In our previous paper, we analyzed the stress state in the solidified region of the heat extraction system from molten magma under the condition of plane strain. In the present paper, we treated the same problem by using the three-dimensional axi-symmetric model in order to take properly account of the effect of body force due to gravity which was treated approximately in our previous paper. The stress field is analyzed by using creep theory for three types of rocks, i.e., granite, olivine and anorthosite, to shed light on the variation of stress field with respect to time after the onset of heat extraction. The usual incremental flow theory are employed, where the second invariant of the stress deviator is used as the creep potential. It was revealed that the normal stresses acting in the circumferential and axial directions on the wellbore wall shifted gradually with time to become compressive. Thus, the formation of the fracture network which is expected to be created by thermal shrinkage of rock due to heat extraction and to work as the flow path of working fluid to extract heat from solidified magma, is mostly determined by the stress field in the early stage of the heat extraction. Based on this fact, we propose a concept of a stress map expressed in the T
s vs. Ea diagram (E: Young's modulus, α : thermal expansion coefficient, T
s: solidus temperature). By using the stress map, a rough estimation on the formation of the fracture network is feasible for any kind of rocks. Among the three rocks mentioned above, olivine is the most potential candidate for extracting heat directly from magma.
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