A sharp transition between liquefaction and transient solidification is observed during impact on a granular suspension depending on the initial packing fraction. We demonstrate, via high-speed pressure measurements and a two-phase modeling, that this transition is controlled by a coupling between the granular pile dilatancy and the interstitial fluid pressure generated by the impact. Our results provide a generic mechanism for explaining the wide variety of impact responses in particulate media, from dry quicksand in powders to impact-hardening in shear-thickening suspensions like cornstarch.Impacts on particulate media like granular materials and suspensions present an astonishingly rich phenomenology [1, 2]. Along with its astrophysical [3] and ballistics applications [4], impact dynamics is an object of active research to understand the high-speed response of granular matter [5]. In dry granular media, impact by a solid object results in the formation of a corona of granular ejecta and a solid-like plastic deformation leading to a permanent crater [6][7][8][9][10][11]. For fine powders in air, granular jets and cavity collapse occur during impact [12,13]. Subsequent studies showed that the ambient pressure of the interstitial fluid (air) is an important element for the observed fluid-like behavior [14][15][16], while for denser packing the impact penetration is much reduced [17]. However, the question of the physical mechanisms and control parameters that give rise to such a wide variety of phenomena is still largely open. Recently, studies on shearthickening suspensions (cornstarch) showed completely different behaviors. Above a critical velocity, an impacting object immediately stops [18], or in some cases generates cracks [19], as if hitting a solid. This phenomenon has been related to the propagation of dynamic jamming fronts in the bulk [18] but the mechanism remains unclear and overlooks the role of fluid/grains couplings, which are known to strongly affect the transient behavior of saturated granular materials [2,20,21]. Whether impact-activated solidification relies on such couplings or on the complex rheology of the suspension is a pivotal question for clarifying the physics of shear-thickening fluids -a still highly debated topic [23][24][25][26][27].The objective of this Letter is to address these questions and elucidate the role of the interstitial fluid and the initial volume fraction on the diverse impact phenomenology observed in granular materials and dense suspensions during the last decade. To avoid difficulties associated with colloidal interactions between particles (like in shear-thickening suspensions) or fluid compressibility (like in powders in air), we study here the impact of a freely-falling rigid sphere on a simple granular suspension [28] made up of macroscopic, heavy particles (glass beads in the range 0.1-1 mm) immersed in an incompressible liquid (water, viscous oil). The initial packing fraction of the suspension φ 0 (the ratio of the volume of the glass beads to the total v...