统一弹塑性本构模型在FLAC^(3D)中的计算格式

Numerical format of elastoplastic constitutive model based on the unified strength theory in FLAC^(3D)

统一强度理论是一个有着坚实理论基础、可表达各种岩土材料强度特性且被广泛应用的新的强度理论。FLAC3D是一个具有强大的计算分析功能且专门针对岩土工程问题开发并被广泛应用的数值分析软件。若能将二者结合起来,无疑会大大促进岩土工程领域相关问题的解决。针对这一问题,研究了统一弹塑性本构模型在有限差分方法中应用的基本理论格式。根据FLAC3D软件中UDM接口计算格式的要求,将统一强度理论引入其中,详细推导了统一弹塑性本构模型在FLAC3D软件中应用的计算公式。由于统一屈服面在应力空间内由12个面组成,在应力角为[0,π/3]的范围内,统一屈服面由两个相交面组成,为计算塑性因子及处理计算中应力超出屈服面的应力调整问题,利用应力角分析了应力空间的分区,推导了区域分界面的公式。最后,编制了相应的UDM接口程序对一圆形隧洞进行了弹塑性分析,对比了计算结果与解析解,结果很好地验证了此计算格式及相应接口程序的正确性。统一强度理论和FLAC3D软件的结合,将使二者的优点得以充分发挥,以解决更多的岩土工程问题。

The unified strength theory is a new theory system which can almost describe the strength characters of most geomaterials and has been applied widely. And FLAC^3D is an excellent geotechnical program. If the former can be integrated in the later, many complex problems in engineering will be settled well. So according to this problem, the numerical scheme of elastoplastic unified constitutive model in FLAC^3D was studied. And the numerical format of the elastoplastic constitutive model based on the unified strength theory was derived. The corresponding UDM interface codes were programmed. Finally, a circle tunnel case is analyzed using this program. The corresponding simulated results are presented and compared with the analytic solution. The comparison expresses a good agreement with the analytic solution and verifies the validity of the numerical scheme and the codes. The merits of the unified strength theory and the FLAC^3D program will be utilized well in geo-engineering after their combination.