Strain softening damage constitutive model and its verification for brittle rocks based on Logistic distribution
GUO Yunpeng1, 2, LIU Dongqiao1, 2, YANG Shengkai3, WANG Yang4, LI Jieyu5, LING Kai1, 2
(1. State Key Laboratory for Tunnel Engineering, China University of Mining and Technology (Beijing), Beijing 100083, China;
2. School of Mechanics and Civil Engineering, China University of Mining and Technology (Beijing), Beijing 100083, China;
3. School of Science, China University of Mining and Technology (Beijing), Beijing 100083, China; 4. Institute of Geomechanics,
Chinese Academy of Geological Sciences, Beijing 100081, China; 5. College of Energy Engineering, Xi'an University
of Science and Technology, Xi'an, Shaanxi 710054, China)
Abstract：The statistical damage constitutive model of rocks and the evaluation methods for brittleness are prominent research topics in the field of rock mechanics. This paper analyzes the nonlinear deformation characteristics during the initial compaction stage of rocks, identifying the full crack compaction point as the critical juncture. First, a constitutive model for the compaction stage is developed based on the changes in tangent modulus and logistic distribution characteristics. Subsequently, drawing on the principles of continuous damage mechanics and statistical damage, we assume that the strength of microelements adheres to the logistic distribution and the Mohr-Coulomb criterion, thereby establishing a damage constitutive model that captures the deformation characteristics post-compaction. Furthermore, a novel brittleness evaluation index is proposed, reflecting the entire damage evolution characteristics. Finally, the proposed constitutive model and brittleness index are validated using uniaxial and conventional triaxial compression test data from glutenite, granodiorite, red sandstone, quartzite, marble, and Maharashtra sandstone. The findings indicate that: (1) The segmented constitutive model based on logistic distribution accurately simulates the complete stress-strain process of various rock types under uniaxial and conventional triaxial compression, effectively describing both peak strength and peak strain of the samples. (2) The speed of damage evolution is inversely proportional to confining pressures; thus, increasing confining pressure can suppress damage development, enhance ductility, and reduce brittleness. (3) The parameters m and f0 influence the degree and length of concavity on the compaction stage curve, while parameters M and F0 affect the degree of brittle failure and peak strength. Collectively, these four model parameters govern the deformation characteristics, strength properties, and brittleness of the rock, ultimately shaping the theoretical constitutive relation curve. (4) The brittleness evaluation index, which comprehensively considers the pre-peak damage degree, peak strain, and post-peak damage evolution speed of rocks, demonstrates rationality, and the feasibility of this new index is corroborated through experimental results across six rock types under varying confining pressures. This research offers valuable insights for constructing brittleness indexes grounded in the rock damage constitutive model, thereby enhancing the analysis and evaluation of rock brittleness.
郭允朋1，2，刘冬桥1，2，杨圣开3，王 炀4，李杰宇5，凌 凯1，2. 基于Logistic分布的脆性岩石应变软化损伤本构模型及其验证[J]. 岩石力学与工程学报, 2025, 44(7): 1828-1845.
GUO Yunpeng1, 2, LIU Dongqiao1, 2, YANG Shengkai3, WANG Yang4, LI Jieyu5, LING Kai1, 2. Strain softening damage constitutive model and its verification for brittle rocks based on Logistic distribution. , 2025, 44(7): 1828-1845.
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2025, Vol. 44 
