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Pyramid Design and Construction - Part I:
The Accretion Theory

Bonnie M. Sampsell

(Originally published in /The Ostracon/, Vol. 11, No. 3, Autumn 2000.
/The Ostracon/ is a Journal of the Egyptian Study Society, Denver, CO.
© Copyright: Bonnie M. Sampsell. No part may be reproduced.)

Pyramids are perennially fascinating to Egyptologists and laymen alike.
Questions about how they were built continue to stimulate new proposals
and provoke debate. Stone pyramids arose as the shape of the royal tomb
in Dynasty III, with Djoser’s Step Pyramid being the earliest one known.
In Dynasty IV, the first true pyramids were built, and tombs continued
to take this form through the rest of the Old Kingdom. During this
450-year period, the substructures composing the burial apartments, as
well as the pyramid superstructures underwent a number of changes in
design. The reason for these changes is not known in most cases. Certain
modifications may have been inspired by changes in the underlying
religious beliefs, while others were the result of a king’s greater
resources and ambitions. Still others appear to have been the
consequences of growing technical capabilities.

*Figure 1*
Accretion layer
*Accretion layer in the Step Pyramid at Saqqara.*

The major shift in external pyramid shape -- from step to true pyramid
-- was accompanied by a change in the internal structure; namely that
the earlier pyramids were built with slanting accretion layers, while
the later ones were built with horizontal courses. While researching Old
Kingdom architecture, I discovered that a major misunderstanding on this
point arose in the 19th Century and has persisted in some literature up
to the present time. One objective of this paper is to counter the
faulty notion that pyramids continued to be built with accretion layers
throughout the Old Kingdom.

In the /accretion /method of building a pyramid, a solid central core
was constructed, then this was expanded outwards on all four sides by
the addition of successive accretion layers (or concentric shells) of
masonry ranging from five to fifteen feet in thickness. The stones in
the accretion layers were small, roughly-rectangular blocks with lengths
ranging up to two feet; they were set on a slant tilting inwards. The
stones of each layer were similar in size and shape except that the
stones at the outer edge of each layer were smoothed to give the layer a
flat surface typically with a slope of 74 - 76°. This was the method
used in Djoser’s Step Pyramid and Sekhemkhet’s unfinished pyramid, both
at Saqqara, and in the ruined Layer Pyramid at Zawyet el-Aryan.

A variation of this approach was to form each accretion layer with two
kinds of blocks: an outer face formed of well-squared blocks of larger
dimensions that served as both a casing for the layer as well as a
retaining wall for an inner portion of roughly-shaped blocks. This is
the pattern seen in the stepped nucleus of the Meidum Pyramid. In either
type of construction, the final or overall “stepped” outline of the
pyramid was achieved by having each accretion layer top-out at a lower
height than the one immediately inward of it. It is worth noting that at
the Meidum Pyramid, the casing blocks of its accretion layers were much
larger than those used at Djoser’s Step Pyramid. Petrie (1892:7) gives
the dimensions of the casing blocks of the steps at Meidum as averaging
32 inches wide by 58 inches long x 20 inches high.

*Figure 2*
Meidum Pyramid
*Cross-section and accretion layers in the Meidum Pyramid.*

The idea that the Egyptians continued building pyramids with accretion
layers to the end of Dynasty VI can be traced to the 19th Century
Egyptologist, Richard Lepsius, who suggested that it provided a way for
a king to add to his tomb over the course of a long reign (Edwards
1993:273). If this had been the practice, we would expect that the
longest-reigning kings, such as Pepi II who ruled for 94 years, would
have built the largest pyramids. But there is no direct relationship
between the size of a king’s pyramid and length of his reign.

*Figure 3*
Sahure's Pyramid
*Cross-section of Sahure's Pyramid according to
Ludwig Borchardt's now discredited accretion theory.*

Lepsius's accretion theory was adopted by the archaeologist Ludwig
Borchardt who excavated in Egypt in the early 1900's. He reported
finding “internal faces” which he interpreted as accretion layers in
Dynasty V pyramids at Abusir. Borchardt 1910:29) presents a diagram of
the internal construction of Sahure’s pyramid showing accretion layers
with sloping internal faces; the pyramid’s casing and core blocks are
set horizontally. This is the diagram that is often copied by authors of
pyramid books (Figure 3). Borchardt also interpreted the “girdle-stones”
in the Ascending Passage of the Great Pyramid at Giza as the faces of
successive accretion layers through which the Ascending Passage had been
excavated following a change in plans (Borchardt 1932). Based on his
1880-2 studies at Giza, Flinders Petrie presented several strong
arguments against Lepsius’s accretion theory (Petrie 1883:163-6). But
Borchardt’s hypothesis about the use of accretion layers in /all/ Old
Kingdom pyramids continued to appear in many books and articles.
Sometimes the authors made an explicit reference to the accretion
theory; in other cases they endorsed it indirectly by using one of
Borchardt’s diagrams, perhaps unaware of its implications. But we must
dispose of this theory once-and-for-all before we can begin to consider
possible methods of pyramid construction.

Our current understanding of pyramid superstructure is based on very
careful surveys by John Perring and Flinders Petrie during the 19th
Century and on additional work of the last half of the 20th Century. In
the 1960’s and 70's, Italians Vito Maragioglio and Celeste Rinaldi
studied the architecture of many Old Kingdom pyramids in great detail.
They paid particular attention to the issue of accretion layers. They
found that for the most part the major pyramids at Dahshur and Giza were
too well preserved to reveal much about their interior structure, but in
every place where they could examine portions of the nucleus of these
pyramids they saw only blocks laid horizontally rather than on a slant.
In fact, they found no evidence for any internal faces that could be
associated with accretion layers in any Dynasty IV or V pyramid.

While Maragioglio and Rinaldi published their results in seven large
volumes with detailed drawings, most nonprofessionals are unfamiliar
with their work. Unfortunately, the books themselves are extremely rare
and their titles obscure the fact that the texts are given in both
Italian /and English/. Here are some excerpts from their reports.

By studying this breach [in the north wall of the burial chamber] we
were able to ascertain that the monument [Red Pyramid] was built in
horizontal courses varying in thickness from one to another
(Maragioglio and Rinaldi 1964:132).

Therefore we believe the nucleus [of Great Pyramid] to be a
homogeneous structure and not to be made in inclined layers as in
Meydum (Maragioglio and Rinaldi 1965:16).

... our surveys in Cheops pyramid have led us to definitely reject
Borchardt’s theory that its nucleus was made in successive
[accretion] layers (Maragioglio and Rinaldi 1965:114). Note: core
blocks in Great Pyramid can be observed in several places: in the
gash on south face, in the area above original entrance on north
face, in Al-Mamoun's passage, in tunnel behind niche in Queen's
Chamber, in a tunnel leading under the King's Chamber.

A careful examination of the masonry of the nucleus [of Khafre's
pyramid], although it was not possible to carry it out thoroughly
owing to the state of the monument, has not provided factors in
favour of the theory of Lepsius and Borchardt, according to which
all pyramids were built in successive sloping layers, and has not
even proved the existence of large steps [stages] in the nucleus
(Maragioglio and Rinaldi 1966:48). In this pyramid they entered the
passages made by grave robbers in the north face and also those
robbers’ passages that intersected the interior passages.

… from the masonry at the sides of the breach [on north face of
Menkaure's pyramid] and the mouth of Vyse's tunnel it is seen that
there is an absolute and unmistakable lack of [accretion] layers of
the type of those at Meydum, ... in Vyse’s tunnel, which we
penetrated for over 15 m. and carefully studied, there is nothing to
make one suspect faces of layers (at least two should have been
seen) (Maragioglio and Rinaldi 1967:34).

Grinsell (/Egyptian Pyramids,/ p 132) states that four internal
facings of the nucleus are visible [in Userkaf’s pyramid] and that
the nucleus was probably in layers. In spite of the most careful
search, both inside the existing cave to the north... and outside
it, we could see nothing to corroborate this hypothesis. Although of
poor quality, the masonry appears homogeneous, with the blocks laid
horizontally (Maragioglio and Rinaldi 1970:12).

The pit and the passage left in the body of the [Sahure’s] pyramid
are alone quite sufficient to exclude the possibility that the
nucleus of the pyramid consisted of a central core against which,
proceeding from the inside outward, layers of gradually decreasing
height were placed. In representing the nucleus as layered in his
section of the pyramid of Sahure, Borchardt was evidently misled by
the steps [stages] that were visible and by what he had noted and
established at Meydum. The sometime very extensive falls of masonry,
which are to be seen, especially on the north, and east faces of the
monument, have shown nothing to make one think of a [accretion]
layer structure. It should moreover be noted that the courses of the
blocks are horizontal and not inclined inwards, as would be normal
if Borchard's [sic] hypothesis (already advanced by Lepsius) had any
foundation (Maragioglio and Rinaldi 1970:86).

Perhaps it is fitting that a final word about accretion layers should
come from an excavator at Abusir, since that is where Lepsius and
Borchardt made their observations and drew their erroneous conclusions.
Miroslav Verner excavated the unfinished pyramid of Dynasty V king,
Raneferef [Neferefre]. Verner reported that this pyramid provides
absolutely no evidence of building by accretion layers saying: “If the
[accretion] theory was valid, then...it should have been possible to
find -- as in cross section -- stone masonry arranged on all four sides
in parallel layers. It would be as if an onion not circular, but square,
had been sliced across horizontally” (Verner 1994:139).

Instead a trench dug into the pyramid's crown revealed a different
method of construction^ as he goes on to explain:

The outer face of the first step of the pyramid core was formed by a
frame made up of huge blocks of dark grey limestone up to 5 m long
and well bound together. Similarly, there was an inner frame built
up of smaller blocks, and making up the walls of the rectangular
trench destined for the underground chambers of the tomb. Between
the two frames pieces of poor-quality limestone had been packed,
sometimes “dry” and sometimes stuck together with clay mortar and
sand ... The core was indeed modelled into steps, but these were
built in horizontal layers and only the stone blocks making up the
outer surface were of high quality and well joined together. The
inner part of the core was filled up with only partially joined
rough stones of varying size and quality (Verner 1994:139-40).

The reports of Maragioglio, Rinaldi, and Verner, taken in conjunction
with personal observations made during several trip to Egypt, make me
confident that the Dynasty IV pyramids at both Dahshur and Giza were
constructed using the new method of horizontal courses rather than with
inclined accretion layers. In this new method the stones of the core
were much larger and were more neatly trimmed into rectangular blocks
although there was a great range in the actual size and shape of these.
These core blocks were set horizontally and ran uniformly through each
course. In some Giza pyramids, such as the Queens’ Pyramids and
Menkaure’s Pyramid, the core blocks did form a “stepped” nucleus, but
this was achieved in a very different manner than described above with
accretion layers. I am going to call these Dynasty IV innovations
"stages" to avoid confusion, since the word “steps" has been used by so
many authors with several different meanings (Figure 4).

*Figure 4*
Dynasty IV pyramids
*(Left) Dynasty IV pyramid with core (shaded) built in four stages with
slanting faces and
setbacks; courses are horizontal. (Right) Pyramid built in horizontal
courses without stages.*

The stages in certain true pyramids were created by setting the stones
at the outer perimeter of each course back slightly from the ones below
creating a gently sloping face with an incline of about 75°. In
addition, after a certain number of courses, an even larger setback
occurred before the next stage began. The object of the stages in this
method of construction was to create a core with an outline
approximating that of the final pyramid to which the casing and backing
blocks could be applied. In some cases, the stages were built of
uniformly large blocks throughout their courses, but in other cases,
large blocks were used at the perimeter of the course while smaller
blocks, even rubble, were used to fill up the center. On eroded pyramids
the vertical faces of stages can be mistaken for accretion layers
without careful study.

I hope that a greater familiarity with recent observations will finally
set the record straight on the important issue of accretion layers. I
have been pleased to note that newer publications on pyramids do
discount the accretion theory. (Some recent books stating that Dynasty
IV pyramids have horizontal courses and no accretion layers: Arnold
1990:159; Lehner 1997:109, 218; Wildung 1997:51.) Unfortunately many of
the older books remain in libraries where they may be the only
references available on this topic. In addition, some authors continue
to use Borchardt’s cross-section of either the Great Pyramid or of
Sahure’s Pyramid without realizing the implications of these drawings.
Readers new to the subject have no way of knowing that the ideas
expressed are outdated.

I am devoting this first paper of the series to this point regarding the
pyramid internal structure because this knowledge is ecessary before one
can discuss construction methods. I believe that the change in the
method of building a pyramid’s nucleus signaled an improvement in
ancient technology and materials. By Dynasty IV, the pyramid builders
found a way to quarry, move, and set in place really enormous blocks of
limestone. It was this capability that changed their entire approach to
pyramid construction and not any disasters or problems encountered
during the construction of any particular monument. Engineering of true
pyramids relies on different principles than used with step pyramids.

Stones employed in building accretion layers were relatively small. This
may have been due to the thin strata in the limestone quarries or the
desire to keep individual stones to a size similar to mud bricks that
could be carried by one or two men, or both. The small stones were set
without adhesive mortar, but only with mud mortar to fill gaps. To
provide the necessary stability to keep the small stones from collapsing
or sliding off one another, the entire layer was tilted to lean on the
one behind it. While the stones within a single accretion layer might
have some adherence to one another due to mortar or overlap, the layers
had no masonry bonding to one another. Their smooth, highly inclined
faces actually represented potential slippage planes.

Without getting involved in a separate debate about the Meidum Pyramid,
I believe that its unbonded accretion layers contributed to its collapse
during an earthquake. Unlike Kurt Mendelssohn who proposed that a
collapse occurred while the pyramid was still under construction and
that this affected the ancient building methods, I believe, as did
pyramid expert

I. E. S. Edwards, that the collapse occurred sometime after Dynasty
XVIII. Nor do I believe that the still-unexplained difficulties which
resulted in the damage observable today at the Bent Pyramid was the
direct stimulus for the abandonment of the accretion method because I
think it had already been abandoned.

I believe that the core of the Bent Pyramid was built from the beginning
using horizontal courses of large blocks. Unfortunately, it is
impossible to confirm this with direct observation. Maragioglio and
Rinaldi found evidence that the lower portion of the Bent Pyramid was
first built with at slope of 60° with a shorter base (Maragioglio and
Rinaldi 1964:60,100). For some reason, an additional layer of masonry
about 50 feet thick was added around the entire base with a slope of
only 54°. There is considerable evidence that this outer layer, which
would not have been bonded to the original 60° surface, slid downward
over the years. Even if the Bent Pyramid's core blocks were set
horizontally, as I believe, it is certainly true that the casing of the
bottom part, is set at an angle. Petrie (quoted in Maragioglio and
Rinaldi 1964:58) reported that the bedding surface of the casing stones
varies from 6° 8' to 13° 27'; while each face, both above and below the
bend is convex not flat. It appears that the builders experienced some
difficulty in cutting and setting these gigantic blocks; alternatively
the variation may be due to the previously-mentioned slippage.

The fact that the Bent Pyramid’s upper portion has casing set almost
horizontally might appear to prove that the change of method of
construction occurred when that pyramid's slope was changed. But, in
fact, blocks had been set horizontally for many years before this. In
early stone structures such as temenos walls, mastabas, and internal
chapels and chambers, the blocks of limestone or granite have horizontal
bedding. In fact, the only place that slanted accretion layers were ever
employed was in step pyramids. (Goneim [1956:53] says that the original
mastaba beneath Djoser’s Step Pyramid had horizontal courses. He
suggests that Imhotep, Djoser’s architect, adopted the slanting layers
for the higher steps as a means of ensuring stability for the layers.)
Interestingly, the size of blocks employed for these non-pyramidal
structures tended to increase in the late Dynasty III to early Dynasty
IV period. Goneim reported that the limestone blocks in the “White Wall”
surrounding the tomb of Sekhemkhet southwest of Djoser’s tomb at Saqqara
were twice as high as those in Djoser’s temenos wall, and he remarked:
“It is certain that already in Djoser’s reign there had been a tendency
to increase the size of the stone blocks, as the builders ultimately
came to learn that an increase in size meant an economy in the work of
cutting out the stones, and lent more strength and a greater degree of
cohesion to walls” (Goneim 1956:46).

When it became possible to quarry and place large blocks of limestone it
was no longer necessary to tilt the blocks; rather, their own weight and
the friction between a block and the ones around it provided stability.
In fact, the larger the individual blocks are, the greater is their
stability, provided they are set horizontal. In this new method of
building with large blocks, the use of inclined layers or internal faces
would render the superstructure less stable, not more. Was Imhotep also
the genius who figured this out?

REFERENCES

Arnold, Dieter. 1990. /Building in Egypt/. New York: Oxford University
Press.

Badawy, Alexander. 1977. “The Periodic System of Building a Pyramid.”
/Journal of Egyptian Archaeology/ 3:52-58.

Baines, John and Jaromir Malek. 1980. /Atlas of Ancient Egypt/. New
York: Facts on File.

Borchardt, Ludwig. 1910. /Das Grabdenkmal des Koniges Sahure, vol I/.
Leipzig: J. C. Hinrichs.

Borchardt, Ludwig. 1932. /Einegies zur dritten Bauperiode der grossen
Pyramide bei Gise/. Berlin: Springer.

Clarke, Somers and R. Engelbach. 1990. /Ancient Egyptian Construction
and Architecture/. New York: Dover Publications, Inc. This is a reissue
of the book /Ancient Egyptian Masonry/ published in 1930 by Oxford
University Press, London. This earlier date should be borne in mind in
evaluating the contents.

Edwards, I. E. S. 1974. “The collapse of the Meidum pyramid.” /Journal
of Egyptian Archaeology/ 60:251-2.

Edwards, I. E. S.1993. /The Pyramids of Egypt/. London: Penguin Books.

Fakhry, Ahmed. 1974. /The Pyramids/. Chicago: University of Chicago Press.

Goneim, M. Zakaria. 1956. /The Buried Pyramid/. London: Longmans, Green
and Co.

Grinsell, Leslie. 1947. /Egyptian Pyramids/. Gloucester: John Bellows
Limited.

Lally, Michael T. 1989. “Engineering a Pyramid.” /Journal of the
American Research Center in Egypt/ XXVI: 207-218.

Lehner, Mark. 1997. /The Complete Pyramids/. New York: Thames and Hudson.

Maragioglio, Vito and Celeste Rinaldi. /L’Architettura delle Piramidi
Menfite (APM)/.

1964. /APM, Parte III/, Rapallo: Tipografia Canessa.

1965. /APM, Parte IV/, Rapallo: Tipografia Canessa.

1966. APM, Parte V, Rapallo: Tipografia Canessa.

1967. /APM, Parte VI/, Rapallo: Officine Grafiche Canessa.

1970. /APM, Parte VII/, Rapallo: Officine Grafiche Canessa.

Mendelssohn, Kurt. 1974. /The Riddle of the Pyramids/. New York: Praeger.

Perring, John S. 1839-40. /The Pyramids of Gizeh/, 2 vol. London: James
Fraser.

Petrie, W. M. Flinders. 1883. /The Pyramids and Temples of Gizeh/.
London: Field & Tuer Ye Leadenhalle Presse.

Verner, Miroslav. 1994. /Forgotten Pharaohs, Lost Pyramids, Abusir/.
Prague: Academia Skodaexport.

Wildung, Dietrich. 1997. /Egypt: From Pre-history to the Romans/. Koln:
Taschen.

© Copyright Bonnie M. Sampsell.
Catchpenny Mysteries © copyright 2000 by //.

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