Numerical modeling and analysis of the ancient pottery kiln from

Numerical modeling and analysis of the ancient pottery kiln from

MATERIAŁY ARCHEOLOGICZNE XXXIX, 2013
JANUSZ P. KOGUT
NUMERICAL MODELING AND ANALYSIS
OF THE ANCIENT POTTERY KILN FROM MAREA (EGYPT)
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 first excavations were carried out on the site
by F. El-Fakharani of the University of Alexandria.
In 1977-79, he identified some of the topographical
elements of the Byzantine town (Szymańska, Babraj 2008). He also described the site as a whole
together with the piers and lake harbors. The investigations 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 fieldwork was undertaken between
1979 and 1981 by K. Petruso from Boston University. This researcher revised Fakharani’s identification
of the discovered buildings. The American team also
explored the harbor facilities and uncovered traces
of a lighthouse on the island that is artificially connected with the mainland. The Byzantine basilica,
a crucial point of the excavations of Polish Archaeological 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 stratigraphical 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 history 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
influence of the soil and foundation and overall stability in every state of kiln and existing structure of
basilica. The kiln structure is one of the largest unveiled 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 dimensions of a pottery kiln.
Figure 2 presents the current state of the kiln’s
grid. The grid is made in such a way that demonstrates the stove underneath as an open one. Author
investigated the results of the archaeological exploration and documentation of works performed on the
site. The centre of the kiln was probably later on cut
out and then filled partially with stones and used as
a part of the construction of the apse staircase. Afterwards, the kiln was filled 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 regular air-holes demanded in a technological process of
pottery production.
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3. Numerical modeling
The finite element model of the kiln is built using
the Finite Element Method (FEM) package ANSYS
(ANSYS 2009) from Academic Computer Centre Cyfronet. The model is based on the representation of relicts, which were reconstructed using the same technology 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)
N
ΣK
where K=
k=1
e
is a total stiffness matrix for N – ele-
ments with element stiffness matrix – Ke, and u is
a nodal displacement vector. Fr is a reaction load vector and Fa is the total applied load vector, which can
be defined by:
N
N
Σ F +Σ F
Fa=Fnd+Fac+
m=1
th
e
m=1
pr
e
(2)
where Fnd – applied nodal load vector, while Fac – acceleration load vector (Fac = −M · ac with M – total
mass matrix and ac – total acceleration vector). Feth is
an element thermal load vector and Fepr is an element
pressure load vector.
Realistically, all structures are non-linear in nature. However, the influence of non-linearities not always
have a significant effect on results obtained. In many engineering problems to obtain accurate result, non-linearities cannot be disregarded and nonlinear analysis is
required. ANSYS program with static analysis provides
ability to simulate complex interaction among different
types of non-linearities such as plasticity, large deflection, 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, Kawecki, 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-
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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 precisely and finally 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 reconstructed 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 burning 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 defined 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 results 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 classified as the
coarse gravel, 4.2% belongs to the fine gravel, 10.1%
of the sample is classified as the coarse sand, 45.4% of
the soil belongs to the medium sand, 33.4% of the sample is classified as the fine sand, and remaining 1.1% is
classified as the fraction of the fine 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 classified as a sand (Sa). From the largest 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 coefficient of active earth pressure of
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 different cases computed for the minimum
and maximum value of Young modulus range. The
maximum displacement under the earth active pressure is nearly 0.3 mm as it is reached for a minimum
value of Young modulus. Figure 9 presents the solution 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
σTmax is well below the strength of the masonry. The
influence of the air-holes on the stresses in this state 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 probably been before the basilica was built. In that model
#2 another circle of holes in the grid has been introduced. 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 floor, which
is also uniform and equal to 10 kN/m2. The vertical
loading is based on the assumption of a sand backfill
of grid and a marble floor, traces of which have been
discovered in the apse. The maximum vertical displacement 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 different numerical models of a unique ancient pottery kiln have been tested here. The initial
analysis of the behaviour of linear model with the
same parameters proved that final results for both
models differ much. While the maximum total displacement 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 stiffness 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 floor of basilica.
4. Final remarks
Two different numerical models of a unique ancient pottery kiln have been discussed in this paper.
Author focused on the initial analysis of the behaviour 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 limit 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 changes 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
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BIBLIOGRAPHY:
ANSYS
2009 Structural analysis guide, ANSYS inc, Canonsburg, PA.
Babraj K. et al.
2008 Babraj K., Mycielska-Dowgiałło E., Szymańska H., Woronko B., Rozwój starożytnego
miasta Marea w Egipcie na tle warunków środowiska, Zeszyty Naukowe Szkoly Wyższej
Przymierza Rodzin, 7–26.
Binda L., ed.
2008 Learning from failure. Long-term behaviour 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 inżynierskich, 194, 131–142, Cracow University of
Technology, Kraków.
Kogut J. P.
2012 Geotechnical data acquisition and analysis for
archaeological appraisal, Archaeologia Polona, 50 (in press).
Majcherek G., El-Shennawi A. A.
1992 Research on amphorae production on the northwestern 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 region 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, symbols, classification and description of the soil, 1986.
Polski Komitet Normalizacji Miar i Jakości, Warszawa. PN-88/B-03004: Brickworked and reinforced concrete chimneys. Static calculation and
design, 1988.
Polski Komitet Normalizacyjny, Warszawa.
PN-EN-ISO 14688-1: Geotechnical investigation and testing – Identification and classification 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 financial
support of the Rector of Cracow University of Technology and a collaboration with Polish Centre of Mediterranean Archaeology of the University of Warsaw is kindly acknowledged.
JANUSZ P. KOGUT
Modelowanie i analiza numeryczna antycznego pieca ceramicznego z Marei w Egipcie
Streszczenie
W niniejszej pracy omówiono próbę modelowania unikalnego w skali światowej antycznego pieca ceramicznego. Konstrukcja, zlokalizowana w egipskiej
Marei, została częściowo odsłonięta przez Polską
Misję Archeologiczną. Misja prowadzi prace wykopaliskowe na terenie bizantyjskiej bazyliki, zlokalizowa-
58
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.
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
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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
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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 floor 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)
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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
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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
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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 floor loading shown
on the deformed model #2 with a maximum displacement more than 4.8 mm
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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 floor loading shown
on the deformed model #2 with a maximum of stress intensity nearly equal to σTmax = 1.02 MPa
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