Stability of the Solidified Magma Region for Direct Utilization of Magma Energy

从固体力学的角度考察了直接从熔融岩浆中提取能量的固化区的稳定性。首先，针对单轴应力-蠕变应变关系，利用Norton定律表示蠕变应变对应力的依赖关系，研究了固化岩浆的本构关系。对于蠕变应变对时间的依赖关系，采用二次蠕变阶段常用的蠕变应变与时间的线性关系，并引入阿累尼乌斯定律来表示蠕变应变的温度相关性。在单轴应力-蠕变应变关系的基础上，利用偏应力的第二不变量-蠕变势，利用J2流动理论建立了本构方程。介绍了花岗岩、斜长岩和橄榄石三种岩石类型。对于温度条件，考虑了以下两种情况。第一种情况是熔融岩浆流动的对流很弱，因此固化区的大小主要由固相线温度决定。第二种情况是岩浆的对流足够强，以至于固化岩浆的大小几乎取决于从固化区外部提取的热量和对流岩浆提供的热量之间的热平衡。分析了两种情况下的温度分布，阐明了应力分布和变形情况，揭示了在上述本构方程和温度场的基础上，凝固区域内断裂网络的形成过程。结果表明，从裂隙网络形成的角度来看，橄榄石和斜长岩都是最有潜力的候选矿物，斜长岩次之。花岗岩不适合直接提取岩浆能量。

Stability of the solidified region for the direct extraction of energy from molten magma was examined from the view point of solid mechanics. Firstly, the constitutive law of the solidified magma was investigated, by using the Norton law to express the dependency of creep strain on stress, for the uni-axial stress-creep strain relation. With regard to the dependency of creep strain on time, the creep strain was set to be linear with respect to time as usually used in the secondary creep stage and the Arrhenius law is introduced to express the temperature dependency of creep strain. Based on the uni-axial stress-creep strain relation, the constitutive equation was constructed by employing the J_2 flow theory which utilized the second invariant of deviatric stress the creep potential. Three kinds of rock, i.e. granite, anorthosite and olivine, were introduced. As for the temperature condition, following two cases was considered. The first case is that convection of molten magma flow is very weak and thus the size of the solidified region is primarily determined by the solidus temperature. The second case is that the convection of magma is sufficiently strong so that the size of the solidified magma is almost determined by the heat balance between the heat extracted and the heat supplied by the convective magma from the outside of the solidified region. The temperature distribution was analyzed for the both cases and the stress distribution and the deformation were clarified, shedding light on the formation of fracture network within the solidified region, based on the constitutive equations and the temperature fields mentioned above. It was revealed that, for both of the two cases, olivine was the most potential candidate from the view point of formation of fracture network and anorthosite came next. Granite would not be appropriate for the direct extraction of magma energy.