55

1. Introduction

The ancient town of Marea, which is located about 45 km on the west of Alexandria, Egypt is an example of a unique ancient construction work. The fi rst excavations were carried out on the site by F. El-Fakharani of the University of Alexandria. In 1977-79, he identifi ed some of the topographical elements of the Byzantine town (Szymańska, Ba-braj 2008). He also described the site as a whole together with the piers and lake harbors. The inve-stigations were preceded by a magnetic survey of the area. Built on a Roman plan, the urban centre developed around two intersecting main streets, the cardo and the decumanus. Egyptian archaeologists focused on their activities on the waterfront where they uncovered a number of important structures. Then, the excavations focused on digging a large three-aisled basilica, the plan of which was drawn by P. Grossmann.

Further fi eldwork was undertaken between 1979 and 1981 by K. Petruso from Boston Universi-ty. This researcher revised Fakharani’s identifi cation of the discovered buildings. The American team also explored the harbor facilities and uncovered traces of a lighthouse on the island that is artifi cially con-nected with the mainland. The Byzantine basilica, a crucial point of the excavations of Polish Archae-ological Mission since year 2000 is located on the north tip of peninsula, and situated on a small hill, descending into the Lake Maryut on the north side, and into the land on the south. Location and scale of the basilica indicates importance of the object in historic times. One of the mysterious constructions revealed by the Polish Archaeological Mission is a pottery kiln dated on the 2nd/3rd century, which is positioned under the level of foundations of basilica.

The kiln was abandoned before construction of the consecutive layers of the basilica, hence the kiln’s date is established on the basis of its stratigraphi-cal position. The pottery kiln is one of the largest in Egypt. In the future, a new museum is planned on the excavations site and hence the estimation of stresses in the kiln structure as well as its stress hi-story is needed.

2. The pottery kiln description

The construction of such a pottery kiln was a real engineering challenge. Due to the size of the kiln structure there are several questions regarding the kiln and the foundations arisen. They contain many engineering topics such as main loading, the infl uence of the soil and foundation and overall sta-bility in every state of kiln and existing structure of basilica. The kiln structure is one of the largest un-veiled so far. It is made of bricks and wrapped with a plaster. Its diameter is about 8.22 meters. Figure 1 presents the drawing of basilica apse with dimen-sions of a pottery kiln.

Figure 2 presents the current state of the kiln’s grid. The grid is made in such a way that demon-strates the stove underneath as an open one. Author investigated the results of the archaeological explora-tion and documentation of works performed on the site. The centre of the kiln was probably later on cut out and then fi lled partially with stones and used as a part of the construction of the apse staircase. After-wards, the kiln was fi lled up with several columns and beams from the basilica, what is visible in Figure 3, which is presenting the photo taken inside the kiln. From Figures 2 and 3 one is able to distinguish regu-lar air-holes demanded in a technological process of pottery production.

MATERIAŁY ARCHEOLOGICZNE XXXIX, 2013

JANUSZ P. KOGUT

NUMERICAL MODELING AND ANALYSIS

OF THE ANCIENT POTTERY KILN FROM MAREA (EGYPT)

56

3. Numerical modeling

The fi nite element model of the kiln is built using the Finite Element Method (FEM) package ANSYS (ANSYS 2009) from Academic Computer Centre Cy-fronet. The model is based on the representation of re-licts, which were reconstructed using the same techno-logy as in the past. It consists of the bricks as in reality.

The overall equilibrium equations for linear structural static analysis in ANSYS program are used to determine the displacements, stresses, strains, and forces that occur in analysing structure as a result of applied loads. All static analysis types are based on the following general equilibrium equation:

K · u = Fr+Fa (1)

where N

K=Σ Ke

k=1

is a total stiff ness matrix for N – ele-

ments with element stiff ness matrix – Ke, and u is

a nodal displacement vector. Fr is a reaction load vec-

tor and Fa is the total applied load vector, which can

be defi ned by:

N N

Fa=Fnd+Fac+Σ Feth+Σ F

epr

m=1 m=1

(2)

where Fnd – applied nodal load vector, while Fac – ac-celeration load vector (Fac = −M · a

c with M – total

mass matrix and ac – total acceleration vector). F

eth is

an element thermal load vector and Fepr is an element

pressure load vector.Realistically, all structures are non-linear in natu-

re. However, the infl uence of non-linearities not always have a signifi cant eff ect on results obtained. In many en-gineering problems to obtain accurate result, non-line-arities cannot be disregarded and nonlinear analysis is required. ANSYS program with static analysis provides ability to simulate complex interaction among diff erent types of non-linearities such as plasticity, large defl ec-tion, creep, large strain, and contact surfaces. However, the initial masonry model used in further analyses here is linear. The walls are homogenized and the following parameters are used: Young modulus (Binda 2008, Ka-wecki, Kogut 1995, PN-88/B-03004) is in the range of

E = 0.01÷0.03 105 MPa,

and the Poisson ratio is in the range of

ν = 0.09÷0.15.

The density of the material is equal to

γk = 20 kN/m3.

The model geometry is taken from the surveying of the structure. Figure 4 displays the horizontal ele-

ments partition. Superimposed on the apse drawing is an ordinary circle with radii at every 12 degrees, which are taking into account the regular air-holes inside the grid. From Figure 4 one is able to notice that the surveying of old designers was marked out very preci-sely and fi nally the pottery kiln was accurately erected.

Figure 5 presents the cross-section of the apse foundation with superimposed on that the model of the pottery kiln structure. The apse walls were recon-structed and the top layer was maintained.

3.1. The model #1

The model #1 geometry is built as a regular ring around the geometrical center with regular air-holes and a central empty space as it is existing now. In the past, the external wall was established as a dome covered the stove, inside of which the process of bur-ning out of the pottery took place, but nowadays it doesn’t exist anymore.

SOLID45 element is used for the 3-D modeling of the kiln solid structure. The element is defi ned by eight nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions. There is an option giving six nodes prism and four nodes tetrahedral elements. Figure 6 displays the element details. The model #1 geometry of half of the kiln is shown in Figure 7a. The bottom of the pottery kiln is clamped and the kinematic boundary conditions of the model of half of the kiln are along the surface of cut assumed as simply supported. The maximum length of the element edge is equal to 0.20 m and the mesh is generated automatically. There are 10537 nodes and 46163 elements in the model mesh. Figure 7b presents FEM mesh model #1 of the analysed structure.

The geomorphologic research at the site of Marea has been conducted since the year 2000 (Babraj et al. 2008; Mycielska-Dowgiałło, Woronko 2008). The re-sults of a granular analysis of typical soil sample taken from the soil surface according to (PN-86/B-02480) show that about 5.8% of the soil is classifi ed as the coarse gravel, 4.2% belongs to the fi ne gravel, 10.1% of the sample is classifi ed as the coarse sand, 45.4% of the soil belongs to the medium sand, 33.4% of the sam-ple is classifi ed as the fi ne sand, and remaining 1.1% is classifi ed as the fraction of the fi ne soil. According to Eurocode 7 (EN 1997-1:2004), which is in compliance with PN-EN-ISO 14688-1 (PN-EN-ISO 14688-1), this means the soil is classifi ed as a sand (Sa). From the lar-gest sand fraction it might be precisely categorized as a medium sand (MSa) in a loose consistency (Kogut 2012). Hence, the loading, which is acting on the kiln structure is based on the value of density index

ID = 0.33,

and internal friction angle equal to φs = 32 deg, which

might be transferred as a linear pressure with coeffi -cient of active earth pressure of

57

Ka = 0.307.

The gravity density of the medium sand is equal to

γs = 16 kN/m3.

The ANSYS solution of the total displacements of the pottery kiln model is shown in Figure 8. The soil loading is changing uniformly from 0 to nearly 20 kN/m2 downwards in the vertical direction. There were two diff erent cases computed for the minimum and maximum value of Young modulus range. The maximum displacement under the earth active pres-sure is nearly 0.3 mm as it is reached for a minimum value of Young modulus. Figure 9 presents the solu-tion of stress intensity due to Tresca theory of strain. Maximum value of equivalent stress is nearly equal to

σTmax

= 0.14 MPa.

It is located at the bottom of the structure near the imaginative foundation is placed. The value of σ

Tmax is well below the strength of the masonry. The

infl uence of the air-holes on the stresses in this sta-te of the loading is negligible, which means that the Byzantine contractors were right utilized the ancient pottery kiln as a part of the foundation of basilica.

3.2. The model #2

In the next step, the structure of the kiln has been modeled as a one similar to that, which had pro-bably been before the basilica was built. In that model #2 another circle of holes in the grid has been intro-duced. In such a way the pottery kiln is similar to the kilns unveiled in Tell al-Haraby (El-Amshawi 1998) and Burg al-Arab (Majcherek, El-Shennawi 1992). All three kilns are probably from the same period of time. Figure 10a presents geometry of model #2 of the pottery kiln, which has its grid extended over the whole plane. Also in that model the bottom of the pottery kiln is clamped and the kinematic boundary conditions of the model of half of the kiln are along the surface of cut assumed as simply supported. The maximum length of the element edge is equal to 0.20 m and the mesh is generated automatically. There are 56462 nodes and 279862 elements in the model mesh. Figure 10b presents FEM mesh of model #2 of the analysed structure. The FEM package solution of the total displacements of the pottery kiln model #2 is shown in Figure 11. The soil loading is changing uniformly from 0 to nearly 20 kN/m2 downwards in the vertical direction. Superimposed on that is the vertical loading of the existing basilica fl oor, which is also uniform and equal to 10 kN/m2. The vertical loading is based on the assumption of a sand backfi ll of grid and a marble fl oor, traces of which have been

discovered in the apse. The maximum vertical displa-cement in this case is more than 4.8 mm. Figure 12 presents the ANSYS solution of stress intensity due to Tresca theory of strain. Maximum value of the stress is nearly equal to

σTmax

= 1.02 MPa.

It is located just inside the holes introduced in the third row around the grid centre. The value of such stress is exceeding the maximum value limiting proper behaviour of the material, which might be, in case of brick wall, equal to

σTlim

= 0.2÷0.3 MPa.

Summing up, in this case the grid might collapse.

3.3. Discussion

Two diff erent numerical models of a unique an-cient pottery kiln have been tested here. The initial analysis of the behaviour of linear model with the same parameters proved that fi nal results for both models diff er much. While the maximum total displa-cement of model #1 is only about 5.6% of model #2, the maximum stress intensity in model #2 increases more than 7 times in comparison to model #1, and at least 3 times exceeds the stress limit of masonry. There is a serious redistribution of stresses due to the higher stiff ness of the structure represented by model #2. That is the reason why the ancient contractors cut out the centre of the kiln and left the remaining part under the fl oor of basilica.

4. Final remarks

Two diff erent numerical models of a unique an-cient pottery kiln have been discussed in this paper. Author focused on the initial analysis of the beha-viour of linear elastic model with typical material parameters. In case of Marea pottery kiln and the soil loading, there is no serious risk of failure and the maximum stresses are below the limits dedicated to masonry structure of kiln. When the centre of the kiln is modeled with the full grid the shear stresses li-mit is exceeded and the centre of the grid might have been collapsed.

In the future, several changes are planned to apply to the model, especially non-linearity with material and geometry, imperfections based on the observed chan-ges and other types of the loading such as temperature as well as external static and dynamic loads.

Instytut Mechaniki Budowli Wydział Inżynierii Lądowej

Politechnika Krakowska

58

BIBLIOGRAPHY:

ANSYS2009 Structural analysis guide, ANSYS inc, Ca-

nonsburg, PA.Babraj K. et al. 2008 Babraj K., Mycielska-Dowgiałło E., Szymań-

ska H., Woronko B., Rozwój starożytnego miasta Marea w Egipcie na tle warunków śro-dowiska, Zeszyty Naukowe Szkoly Wyższej Przymierza Rodzin, 7–26.

Binda L., ed.2008 Learning from failure. Long-term behavio-

ur of heavy masonry structures, WIT Press, Southampton, Boston, 2008.

European Committee for Standardization, Brussels. EN 1997-1:2004 Geotechnical design - Part 1: General rules, 2004.

El-Amshawi F.1998 Pottery kiln and wine-factory at Burg el-Arab,

Bulletin de Correspondance Hellénique, Supplément 33, 55–64.

Kawecki J., Kogut J. P.1995 Dynamic characteristics of low buildings, [in:]

Problemy naukowo-badawcze konstrukcji inży-nierskich, 194, 131–142, Cracow University of Technology, Kraków.

Kogut J. P.2012 Geotechnical data acquisition and analysis for

archaeological appraisal, Archaeologia Polo-na, 50 (in press).

Majcherek G., El-Shennawi A. A.1992 Research on amphorae production on the north-

western coast of Egypt, Extrait des Cahiers de la Céramique Égyptienne, 3, 129–136.

Mycielska-Dowgiałło E., Woronko B.2008 Evolution of the natural environment in the re-

gion of Marea, [in:] H. Szymańska, K. Babraj, ed., Marea vol. 1 Byzantine Marea. Excavations in 2000-2003 and 2006, Kraków, 17–26.

Polski Komitet Normalizacji Miar i Jakości,Warszawa. PN-86/B-02480: Building soils. Nomenclature, sym-bols, classifi cation and description of the soil, 1986.

Polski Komitet Normalizacji Miar i Jakości, Warsza-wa. PN-88/B-03004: Brickworked and reinfor-ced concrete chimneys. Static calculation and design, 1988.

Polski Komitet Normalizacyjny, Warszawa. PN-EN-ISO 14688-1: Geotechnical investiga-

tion and testing – Identifi cation and classifi ca-tion of soil, 2004.

Szymańska H., Babraj K., ed.2008 Marea vol. 1 Byzantine Marea. Excavations in

2000-2003 and 2006, Kraków.

ACKNOWLEDGMENT

Author would like to thanks Mr. Krzysztof Babraj from Archaeological Museum in Kraków, the Head of Polish Archaeological Mission in Marea (Egypt). All the pictures of the pottery kiln are taken by Mr. J. Kucy from NYC. All the drawings are made by Ms. D.Tarara from Dublin. The computations are made by Mr. Jakub Zięba – PhD Student at the Department of Civil Engineering, Cracow University of Technology. The fi nancial support of the Rector of Cracow University of Technology and a collaboration with Polish Centre of Mediter-ranean Archaeology of the University of Warsaw is kindly acknowledged.

JANUSZ P. KOGUT

Modelowanie i analiza numeryczna antycznego pieca ceramicznego z Marei w EgipcieStreszczenie

W niniejszej pracy omówiono próbę modelowa-nia unikalnego w skali światowej antycznego pieca ce-ramicznego. Konstrukcja, zlokalizowana w egipskiej Marei, została częściowo odsłonięta przez Polską Misję Archeologiczną. Misja prowadzi prace wykopa-liskowe na terenie bizantyjskiej bazyliki, zlokalizowa-

nej nad brzegiem jeziora Maryut. Model numeryczny pieca ceramicznego obejmuje kilka faz jego pracy, zaś obliczenia analizują zachowanie się konstrukcji pieca i sił wewnętrznych w nim występujących oraz sprawdzają jego ogólną stateczność.

59

Rys. 1. Rzut poziomy absydy bazyliki z Marei wraz z wymiarami pieca ceramicznego

Fig. 1. The drawing of the Marea basilica apse with the horizontal dimensions of the pottery kiln

Rys. 2. Widok pieca ceramicznego przed wykonaniem robót konserwatorskich

Fig. 2. The pottery kiln’s grid prior to the conservation works

60

Rys. 3. Wnętrze pieca widziane od strony paleniska

Fig. 3. The pottery kiln inside picture taken from the position of a stove

Rys. 4. Fragment absydy bazyliki z Marei wraz ze wstępnym podziałem pieca na elementy

Fig. 4. The drawing of the Marea basilica apse with the initial elements partition of the pottery kiln

61

Rys. 5. Przekrój absydy bazyliki z Marei wraz z zakonserwowanymi ścianami i reliktami podłóg oraz zaznaczonym modelem pieca

Fig. 5. The sketch of a cross-section of the Marea basilica apse including the wall reconstruction and fl oor relicts with the elements of the pottery kiln model

Rys. 6. Elementy skończone użyte do analizy (ANSYS 2009)

Fig. 6. FEM element details (ANSYS 2009)

62

Rys. 7. Geometria modelu #1 (a) i odpowiadająca jej siatka MES (b) widoczna w przekroju pieca

Fig. 7. Geometry of the model (a) of half of the pottery kiln and FEM mesh (b)

Rys. 8. Przemieszczenia całkowite pieca ceramicznego przy obciążeniu parciem gruntu, widoczne na odkształconym modelu #1 z zaznaczonym przemieszczeniem maksymalnym dochodzącym do 0,3 mm

Fig. 8. Solution of the total displacements of the half of the pottery kiln under the soil loading shown on the deformed model with a maximum displacement nearly to 0.3 mm

63

Rys. 9. Wartości wytężeń pieca ceramicznego, zgodnych z hipotezą Tresci, przy obciążeniu parciem gruntu widoczne na odkształconym modelu #1 z zaznaczonym maksymalnym wytężeniem dochodzącym do σTmax = 0,14 MPa

Fig. 9. Solution of the stress intensity of the half of the pottery kiln under the soil loading shown on the deformed model #1 with a maximum of stress intensity equal nearly to σTmax = 0.14 MPa

64

Rys. 10. Geometria modelu #2 (a) i i odpowiadająca jej siatka MES (b) widoczna w przekroju pieca

Fig. 10. Geometry of the model #2 (a) of half of the pottery kiln and FEM mesh (b)

Rys. 11. Przemieszczenia całkowite pieca ceramicznego przy obciążeniu parciem gruntu oraz ciężarem posadzki, widoczne na odkształconym modelu #2 z zaznaczonym przemieszczeniem maksymalnym wynoszącym 4,8 mm

Fig. 11. Solution of the total displacements of the half of the pottery kiln under the soil and fl oor loading shown on the deformed model #2 with a maximum displacement more than 4.8 mm

65

Rys. 12. Wartości wytężeń pieca ceramicznego, zgodnych z hipotezą Tresci, przy obciążeniu parciem gruntu oraz ciężarem posadzki, widoczne na odkształconym modelu #2 z zaznaczonym maksymalnym wytężeniem dochodzącym

do σTmax = 1,02 MPa

Fig. 12. Solution of the stress intensity of the half of the pottery kiln under the soil and fl oor loading shown on the deformed model #2 with a maximum of stress intensity nearly equal to σTmax = 1.02 MPa