A whole process damage constitutive model for layered sandstone under uniaxial compression based on Logistic function

基于Logistic函数的层状砂岩单轴压缩全过程损伤本构模型

Bedding structural planes significantly influence the mechanical properties and stability of engineering rock masses.This study conducts uniaxial compression tests on layered sandstone with various bedding angles(0°,15°,30°,45°,60°,75°and 90°)to explore the impact of bedding angle on the deformational mechanical response,failure mode,and damage evolution processes of rocks.It develops a damage model based on the Logistic equation derived from the modulus’s degradation considering the combined effect of the sandstone bedding dip angle and load.This model is employed to study the damage accumulation state and its evolution within the layered rock mass.This research also introduces a piecewise constitutive model that considers the initial compaction characteristics to simulate the whole deformation process of layered sandstone under uniaxial compression.The results revealed that as the bedding angle increases from 0°to 90°,the uniaxial compressive strength and elastic modulus of layered sandstone significantly decrease,slightly increase,and then decline again.The corresponding failure modes transition from splitting tensile failure to slipping shear failure and back to splitting tensile failure.As indicated by the modulus’s degradation,the damage characteristics can be categorized into four stages:initial no damage,damage initiation,damage acceleration,and damage deceleration termination.The theoretical damage model based on the Logistic equation effectively simulates and predicts the entire damage evolution process.Moreover,the theoretical constitutive model curves closely align with the actual stress−strain curves of layered sandstone under uniaxial compression.The introduced constitutive model is concise,with fewer parameters,a straightforward parameter determination process,and a clear physical interpretation.This study offers valuable insights into the theory of layered rock mechanics and holds implications for ensuring the safety of rock engineering.

层理结构面影响工程岩体力学性质和稳定性。为研究层理倾角对岩石变形力学特性、破坏模式和损伤演化过程的影响,对7种不同层理倾角的层状砂岩开展单轴压缩试验。综合考虑砂岩层理倾角效应与荷载耦合作用,建立基于弹性模量衰减法的Logistic损伤演化模型,并结合损伤力学理论与有效介质理论引入考虑初始压密非线性变形特征的分段本构模型。研究结果表明:随着层理倾角从0°增加到90°,砂岩峰值强度和弹性模量均呈现先大幅降低、后增加再降低的趋势,对应破坏模式由劈裂型张拉破坏变为剪切滑移破坏,再变为劈裂张拉破坏;不同层理倾角砂岩均大致经历了初始损伤保持、损伤逐渐开始、损伤加速增长及损伤减速终止四个阶段;基于Logistic函数建立的理论损伤模型能够很好地模拟和预测层状砂岩损伤演化全过程;理论本构模型曲线与试验数据吻合度高,能够较好地模拟层状砂岩单轴压缩变形破坏全过程;本文所建模型形式简洁,参数较少,参数确定过程简单且物理意义明确。研究成果可为层状岩石力学理论和保证岩石工程安全提供参考。