Particle dynamics simulations of granular piles constructed upon planar substrates with different shear strengths model the gravitational deformation of natural volcanoes. Results reveal direct correlations among pile morphology, layer stratigraphy, deformation structures, and stress field, dependent upon the shear strength along the base of the pile. Piles constructed above a strong, cohesive substrate that prevents basal slip develop outward dipping layers through particle avalanching down angle of repose slopes. In the absence of basal cohesion, slip occurs along a basal décollement if the topographically induced shear stresses exceed the basal shear strength. For friction coefficients decreasing from 0.3 to 0.1, fault planes migrate progressively inward, defining a transition in deformation mode from shallow slumping to deep-seated landsliding and, finally, to full gravitational spreading. The variations in deformation mode reflect the dependence of internal fault geometry on basal strength in accordance with critical Coulomb wedge theory. In order for slip to occur both internal and basal failure criteria must be met simultaneously. Topographically induced shear stresses increase outward along the base of the pile, enabling décollement sliding once the basal failure criterion is met. Normal faults arise from the inside edge of the slipping décollement, accommodating downward and outward displacements of the flanks. Surface slopes evolve to maintain equilibrium between gravitational driving and basal resisting stresses. This simple mechanical understanding of gravitational deformation of granular piles provides insight into the controls on modes of volcanic deformation, providing a predictive tool for understanding volcanic evolution and hazards in many settings.