the funicular polygon method ofthrust line analysis became a standard way of analyzing arches in the nineteenth century when the introduction of graphical methods made it more user-friendly than the mathematical methods with which the principles were developed. I use it in Chapter 8 to test the efficacy of various techniques discussed in this study. In what follows, I provide an example of how to perform a simple thrust line analysis for a barrel vault. It can be done with a pencil and paper, but I use AutoCad for greater accuracy and ease.

PART 1

STEPS FOR CONSTRUCTING THE THRUST LINE THROUGH A BARREL VAULT (FIG. 145):

1. Draw a scaled profile of the vault to be analyzed (shaded area in Drawing 1).

2. Divide the vault into an odd number of vertical sections (the more sections the more accurate the final curve) so that the middle section is centered on the crown of the vault. Number each section starting with “1” at the far left.

3. 3a. Determine the unit weight of the material used for each section in kg/m3. Calculate the mass (M) of each section in m3 and multiply it times the unit weight of the material used. The weight (W) in kg must then be translated into units of force in Newtons (N) by multiplying by 9.8 m/sec/sec. These are the force vectors, each of which is referred to by the number of its corresponding section, for example, F1, F2, F3, and so on.

4. 3b. To draw the force vectors, choose a convenient scale for the vectors so that each unit in the drawing equals a certain number of Newtons (e.g., scale above Drawing 2). Draw each calculated force vector as point load located at the center of gravity of its section. (A program such as AutoCad can calculate the center of gravity of unsymmetrical shapes automatically.)

5. […]

The first task after setting up the centering was to mix the mortar and choose the caementa. The best-quality Roman concrete during the imperial period was extraordinarily strong and durable. This is in part due to the addition of pozzolana but also to the high-quality lime that was available. In addition, the choice of caementa played a significant role in the stability of the structures as did the care in placing them within the mortar and ensuring that the mixture was very compact. In the following sections, I examine the individual ingredients of the concrete mixture to show how they interacted with each other and how and why the builders chose the varieties that appear in the extant remains.

MORTAR

The mortar used by the Romans employed pozzolana, a volcanic ash that imparted added strength and hydraulic qualities (the ability to harden under water) that were lacking in the simple lime mortar used by the Greeks. Recent studies show that the resistance to compression of pozzolana-lime mortar is five to eight times stronger than that of lime mortar. A simple lime mortar made of siliceous quartz sand (SiO2), slaked lime (Ca(OH)2), and water (H2O) hardens and gains strength through its contact with carbon dioxide (CO2) in the air as the water evaporates; as a result, the mortar at the center of a mass does not develop the same degree of strength as that in contact with the air.

Roman concrete vaults are praised for the impressive distances they were able to span, but one often forgets that the wooden structures on which the concrete was first laid is what determined the size of the final vaulted structure. Much of the technology for building large concrete vaults was based on woodworking techniques; this aspect of concrete vaulting has not received much attention, in part, because very little remains of these wooden structures. In this chapter, I examine the evidence that exists for the wooden centering and formwork and pose the questions: How were the centerings constructed? How were they lifted into place? How were they supported? How were they removed without damaging the work below? The sources used to answer these questions include the impressions of the boards left in the concrete, pieces of the actual wood (which are rare), ancient pictorial representations of wooden structures (albeit not centering structures), literary descriptions of wooden construction for bridges and siege towers, and comparisons of centering structures from later periods.

ASSEMBLING THE CENTERING

The construction of the most impressive Roman vaults was dependent on the builder's ability to erect large wooden centerings capable of taking the weight of the concrete. These wooden structures differed from wooden roof structures in that they did not require clear spans and had to take a much greater load with minimum deflection, but many of the joinery techniques and the structural principles were no doubt the same.

the following catalogue includes the major monuments from Rome and environs discussed in this study. The purpose of the catalogue is threefold. First, each entry introduces the location, date, purpose, and, if relevant, the later history of the monument. Second, the details of the various constructional issues relevant to this study are summarized together. If the issue is discussed at length in the main text, a cross reference is provided rather than repeat the information. In cases where the observations are my own unpublished on-site observations, I include more details than if the information is published elsewhere. Third, the relevant bibliography that deals with the construction techniques used in the monument is included at the end of each entry. I also cite the references from the Lexicon Topographicum urbis Romae (LTUR), which the reader can consult for a more comprehensive bibliography. Each monument is located on Map 1 (p. 4) according to its catalogue number.

PONS FABRICIUS (62 b.c.)

COMMENTS: The Pons Fabricius consists of two arches (24.5-m span) and connects the left bank of the Tiber to Tiber Island. Identical inscriptions on both sides of one of the arches indicate that it was built by L. Fabricus in 62 b.c.

Materials. The arches, approximately 6 m thick, are built of peperino (lapis Gabinus) blocks with an outer facing of travertine voussoirs.

Centering. The arch connecting to the left bank has two cuttings, spaced approximately 4.5 m apart, along the impost at either side of the intrados.

The use of amphoras in the concrete vaults of buildings around Rome is a phenomenon that has been recognized for centuries largely because of the ruined state of some monuments that has left the amphoras exposed. The most renowned example is the Mausoleum of Helena, which by the sixteenth century was dubbed the “Tor Pignattara” from the visible remains of the amphoras (or “pignatte”) in its partially fallen dome (Fig. 47). The monument made such an impression in the past that it now provides the name for the surrounding suburban area. This technique of placing amphoras in the vaults has thus been long recognized, but it has sometimes been equated with or confused with another vaulting technique in which specially made terracotta tubes (tubi fittili) were inserted into each other to form the permanent centering of the vault. They are, in fact, two quite separate techniques. The amphoras are reused material within the vault whereas the tubes are made specifically to act as the permanent centering. The use of tubi fittili is a technique that only became common in Rome in the fifth century and later and is, therefore, beyond the scope of the present study. In the following discussion, I focus exclusively on the phenomenon of inserting reused amphoras into the core of the vaults.

Roman builders had an intuitive understanding of vault behavior and structural form as seen through their use of lightweight caementa, vaulting ribs, and iron tie bars. They had no means of quantifying and calculating vault thrusts, but they had developed ways of controlling behavior through long experience with the problems that could occur. Because most readers do not have the same benefits of firsthand experience of vault construction, I present some basic principles of vault behavior and examine how the Roman builders and designers developed techniques to control it. In Chapter 8, I then give an overview of the historical development of the modern understanding of vault behavior and methods of analysis that have been developed to study it.

The way Roman architects and builders approached design would have influenced how they determined the appropriate size and form for their vaulted structures. M. Wilson Jones has recently examined the design methods used by Roman architects and has pointed out that they typically used rules based on numerical proportions and/or geometrical relationships, both of which were principles used by Vitruvius for attaining symmetria, or mathematical harmony. Vitruvius's concept of symmetria was an aesthetic principle rather than a structural one, but when Roman architects and engineers were faced with determining the form of an arch or the appropriate wall thickness for a given structure, they would have likely resorted to the same type of proportional system that was used to ensure symmetria.

Structural analysis is often viewed by the nonengineer as a mysterious and magical process leading to the Truth. Attempts by engineers to demystify the process have not always been successful, which has led many nonengineers interested in ancient structures to the conclusion that if one can simply find an amiable engineer competent with a computer all structural questions can be readily answered. In fact, much of the basic understanding of arch and vault behavior was developed long before computers became available. In any case, the computer provides answers only as accurate as the information entered. Moreover, different approaches can be applied to structural analysis, and there is some debate regarding which approach yields the most useful information. My goal in this chapter is to make yet another attempt to demystify the basics of structural analysis and to present the two major approaches most often applied to the analysis of historical structures, finite element modeling and thrust line analysis. Each approach makes different assumptions about the structure and asks different questions; therefore, the answers are not always comparable. The choice of approach depends in part on the question one is trying to answer. For the nonengineer interested in the structural behavior of historical buildings, understanding the fundamental differences provides some basis for evaluating the results. After discussing the historical development of arch analysis and the modern approaches to it, I present a series of case studies intended to demonstrate various ways in which structural analysis can be useful to the archaeologist examining ancient buildings.

Concrete vaulted structures represent one of the ancient Romans' most original and enduring contributions to the artistic and architectural patrimony of the Mediterranean world. A combination of factors led to the development of the large spans and curvilinear forms still visible in buildings such as the Pantheon and the Basilica of Maxentius. Rome was endowed with a wealth of natural resources in its immediate environs, and what it could not supply for itself it could bring in from afar through the development of extensive trade networks. Along with the financial benefits of conquest came the architectural, technological, and mathematical expertise of the architects, builders, and engineers from the conquered territories. Augustus, in bringing the civil wars to an end, also brought a vision of urban renewal for Rome that provided incentive for more grandiose schemes than had previously been possible. By that time, the architects and builders had over a century of collective experience with concrete construction, but Augustus's creation of an organizational infrastructure provided a context in which new ideas and larger building schemes were possible. As emphasized by W. L. MacDonald, the fire that devastated much of Rome during Nero's reign in a.d. 64 effectively cleared the slate and provided opportunities to exploit the fireproof nature of concrete and in doing so created a new aesthetic based on the plastic potential inherent in the material.

One of the hidden but nevertheless crucial elements in the development of the architectural vocabulary of imperial Rome was the use of metal fittings, such as clamps, dowels, and tie bars. These elements became particularly important when marble was introduced into Rome as a major building material. The growth of the marble trade during the imperial period created an environment where, on the one hand, Greek classicism provided models of trabeated structures that had developed in the marble-rich areas of the Aegean and, on the other, concrete provided the potential of creating new types of interior spaces. The marriage of these two was ultimately made possible by the hidden metal fittings that allowed the concrete vaults to be securely attached to the marble support structure.

Metal clamps and other experimental uses of metal in architectural contexts had appeared in Greece by the fifth century b.c., but they only appeared in Rome at the end of the second century b.c. when travertine and imported Greek marbles began to be used there. The Romans had access to the Etruscan iron resources from Elba and Populonia from the mid-third century b.c., so the late development of the use of iron for clamps seems to have more to do with the supply of stone than with the supply of metal. The earliest datable use of clamps in Rome are the iron pi clamps used to attach the travertine facing of the Metellan rebuilding of the Temple of Castor in the Forum just after 117 b.c. Other examples occur sporadically during the late Republic such as in the round temple in the Forum Boarium (c. 100 b.c.), where iron pi clamps were used to attach the Pentelic marble facing of the cella to the travertine backer blocks.

The focus of the preceding chapters has been on the innovations in the use of materials and construction techniques involved in the creation of large and technologically advanced concrete vaulted structures in imperial Rome. The period from Augustus to Constantine is one in which the Roman world underwent great transformation, the nature and causes of which are often the subjects of debate. As a means of generating an overview and putting the conclusions into context, I employ the four criteria for technological innovation described at the end of Chapter 1: (1) accumulated knowledge, (2) evident need, (3) economic possibility, and (4) cultural/social/political acceptability. In what follows, I use these four criteria to explore some of the most salient issues involved in understanding the changes that affected vaulted construction during the three and half centuries under investigation.

ACCUMULATED KNOWLEDGE

Perceptible changes can be seen in the way builders approached vaulted construction during the imperial period including the understanding of the properties of materials, of centering construction, and of the effect of form and mass on vault behavior. Much of the increased understanding no doubt came from years of experience with materials. Another, less direct, influence is that of military technology, which manifested itself largely in the use of timber construction and in metallurgy for making tools and connectors used on the building site.

The quality of the mortar gradually improved from the second century b.c. to the first century a.d.

the intention of the analysis was to determine the most likely provenance of the scoria samples taken from the caementa of vaults of five buildings in Rome dating from the mid-first century b.c. to the late third century a.d. The samples are visually very similar to the scoria used in the dome of the Pantheon, which was determined by Gioacchino De Angelis d'Ossat in 1930 to have been a product of Vesuvius. Because there has recently been some suggestion that a similar looking material produced by the Colli Albani system just south of Rome also may have been used for vaulting in Rome, this analysis is designed to determine whether the material from Vesuvius continued to be imported over a long period or whether it was replaced by a local but similar-looking material. In his later study of the lightweight material from the “Temple of Minerva Medica,” De Angelis d'Ossat found pumice produced by the Sabatini system north of Rome. In the present study, petrographical analyses of thin sections were used to identify the crystal fragments within each sample, and then the resulting mineralogical profile was compared to the compositional data for volcanic deposits from the three most likely volcanic districts to have supplied the Roman builders: Vesuvius, Colli Albani, and Sabatini.

Because the color of the scoria varies from dark brown to reddish brown (Pl. VIII, IX), samples from each end of the spectrum were included.

FOUR POPULAR PLANS

The temple seems to us the most characteristic of all Greek buildings, and it would be natural to conclude that the Greeks regarded such buildings as requirements for the worship of their gods and goddesses. In fact, nothing more than an open-air altar was really necessary. However, once the Greeks began to make statues of their deities, they had to provide a shelter to protect them, and it was to serve this function that a temple was constructed. It was not built to accommodate a congregation, since religious ceremonies and rituals still took place at an altar outside the front (usually the east end) of the temple, and few people ever went inside.

A temple, whether made of wood or stone, could be very simple. A single room entered through a porch would suffice (Fig. 33). The room in which the statue of the god was kept was called a naos (the Romans called it a cella, and this term is sometimes also used of Greek temples). The porch was called a pronaos (literally ‘in front of the naos’).

When a temple could easily be seen from more than one side, the Greeks disliked having the front and the back look different, so they added another porch at the rear (Fig. 34). There was usually no way into the temple from the back porch (called the opisthodomos); its only purpose was to give the temple a more symmetrical appearance.

WORLD ARCHITECTURE FOR WORLD RULERS

The Romans were great organisers and great builders. Wherever they went – and they went all over the western part of the civilised world (Map 3) – they established colonies and built cities. These cities were then graced with the amenities that made Roman civilisation attractive to conquered people. To house such amenities, the same types of buildings as had been created in Rome were erected outside the city in the newly acquired domains, although local methods and materials often had to be used to construct them.

We have already seen how a theatre in the Roman style was built at Orange in southern France (Fig. 123). Similar theatres can be found throughout the Roman empire. The best preserved is at Aspendos in Asia Minor (Fig. 130). As at Orange, the scaenae frons still stands up to its full height and is linked to the top of the cavea. The audience was, therefore, contained within an enclosed space, isolated from the outside world; this was very different from the open aspect of the Greek theatre at Epidauros (Fig. 88).

The scaenae frons was, in its original state, a glamorous affair. Statues stood in niches framed by columns, each pair of columns topped by its own entablature. This lively decorative scheme was on two levels, supported by the outcroppings still protruding from the back wall of the scaenae frons.