深部硬岩脆-延性转化行为的细观损伤模型

Micromechanical Damage Model for the Brittle-Ductile Transition in Deep Hard Rock

既有试验研究表明,在压缩荷载作用下,围压对低孔隙率硬岩的强度、破坏模式、剪胀性等具有重要影响。在围压不断增大的条件下,硬岩的破坏特性将呈现由脆性向延性转变的趋势。本文基于细观力学方法分析硬岩的脆-延性破坏机理,探究脆-延性转化过程中非弹性变形、损伤与围压的定量关系,继而构建细观损伤力学模型以描述深部硬岩在不同压缩荷载作用下的脆-延性转化力学行为。为了验证所构建模型的合理性和有效性,通过UMAT子程序将其嵌入有限元软件Abaqus模拟低孔隙率砂岩(围压10~120 MPa)和Tavel石灰岩(围压10~150 MPa)在常规三轴加载下的力学行为。对比发现,数值模拟结果与试验数据具有较好的一致性,说明细观损伤力学模型能够较好地捕捉硬岩随着围压增加表现出的从脆性到延性转化的力学特性,也初步表明基于细观力学的分析方法可以为解译深部岩石的力学行为提供理论支撑。

Objective This comprehensive exploration delves into the intricate domain of confining pressure’s influence on the mechanical complexities found in low-porosity,resilient rocks under compressive loading.It seeks to elucidate the transition from brittleness to ductility induced by in-creasing confining pressure.Additionally,it sheds light on the variations in strength,failure modes,and shear dilation across a wide range of con-fining pressure conditions in these rocks.As confining pressure increases,a transformative process unfolds,leading to a dramatic shift in the fail-ure characteristics of these rocks—From the fragility of brittleness to the flexible embrace of ductility.The paper aims to unravel the intricate mechanism of the brittle-ductile transition by delving into the micro-mechanical landscape.This detailed expedition meticulously charts the nu-anced relationship among non-elastic deformation,damage evolution,and the pervasive influence of confining pressure.Arising from the intrica-cies of our micro-mechanical analysis is a skillfully crafted micro-damage mechanics model,serving as a guide through the challenging terrain of hard rocks under compressive loading.Methods In our meticulous mechanical scrutiny,we intentionally choose the representative elementary volume(REV),characterized by the volu-minousΩand the peripheral boundaryΩ,as the focal point of our investigative efforts.The articulation of micromechanical constitutive equa-tions is meticulously forged by the nuanced contemplation of microstructural idiosyncrasies and indigenous mechanical properties.The distinct-ive elementary volume emerges as an amalgamation of an isotropic rock matrix and a profusion of penny-shaped microcracks.Its examination is steeped in the resolution of the Eshelby inclusion problem,unfurling the tapestry of the aforementioned heterogeneity.The formulation of mi-cromechanical constitutive equations is carefully crafted through thoughtful consideration of microstructural idiosyncrasies and inherent mechan-ical properties.In conceptualizing a micromechanical damage paradigm,we use a scalar damage variable intricately linked to crack density,serving as a clear descriptor of the wide spectrum encompassing material breakdown.The nonlinear coordination of mechanical behavior in rock materials under compressive stress orchestrates a ballet involving two antagonistic energy dissipation mechanisms:Frictional slip and crack propagation.Frictional slip upon microcrack canvases performs a graceful mechanism marked by voluminous expansion.In contrast,the cres-cendo of sealed crack expansion weakens the material,serving as a prelude to the emergence of damage.Within the domain of the free energy function,this manuscript orchestrates the derivation of a nuanced dance performed by the local stress field on the crack surface.The detailed de-rivation establishes the foundation for a sophisticated multiscale bridge,smoothly transitioning from microscopic stress nuances on the crack sur-face to the comprehensive realm of macroscopic material stress.The evolution of the frictional slip criterion,once confined to the micro-mechan-ic crack surface,transforms into the realm of a macroscopic strength criterion.The melodious findings from the research chorale reveal a harmoni-ous correlation,a sonorous concord,between non-elastic strains reaching the stress peak and the encompassing embrace of confining pressure.Thus,within a symphony of formulation derivations,it crystallizes that the pivotal nexus of critical damage shows a positive correlation with the surrounding cocoon of confining pressure.We present a sonnet in the form of a power-law function,meticulously crafted upon the scaffold of ex-isting research,cohesively narrating the quantitative connection between the critical damage threshold and the unwavering influence of confining pressure during the metamorphosis of material breakdown,transcending from the realm of fragility to the dominion of ductility.This model stands as a testament to the fusion of scientific inquiry and engineering ingenuity,a synthesis that tries to encapsulate the dynamic essence of mechanic-al responses within the core of unyielding geological formations.Results and Discussions To scrutinize and affirm the validity of our conceptual masterpiece,we employ robust numerical simulations using the renowned Abaqus software,complemented by the sophisticated UMAT subroutine.The conventional triaxial compressive mechanical behavior of low-porosity sandstone(10~120 MPa)and limestone(10~150 MPa)is simulated under various confining pressure conditions.It is found that the numerical simulation results are consistent with experimental data,indicating that the micro-damage mechanics model can effectively capture the mechanical characteristics of the transition from brittleness to ductility of hard rocks as confining pressure increases.This also preliminarily suggests that the analysis method based on micro-mechanics may provide theoretical support for the mechanical behavior of deep-seated rocks.Conclusions This opulent tapestry of exploration,a magnum opus,reveals the evolution laws of damage during the transition process from brittle-ness to ductility in the failure mode of hard rocks within constantly changing pressure conditions.The research carries positive implications for the theoretical advancement in rock mechanics and offers valuable insights for practical applications in rock engineering.Deepening our compre-hension of rock mechanical behavior is expected to provide more accurate rock mechanics parameters,improving the precision and reliability of geotechnical engineering design.The application of micro-damage mechanics models in real engineering projects will better guide the design and construction of rock engineering.