The Fractal and Non-Fractal Design of the Retaining Walls Built by Incas at Machu Picchu, Pisac and Moray in Peru

The retaining walls of the agricultural terraces at Machu Picchu Pisac and Moray were constructed by the Incas of dry stacked granite blocks. The walls at Machu Picchu have remained stable for more than 500 years. The walls at Pisac and Moray have failed. This study involves field, fractal and numerical analyses designed to understand why the walls at Machu Picchu are stable and why the walls at Pisac and Moray have failed. Walls at Machu Picchu, Pisac and Moray were photographed and digitized. The number and area of each individual stones were measured for an analyses of the stone size distribution in the walls. An analysis of the stones' boundaries indicated that they were relatively rough. The stone size distribution of the walls at Machu Picchu was determined to be fractal in nature. The walls at this location were made of a mixture of large, medium and small rock pieces. However, the stone size distribution of the walls at Pisac and Moray were found to be non-fractal. The walls at Pisac and Moray were made of the same size rock pieces. The source of stability of the walls at Machu Picchu rested on the gravity- induced frictional resistance developed between the many contacts between the large and medium sized rock pieces and the small ones. The large frictional resistance developed by the walls at Machu Picchu prevented their removal by the soil pressures behind these walls. The Pisac and Moray walls made of uniform rock pieces had average number of contacts equal to 5. With these few number of contacts, the gravity-induced frictional resistance was found to be small and the pressure of the soil behind these walls easily removed the rock pieces causing their failure.