Analysis of Compressive Behaviors of Concrete Mesoscale Models Based on the SISSO Algorithm
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摘要: 混凝土在外载荷作用下的力学性能受细观组分特性影响，其典型非均质性使得传统实验或数值方法难以揭示细观结构对宏观力学性能的影响规律.为有效分析混凝土骨料-砂浆-孔隙三相细观模型在单轴压缩下的峰值应力，使用PYTHON和ABAQUS构建混凝土细观模型的二次开发框架，生成了包含不同骨料体积分数、孔隙率和受压峰值应力的模型数据集.基于固定描述符压缩筛选(sure independence screening and sparsifying operator, SISSO)的机器学习算法，结合K折交叉验证筛选最优物理描述符，给出了不同骨料体积分数与孔隙率对峰值应力的影响公式.该公式不仅可准确计算目标参数，还具备一定物理意义，能够清晰描述峰值应力的变化趋势.与传统机器学习算法相比，SISSO在保证精度的同时具有计算成本低、可解释性高的明显优势，克服了经典机器学习的“黑盒”局限性，为复合材料的多尺度力学分析提供了新方法.Abstract: The mechanical properties of concrete under external loads are influenced by its mesoscale components. Due to their heterogeneity, experimental and numerical methods struggle to reveal the impacts of mesoscale structures on the macroscopic mechanical behaviors of concrete. To effectively predict the peak stress of a 3-phase (aggregate, mortar and voids) mesoscale model of concrete under uniaxial compression, a framework for mesoscopic concrete was established with PYTHON and ABAQUS, to generate a dataset of models with varying aggregate volume fractions, porosities and peak compressive stresses. The sure independence screening and sparsifying operator (SISSO) machine learning algorithm, combined with the K-fold cross validation for hyperparameter optimization, was employed to derive a formula describing the effects of the aggregate volume fraction and the porosity on the peak stress. The formula accurately describes the peak stress variation trend, thereby achieving precise predictions and offering physical interpretability. Compared to traditional machine learning algorithms, the SISSO demonstrates advantages of maintaining precision while reducing computation costs and improving interpretability. It overcomes the "black box" limitations of conventional methods, offering new insights for multiscale mechanical analyses of composite materials.
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图 1 不同类型的混凝土细观形态
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 1. Different types of meso-scale concrete
图 5 不同特征复杂度和维数下SISSO模型的预测性能
Figure 5. Performances of the SISSO model with different values of feature complexity and dimension
图 7 不同特征复杂度下SISSO模型的预测表现
Figure 7. SISSO model prediction performances under different-feature complexities
图 9 不同算法在测试集上的R2与计算时间
Figure 9. R2 values and computation durations of different algorithms on the test set
表 1 骨料和砂浆的力学参量
Table 1. Mechanical parameters of aggregate and mortar
compressive strength/MPa density /(kg·cm-3) dilatancy angle/(°) elasticity modulus/GPa eccentricity/(%) stress ratio Poisson’s ratio aggregate - 2.67 - 43 - - 0.23 mortar 35 2.40 38 25 0.1 1.16 0.2 
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表 2 文献中混凝土单轴压缩的试验参数[36]
Table 2. Experimental parameters for uniaxial compression tests on concrete[36]
parameter symbol/unit value concrete compressive strength FC/MPa 35.46 water-cement ratio w/c 0.37 coarse aggregate particle size d/mm 5~20 specimen size l/mm 150×150×300 cement density ρc/(g·cm-3) 3.1 coarse aggregate density ρm/(g·cm-3) 2.71 mortar elasticity modulus Em/GPa 23 concrete elasticity modulus Ec/GPa 32.4 mortar Poisson’s ratio υm 0.2 coarse aggregate Poisson’s ratio υc 0.2
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表 3 特征复杂度为2时10折验证识别的描述符
Table 3. Descriptors identified through 10-fold cross validation with 2-feature complexity
frequency 1st descriptor 2nd descriptor 3rd descriptor 4 Pp+PaPp e2Pa e－Pp2 1 e-3Pp Pa+Pp2 $ \frac{P_{\mathrm{p}}^2}{P_{\mathrm{a}}}$ 1 Pa+Pp2 2Pa+Pp $\frac{P_{\mathrm{p}}^2}{P_{\mathrm{a}}} $ 1 Pp+PaPp PaePa e－Pp2 1 Pp+PaPp Pp3-Pa Pp2-Pa 1 Pp+PaPp Pa3/2 e－Pp2 1 $\frac{P_{\mathrm{p}}}{\mathrm{e}^{p_{\mathrm{a}}}} $ Pa+Pp2 2Pa+Pp
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表 4 特征复杂度为3时10折验证识别的描述符
Table 4. Descriptors identified through 10-fold cross validation with 3-feature complexity
frequency 1st descriptor 2nd descriptor 3rd descriptor 9 $\frac{P_{\mathrm{a}} P_{\mathrm{p}}}{P_{\mathrm{a}}+P_{\mathrm{p}}}$ Pa+Pp2 (Pa+Pp)Pp2 1 $\frac{P_{\mathrm{a}} P_{\mathrm{p}}}{P_{\mathrm{a}}+P_{\mathrm{p}}} $ Pa+Pp2 PaPp2
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表 5 式(6)中的参数项(单位: MPa)
Table 5. The parameters in formula (6) (unit: MPa)
C1 C2 C3 b -283.373 15.245 738.123 32.558
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表 6 计算环境及软硬件参数
Table 6. Computational environment and hardware/software parameters
parameter value central processing unit Intel(R) Core(TM) i7-9750H CPU @ 2.60 GHz memory RAM 8 GB graphics card NIVIDA GeForce GTX 1650 system Windows 10 environment PYTHON 3.8 Scikit-learn 0.23.2 NUMPY 1.22.4
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