Abstract: Cracking of arch dams and control of it remain a technical difficulty in design, construction and operation. A mechanism for arch dam cracking caused by gradients in temperature, deformation and stiffness is revealed in this paper, based on observations and analyses on the stress cracks, temperature cracks, special local cracks, and foundation block cracks in arch dams. In the analysis, gradients are considered as a measure of material state or a control factor in the control system, including stress gradients in dam structures, temperature gradients between inside and outside of dam blocks, material function gradients, and gradients in foundation dam block lifting. Through decomposition of problems from multiple dimensions, including time, space, and functions, we construct a multi-dimensional gradient control method system for multi-physical quantity fields. It provides a key theory and technical support for reliable design, controllable construction and safe operation of arch dams.