Abstract Most of ancient Rome was settled on the Tiber River Holocene flood plain. Monuments of Imperial age (I to V century) show evidence of significant ...
Bulletin of the Seismological Society of America, Vol. 85, No. 1, pp. 320-324, February 1995
Short Notes
Resonance of Subsurface Sediments: an Unforeseen Complication for Designers of Roman Columns by E. Boschi, A. Caserta, C. Conti, M. Di Bona, R. Funiciello, L. Malagnini, F. Marra, G. Martines, A. Rovelli and S. Salvi
Abstract
Most of ancient Rome was settled on the Tiber River Holocene flood plain. Monuments of Imperial age (I to V century) show evidence of significant damage, mainly produced by earthquakes generated in the seismogenic areas of the Central Apennines, 70 to 130 k m away from Rome. The different level of damage suffered by the two most important honorary columns in Rome, those of Trajan and Marcus Aurelius, located 700 m apart, suggests the occurrence of strong variations of ground motion across a narrow zone due to changes in the local geology. In order to check this hypothesis, we investigate the details of surface and subsurface geology of the area. We construct a 2D geological profile which includes topographic variations and heterogeneities of the elastic and anelastic parameters. A finite-difference technique is used to compute the SH-wave response along the profile. Numerical modeling of seismic response at the site of Marcus Aurelius' column shows a significant spectral amplification in a narrow frequency band corresponding to the natural vibrational mode of the column. The amplification attains much lower values at the Trajan's column site.
unveiled in the year 113 A.D. The latter was erected following the death of Marcus Aurelius; according to historical sources the column was already completed in the year 193 A.D. Both were honorary columns storied with scenes from the wars won by the two emperors:
The columns of Trajan and Marcus Aurelius (hereinafter TC and AC, respectively) are very similar Imperial Age monuments located less than 700 m apart in Rome's historical center (Figs. la and lb). The former was commissioned by Emperor Trajan and was officially
b
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7-
V Figure 1. The columns of (a) Trajan and (b) Marcus Aurelius are among the tallest monuments of ancient Rome. The two colunms consist of (c) a base, a shaft, and a capital. (d) The column's interior is hollow, and houses a helicoidal staircase. 320
d
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they were intended not only to ruthlessly represent the fate in store for the enemies of R o m e but, more importantly, to raise the emperor's statue above all mortals and above every building in the city. During the sixteenth century other statues were placed on top of the monuments: those of Saint Peter and Saint Paul (on TC and AC, respectively). The mean diameter of each column is 360 cm and they are both approximately 40-m high from the bottom to the top of the apostles' statues. The columns' shafts were built by superimposing 17 blocks of white Carrara marble (see Fig. lc). The blocks were placed one over the other with no mortar. They were originally dowelled by metal pins driven into holes drilled in the marble (black squares) and subsequently sealed in place with fused lead (see Fig. ld). Dowels and lead were stolen during the Middle Ages, a time when monuments presented an easy source of metal for forging swords and daggers. While an equal state of preservation would be expected for the two monuments so closely set and so similar in architecture, age, size, and building materials, AC experienced much greater damage, requiring a number of drastic restorations (Martines, 1985). The most important damage involved significant fracturing and dislocations of large marble blocks. Prints dating back to the early sixteenth century portray the column with two deep cracks running up its shaft, but this is no longer easily perceived because of the restoration commissioned by Pontiff Sixtus V (1585 through 1588). Even after restorations, considerable local damage can still be observed on this column (Fig. 2). TC, however, never required any structural restoration. The observed damage to AC can reasonably be explained as due to ground shaking produced by one or more large earthquakes that may have occurred 40 to 150 km away in any of the seismogenic areas located to the northeast, east, and southeast of Rome (Salvi et al., 1991). Indeed, only earthquakes could produce enough energy to shift marble blocks that each weigh 30 tons. Unfortunately, the available historical sources do not explicitly assign the damage to one or more specific earthquakes (Molin and Guidoboni, 1989). However, a reasonable objection to this interpretation is that if earthquakes were indeed the principal cause of deterioration of AC, then TC, which is so similar and located only 700 m away, should have suffered a comparable amount of damage. The following two possibilities can answer this objection: (1) a difference in structure or constructive modalities between the two columns; and (2) a difference in ground-motion characteristics due to the local geological conditions at the sites where the columns stand. Based on the evidence of a close structural similarity (similar age, size, architecture, and origin of the marbles from the same quarry, see Lazzarini et al., 1988), we discard the former. On the other hand, it has long been
known that significant ground-motion differences during earthquakes may be expected at sites characterized by different local geological conditions (Baratta, 1901; Wood, 1933; Borcherdt, 1970; Singh et al., 1988; Cranswick et al., 1990). To check the extent to which ground-motion intensity may vary locally in R o m e ' s historical center we performed a detailed investigation of both geometrical and lithological characters of the near-surface geology. In order to reconstruct the three-dimensional (3D) geological structure, we analyzed data from more than 100 boreholes drilled for construction and engineering purposes in the area encompassing the two columns, approximately 4 km 2 (Feroci et al., 1991). Our investigation showed that while AC stands on unconsolidated Holocene sediments of the Tiber alluvial plain, TC stands on a much harder sequence of volcanic deposits and Quaternary sediments. Both sequences overlie a consolidated Pliocene clayey bedrock. Figure 3 (top) shows a W-E-oriented cross section of the Tiber river valley through the site of AC. TC is located 300 m south of the section; in the figure the arrow indicates its projection onto the section to a point with equivalent stratigraphy. The borehole data were used to construct a two-dimensional (2D) model including topographic variations and heterogeneities of the elastic and anelastic parameters (see Table 1). Density, quality factor, and shear-wave velocity of Holocene sediments are
Figure 2. Even after restorations, traces of previous significant damages are still evident on the column of Marcus Aurelius. The offset in the carved figures amounts to 8.2 cm and is mainly due to dislocation; a minor rotational component is also present. The white S-shaped plastering visible inside the shield of the winged Victory fills one of the holes excavated in the Middle Ages for the theft of the metal dowels (photo by Lino Rizzi).
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from in situ down-hole measurements taken in the Tiber river valley at a site 20 km out of the city, on the same alluvial deposits as those underlying AC; for the other terrains, the parameter values were obtained from the literature (see Salvi et a l . , 1991). We used the 2D model shown in Figure 3 (top) to simulate the seismic response of the local near-surface geology to a deltalike seismic input incident to the bedrock (Fig. 3, bottom). A finite-difference technique was developed (see Mitchell and Griffith, 1980) and used to compute the out-of-plane S H response to a vertically incident plane S H wave. Following Emmerich and Korn
(1987), anelastic attenuation has been included using the rheological model of the generalized Maxwell body. The time function of the forcing input was given by a Gabor impulse G(t) = exp [ - (toe(t - ts)/302] cos [toe(t - ts) + ~O], where toe = 27rfp and ts = 0.453,/fm The values = 0.24, ~0 = ~r/2, andfe = 0.45 Hz were used in our modeling to simulate a deltalike function. The grid size was chosen to allow a frequency range of validity up to 8 Hz. Figure 3 shows the pseudo-impulse responses of our model across the Tiber river valley. This numerical simulation shows that the response of Holocene sediments is characterized by a significant magnification of
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Figure 3. Section drawn across the Tiber river valley showing the local geological setting of the sites of the two monuments. Horizontal to vertical scale is 1 : 5. Based on a 2D model including topographical variations and heterogeneities of elastic and anelastic parameters, the synthetic displacement across the valley was numerically computed using a finite-difference technique. The pseudo-impulse responses to a vertically incident plane S H wave are shown for the sites along the free surface. Higher amplitudes and larger durations of seismic waves characterize the response of sites within the Tiber river valley.
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Table 1 Elastic and Anelastic Parameters Used in the Numerical Modeling
Geological Unit
a b c
Holocene alluvium Volcanic deposits and Pleistocene sediments Plio-Pleistocene clays
Density (g/cm 3)
Shear Velocity (m/sec)
Quality Factor
1.95 2.0
300 500
10 20
1000
50
2.1
both amplitudes and durations. In particular, the synthetic seismograms calculated for the sites of the two columns exhibit a markedly different behavior (Fig. 3, bottom). The amplitude spectra at the two sites were divided by the amplitude spectrum of the wavelet used as the bedrock input in the numerical modeling (see Fig. 4a). These spectral ratios provide an estimate of the near-surface amplification of the two sites due to the wave propagation in the uppermost soil layers. Based on our model (see Fig. 3 and Table 1), the soft Holocene sediments show a resonance effect at 1.1 Hz with an amplification reaching a factor of 7. This resonance peak occurs at the same frequency as predicted by one-dimensional (ID) theory. It is directly proportional to the shear-wave velocity and inversely proportional to the upper-layer thickness. While the latter is accurately defined by welllog data, the measured values of the former show a variability between 300 and 360 m/sec. The resulting variability for the sediment resonance frequency ranges from 1.1 to 1.3 Hz, approximately. Amplification of spectral amplitudes and larger durations over the Holocene sediments could locally produce significant damage, especially when the vibrational modes of the structure lie in the same frequency band as that of the sediment resonance. To check this possibility
10
Figure 4. (a) Ratios between the spectrum of the synthetic seismogram at the sites of the two columns and the spectrum of the theoretical input at the bedrock: these spectral ratios quantify the site amplification due to the wave propagation in the uppermost soil layers. (b) Ratios between the spectra of recordings of horizontal motions produced by ambient noise at the top and at the base of the columns: these spectral ratios quantify the natural vibrational mode of the columns. The fundamental mode does not appear to differ significantly for the two columns, as we could expect knowing that they are equal in size and similarly built. The small spectral differences are probably due to the effects of a different soil-generated damping at the column basement.
for AC, we measured the natural vibrational frequency of the columns (Fig. 4b). These measurements were carded out by recording ambient noise simultaneously at the base and at the top using two Mark Products L4-3D seismometers with natural period of 1 sec. The ambient noise recordings were --~10-min long. From the computed Fourier amplitude spectrum of the two horizontal components of motion recorded at the top of the columns, we calculated the square root of the sum of the squared amplitudes. This spectrum was divided by the spectrum computed in the same way for the base of the column. The fundamental mode does not appear to differ significantly for the two columns (see Fig. 4b), as we could expect knowing that they are equal in size and similarly built. On top of AC, the horizontal motion due to ambient noise is amplified by a factor of more than 50 compared to the base, in a narrow frequency band around 1.3 Hz (Fig. 4b). This frequency is very similar to the resonance of the upper sediments beneath AC. For strong inputs, as in the case of earthquakes, nonlinear effects can decrease both the fundamental-mode frequency and the amplification at the top of the columns compared with those obtained from measurements of weak motions. For a decrease up to 30% (given the construction details and the weight of the column blocks this value represents a realistic bound), the overlapping of the fundamental mode of AC over the sediment resonance band is larger or comparable with that observed in the case of ambient noise. The coupling of the two resonances indeed appears an unfavorable feature for AC: strong shaking of the column could occur even for a moderate seismic excitation at the bedrock. At the site of TC, the same bedrock input would likely produce horizontal ground shaking that is several times smaller than that suffered by AC (Fig. 4a). Source scaling laws estimated for central Italy earthquakes predict, for a M 7 event, spectral amplitudes of the order of 10 g a l / H z at 1 Hz at a distance of 100 km (Rovelli et al., 1988). A crude estimate
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based on the assumption of linearity would suggest that the upper portion of AC could have been subject to an acceleration of 1.5 g, roughly. This estimate is simply obtained by inverse Fourier transform after spectral convolution. Of course, the hypothesis of linearity is certainly not applicable in this case where an important role is played by the friction between the blocks. Therefore, the value of 1.5 g is significantly overestimated: it nevertheless suggests that strong seismic effects can be expected even for relatively small bedrock inputs. The Italian seismic catalog (spanning more than 2000 yr) reports that several strong earthquakes of the central Apennines were felt in Rome through the centuries (Molin and Guidoboni, 1989). We sought the causative earthquake for the damage on AC in a temporal window defined by two well-dated events: the theft of metal dowels (XIII to XIV century) and the restoration by Pontiff Sixtus V (1585 through 1588). The former fixes the time when AC's structure was weakened and made more vulnerable to earthquakes; the latter is represented by the extensive plastering and bas-relief reconstruction (Fig. 2) whose present integrity excludes any successive significant damage on the column. The only strong earthquake felt in Rome during that time span occurred in 1349 and produced widespread damage as documented by many authors (the most famous one is Petrarca, 1351, 1352). Lacking, at present, any alternative explanation, the most likely explanation of the described damage to AC appears to be the coupling of soil and column resonances during this earthquake. Aside from representing an important part of the archeological history of Rome, these two ancient columns convey an important warning concerning the modern structures located on the alluvial substrate of the city, especially those structures whose natural frequencies lie near 1 Hz which, typically, correspond to 10-story buildings.
Borcherdt, R. D. (1970). Effects of local geology on ground motion near San Francisco Bay, Bull. Seism. Soc. Am. 60, 29-61. Cranswick, E., K. King, D. Carver, D. Wodey, R. Williams, P. Spudieh, and R. Banfill (1990). Site response across downtown Santa Cruz, California, Geophys. Res. Lett. 17, 1793-1796. Emmerich, H. and M. Korn (1987). Incorporation of attenuation into time-domain computations of seismic wave fields, Geophysics 52, 1252-1264. Feroci, M., R. Funiciello, F. Marra, and S. Salvi (1991). Nuovi Dati suU'Assetto Geologico dell'Area Romana, ll Quaternario, 3, 141158 (in Italian). Lazzarini, L., M. Mariottini, M. Pecoraro, and P. Pensabene (1988). Determination of the provenance of marbles used in some ancient monuments in Rome, in Classical Marble: Geochemistry, Technology, Trade, N. Herz and M. Waelkens (Editors), Asi NATO Series, Kluwer Academic Publishers, 399-409. Martines, G. (1985). Restauri storici di monumenti antichi: un esempio, la Colonna di Marco Aurelio, in Forma. La Cillgt Antica e il Suo Avvenire, catalogue of the exhibition jointly organized by Soprintendenza Archeologica di Roma and by Caisse Nationale des Monuments Historiques e des Rites of France, Rome, Italy, 191-196. Mitchell, A. R. and D. F. Griffith (1980). The Finite Difference Method in Partial Differential Equations, John Wiley & Sons, New York. Molin, D. and E. Guidoboni (1989). Effetto fonti, effetto monumenti a Roma: i terremoti dell'antichita a oggi, in 1 Terremoti prima del Mille in Italia e nell'Area Mediterranea, E. Guidoboni (Editor), SGA, Bologna, Italy, 194-223. Petrarca, F. (1351). Familiarum Rerum Libri, Vol. ! 1, Letter no. 7. Petrarca, F. (1352). Familiarum Rerum Libri, Vol. 15, Letter no. 9. Rovelli, A., O. Bonamassa, M. Cocco, M. Di Bona, and S. Mazza (1988). Scaling laws and spectral parameters of the ground motion in active extensional areas in Italy, Bull. Seism. Soc. Am. 78, 530-560. Salvi, S., E. Boschi, M. Di Bona, R. Foniciello, L. Malagnini, F. Marra and A. Rovelli (1991). Subsurface geology and variations of seismic response in the city of Rome, in Fourth International Conf. on Seismic Zonation, EERI, Stanford, California, 115122. Singh, S. K., E. Mena, and R. Castro (1988). Some aspect of source characteristics of the 19 September 1985 Michoacan earthquake and ground motion amplification in and near Mexico City from strong motion data, Bull. Seism. Soc. Am. 78, 451-477. Wood, H. D. (1933). Preliminary report on the Long Beach earthquake, Bull. Seism. Soc. Am. 23, 43-56.
Acknowledgments Discussions with Amos Nut, Dave Boore, Shri K. Singh, Peter Moczo, Raniero Berardi, and Luca Valensise were very helpful throughout the development of the work. Peter Moczo, Shri K. Singh, and Pierre-Yves Bard provided many critical suggestions that significantly improved the quality of the final version of the text. Appreciation is expressed to Daniela Riposati for constructing many of the figures. References Baratta, M. (1901). l Terremoti d'ltalia, Fratelli Bocca, Torino, Italy, 278.
Istituto Nazionale di Geofisica Via di Vigna Murata 605 00143 Rome, Italy (E.B., A.C., M.D.B., R.F., L.M., F.M., A.R., S.S.) Soprintendenza Archeologica di Roma Piazza S. Maria Nova 53 00186 Rome, Italy (C.C., G.M.) Manuscript received 28 June 1993.
