THE DECLINING RAMP THEORY

MORTUARY COMPLEX - RAISING GRANITE THEORY

CONSTRUCTION OF THE GREAT PYRAMID

By Aymen Ibrahim

1. Overview……………………………………………………………………..Page 1

2. Background…………………………………………………………………..Page 3

3. Geology – area makeup……………………………………………………...Page 4

4. Pyramid and Building site…………………………………………………...Page 10

5. DECLINING RAMP THEORY……………………………………………..Page 10i. Preparationii. Construction of declining rampsiii. part two, flat to inclining ramp

6. Kings Chamber and granite Blocks………………………………………… Page 19

7. Mortuary complex - Raising Granite………………………….……………..Page 20

8. Nile valley canal stream way and delivery of materials……………………..page 24 i. Nile harbour waterway

Preliminary study by Aymen Ibrahim, London, 2010 - Aymsmail@ymail.com.Contact for discussion, additional information and defined material.

OVERVIEW

Using geographical and geomorphilogical observations of local environments, in relation tothe construction of the great pyramid. This research composes a Complete preliminary studyproposing a: i) Declining ramp theory, ii). Raising granite - Mortuary temple theory. iii) Useof “air-shafts” theory.

With results correlated with those of former studies, demonstrating the existence of naturalhills and rocky formations used for quarrying and to build declining ramps for thetransportation of materials to the maximum height of upto 50 meters (1/3rd), 33% of the totalheight and respectively a maximum volume of 82% of total building substance > Toeventually flat, leading to a slight angle of incline of 3 degrees to construct upto 70-75meters (1/2), 50 % of the total height.

This study and model is based on, composes & represents work, which would have beenmechanically feasible with means at the disposal of the ancient builders. Based on humanpower including what is relatively mathematically possible and within human capabilities, toconstruct the cyclopean structure within 20 years. This paper shows:

1. The use of a declining ramp to build a minimum of 50 meters total height, andcomplete the majority, over 80%, of the total building substance. Providing aworking model to achieve the raising of the large granite blocks up to a maximum of65 meters, 46% of the pyramids total height. Also showing a practical use of the “air-shafts”.

2. The nature and organization of the sedimentary levels making up the original plateaucorrelating with the declining ramp, outcropped from the local Mokattam formation

3. To show the ability to use quarries at higher levels than once thought, for the bulk ofthe Pyramids core blocks.

4. To clearly demonstrate the geological difference at the Giza plateau, and the pre-existence of a wider and larger natural rock formation of the Mokattam formation tothe west of the Giza plateau, and show the pyramids in the context of their setting.

5. To demonstrate the morphology of these worked rock hills where they are clearlyvisible. And map the outcrops of natural stone of the Mokattam formation andpropose a model of size and morphology for the original hills as worked for theconstruction of the construction of the great pyramid.

As direct access to the inner parts of the monument is not possible, and as the ancients left noclear account of the construction, this work focuses on:External observations and measurements. Petrological, sedimentary and structural

characteristics of local geological formations were studied using detailed field observationand dip measurements, and correlated with the geomorphology and topography of the sites.

These observations were cross-referenced with an amalgamation of literature on Egyptianlimestone formations and quarries, and from this general conclusions were made regardinglimestone provenance.

Study of the monument itself relied principally on detailed visual observation,photographs and photomontages. In order to propose a model for the morphology of the rockoutcrops, the results have been correlated with earlier geological and architectural studies ofthe geology of the monument. Inspection of artefacts and connecting them with conceivablehuman engineering capabilities. With the geology of Giza and demographics of the quarriesand materials used, this study concludes the following from these observations.

BACKGROUND

The declining ramp theory (DRT) concentrates on the main bulk of stones used to build thegreat pyramid. The stones used for Khufu's pyramid are a gray-yellow colored nummulitelimestone and belongs to the local Mokattam formation.

We know by actual measurement the size and weight of the blocks of stone commonlyemployed at this time, as well as the methods of quarrying them and the location of at leastsome of the quarries.

There were many Quarries for many different types of stones, which are mainly locatedalong the Nile. Quarries for Limestone, sandstone, granite, alabastar, basalt, gneiss, quartzite,greywacke, copper, lead, iron and gold.Most stones were transported on barges down the Nile

A few of the main ones are:

LIMESTONE, used for the stone blocks were quarried locally in the Giza quarries.ROSE GRANITE used in the king’s chamber was quarried and brought in from the Aswanquarries over 900km away. Weighing approx. 50 tonsWHITE LIMESTONE for the casing was quarried about 15km away at the Tura quarries

All figures are approx:

A total of over 2,300,000 (or only 590,712)* blocks of limestone and granite were used in itsconstruction with the average block weighing 2.5 tons and none weighing less than 2 tons.The large blocks used in the ceiling of the King's Chamber weigh as much as 50 tons.

Construction date (Estimated): 2589 B.C.Construction time (Estimated): 20 years.Total weight (Estimated): 6.5 million tons.

The original height was 481 feet tall, but is now only 449 feet.Total layers: 210Total height: 146 meters

The base of the pyramid covers 13 acres, 568,500 square feet andThe length of each side was originally 754 feet, but is now 745 feet.

The King's chamber, which is the definitive part of the structure lies on 43.03m and is linedwith granite

Kings chamber.Base of the kings chamber: 43.03m ceiling: 48.36m.Heavy granite gables: up to 70 metersKings chamber Shafts: 79 meters Approx. 90 layers of stone

Queens chamber.Base of queens chamber: 20 meters.Tip of gable of the queen’s chamber: 28 meters Approx. Up to 40 layers of stone

GEOLOGY AND MAKE UP OF AREA

The geology of the Giza plateau, and Egypt as a whole, was vastly different at the time ofKhufu then what we see today. In approximately 2,500bc this area of Egypt was austere andbarren, only the Sahara desert and profusion of windblown shifting sand could be seen inabundance on this part of the plateau.

Beneath this sand is a rock plateau, a solid limestone bedrock. On this rock shelf, today, arenine pyramids, as well as a few other ancient buildings and monuments.

The rock plateau currently sits at 60meters above sea level. Sloping from N.West downhill toS.East to the valley floor. Immediately to the west to southwest of this location are the localhigher grounds of the Mokkattam and Maadi rock formations, with significant levels of sandaccumulation on and against these surrounding cliffs.

The Khamaseen is a wind that blows from the south in Egypt, bringing sand and dust, whichaccumulated onto the north westerly cliff face. The plateaus lower ground local to theseformations acted as a semi-enclosed basin holding a large collection of windblown sand.The prolific sand accumulation and surrounding cliffs at Giza provide the greatestcontribution to the ramp declination theory.

These geomorphological and geological characteristics led fourth dynasty architects tochoose these hills as natural bases for the monuments.

The geomorphology of these formations, seen today, is the result of the interaction of threemajor factors,

1. The nature of the rock and the arrangement of the sedimentary series;2. The tectonic fracturation which has affected this series3. The effects of weathering on these formations.

And as this study will prove, 4. The human affect on the plateau - via surface quarrying ofthe formation and human manipulation of the plateau as a whole.

The Pyramids are in an area where cropping out of geological formations are dated betweenthe Late Cretaceous and Quaternary eras. The plateau is positioned on the Middle Eoceneseries (Mokattam formation). The arrangement and structure of the plateau is part of, a groupof synclines and anticlines, formed during Late Cretaceous compression.

The Giza Plateau is located at 29° 59’ N and 31° 08’ E, which places it at the northeastcorner of the African plate, which meets the Arabian and the Eurasian plate.As a result, the plateau is based in the Mokattam formation of the Middle Eocene, linked inthe south by faults with the Maadi formation of the Late Eocene. The weak throw and theorientation of these faults essentially suggest (Guiraud, oral communication) a discretedeformation by sedimentary normal faults during the Eocene deposition period.

The ancient loss of ground water, along with the resulting earth movement has created anumber of geological faults in the Valley, mainly the outcrop of rock sequences which waskey to this site being chosen.

“The Giza plateau and the surrounding cliffs have been the subject of numerous geological studies,among them, structural stratigraphic and sedimentological studies by [Zittel, 1883] [Blanckenhorn,1921] [Cuvillier,1930] [Said, 1962, 1990] [OMara, 1952] [Aigner, 1983] [Strougo, 1985]. Thesestudies show that the monuments of the fourth dynasty of the plateau of Giza are built on asedimentary sequence with dominant carbonated formations deposited in an epicontinent al sea ofvariable depth. All the authors agree that these sedimentary layers have the characteristics of theMokattam formation and Maadi formation, from Middle to Late Eocene age.”

“These tectonic processes have added to the geological attributes of the Nile Valley basin. Since thelate Cretaceous these movements have been responsible for structural uplifts and basins throughoutthe northern part of Egypt, and have strongly affected the paleogeography and sedimentationpatterns [Hume, 1912] [Shukri,1954] [Salem, 1976].sediments unconformably overlay these folds {Guiraud, 1999 #48}, which were slightly accentuatedin Late Eocene.”

The limestone Sediments deposited in layers as a strata, accumulated by natural forces,forming an encrusted structure consisting of many units. These sedimentary units wereraised, the layers of rock bent into folds due to pressure from tectonic activity, resulting inoutcropping.

Parts of this bedding were raised to an unspecified height due to the tectonic uplift. Thebedrock and superficial deposits could have been exposed at the Earth's surface due thequarrying and building of transport routes.

Geological features of the limestone in the strata are depositional history, evolution ofporosity, and development of joints. Where these joints intersect, there is raising of materialat the core. The limestone in the pyramid, in terms of both texture and composition, areidentical to varieties commonly found in the Lower to Middle Eocene limestone sequence ofthe Nile River. The local Mokattam was heterogeneous enough to accommodate all thelimestone varieties in the construction.

The sediment layers and resulting limestone differed in density relative to height.The fault lines in this location would of allowed Most layers of the sedimentary rocks to begreatly distorted-- squeezed into curves and tilted at great angles, with layers formed aroundfault lines, varying from horizontal layers to vertical, with steep dips and twisted strata allvarying at the height of each layer

Simplified -image not to scale

This would indicate that the relevant quality lime/sand stone sediments, needed for thepyramids where pushed up due to tectonic activity. The raised sedimentary bedding settledfrom high winds and local flooding, resulting into this Mokattam formation.Allowing the ancient builders to find the materials needed, going up hill, to a height of up to45 meters above the plateau (105 meters above sea level).

The bulk of soft limestone came from the same natural Mokattam Formation quarries foundby geologists, though due to tectonic activity pushing this bedrock upwards in the Mokattamformation, The sedimentary limestone available on the lower eastern side on the plateau wasavailable in the resulting outcrop at up to 45 meters above the plateau floor west of thepyramid.

Quarried from within the local formation, the stones used for Khufu's pyramid is a gray-yellow colored nummulite limestone and belongs to this Mokattam formation. Thisformation, with the anticline of sedimentary layers, allowed the ancient builders to quarry therelevant limestone needed for the bulk of the pyramid at higher levels than once thought.

The dip and the sedimentary make-up of the layers of this monocline mountain ishomogeneous, having the same kind of constituent elements and uniform composition,consistent and being similar in nature with materials composing the great pyramid

What we see today at Giza is remnants of the original formation where the overlying cover isremoved through the quarrying process. When the builders extracted the higher levelNummilite limestone, the local Mokkatam formation eventually resided to its current height.This quarrying was rapid and exceeded the weathering rate, which caused steeper hillsidesand mountain ridges of the higher parts of the formation to the SW of the pyramid.

The current residual Mokattam formation consists of a highly fractured, crumbly nature ofstone at the fault line itself. This is where rock shattered and crumbled as the two rock faces

ground against one another. The current strata is a series of massive grey to white Limestone,the upper unit is a reddish brown Limestone. The local Maadi formation is composed ofwell-developed brownish Lime stone beds exposed and observed at the top. The mokattamformation, as a whole, forms the walls of the Nile and ranges approx 160 km, 95m above theplateau and is widely disseminated across the eastern desert, east to the red sea coast.

“The local series presents an alternation of bioclastic and marly limestone, separated by decimetremarly levels. It is dated from Middle Eocene and called the Mokkatam seriesevolves from a bioclastic nummulitic packstone (Khufu area) to more argillaceous formations(between Khufu and Khafre) and finally to a detritic nummulitic wackestone (Khafre area). Thepackstone of the Khufu area. It has an argillaceous and calcareous matrix including two differentsizes of gizehensis nummulites. This packstone is found in some of Khufus blocks”

The petrographic facies of the nummulitic sandy limestone levels alternating with clayeylevels are consistent in the cliffs as in the base steps of the pyramid.

According to geologist Thomas Aigner and Egyptologist Mark Lehner, the original groundsurface of the Mokattam Formation at the pyramid site constitutes a very hard and massivelimestone bank of the nummulite type. Though there is a distinction in the materials based onits location on the plateau, suggesting that the surface layer west of the pyramid differs tothat on the east, using the Pyramid as a marker. This indicates and shows evidence thathuman effects (ie quarrying) effected the current make up of soft-hard stone sediments foundaround the pyramid.

Extrapolating from these observations it is apparent that the surrounding cliffs were apromenade, an esplanade to the monument, which was carved away from between cliffs andthe resulting material was moved from the formation constituting the quarry and decliningramp of the pyramid.(pg.13)

Differential weathering in the natural layers of rock "hard-soft" sequence of layers at thistime, In this part of the plateau, would have made it easy for the builders to extract therelevant blocks of stone for building.

The resulting construction has differentially modified the morphology of the surface rock,with layers carved out and more rigid rock left in relief, as a stabilizer of the ramp. Thisdifferential quarrying and the alignment of dip of natural bedding, is consistent with themeasured dip of the strata of the cliffs. Therefore it is clear that the ramp and the cliffformations are in continuity. (pg.13)

Sloping in situ with the cliffs and ramp, the plateau and the rocky remnants of the slope arevisible at the base of the four sides of the Pyramid. These observations suggest anddemonstrate that the declining ramps were part of the local geological formation.

Observations at Khufu show the presence of the original sloping nature of the rocky plateausloping towards the pyramid, visible in the boat pits at eh NE corner of the pyramid, and onthe promenade around the pyramid. The rock base of the pyramid is mainly composed ofnummulitic packstone.(pg.17)

Extrapolating from these observations it is apparent that the surrounding cliff promenade ofthe Pyramid has been chiselled out, quarried between cliffs constituting the pyramids mainmaterials.

left -Khafres pyramid as seen from the surrounding formations. Right - khufus pyramidimage sused for representation courtesy of google.

There is evidence on the plateau of two other monuments that use the geology of the plateauas higher-level access points (esplanades) to a monument, the sphinx and queen Khentkawestomb, consisting of natural rock carved out of the local geological series.It is evident, with addition of a slight manipulation of location from the surroundingformations, that the same could be done for the pyramids themselves and for the Giza plateauas a whole.

These geomorphological and geological characteristics led fourth dynasty architects tochoose these hills as natural bases for the monuments. The site including the finishedpyramid, seems to be related geologically and hydrologically.

The rock structures, the sequence of events that created it, raising of layers, tectonic activityof the lower igneous rocks, the shifting sands and winds contribute to the declining ramptheory. The main other contribution and to the make-up of the outcrop is the geologicalchange of the local inundation.

The Nile was essential to sedimentary build up of deposits and the formation of outcrops.The Nile valley stands in great contrast to the rocky desert necropolis above, sitting at around20m above sea level. Geological investigations revealed that Egypt had higher levels offloods during the time if Khufu and then suffered from a series of catastrophically low Nilefloods due to abrupt climate change.

The course of the Nile in early dynastic period was closer to the Pyramid sites, having latershifted to its current location only gradually (eonile). The old course and geology of theinundation allowed Nummilite limestone and other sedimentary bedding to be found furtherinland on the banks of the Nile.

Along most of its length through Egypt, the Nile has scoured a deep, wide gorge in the desertplateau, with a floodplain fringed with manmade sand dunes, limestone dams and canals.

With a very high level of fluctuation from year to year, the ancient Egyptians knew when theflood would come to the day, but they never knew how much water it would bring, no onecould tell exactly when the flood would reach its peak.

Records reveal that the last kings of the old kingdom were faced with a declining level ofNile floods, the drop of the Nile floods was rapid and traumatic. The level declined evenfurther in the middle, and further in the new kingdom, though by then the Egyptians had vastknowledge in how to manipulate the inundation for there own needs. (pg 25)

The ups and downs of Nile floods in response to climatic change beyond human reckoninghad on occasion led to misery and the collapse of centralized government. The Nile recordconfirms that climate changes can be abrupt and severe, these records indicate that onaverage, one year of out every five saw an inundation that was either over-abundant or fellshort of expectations. The sand covered plateau was inundated with the Nile flooding theplain.

Evidence of this change in the water table is evident all over Egypt, examples are in thehistorical records of lake Meroe and lake Fayoum.To add, “in approximately 4000B.C Herodotus visited what is now Libya and Egypt andobserved the pyramids of limestone, probably in the Giza area. He noted that the limestonecontains seashells and concluded that the sea, at one time, covered part of northern Africabecause of similarities of the fossil shells to those of organisms then living along the shoresof the Mediterranean Sea. He also noted the small fusiform fossils, now known asnummulites, which are common in some blocks.”

PYRAMID AND BUILDING SITE

Neither built on the highest or most central, flat or most ideal location, instead Khufuspyramid is built on the lowest part of the plateau (Khafres pyramid base has 30ft heightadvantage over Khufus pyramid) In the most northerly location, on the northern edge of theplateau, near to the Mokattam and Maadi formation. The sand accumulation against and onthis rock cliff was also the key to the height of the first pyramid, and the reason why no otherpyramid could reach this height

Built on a rock core, the builders of this pyramid were very wise to choose this site as mostof the stones, with the exception of the casing stones, some granite and basalt stones wereavailable in the nearby quarry. This practical choice made it possible to reduce, considerably,the time and labour needed to drag the stones from distant quarries across the Nile. Includingan apparent internal hillock the pyramid sits on a manmade limestone base, which is built onan unlevelled rocky ground with a slope to one side. This limestone base is impressively flat,off by less than half an inch.

DECLINING RAMP THEORY

The pyramid was built in two parts, with a series of declining ramps, sand in-fill, dunes, withadditional dams, canals and an extensive harbour used to bring relevant materials to the site.

There were two main declining ramps, the shortest with the greatest level of declinationheading down from the western heights of the local Eocene Mokottam formation, Thesecond longer ramp, ascending from the southwest heading to the southern side of thepyramid.

The ramp transformed as work progressed on the pyramid, with a Varying angle, height andlength of the ramp

The current peak of the local Mokattam series sits at 105 meters above sea level a fewhundred meters away from the pyramid base, which lies at 60 meters above sea level. Givinga height of 45 meters for the formation, above the plateau floor.

For the purpose of this study, we will use the maximum height of the local Mokattam hills at45 meters above the plateau, which is its current height. Geomorphic observations proposethat this height would be the minimum suggested height at the time of construction.

The following extrapolated observations suggest that the pyramid was built:1) Using a declining ramp, from the surrounding formations to complete 45 meters, upto

33% of the pyramids height and over 80% of the total building substance. I.e. heightof the kings chamber.

2) Using an eventually flat ramp and upto 4 degrees angle of inclination to completeupto 70-75 meters, 50% of the pyramid height, ie completing kings chamber.

3) Using an inclining ramp to complete the top 50% of the pyramids height, and theremaining 20% of the total building substance

4) Using a different technique in Raising Granite to 65 meters.(pg.20)

A minimum of 1/3 of the total height was built using the abound levels of sand and the localgeology to form a declining ramp. Transporting material quarried from within the localMokattam formation, down through the sand to the bedrock floor.Which led onto a flat to slight level of inclination (under 4 degrees), to build a further 20meters up to 70-75 meters, 1/2 of the total height, which is over 90% of the total buildingsubstance. This would mean that the Queens chamber and base of Kings chamber was builtwith a declining ramp.

The second part of the theory uses the traditional inclining ramp theory, which would bebuilt and extended onto the existing declining ramp, to complete the rest of the pyramid.(pg.19)

Preparation

Preparing the 13-acre site (5.2 hectares) to host the pyramid would have been its own majorfeat. A trench in the abound sand against the surrounding cliffs was needed, dug down to thestone plateau bedrock, varying in depth with the sand accumulation approx. 20 meters (max.)deep on western side, sloping in situ with the declining plain of the plateau bedrock to theeastern side, which was up to 10 meters deep.

Once the sand, gravel and loose rocks had been removed, down to the solid bedrock of theplateau, the whole pyramid site was opencast, immediately allowing the use of decliningramps to the bedrock of the plateau.

Labourers moved massive levels of debris, sand and dirt, for making these huge trenches andramps and so on. This was done on a regular basis, not only for raising large monuments, butalso for creating the dikes and canals on which Egypt's irrigation and agriculture depended.Moving dirt for their basic infrastructure was very common.

images not to scale.As the location for the pyramid is based at the lowest part of the plateau, at this time, theclose bases of the Mokattam cliffs and local quarries for the bulk of the core limestoneblocks, laid above this trench to the bedrock floor, west to southwest of the pyramid.Immediately allowing the first twenty meters to be built with a declining ramp. The rampsheight lay at the initial plane of ground, up to 20 meters above the new trench to the bedrockfloor. Before ascending the formation.

This cleft technique was only used in the construction of the first and largest pyramid. Theheight of khufus pyramid could not be replicated in the immediate area. Once the sand wascleared, and levelled (by flooding) the approach needed for the next pyramid would slightlychange.

Construction of declining ramps

Dominating the plain are the natural limits of the plateau and old quarry worked faces. Thespaces between the monuments and the plateau can be related to natural fractures widened &morphed by human action, with the remains of a much more resistant, higher level of theoriginal hill used to construct the pyramid.

The declining mountain formation is oriented NE-SW and has a dipping SE monocline. Thismonocline is the SE anticlinal progression of the declining plateau and resulting ramp.The outcrop formation, with the anticline of sedimentary layers, allowed the ancient buildersto quarry the relevant limestone needed for the bulk of the pyramid at higher levels than oncethought.

The dip and the sedimentary of the layers of this monocline mountain is homogeneous,having the same kind of constituent elements and uniform composition, consistent and beingsimilar in nature with materials composing the great pyramid

To the north and east, the Mokattam Formation is characterized by two steep escarpments,the majority of which are mainly over 30 meters high. It continues to the Great Sphinx ditch,these steep escarpments are much more severe than the local Maadi formation, which couldindicate human activity

The images below show possible progression of the causeway made from observations in themountainous cliffs, highlighting the basic possible appearance of the local formation before theramp ascended onto the resulting cliff face via the quarrying of the inner parts of the outcrop.

The first image in the below series illustrates the possible representation of the minimum heightof the contour levels our observations indicated, pre-construction. The outcrop had potential tobe more cubic with a higher volume and capacity. The final image shows the current formationwith the relevant contour lines.

.

As work progressed, the height of the declining ramp was increased, by extending the rampinto and heading up the hill of the Mokattam formation; a pathway was forged into and upthe formation, as the rock face of the cliff was chiselled away. Eventually separating theridges into chains of isolated hills.

An ascending causeway was carved through to the relevant materials as work progressed,leaving a broader geography and range of rock features, steep-sided isolated hills risingrelatively abruptly above gently sloping ground.

The existing isolated hills and lone mountains that remain in these formations have survivedthe building project. Covered in rubble and sand that have accumulated here after thequarries were abandoned, and formed into its current physical make up through naturalforces. Differential weathering in the natural layers of rock "hard-soft" sequence of layers atthis time, in this part of the plateau would have made it easy for the builders to extract therelevant blocks of stone for building

When the top layer of less resistant rock is carved away to form a plain, the more resistantrock is left behind as a root structure of the ramp, resulting in isolated mountains and rockformations. As seen above in the mapping and correlation of features between certain areasof the formation. The use of worked rocks hills appears to be a characteristic of theconstruction methods in the fourth dynasty. (pg17)

When we reconstitute the topography of the carved outcrop, we see a very good match of thelevel lines of the original hill with the level lines of the pyramid up to the kings chamber. Italso shows the importance of the carving work carried out W and N of the pyramid

The labourers quarried into the outcrop formation, to the relevant distance to reach thelimestone, then up the outcrop carving and leaving a new rock face which has now morphedand moulded by natural forces leaving the current sedimentary layer of rock, with highlyfractured, crumbly nature of stone at the fault line itself.

The ramp transformed as work progressed on the pyramid, with a Varying angle, height andlength of the ramp, ascending the cliff face as the pyramid grew in stature. Manipulation ofthe ramp happened through the use of landfill.The est. maximum length is 900 meters to the peak at 45 meters with the majority of theramp at 35 meters height and 600 meters in length. The main concern of the labourers, wasto keep the ascending ramp under 30 degrees to allow controlled movement of materials andto maximise the amount of material quarried at that height before the ramp was extended.

The peak of the local Mokkatam formation currently lies up to 45 meters above the plateau.For this study we will use this height with a variance of up to 5 meters. Resulting in 50meters maximum for the total height. This would complete the kings chamber

The King's chamber is the definitive part of the structure and its base lies on 43.03m, to 48meters. Once the height of the kings chamber had been reached, the declining ramp levelledup and flattened out and began a gentle incline to 70 meters. With a subtle angle ofinclination, under 4 degrees.

It is evident from the study that the height of the Mokattam and Maadi formations had thepotential of being up to 10 meters higher than this study suggests. Which would allow theuse of a declining ramp for the kings chamber, though to reach the heavy granite blocks fromthe harbour to this height, needed a different method (see “ kings chamber and granite”pg.20)

Upto 20 meters built via a trench, through sand plane to bedrock.1/3rd of height (50m) built using a declining ramp.

1/2 of height (75m) built with upto a 4 degree angle of incline, extended on existing ramp.Top 1/2 built using an inclining ramp.

At 30 meters height, 52% of entire pyramid built - At 50 meters height 1/3rd, 82% of theentire pyramid was built- At 100 meters height 2/3rd, 97`% of entire pyramid was built.The higher the pyramid grew, the less work is needed. At 50 meters the quantity of blocksalready laid would have been vast.

The amount quarried from the Mokattam outcrop for khufus pyramid could vary drastically,as a complete assessment of the interior of the pyramid, has not yet been made.A total of 5 million tons (est.) or as little as >1 million. of sedimentary Nummilite limestonewas carved away from under the surface of the cliff face.

Ramp augmentation using sand infill, ranging across a wide outcrop formation. Showing construction of 1/3rd upto 1/2 of the total height.

Fig. 6 – image not to scale- Decline of ramp and progression carving of rock face, showing the human effect onthe mokattam formation

The ramp with the use of sand infill, would have effectively buried the western side of thepyramid in sand as it grew. Sand infill would be used only for changing the angle of theramp meeting the pyramid (also used in parts of the core), as a complete land infill of the sitewould have been inconceivable, the ancient builders only used sand infill of the ramps toallow manoeuvring, placing and for all other building needs.

With simple manipulation, the angle for decline could be increased. Which allowed them toreach and build the kings chamber, at 45 meters minimum, before the angle of declinationlevelled to become flat. Then for 50 meters plus the pyramid was built with a slightlyinclining ramp. Though at this time 80% of build would have been completed.

The ramps where made from a mixture of sand, limestone rubble, and rock/stone rubbledebris cemented through pressure to form a rock. This compressed and fused sand rubblewas used for stability, which could fluctuate in size with simple manipulation. When needed,it could be lined with timber, with the sledges carrying the blocks greased.

Existing example of a limestone ramp, declining into limestone bedrock

As well as the two monuments at Giza that use a rock hill out crop, the sphinx and queenkhentkawes tomb, consisting of natural rock carved out of the local geological series, moreevidence of the sloping plateau is seen at the base of the pyramid, the declining plateau andresulting ramp are visible at the level of the esplanades around the pyramids, seen at the boatpits located at the NE of the pyramid, indicating and supporting the declined ramp theory,

The existing quarry, which is originally believed to be that for the pyramid, sits 30 metersbelow the plateau surface, housing hard limestone. Though it is not certain if this quarry was

only used for khufus pyramid. The quarry is uneven, appearing to slope up to the north. Thequarry’s southern outlet disappears beneath the sand-filled wadi situated between theMokkatam and Maadi geological formations. Therefore, we do not know the entire length ofthe quarry in that direction. Possibly to a height as high as the wider range of themountainous formations, 95 meters above the plateau floor.

This slope is further evidence of the declining ramp theory. This 30 meter deep canyon hasmore evidence to suggest that it was built/dugout for a tomb, as it houses and the tombs ofkhafres children, this suggests that it was used and dug to this depth during khafres pyramidbuild not khufus great pyramid

Aerial view - ramp ascending up local formation, courtesy of google earth,

Below is a “Possible” extension of the ramp to other local quarry sites, at above 60 metersabove sea level. 3 miles away - the “White desert” includes many outcrop features-plausible location for additional materials.

Images courtesy of google earth.

SECOND PART – INCLINING RAMP

We know that inclined planes or ramps were used in raising stones, which we employed asthe second part of this pyramid build.

The second part began at 65-70 meters. In-between the tip of the kings chamber and theheight of the shafts. Ie top half (50%). Using an inclining ramp to build the remaining 20%of the total building substance. The higher the inclination, the less blocks needed to be takenup this ramp, the width of the ramp was reduced for stability when they reach the upperportion of the pyramid.

If the ramps length was 800 meters (min.) at 45-50 meters height, then to reach 75-80 metersheight the angle of inclination would of have been minimal at around 2 to 3 degrees.

At 30 meters height, 52% of entire pyramid builtAt 50 meters height 1/3rd, 82% of the entire pyramid was builtAt 75 meters height 1/2, over 85% of the entire pyramid was builtAt 100 meters height 2/3rd, 97`% of entire pyramid was built

The higher the pyramid grew, the less work is needed. At 50 meters the quantity of blocksalready laid would have been vast. At 75 meters the majority of work would have beencompleted.

The limestone casing was added on the way down

KINGS CHAMBER AND GRANITE

Airshafts

Granite was used in the Grand Gallery and the King's chamber. Large Granite beams (1.3 x1.8 x 8m, 50-60t) for the relieving chambers and granite portcullis slabs. The Pyramidtemple (mortuary temple) has granite columns and basalt pavement around the pyramid.

The use of the core sand infill method was mainly applied to lower the granite blocks of the“relieving chambers” into place. This sand infill of the core technique also demonstrates anoperational function for the shafts of the Kings chamber.

The so-called “air-shafts” never actually pierced the outer casing of the pyramid, and fellshort, terminating about 6 meters, from the existing core structure outer layer.

The following method and conclusions was devised from our observations:

1. The portcullis (granite slabs at entrance of kings chamber) would be lowered and theshafts would be plugged/blocked up from the shafts exiting point. The chamberwould then be filled with sand from the top downwards.

2. The granite beam would be placed on this infill, the shafts plugs would be removedand the granite beam would begin to slowly descend into position as the pressuresends the sand spurting out of the shafts. A sort of sand pressure hydraulics system.

This method was used for placing the granite blocks as to minimise cracking of the materialdue to exerted weight and pressure as well as to actively measure how much of the granitewas needed.

RAISING GRANITE AND MORTUARY TEMPLE

Granite was used in the Grand Gallery and the King's chamber. Granite beams weighedapprox. 50 tons for the relieving chambers and granite portcullis slabs.

The heaviest Granite blocks had to be raised to a height of 43 to 65 meters. This wasaccomplished by a different technique as apposed to the declining ramp.Relevant materials were brought to the foot of the pyramid via a local harbour (pg.24).

Today, at the east side of the pyramid, is a courtyard, known as the Mortuary temple, pavedwith patches of black basalt, with sockets, which held huge granite pillars that formed acolonnade around the courtyard. At the western end of the temple there is a alcove (possiblya sanctuary) flanked by two storerooms. The interior walls were made of limestone. Thistemple is the first known temple to make use of limestone, granite and basalt. There is alsoan area of basalt pavement at the far end of the causeway.

This Old Kingdom complex at Giza, during the construction of the pyramids, would haveserved as a main structure used in raising the Granite beams.A large enclosure that holds water and accommodates the granite blocks to raise them to ahigher level. The main feature of the complex was a watertight limestone enclosure,reinforced and paved with basalt, which can be sealed off at ground level.

The complex was used as a single large water lock, with a simple purpose - to raise the waterlevel. The single large lock was used to raise the 50-ton granite blocks, and other materials tothe relevant height of 50 – 65 meters.The kings chamber is the definitive point in the structure, starting at 40> meters, theconstruct allowed for the granite to be elevated and used at up to 65 meters, which is thehighest point of the kings chamber The upper pound of the lock would vary as the pyramidgrew. For the purpose of the study we will use the maximum height of 65 meters.

The granite beams were placed at ground level within the mortuary temple. Dimensions ofthe mortuary temple is approx. 52 meters by 40 meters, which was wide enough to house anyof the granite beams located in the pyramid structure.

As work progressed on the pyramid, additional limestone and basalt blocks were added tothe mortuary temple, the height of which increased in situ with the pyramid.Extended in height with limestone blocks stacked upon each other, similar in dimensions tothe Limestone blocks of the pyramid, then lined & paved with basalt to accommodateleakage and subsidence.

Attached to a flat ramp at 60-65 meters in height, the granite blocks were moved into place.

The maximum dimensions of the structure was 52 x 40x 65 m^3Additional cubes stacked one on top of the other up to 65m tall = depth of chamberWhen filled solely with water = 65000 kilograms per cubic meter (kg/m^3).Supported by the bottom cube that is 52m x 40m = 2080 square meters (m^2).The pressure at the bottom of the Chamber is therefore 65000 kg spread over an area of2080m^2.Pressure = weight divided by area = 65000 kg/ 2080m^2 = 31.25 kg/m^2.

The pressure on the floor over the area of contact= 31.25 kg per square meter when the wateris filled without the granite. Remnants of the paved floor represent efforts to stabilize theground, and lesson the sinking due to subsidence. Despite its cyclopean size, in comparison alow amount of weight is at point of contact, 31.25 kg/m^2, which allows for use ofreinforced limestone to be adequate when supporting the extra pressure of the 50 ton graniteblocks.

The sealed reinforced chamber, with rafts attached to the granite, allowed for neutralbuoyancy. The completed box chamber would have been strong enough to withstand thepressure of the filled enclosure. This allowed the builders to use the very heavy granitebeams at this impressive height.In addition leakage will be less in a single lock of larger size,than in double ones of lesser size.Sealed and then filled with water, the water level was raised to the relevant height of up to 65meters

Approx. 65 meters in height max. and ten yrs construction time was needed, to reach therequired height those materials were needed in the pyramid.

Covered on the inside faces by well-hewn ashlars of limestone and basalt, which weretransported to the slowly growing lock by way of ramp. The limestone and basalt blocks thatcompose the inners wall vary in size. The foundations of these walls may have been built uphigher with inclined sides, formed with a casing of basalt or limestone and having a core ofpacked limestone chips.

Fluctuating in height as the pyramid grew, this dry-dock was built into the plateaus plain, toallow easy loading of the granite. The dry/floating dock raised over the water rather thanwithin it. This was used to keep the floating dock at the same level to the pyramid evenduring changing heights.

Observations and methodology suggests the builders would use the granite poles as oldkingdom nilometer pylons and to secure the platform of the flotation device (The Egyptianslearned a method of measuring the height of the Nile, reinvented in the middle kingdom andlater, known as the Nilometer)

The whole operation for one granite beam to be elevated depended mainly on the lock beingfilled. There where many ways to raise the water level in the old kingdom. I.e. A chaduf.

On completion of the whole pyramid complex, these basalt and limestone blocks wereremoved, down to their lowest units. The structure was then renovated for another practicaluse, in relation to the completed pyramid complex as a whole.

The large granite blocks arrived in the harbour of Giza (the Nile channel lies on approx. 17mabove sea level, the exact position of the harbour is unknown) and had to be transported overa distance of 500-600 meters. The builders prepared the harbour for the coming flood and thetransportation and delivery of the blocks from the quarries.

Attached to a waterway, canal valley stream ways were used to bring water and materials tothe foot of pyramid. When the water level reached the mouths of the canals, the damsseparating the canals from the river were opened and the basins and canals flooded fillingthese valley pathways.

The ancient Egyptians cut this canal from the nearby river to connect it with the harbourdiscovered at Giza (pg 24). The walls of the channel and the harbour were probably used tomoor ships transporting building materials. The piers found around this site is evidence of aquay, a structure on navigable water used for loading and unloading vessels; a wharf (wiki)

Blocks were not lowered onto boats or lifted off. Instead, when they were quarried theywould be fixed to sledges from quarry to placement, most likely dragged by a boat, and leftin the harbour at Giza for the peak of the flood

The harbour with a dry-dock was built into the flood plain during the recession, blocks wereloaded. Then when the inundation happens the transportation can begin. The water was alsoused to flood large tracts of land while the Nile was flowing high.

The ancient workers moved the massive artefacts directly to their final destinations overwaterways. Evidence of cut-stone revetments, large piers, and extensive, artificial basinshave been excavated all over Egypt.

Evidence of large-scale water-control earthen works such as dikes were found along theriver, used to control the course of the water and to allow the creation of irrigation canals,levees, dams dating from before King Scorpion in Predynastic Egypt. The embankments ofthe abandoned canals are still present.

Canals have been discovered at both significant granite quarries in Aswan and at thedestination harbour in Giza. The canals likely filled in with water during Nile's annualfloods. Workers would have dragged the large stone Blocks onto rafts, before, at a pointbelow the floodwater level, allowing the artefacts to float when the water level rose.

FURTHER READING:

CANAL STREAM WATERWAYS COMING FROM THE NILE

Transportation of the blocks only occurred during the flood of the Nile. The annualinundation allowed the builders to bring certain blocks, quarried at further quarries to theharbour at Giza, and to be loaded onto the ramp at the manmade limestone dam style harbourat the right time, when the water level is at its peak.

This Old Kingdom harbour and quay’s at Giza, during the construction of the pyramids,would have served as a main quay for a deep water harbour at the lowest point of the plateau,where the bedrock was being exploited meet the general level of the flood plain.Harbours & canal valley stream way, canals have also been discovered at the Giza pyramids,and at the significant granite quarry in Aswan.

A large dam was forged at the harbour as work progressed on the pyramid, from limestone tocapitalise on the flood to reach the higher level of the pyramid. The dune and resultingharbour and canal stream ways contributed to a water filled ramp aqueduct declination,leading to the base of the pyramid brining materials the plateauThe builders prepared the harbour for the coming flood and the transportation and delivery ofthe blocks from the quarries.

Dams/canals were used at both quarry and the destination harbour at Giza. The ancientworkers moved the massive Blocks directly to Giza over waterways. Evidence of cut-stonerevetments, large piers, and extensive, artificial basins have been excavated all over Egypt.

At Giza, the walls of the channel and the harbour that were discovered, were probably usedto moor ships transporting building materials. The piers found at this site is evidence of aquay, A limestone structure on navigable water used for loading and unloading vessels; awharf

The canal likely filled in with water during Nile's annual floods. Workers would havedragged the large stone monuments onto rafts, before, at a point below the floodwater level,allowing the artefacts to float when the water level rose.

With a centralised government in place at the time the pyramids, predating the4th dynastyone of the first duties of provincial governors was the digging and repair of canals,They built a series of diversion dams (barrages or weirs) across the Nile so as to raise thelevel of water upstream to supply the stream valley canals and to regulate navigation. TheManmade dune, like the one at wadi Haifa.

The limestone harbour and dune went from being a small type weir to a larger type barrage.Weirs and barrages are different types of ’run–of–river’ dams, not a storage dam. This meansthat while they raise the water level upstream they create only a small reservoir (’headpond’) and cannot effectively regulate the downstream flow. A weir is normally a low wall

of basalt or limestone. A barrage can be a huge structure ten or twenty metres high extendingfor hundreds of metres across

A weir or barrage was constructed across the river to raise the water level and divert waterinto the canal. A Barrage would be used when water level on the up stream side of the weiris required to be raised to different levels at different times. Attached to a pier.

With a Divide wall constructed perpendicular to weir or barrage, made of limestonereinforced with basalt.To help form a still water pocket in front of the canal head. To control the current and toprovide a straight approach. This helped resist the overturning effect of the weir or barrage.

The run of river dam at Giza would be at right angle to the Nile flow, the building of dams atright angles to the flow of the Nile, separating the Nile Valley into basins, precedes the OldKingdom. Dikes were built along the banks of the river and the basins which coveredbetween 400 and 1700 hectares, were carefully levelled. The river water was diverted intocanals on either side of the Nile

“The Sadd el-Kafara in Wadi Garawi, the oldest known dam in the world, collapsed not longafter its erection(2,500>2600 bc.) the 110m long dam, 98 m wide at base, 56 m at top, 14meters high from the wadi floor. . Downstream face is constantly inclined at a slope of 30degrees, while the upstream face is curved. With a core of rubble, gravel, silty sand,embedded with layers of stone and rubble…”

Even today, Earth and rock embankments, which are usually the cheapest to build, make upmore than 80 per cent of all large dams. These Embankments where generally built acrossbroad valleys near sites where the large amounts of construction material they need can bequarried.

Different dykes and levees where used to confine the flow of the river, resulting in higherand faster water flow. Levees where used where dunes where not strong enough, placedalong the river for protection against high-floods, a network of levees were constructed over3,000 years ago in ancient Egypt, where a system of levees was built along the left bank ofthe River Nile for more than 600 miles (970 km), stretching from modern Aswan to the NileDelta on the shores of the Mediterranean

Though efforts to completely control the flood was met by failure many times, which is welldocumented. The floods levels were unpredictable, aggressive. When the Nile receded theappearance of the land had radically changed and there was a great rush to restoreboundaries, there where many disputes as markers had moved, banks had collapsed anddistinguishable features had disappeared.

BIBLEOGRAPHY

The Giza Plateau Mapping Project at the University of Chicago's Oriental Institute – MarkLehner

The Complete Pyramids of Egypt (Thames and Hudson 1997, ISBN 0-500-05084-8)Secrets of lost empires (Sterling Publications 1997, 080699584X)Development of the Giza Necropolis (1985)

Petrie, William Matthew FlindersPetrie Online Book: The Pyramids and Temples of Gizeh, 1883

The oxford history of Ancient Egypt – Ian Shaw

A Bibliography on the River Nile Vol. I The River Nile and its Economic, Political,Social and Cultural Role An Annotated Bibliography Terje Tvedt

Geological and geomorphological study of the original hill at the base of the 4th dynastyEgyptian monuements – Suzanne Raynaud, Henri de la Boisse, Farid Mahmoud Makroum,Joel Bertho.

A HISTORICAL PERSPECTIVE Fekri A. Hassan Water Ethics World Commission on theEthics of Scientific Knowledge and TechnologyUNESCO International HydrologicalProgramme and

ORIENTALIA MONSPELIENSIA IX CENTRE D'EGYPTOLOGIE FRANCOISDAUMAS INSTlTUT D'EGYPTOLOGIE - UPRES-A 5052 DU CNRS Etudes sur l' AncienEmpire et la necropole de Saqqara dediees aJean-Philippe Lauer reunies par CatherineBERGER et Bernard MATHIEU pubIh~es avec Ie concours de l'URA 995 du CNRS

Petrographic investigation of Coptic limestone sculptures and reliefs in the BrooklynMuseum of Art J.A. Harrell Professor of Archaeological Geology Department of Earth,Ecological and Environmental Sciences The University of Toledo 2801 West Bancroft St.Toledo, Ohio 43606-3390, USA

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Franz Löhner www.cheops-pyramide.chWikipediaGoogle earth

Geopolymer institute– joseph davidovits

Arnold, DieterEncyclopedia of Ancient Egyptian Architecture (2003, Princeton University Press, ISBN 0-691-11488-9)Building in Egypt, Pharaonic Stone Masonry (1991, Oxford University Press ISBN 0-19-506350-3)

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Hawass, ZaniKhufu Pyramid Complex 1999