The stopping of a rising, liquid‐filled crack in the Earth's crust by a freely slipping horizontal joint

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Abstract
The stress intensity factor K at the upper tip of a vertical, liquid‐filled crack in the earth's crust is large for relatively small cracks (K>3 MPa m½when the crack length is larger than about 40 m). Consequently, the large water‐filled cracks considered for use in the extraction of geothermal heat might be expected to pop to the earth' surface. In this paper it is shown that a freely slipping horizontal joint (as well as a not so freely slipping joint) can stop the upward motion of a large liquid‐filled crack. If the joint is tightly fitting, there is no limit to the length of a stopped crack. If slip on a joint results in the joint being propped open, the maximum crack length of a stopped crack is given by the crevasse expression: total crack length = πT/2(ρ −ρ ′)g, where T is the tectonic stress, g is the gravitational acceleration, and ρ −ρ′ is the difference between the rock and liquid density. The results can also be applied to the problem of magma transport in the earth's crust. In particular, laccolith emplacement is favored when the nonhydrostatic tectonic stress component is compressive in character.