With the advancement of ultrashort pulsed-laser processing technologies, greater control of processing conditions has come into demand. A factor which particularly complicates ablation situations is "damage incubation," a phenomenon in which the intrinsic optical properties of the processed material change due to accumulated defects from repeated laser excitation. Damage incubation can induce striking changes in the observed morphology during ablation and should be an important factor governing processing results. However, only a few studies have incorporated these effects into multiple-pulse ablation models due to its complexity. Here, in order to quantify the effects of damage incubation in a practical processing setting, we study ablation morphologies of shallow grooves formed on the surface of sapphire (alpha-Al2O3) with varying laser pulse number and energy in a purpose-made experiment. We observe clear evidence of incubation-induced changes in ablation phase and nonlinear dependence of depth on the incident total energy density. To understand the results, we create a simple empirical model for material energy absorption by characterizing interpulse absorption changes and analytically derive solutions for two limiting cases in which the material has either a very low (quasistatic absorption) or very high (accumulative absorption) damage incubation characteristic. By following the energy absorption characteristics predicted by the latter model, we were able to derive universal relations between ablated depth and incident energy density for sapphire. This work serves to highlight the effects of damage incubation on multiple-pulse ablation situations and provides a simple and practical method to predict such morphological characteristics of an arbitrary material. (c) 2019 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).