A Case Study in Costing Late Antique Circuits

By Christopher Williams


I. Introduction

Throughout Late Antiquity, spoliated material became a more common feature in many building projects across the Roman Empire. While it is often assumed that this increase in spolia is linked with economic degradation, this may not be the case. Estimating the costs of Roman buildings is no easy task, due to the questionable accuracy of price data and complexity of building processes. Nevertheless, estimating the costs of these buildings may open a window into some of the decision-making behind construction materials. Focusing on the mid-fourth century wall circuit of Aphrodisias can serve as a case study in the usage of spolia and costing Roman walls. Several questions could be addressed with this information: What were the costs associated with building the circuit? Which phases of construction make up the largest portions of these costs? Why did they choose to use spolia and other construction materials? What might this tell us about the town or its economy?

The city of Aphrodisias built its circuit in the 350’s or 360’s, before which it had no fortifications (Aphrodisias Excavations Project 2019). This was a period of relative peace and stability for the empire, and the city most likely saw residential expansion while undergoing urban revitalization. Aphrodisias had become the capital of the province of Caria under Diocletian some sixty years before the construction of the walls (De Staebler 2008). Significantly for the goal of a quantity survey, Aphrodisias is one of the sites in which fragments of Diocletian’s Maximum Price Edict have been found (Kropff 2016). This can, with some qualifications, provide information about wages necessary for the calculation of labor costs.


II. Data Sources and Methodology

The circuit of Aphrodisias is approximately 3.5 km long and 10 m tall. The width of the wall is on average 3 m. Roughly three sections comprise the wall: an exterior face, fill, and interior face. All three of these sections are primarily composed of local white marble with lime mortar used for the fill and interior face. The exterior face is primarily composed of pseudo-isodomic Ashlar masonry making use of spoliated material from nearby monuments. The fill is composed of local stones, mostly white marble. The interior face is sub-Ashlar masonry making use of fresh quarried white marble (De Staebler 2008). The local white marble quarries were close to the city, approximately 2.5 km to the north-east (Aphrodisias Excavations Project 2019). While limestone appears to be found locally, specific locations were not mentioned (Long 2012). Thus, for the purposes of this quantity survey, an assumed distance of 3 km will be used for the distance of sand and limestone.

Figure 1 — Aphrodisias, plan: (a) ‘acropolis’; (b) necropoleis; (c) agora; (d) Temple of Aphrodite; (e) odeion-bouleuterion; (f) Portico of Tiberius; (g) Baths of Hadrian; (h) theatre; (i) bath complex; (j) market area; (k) stadium; (l) Sebasteion; (m) tetrapylon (Erim and Huber 2003)

To perform a quantity survey, the quantity of materials from the wall data will first be assessed. The volume of marble and mortar needed requires assumptions about the proportions of the three components of the wall. Through an assessment of photographs, it was assumed that the exterior face is on average .15 m thick, the interior face .3 m, and the rubble composing the remaining portion. While De Staebler agrees with the assumption of .3 m, he assumes that the rubble fill is approximately 2.1 m, implicitly making the exterior face .6 meters thick (De Staebler 2008). This, judging from photographs, seems unlikely and would make the exterior face twice the width of the interior face, on average. The mortar is assumed to represent 10% of the rubble fill and a negligible amount of the interior face. Once the quantities of material needed have been established, the mortar can be decomposed into necessary quicklime, a derivative of limestone, and sand, in lieu of pozzolana. The assumed proportions will be one-part quicklime to three-parts sand, as specified in Vitruvius (Vitruvius 1914). Thus, total needed volumes of marble, both spoliated and freshly mined, limestone, and sand have been calculated.

Figure 2 — Side View of Wall North of the Northeast Gate (De Staebler 2008)

Now, the total man-hours to collect these raw resources will be calculated. For the quarrying of fresh marble, numbers will be taken from DeLaine, who performed a similar quantity survey on the Baths of Caracalla (DeLaine 1997). Man-hours will be split into skilled labor, unskilled labor, and supervision and administration. The man-hours of supervision and administration are assumed to be one supervisor per twenty workers. While DeLaine estimates 234 unskilled and skilled man-hours per cubic meter quarried and squared (DeLaine 1997), it is interesting to note that experiments on Thasos suggest that it took 176 man-hours to quarry one cubic meter (Long 2012). Nonetheless, DeLaine’s numbers will be used. For spoliated material, it was assumed that ‘quarrying’ took ten percent of the time and that ‘squaring’ took twenty percent of the time, in order to account for the significant reduction in labor. This amounts to a roughly 84% reduction in labor compared to freshly quarried marble. For rubble collection, the rate of collection of hard, dry clay found by the United Nations and posted on the EnCAB website was used as an approximation (UN 1957). The man-hour cost of sand was assumed to be roughly the rate of collection of soft clay from the same study and website (UN 1957). Quicklime costs were taken from DeLaine’s study, which included the cost of mining the limestone and baking it (DeLaine 1997). It is important to note that this does require wood as fuel, but this cost will be discounted for simplicity. Thus, the cubic meter to man-hour conversions have been found for all required materials. Using these conversions, with the previously found volume, total man-hours have been estimated.

Figure 3 — Composition of Costs Found by DeLaine (DeLaine 1997)

With these man-hour productions in unskilled labor, skilled labor, and supervision, a price can now be calculated with the use of the Price Edict of Diocletian. The wage for a farm laborer will be assumed to represent the wage of an unskilled laborer cited in the text. The wages for stonemasons will stand in for the skilled labor of quarrying and squaring. The wage for a marble layer will stand in for the skilled labor of constructing an Ashlar and sub-Ashlar masonry (Kropff 2016). With these three approximate wages, the prices of production can be calculated.

With the completion of the calculations of material production, the costs associated with transportation to the proper location in the wall will be examined. The cost of all transportation is supplied from the Price Edict of Diocletian, which specifies a price for wagon loads of 1,200 pounds (Kropff 2016). The freshly quarried marble is transported from the local marble quarries, at 2.5 km distance from the city (Aphrodisias Excavations Project 2019). The spoliated marble is assumed to have been found uniformly distributed somewhere inside a 3 km ring surrounding the city walls. The average distance is then found using a trick of geometry. Finding the difference in volume between a cylinder, representing the total area if the circuit is assumed to be a circle, and a truncated cone, representing the distance between the nearest point of the wall and any point in the 3 km ring, and dividing by the total volume of the cylinder provides the average distances from any point in the ring to the nearest point on the wall. This was used to approximate the distance of transportation for both the spoliated marble and the rubble fill, except with an assumed distance of at most 1.5 km from the wall to allow for more frequent rubble findings. Finally, the distance for the limestone and sand were both assumed to be 3 km. Lastly, volumes need to be converted to weights, which was done using conversions provided by Aqua-Calc (Aqua-Calc n.d.), a website with a large list of conversions, and a marble weight conversion provided by De Staebler (De Staebler 2008). With these weights and distances, the cost of transportation can now be calculated.

Finally, the man hours and cost of building need to be approximated. The man-hours per cubic meter of Ashlar masonry conversion is taken from a study by Harper on the EnCAB website (Harper, Alg. Harper 2016 525 3 2016). The conversion for sub-Ashlar masonry is assumed to be 50% that of Ashlar masonry, to account for the lower labor requirement. Harper’s study, listed on the EnCAB website, also provides a conversion for building a rubble wall, including time to mix mortar, which will be used to approximate constructing the rubble fill (Harper, Alg. Harper 2016 526 2 2016). This algorithm does not, it should be noted, specify the amount of mortar used and does not include time to collect water for the mortar. With these three algorithms, representing the three portions of the wall, the man-hour costs of the wall can be calculated. The further calculation of the cost of labor can be found trivially in the same way specified earlier.

With these final calculations, a total cost estimate can be achieved. Thus, this represents a relatively general method of calculation, in which we can enter various parameters to hopefully compare different potential construction compositions. As a final point of comparison, total cost was translated into k. mod. of wheat, much like in DeLaine, and then translated, using Sallare’s assumption of 40kg of wheat per hectare, into hectares required to ‘produce’ the cost of the wall (Sallares 2007).


III. Model Specifications

With this general methodology outlined, different specific models were created and tested. To this end, five models have been evaluated, one of which represents a significant departure from the rest. The initial ‘control’, Model 1, is an attempt to best represent the reality of the wall as possible. This represents the methodology outlined above with the specified values. Model 2, with changing only a single variable, assumed that the exterior face was not spoliated material, but freshly quarried. The rubble fill will still be assumed to have been collected from a ring surrounding the city. This model will hopefully shed some light on the decision to use spoliated material. Model 3, again with changing only a single variable, will return to Model 1’s assumption of spoliated material, but instead of the current approximation of a .15 m thick exterior face, De Staebler’s assumption of a .6 m thick exterior face will be used (De Staebler 2008). This change will indicate the effects of changing wall portions on the final cost. Finally, Model 4 will combine the assumptions of both Model 2 and Model 3. It will assume a .6 m think exterior face which has been freshly mined.

Model 5, in a great departure from previous models, represents a wall very different from the reality of Aphrodisias. It will be assumed that this wall was produced with brick for the fill and interior face and imported marble from Lesbos for the exterior face. No mortar will be assumed to have been used in this model, as it is not listed in the Price Edict. This model, composed only of materials explicitly listed in the Price Edict, represents a comparison point of a couple things. Chiefly, it will serve as an example of the magnitude of the transportation costs of important goods vs. local goods. Secondly, it will hopefully allow a comparison of the Price Edict to the enumerated method of costing the production of these materials. Lastly, it may inform some decisions of building materials. While the methodology of this model is largely analogous to that of what has already been described, it differs in a few key areas. Firstly, brick production man-hour costs will be furnished by DeLaine’s study of the Baths of Caracalla (DeLaine 1997). Secondly, the marble will be transported not only over land, but also over sea. To this end, the cost of shipping from Nicomedia to Ephesus, specified in the Price Edict, will be used as a surrogate for the cost of shipping from Lesbos to Ephesus (Kropff 2016). Lastly, the bricks are assumed to be produced on site, with clay on site, so no transportation costs are assumed in brick production or construction. Besides these points, the process of model 5 will largely resemble that of the other models.


IV. Model Analysis

Figure 4 — Summary of Cost Breakdown of Each Model (Author Generated)


Model 1:

The total cost of the project was found to be roughly 20.7 million Denarius Communius. To place this amount in context, it is roughly 1.7% of the cost of the Baths of Caracalla (DeLaine 1997). The Baths would have been a significantly more expensive project funded by the Imperial purse, as compared to the city circuit, which was in large-part paid for by governors and perhaps supplied by the city council (De Staebler 2008). Thus, this result is expected and indicates that the analysis is not widely over-estimating, assuming DeLaine’s calculations are correct. Material production represents roughly 48% of the total cost, with transportation coming in second at about 38% of the cost. The smallest cost in the project is that of building, which only costs 13% of the project. It is interesting to note how much of the project cost is represented in transportation, given the relatively short distances that are needed. At the farthest, nothing is travelling more than 3 km from the city. Of the transportation, the fill represents the largest cost, making up 65% of the transportation cost. This appears to be because of the large quantity of fill needed. Thus, despite the low distances of transport, the costs end up quite high. It is also notable that the interior marble makes up 87% of the cost of material production, because quarrying fresh marble is so much more labor intensive than using spoliated material. Interestingly, the division of building costs between the three components is relatively even.


Model 2:

The total cost of the project was found to be roughly 25 million Denarius Communius. This represents an approximate 20% increase in cost of Model 1. Now, the wall represents 2% of the cost of the Baths of Caracalla (DeLaine 1997). Since the costs of the Baths are so high, a 20% increase in the project price is comparatively small, so future mention of the price compared to the Baths will be eschewed. The overall breakdown of the cost of production, transportation, and construction do not change significantly from Model 1. The most noteworthy change is in the breakdown of the production costs (which are now 55% of the total cost). The exterior marble now represents 32% of the production cost, with the percentage of the cost held by interior marble going down but remaining at 64%. The percentage of transportation cost represented by exterior marble nearly doubles to 13% but fill remains the largest component cost. The percentage of overall cost which the exterior face represents increased from 10% to 25%. Thus, while the overall price of the project increased, the breakdown of cost between sections did not significantly alter. The components that had made up much of the cost previously retained the lion-share of the costs even with freshly quarried material for the exterior face.


Model 3:

The total cost of the project was found to be roughly 25.8 million Denarius Communius. This is roughly 24.6% higher than the cost of Model 1. Thus, we can see that the cost of increasing the width of the exterior face is relatively high compared to changing the same width to fresh marble. The cost of the exterior face in relation to the total cost increased to 32%, up from 10% in Model 1. While the breakdown in cost between the phases of construction did not alter significantly, some noteworthy changes occurred. The exterior face now represents the majority (65%) of the cost of construction, up from 29%. Additionally, the share of transportation and production costs contributed by the exterior face increased to nearly 25% from 7% for both. Thus, altering the width of the exterior face, while still using spoliated material, had a large effect on the cost because of the still high cost of transportation and construction.


Model 4:

The total cost of the project was found to be roughly 42.7 million Denarius Communius in this model. This is an 106% increase in price from Model 1 and a 65.5% increase from Model 3. As is to be expected from the result of Model 2 and Model 3, the percentage share of the cost of the project held by the exterior face becomes the majority share of the project at 59%. The breakdown of cost of construction remains the same from Model 3, but we see an increased affect present in Model 2 for the breakdown of production costs because of the massive increase in material in the outer face. The production of so much marble for the exterior face represents a 2,200% increase from the cost of production for the exterior face in Model 1. Thus, as the amount of needed material increases, the cost saving measures of spolia begin to have a larger effect. When the amount of spoliated material is relatively low, and transportation costs are low because of distance (or other reasons), the cost benefit of using spolia is relatively small.


Model 5:

The total cost of the project was found to be roughly 49.4 million Denarius Communius. This represents an approximate 138% increase from Model 1 and 15.6% increase from Model 4. Comparing the costs of producing materials against the prices listed in Diocletian’s Price Edict, it is found that the price listed for bricks is roughly 1,180% higher than the price found through the production calculations. It should be noted that several assumptions are made concerning the size of the bricks in the edict. It is also found that the price listed for Lesbos Marble is twice the price found through production calculations for generic marble. The cost for marble transportation is 1,060% the cost of marble transportation in Model 2, in which all marble was transported from the quarry. It is noteworthy that in this model, transportation comprises 79% of the total cost. This is significantly larger than in any of the other models. Interestingly, the cost is not so much larger than Model 4, which perhaps indicates that the cost of quarrying and laying so much new marble is akin to transporting a smaller amount of marble a long distance. It should be noted, however, that this model is notably simpler so that the Price Edict can be used for total comparison.


V. Discussion

There exist some potential shortcomings in the data used. As shown by the price differences between Model 1 and Model 3, the width of the exterior facing makes a large difference in the overall cost of the wall. This result calls into question many of the assumptions of the physical specification of the wall. For example, changing the percentage of mortar used in the wall construction may have a non-negligible effect. Returning to the question of the exterior face width, a discussion can be had on the assumption of .15 m as opposed to De Staebler’s apparent assumption of .6 m. First, it should again be noted that De Staebler never explicitly lists an average width of the exterior face. Doing so, in many ways, would have been meaningless for his description of the wall. As De Staebler was not calculating volumes for the various components of the wall, the composition of the exterior face made ‘average’ blocks pointless. The exterior face is composed of ‘risers’ and ‘stringers’ which serve different purposes and are vastly different sizes. While ‘risers’ are thin and tall, ‘stringers’ are wide and short (De Staebler 2008). This creates large variation which would make finding an average block only useful for a calculation of volume. De Staebler does list an average interior face block and the width of the rubble core, by which we can back calculate a ‘width’ for the exterior face, using the average width of the wall. With this method, the exterior wall is much larger, which may suggest that De Staebler measures the rubble core width from the end of the ‘stringer’ instead of from an ‘average’ point of the exterior face. This would then, in calculations, assume that the entire exterior face is the width of the ‘stringer’. Thus, a smaller assumption, such as .15 m seems much more reasonable as an ‘average’. Furthermore, many assumptions were made about the mortar out of a lack of information, such as the ballast used and an assumed distance of transportation for limestone. If limestone is not, in fact, local, but imported from a nearby city, this would impact costs greatly, as can be seen through the outsized effect of transportation costs in the models.

Most troublesome of all the data is the Maximum Price Edict of Diocletian, which serves mainly as a way of setting maximum prices which can be charged for army procurers. With its introductory references to greed and moral degradation, it’s not clear exactly how the Price Edict was meant to be applied (Kropff 2016). Certainly, the Price Edict represents price ceilings, as suggested by its name, so the use of its listed prices in calculations produce a ceiling total cost. Despite these issues, the location of a Price Edict fragment in Aphrodisias does alleviate some of the common issues when applying the Edict, namely geographic location. What remains, however, is an issue of chronology. The price edict was issued under Diocletian, around the same time that Aphrodisias was made into a provincial capital. This is over half a century before the wall circuit is built. Thus, it is feasible that the wage data furnished by the Edict is not reliable. Model 5 attempted to evaluate some of these issues. While the result of the marble was encouraging, the price comparison of brick left much to be desired. There are further potential issues with this model, ranging from any number of assumptions from scalars on production functions to the production functions themselves.

Despite these many issues, comparing the models to each other allows a discussion of like-terms by which isolated variables can be manipulated. It is important to note that, depending on the width of the spoliated material, using spolia was not significantly cheaper than using newly quarried material. Furthermore, even with the spoliated material, the newly quarried material of the interior face composed a large portion of overall cost. If the spoliated material was used for the sake of cutting costs, then the use of new material in the interior face undermines this decision. Another factor, more qualitative than quantitative, is the use of pseudo-isodomic masonry on the exterior face, which is certainly more time intensive to construct than normal Ashlar, although this was not included as a scalar specifically (De Staebler 2008). While this was not included as a model, the findings from the other models suggest that for true budget optimizing, assuming that there was a limit to spoliated material, the spolia would be used for the interior face rather than the exterior face, due to the larger width, if not using De Staebler’s assumption. At the very least, it is clearly demonstrated through these models that having such accessible, local quarries was a boon to Aphrodisias. It allowed them to avoid the normally immense costs of transportation.


VI. Conclusion

Ultimately, these models suggest that the decision to use spoliated material in the Aphrodisiac circuit was not one of budget optimization. Additionally, it is quantitatively shown that the relative benefit of using spoliated material, from a budget prospective, largely depends on the quantity of spoliated material relative to new material. For Aphrodisias, the use of freshly quarried material in place of spolia would not represent an enormous increase in costs, especially in relation to the amount already being spent on the non-spoliated interior face. These findings certainly suggest that building for Aphrodisias was made much easier through the location of a nearby quarry. Further lines of research would be to refine the models and include more granular data, such as specifics about mortar usage and sourcing. A minor point not yet discussed is the cost of these models in terms of hectares. While these calculations are flawed for reasons of assumed grain yields, the assumed required hectares for Model 1 would be roughly 7,000 ha. A further extension, although, again, flawed, would be to find the “fields” around Aphrodisias which could represent this acreage. More interesting, rather than finding “fields” is finding a region of “influence” around the city which represents 7,000 ha of arable land, in a method perhaps resembling that of Bevan in Minoan Crete (Bevan 2010). If this region overlaps or intersects with other cities, then this may suggest a fault somewhere in the calculation, although production for the wall most likely spanned a number of years (De Staebler 2008). This research potentially helps provide quantitative analysis to a subject long under debate: the nature of spoliated material in building projects. While this research does suggest some initial findings, there are many further avenues for research.



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Table 1 — Model 1 Costs Broken Down by Phase of Construction

Table 2 — Model 1 Costs Broken Down by Component of the Wall


Table 3 — Model 2 Costs Broken Down by Phase of Construction


Table 4 — Model 2 Costs Broken Down by Component of the Wall


Table 5 — Model 3 Costs Broken Down by Phase of Construction


Table 6 — Model 3 Costs Broken Down by Component of the Wall


Table 7 — Model 4 Costs Broken Down by Phase of Construction


Table 8 — Model 4 Costs Broken Down by Component of the Wall


Table 9 — Model 5 Costs Broken Down by Phase of Construction

Table 10 — Model 5 Costs Broken Down by Component of the Wall


Christopher Williams (College ’21) is a student at the University of Pennsylvania studying Economics, Computer Science, and Ancient History and is a candidate for M.S.E. in Computer Science (’22).

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