The modified mesoscopic stochastic fracture model incorporating the random field of Young's modulus for the uniaxial constitutive law of concrete考虑混凝土单轴本构关系 Young 氏模量随机场的修正细观随机断裂模型
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Liu YY, Chen JB, Li J, 2024. The modified mesoscopic stochastic fracture model incorporating the random field of Young's modulus for the uniaxial constitutive law of concrete. Probabilistic Engineering Mechanics, 75: 103585.DOI: 10.1016/j.probengmech.2024.103585
摘要 | Abstract
混凝土是一种多相复合材料，在不同情形下表现出非线性和随机性。细观随机断裂模型 (mesoscopic stochastic fracture model, MSFM) 用于刻划混凝土的本构行为。然而，它在量化上升段应力—应变曲线随机性方面仍不够准确，可能会显著低估强度的变异性。为了解决上述缺陷，本文提出了细观随机断裂模型的两类修正。在修正模型中，除细观尺度断裂应变的随机场外，细观弹簧的 Young 氏模量也分别由单一随机变量或随机场来量化。推导了修正模型中混凝土单轴受压应力—应变曲线的均值和标准差数学表达。此外，基于不同强度等级混凝土的完整受压应力—应变关系试验数据，结合遗传算法和降维算法，确定了两类修正细观随机断裂模型的参数。结果表明，涉及细观尺度断裂应变和细观 Young 氏模量随机性的修正模型在捕捉混凝土强度变异性和上升段应力—应变关系标准差方面，精度比现有细观随机断裂模型大大提高。关键词: 随机损伤力学, 混凝土本构模型, 细观尺度 Young 氏模量, 随机场, 参数识别Concrete is a multi-phase composite material that exhibits nonlinear and random characteristics in various contexts. The mesoscopic stochastic fracture model (MSFM) was developed to capture the constitutive behaviors of concrete. However, it is still not accurate enough to quantify the randomness of stress-strain curves in the ascending phase, and the variability of the strength might be considerably underestimated. In this paper, to remedy the above deficiencies, two alternative modifications to the MSFM are proposed. In the modified models, in addition to the random field of mesoscale fracture strain, Young's modulus of meso-springs is also quantified by a single random variable or a random field, respectively. The mathematical expressions for the mean and standard deviation of the uni-axial compressive stress-strain curves of concrete in the modified models are derived. Furthermore, based on the data from tested complete compressive stress-strain relationships of concrete with different strength grades, the parameters in the two modified MSFMs are identified by combining the genetic algorithm and a dimension-reduction algorithm. The results show that the accuracy of the modified models involving the randomness from both the mesoscale fracture strain and the mesoscale Young's modulus is greatly improved compared to the existing MSFM in capturing both the variability of concrete strength and the standard deviation in the ascending phase of the stress-strain relationship of concrete.Keywords: Stochastic damage mechanics; Concrete constitutive model; Mesoscale Young's modulus; Random field; Parameter identification创新点 | Highlights
- 将细观尺度 Young 氏模量随机性纳入细观随机断裂模型
在量化混凝土强度变异性方面，精度大幅提高
- Two modifications to the mesoscopic stochastic fracture model (MSFM) for concrete
- Incorporating the randomness of mesoscale Young's modulus into MSFM
- Expressions of the mean and standard deviation of stress-strain curve of concrete
- The accuracy of quantifying the variability of concrete strength greatly improved
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Fig. 1. Mesoscopic stochastic fracture model
Fig. 2. Mesoscopic stochastic fracture model
Fig. 3. Stress-strain responses of discrete bundle and continuum bundle
图 4: 两类修正细观随机断裂模型的参数识别流程图Fig. 4. Flow chart for parameter identification of MSFM-M1 and MSFM-M2
Fig. 5. Histograms of Young's modulus
Fig. 6. Comparison of standard deviation of stress-strain curves
Fig. 7. Comparison of standard deviation of stress-strain curves of data subset
Fig. 8. Comparison of the area covered by the mean plus or minus two times standard deviation
Fig. 9. Comparison of errors between three models and experimental results
图 10: 基于陶金聚等人数据的不同分布类型概率密度函数Fig. 10. PDFs of different distribution types based on data from Tao et al. (2021)
图 11: 基于李杰等人数据的不同分布类型概率密度函数Fig. 11. PDFs of different distribution types based on data from Li et al. (2021)
图 12: 基于晏小欢等人 C30 数据的不同分布类型概率密度函数Fig. 12. PDFs of different distribution types based on data from Yan et al. (2015) - C30
图 13: 基于晏小欢等人 C40 数据的不同分布类型概率密度函数Fig. 13. PDFs of different distribution types based on data from Yan et al. (2015) - C40
图 14: 基于晏小欢等人 C50 数据的不同分布类型概率密度函数Fig. 14. PDFs of different distribution types based on data from Yan et al. (2015) - C50
图 15: 基于陈建兵等人数据的不同分布类型概率密度函数Fig. 15. PDFs of different distribution types based on data from of Chen et al. (2018)
图 16: 基于陶金聚等人数据的不同应变处应力概率密度函数Fig. 16. PDFs of stress at corresponding strains based on data from Tao et al. (2021)
图 17: 基于李杰等人数据的不同应变处应力概率密度函数Fig. 17. PDFs of stress at corresponding strains based on data from Li et al. (2021)
图 18: 基于晏小欢等人 C30 数据的不同应变处应力概率密度函数Fig. 18. PDFs of stress at corresponding strains based on data from Yan et al. (2015) - C30
图 19: 基于晏小欢等人 C40 数据的不同应变处应力概率密度函数Fig. 19. PDFs of stress at corresponding strains based on data from Yan et al. (2015) - C40
图 20: 基于晏小欢等人 C50 数据的不同应变处应力概率密度函数Fig. 20. PDFs of stress at corresponding strains based on data from Yan et al. (2015) - C50
图 21: 基于陈建兵等人数据的不同应变处应力概率密度函数Fig. 21. PDFs of stress at corresponding strains based on data from Chen et al. (2018)
作者信息 | Authors
同济大学 (Tongji University) 土木工程学院
陈建兵 Jian-Bing Chen, 通讯作者 (Corresp.) 同济大学 (Tongji University) 土木工程学院Email: chenjb@tongji.edu.cn
中国科学院院士
同济大学 (Tongji University) 土木工程学院
律梦泽 M.Z. Lyu | 编辑 (Ed)
P.D. Spanos | 审校 (Rev)
陈建兵 J.B. Chen | 审校 (Rev)
彭勇波 Y.B. Peng | 审校 (Rev)
