基于重整化群有限原胞级整体安全性分级评价
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国家自然科学基金(51179107)


Safety classification evaluation of an overall structure based on limited primitive cell level using renormalization group theory
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    摘要:

    为解决重整化群理论研究对象在理论上应具有无标度性(即原胞级数趋于无限大),但实际工程中原胞级数不可能取很大这一问题,基于重整化群理论的逾渗模型、断层破裂分形树模型、岩石破碎模型、重力坝三棱柱结构破坏概率模型,开展有限原胞级数的破坏概率规律研究。研究表明,原胞级数即迭代次数取3可满足实际工程需要。提出基于三级原胞破坏概率值的实际结构整体安全性分级方法,并给出应用三棱柱模型判别重力坝结构整体安全性状态步骤。依据三级原胞破坏概率关键点、不动点将结构整体安全状态划分为3个级别:(a)Ⅰ状态,结构整体安全;(b)Ⅱ状态,结构整体安全性较低,结构整体由安全向破坏过渡,处于亚健康状态;(c)Ⅲ状态,结构整体破坏。

    Abstract:

    The study subject of the renormalization group theory is supposed to have a scaleless property in theory. In other words, the primitive cell level tends to be infinite. However, the level cannot be set at a very high value in actual engineering projects. In order to solve this problem, comparative studies of damage probability of limited primitive cell levels were carried out using the percolation model, the fault rupture model, the rock breaking model, and the structural damage probability model of a triangular prism unit for a gravity dam based on the renormalization group theory. The results of iterative computations show that level 3 of a primitive cell or three iterations can be applicable to actual engineering projects. A safety evaluation classification method for an overall structure is proposed based on the damage probability of a primitive cell of level 3. The steps of determing the overall safety of a gravity dam using the triangular prism model are presented. According to the key points and fixed points of the damage probability, three safety states of the overall structure were classified as follows: (a)a safe state; (b)an intermediate state, between safey and overall collapse; and(c)an overall collapse state.

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顾培英,邓昌,汤雷.基于重整化群有限原胞级整体安全性分级评价[J].河海大学学报(自然科学版),2014,42(4):355-360.(GU Peiying, DENG Chang, TANG Lei. Safety classification evaluation of an overall structure based on limited primitive cell level using renormalization group theory[J]. Journal of Hohai University (Natural Sciences),2014,42(4):355-360.(in Chinese))

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  • 收稿日期:2013-05-31
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  • 在线发布日期: 2015-05-20
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