Evaluation study on structural fault of a Renaissance Italian palace

Engineering Structures 32 (2010) 1801–1813

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Evaluation study on structural fault of a Renaissance Italian palace Michele Betti ∗ , Gianni Bartoli, Maurizio Orlando Department of Civil and Environmental Engineering (DICeA), University of Florence, Via di Santa Marta, 3, I-50139 Firenze, Italy

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Article history: Available online 3 April 2010 Keywords: Masonry buildings Damage assessment Finite element analysis Limit analysis

abstract This paper discusses the cracking pattern in a historical Italian palace proposing a diagnosis for the origin of the actual damage state. The analyzed building, which dates back to the seventeenth century, is a masonry building with a rectangular plan section located in Piancastagnaio (South Tuscany, Italy). The building exhibits a severe and variegated vertical and horizontal cracking pattern mainly affecting the southern and eastern façades. Due to the damage, the palace was evacuated by the Public Authorities during the 1980s and a series of provisional remedies (mainly steel chains) was added. Through the use of the finite element technique, the paper provides an interpretation of the manifested damage. The aim of the diagnosis, supported by the numerical results, is to design an extensive in-situ investigation on the palace. Moreover, the paper aims at evaluating the effectiveness of the actual temporary retrofitting (mainly steel chains) used to freeze the present damage. At the end of the paper the in-situ investigation is presented and discussed. © 2010 Elsevier Ltd. All rights reserved.

1. Introduction In civilized countries the exploitation of the historical built heritage is a key issue, as it represents an economic concern especially in contexts where tourism has become a major source of wealth. Normally the conservation or rehabilitation of a historic masonry building requires a deeper knowledge of the understanding of the historical process. While the structural behaviour of a new masonry construction is a relatively simple task (due to the presence of standard codes, inherent literature and accurate knowledge of material properties), the prediction of the structural response of monumental buildings is still a challenging task [1,2]. As a matter of fact, historic buildings cannot be easily reduced to standard structural schemes because of the uncertainties affecting both the structural behaviour and the mechanical properties [3]. Due to these aspects, the maintenance of historical buildings has become in the last decades a very topical scientific issue that has attracted the interest of a plethora of researchers all over the worldwide community. Nowadays several computational and theoretical approaches are available both in the specialized scientific literature and in the National Standards [4,5]. As to the numerical developments, in particular the last few decades have seen the growth in the scientific literature of both new numerical tools [6–9] and illustrative case studies for the analysis of the structural response of historic masonry structures. These case studies are significant for both the research community

∗

Corresponding author. E-mail addresses: [email protected] (M. Betti), [email protected] (G. Bartoli), [email protected] (M. Orlando). 0141-0296/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2010.03.001

and the practitioners as they represent a wide state-of-the-art of the engineering approach to the evaluation of safety and assessment of historical buildings. Lourenço et al. [10] discuss the case study of the Monastery of Jerónimos in Lisbon (Portugal). The authors show how, by means of advanced numerical analyses, it is possible to reach an understanding on both the behaviour and the damage of a complex historical construction. The numerical modelling strategies, combined with a sensitivity analysis of the results, allow for a proper design of the remedial measures. Moreover the authors show that the numerical model is an invaluable tool in the conception and understanding of in-situ testing and monitoring. The importance of a numerical iterative approach to the analysis of historic masonry constructions is also pointed out by Antonelli et al. [11] discussing the case study of the Cappella dei Principi in Firenze (Italy). The authors, with the aim to assess the causes of the failure of an internal stone arch, build a numerical model of the masonry dome whose complexity (geometrical and mechanical) has been progressively increased in different steps. Firstly, simplified elastic linear models have been used to obtain information (mainly stress concentration) for both the planning of a subsequent experimental campaign and the position of monitoring instruments (mainly temperature and displacement transducers). Secondly, results of the in-situ experimental campaign have been used to fit the properties of the numerical model. The authors show how by means of an iterative numerical modelling it is possible to obtain a proper identification of the structural behaviour of the analysed building. A successful and illustrative employment of the finite element method in the assessment and strengthening of a historic building (a masonry church) is proposed in [12] where the author shows how advanced structural analyses are a reliable tool that offers both a clear

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understanding of the structural behaviour and a minimum and adequate design of strengthening. Betti & Vignoli [13], by means of a finite element model, analyse the structural behaviour of a Romanesque church to assess the origin of the actual damage and the seismic vulnerability of the church. The finite element model has been used to evaluate the benefit of different strengthening restoration proposals, offering an insight into an understanding of the minimum and adequate design of strengthening. Cardoso et al. [14,15] propose an iterative method for the seismic assessment of old masonry buildings: in each iteration damage in the structural elements (or connections between them) is identified and the structural system changed accordingly. Each iteration comprises only a linear elastic analysis and that allows its use in current design practice. The method has been applied by the authors to an old masonry building (named ‘Pombalino’, typical in downtown Lisbon). Discussion of the results shows the method’s effectiveness and its limitations. Recently Mallardo et al. [16] discuss the seismic behaviour of a Renaissance palace in Ferrara (Italy). Firstly a full 3D non-linear model of the palace is discussed to obtain an insight into the structural performance of the palace. Next, by means of three reduced 2D non-linear models, a detailed study of the main façade of the palace is presented. The combining of different modelling strategies allows a critical evaluation of the seismic vulnerability of the main elements. Nevertheless, despite the significant development of strategies or adequate tools for the numerical analyses of masonry buildings [17,18], the conservation and restoration of historical structures still remain a challenge to modern engineering since a correct structural evaluation of masonry buildings should be based on a deep knowledge of: (i) the building’s history and evolution, (ii) geometry, (iii) structural details, (iv) crack patterns and material damage map, (v) masonry construction techniques and materials, and (vi) material properties [19]. This knowledge can be reached combining in-situ and laboratory experimental investigations jointly with structural analyses with appropriate models. Since it is extremely difficult to get all the information necessary for a correct definition of a numerical (non-linear) model it is necessary to have a simplified, often iterative, procedure for the evaluation of the static and seismic reliability. Taking into account only a reduced amount of information this procedure should be able to address the relevant aspects of the problem and provide guidance in analyses and experiments. As a general remark, it is possible to state that when dealing with historic masonry buildings different approaches are needed to analyse different aspects, and that the analysis of an ancient structure asks for a multidisciplinary study [20,21]. The paper illustrating a significant case study deals with the above-mentioned problems. Results are reported of research aimed to assess the damage caused on a historical Italian palace and to plan an effective experimental investigation. In the first part of the paper a description of the building together with a review of the main historical steps and the actual damage is reported. A topographic survey performed over the whole palace is used to build a 3D finite element model, and the numerical model is then used to discuss the damage causes. The second aim of the modelling strategies is to offer indication for the design of a subsequent effective in-situ experimental campaign that is a crucial point since an erroneous design might compromise a study and excessive in-situ measurements have high costs. In the second part of the paper the benefits have been discussed derived by the temporary provisional measures (mainly steel chains installed during the 1980s) to prevent the ruin of the palace. Global out-ofplane mechanisms of the main façades in the case of seismic load (as the palace was built in a seismic area) have been analysed. The benefits are estimated by comparing the case with and without the steel chains. Results are used to evaluate if additional provisional

A

MONUMENTAL ROOM

N

0 0.5 1

2

3

4

5m

C

D

A

B

A

Fig. 1. First floor layout (‘‘piano nobile’’).

measures are necessary to ensure the stability of the main façades in case of a seismic event, before planning a global retrofitting. This paper contributes to the issue of modelling and analysis of historic masonry buildings of cultural importance, presenting a careful use of numerical analyses to deal with practical engineering problems in the field. The study suggests that the comprehension of the structural behaviour of historic buildings is an iterative procedure that starts from preliminary simplified modelling strategies (i.e. not computationally expensive, compared to the available experimental data). The comprehension of the static behaviour (and proposal for remedial measures) of cultural heritage buildings requires an iterative approach, aimed at gathering all the information (numerical and experimental) necessary to issue a proper and critical judgment. 2. The case study The analysed building is located in Piancastagnaio (South Tuscany, Italy). The original structure dates back to the beginning of the seventeenth century and it was built under the supervision of the architect Valentino Martelli (about 1550–1630), a Michelangelo disciple [22]. The palace was edified by the family BourbonDel Monte, feudatory of the Grand Duke Ferdinando I Medici, to represent its political and economical importance in the area, with dimensions and architectural details reflecting such an intent. The building is a rectangular three-story masonry construction, with a length of about 34 m and a width of about 31 m (Figs. 1 and 2) and an external masonry wall thickness of about 1.2 m. At the level of the first floor (the so-called ‘‘piano nobile’’) there is a large monumental room (Fig. 3). A monumental stone stair connects each level of the palace. The foundations of the palace are not at the same level and an underground level (a storage basement) is present in the southern area (Fig. 3), as part of the building (the northern part) was partially built over the old city walls. The floor levels are made of several types of masonry vaults, depending on the dimension and importance of the room (Figs. 1 and 2). Smaller rooms are usually covered by cross vaults, while the monumental room is roofed by a cloister vault. Noteworthy is the regularity of the geometrical configuration of the building characterized by well connected orthogonal masonry walls. The only geometrical irregularities are

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vertical and affect the walls perpendicular to the eastern façade (Figs. 4 and 5). These walls in particular (AB and BC in Fig. 1), having a thickness of about 0.7 m, do not reach the foundation level, as they end at ground floor and their vertical load is transferred to the ground by two large arches. Concerning the foundation, the northern part of the building is founded on rock soil and the southern one on an alluvial deposit (Fig. 6). During the 1980s some walls underwent vertical settlement, probably due to ground sinking, and diffused crack patterns arose in several masonry walls. At the end of the 1980s the damage became so critical that the palace was evacuated by the Public Authorities [23].

(Figs. 4 and 5) and on the corresponding internal masonry walls. In contrast, the northern and the western façades are substantially in a good state of conservation. Fig. 4 shows cracks on the eastern façade which are concentrated on the central part that is the most damaged area. It is noteworthy to underline that, in order to prevent the global ruin of the palace, a reinforced concrete plinth was built in the 1970s under this façade [23] to sustain the underground impost of the masonry arch lying under wall CD (Fig. 1) that has undergone a differential vertical displacement of about 10 cm. Fig. 3 shows cracks on the internal wall parallel to the eastern façades. On the southern façade cracks are substantially vertical (Figs. 7 and 9), as an external out-of-plane rotation of the wall (with partial separation of the façade) was activated. Figs. 10 and 11 show the main cracks in the monumental room on the first floor, while Figs. 12 and 13 report details of the cracks present at the ground floor in the southern area of the palace. As a general remark, it is possible to observe that the damage does not affect the whole palace, but mainly the southern and eastern parts of the building. The remaining part, even though it reflects the abandonment and the damage due to the total absence of ordinary maintenance, is mostly intact. After the evacuation, some provisional measures to temporarily freeze the damage were implemented to prevent the palace’s global ruin. In addition to the plinth at the underground level, a series of steel chains (with a diameter of about 22 mm) were inserted to connect the southern and eastern façades to the internal walls [23]. Since May 2007 a large automatic digital monitoring system including about 20 instruments is installed on the building. This system allows both the logging of the temperature value (thermometer) and the crack movement (to record their time evolution) by using displacement transducers and strain gauges placed across the main cracks. The aim of this system is to provide a correlation between movement and crack widths and temperatures. In addition, piezometers and clinometers have been disposed to record both the level of water table and the rotation of the eastern and southern façades. Moreover four triaxial accelerometers have also been installed to record possible seismic activity (whose sensitivity has been selected to record microevents too).

3. The damage survey

4. Numerical simulations (global analysis)

The crack pattern of the palace is quite complex. Major cracks are observable on the southern (Figs. 7 and 8) and eastern façades

In this paragraph the numerical model and the iterative procedure adopted in this study are presented. The analyses

A

MONUMENTAL ROOM

N

0 0.5 1

2

3

4

A

5m

Fig. 2. Third floor layout.

1

0 0.5 1

2

3

4

MONUMENTAL ROOM

2

5m

Fig. 3. Section A–A (red lines highlight major cracks). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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760

760

1 I

R

755

755

Tra

750 Sa+Tra

3-5-5

750

1/2 15-19-RIF 4

745 Sa

740 rock area

Ls

I

R

745 740

Tra

735

L

730 L

725

Fig. 4. Eastern façade (red lines highlight the crack pattern). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

720 715

735

alluvial deposit

730 725 720 715

Fig. 6. Cross section of the palace and subsoil profile: geological characteristics of the ground (R, Sa: superficial soil; Sa + Tra: sand with trachyte; Tra: trachyte; Ls: sandy silt; SI: silty sand; L: silt).

Fig. 5. Eastern façade.

herein discussed have a double aim: (i) to assess the potential causes of the palace’s damage and (ii) to plan a subsequent insitu experimental campaign (both on the masonry wall texture and on the ground). To this end, the finite element technique has been used. A finite element model of the whole palace has been intentionally built with the commercial code SAP2000 [24], a program that performs essentially linear analyses. However since the study asks us to model a historic masonry building this choice led to the need of a step-by-step iterative procedure to simulate, even if in an approximate manner, the non-linear behaviour of the entire masonry structure. By introducing a number of changes in the structural configuration it is possible to simulate the principal sources of non-linear material behaviour (i.e. cracking of the masonry elements and failure of the connections between masonry walls). It is also possible, if relevant, to simulate the respective sequence of ruptures [25]. This approach could be considered quite reasonable, given the variability of material properties and the unknowns at the present time. Despite its disadvantages (for example the selection of the damaged elements is made by a visual inspection of the element stress state) the approach has the main advantage that it can be easily implemented in commercial codes (such as the one used in this study) as it basically requires us to develop a series of linear analyses. This method has been used successfully in the past (starting from the 1980s) with reduced computer power, and the corresponding scientific literature reports both the theoretical basis of the approach and many illustrative case studies. Today, with more computer power and sophisticated numerical tools, is possible to model a wide range of non-linear phenomena (including cracking and crushing

Fig. 7. Southern façade (red lines highlight the crack pattern). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

that occurs in masonry under severe loads). It is then obvious that the procedure is not competitive (in a general sense) if aimed at a concluding diagnosis. Nevertheless, in the authors’ opinion the finite element procedure remains competitive if used, as in the proposed case study, to obtain preliminary results to address the subsequent steps of the research. Next a preliminary discussion on the adopted mesh is reported before specifying the application of the iterative procedure with respect to the case study and discussing the adopted parameter value (both for the masonry material and for the ground). The finite element model, built at this step of the investigation by two-dimensional shell elements, aims to reproduce accurately the geometry of the structure. The results of a topographic survey performed over the whole palace [26] have been used to build a first (not computationally expensive) numerical model of the building. All the variations in wall thickness, geometrical irregularities and wall connections were taken into account. The major openings in the building are reproduced. Windows have been modelled taking into account their actual dimensions

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Fig. 8. Southern façade.

Fig. 10. Monumental room (#1 in Fig. 3).

Fig. 9. Southern façade (cracks details).

(Fig. 12). Vaults have been modelled (assuming the fill material as a dead load) to consider their thrust effect on the confining walls. Masonry walls and vaults were modelled by means linear elastic shell elements. In contrast the roof’s timber trusses were not modelled and their self-weight was applied to the model as vertical loads acting directly on the corresponding masonry walls. The final model is able to reproduce, with acceptable confidence (i.e. compared to the available data), the overall spatial configuration of masonry walls together with the entire set of architectural elements that are of structural relevance. This attention is particularly required in historic buildings where differences between architectural and structural elements are not always clear. A preliminary study on the mesh size of the shell elements has also been made. This preliminary study has led us to decide the mesh size for masonry elements. It was concluded that it was not worth refining the mesh more than the one reported in Fig. 14 (with a refinement around windows and doors) for two major reasons: (i) the main objective in studying cracking in masonry elements was to evaluate the trend in the location of masonry damage rather than its exact position and (ii) the level of accuracy does not need to go beyond the knowledge of material properties. The adopted mesh size seems to be appropriate for these purposes; moreover the results obtained with the adopted mesh are similar to those obtained with a preliminary local model where a more refined mesh was assumed.

Fig. 11. Monumental room (#2 in Fig. 3).

To have a preliminary evaluation of the load transfer mechanisms from the building to the ground taking into account the effects of the soil–structure interactions, a simplified iterative procedure, as previously introduced, has been intentionally applied. The proposed iterative procedure, needed to consider the nonlinear material behaviour of masonry (mainly the low tensile resistance of the masonry), has been applied as follows: (a) a linear model of the whole structure is built by means of 2D isoparametric shell elements; (b) a linear static analysis is performed considering the own weight (and the service loads); (c) for each structural element (or connection) the design action effects F (principal tensile stresses on masonry walls) will be compared with respective re-

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Fig. 12. Internal room (and windows detail).

Fig. 13. Eastern–southern edge (internal view).

data for historic masonry (i.e. buildings with similar masonry texture [27,28]) and normative reference [4] deriving conservative values from these experiences. In particular, since the masonry texture seems to be an infilled one, typical values of infilled masonry have been assumed: the Young’s modulus of masonry Em has been assumed equal to 15, 000 N/mm2 (considering a range of variation between 1440 and 1980 N/mm2 ); its own weight γm has been assumed equal to 20 kN/m3 (considering a range of variation between 19 and 21 kN/m3 ). The Poisson coefficient was assigned the value 0.2. In the present case study a parametric study varying the properties of the masonry (mainly the Young’s modulus) was not planned. In the absence of experimental results that can account for the spatial distribution of the building’s masonry typologies it is, at this step, only rational to assume a uniform distribution of masonry properties (i.e. without differentiating the masonry parameters along the main elements of the building) as any variation could be totally arbitrary. Being the non-linear analyses conducted as a sequence of linear ones, a scaling on the Young’s modulus could produce only a scaling on the corresponding results. A test was made assuming Em equal to 20, 000 N/mm2 , and no appreciable differences were observed in the building behaviour. Masonry strength (R) has been assumed about 0.2 N/mm2 (considering a range of variation between 0.1 and 0.4 N/mm2 as suggested by [4]). Due to the variability in the properties of structural materials and due to the variety of structural solutions that is possible to find in an old masonry building, strength values are always average values. Designers could adopt different values but a definitive decision can be delivered only after experimental tests. With respect to the foundation soil modelling, due to the differences in mechanical properties [29], different values have also been considered for ground characteristics. In the southern part of the building, where the ground is characterized by the presence of silty sand and sandy silt, a linear elastic Winkler model has been considered by means of spring elements whose stiffness changes according to the corresponding ground properties. In contrast, in the northern area, a layer of membrane elements has been inserted at the foundation level under the masonry walls, in order to take into account the high cohesion (about 200 kPa, see Table 1) of the rocky ground (Fig. 6). Additional elements have been inserted underneath the walls, whose vertical stiffness R∗ is given by: R∗ =

Fig. 14. Global view of the numerical model of the palace.

sistances R (tensile strength of masonry) identifying their rupture (cracking if F > R); (d) the damage state is modelled by reducing the stiffness of the collapsed elements (or connections) which suffered significant cracking. The number of elements where the stiffness is reduced at each time depends on the precision required in the analysis; (e) the process is repeated (i.e. changes in Young’s stiffness of the elements of the structural model) and it stops if for all the elements F < R. The structural elements where damage was analyzed are masonry walls and connections of masonry walls with vaults. In this study, a reduction of about a tenth of the elastic modulus was considered to model the cracking damage on masonry elements. However a designer may wish to adopt a different criterion for the stiffness reduction for higher or lower precision. Concerning the masonry properties, as no in-situ tests are available at this step (the results herein obtained will be used to plan the experimental campaign), assumptions on the masonry material properties have been made taking into account literature

E·A h

=

E · i · sm h

(1)

where E is the elastic modulus, h is the height of the element; sm is the thickness of the masonry and i is the reference length of each node of the element. By using a linear elastic model the stiffness of each spring is given by R = ks · sm · i (where ks is the Winkler assumed constant and equal to 0.20 N/mm3 as suggested in [29]); therefore the expression to evaluate the vertical stiffness E becomes: R = R∗ ⇒ E = ks · h [N/mm3 ]

(2)

Finally the numerical model has been built to account for both the geometric irregularities (using the results of the geometric survey [26]) and the differential ground settlements (using the results of a geological/geotechnical survey [29]). The final threedimensional model consists of 16,210 shell elements, 832 spring elements and 16,486 joints (Fig. 14). The model has been used to assess the influence on the actual damage of both the differential settlements of foundations and the vault thrusts. Due to the differences in shape and dimension and as the imposts of the vaults are not at the same level, these elements produce an unbalanced thrust on the supporting walls (especially in correspondence of

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Table 1 Geotechnical characterization of ground (R, Sa: superficial soil; Sa + Tra: sand with trachyte; Tra: trachyte; Ls: sandy silt; SI: silty sand; L: silt). Lithotype Weight (kN/m3 ) Friction angle (°) Cohesion (kPa)

R

Sa

Sa + Tra

Tra

Ls

SI

L

17.5 28° 0

18 32° 0

18.5 33° 0

22 40° 200

20 30° 1

19 29° 0

21 28° 5

Fig. 16. Fixed-base model, principal tensile stresses on East façade [N/mm2 ].

Fig. 15. Fixed-base model, principal tensile stresses on masonry [N/mm2 ].

the monumental room). The effect of the differential settlements of the foundations has been taken into account by a series of parametric analyses, where the ground stiffness of the alluvial deposit (mainly characterized by the Winkler constant value reported in the geotechnical survey [29]) has been changed within a physical range. In particular, assuming as a mean value for ks the value reported in [29], a range of variation between 0.10 N/mm3 (corresponding to 1/2 of the experimental value) and 0.40 N/mm3 (corresponding to double the experimental value) has been considered. To identify the damage state, the following models have been analysed: (i) model A is the model of the building with fixed base assumption; (ii) model B is the model that accounts for the soil–structure interaction and (iii) model C is similar to model B but with the addition of a localized ground sinking. They are next described.

Fig. 17. Soil–structure interaction, model without reduced modulus. Principal tensile stresses on masonry [N/mm2 ].

4.1. Model A. Fixed base model The first series of analyses have been performed assuming a rigid ground foundation, i.e. a fixed base model has been considered under vertical loads mainly due to its own weight (masonry walls, vaults and fillings, wooden roof). The service loads have also been taken into account assuming a uniform load at each level equal to 2 kN/m2 . Results of these preliminary analyses are reported in Figs. 15 and 16. The figures show the principal tensile stresses which are relatively low except for a limited zone (circled in Fig. 16). This means that the own weight and service loads alone cannot account for the damage on the building; results do not change even if the masonry strength is reduced by one-half to take into account the degradation of masonry properties with time. 4.2. Model B. Soil–structure interaction Results from model A suggest that the effect of the differential ground settlements should be introduced in the F.E. analysis. To evaluate the effects of the soft properties of the ground, parametric variations of the Winkler constant on the alluvial deposit have been taken into account. A range of variation between 0.10 N/mm3 (corresponding to 1/2 of the experimental value) and 0.40 N/mm3 (corresponding to double the experimental value) has been considered, but the results of the analyses don’t show

Fig. 18. Soil–structure interaction, model without reduced modulus. Principal tensile stresses on eastern façade [N/mm2 ].

appreciable variability in the building response. Consequently the value of the Winkler constant reported in [29] has been used, since to justify different values it is necessary to have, e.g., information about the shape of the foundations. Fig. 17 reports the principal tensile stresses on the masonry at the start of the iterative procedure; in particular Fig. 18 shows a high tensile stress state on the masonry in the eastern façade. In order to consider the no tensile resistance of masonry, the original model has been consequently modified by following the previously described step-by-step procedure. In the elements where tensile stresses exceed the masonry strength (assumed to be equal to 0.2 N/mm2 ) the elastic modulus has been fictitiously reduced (of a tenth). This reduction has been made iteratively until the redistribution of the internal stresses allows acceptable values of tensile stresses (lower or equal to 0.2 N/mm2 ) on all the masonry walls. Seven steps are enough to reach a stable configuration. Fig. 19 shows the elements where the stiffness has been reduced (grey elements) at the end of the iterative stiffness

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Fig. 19. Soil–structure interaction, model with reduced modulus. Element with reduced modulus (dark).

Fig. 20. Soil–structure interaction, model with reduced modulus. Principal tensile stresses on East façade [N/mm2 ].

Fig. 21. Global view of the numerical model of the palace (view of the assumed boundary condition).

Fig. 22. Soil–structure interaction, model without reduced modulus. Principal tensile stresses on East façade [N/mm2 ].

reduction; Fig. 20 reports the corresponding tensile stresses on the eastern façade of the palace. As stated before several models have been analysed opportunely changing the ground stiffness on the alluvial area based on the indication reported in [29], but all of them led to the same damage pattern, identified by the elements with the reduced modulus (Fig. 19). The damage configuration obtained considering only the different spatial distribution of ground properties does not account for the actual damage; this means that also taking into account the ground properties it is not possible to explain the present damage state. 4.3. Model C. Soil–structure interaction with local sinking Taking into account the results of the diagnosis made in the late 1980s (when a differential movement on the eastern façade of about 100 mm was found between the internal and external walls) a new series of analyses has been performed removing the springs under the central part of the eastern façade (Fig. 21) with the goal of simulating a local sinking. The tensile stress state obtained at the start of the iterative procedure is reported in Fig. 22. This stress map is characterized by the presence of a high level of tensile stress, much higher than the adopted tensile strength. As in the previous analyses the iterative procedure has been repeated until in all the elements tensile stresses were lower than the masonry strength. The damage pattern obtained at the end of the procedure, after 11 iterations, is shown in Fig. 23 while the corresponding tensile stress state in the masonry is shown in Fig. 24. The element pattern with reduced elastic modulus in Fig. 23 moves to the left embracing the area of the present damage on the eastern façade. 4.4. FEM: key point results The finite element analyses highlight some points. The first is that its own weight alone (Model A) induces a very localized stress

Fig. 23. Soil–structure interaction, model with reduced modulus. Element with reduced modulus (dark).

state, while models accounting for differential ground settlements reproduce a damage state that do not match the present one. Model B, which accounts for the different soil properties under the palace in the alluvial area, is not able to justify the actual damage. The palace dates back to the seventeenth century, and the major effects of the damage were recorded during the 1980s. It is reasonable to expect that accidental effects due to differences in ground properties took place during, or immediately after, the construction of the palace. This is confirmed by the numerical results (Model B). On the other hand, researches on the historical seismicity of the area do not show significant earthquake events in the past 200 years. The last strong earthquake in the area was recorded in 1919 (with an intensity IS = 7 according to Mercalli Intensity Scale), but it is not believed to be the cause of the actual damage of the palace since the building continued to be used as private houses and a public gymnasium. This means that at that

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Fig. 25. Partial collapse of foundation under the eastern façade. Fig. 24. Soil–structure interaction, model with reduced modulus. Principal tensile stresses on eastern façade [N/mm2 ].

time the present damage was not present. The time during which the damage of the palace has developed is quite short, probably less than 4–5 years [23]. Previous observations, along with the results obtained with the last numerical analyses (Model C), seem to suggest that the origin of the present damage is due to a local collapse of the ground under the central part of the eastern façade. Moreover, historic literature data report that all the area where the palace is built is characterized by the presence of underground cavities [22]; it is then reasonable to suppose that local sinking has happened under the eastern façade due to the collapse of one of these cavities. Nevertheless this hypothesis must to be confirmed by a new soil investigation campaign, which has been already designed considering the results of this study. As an additional result the numerical analyses show a high value of the vertical (compressive) stresses under the eastern and southern façades. In particular the average compressive stresses at the base of the western and northern façades, founded on rock, are about 0.3 N/mm2 , while on the eastern and southern façade, founded on the alluvial deposit (Fig. 6), are about 0.5 N/mm2 . These values seem very high if compared with the alluvial deposit resistance, so that a deeper investigation on both soil and overlaying walls and corresponding foundation typologies is planned to confirm and check the numerical results. Coring tests and single/double flat-jack tests are planned in this area to assess the exact composition of masonry walls and to evaluate both the stress state and the masonry Young’s modulus. Hence the applied iterative approach, making use of accessible computational tools, has the advantage of identifying the weakest and critical parts of the structure providing useful information to plan effective investigation. 5. Limit analysis (local analysis) Results of previous analyses allow us to exclude that the origin of the present damage is due to the different soil properties under the palace or to a seismic event. At the same time they suggest that the origin of the damage is due to a local ground sinking (probably a local collapse of an underground cavity) in the middle part of the eastern façade. Even if it is possible to exclude the earthquake as the cause of the present damage, the palace is built in a seismic area (classified with respect to the Italian Recommendation in medium seismicity [4]) then evaluation of its seismic safety should be a primary concern. In order to evaluate the safety levels of the palace some representative macro-elements have been analyzed. The attention has been paid to the area where damage is present to assess the effectiveness of the temporary retrofitting with steel chains made in the 1980s. The out-of-plane collapse multipliers of the macro-elements were compared with and without the provisional steel chains.

Fig. 26. Mechanism #1: partial overturning of the eastern façade.

Fig. 27. Mechanism #2: overturning of the eastern façade.

To this end is verified if horizontal load multipliers for out-ofplane mechanisms are higher than the corresponding threshold proposed by the Italian Recommendations [4,5]. Previous research works [30,31] show the validity of a limit-state approach in the assessment of the seismic behaviour of unreinforced masonry buildings. When analyzing out-of-plane mechanisms (the socalled first type mechanisms), masonry walls are modelled as a system of rigid bodies, articulated by hinges, whose geometry and distribution are defined according to potential failure mechanism. Substantially the structure is considered as the assemblage of a certain number of components depending on the structural compound geometry and shape (e.g. the whole façade) and on the details (e.g. quality of existing connections) whose behaviour is similar to that of analogous macro-elements in similar buildings. In this study, several possible out-of-plane mechanisms which best represent the surveyed damage patterns have been taken into account (Figs. 25–30). All of the mechanisms herein considered take into account global overturning of masonry façades. After the selection of the elementary macro-elements, the collapse multiplier (λ) can be evaluated by applying the Theorem of Virtual Work (TVW) on the rigid-body system, where the seismic load is assumed as an overturning force while the gravity load is

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M. Betti et al. / Engineering Structures 32 (2010) 1801–1813

Fig. 28. Mechanism #3: partial overturning of the southern façade.

hinge

Fig. 31. Out-of-plane mechanism (western façade); Fh : vault thrust; Fv : own weight; λFv : seismic loads.

Fig. 29. Mechanism #4: global overturning of the southern façade.

Table 2 Vulnerability indexes, kinematic analysis results (λ: collapse multiplier; a∗0 : seismic spectral acceleration corresponding to λ; a1SLU : seismic acceleration demands corresponding to the ultimate limit state).

Mechanism 1 Mechanism 2 Mechanism 3 Mechanism 4 Mechanism 5

λ

a∗0

a1SLU

Check

0.028 0.024 0.012 0.011 0.175

0.286 0.243 0.122 0.115 1.811

1.261 1.343 1.348 1.325 1.472

NO NO NO NO YES

limit state (SLU) [4,5]. The verification of the considered limit state is satisfied if the following inequality yields: Fig. 30. Mechanism #5: corner overturning.

ag · S a∗0 ≥ a∗1SLU = · q

assumed as a stabilization load [5]:

λ·

" n X

#

n+m

Pi · δix +

i=1

X

Pj · δjx

j=n+1

−

n X i =1

Pi · δiy −

l X

Fh · δh = Lfi (3)

h=1

For the meaning of the terms in Eq. (3) see Fig. 31. Fig. 31 shows the loads acting on the western façade with respect to the overturning mechanism (Fig. 27) where the thrusts of the vaults have been also considered. For the western façade, Eq. (3) assumes the form given in Box I: After the evaluation of the collapse multiplier λ corresponding to each mechanism, the corresponding seismic spectral acceleration a∗0 (an effective static threshold acceleration corresponding to the onset of the mechanism) has been evaluated by means of Eq. (4):

λ· a∗0 =

n +m

P i=1

M∗

Fv i

=

λ·g e∗

(4)

where M ∗ is the effective mass and g denote the gravity acceleration. The safety of the building with respect to the selected mechanism has been evaluated taking into account the collapse



1 + 1.5 ·

Z H

 (5)

where ag S is the design elastic acceleration spectral ordinate (at T = 0), q is the behaviour factor (assumed equal to 2.0 [4]); Z is the height, with respect to the ground, of the centroid of all inertial masses involved in the mechanism and H is the total height of the building. Table 2 summarizes the collapse multipliers λ and the spectral acceleration values a∗0 together with the seismic acceleration demands corresponding to the ultimate limit state a1SLU as required by the Italian Recommendations [4]. The results of Table 2 refer to the conservation state of the palace before the temporary retrofitting with steel chains. Fig. 25 shows the mechanism activated by the subsiding of the ground under the eastern façade, which produce the arch-type cracking pattern. These cracks can allow the appearance of the mechanism sketched in Fig. 27 and those of the southern façade sketched in Figs. 28 and 29. The low values of the collapse multipliers seem to confirm a high intrinsic vulnerability of the façades itself. Next the identified mechanisms have been analyzed to take into account the presence of the steel chains inserted in the 1980s soon after the development of the actual damage [23]. To prevent the slip of these steel chains bolted end-plates have been disposed of the façades (Fig. 9). To this aim the reference

M. Betti et al. / Engineering Structures 32 (2010) 1801–1813

λ=

1811

(W · dW ) + (FV 1 · dV 1 ) + (FV 2 · dV 2 ) + (FV 3 · dV 3 ) + (FVcop · dcop ) − (FH1 · hV 1 ) − (FH2 · hV 2 ) − (FH3 · hV 3 ) − (FHcop · hcop ) (W · yG ) + (FV 1 · hV 1 ) + (FV 2 · hV 2 ) + (FV 3 · hV 3 ) + (FVcop · hcop ) Box I.

at the different levels. At each ∆θ both the ∆Li and the deformation εi in the chains (Fig. 33) have been calculated. Figs. 34 and 35 report the diagrams of the collapse multiplier λ (expressed as spectral acceleration a∗0 ) at varying rotation angle θ for the mechanisms shown in Figs. 27 and 29. These diagrams show for both the eastern and western façades that very small rotations are required to make the seismic capacity higher than the seismic demand. It is then possible to state that, for the considered mechanisms, the steel chains seem to offer a proper (but provisional) remedial in the case of a seismic event. It seems that the temporary retrofitting is able to ensure the stability of the palace with respect to a global overturning of the main walls and consequently it is possible to exclude additional provisional measures to ensure the safety of the palace while awaiting an effective global retrofitting. Nevertheless, an exhaustive study of the overall stability of masonry walls with respect to the seismic loads needs to consider that, after preventing the original mechanism, it is still possible that other mechanisms will develop with hinges in different positions. These analyses will be developed in parallel with the investigation campaign when the exact internal composition of the masonry walls will be investigated. hinge

6. Conclusions and future works Fig. 32. Out-of-plane mechanism (western façade); Fh : vault thrust; Fv : own weight; λFv : seismic loads; Ti : chain forces.

TVW scheme has been modified (Fig. 32) to take into account the chain forces Ti . The evaluation of the collapse load multiplier λ has been made, considering several possible configurations of the mechanism (Fig. 33). To this aim the progressive modification of the external chain forces acting at each level during the development of the mechanism has been taken into account considering the elongation of the chains and assuming an elasticperfectly plastic behaviour. The analyses have been carried out until the chains at the last level are yielded. Fig. 33 reports the development of the considered mechanism for a generic wall as a function of the angle θ ; ∆Li denotes the elongations of the chains

In this paper, the main results of research aiming at interpreting the cracking pattern on an historic Italian palace have been presented. After a discussion on the building geometry, ground typology and the present cracking pattern, the diagnosis has been presented together with the adopted procedure for static assessment. The approach includes the use of a commercial code that performs basically linear analyses. Consequently an iterative procedure has been applied, and in each iteration the Young’s modulus of the damaged elements (i.e. the element where the tensile strength exceeds the selected tensile strength of the masonry) is reduced and the structural system changed accordingly. The analysis is then repeated until a distribution of admissible principal tensile stresses is obtained on the building. Despite the method’s disadvantage since each step

Fig. 33. Mechanism configuration at varying rotation angle θ .

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M. Betti et al. / Engineering Structures 32 (2010) 1801–1813 Eastern façade 3

spectral acceleration a0*

2.5

2

1.5

1

0.5

a0* a1SLU

0

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 angle [θ°]

1

1.1 1.2 1.3 1.4 1.5

Fig. 34. Spectral acceleration evolution eastern façade. Southern façade

Acknowledgement

3

The authors kindly acknowledge the Municipality of Piancastagnaio, who supported the research through financial support.

spectral acceleration a0*

2.5

2

References

1.5

1

0.5

a0* a1SLU

0

The next steps of the research will include an in-situ survey on the ground and masonry texture. The ground survey aims to check the presence of underground cavities (to verify the hypothesis herein developed) and it will be realized by geo-electrical or geoseismic methods. The masonry survey will include single/double flat-jack tests aiming at evaluating both the elastic modulus of masonry and the compressive stress state. Investigation is planned on the masonry walls’ foundation due to the high compressions found in the numerical models. Analyzing an illustrative case study, the importance is stressed of using simple (i.e. not computationally expensive) but effective instruments to evaluate the structural state of historic masonry buildings. The complexity of the instruments used to assess the structural behaviour of masonry buildings needs necessarily to be compared with the quality and quantity of available information (i.e. experimental results). Sophisticated analyses may produce meaningless results if not supported by a properly designed investigation; on the other hand, the applied approach when no experimental results are available can be a very useful instrument for a first assessment of both the building’s behaviour and the experimental demands.

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 angle [θ°]

1

1.1 1.2 1.3 1.4 1.5

Fig. 35. Spectral acceleration evolution southern façade.

of the procedure is only a linear analysis the method is not computationally expensive and could be reasonably proposed as an effective instrument to identify the weakest or critical area of the building. Results of the analyses offer effective information for a subsequent investigation (and more refined analyses with more powerful tools). In this case study, the effects of differential ground settlements have been considered and the analyses indicate that the damage in the palace is due to a local failure of an underground cavity under the middle part of the eastern façade of the palace. The activation of an arch-type cracking pattern on this wall can be responsible for a sequence of mechanisms that might account for the present damage. The procedure is effective especially if compared with the available experimental data and allows us to have engineering results in a few iterations. The second part of the paper provides an estimation of the seismic safety of the southern and western façades (the damaged area) with respect to the limit analysis scheme. The palace is in a seismic area and the effectiveness of the temporary measures positioned during the 1980s has been evaluated to assess the need of additional retrofitting. Results show that the temporary retrofitting can ensure the stability of the façades with respect to a global overturning.

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