification sys-tem are summarized. The advantage of the present

Figure 12. Deformations of a wall dimensioned L = 20 m,H = 6.5 m at volume loss 3, (a) with rough interface but nolive load, (b) with rough interface and live load and (c) smoothinterface but no live load.

study is the possible consideration of all major nonlin-ear factors in the numerical analyses. It is found thatthe inclusion of the soil-structure interface model inthe numerical analyses is essential for quantifying themagnitude of strain transmitted from the soil to thebuildings. This better insight of soilstructure responsedue to tunnelling enables the future translation of thepresent parametric studies to the development of animproved damage classification system.

REFERENCES

Addenbrooke, T.I. 1995. Numerical analysis of tunnellingin stiff clay, Ph.D. Dissertation, University of London(Imperial College of Science Technology and Medicine),London, UK.

Boonpichetvong, M. & Rots, J.G. 2002. Settlement dam-age of masonry buildings in soft-ground tunnelling, inMax A.N. Hendriks and Jan G. Rots (eds), Finite Ele-ment in Civil Engineering Applications, 3rd DIANAWorld Conference on Finite Elements in Civil EngineeringApplications, Tokyo, Japan: 285–293.

Boonpichetvong, M., Rots, J.G. & Netzel, H. 2003. Onmodelling of masonry buildings response in Dutch soft-ground tunnelling, in J. Saveur (ed), (Re)Claiming theUnderground Space, Proceedings of ITAWorldTunnellingCongress, Amsterdam, the Netherlands, Vol.2: 799–805.

Boonpichetvong, M. & Rots, J.G. 2004a. Numerical anal-yses of size effect in settlement damage prediction, InJ. Walraven et al. (eds), Proc. 5th Int. PhD Symposium inCivil Engineering, Delft, the Netherlands: 1337–1346.

Boonpichetvong, M. & Rots, J.G. 2004b. Fracture analy-ses of walls under non-proportional loadings, in V.C. Li

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et al. (ed), Fracture Mechanics of Concrete Structures,Proceeding of the Fifth International Conference on Frac-ture Mechanics of Concrete and Concrete Structures,Colorado, USA: 941–948.

Boonpichetvong, M. & Netzel, H. 2005. 2D soil-foundation-facade interaction due to tunnelling: numeri-cal analyses and interpretations, Internal Report, Facultyof Architecture, Delft University of Technology, Delft, theNetherlands.

Liu, G. 1997. Numerical modelling of damage to masonrybuildings due to tunnelling, Ph.D. Dissertation, Universityof Oxford, Oxford, UK.

Netzel, H. 2004. Building settlement damage criteria, angu-lar distortion or deflection ratio?, in D. Martens andA. Vermeltfoort (eds), Proceeding of the 13th Interna-tional Brick/Block Masonry Conference, Amsterdam, theNetherlands, Vol. 3: 1235–1244.

Rots, J.G. 1988. Computational modelling of concrete frac-ture, Ph.D. Dissertation, Delft University of Technology,Delft, the Netherlands.

Son, M. & Cording, E.J. 2005. Estimation of buildingdamage due to excavation-induced ground movements,ASCE Journal of Geotechnical Engineering, 131(2):162–177.

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