Abstract
Using linear fracture mechanics and fluid dynamics, we studied [1] the static stability of an edge crack connected with a fluid (magma or aqueous fluid) reservoir and [2] the propagation dynamics of the crack filled with magma denser than the surrounding rock. Our purpose is to elucidate [1] onset conditions for magmatic (aqueous) fluid transport by crack propagation in magmatism (metamorphism) and [2] the dynamics of dense magma dyke formation which probably occurs in the lower crust. The results are as follows. [1] The quantitative onset conditions are obtained; they are expressed by five factors (reservoir's excess pressure, vertical crack length, fracture toughness of the rock, density difference between the rock and the fluid, and gravitational acceleration). [2] The temporal behavior of the dyke length and width for given magma injection rates is elucidated for dense magma dyke formation. At an early stage of the dyke formation (i.e., while the dyke size is small), the crack propagation is controlled by the viscous flow resistance of magma. Eventually it is controlled by the negative buoyancy of the dense magma, to which the static discussion without the viscous flow resistance is applicable.
