Tunnelling-induced deformation and damage on historical masonry structures

118

Amorosi, A. et al. (2014). Geotechnique 64, No. 2, 118–130 [http://dx.doi.org/10.1680/geot.13.P.032]

Tunnelling-induced deformation and damage on historical masonrystructures

A. AMOROSI�, D. BOLDINI†, G. DE FELICE‡, M. MALENA‡ and M. SEBASTIANELLI‡

The analysis of deformation and damage mechanisms induced by shallow tunnelling on masonrystructures is carried out using an integrated, geotechnical and structural, numerical approach based ontwo-dimensional finite-element analyses. The masonry construction, schematised as a block structurewith periodic texture, is regarded at a macroscopic scale as a homogenised anisotropic medium. Theoverall mechanical properties display anisotropy and singularities in the yield surface, arising from thediscrete nature of the block structure and the geometrical arrangement of the blocks. The soil ismodelled by means of a linear elastic-perfectly plastic model. The numerical analyses are performedassuming plane strain and plane stress conditions for the soil and the masonry structure, respectively.A displacement-controlled technique is adopted to simulate the tunnel construction, which producessettlement troughs in agreement with the empirical Gaussian predictions at different volume lossesunder free-field conditions. In order to test the numerical approach, a preliminary set of parametricanalyses is carried out considering a simple masonry wall, characterised by different geometrical andmechanical properties, founded on a clayey deposit. Then, the case study of the Felice aqueduct inRome (Italy), undercrossed by two tunnels of a new metro line, is considered. Significant differencesare observed between the uncoupled analysis, where displacements predicted under free-field condi-tions are simply applied at the foundation level of the structure, and the interaction-based one, thelatter being characterised by a reduced amount of tensile plastic strain. Numerical results in terms ofvertical displacements at the ground level and on the structure are found to be in good agreementwith monitoring data, thus validating the numerical model for this class of soil–structure interactionproblems.

KEYWORDS: numerical modelling; soil/structure interaction; tunnels

INTRODUCTIONThe prediction of settlements is one of the main tasks in thedesign of underground infrastructures, as it allows estimationof the related damage induced on surface structures andprovides a key ingredient to select the most appropriatemitigation techniques to be eventually adopted in order tominimise it (e.g. Mair & Taylor, 1997; Mair, 1998; Puzrin etal., 2012). This holds particularly true for shallow tunnels inurban areas, especially in the presence of cultural heritagebuildings for which the preservation has to be guaranteed(e.g. Burghignoli, 2012; Rampello et al., 2012).

The conventional approach to evaluate possible induceddamage, which is currently in use for a preliminary assess-ment of building performance, is based on the empiricalprediction of the subsidence curve under free-field condi-tions (Peck, 1969; O’Reilly & New, 1982; Fargnoli et al.,2013). The building is represented by a simple, weightless,two-dimensional (2D) deep elastic beam undergoing saggingand hogging modes of deformation according to the soildisplacement profile; the onset of cracking is related to thecritical tensile strain within the beam associated with shearand bending (Burland & Wroth, 1974; Burland et al., 1977).This model was then improved to incorporate the influenceof horizontal strain in the foundation soil (Boscardin &Cording, 1989; Burland, 1997).

More recently, an extension of this approach to a three-dimensional (3D) schematisation of the structure was pro-posed, adopting an analytical thick plate model to includethe effect of both in-plane and out-of-plane ground move-ments (Namazi & Mohamad, 2013).

These uncoupled approaches disregard the mutual inter-action between the soil and the structure and the influenceof structure stiffness and weight on the tunnelling-relateddisplacement field; as such they frequently lead to over-estimated differential settlements and, consequently, to pre-dictions of the induced damage that can be far more severewhen compared to what is typically observed in real cases.

An attempt to include building stiffness into the designapproach was proposed in Potts & Addenbrooke (1997), onthe basis of a parametric finite-element study representativeof the typical conditions encountered during tunnel excava-tions in London Clay. Franzius et al. (2004) extended thislatter study to include the role of the building weight.

In general, the use of numerical methods (finite-elementor finite-difference methods) is nowadays common; neverthe-less their success in practical application strongly dependson different factors, which include 2D or 3D geometricaldiscretisation (e.g. Kasper & Meschke, 2004), correct re-presentation of the construction stages (e.g. Contini et al.,2007; Moller & Vermeer, 2008), initial state of the soil (e.g.Franzius et al., 2005; Grammatikopoulou et al., 2008),drainage conditions (e.g. Wongsaroj et al., 2007), numericaltechniques and constitutive hypotheses (e.g. Gonzalez et al.,2012).

Referring to masonry buildings, 2D finite-element ap-proaches based on a non-linear model for both soil andsurface structure were developed in Liu et al. (2000), Son &Cording (2011) and Amorosi et al. (2012), while more

Manuscript received 21 May 2013; revised manuscript accepted 16October 2013. Published online ahead of print 9 December 2013.Discussion on this paper closes on 1 July 2014, for further details seep. ii.� Technical University of Bari, Italy.† University of Bologna, Italy.‡ University of Roma Tre, Italy.

complex 3D simulations accounting for the non-linear andirreversible behaviour of the soil, the structure and their inter-action, were presented in Burd et al. (2000) and Giardina etal. (2010).

In this paper the results are summarised for a multi-disciplinary research programme aimed at combining theadvances in geotechnical and structural engineering withreference to the numerical analyses of tunnel excavationsinteracting with masonry surface structures. Major emphasisis given here to the effects of the advanced constitutivemodel adopted for the masonry (de Buhan & de Felice,1997; de Felice et al., 2010), while a more conventionalhypothesis is considered for the soil. The long-term objec-tive of the research is to provide an insight into the damagepatterns of ancient masonry structures interacting with un-derground constructions, by means of up-to-date constitutivemodels and numerical finite-element tools.

In the first part of the paper the results of 2D finite-element simulations of the excavation of an ideal shallowtunnel in a medium consistency clayey soil are presented,first with reference to free-field conditions and then assum-ing the pre-existence of a surface masonry wall. Theanalyses were aimed at establishing the role of the masonrystructure on the resulting surface settlement profile and atinvestigating the evolution of the tensile plastic strain accu-mulation into the wall. In particular, a number of parametricanalyses were carried out to investigate the influence ofgeometry (i.e. height and length), eccentricity and strengthproperties of the masonry structure. The tunnel-inducedplastic strain distribution within the structure is associatedwith typical bending or shear damage mechanisms and theresulting subsidence profiles are compared to those obtainedunder free-field conditions to explore the relevance of soil–structure interaction phenomena.

All of the above was preparatory to the study of a realancient masonry structure, the Felice aqueduct of Rome(Italy), undercrossed by two tunnels of the new C metro line.The tunnels were excavated in pyroclastic soils with earthpressure balance (EPB) machines, which guaranteed volumelosses at the surface lower than 0.5%. Uncoupled and inter-action 2D finite-element analyses were carried out and theresults of these class C back-predictions are here discussedtaking advantage of the available monitoring data providedby the tunnel contractor.

STATEMENT OF THE PROBLEMAs discussed above, in this study a 2D numerical

approach is followed to investigate the interaction betweenthe excavation of a shallow tunnel and the response of asurface masonry structure. This assumption confines thestudy of the problem to the case of a tunnel being excavatedperpendicular to the principal plane of the structure. Thesegeometrical conditions can be considered as sufficientlyrepresentative for the case study presented in the second partof the paper.

Owing to the very different geometric and boundaryconditions of soil and masonry structures, a plane strainbehaviour is assumed for the former, whereas a plane stresscondition is adopted for the latter. This assumption is con-sidered appropriate when modelling the problem in twodimensions, because plane strain elements, if assumed forthe wall, would induce a slight enhancement of its stiffness(estimated in the order of about 1.5% for the parametricanalyses described in the first part of the paper and about5% for the Felice aqueduct).

As a direct consequence of the above assumption, careshould be taken in selecting the appropriate dimension inthe out-of-plane direction (i.e. element thickness) of the soil

elements adopted in the analysis. In fact, by means of thisoption, which is neglected in fully plane strain conditions,the user controls the volume of soil effectively involved inthe deformation process induced by the presence of theplane stress surface structure, as such influencing the overallsoil–structure interaction process.

In the following, the thickness of the plane stress elementscorresponds to that of the structure, while that of the under-lying plane strain elements is calibrated in order to match theexpected settlements experienced by the structure under itsown weight, the latter being evaluated by simple analyticalapproaches. It is worth noting that the above calibrationprocedure does not significantly affect the results of the tunnelexcavation stage of the analysis, given the displacement-controlled technique employed in its simulation.

The numerical study is performed by the finite-elementprogram Abaqus. The mesh is composed of eight-nodequadrangular plane strain elements for the soil and four-nodequadrangular plane stress elements for the masonry. Thestructure is assumed to be connected to the soil such thatthe full soil strength can be mobilised at the interface.

An advanced constitutive model for the masonry wasimplemented in the code to accurately simulate the initiationand propagation of the settlements-induced damage causedby tunnelling excavation. In comparison, a relatively simpleconstitutive model was adopted for the soil. Related to this,a specific preliminary study has been performed to evaluatethe capabilities of the numerical model to correctly predictthe effects of tunnel excavation in terms of displacements atthe surface and subsurface. A good match with the well-known Gaussian curves for green-field conditions was con-sidered as being representative of this goal.

Modelling of excavationThe excavation of the tunnel was simulated in the follow-

ing steps

(a) initialisation of the stress field in the soil(b) activation of gravity in the masonry structure in several

steps(c) deactivation of soil elements inside the tunnel section and

application of a displacement field at the boundary nodes,in order to obtain the target volume loss.

Following the procedure described in Rowe et al. (1983),the imposed displacements are calculated considering ahomothetic reduction in the tunnel section corresponding tothe target volume loss together with a vertical translationsuch that the lower point of the tunnel remains in its initialposition (Fig. 1). The resulting displacement field is thuscharacterised by both vertical and horizontal components.

In the numerical analyses the application of the nodaldisplacements is performed in several steps of variable size,

Fig. 1. Initial and final configurations of the tunnel section (not toscale; gravity is disregarded in this plot)

TUNNELLING-INDUCED DEFORMATION AND DAMAGE ON HISTORICAL MASONRY STRUCTURES 119

due to the non-linear behaviour of both soil and masonrystructure.

In the preliminary parametric analyses, the volume lossat the tunnel section matches the subsidence volume at theground surface, as calculations are performed consideringundrained conditions for the soil layer. On the contrary, inthe analyses of the case study of the Felice aqueductdrained conditions are assumed during excavation, leadingto different subsidence volume as compared to the volumereduction imposed at the tunnel section. In this latter case,green-field analyses were first carried out in which thevolume reduction at the tunnel section was calibrated toobtain the target subsidence volume as observed at thesurface. Then, the same volume reduction at the tunnelsection was applied in the coupled analysis, that is, in thepresence of the structure.

Constitutive modelsThe constitutive models for soil and masonry are formu-

lated in the framework of classical rate-independent plasti-city. A linear elastic-perfectly plastic constitutive model wasselected for the soil, characterised by a Mohr–Coulombyield criterion and a null dilatancy angle. Although verysimple and often inappropriate, the above hypothesis provedto be sufficient in the context of the present study, asdiscussed later in the subsection entitled ‘Free-field analysisresults’.

A linear elastic-perfectly plastic constitutive model wasalso selected for masonry where, however, anisotropy in bothelastic properties and strength envelope are taken intoaccount. The model is formulated in the framework ofhomogenisation theory of periodic media, referring to ablock masonry structure, consisting of a periodic pattern ofelastic blocks with cohesive and frictional joints. In such acase, a closed-form approximated expression for the elasticstrain energy is provided in de Felice et al. (2010) that takesthe following form

W (�e) ¼ 1

2

Ex

1� vxzvzx

(�exx)

2 þ Ez

1� vxzvzx

(�ezz)

2

� �

þ 1

2

2vxzEz

1� vxzvzx

�exx�

ezz þ 4G(�e

xz)2

� � (1)

where x and z are the horizontal and vertical directions,respectively. The coefficients in equation (1) depend on theelastic Lame coefficients of the blocks (º9b, �b) and thenormal Kn and tangential Kt stiffness of the joints, as well ason the height a and width b of the blocks as follows

1

Ex

¼ 4a

4abKn þ b2K t

þ 1

4�b

þ 1

4(º9b þ �b)(2)

1

Ez

¼ 1

aKn

þ 1

4�b

þ 1

4(º9b þ �b)(3)

1

G¼ 1

aK t

þ 4a

4abK t þ b2Kn

þ 1

�b

(4)

vxz

Ex

¼ vzx

Ez

¼ º9b

4�b(º9b þ �b)(5)

The elastic domain is defined in the context of multi-surface perfect plasticity as

Es ¼ f�j f a(�) :¼ na : �–ca < 08 2 1, . . ., m½ �g (6)

where f a(�) are m independent planes, intersecting in anon-smooth way, which define the yield surface. The expres-sion for the yield surface of block masonry is provided in deBuhan & de Felice (1997) on the basis of the yield design

homogenisation method. In particular, in the case of historicmasonry the blocks can be assumed as infinitely resistantbodies and the mortar joints as interfaces with cohesion cand friction angle �. In such a case, the yield surfacecomprises m ¼ 4 planes, which can be written in terms ofstress components in the Oxz reference adopted for the jointsas follows

f 1 :¼�� xx þ tg(�)� zz þ 1þ tg(�)�½ �� xz � c� c�=tg(�)

< 0

f 2 :¼�� xx þ tg(�)� zz � 1þ tg(�)�½ �� xz � c� c�=tg(�)

< 0

f 3 :¼� zz þ 1=tg(�)� xz � c=tg(�) < 0

f 4 :¼� zz � 1=tg(�)� xz � c=tg(�) < 0

(7)

where � ¼ 2a/b is the aspect ratio height-to-width of theblocks.

The model is integrated at the Gauss point level by meansof a numerical procedure based on quadratic minimisation(Goldfard & Idnani, 1983).

PARAMETRIC STUDYIn the following section the results of a preliminary

parametric study on the behaviour of a simple masonrystructure affected by the excavation of a shallow tunnel arediscussed. The aim of the analyses is to highlight the role ofgeometry, eccentricity and joint cohesion of the structure onits overall behaviour as predicted in the specific soil–structureinteraction process under study.

Geometry, boundary and initial conditions, constitutiveparameters

A schematic sketch of the numerical model is shown inFig. 2. The coordinate system is defined such that x is thedistance from the tunnel axis in the horizontal direction andz is the depth below the ground surface.

The tunnel is located at a depth of z0 ¼ 20 m and ischaracterised by a diameter D ¼ 10 m. It is excavated in ahomogeneous clayey layer of medium consistency, withground-water level coincident to the ground surface. Theassumed value of K0 is 0.593, as predicted by the well-known expression by Jaky (1948). All the simulations of theexcavation process are performed in undrained conditions.

The masonry structure represents a typical ancient wall.The geometric and mechanical properties of the structure, aswell as its position with respect to the tunnel, were varied inthe parametric study.

In the reference analysis, the structure is characterised bya width of 40 m, a height of 5 m and a thickness of 1 m. Theoffset distance between the centre of the wall and the tunnelcentre-line, that is its eccentricity, is equal to 20 m; its rightcorner has the same x-coordinate as the tunnel axis. Consis-tently with the procedure discussed in the previous section,‘Statement of the problem’, a thickness of 10 m is assumedfor the plane strain elements, this value being kept constantin all the parametric analyses described hereafter. Themechanical parameters adopted for the masonry structure inthe reference simulation are: ª ¼ 18 kN/m3, a ¼ 8 cm,b ¼ 30 cm, Eb ¼ 3.18 GPa, �b ¼ 0.23, Kn ¼ 30.6 GN/m3,Kt ¼ 12.80 GN/m3, c ¼ 5 kPa and � ¼ 318 (de Felice et al.,2010). Eb and �b indicate the Young’s modulus and thePoisson ratio, respectively.

120 AMOROSI, BOLDINI, DE FELICE, MALENA AND SEBASTIANELLI

The soil parameters, assumed for all the simulations, areindicated in Fig. 2.

Free-field analysis resultsFigure 3 shows the free-field surface settlements for values

of the volume loss, VL, equal to 0.59% and 1.66%. The firstvalue is considered typical for a well-performing EPB ex-cavation whereas the second would be appropriate for aworse scenario for the excavation process. The settlementprofile calculated in the numerical analysis for a volume lossof 0.59% is in good agreement with those predicted by theGaussian distributions (Peck, 1969) for trough width param-eter K in the range 0.5–0.6. The accordance between thenumerical results and the empirical predictions decreases inthe case of VL ¼ 1.66%, probably due to the slight heave ofthe subsidence profile as predicted numerically, which in-duces some differences between the subsidence volume andthe volume loss at the tunnel section.

In general, the satisfactory comparison between the pro-files of the empirical and numerical solutions indicates thatthe relatively simple constitutive assumptions and the simu-lation technique adopted for the tunnel excavation are ade-quate to the purpose of the present study, provided lowvalues of K0 are adopted.

Results of the interaction analysesReference analysis. Figure 4 shows the results obtained forthe reference analysis. The two curves in the upper portion of

the figure refer to the ground surface vertical settlements aspredicted at the end of the gravity activation for the wall andat the end of the tunnel excavation simulation. In the lowerpart of the figure, the distribution of principal tensile plasticstrain for the masonry wall as induced by the excavation (i.e.disregarding the effect of gravity loading) is provided, thesmall segments superimposed on the strain contours repre-senting the corresponding principal direction.

The aforementioned representation, adopted throughoutthe rest of the paper, stems from the homogenisation ap-proach for the masonry, where the development of cracks isrepresented by an equivalent plastic strain. For the class ofproblems under study, damage is typically associated withthe opening of tensile cracks and, as such, the contour oftensile plastic strain can be considered as an appropriateindicator of this phenomenon. According to Boscardin &Cording (1989) different categories of damage can in fact beassociated with different levels of tensile strain (i.e. aboutequivalent in magnitude to the tensile plastic strain used inthe representation). In this context, the superposition of theprincipal direction segments provides an indication of thepossible crack openings’ direction.

At the end of the gravity activation, the structure isinflected symmetrically with respect to its centre. As aconsequence of tunnel excavation, the wall shows a displace-ment pattern characterised by the superposition of a prevail-ing rigid rotation towards the tunnel centre and a deformativeresponse concentrated within the range �20 m < x < �10 m.This induces a concentration of plastic strain characterisedby two different patterns: a shear-induced pattern, diffused

VL 0·59%�

50250�25x: m

VL 1·66%�

50250�25x: m

�50

K 0·5�

K 0·6�

�50

25

20

15

10

5

0

�5

Set

tlem

ent,

: mm

Sv

75

50

25

0

K 0·5�

K 0·6�

Fig. 3. Net vertical settlement for a volume loss of 0.59% (on the left) and 1.66% (on the right) for the free-field analysis andcomparison with empirical solutions

z0 20 m�

D 10 m�

50 m

400 m

γ

νψ

20 kN/m

0·59335000 kPa, 0·25

5 kPa, 24°, 0°

�

�

� � � �

� � � � � �

3

0KE

c ϕ

Fig. 2. Geometry of the problem (reference analysis) and soil parameters adopted in the numerical analyses

TUNNELLING-INDUCED DEFORMATION AND DAMAGE ON HISTORICAL MASONRY STRUCTURES 121

from the base to the upper portion of the wall with prevailingprincipal tensile plastic strain direction equal to 458 andaverage magnitude of 0.7%, and a bending-induced pattern,associated with the sagging portion of the settlement curve,concentrated in the lower-right portion of the wall, withaverage vertical direction and magnitude of 1.0%. It is worthobserving that such values of strain would lead to very severedamage according to the categories proposed by Boscardin &Cording (1989); these extreme conditions are related to thespecific ideal interaction problem under study, appropriatelyselected to enhance the damage-related effects due to under-ground excavations.

Parametric study. The parametric study was aimed atinvestigating the role of the mortar joints’ cohesion (0, 5and 10 kPa) and that of height (1, 5, 10 and 20 m), length(20, 40, 80 and 400 m) and eccentricity of the wall (0, 10 and20 m with respect to tunnel axis). This latter quantity isdefined as the horizontal distance between the tunnel axis andthe structure centre.

The results of the complete parametric study are sum-marised in Figs 5 and 6. Fig. 5 shows the profiles of groundsurface settlements at the end of gravity activation in thestructure and the corresponding incremental settlement pro-files as induced by the tunnel construction (i.e. disregardingthe effect of gravity loading). It can be observed that in mostcases those latter settlement profiles deviate from the Gaus-sian free-field pattern, as a consequence of the soil–structureinteraction (e.g. Potts & Addenbrooke, 1997; Shahin et al.,2011). The results of the reference analysis are indicated inall the plots by thick black lines. In Fig. 6 the contour ofprincipal tensile plastic strain and its direction are reported.

The influence of structure cohesion appears negligible interms of overall displacement pattern, but more relevant forthe damage development within the masonry wall. The analy-sis for a null cohesion displays a severe shear-induceddamage pattern, characterised by an average tensile plasticstrain value of 0.8% and a corresponding bending-inducedvalue of 0.6%, this latter being lower than that of thereference case due to the prevailing shearing mode. No sig-nificant differences are observed between the reference analy-sis and that carried out with cohesion c ¼ 10 kPa. This set of

analyses clearly demonstrates the role of non-linear structuralbehaviour on the correct assessment of the masonry response.In fact, a linear anisotropic-elastic analysis would have pre-dicted the same level of damage in all the investigated cases.

The height of the wall clearly affects both structuralstiffness and weight. Increasing height values are associatedwith larger settlements due to weight, but lower deflectionsin relation to larger stiffness. The deflection of the 1-m-highwall resembles that of a Gaussian curve, while the analysesconsidering wall heights of 5 and 10 m are characterised byan almost bilinear deflection pattern in the right portion ofthe subsidence curve, with a corner point located at about15 m left from the tunnel axis. A rigid rotation prevails forthe tallest structure, in which case almost no damage isobserved in the structure apart from some minor plasticstrain accumulation on the lower left side of the wall. Thetunnel excavation induces prevailing shear damage in the10-m-high structure, while a bending-type damage patternresults in the case of the shortest wall, where possiblevertical cracks are expected in plastic regions characterisedby very large average plastic strain values of about 3%.

The influence of length is strictly related to the relativeposition of the tunnel and the structure, and to the extent ofthe soil volume affected by the tunnelling construction. Theresponse of the shortest structure (length ¼ 20 m) is charac-terised by a relatively rigid behaviour which induces arelatively moderate tensile plastic accumulation during thetunnel excavation (0.3 and 0.6% for shear and bending,respectively). In fact, the masonry wall is entirely located onthe portion of the ground surface displaying a sagging modeof deformation under green-field conditions. Longer struc-tures, conversely, show significant shear-induced damagemainly concentrated at a distance of about 15 m left fromthe tunnel axis, associated with the bending-induced damageconcentrated at the bottom right side of the wall, with anoverall response very similar to that of the reference analy-sis. In particular, for the 80-m-long wall, the impact of thetunnel excavation only affects less than 25% of its length; itsleft portion does not experience any significant excavation-related damage. The special case of a 400-m-long structure,perfectly symmetrical with respect to the tunnel (eccentricityequal to 0 m), is also displayed; in this case the incrementalsettlement profile is characterised by a Gaussian-like shape.

20100�10�20�30�40

0�10�20�30

�50

: mx

75

50

25

0

Set

tlem

ent,

: mm

Sv

Gravity

VL 1·66 %�

0

2·00 10� �3

4·00 10� �3

6·00 10� �3

8·00 10� �3

1·00 10� �2

5

0�40

Fig. 4. Vertical displacement at ground surface and distribution of principal tensile plastic strainin structure for the reference analysis

122 AMOROSI, BOLDINI, DE FELICE, MALENA AND SEBASTIANELLI

This result should be related to the adopted length andeccentricity, as the relative soil–structure stiffness coincideswith that assumed in the other cases. The plastic straindistribution is symmetric with respect to the tunnel axis andis characterised by the two-fold damage patterns associatedwith bending in the sagging zone (average plastic strain

value equal to 3%) and to shearing at a distance of about15 m from the tunnel axis (average plastic strain equal to1%). Once again, where present, the shear-induced damageis diffuse along the height of the wall.

Finally, eccentricity is also found to play an importantrole in the interaction problem. A structure with zero

Set

tlem

ent,

: mm

Sv

Set

tlem

ent,

: mm

Sv

Set

tlem

ent,

: mm

Sv

VL 1·66%�

250�25x: m

250�25x: m

�50

250�25x: m

250�25x: m

�50�50

250�25x: m

250�25x: m

�50�50

250�25x: m

250�25x: m

�50�50

�50

75

50

25

0

Set

tlem

ent,

: mm

Sv

75

50

25

0

Cohesion:

0 kPa

5 kPa

10 kPa

75

50

25

0

75

50

25

0

Height:

1 m

5 m

10 m

20 m

75

50

25

0

75

50

25

0

Length:

20 m

40 m

80 m

400 m

75

50

25

0

75

50

25

0

Eccentricity:

0 m

10 m

20 m

Fig. 5. Vertical displacement at ground surface obtained in the different parametric analyses

TUNNELLING-INDUCED DEFORMATION AND DAMAGE ON HISTORICAL MASONRY STRUCTURES 123

eccentricity exhibits a deformation pattern similar to thatobserved for the 400-m-long structure, with a comparabledistribution of tensile plastic strain. The analysis relative tothe intermediate eccentricity produces a settlement troughwhich is, in part, on the left side with respect to the tunnelaxis, superimposed on the one observed for the zero eccen-tricity case. On the right side, the structure is exposedto a moderate sagging deformation pattern associated withbending-induced damage (average plastic strain equal to 2%)in the lower portion of the wall.

CASE STUDYDescription of the case study

The undercrossing of the Felice aqueduct by the twintunnels of the new C underground line, currently underconstruction in Rome (Italy), is analysed in the following.The Felice aqueduct (Fig. 7) is a historical construction builtin 1585 on the ruins of Circo Variano, an amphitheatredating back to the third century B.C. The structure is madeof a sequence of arches with 2.3 m span and height of9.3 m. In the early twentieth century, some of the originalarches were replaced by five larger ones, characterised by5.5 m span and 8.0 m height, separated by rectangular piersof dimensions 1.5 m 3 2.3 m. The original structure is madeof combined tuff and brick masonry, while the more recentadditions are made of brick masonry. The underlying CircoVariano, embedded below the ground level, is characterisedby an 8-m-thick wall made out of poorly bonded tuff blocks,whose continuity is interrupted by a sequence of little open-ings in its upper portion. In the case under study, it playsthe role of a stiff foundation for the aqueduct.

The two tunnels have a diameter D ¼ 6.7 m, inter-axisi ¼ 22.8 m and are located at a depth z0 ¼ 25.8 m from theground surface. They were excavated by two identical EPBmachines, underpassing the aqueduct in two different stages(odd line first, indicated as OL, followed after 10 days bythe even one, EL).

A monitoring system was installed prior to the excavation,aimed at registering the movements at the ground surfaces andon the aqueduct. The details of this system are given later.

An extensive physical and mechanical characterisation ofthe soils and the masonries involved in the problem wascarried out during the design of the new underground line.For sake of brevity in the following, only the main resultsare summarised.

The subsoil in the area under study was investigated bymeans of eight boreholes which showed the presence of sixdifferent layers (Table 1): made ground (R), whose maincharacteristic is its variability due to the anthropic origin;Villa Senni tuff (VS-PN), a lightly cemented sandy tuff;alternate levels of cemented sandy tuffs (T1/T2) and partlycemented (TA) silty tuff and a stratum of relatively stiff clayeysilt (ST-AR). All the above materials are characterised byrelatively large permeability coefficients, in the order of10�6 m/s for the tuffs and 10�7 m/s for the silt, as observed bynine Lefranc tests carried out along five different boreholes.

Four piezometers were installed at different depths alongtwo verticals, showing the existence of a permanent verticalflow from the upper layers across the silty one, leading tothe pore-water pressure profile shown in Fig. 8.

A set of laboratory tests was carried out to identify theshear strength parameters of those strata for which undis-turbed soil samples could be retrieved, namely VS-PN, T1,T2, TA and ST-AR. Forty standard penetrometer tests werealso performed to complete the overall picture in terms ofshear strength and stiffness of the subsoil, actually leadingto rather dispersed results, especially in the semi-lithoid tuffstrata. The profile of the very small strain stiffness was

Reference analysis

Influence of cohesion

c 0 kPa�

H 1 m�

Influence of height

H � 10 m

H 20 m�

Influence of length

L 20 m�

L 80 m�

L 400 m�

Influence of eccentricity

c 10 kPa�

e 0 m�

e 10 m�

5

0

�40

5

0

5

0

10

5

0

5

0

10

10

15

20

5

0

5

0

5

0

�25 �5 15

5

0

5

0

10

1 10� �2

8 10� �3

6 10� �3

4 10� �3

2 10� �3

0

0�10�20�30

�40 0�10�20�30

�40 0�10�20�30

�40 0�10�20�30

�40 0�10�20�30

0�10�20

�40 0�10�20�30

2520�15

200�10�20

100�10�30 �20

�40 0�10�20�30

Fig. 6. Distribution of principal tensile plastic strain in structureobtained in the different parametric analyses

124 AMOROSI, BOLDINI, DE FELICE, MALENA AND SEBASTIANELLI

obtained by performing a specific cross-hole test; the aver-age G0 values for each stratum were further elaborated toevaluate the corresponding G values appropriate to the strainlevel expected for the class of problem under study (0.01%< �s < 0.1%), with reference to stiffness decay curves takenfrom the literature (Vucetic & Dobry, 1991). K0 values forthe different strata are assumed to equal those predicted bythe well-known expression by Jaky (1948) assuming anoverconsolidation ration (OCR) equal to one. In fact, for thetuff strata (VS-PN, T1, TA and T2) it appears that theprevious stress history has not been significantly charac-terised by relevant erosion and deposition cycles, consis-tently with their geological age (they date back to less than0.5 million years ago). This assumption is partly confirmedby the unique pressuremeter test successfully carried out onone of them, the TA stratum, the interpretation of whichleads to a value of K0 ¼ 0.5, fairly similar to the oneassumed here (Table 1). A slightly less satisfactory compari-son characterises the coefficient at rest of the cohesiveST-AR stratum, for which the assumed value, equal to 0.6,is lower than that observed in a pressuremeter test carried

out in this soil, indicating for K0 a value of 0.8 (consistentwith an OCR value of about 2).

An extensive characterisation of the masonries was alsocarried out, including careful identification of the geometri-cal characteristics of the blocks and the execution of severalflat jack tests to detect their stiffness. The values of theparameters adopted in the analyses were selected withreference to the above results. For the selection of the jointstrength parameters specific reference was also made to theavailable data on Roman age construction materials (e.g.Mastrodicasa, 1993).

The selected parameters ª, K0, G, ı, c9, j9 for each soillayer are summarised in Table 1, while those adopted for themasonry structure are reported in Table 2.

The whole system consisting of the Felice aqueduct, theCirco Variano and the soil layers was incorporated into a 2Dfinite-element model. The geometry of the model is shown inFig. 8, together with the position of the two tunnels. Thedomain is characterised by a height of 44 m and a width of163.5 m; the latter dimension being evaluated considering adistance of ten diameters from each of the two tunnels, in

Table 1. Geotechnical properties of soil layers at the construction site (ª unit weight of volume; e void ratio; w natural watercontent; K0 coefficient at rest; k permeability coefficient; � Poisson ratio; G0 shear modulus at small strains; G shear modulus;jj9 friction angle; c9 cohesion; cu undrained strength)

Unit ª: kN/m3 e w: % K0 k: m/s ı G0: MPa G: MPa j9: 8 c9: kPa cu: kPa

R 17.0 1.2 43 0.5 1.0 3 10�5 0.3 40 16 31 10 –VS-PN 17.5 0.9 35 0.4 3.0 3 10�6 0.3 80 32 37 12 –T2 16.0 1.5 45 0.4 4.0 3 10�6 0.3 250 150 35 40 –TA 16.0 1.5 47 0.6 9.0 3 10�6 0.3 210 84 25 27 –T1 16.0 1.5 45 0.4 4.0 3 10�6 0.3 250 150 35 40 –ST-AR 19.5 0.7 25 0.6 3.0 3 10�7 0.3 150 60 25 15 130

z0z0

EL

VS - PN

T2TA

T1

ST - AR

D D

i

OL

�12·5 m p.c.

0·0 m

�8·0 m

�17·5 m

�21·5 m

�44·0 m

�29·8 m

�23·5 m

u

68·85 68·706·70 6·7016·35

Fig. 8. Schematisation of the Felice aqueduct and of the geotechnical conditions

Fig. 7. View of the Felice aqueduct

TUNNELLING-INDUCED DEFORMATION AND DAMAGE ON HISTORICAL MASONRY STRUCTURES 125

order to minimise boundary effects. With reference to theprocedure discussed in the earlier sections, a thickness of11.5 m is assumed for the soil plane strain elements, while thatof 2.3 m is adopted for the masonry structures. Some details ofthe finite-element discretisation are provided in Fig. 9.

Numerical resultsThe case study was first analysed by means of an un-

coupled approach, followed by the more complete interactionone. In the uncoupled analysis the effects of tunnel excava-tion on the structure are evaluated imposing vertical andhorizontal free-field ground displacements at the base of thestructure. These were derived from a free-field analysiscarried out with reference to the observed subsidence vo-lumes VS ¼ 0.49% and VS ¼ 0.48%, for the OL and ELtunnels, respectively. These values were obtained by impos-ing maximum vertical displacements of 25 and 26 mm at thetunnel crown, compatible with the available gap of theadopted tunnel-boring machine. Results in terms of displace-ments were extracted with reference to a depth of 8 m,corresponding to that of the Circo Variano base. The samevolume losses were adopted in the interaction analysisaccording to the sequence of stages described in the earliersubsection ‘Modelling of excavation’.

Figure 10 shows the comparisons between vertical and

horizontal displacement distributions as obtained by the twoanalyses: the vertical trough is smoothed by the presence ofthe structure, leading to a single-peak curve as opposed tothe two-peaks curve characterising the green-field result. Theinteraction analysis also induces a slightly wider settlementtrough, for a lower value of the maximum settlement. As anoverall picture it can be observed that the structure does notsignificantly modify the vertical trough as obtained by thecoupled analysis, irrespectively of its stiffness. This shouldbe ascribed to the length of the structure, which extendsalong the full width of the model (Fig. 8), leading to aGaussian-like settlement profile, consistently with what wasdiscussed in the parametric study with reference to a struc-ture’s length of 400 m. Conversely, the corresponding com-parison in terms of horizontal displacements, also shown inFig. 10, indicates that the interaction analysis significantlyreduces this displacement component, inducing a much low-er amount of horizontal strain in the structure which, accord-ing to Boscardin & Cording (1989) and Burland (1997),plays a relevant role in its damage pattern.

Figure 11 shows the distribution of the principal tensileplastic strain for the structure as predicted by the uncoupledapproach, while Fig. 12 illustrates the corresponding distri-bution for the coupled analysis. In the uncoupled analysis,plastic strain mainly develops within the Circo Variano, nearto the small openings of its upper section, with an averagevalue of about 0.1%, corresponding to a slight degree ofdamage according to Boscardin & Cording (1989). A lower

(a)

(b)

Fig. 9. Masonry discretisation of Felice aqueduct

7550250�25�50

7550250�25�50�75: mx

�75: mx

�8

�6

�4

�2

0

Set

tlem

ent,

: mm

Sv

Green-field

Interaction

OL EL

�2

�1

0

1

2

Hor

izon

tal d

ispl

acem

ent,

: mm

Sh

OL EL

Fig. 10. Comparison between free-field and interaction settle-ments and horizontal displacements at the foundation level (i.e. atthe base of Circo Variano)

Table 2. Mechanical parameters of masonry structure

ª: kN/m3 � Eb: GPa vb Kn: GN/m3 Kt: GN/m3 c: kPa �: deg

Brick masonry 18 0.333 2.0 0.2 57.14 23.81 25 31Tuff masonry 18 0.320 1.5 0.3 37.50 14.42 10 31

126 AMOROSI, BOLDINI, DE FELICE, MALENA AND SEBASTIANELLI

amount of principal tensile plastic strain also cumulates inthe upper portion of the Felice aqueduct, over its arches.The coupled analysis results in less intense tensile plasticstrains, which are almost exclusively cumulated in the CircoVariano with a maximum intensity of 0.05%, correspondingto a negligible to very slight level of damage.

The presence of openings in the aqueduct and CircoVariano strongly influences the plastic deformation pattern asinduced by the non-uniform settlement of the aqueduct’s piers.

Damage tends to localise in the region between two verticaladjacent openings, characterised by lower compression andrelated shear strength. The observed deformation patternsindicate that a prevailing shear response is characterising thebehaviour at the local level, while a more complex overallresponse appears to take place, where both shear and bendingare playing their role. Given the peculiar geometric characterof the aqueduct, this latter would only roughly be accountedfor when adopting the simple equivalent beam analogy.

12011010090

2·00 10� �3

1·80 10� �3

1·60 10� �3

1·40 10� �3

1·20 10� �3

1·00 10� �3

8·00 10� �4

6·00 10� �4

4·00 10� �4

2·00 10� �4

0

OL EL

70: mx

605040 80

Fig. 11. Tensile plastic strain distribution obtained in the uncoupled analysis

12011010090

OL EL

2·00 10� �3

1·80 10� �3

1·60 10� �3

1·40 10� �3

1·20 10� �3

1·00 10� �3

8·00 10� �4

6·00 10� �4

4·00 10� �4

2·00 10� �4

0

70: mx

605040 80

Fig. 12. Tensile plastic strain distribution obtained in the interaction analysis

TUNNELLING-INDUCED DEFORMATION AND DAMAGE ON HISTORICAL MASONRY STRUCTURES 127

The interpretation of the coupled analysis clearly indicatesthat the Circo Variano plays a key role in reducing thehorizontal strain, thus preserving the aqueduct from experi-encing significant excavation-related damage.

Comparison with monitoring dataA comparison between the numerical results and the

monitoring data collected by the contractor during the con-struction of the tunnel is presented here. Vertical displace-ments in the structure and at the ground level were acquiredduring the tunnel undercrossing, by monitoring benchmarksat the base of the structure (Fig. 13 – section D) and targetson it (Fig. 13 – sections A, B, C).

The observed vertical displacements at the four sectionsfrom the top of the structure down to the ground surface are

reported in Fig. 13, together with the corresponding numer-ical predictions. In particular, only a slight reduction of themaximum settlement value is observed from the base (sec-tion D) to the top of the aqueduct (section A), together witha modest overall increase in the lateral uplift.

It is worth noting that, despite some little differences andlocalised phenomena, the numerical outcomes compare wellwith the monitoring data. No evidence of damage wasdetected on the aqueduct, consistent with what was discussedin the earlier subsection ‘Numerical results’.

CONCLUSIONThis paper presents the results of an interdisciplinary,

geotechnical and structural, study devoted to the analysis ofthe response of masonry structures affected by tunnelling-induced ground displacements. This topic is of great rele-vance for tunnel excavation in urban areas where possiblyseveral structures, sometimes of inestimable value, mightinteract with underground developments.

The study, conducted with the finite-element code Abaqus,was performed in 2D conditions assuming plane strain andplane stress conditions for the soil and the structure, respec-tively. As such, the analysed class of problems is that of a tunnelexcavated under a masonry structure, this latter being charac-terised by its plane oriented perpendicularly to the tunnel axis.

The modelled structure represents an ancient masonrywall, schematised as a block structure with periodic texture.Its continuum behaviour at the macro scale (i.e. at the scaleof the analysis) was derived by a homogenisation procedurebased on relatively simple assumption at the local scale (i.e.at the scale of blocks and joints). The resulting model ischaracterised by a non-linear anisotropic mechanical re-sponse. The soil was modelled using a simple elasto-plasticconstitutive assumption.

The first part of the paper describes the results of a setof parametric analyses, aimed at verifying the capability ofthe numerical model in simulating the tunnel excavationand the related soil–structure interaction. A simple masonrywall founded on a clayey deposit was considered, and theinfluences of the mechanical and geometrical properties ofthe structure, as well as of its eccentricity with respect totunnel axis, were investigated. Free-field preliminary ana-lyses demonstrated that, despite the relatively simple con-stitutive hypothesis adopted for the soil, the displacement-controlled technique used to reproduce the tunnel construc-tion well captured the induced ground displacements, asdemonstrated by the comparison with the Gaussian curvesfor surface settlements at different volume losses. Thenumerical results were able to mimic the main features ofthe soil–structure interaction, including the modifications inthe subsidence profile and the related deformative pattern inthe structure.

In the second part of the paper a class C numericalprediction of the settlements induced in a complex historicalmasonry structure (the Felice aqueduct in Rome, Italy) bythe excavation of shallow twin tunnels is presented. First, anuncoupled analysis was performed, applying at the base ofthe structure the displacements obtained by the model underfree-field conditions. Then, a fully coupled simulation wascarried out, thus highlighting the influence of soil–structureinteraction on the computed deformative response of thestructure, characterised by a reduced amount of tensileplastic strains, and in the ground, where horizontal displace-ments were dramatically decreased. The satisfactory com-parison with available monitoring data proved the soundnessof the numerical model.

It is worth commenting on the novelty and potential ofthe presented approach, in which all the important ingredi-

Set

tlem

ent,

: mm

Sv

Set

tlem

ent,

: mm

Sv

Set

tlem

ent,

: mm

Sv

50250�25

50250�25�50x: m

50250�25�50x: m

50250�25�50x: m

6

4

2

0

Set

tlem

ent,

: mm

Sv

Monitoring data (06/10/2011)Numerical results

Section A

6

4

2

0

Section B

6

4

2

0

Section C

�50x: m

6

4

2

0

Section D

Section A

Sec CtionSec Dtion

Sec BtionPrisms Datum point

Fig. 13. Comparison between numerical predictions and monitor-ing data in terms of vertical settlements

128 AMOROSI, BOLDINI, DE FELICE, MALENA AND SEBASTIANELLI

ents of the problem (i.e. the tunnels, the soil and thestructure) are incorporated in a unique model without theneed for cumbersome, or sometimes obscure, links betweenthe ‘geotechnical’ and the ‘structural’ responses. In addition,the masonry constitutive law allows the evaluation of plasticstrain initiation and accumulation within the structure andthe estimation of the induced damage using a realistic (i.e.inelastic and anisotropic) material model.

Should the present approach be further validated for dif-ferent geotechnical and structural conditions, it would beamenable for future use as a class A predictive tool forsimilar soil–structure interaction processes.

ACKNOWLEDGEMENTSSpecial thanks are owed to Eng. Grazia Di Mucci of

Metro C S.p.c.A. for providing monitoring data of the Feliceaqueduct and technical support during the site activity, andto Eng. Marco Ferrandino for carrying out some of theanalyses. Financial support provided by the research pro-grams Reluis, funded by the Italian Civil Protection Depart-ment and PRIN 2009, funded by the Ministry for Researchand Higher Education, is gratefully acknowledged.

NOTATIONa, b height and width of blocks

c mortar joints cohesionc9 soil cohesioncÆ intercept of Æ – plane constituting elastic domain of

masonrycu undrained strengthD tunnel diameter

Eb Young’s modulus of blocksEx, Ez Young’s moduli of masonry in x and z directions

E� elastic domain of masonrye void ratio; eccentricity of the masonry wall

fÆ independent planes constituting elastic domain ofmasonry

G0 shear modulus at small strainsG shear modulusH height of masonry walli tunnel inter-axis

K trough width parameterKn, Kt normal and tangential stiffness of joints

K0 coefficient of earth pressure at restk permeability coefficientL length of masonry wallm number of independent planes constituting elastic

domain of masonrynÆ normal to Æ – plane constituting the elastic domain of

the masonrySv settlementVL volume lossVS subsidence volumeW elastic strain energyw natural water contentx horizontal distance from tunnel axisz depth below ground surface

z0 depth of tunnel axisª unit weight of volume

�e elastic strain tensor�s deviatoric strain

�exx, �e

zz, �exz normal and shear components of elastic strain tensor

º9b, �b elastic Lame coefficients of blocks� 2a/b aspect ratio height-to-width of blocks� Poisson ratio�b Poisson ratio of blocks

�xz, �zx Poisson ratios between x and z directions� stress tensor

�xx, �zz, �xz normal and shear components of the stress tensor� mortar joints friction anglej9 soil friction angle

REFERENCESAmorosi, A., Boldini, D., de Felice, G. & Malena, M. (2012).

Tunnelling-induced deformation in a masonry structure: a nu-merical approach. Proceedings of the 7th international sympo-sium on geotechnical aspects of underground construction insoft ground, Rome (ed. G. Viggiani), pp. 353–359. London, UK:Taylor & Francis.

Boscardin, M. D. & Cording, E. J. (1989). Building response toexcavation induced settlement. J. Geotech. Engng 115, No. 1,1–21.

Burd, H. J., Houlsby, G. T., Augarde, C. E. & Liu, G. (2000).Modelling tunnelling-induced settlement of masonry buildings.Proc. Instn Civ. Engrs – Geotech. Engng 143, No. 1, 17–29.

Burghignoli, A. (2012). L’attraversamento sotterraneo del centrostorico di Roma. Riv. Ital. Geotec. 3, 13–50 (in Italian).

Burland, J. B. (1997). Assessment of risk of damage to buildingsdue to tunnelling and excavation. invited special lecture. Pro-ceedings of 1st international conference on earthquake geotech-nical engineering, IS-Tokyo 95 (ed. K. Ishihara), pp. 1189–1201. Rotterdam, the Netherlands: Balkema

Burland, J. B. & Wroth, C. P. (1974). Settlements on buildings andassociated damage. Proceedings of conference on settlement ofstructures, Cambridge, pp. 611–54. London, UK: Pentech Press.

Burland, J. B., Broms, B. B. & de Mello, V. F. B. (1977). Behaviorof foundations and structures. Proceedings of the 9th interna-tional conference on soil mechanics and foundation engineering,IS-Tokyo 77, vol. 2, pp. 495–546.

Contini, A., Cividini, A. & Gioda, G. (2007). Numerical evaluationof the surface displacements due to soil grouting and to tunnelexcavation. Int. J. Geomech. 7, No. 3, 217–226.

de Buhan, P. & de Felice, G. (1997). A homogenisation approach tothe ultimate strength of brick masonry. J. Mech. Phys. Solids 45,No. 7, 1085–1104.

de Felice, G., Amorosi, A. & Malena, M. (2010). Elasto-plasticanalysis of block structures through a homogeneization method.Int. J. Numer. Analyt. Methods Geomech. 34, No. 3, 221–247.

Fargnoli, V., Boldini, D. & Amorosi, A. (2013). TBM tunnelling-induced settlements in coarse-grained soils: the case of the newMilan underground line 5. Tunnelling Underground Space Tech-nol. 38, 336–347.

Franzius, J. N., Potts, D. M., Addenbrooke, T. I. & Burland, J. B.(2004). The influence of building weight on tunnelling-inducedground and building deformation. Soils Found. 44, No. 1,25–38.

Franzius, J. N., Potts, D. M. & Burland, J. B. (2005). The influenceof soil anisotropy and K0 on ground surface movements result-ing from tunnel excavation. Geotechnique 55, No. 3, 189–199,http://dx.doi.org/10.1680/geot.2005.55.3.189.

Giardina, G., Hendriks, M. A. N. & Rots, J. G. (2010). Numericalanalysis of tunnelling effects on masonry buildings: the influ-ence of tunnel location on damage assessment. Advd Mater. Res.133–134, 289–294.

Goldfard, D. & Idnani, A. (1983). A numerical stable dual methodfor solving strictly convex quadratic programs. Math. Program-ming 27, No. 1, 1–33.

Gonzalez, N. A., Rouainia, M., Arroyo, M. & Gens, A. (2012).Analysis of tunnel excavation in London Clay incorporating soilstructure. Geotechnique 62, No. 12, 1095–1109, http://dx.doi.org/10.1680/geot.11.P.030.

Grammatikopoulou, A., Zdravkovic, L. & Potts, D. M. (2008). Theinfluence of previous stress history and stress path direction onthe surface settlement trough induced by tunnelling. Geotech-nique 58, No. 4, 269–281, http://dx.doi.org/10.1680/geot.2008.58.4.269.

Jaky, J. (1948). The coefficient of earth pressure at rest. J. UnionHungarian Engrs Architects 78, No. 22, 355–358.

Kasper, T. & Meschke, T. (2004). A 3D finite element simulationmodel for TBM tunnelling in soft ground. Int. J. Numer. Analyt.Methods Geomech. 28, No. 14, 1441–1460.

Liu, G., Houlsby, G. T. & Augarde, C. E. (2000). 2-dimensionalanalysis of settlement damage to masonry buildings caused bytunnelling. The Struct. Engr 79, No. 1, 19–25.

Mair, R. J. (1998). 46th Rankine Lecture. Tunnelling and geotech-nics: new horizons. Geotechnique 58, No. 9, 695–736, http://dx.doi.org/10.1680/geot.2008.58.9.695.

Mair, R. J. & Taylor, R. N. (1997). Bored tunnelling in the urban

TUNNELLING-INDUCED DEFORMATION AND DAMAGE ON HISTORICAL MASONRY STRUCTURES 129

environment: State-of-the-art report and theme lecture. Proceed-ings of the 14th international conference on soil mechanicsand foundation engineering, Hamburg, vol. 4, pp. 2353–2385.Rotterdam, the Netherlands: Balkema.

Mastrodicasa, S. (1993). Dissesti statici delle strutture edilizie.Milan, Italy: Hoepli Editore (in Italian).

Moller, S. C. & Vermeer, P. A. (2008). On numerical simulation oftunnel installation. Tunnelling Underground Space Technol. 23,461–475.

Namazi, E. & Mohamad, H. (2013). Assessment of building damageinduced by three-dimensional ground movements. J. Geotech.Geoenviron. Engng ASCE 139, No. 4, 608–618.

O’Reilly, M. P. & New, B. M. (1982). Settlements above tunnels inthe United Kindom – Their magnitudes and prediction. Proceed-ings of tunnelling ’82 symposium, London (ed. M. J. Jones), pp.173–181. London, UK: Institution of Mining and Metallurgy.

Peck, R. B. (1969). Deep excavations and tunneling in soft ground.State of the art volume. Proceedings of the 7th internationalconference on soil mechanics and foundation engineering,Mexico City, pp. 225–290. Mexico City, Mexico: SociedadMexicana de Mecanica.

Potts, D. M. & Addenbrooke, T. I. (1997). A structure’s influenceon tunnelling-induced ground movements. Proc. Instn Civ.Engrs – Geotech. Engng 125, No. 2, 109–125.

Puzrin, A. M., Burland, J. B. & Standing, J. R. (2012). Simpleapproach to predicting ground displacements caused by tunnel-ling in undrained anisotropic elastic soil. Geotechnique 62, No.4, 341–352, http://dx.doi.org/10.1680/geot.10.P.127.

Rampello, S., Callisto, L., Viggiani, G. & Soccodato, F. (2012).Evaluating the effects of tunnelling on historical buildings: theexample of a new subway in Rome. Geomech. Tunnelling 5, No.3, 275–299.

Rowe, R. K., Lo, K. Y. & Kack, G. J. (1983). A method ofestimating surface settlement tunnels constructed in soft ground.Can. Geotech. J. 20, No. 1, 11–22.

Shahin, H. M., Nakai, T., Zhang, F., Kikumoto, M. & Nakahara, E.(2011). Behaviour of ground and response of existing foundationdue to tunneling. Soils Found. 51, No. 3, 395–409.

Son, M. & Cording, E. J. (2011). Responses of buildings withdifferent structural types to excavation-induced ground settle-ments. J. Geotech. Geoenviron. Engng 137, No. 4, 323–344.

Vucetic, M. & Dobry, R. (1991). Effects of the soil plasticity oncyclic response. J. Geotech. Engng Div. ASCE 117, No. 1, 89–107.

Wongsaroj, J., Soga, K. & Mair, R. J. (2007). Modelling of long-term ground response to tunnelling under St James’s Park,London. Geotechnique 57, No. 1, 75–90, http://dx.doi.org/10.1680/geot.2007.57.1.75.

130 AMOROSI, BOLDINI, DE FELICE, MALENA AND SEBASTIANELLI