Structural resistance of reinforced concrete buildings under pyroclastic flows: a study of the Vesuvian area

Structural resistance of reinforced concrete buildings underpyroclastic £ows: a study of the Vesuvian area

S.M. Petrazzuoli, G. Zuccaro �

Dept. ‘Scienza delle Costruzioni’, University of Naples ‘Federico II’, Via Claudio 21, 80125 Naples, Italy

Received 1 May 2002; accepted 21 April 2003

Abstract

The analysis of the effects of pyroclastic flows on humans and on buildings represents the main tool to define theboundary of the most hazardous area around an active volcano such as Somma^Vesuvius. Estimation of the lateralpressure on buildings derived from analogies with the damages observed after a nuclear explosion [Valentine (1998)J. Volcanol. Geotherm. Res. 87, 117^140] lead to pressure values and/or structural resistance which are not realistic(too high). Recent evidence [Baxter (2000) Human and Structural Vulnerability Assessment for Emergency Planningin a Future Eruption of Vesuvius. Final Report EC Project ENV4-CT98-0699; Young et al. (1997) EOS, Trans. Am.Geophys. Union, 78, 401] have shown that beyond 2^3 km from the vent, even after a great eruption, resistance tocollapse of buildings affected by a pyroclastic flow is still possible. Neri et al. [(2000) Numerical simulation ofpyroclastic flows. In: Human and Human and Structural Vulnerability Assessment for Emergency Planning in aFuture Eruption of Vesuvius. Final Report EC Project ENV4-CT98-0699], by means of a numerical model of acollapsing column, show that the peak overpressures of the pyroclastic flows range from 1 to 2 kPa at a distance fromthe vent of about 4^5 km, where important historical centres of the Vesuvian area are located. A detailed analysis ofurban settlement of the area [Cherubini et al. (2001) Vulnerabilita’ Sismica dell’Area Vesuviana. Gruppo Nazionaleper la Difesa dai Terremoti, CNR, Roma] has shown that most of the people live in reinforced concrete (r.c.)structures, not designed to resist horizontal seismic actions. The present work is aimed at analyzing the collapse limitload of r.c. structures to horizontal pressure for different structural design typologies (strong aseismic, weak aseismic,strong non-aseismic, weak non-aseismic). The simulations performed have also taken into account the specific featuresof the r.c. structures of the area (local building practice). The limits of resistance for each typology, in case of regularand irregular buildings, are provided. Such limits of resistance are in good agreement with the literature data comingfrom collapse simulation of buildings under seismic actions.F 2003 Elsevier B.V. All rights reserved.

Keywords: structural damage; reinforced concrete; pyroclastic £ow

1. Introduction

The existence around the world of wide urban

settlements nearby active volcanoes, like in theNeapolitan area (Vesuvius and Phlegraean Field)of Italy, Sakurajima of Japan, and Popocateptl ofMexico, emphasises the importance of estimatingthe e¡ects of pyroclastic £ows on buildings, inorder to acquire useful indications for emergency

0377-0273 / 03 / $ ^ see front matter F 2003 Elsevier B.V. All rights reserved.doi:10.1016/S0377-0273(03)00407-4

* Corresponding author. Fax: +39-081-768-3332.E-mail address: [email protected] (G. Zuccaro).

VOLGEO 3035 6-4-04 Cyaan Magenta Geel Zwart

Journal of Volcanology and Geothermal Research 133 (2004) 353^367

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planning and to tune the alternative measures forrisk mitigation such as: (1) restraining the in-crease of people in the entire area exposed; (2)forbidding the construction of new buildings inthose areas where total destruction is expected;(3) encouraging new human settlements beyondthe dangerous area; (4) shifting strategic industri-al installations to areas where no or little damagecan be expected.The Vesuvius Emergency Plan (Department of

Civil Protection, 2001) indicates two hazardousareas, called the red zone and the yellow zone(Fig. 1). The red zone represents the area aroundthe volcano (0^10 km) a¡ected by pyroclastic£ows where huge damage to buildings may occur,whilst the yellow zone represents the area wherelarge thicknesses (tens of centimetres) of pyro-clastic fall out can be expected. The VEP doesnot take into account di¡erent levels of hazardwithin the red zone; in fact, should an erup-

Fig. 1. Map of the red and yellow zones de¢ned by the VEP.


S.M. Petrazzuoli, G. Zuccaro / Journal of Volcanology and Geothermal Research 133 (2004) 353^367354

tion approach this area, it must be totally evac-uated.Baxter (2000) and Young et al. (1997) found at

Monserrat, after the 1997 eruption, that not allbuildings near the volcano (within 2^3 km) weredestroyed and that some damages observed couldbe considered to result from the in¢ltration ofhot pyroclastic £ows through windows, doors,and in¢ll panels, instead of structural collapse.These remarks stimulated an international proj-ect supported by the European Union (ENV4-CT98-0699) devoted to evaluate the humanand structural vulnerability to pyroclastic £ow ac-tion.Valentine (1998), with reference to nuclear

weapons experiments, indicated that about 7 kPa

was the value of pressure at which damage atreinforced concrete (r.c.) buildings begins, andthat 35 kPa was the upper limit of any kind ofstructures. Comparing the description of the dam-ages caused by nuclear explosions with the struc-tural damages described by Sigurdsson et al.(1985) and Valentine (1998), the lateral pressurewhich occurred at Erculaneum (5 km from thevent) in the 79-AD eruption of the Vesuvius canbe estimated as V10 kPa. Such an amplitude ismuch larger than the wind pressure (V1^3 kPa)and induces horizontal forces on buildings evenlarger than a strong earthquake (0.2^0.3 g peakground acceleration). At ¢rst glance the overpres-sure value at Erculaneum seems to be very high,considering that the Roman buildings were not all

Fig. 2. Peak values of dynamic pressure of simulation LL-w2-t950-A (top), LM-w2-t950-A (middle), and L-w2-t950-A (bottom),at 5 and 15 m above the aerodynamic ground plane, and as a function of distance from the vent (after Neri et al., 2000).


S.M. Petrazzuoli, G. Zuccaro / Journal of Volcanology and Geothermal Research 133 (2004) 353^367 355

destroyed and that it is still possible to ¢nd nu-merous undamaged buildings. Even the damageresistance threshold for r.c. structures appearsoverestimated. A possible explanation could befound in the duration of dynamic pressure aftera nuclear explosion (milliseconds) that is threeorders of magnitude smaller than the durationof dynamic pressure due to pyroclastic £ows (sec-onds).Neri et al. (2000) performed numerical model-

ing of the collapsing column pyroclastic £ow ofthe Vesuvius obtaining an estimation of dynamicpressure in the range of 5^15 m above the groundlevel with reference to a 1631 size eruption (sub-plinian). In Fig. 2 the peak of dynamic pressure isplotted vs. distance from the vent: at close dis-tance (2 km) the dynamic pressure is very strongwith values of about 7^10 kPa, whereas it decaysvery rapidly with distance (W1 kPa for ds 5 km).Taking into account that most of the buildingsare located at a distance of 4^5 km from thevent, the peak of dynamic pressure a¡ecting thestructures could be estimated as V1^2 kPa. Themodeling of Neri et al. (2000) assumes that thepyroclastic current a¡ects an angle sector of 90‡;but since then it has been observed that someeruptions concentrate £ow in smaller angles (30^45‡), the peak of overpressure may increase to 3^5

kPa, large enough to induce serious damages onbuildings.A careful study of the main features of the

buildings in the Vesuvian area has been carriedout by Zuccaro (2000), Zuccaro et al. (2002),and Cherubini et al. (2001). The results of thissurvey indicate that almost 70^80% of the peoplelive in r.c. structures built from 1960 to 1975,most of them non-designed to resist seismic ac-tions. Therefore, the resistance of r.c. buildingsagainst the action of pyroclastic £ows plays acrucial role in estimating damage scenarios.The work to evaluate the limit resistance of real

buildings to horizontal forces has been limited,since it requires complex elasto-plastic analyses.Moreover, in order to evaluate the equivalentaverage collapse pressure plan dimensions and in-terstory height are required. Some data can befound in the works of Meli (1991), Dai et al.(1996) and Cosenza et al. (2000).Meli (1991) analyses the performance of two

strong r.c. aseismic buildings, one located in Mex-ico City and another one in San Salvador, struckby strong earthquakes. By means of an elasto-plastic analysis, the author estimates the maxi-mum horizontal shear force allowable. Cosenzaet al. (2000) carries out a similar analysis withreference to two non-aseismic r.c. buildings in

Fig. 3. HPL of real buildings evaluated by means of non-linear simulations.



the historical centre of Catania (Sicily, southernItaly). Dai et al. (1996) performes a non-linearanalysis of an aseismic six-storey building withcomposite structures.The results of these analyses have been trans-

formed into limit pressure (qx;y) dividing the limit-shear force (Sx;y) and the building surface (Ax;y)exposed in that direction:

qx;y ¼ Sx;y=Ax;y ð1Þ

The values of Horizontal Pressure Limit (HPL)range from 1 to 7 kPa (Fig. 3). The HPL valuesfor non-aseismic buildings (1^2 kPa), withoutconsidering the resistance of the in¢ll wall panels(bare frame), are surprisingly low, comparable tothe magnitude of the wind pressure.Obviously, the r.c. structures can provide a very

wide range of resistance values according to dif-ferences in design and the contractional criteriaadopted. Therefore, in order to obtain an estima-tion of the average resistance of the r.c. buildingtypologies (aseismic and non-aseismic, strong andweak), in this work an analytical study of thestructures in the Vesuvian area has been carriedout using the widely-known structural modelsmainly used in seismic engineering. The character-

istics of the materials and the usual constructionalmethods of that age have been taken into accountby performing the analyses on the existing build-ings (i.e. percentage of reinforcement in the col-umns and the beams, dimensional increments ofthe geometry of the structures by storey levels,mechanical characteristics of the concrete andthe steel bars, etc.). The increment of the horizon-tal resistance of the framed structures due to theshear strength provided by the in¢ll panels hasbeen neglected since it is reasonable to thinkthey could be seriously damaged by the £ow.

2. Reinforced concrete limit state analysis

The analysis has been carried out by means ofthe fundamental theorems of limit analysis (Mas-sonet and Save, 1967) applied to r.c. frames, as-suming for each frame two failure mechanisms(Fig. 4) ; the resistance of the structure as a wholeis assumed to be the contribution of all framesaligned with the pyroclastic £ow, neglecting tor-sional e¡ects. The procedure has been calledStructure Horizontal Resistance Evaluation atCollapse (SHREC).

Fig. 4. Failure mechanisms considered in SHREC simulation: type 1 (strong beams and weak columns); type 2 (strong columnsand weak beams); where: HPL=Horizontal Pressure Limit; Ht = frame total heigth; h1 =¢rst £oor heigth; Tmax =HPL*Ht (Lim-it Shear Force); Lt = frame total length; Mi (Ma, T, Mc) = bending moment at column node; Mk

ij (M1a2, T, M

nc1) = bending moment

at beam node, k=£oor number, i = column n. (a, b, c), j = beam side (1= left, 2 = right).



Because of their complexity, the failure mecha-nisms analysed should have required a more de-tailed analysis in order to take into account thelarge number of mechanical and geometric pa-rameters in£uencing the collapse of r.c. structures.However, the development of such a kind of mod-elling would have been too much time consumingand it would have not allowed the opportunity toperform a parametric analysis in order to estimatethe e¡ects on the collapse of the main structuralfeatures of r.c. framed buildings, such as height,number of stories, dimensions of structural ele-ments, amount of reinforcement, typology, andstrength of beams. Although the modelling isbased on a limited number of factors, the resultsobtained are in good agreement with more com-plex analyses considered as check points.As mentioned before, two mechanisms have

been considered: (1) the failure mechanism type1 (called strong beams and weak columns) occursby formation of plastic hinges at the ends of the¢rst £oor columns, and (2) the mechanism type 2(called strong columns and weak beams) due tothe formation of plastic hinges at the ends of thebeams and at the base of columns. The lattermechanism is much more energy consumingthan type 1.The HPL for each mechanism is:

Mechanism 1 : HPL ¼ 2

Xi

Mi=h1

BHt; ð2Þ

Mechanism 2 : HPL ¼Xi;j;k

mki;j þ

Xi

Mi

!=ðBH2

t Þ; ð3Þ

where: k= the storey level (1,Tn), i= the columnconsidered (a, b, c,T.), j= the side of the column-beam node (1= left, 2 = right), Mk

i;j = the bendingmoment at the frame node, Mi = the bending mo-ment at column node, B= the building width, andother dimensions are shown in Fig. 4.

3. Main features of r.c. structures

The building technique of r.c. structures for

civil engineering spread over the Vesuvian areamainly after the Second World War (1939^1945)and in particular from 1960 to 1975. During thistime most of the r.c. structures were built, havingan height ranging from 10 to 20^25 m. It is im-portant to point out that the area has not beenclassi¢ed as a seismic zone hazard since 1981.Afterwards, most of the towns were classi¢ed inthe second seismic category, characterised by adesign seismic acceleration: ad =0.07 g. Therefore,after this time the constructional techniques anddesign criteria substantially changed. The newcode for r.c. structures issued in 1976 (D.M. 16/6/1976), which de¢ned exactly the characteristicsof the materials to be used in building rather thansome general rules for mixing the components ofthe concrete (sand, cement, water), also resultedin changes in practice.Before these new codes came into force (1960^

1975), the strength of the r.c. structures in theregion could be very di¡erent from one to anoth-er, depending on the awareness of the builder anddesigner about structural hazards. The introduc-tion of the new codes (after 1981) led to a moreuniform design and standardised constructionalmethods.

3.1. Column: dimensions and reinforcements

In general, the smallest dimensions for columnsare 30 by 30 cm, used for most single-storeybuildings. Larger dimensions are required for in-creasing numbers of £oors.The enlargements of the column dimensions,

moving from the upper to the ground £oors,have been assumed by an increment of one sidedimension of the columns every two stories, rang-ing from 15 to 5 cm as a function of buildingtypology (see Table 1). The total area of steelbars (Ast) ranges from 0.7 to 2% of the crosssection of columns, for non-aseismic structures,and up to 2^3% for aseismic structures. Aseismicbuildings taller than 7^8 stories require shearwalls that induce a remarkable change of struc-tural scheme.It must be pointed out that in the evaluation of

the yield interaction surface (N-axial force,M-bending moment) only the e¡ective reinforce-



ment for each direction has been considered. Infact, since some steel bars are placed along theperimeter of a column they will not be consideredfully e¡ective in both directions (Fig. 5). There-fore, the reinforcement used to evaluate the yieldsurface was a fraction of the total amount of re-inforcement.Since it is not possible to take into account the

position of each steel bar, the following empiricalrule has been adopted. De¢ning: Ast = totalamount of steel bars expressed as a percentageof the cross section area of the column; As = steelbars in tensile zone; APs = steel bars in compres-sion zone; for low total reinforcements (Ast) lessthan 1% of the cross section, arranged with fewsteel bars located at the corners of the column:APs =As =Ast/2 (Fig. 5a) has been assumed; forhigh total reinforcements (Ast) around 2.5^5%,with many bars located along the border of thecolumn (Fig. 5c): APs =As =Ast/3 has been as-

sumed; for medium total reinforcements (Ast)around 1^2.5% (Fig. 5b): APs =As =Ast/2.5 hasbeen assumed.Therefore, the percentage of steel bars used in

the modeling ranges from 0.5 to 1.5% correspond-ing to a total reinforcement in the range 1^5%.The axial load in the columns at ¢rst £oor (Ni)

was estimated considering the contribution ofdead weight (Ndwi), and the variation of axialload due to lateral pressure (NHPLi) :

Ni ¼ Ndwi þNHPLi; ði ¼ a; b; cÞ

The contribution of dead weight, Ndwi was es-timated as 80 kN per £oor: Ndwi, where n is thetotal number of storeys. The e¡ects of horizontalpressure are given in (Fig. 6):Failure mechanism 1: the axial load in the col-

umns due to the lateral load is evaluated bymeans of the rotation equilibrium of the totalframe, and assuming as zero the axial load varia-

Table 1

Building type Columnssteel bars

Columns dimensionincremented every two stories

Limiting bending moment

(%) (cm) Thickbeams Mlim

Flatbeams Mlim

Beams Mlim incrementevery two stories Mincr

(kN m) (kN m) (%)

A ^ strong aseismic 1.5 15 150 75 15B ^ weak aseismic 1 10 150 75 10C ^ dtrong non-aseismic 0.75 10 150 75 5D ^ weak non-aseismic 0.35 5 100 50 5

Fig. 5. Steel bars distribution as a function of reinforcement percentage; where: APs = steel bars in compressive zone; As = steelbars in tensile zone.



tion for internal columns. With reference to Fig. 6symbols:

NHPLa ¼ 3NHPLc ¼HPL

H2t

2þXci¼a

Mi

Lt;

NHPLbw0 ð4Þ

Since the axial force in a column (NHPLa ,NHPLc) in£uences the limit bending moment ofthe column (yield interaction surface N^M) anddepends on HPL, an iterative procedure has beenset up.Failure mechanism 2: since the shear forces

transmitted by each beam to the column are lim-ited by the plastic hinges, the axial load in thecolumn (Tk

i;j) is the summation of these limitshear forces:

Tki;j ¼

2Mki;j

Li;iþ1ð5Þ

where k= the storey level (1,Tn), i= the columnconsidered (a, b, c), j= identi¢es the side of thecolumn-beam node (1= left, 2 = right). Hence:

NHPLa ¼Xnk¼1

Tka2; NHPLbw0; NHPLc ¼

Xnk¼1

Tkc1 ð6Þ

The yield interaction surface (N^M) was esti-mated according to the EC-2 code (EuropeanCommittee for Standardization, 1999), see Ap-pendix for details.

3.2. Beam dimensions and reinforcements

Before the coming in force of the seismic codeusually only load-bearing beams, often alignedalong the same direction, and border in¢ll panelbeams were made. Usually linkage beams betweencolumns were not built ; however, some bendinglinkage of the £oor is not negligible. In fact, thetotal lack of damages observed to this kind of r.c.structure after the 1980 earthquake, that struckthe area with an VII MCS intensity, as well asthe very light damages surveyed on the in¢ll pan-els, possibly due to very small interstorey drifts,could be justi¢ed by assuming that the £oor canprovide a bending sti¡ness su⁄cient to resist sig-ni¢cant lateral forces.It is well known that the in¢ll panels play an

important role in the frame structure response tothe horizontal actions. However, in this study thecontribution of the panels has not been taken intoaccount since the pyroclastic £ow, once in thesettlement, might have a turbulent behaviour

Fig. 6. Variation of axial load in columns due to horizontal loads; where: NHPLa, NHPLc = axial load in column; Tki;j (T1a2, T,

Tnc1) = beam limit shear forces; HPL=Horizontal Pressure Limit; Ht= frame total heigth; h1 =¢rst £oor heigth; Lt = frame totallength; Mi (Ma, T Mc)=bending moment at column node; Mk

ij (M1a2, T., M

nc1) = bending moment at beam node, k= £oor number,

i = column n. (a, b, c), j = beam side (1= left, 2= right).



and the panels might be heavily damaged by thee¡ect of lateral pressure and heat. In order toestimate the bending e¡ect of £oors, a £oor belt2 m in width contributing to the bending sti¡nessmay be assumed for each column. Consideringsome practical building rules shown in Fig. 7,the bending resistance of such a £oor belt mightbe evaluated as about 50 kN m.Whether linking beams are present or not: lim-

iting bending moment Mlim = 75 kN m for £atbeams, 100 kN m for thick beams of mediumsize and 150 kN m for well-reinforced thick beamshave been assumed. In aseismic structures beamsin both directions are considered and their dimen-sions and reinforcement increase from upper tolower £oors; the previous Mlim values for beamsof non-aseimic structures, as they are designed tosupport only vertical loads, have to be consideredrepresentative of upper £oors of aseismic build-ings.Therefore, we de¢ned an incremental coe⁄cient

of Mlim (Mincr) that increases the limit bendingmoment every two £oors (Fig. 8). This incremen-tal coe⁄cient ranges for aseismic buildings from10 to 15%, inducing in a ¢ve-£oor building anMlim increase at the ¢rst £oor of about 20^30%.Also in non-aseismic buildings larger dimensionsand stronger reinforcements at lower £oors as aconsequence of the increasing of the overloadshave been observed. In that case the Mincr coef-¢cient has been limited to 5%.

4. Simulations

Although a limited number of parameters havebeen used, the number of possible combinationsare still very high and as a consequence it was not

possible to carry out a complete parametric study.Therefore, a simulation considering four di¡erenttypes of buildings has been performed, de¢ningfour extreme limits of resistance to lateral loads.Most of the existing buildings should be includedwithin this range: (A) weak aseismic structures;(B) strong aseismic structures; (C) strong non-aseismic structures; (D) weak non-aseismic struc-tures.Each of these categories has di¡erent character-

istics of structural elements (beams and columns),as reported in Table 1.Structures (C) and (D) are the extremes of not-

aseismic buildings: (C) represents a well-built ed-i¢ce with good concrete and strongly reinforced;it has been designed to resist non-seismic horizon-tal actions such as the wind. (D) represents abadly built edi¢ce with poor materials (steel andconcrete) not designed to resist any horizontalaction. Buildings (A) and (B) represent well-builtand designed aseismic structures for the secondand the third seismic category according to theItalian seismic code. (A) represents a structuredesigned to resist a horizontal force equal toV10% of the dead weight. (B) represents a struc-ture designed to resist a horizontal force equal to5% of the dead weight. Badly designed and/orbuilt aseismic structures could be associated withstructure (D), previously de¢ned.

Fig. 8. Variation of columns dimensions (v) and limit bend-ing moment (Mk

ij) of beam as function of £oor; where: Mkij

(M1a2, T., M

nc1) = bending moment at frame node; h

ki (h

1a, h

1b,

T, hnc ) = column dimensions, k=£oor number, i = column n.(a, b, c).

Fig. 7. Typical reinforcement of a £oor r.c. rafter.



In order to evaluate the e¡ects of irregularshape of structures (planimetric irregularities),two types of plan con¢gurations have been de-¢ned (Fig. 9). The irregular structure has beenderived from the regular one by cutting awaysome columns, so that results are directly compa-rable. Moreover, to take into account the di¡erentmaterials used for the buildings made before andafter 1980, two classes of materials have beenconsidered:Class 1 ^ good materials and/or new buildings,

less than 25 years (corresponding to Rck= 25MPa for concrete and Feb 38 K for steel bars):concrete (cc = 13.5 MPa); and steel (cs = 330MPa).Class 2 ^ poor materials and/or old buildings,

more than 25 years (corresponding to Rck= 20MPa for concrete and Feb 32 K for steel bars):concrete (cc = 10.6 MPa), and steel (cs = 272MPa).Eventually the simulations have been per-

formed on four di¡erent structural typologiesand assuming two classes for materials (A1, A2,B1, B2, C1, C2, D1, D2) and for each structuralmodel (regular, irregular). The number of £oorsvaries from 1 to 9. The inter-storey height wasassumed 3.2 m for all buildings. The £ow diagramof the computation programme is shown in Fig.10.

5. Results

Figs. 11^13 show the results obtained by theSHREC simulations. It can be observed that theupper and lower limits of resistance for each ty-pology correspond to the classes of materials 1and 2, respectively. The analysis has shown thatmechanism type 2 is by far less frequent than type1, in good agreement with some observationsgathered from recent earthquakes in Europe (Zuc-caro et al., 2002).Aseismic buildings are found to be 2^3 times

stronger than not-aseismic ones. The limit loadsfor regular buildings are 30% larger than irregularones. In particular resistance for all typologies isalways larger than 5 kPa and greater than 10 kPafor aseismic buildings.It is worth pointing out that by ‘regular build-

ings’ we mean edi¢ces not only with a regularplan but also having homogenous material char-acteristics, structural dimensions and details. Ac-tually all these characteristics are di⁄cult to ¢ndin reality, therefore resistance values for irregularbuildings seem more reliable in order to charac-terise the r.c. structures as a whole.Comparing the resistance interval calculated

with the literature data referenced in the introduc-tion (Fig. 12), we can observe that some of themare in good agreement with the limit range (Meli,

Fig. 9. Floor plans of regular and irregular structures.



1991; Dai et al., 1996), whereas the data relevantto non-aseismic buildings from Cosenza et al.(2000) are much lower.The disagreement with Cosenza et al. (2000) is

probably due to the assumption, in our simula-tions, of some bending resistance of the slab incase of lacking linking beams in aseismic buildings.In order to validate the results obtained, the

authors performed elasto-plastic numerical analy-ses on eight structural models having equal geo-metric characteristics as those introduced into theSHREC simulation, assuming a uniform lateralload and Class 1 for materials. These tests werecarried out by means of NOLIAN (Softing, 2001),a computer code for non-linear structural analy-

sis. The code performs a step-by-step elasto-plas-tic analysis assuming a prescribed limit moment atthe end of each element (beam and column). Thecompatibility of limit moments with yield surfacehas been followed manually.The comparison between the NOLIAN analy-

ses and the SHREC simulations shows a reason-able agreement; the percentage error is estimatedwithin 20% in spite of the considerable di¡erencesin the collapse mechanism found by NOLIAN,which is much more complex.Overall the literature data and the tests per-

formed have shown that the resistance limits eval-uated are a reliable estimation of real r.c. struc-tures.

Fig. 10. Flow chart of the computer programme SHREC used to evaluate the horizontal pressure limit (HPL).



Some data from the current literature (Cosenzaet al., 2000) highlight the sensitivity of the limitloads to the typological details of the structureconsidered, in particular for non-aseismic struc-tures, indicating a need for caution in extendingthe results of this study to di¡erent areas orpoorly built structures.

6. Conclusions

Recent experiences derived from studies on thedamage to structures caused by pyroclastic £owsfollowing great eruptions in volcanic areas (Pina-tubo, Monserrat, etc.) have produced researchaimed to de¢ne mechanisms of damage to the

Fig. 11. HPL vs. the n. of stories for di¡erent structural design typologies.

Fig. 12. Comparison among limit resistance calculated, literature data and test cases.



buildings. The European Project ENV4-CT98-0699 (Baxter, 2000; Neri et al., 2000; Zuccaro,2000) has traced a ¢rst methodological approachto the vulnerability of buildings in volcanic areas.It has to be underlined that this research does

not include all the aspects de¢ning destructive sce-narios after an eruptive event. These include otherfactors such as seismic events, pyroclastic fall out,lahars and so on.This topic is largely treated in the scienti¢c lit-

erature dealing with seismic horizontal actions;however, despite some analogies, the di¡erent na-ture of the phenomenon (the dynamic seismic ac-tion, the quasi static £ow pressure), requires cau-tion in applying the seismic engineering results tothe volcanic vulnerability of buildings, and re-quires the development of speci¢c numerical tech-niques.The present work, in spite of its limits deriving

from the simpli¢cations assumed in the analysis,has allowed us to ¢nd credible values for the limitresistance of r.c. buildings, subdivided into cate-gories based on di¡erent constructional tech-niques and on di¡erent periods of construction.With reference to the Vesuvian area, most of theurban settlements are located 4^5 km from thevent and if the dynamic peak pressure is assumedto be in the range 3^5 kPa, it can be stated that:(1) the r.c. structures designed in agreement to

the seismic code, even for zones classi¢ed in thethird category (weak aseismic, acceleration design0.04 g), provide collapse loads greater than 3^5kPa;(2) the 1^2-£oor r.c. structures, of any typol-

ogy, show a low vulnerability (HPLs 5 kPa);(3) the non-engineered structures (non-aseismic)

are quite vulnerable to pyroclastic £ow action,and their vulnerability increases with the numberof £oors.

Appendix. Yield interaction surface (N^M)

The yield interaction surface (N^M) was esti-mated according to the EC-2 code (EuropeanCommittee for Standardization, 1999), with refer-ence to the symbols of Fig. 13:(1) from limit strain diagram 1 to 2:ultimate concrete compressive strain:

O c ¼ 0:003

steel tensile strain:

O s ¼ 0! 30:01

position of neutral axis:d = cover

xc ¼ 0:003Wðh3dÞ

0:003þ O s

Fig. 13. Evaluation of ultimate strength of steel reinforced concrete column subjected to axial thrust (N) and bending moment(M) simultaneously; where: b, h= cross section dimensions; cc = concrete yield stress, cPs = steel compressive stress, cs = steel ten-sile yield stress; xc = coordinate neutral axis, Oc = ultimate concrete strain; Os = steel tensile strain, OPs = steel compressive strain;APs = steel bars in compressive zone; As = steel bars in tensile zone; d= steel bars cover.



steel compressive strain:

O0s ¼ 0:0033

0:003xc

Wd

steel tensile stress :

c s ¼ EsWO s

if csscsy, then cs =csy (steel tensile yield stress)where Es = steel Young modulussteel compressive stress:

c0s ¼ Es O

0s

if cPsscsy, then cPs =csy (steel compressive yieldstress)

K ¼ 0:85

N ¼ 1c 0sWA0

s þ c cWAs þ 0:85WxcWc cyWb ðA1Þ

M ¼ c0sWA0

sWðh32WdÞþ

0:85WxcWc cWbW h3xc23d

� �3N W

h23d

� �ðA2Þ

where ccy = concrete compressive yield stress.

(2) from limit strain diagram 2 to 1:ultimate concrete compressive strain:

O c ¼ 0:003! 0

steel tensile strain:

O s ¼ 30:01

position of neutral axis:

xc ¼ O cWðh3dÞ=ðO c3O sÞ

steel compressive strain:

O0s ¼ O c3O c=xcWd

steel tensile stress :

c s ¼ c sy

steel compressive stress:

c0s ¼ EsWO 0

s if c 0ssc sy; then c

0s ¼ c sy

concrete compressive stress :

c c ¼ EcWO c; if c csc cy; then c c ¼ c cy

where Ec = concrete Young modulus

K ¼ 0:5þ 0:35=0:003 O b

N ¼ c0sWA0

s þ c cWAs þ K WxcWc cWb ðA4Þ

M ¼ c0sWA0

sWðh32WdÞþ

K WxcWc cWbW h3xc23d

� �3N W

h23d

� �ðA5Þ

References

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Structural resistance of reinforced concrete buildings under pyroclastic flows: a study of the Vesuvian area