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本文给出了在球层模型下,地球岩石层对表面荷载响应的解析解。计算了地球岩石层对圆盘形荷载和正弦型荷载的响应,及由此产生的重力异常。结果表明:1.岩石层弯曲不仅与其厚度有密切关系,而且与荷载尺度有关。当岩石层厚度与荷载尺度相比很小时,其弯曲与厚度关系不大,并呈现薄板效应。2.弹性模型岩石层在外加荷载下能承受数千巴的弯曲应力。3.弯曲应力在岩石层中的分布较为规则。由于大尺度荷载下岩石层出现薄板效应,传统的由弯曲刚度估算等效岩石层厚度的部分结果需要重新估价。
In this paper, we give the analytical solution of the Earth’s rock layer to the surface load response under the spherical model. The response of the Earth’s rock layer to the disc-shaped and sinusoidal loads and the resulting gravity anomalies were calculated. The results show that: 1. The bending of rock layers is not only closely related to its thickness, but also related to the load scale. When the thickness of rock layer is small compared with the load scale, its bending has little to do with the thickness, and shows a thin plate effect. 2. Elastic model The rock layer can withstand bending stresses of several thousand bar under applied load. 3. The distribution of bending stress in the rock is more regular. Due to the sheet effect of rock layers under large-scale loading, some of the traditional results of estimating the equivalent rock layer thickness by bending stiffness need to be re-evaluated.