Static stability of monumental moai–pukao assemblies on the ahu of Rapa Nui: a closed-form structural model for built heritage conservation

Abstract The monumental statues (moai) of Rapa Nui (Easter Island) and their cylindrical scoria topknots (pukao) constitute, together with the stone platforms (ahu) on which they were installed, one of the most distinctive bodies of monumental built heritage in the Pacific. Approximately 100 moai carried pukao during the late phase of construction (15th–16th centuries CE). Since 1956, approximately 50 moai have been re-erected on their ahu by conservation programmes, several with pukao reinstalled, yet the static stability of the installed moai + pukao assembly as a built structure has not been derived analytically. This paper develops a closed-form structural model of the assembly, building on the established tradition of overturning-stability analysis for megalithic monuments and the two-block rocking literature while extending it to include explicit directional analysis. The centre of mass is elevated from approximately 0.522 (moai alone) to approximately 0.671 H m for the assembly. The critical tipping angle is directionally anisotropic: lateral θ crit is reduced from approximately 17.7 to 13.9° by the pukao, whereas frontal θ crit —the direction of observed face-down toppling—is reduced from approximately 10.8 to 8.5°. The pseudostatic seismic thresholds for frontal tipping decrease from approximately 0.19 to 0.15 g. The minimum tipping energy for frontal toppling is approximately 6.7–6.9 kJ, which is only about 37% of the lateral value, indicating that the frontal mode is favoured due to both the smaller angular margin and the lower energy barrier. The principal contribution is a directionally anisotropic structural envelope within which any toppling mechanism—seismic, ritual, postcontact neglect, or applied force—must operate. Beyond interpretation, the model functions as a first-order screening tool for built heritage conservation: it allows restored moai–pukao–ahu assemblies to be ranked by frontal stability margin, supports preventive conservation prioritisation for structural health monitoring, and provides quantitative criteria for evaluating future restoration decisions involving pukao reinstallation. All numerical values are reproducible from the Python script provided as a supplementary file.