DeJong, Matthew J.

Giardina, Giorgia

Mair, Robert J.

Ritter, Stefan

Masonry buildings in urban areas can be damaged by differential ground movements caused by underground excavations. Existing procedures for the assessment of building damage due to excavation-induced settlements include the effect of the building on the settlement trough in terms of building stiffness relative to soil stiffness. In these procedures, the relative stiffness is calculated by considering either the bending stiffness or the shear stiffness of the building. In this paper, finite element modelling of buildings subjected to tunneling-induced settlements is used to determine the relative importance of shear and bending deformations in damage predictions. Computational modelling was first validated by simulating centrifuge tests on 3D printed small scale models of masonry buildings subjected to tunneling in sand. Using a similar modelling approach, a sensitivity study was then conducted on the governing effect of shear or bending deformations for different amounts of facade openings. Results indicate the need to include both shear and bending deformation in assessment procedures, and provide essential data towards this objective

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        Citation for published version:Giardina, G, Ritter, S, DeJong, MJ & Mair, RJ 2017, 'Influence of building geometry on bending and sheardeformations of buildings subject to tunnelling subsidence: numerical modelling' Paper presented at EURO:TUN2017, Innsbruck, Austria, 18/04/17 - 20/04/17, .Publication date:2017Document VersionPublisher's PDF, also known as Version of recordLink to publicationPublisher RightsUnspecifiedUniversity of BathGeneral rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Download date: 13. May. 2019EURO:TUN 2017, Innsbruck University, AustriaInfluence of building geometry on bending and sheardeformations of buildings subject to tunnellingsubsidence: numerical modellingGiorgia Giardina1,2, Stefan Ritter2, Matthew J. DeJong2 and Robert J. Mair21University of Bath, UK2University of Cambridge, UKAbstract: Masonry buildings in urban areas can be damaged by differential ground move-ments caused by underground excavations. Existing procedures for the assessment of build-ing damage due to excavation-induced settlements include the effect of the building on thesettlement trough in terms of building stiffness relative to soil stiffness. In these proce-dures, the relative stiffness is calculated by considering either the bending stiffness or theshear stiffness of the building. In this paper, finite element modelling of buildings subjectedto tunnelling-induced settlements is used to determine the relative importance of shear andbending deformations in damage predictions. Computational modelling was first validatedby simulating centrifuge tests on 3D printed small scale models of masonry buildings sub-jected to tunnelling in sand. Using a similar modelling approach, a sensitivity study was thenconducted on the governing effect of shear or bending deformations for different amounts offac¸ade openings. Results indicate the need to include both shear and bending deformation inassessment procedures, and provide essential data towards this objective.1 INTRODUCTIONUrban underground projects typically require the assessment of a large number of surfacebuildings against the risk of being damaged by excavation-induced ground settlements. Forthis reason, damage assessment procedures need to guarantee an expeditious and conservativeprediction which does not require highly detailed inputs (e.g. [1, 2, 3]).Available assessment procedures tend to focus on the potential damage caused to the buildingby either the bending or the shear component of the settlement-induced deformation. Thebending or shear focus is attested by the way of measuring the building influence on theexcavation-induced settlement profile [4, 3]. The magnitude of this influence is associatedto the relative stiffness between the building and the soil, which can be evaluated as a ratiobetween either the building bending [4, 5, 6] or shear [3] stiffness to the soil stiffness.This paper aims at providing numerical data to develop a more consistent assessment proce-dure. It investigates the relative contribution of bending and shear deformation in buildingsundergoing tunnelling-induced settlements. A finite element model of masonry buildingsLGEBA ωΔ βmax θ(a) Sagging modeLGEBAωΔβmaxθ(b) Hogging modeFigure 1: Deformation parameters: relative deflection ∆, deflection ratio ∆/L, rotation θ,angular distortion (or relative rotation) β and tilt ω.adjacent to a tunnel excavation in sand is first validated by comparison with the results ofcentrifuge testing and then used to perform a sensitivity study on the effect of window open-ings.2 NUMERICAL MODELThe numerical models reproduced two centrifuge tests which were performed at the Univer-sity of Cambridge on 3D printed structures subjected to tunnelling in sand (Fig. 2a). In bothexperiments, the box containing the soil, tunnel and building model was subjected to an ac-celeration of 75 g, therefore reproducing the response of a real scale structure 75 times larger.The experimental testing is described in Ritter et al. [7].(a) model geometryXYZModel: TEST08_20_SUPPRE_0109 NOV 2016 17:03:46 test08_20_meshiDIANA 10.0-07 : Univ. of Cambridge (b) 20% opening fac¸ade meshXYZModel: TEST08_40_SUPPRE_0109 NOV 2016 17:04:16 test08_40_meshiDIANA 10.0-07 : Univ. of Cambridge (c) 40% opening fac¸ade meshFigure 2: Numerical models reproducing the experimentally tested structures.In the numerical model, the centrifuge spin-up was simulated by incrementally increasing thegravity acceleration up to 75 g, while the tunnelling-induced settlement profile was obtainedby gradually reducing the outward equilibrium radial pressure applied at the tunnel boundary.Both the soil and the building were modelled by quadratic plane strain elements. A nonlinearelastic power low was used to simulate the relationship between the soil strains and stresses;the parameters were calibrated by comparison with the greenfield soil surface displacementsmeasured during the centrifuge spin-up. Giardina et al. [8] reported details and validation ofthe soil model.Table 1: Material inputs for the numerical model. See [8] for further details.StructureYoung’s modulus Ew = 0.8× 103 N/mm2Density ρw = 1.28× 10−6 kg/mm3Poisson’s ratio νw = 0.2Tensile strength ftw = 1.27Ultimate strain εw = 0.31%SoilRef. Young’s modul. E0 = 25 N/mm2Density ρm = 1.59× 10−6 kg/mm3Poisson’s ratio νm = 0.25Ref. shear modulus G1 = 1 N/mm2Ref. compr. modulus K1 = 2.5 N/mm2Power constant n = 0.53Ref. pressure p0 = −1× 10−3 N/mm2InterfaceNormal stiffness kn = 100 N/mm3Tangent stiffness kt = 1 N/mm3Cohesion c = 0MPaFriction angle φ = 30◦Dilatancy angle ψ = 0◦The building was connected to the soil through line interface elements with zero tensilestrength and frictional behaviour (Tab. 1). The latter feature reproduced the transmissionof shear stresses due to the rough base interface of the centrifuge models; shear parameterswere calibrated by using the tunnelling-induced horizontal displacements of the soil surfaceobserved in the centrifuge model [8].The building model reproduced a two storey masonry Georgian house on strip foundations;it included two internal transverse walls and windows openings covering 20% (Fig. 2b) and40% (Fig. 2c) of the total fac¸ade area. The plaster-based 3D printed material, used in thecentrifuge model to capture potential cracking of masonry, was simulated by a smeared rotat-ing crack model with elastic behaviour in compression and post-cracking linear softening intension. The material parameters (Tab. 1) were derived by four point bending tests performedon 3D printed material samples [7].3 DEFORMATION PARAMETERSThis section describes the procedure adopted to separate the bending and shear componentsof the total tunnelling-induced building deformation. According to Cook [9] the buildingwas divided in three units (Fig. 3a). For each unit the vertical differential displacement wasdecomposed in tilt, bending and shear deformation (Fig. 3b).The total deformation was measured asytot = ∆yA −∆yB (1)with positive downwards vertical displacements.A BCDEFGH(a) Building bay divisiontsbω1 ω2ω2(b) Bay 1 deformation parameters (after Son and Cording [3]).Figure 3: Building reference points and deformation parameters.The tilt deformation ∆yt is the contribution due to the rigid body rotation. For bay 1:ω1 = arctg [(∆xA −∆xD)/H] (2) ω2 = arctg [(∆xB − ∆xC)/H] (3)with ω positive if anticlockwise, and∆yt = sin(ω2)× L (4)The bending deformation was calculated as∆yb = tg(ω1 − ω2)× L (5)and the contribution due to shear was derived as∆ys = ytot −∆yt − ∆yb (6)4 RESULTSFigures 4 and 5 compare the experimental and numerical displacements of the models with20% and 40% of window openings. To improve readability, only the four left points (A B CD) and the four base points (A B E G) are shown for the vertical (Fig. 4) and horizontal (Fig.5) displacement, respectively.The soil numerical model has been previously validated against centrifuge testing with nobuildings or including simplified surface structures [8]. The good fit to the experimentalcurves in Figures 4 confirms that the overall model can capture the soil-structure interactioneffect on building settlements. The increasing difference between the corresponding base andtop point displacements (e.g. ∆yA and ∆yD) indicates the shear and bending deformation ofthe building portion included between the external right wall and the considered points (e.g.the whole building for ∆yA and ∆yD, bays 2 and 3 for ∆yB and ∆yC).Figures 5a and 5b indicate a correct simulation also of the horizontal displacement trend,with a consistently larger magnitude with respect to the experimental values. The impactof this difference on the building deformation modelling is limited to the actual discrepancybetween the reference point relative displacements; for this reason, the numerical horizontal0 2 4 600.10.20.30.4Volume loss (%)Displacement (mm)  A expB expC expD numA numB numC numD num(a) 20% opening0 2 4 600.10.20.30.4Volume loss (%)Displacement (mm)  A expB expC expD numA numB numC numD num(b) 40% openingFigure 4: Vertical displacements of bay 1 reference points, comparison between experimentaland numerical model.0 2 4 6−0.25−0.2−0.15−0.1−0.050Volume loss (%)Displacement (mm)  A expB expE expG numA numB numE numG num(a) 20% opening0 2 4 6−0.25−0.2−0.15−0.1−0.050Volume loss (%)Displacement (mm)  A expB expE expG numA numB numE numG num(b) 40% opening0 2 4 62345Volume loss (%)Normalised displacement (−)  ABEG(c) normalised, 20% opening0 2 4 62345Volume loss (%)Normalised displacement (−)  ABEG(d) normalised, 40% openingFigure 5: Horizontal displacements of base reference points, comparison between experimen-tal and numerical model.displacements are plotted in Figures 5c and 5d as normalised with respect to the experimentalvalues. After an initial adjustment, up to 0.5% of volume loss, the ratio between numericaland experimental values tends to remain constant, suggesting an appropriate modelling of therelative displacement between the reference points.Following the procedure described in Section 3, Figure 6 reports the relative contribution ofshear and bending deformations for each bay of the 20% and 40% window opening models.The trend of increasing deformation with larger volume losses is in line with the experimentalobservations, as well as the absolute and relative deformation magnitude.Both the experimental and numerical results show a dominant contribution of the shear com-0 2 4 6−0.0100.010.020.030.04tunnel volume loss (%)deflection (mm)  shearbending(a) Bay 1, 20% opening0 2 4 6−0.015−0.01−0.00500.0050.01tunnel volume loss (%)deflection (mm)  shearbending(b) Bay 2, 20% opening0 2 4 6−0.04−0.03−0.02−0.0100.01tunnel volume loss (%)deflection (mm)  shearbending(c) Bay 3, 20% opening0 2 4 6−0.0200.020.040.060.08tunnel volume loss (%)deflection (mm)  shearbending(d) Bay 1, 40% opening0 2 4 6−0.02−0.0100.010.02tunnel volume loss (%)deflection (mm)  shearbending(e) Bay 2, 40% opening0 2 4 6−0.06−0.04−0.0200.02tunnel volume loss (%)deflection (mm)  shearbending(f) Bay 3, 40% openingFigure 6: Separation of bending and shear components, comparison between experimentaland numerical model.XYZModel: TEST08_20_SUPPRE_0109 NOV 2016 17:03:46 test08_20_meshiDIANA 10.0-07 : Univ. of Cambridge (a) 20% openingsXYZModel: TEST08_30_SUPPRE_0109 NOV 2016 17:04:02 test08_30_meshiDIANA 10.0-07 : Univ. of Cambridge (b) 30% openingsXYZModel: TEST08_40_SUPPRE_0109 NOV 2016 17:04:16 test08_40_meshiDIANA 10.0-07 : Univ. of Cambridge (c) 40% openingsXYZModel: TEST08_50_SUPPRE_0109 NOV 2016 17:04:36 test08_50_meshiDIANA 10.0-07 : Univ. of Cambridge (d) 50% openingsFigure 7: Fac¸ade meshes for the parametric study variations.ponent, which significantly increases for increasing volume losses, while the bending defor-mation remains generally small. According to the adopted sign convention, negative bendingindicates a concave building deflection (i.e. sagging mode, see Fig. 1). A hogging type de-formation would be expected for the entire building, due to its position within the tunnelling-induced settlement profile; however, the centrifuge model exhibits a small degree of saggingdeflection in the second and third bay, for both the 20% and 40% opening cases. This be-haviour is not completely captured by the numerical model, which shows a small saggingdeflection only in the third bays. However, the general good agreement between the exper-imental and numerical deflection contributions enable the use of the numerical model as areliable tool to investigate different scenarios.Figure 7 shows the geometrical variations included in a sensitivity study which was per-formed on the effect of window openings. In the building portion closer to the tunnel centre-line (bay 1, Fig. 8a), larger openings lead to a reduced hogging bending deformation, whichbecomes almost negligible for the extreme case of 50% openings. In the central bay (Fig. 8b),after a similar reduction between 20% and 30% of windows openings, the bending deflectionchanges in shape and becomes of the sagging type. This behaviour is due to the combination0 2 4 6−0.0200.020.040.060.08tunnel volume loss (%)deflection (mm)  20%30%40%50%shearbending(a) Bay 10 2 4 6−15−10−505 x 10−3tunnel volume loss (%)deflection (mm)  20%30%40%50%shearbending(b) Bay 20 2 4 6−0.06−0.04−0.020tunnel volume loss (%)deflection (mm)  20%30%40%50%shearbending(c) Bay 3Figure 8: Separation of bending and shear components, variation of opening percentage.XYZModel: TEST08_20_SUPPRE_02LC6: Load case 6Step: 97  LOAD: 9.6Nodal PDTX...G RESPDTMax/Min on model set:Max = .653  Min = .245Factor =  10020 NOV 2016 17:32:27 def_08_20iDIANA 10.0-07 : Univ. of Cambridge (a) 20% openingsXYZModel: TEST08_30_SUPPRE_02LC6: Load case 6Step: 97  LOAD: 9.6Nodal PDTX...G RESPDTMax/Min on model set:Max = .66  Min = .242Factor =  10020 NOV 2016 17:32:37 def_08_30iDIANA 10.0-07 : Univ. of Cambridge (b) 30% openingsXYZModel: TEST08_40_SUPPRE_02LC6: Load case 6Step: 97  LOAD: 9.6Nodal PDTX...G RESPDTMax/Min on model set:Max = .664  Min = .241Factor =  10020 NOV 2016 17:32:51 def_08_40iDIANA 10.0-07 : Univ. of Cambridge (c) 40% openingsXYZModel: TEST08_50_SUPPRE_02LC6: Load case 6Step: 97  LOAD: 9.6Nodal PDTX...G RESPDTMax/Min on model set:Max = .671  Min = .239Factor =  10020 NOV 2016 17:33:00 def_08_50iDIANA 10.0-07 : Univ. of Cambridge (d) 50% openingsFigure 9: Fac¸ade deformed shape for the parametric study variations, magnitude factor=100.between the higher flexibility of the building with larger openings and the influence of thehorizontal component of the tunnelling-induced soil displacements. Figure 9 indicates thatthis effect is limited to the lower side of the building, and it does not affect the global de-formation mode of the fac¸ade, which remains predominantly in hogging. In bay 3 (Fig. 8c)the trend is confirmed by an increasing sagging type deformation of the bending deflection.For all bays the shear component keeps increasing with increasing opening percentage, andrepresents the larger contribution to the total building deflection.5 CONCLUSIONSThis paper analyses the relative contribution of bending and shear deflection to the tunnelling-induced deformation of surface masonry buildings. Finite element modelling is used to sim-ulate the response of 3D printed models of complex structures adjacent to tunnel excavations,which was modelled in a geotechnical centrifuge. For the first time, numerical results arevalidated not only by comparison with soil and building displacements, but also by verifyingthe model capability of reproducing the experimentally observed proportion between bendingand shear deformations.The model is used to evaluate the effect of windows openings on these deformations for astructure located in the hogging portion of the tunnelling-induced settlement profile. Theresults emphasize the governing contribution of the shear component and indicate the needto reconsider current assessment procedures, which relate the effect of openings solely to areduction in bending stiffness (e.g. [10]).6 AcknowledgmentsThe authors are grateful to EPSRC grant EP/KP018221/1 and Crossrail for providing finan-cial support. The related research data is available at http://dx.doi.org/10.17863/CAM.6492.References[1] J B Burland, Standing J R, and Jardine F M. Building response to tunnelling: case stud-ies from construction of the Jubilee Line Extension, London. CIRIA Special PublicationSeries. Thomas Telford, London, 2001.[2] R J Mair, R N. Taylor, and J B Burland. Prediction of ground movements and assessmentof risk of building damage due to bored tunnelling. In R.J. Mair and R.N. Taylor, editors,Geotechnical Aspects of Underground Construction in Soft Ground. Proceedings of theInternational Symposium, pages 713–718, Rotterdam, 1996. Balkema.[3] M Son and E J Cording. Estimation of building damage due to excavation-inducedground movements. Journal of Geotechnical and Geoenvironmental Engineering,131(2):162–177, 2005.[4] D M Potts and T I Addenbrooke. A structure’s influence on tunnelling-induced groundmovements. Proceedings of the Institution of Civil Engineers: Geotechnical Engineer-ing, 125(2):109–125, 1997.[5] J N Franzius, D M Potts, and J B Burland. The response of surface structures to tunnelconstruction. Proc Inst Civil Eng: Geotech Eng, 159(1):3–17, 2006.[6] K H Goh and R J Mair. The response of buildings to movements induced by deepexcavations. Geotechnical Engineering Journal of the SEAGS and AGSSEA, 42(3),2011.[7] S. Ritter, G. Giardina, M.J. DeJong, and Mair R.J. Centrifuge modelling of buildingresponse to tunnel excavation. (Submitted for review to the International Journal ofPhysical Modelling in Geotechnics).[8] G. Giardina, M.J. DeJong, and R.J. Mair. Interaction between surface structures andtunnelling in sand: Centrifuge and computational modelling. Tunnelling and Under-ground Space Technology, 50:465–478, 2015.[9] D Cook. Studies of settlement and crack damage in old and new facades. In Proc., 3rdInt. Masonry Conf., volume 6, pages 203–211, London, 1994.[10] M Melis and J Rodriguez Ortiz. Consideration of the stiffness of buildings in the esti-mation of subsidence damage by epb tunnelling in the madrid subway. In Response ofBuildings to Excavation Induced Ground Movements Conference, London, 2001.

Influence of building geometry on bending and shear deformations of buildings subject to tunnelling subsidence:numerical modelling

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Influence of building geometry on bending and shear deformations of buildings subject to tunnelling subsidence:numerical modelling

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