Shao-Zhu-Su岩石流变模型的快速显式积分算法及比较研究

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摘要基于对Shao-Zhu-Su岩石力学流变模型及其数值算法的分析，发现传统积分算法在处理流变卷积方程时存在变量存储量大和计算效率低的缺点。运用数学变换和Taylor展开提出2种显式积分算法，即非线性显式积分算法(NEIA)和线性显式积分算法(LEIA)。通过蠕变和松弛数值试验对新算法进行验证和比较。提出的显式积分算法变量存储量较少，且避免与加载历史有关的累积求和运算，从而明显提高计算效率，使得此类内时流变模型更适合于大型岩体结构分析。需要指出的是，建议的数值积分方法也可用于其他积分型流变模型的数值处理。

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关键词 ：岩石力学, 流变模型, 时效损伤变量, 快速显式积分算法

Abstract：Based on the analysis to the rheological model proposed by Shao-Zhu-Su for geomaterials，it was found that the traditional computational algorithm for solving the convolution integral had obvious shortcomings regarding the storage of time-dependent variables and computational efficiency. In this paper，a nonlinear explicit integral algorithm(NEIA) and a simplified linear explicit integral algorithm(LEIA) were developed with the help of mathematical transformation and Taylor expansion. The proposed algorithms were validated and compared through numerical creep tests and relaxation tests. Since the new method reduced significantly the number of variables to be stored and avoided the accumulation operation over loading history，its computational efficiency was improved remarkably and therefore more suitable for large-scale numerical analyses of rock structures. It is pointed out that the proposed numerical treatment is also applicable to other integral-type rheological models.

Key words： rock mechanics rheological constitutive model time-dependent damage variable fast explicit integral algorithms

引用本文:

朱其志1，2，赵伦洋1，2，刘海旭1，2，邵建富1，2. Shao-Zhu-Su岩石流变模型的快速显式积分算法及比较研究[J]. 岩石力学与工程学报, 2016, 35(2): 242-249.
ZHU Qizhi1，2，ZHAO Lunyang1，2，LIU Haixu1，2，SHAO Jianfu1，2. Fast explicit integral algorithms with comparative studies for Shao-Zhu-Su?s rock rheological model. , 2016, 35(2): 242-249.

链接本文:

http://www.rockmech.org/CN/Y2016/V35/I2/242

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