A variety of building methods is described by Müller-Römer (2011, 261–348). In a similar, but less detailed, review by De Haan (2010, 59–78), the emphasis is more on the quantitative aspects of these methods. These methods can be roughly subdivided in three groups: (1) methods without ramps; (2) straight or linear ramps; and (3) ramps built parallel to the sides of the pyramid (‘parallel’ ramps).
Methods without ramps
These methods have the obvious advantage that only the material for the construction of the pyramid has to be lifted. Naturally, without a ramp, the building material must be lifted somehow along the sides of the pyramid. A method proposed and proved experimentally is levering (Hodges 1989). He proposed that the building blocks are lifted along the side walls of the pyramid by means of staircases. In other concepts, the blocks are lifted by means of cranes mounted on the steps of the pyramid (Croon 1925) or pulled up along a lubricated wooden plank, assisted by levering (Isler 2001, 259–61). Illig and Löhner (1994) suggest the use of a pulley fixed at the top to reverse the direction of the pull, so that the hauliers can benefit from their own weight. Riedl's concept (1980) relies on the use of winches—which, however, were not known to the Egyptians prior to the 12th Dynasty (Arnold 1991, 71).
There is ample evidence that linear ramps were used for construction purposes in ancient Egypt. Various ramp concepts are reviewed by Arnold (1991, 79–101). The oldest construction ramps, made of pebbles, are found at Sakkara and belong to Sekhemkhet's complex. There are four ramps around the pyramid of Sinki, 12 m long, with a gradient of 21–26%, which seems acceptable for the transportation of the small blocks used. The height would have been 6 m, if finished. Presumably the later use of brick (rather than rubble) ramps is related to the use of large building stones. Two large ramps at Meidum were heightened several times. There are also short ramps to the roofs of mastabas, made of bricks and pebbles that were needed for the construction of the mastaba and for the installation of a sarcophagus. A ramp is also pictured in the tomb of Rekhmire. Remains of a ramp can still be observed at the temple of Karnak.
Probings suggest that the whole south edge of the Giza plateau is a gigantic rubbish infilling, consisting of ramp debris and remains of building sites and additional work camps (Lehner 1997, 132; Kemp 2006, 191). At Giza, there is also a ramp with stone walls near Khufu's pyramid, connecting the quarries west of the Sphinx to the plateau. Nevertheless, as pointed out by Arnold (1991, 98), there is no indication as to which type of ramp may have been used for the construction of Khufu's pyramid. That is, of course, not surprising, as the ramps would have been demolished after completion of the pyramid. Linear ramps have been proposed by several authors (Borchardt 1928; Arnold 1991, 98; Lehner 1997, 129–32; Stadelmann 2003, 128). In some cases, multiple ramps were proposed, or a combination of a linear ramp with a parallel ramp wrapping round the pyramid. The linear ramp is illustrated in Figure 10, but there is no reason why the ramp must be oriented perpendicular to the pyramid.
Müller-Römer (2011, 238–9) discards the possibility of a linear ramp on the grounds that its construction would take a disproportional amount of effort, that it would lead to interruptions in transportation, and that it would allow insufficient transportation capacity and that therefore four ramps would be required to achieve the necessary high initial building rate. Moreover, he points out that the linear ramp does not do justice to the stepped shape of the core of Menkaure's pyramid. By contrast, De Haan (2010, 228, 37 and 44–6) showed that a single 82 m high ramp would require a relatively small fraction of the total effort in man-years, but would suffice for the completion of more than 90% of Khufu's pyramid. The top 10% of the pyramid would have to be completed by means of another method; for instance, levering or the zig-zag ramp system proposed by Müller-Römer. This combination would provide sufficient transportation capacity for completion of the pyramid in 20 years. The ramp would only cover less than 20% of the pyramid surface, so that the ramp would not seriously hamper its alignment. Admittedly, the proponents of the linear ramp are left with the question of why the core of Menkaure's pyramid was apparently constructed with steps that are 4–5 m wide. On the other hand, one cannot perhaps exclude the possibility that the steps of the core structure were filled in concurrently with the construction of the pyramid by means of a linear ramp.
In this connection, one specific aspect of Menkaure's pyramid should not be overlooked, namely that in contrast to the other pyramids, a large part—that is, the first 16 courses—of its casing consists of granite. This corresponds with a height of 16 m according to Müller-Römer (2011, 192, fig. 126.96.36.199.4). For a thickness dc of 1 m and a slope γ of the pyramid, this corresponds to a volume of
In addition, the limestone for the pyramid had to be quarried, with a volume of
Based on experiments reported in the literature, De Haan (2010, 13) estimated a quarrying efficiency for granite of 0.00024 m3 per man-hour = 2624 × 0.00024 = 0.63 m3 per man-year, and for limestone 0.03 m3 per man-hour = 2624 × 0.03 = 78.7 m3 per man-year. Thus it would take 7433/0.63 = 11 800 man-years to produce the granite and 234 000/78.7 = 3014 man-years to produce the limestone. This compares with a mere 937 man-years to build the actual pyramid (Table 3). In other words, the effort to quarry the material for the casing far exceeded the combined effort required to build the pyramid and provide the necessary limestone. Thus the supply of the casing material was in fact a bottleneck in the building process, and one can well imagine that Menkaure wanted to have the bulk of his pyramid—the stepped core—completed first and the casing installed later. This problem did not occur for the other pyramids and thus did not interfere with the simultaneous construction of the core and the ‘shell’. In fact, Arnold (1991, 160, 161) believes that, in general, the 4th Dynasty pyramids, such as those of Khufu and Khafre, consist of horizontal layers, presumably constructed in a single phase. It would seem that the presence of a granite, rather than a limestone casing, also casts some doubt on Müller-Römer's supposition that the casing was smoothed at the end, from the top down, bearing in mind how difficult it is to work granite. It seems more logical that the blocks were finished on the ground, so as to ensure a more or less smooth surface, sloping at the correct angle (Arnold 1991, 169).