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基于弹性理论,推导得到了立井内外壁温度差引起的温度应力解答。数学分析表明,立井内壁温度高于外壁温度时,温度应力分量σθ与σz在内壁处取得最大值,在外壁处取得最小值。温度应力分量σz随着立井的弹性模量E、泊松比μ、膨胀系数αf、立井深度z的增大而增大,随着温差ΔT=Tb?Ta的增大而减小。进一步分析表明,温度应力导致立井内壁处最先发生破裂,这与大量实际立井破裂现象完全吻合。诱发立井破坏的因素中,温度应力的权重大于立井自重荷载的权重,可见温度应力是导致立井破裂的重要因素。
Based on the elastic theory, the temperature stress induced by the temperature difference between the inner and outer walls of shaft is derived. Mathematical analysis shows that when the inner wall temperature is higher than the outer wall temperature, the temperature stress components σθ and σz get the maximum value at the inner wall and the minimum value at the outer wall. The temperature stress component σz increases with the increase of the elastic modulus E, Poisson’s ratio μ, expansion coefficient αf and vertical shaft depth z of shaft, and decreases with increasing temperature difference ΔT = Tb-Ta. Further analysis shows that temperature stress causes the first rupture in the inner wall of vertical shaft, which is in good agreement with a large number of actual vertical shaft ruptures. Among the factors that induced the failure of vertical shaft, the weight of temperature stress is greater than the weight of vertical shaft self-weight load, so it can be seen that temperature stress is an important factor leading to the failure of vertical shaft.