The Engineering and Influence of the Pantheon

By Emily Worthy

History of the Pantheon

Lying in the heart of Rome is the Pantheon, considered one of the most influential buildings in history. Its dome has remained the largest unreinforced concrete dome in the world (Masi, et al., 2018), with this feat of engineering continuing to be an inspiration to architects and engineers to this day.

However, the Pantheon today is not the original. The structure as it is now has undergone several reconstructions due to damage throughout the years. Travertine, a material contained in most Roman buildings, cracks easily in fire (Dewidar, 2016) and the Pantheon was no exception. The original Pantheon, constructed by Marcus Agrippa (son-in-law of Augustus, the first emperor of Rome) was damaged by fire in 80 CE (Fletcher, 2019). After a partial reconstruction under emperor Domitian, lightning struck in 110 CE and reconstruction began again under emperor Trajan. Reconstruction concluded in 125 CE during Emperor Hadrian’s rule, resulting in the version of the Pantheon we see today. (Fletcher, 2019). The majority of brickstamps from the structure date to late Trajanic or early Hadrianic periods (Jones, 2009), some of the components are original, but it can be concluded that the structure we see today was almost completely constructed in this time frame. The inscription on the portico roof shown in image 12 mentions Agrippa by name which can be misleading because brickstamps date the structure to a different time period. As a result, today we see the Trajanic-Hadrianic version of the Pantheon which has survived nearly 2000 years. 

The location of the Pantheon is fairly central to Rome, located near the large bend in the Tiber River. This location, chosen by Augustus, was not chosen by accident. It was “the same place of Romulus divinization, the legendary founder of Rome” (Nicoletta and Virgili, 2016). The location of the Pantheon is shown in figure 1.

Figure 1: Map showing the location of the Pantheon

One might wonder: how did a pagan temple survive for so many centuries? The word Pantheon means “all the gods” in Greek (Nicoletta and Virgili, 2016), and many pagan temples did not survive from ancient times. However it was the conversion of the Pantheon to a Catholic place of worship, the Basilica of St. Mary and the Martyrs, that has allowed it to remain largely intact throughout the years. This paper will explore the incredible engineering that the Romans achieved by constructing the Pantheon, focusing on its structural elements, engineering, mathematical and celestial relationships in geometry, and lastly, the influence of the Pantheon throughout history.

How Astronomy Influenced Design

Understanding the geometry of the Pantheon requires investigating its origins as a temple to the gods. Filled with symbolism, the geometry of the Pantheon’s design dictated how it was engineered. Sunlight is the main light source in the Pantheon, and this is also shown symbolically in the mathematical relationships between celestial bodies and the geometry of the Pantheon. (Fletcher, 2019). 

Celestial patterns can be observed everywhere in the design. Five rings of coffers encircle the dome, getting progressively smaller as they ascend. These coffers represent “the number of phases recognized in a lunar cycle” (Fletcher, 2019) and the seven chapels around the rotunda could “symbolize the seven visible “planets” recognized in the ancient world – Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn.” (Fletcher, 2019). Image 1 shows the circle of sunlight cast from the oculus above. This circle moves along the walls with the passage of the sun throughout the days and seasons. 

Walking through the rotunda, it is easy to imagine the sun holds great significance in the structure. Your eyes get drawn to the huge circle of light projected on the wall from the oculus which seems like it could be a sundial. The Pantheon is not oriented exactly along the north-south line, so the circle of sunlight does not align straight at noon (Nicoletta and Virgili, 2016). Despite this, there is still symbolism in where the sun strikes within the structure at midday and other days of the year important to the Romans. The sunlight shining through the oculus “marks a calendar, in the days of Equinoxes and Solstices, in addition to the April 21 birthday of Rome, at noon the spot of light in special architectural points” (Nicoletta and Virgili, 2016).

Moving around the circular rotunda, closer observation reveals the pattern of repeated circles and squares in the design and decoration. Mathematical patterns within the Pantheon’s plans show up in the use of the geometric construction technique known as ad quadratum which means “to the square” in Latin (Fletcher, 2019). The pattern consists of alternating squares and circles where the sides of the squares relate in a root two ratio (Fletcher, 2019). The ratio of root two is known as the golden ratio and is derived from the Fibonacci sequence which is seen frequently in nature. The ad quadratum pattern relates the inside and outside surfaces of the rotunda (Fletcher, 2019). The root two proportions also appear in the rotunda and portico floors (Fletcher, 2019). The rotunda tiles are pictured in image 2.

Structure and Load Path

The aboveground structure has three main parts: the rotunda, the grottoni and the portico. The rotunda supports the dome and connects to the rectangular portico at the front. The grottoni structure is located to the south, behind the rotunda. The following paragraphs describe the engineering of these three main structures as well as the foundation.

The Grottoni

Attached to the south part of the rotunda is a structure that is often overlooked but plays a vital role in the structural support of the Pantheon. The name grottoni in this context refers to the space between the rotunda and basilica to the south of the Pantheon (Jones, 2009).  According to observation, the grottoni may have been added as an intervention to mitigate vertical cracks in the rotunda structure (Jones, 2009). The grottoni structure is not open to the public, but is visible at the south side of the Pantheon pictured in image 3. Its purpose seems to have been to support the main rotunda structure and therefore may not have been originally planned as part of the structure due to the fact it was added after construction began.

The Rotunda

Walls and Relieving Arches

Roman engineers employed various techniques in engineering the walls in order to support the massive weight of the dome. Outside height of the Pantheon’s walls measures 104 feet (Dewidar, 2016). Because of the height of the walls, a lower center of mass helps stabilize them. The Romans achieved this through aggregate gradation. The walls and the lower, middle and upper parts of the dome are all made up of concrete faced with brick (Masi et al., 2018). Aggregates in the concrete are graded starting with travertine at the bottom, then tuff and travertine, then tuff and brick fragments up to where the dome begins (Masi et al., 2018). The walls start with heavy materials such as travertine and get lighter with height.

Unobstructed, the load path from the massive dome would carry the self weight and any other loading directly down through the walls to the foundation. Load path is how the loads on a structure are conveyed through its members to the ground. Relieving arches serve to direct the heavy load of the dome to the sides around the interior niches (Lancaster, 2009). Placement of relieving arches redirects the load path around the thinner, weaker areas instead of the load traveling through these areas from the dome to the ground. Since the distributed load on an arch is transferred to either side, this allows the weaker spaces beneath the arches to either hold a lighter load, or no load at all. There are eight piers between the cutouts around the interior. These piers are where the loads taken by the relieving arches were directed (Lancaster, 2009). Masonry relieving arches are visible outside the Pantheon’s rotunda, shown in images 3, 4 and 6.

Arches of this kind are also visible from the inside as shown in image 5. Each of the seven interior niches need relieving arches where the walls are thinner in order to support the load. In image 5, it is possible to see the size of the interior niches and why the relieving arches are necessary in these locations. In image 5, two relieving arches are used.

The function of masonry arches can be understood with statics using equilibrium equations. Using equilibrium analysis of an arch, it is possible to see why they were used to relieve the load in the Pantheon structure. Arches, as compression members, are effective in concrete and masonry construction as these materials function well in compression. Figure 2 below shows a free body diagram of a masonry arch, and illustrates its function in compression.

The Dome

The dome of the Pantheon famously remains the largest unreinforced concrete dome in the world. Shown in image 7, the circular rotunda measures 43.30m from side to side and is designed to fit a sphere whose top touches the dome and bottom touches the floor (Masi, et al., 2018). Pouring concrete for a dome this large required the use of wooden formwork. The system of scaffolding used to support the dome would have been massive. The Romans are described as having “a high mastery in using timber framing in a way no other earlier cultures had developed” (Perucchio cited in Clarke, 2022). Once the formwork was removed and the concrete had cured, the dome would need to support its own self weight. However, cracks did occur in the structure. On a dome of this size, the combined effects of gravity and concrete shrinkage explains the presence of cracks in the dome (Masi et al., 2018). To combat the cracks worsening, step-rings were added to the base.

Step-Rings

Circling the base of the dome are concentric step-rings. According to Masi et al., the Romans expected the dome to crack initially, and, as a result of this hoop stresses can’t be transmitted through the dome (2018). Image 8 shows possible patches to cracks in the lower dome area. Visiting the Pantheon, and searching for the cracks it is possible to see slightly lighter areas where cracks may have been patched over. The function of the concentric hoops is to “add to the load over the critical or haunch portion of the great vault and function as buttresses, helping to bring the structure into stability through compression.” (MacDonald cited in Hutchinson and Mark, 1986).

Adding more gravity load over the support reactions shown in figure 2 will help counteract the horizontal thrust and prevent collapse, which is essentially the function of the stepped rings, pictured in images 9 and 10. As hypothesized by Hutchinson and Mark, the stepped rings may have been placed to counteract initial cracking in the structure (1986). As shown by Masi et al., modeling cracked and uncracked versions of the Pantheon, it can be seen that the addition of step-rings decreases hoop stress as opposed to a model without them (Masi et al., 2018). From the models, it can be concluded that the dome behaves like a series of wedge-shaped arches (Masi et al., 2018). This allows the use of a free body diagram of an arch, such as figure 2, as an illustration of the function of stepped rings.

Each part of the structure must be in static equilibrium, including the arches. While the ancient Romans did not have the analysis methods we do today, we are able to use them to understand the techniques they employed and why they work. Visualizing the equilibrium of a masonry arch is made possible using the line of thrust method (Block et al., 2006). The method consists of using a theoretical line to represent compressive resultant forces through the arch (Block et al., 2006). If the line of thrust lies within the physical structure, then the structure will be in equilibrium (Block et al., 2006). The line of thrust method was conducted on the Pantheon’s dome by Lancaster and it was concluded that “elimination of the step-rings has a much more substantial effect on the thrust line, pushing it further outwards, though again not so far as to cause the structure to fail” (Lancaster, 2009). This shows that by analyzing the dome like masonry arches, the step-rings greatly improve the safety of the structure. The Romans did not have this advanced knowledge of arch analysis and likely relied on lessons learned from past experience to guide their designs.

Coffering

Concentric rings of coffers (square, empty spaces cut away in the concrete) continue up the interior of the dome, as shown in image 7. The coffers serve to reduce the weight of the dome (Masi et al, 2018). In addition to the structural purpose of the coffers, they also serve the symbolic purpose of representing phases of a lunar cycle as mentioned previously. The dome culminates in an open air oculus measuring 9 meters in diameter (Hutchinson and Mark, 1986), decreasing the weight of the dome further.

Concrete

The Romans are famous for their use of concrete. The concrete they used and its properties are part of what has preserved so many Roman structures through the centuries. The Pantheon marked the culmination of a “Roman architectural revolution” (Hutchinson and Mark, 1986). This was due to the use of concrete in the structure. The Roman pozzolana sets similarly to modern Portland cement (Hutchinson and Mark, 1986). Pozzolana and Portland cement are hydraulic, meaning they will set in water and damp conditions allowing their use for large structural elements (Hutchinson and Mark, 1986). The unreinforced concrete dome of the Pantheon was by far the largest of its time. The rotunda walls took a period of 4-5 years to build and the dome required a similar length of time (Dewidar, 2016). Long construction times helped the concrete to cure and gain the strength needed to support the structure.

Aggregate

In the Pantheon, clever use of aggregate served to lighten the load of the dome. At the base of the dome heavy travertine was used as aggregate, then alternating layers of light tuff, pumice and amphorae (clay vases) were mixed into the concrete to decrease the weight further (Clarke, 2022). As the aggregate decreased in weight, so did the thickness of the dome and the density of the concrete. Thickness ranges from approximately 5.9 m to 1.5 m, and the concrete densities at the bottom, middle and top respectively are: 1600 kg/m^3, 1500 kg/m^3 and 1350 kg/m^3 (Masi et al, 2018). These values reflect the varying aggregate materials used at each level. Density of modern concrete is generally taken as 150 lb/ft^3 or 2400 kg/m^3 but is almost always reinforced and therefore can support the higher density more easily. 

The step-rings provided extra weight over the edges of the dome, but the aggregate gradation also played a role in adding load in this area to resist outward pressure. The Romans understood the importance of keeping the top of the dome light, while keeping the outer portions heavy to counteract lateral forces (Lancaster, 2009). The combination of lighter and lighter aggregate going up, and the heavy outer aggregate with the weight of the step rings on the outer portions of the dome helped the structure resist the outward forces exerted by the dome. 

Cement

It was the Roman cement and its chemical properties that helped their concrete achieve its incredible durability. The concrete recipe used by the Romans consisted of the aggregates described above as well as lime and pozzolana sand (Clarke, 2022). Pozzolans have little value as a cementitious material except when mixed with water where they react with calcium hydroxide which forms cementitious compounds (Clarke, 2022). The chemistry of these compounds contributed to the survival of the dome for nearly two thousand years without reinforcement. (Clarke, 2022). 

The Portico

Sixteen columns support the roof of the portico. Columns are designed to carry compressive axial load, so the load path goes straight through the columns to the foundations then disperses to the ground. There are three kinds of columns: Doric, Ionic and Corinthian. The Pantheon uses Corinthian columns, the most ornate kind, shown in images 6, 11 and 12. These columns, made of granite and marble, were imported from Egypt (Craven, 2019). The portico, transitional block and rotunda were part of one sequence of construction (Jones, 2009) with the transitional block representing the connection between the portico and the rotunda. The portico’s granite columns hold up a roof of stone beams and slabs (Dewidar, 2016). Originally, the roof of the portico was made of bronze, however that was stripped away and replaced with wooden beams (Dewidar, 2016). The wooden beams, columns and portico roof are shown in image 11.

The Foundation

The grottoni and the step rings were both counteractive measures to prevent the worsening of cracks in the structure. Cracks could have originated because of self-weight or other reasons, but they also could have been caused by settling of the ground under the weight of the structure. In fact, foundation settlements seem to be the most likely cause for cracks (Masi et al., 2018). Since the components of the structure were heavily influenced by the appearance of cracks, it is important to understand where the cracks may have originated. Even if the foundations are not part of the visible structure, they still played an integral role in influencing what we see above. 

Geotechnical soil conditions are important for understanding the foundations and overall stability of the structure. The soil conditions are described as “marshy, unstable earth which gave a serious supporting problem to its builders” (Dewidar, 2016). These conditions may lead to differential settling of the structure. If part of the building settles more than a different part, bending stresses occur between the two parts which can result in cracking (Dewidar, 2016). Pile foundations are typically used in modern times to support the structure from the level of the bedrock, however the Romans chose to use two rings for the foundations to support the structure over a larger area (Dewidar, 2016). The second ring foundation was built to prevent the first one from cracking (Dewidar, 2016). The width of the first ring foundation is about 23 feet 7 inches and the second about 10 feet (Dewidar, 2016). While pile foundations reaching the bedrock would be the modern solution for preventing settling in the given soil conditions, the Romans employed a ring-shaped spread footing in order to support the load.

The load path travels through the foundation so it has to be strong enough to support everything that we see above ground. Because of this, the concrete used in the foundation has a density of 2000 kg/m^3 (Masi et al., 2018). This concrete was some of the densest concrete used in the structure, and is closer to the density of modern concrete. 

The Influence of the Pantheon

As an aspiring structural engineer, it is incredible to see a building which has made such a mark on history. For me and other engineers, the biggest influence of the Pantheon may be the intention with which it was engineered. It was clearly built to be beautiful and to last for centuries.

Architectural similarities between modern government and public buildings and Greco-Roman designs are common. Classical architecture including domes, arches and columns continue to influence the design of famous buildings to this day. Thomas Jefferson, inspired by the architecture of the Pantheon, brought this form of architecture to America (Craven, 2019). Inspiration was taken from the Pantheon for buildings such as the U.S. Capitol, the Jefferson memorial and National Gallery (Craven, 2019). The National Gallery of Art in Washington D.C. also houses Giovanni Paolo Panini’s famous painting, Interior of the Pantheon in Rome, in its collections. The ad quadratum pattern of rotated squares showed up in the version of the Pantheon’s plans used as inspiration for Thomas Jefferson’s University of Virginia Rotunda (Fletcher, 2019).

In addition to the architectural influence of roman structures such as the Pantheon, the materials that the Romans used in their construction continue to be used. Considering the fact that concrete structures like the Pantheon have lasted for thousands of years, there is still much that can be learned from Roman use of the material. Research on Roman concrete is still influencing how we produce concrete today.

Materials the Romans used may also influence sustainability in modern construction. Manufacture of Portland Cement accounts for “up to 8% of global greenhouse gas emissions” (Seymour et al., 2023). Improving the durability and longevity of modern concrete would reduce emissions from a decreased need for new concrete. As explained by Seymour et al., “In contrast to their modern counterparts, ancient Roman mortars and concretes have remained durable in a variety of climates, seismic zones and even in direct contact with seawater” (Seymour, et al., 2023). This shows that there is much to learn from the Romans in terms of making concrete construction more sustainable.

Why was Roman concrete so durable? The answers lie in the chemical composition of the material. Volcanic aggregates have prolonged reactivity and the role that they can play in longevity and durability of concrete is a main focus of studies on Roman concrete (Seymour et al., 2023). Reactive calcium helps to fill cracks in concrete and gives Roman concrete self-healing mechanisms (Seymour et al., 2023). According to Seymour et al., “the high abundance of aggregate-scale lime clasts in ancient Roman mortars could thus serve as a source of calcium for post-pozzolanic processes in a pore- and crack-filling “self-healing” mechanism that combats progressive degradation of these cementitious materials” (2023). If modern concrete with the ability to self-heal small cracks was widely used, concrete structures would last longer and need less repairs. Creation of more durable structures would facilitate less production of concrete, in turn decreasing carbon emissions and increasing sustainability of construction. From architecture to engineering and materials, so much can still be learned from the Romans’ enduring structures.

2000 Years Later

Physically and metaphorically the Pantheon is still at the heart of Rome. Its structure endures in modern times as a monument to Roman engineering that is still in use today. Beyond its historical significance, the materials used are still being studied in the present day. Lancaster describes the Pantheon as a “result of a century of experimentation with the use of advanced building elements such as the relieving arch, vaulting rib, lightweight caementa and step rings.” (Lancaster, 2009) Each structural element of the Pantheon shows how the Romans overcame engineering challenges. They learned from past mistakes to engineer a structure that remains awe-inspiring to this day and has influenced architecture and engineering for thousands of years.

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