考虑理想弹塑性弯扭-Mohr-Coulomb-最大拉应力破坏准则,以及拉伸失效、压剪失效、转动屈服和扭转屈服4种失效模式,提出一种新的离散元弹塑性本构模型。该模型植入二次开发的三维颗粒流程序,通过数值试验研究宏细观参数关系,模拟Lac du Bonnet(LDB)花岗岩试样压剪和拉伸强度试验。研究表明:颗粒转动弹塑性弯扭矩对宏观内摩擦角和黏聚力具有显著影响;宏观黏聚力随细观黏聚力和屈服弯扭矩增加而趋于恒定;宏观内摩擦角随屈服弯扭矩和细观摩擦系数增加而增加;岩石宏观单轴抗拉强度随细观极限拉应力的增加而趋于恒定;宏观弹性模量和泊松比主要受细观弹性模量和刚度比影响。弹塑性颗粒流本构模型模拟的LDB花岗岩的强度参数和变形参数,以及压拉强度比和裂缝分布与室内试验结果吻合较好。LDB花岗岩单轴压剪模拟试验在达到峰值应力前,试样内部裂缝以细观拉伸裂缝为主,从试样端部向中部发展成近似X状;在接近或超过峰值应力后,试样内部开始出现压剪裂缝、转动屈服裂缝和扭转屈服裂缝,从试样一端向另一端发展成单斜状,其倾角与宏观破坏倾角接近,发展成宏观压剪破坏面,从而揭示了宏观裂缝形成的细观机理。
Abstract
A novel constitutive model was presented in line with the ideal elasto-plastic rolling and twisting moment and the Mohr-Coulomb-maximum-tensile failure criterion. The model could reflect four failure modes: tensile failure, compression-shear failure, rolling yielding, and twisting yielding. The model was incorporated into PFC3D with secondary development to set up the equations of macro-and-mesoscopic parameters and to simulate the mesoscopic failure mechanism of Lac du Bonnet (LDB) granite in compression-shear test and tensile test. According to the results, the significant effects of particle rolling and twisting on the macro-cohesion and frictional angle of rock were observed. The macro-cohesion also increased to a constant value with the growth of mesoscopic ultimate moment and torque and meso-cohesion. The macroscopic internal friction angle increased with the increasing of mesoscopic ultimate moment and torque and mesoscopic frictional coefficient. The macroscopic tensile strength increased with the increase of microscopic tensile stress until reaching a constant value. The macroscopic elastic modulus and the Poisson’s ratio were mainly determined by mesoscopic elastic modulus of particles and their stiffness ratio. The numerical simulation result of LDB granite by the presented model was well consistent with indoor experimental results in terms of strength and deformation behaviors, compressive strength to tensile strength ratio as well as crack distribution. Before reaching to the peak value, the mesoscopic tensile cracks were dominant cracks in the LDB granite extending in an “X” shape from the end of specimen towards the middle of specimen under the condition of vertical-low pressure. Under the conditions of vertical pressure close to the peak value or exceeding the peak value, meso-cracks of compression-shear, and meso-failure of rolling and twisting were found. The cracks developed from the bottom to the top of specimen, with dip angles equal to the macro failure angle of LDB granite. And that reveals the mesoscopic mechanism of macro-cracks of LDB granite.
关键词
Lac du Bonnet花岗岩 /
理想弹塑性弯扭 /
Mohr-Coulomb-最大拉应力准则 /
离散元弹塑性本构模型 /
三维颗粒流 /
宏细观参数 /
裂缝
Key words
Lac du Bonnet granite /
ideal elasto-plastic rolling-twisting model /
Mohr-Coulomb maximum-tensile criterion /
discrete element /
3D particle flow /
macroscopic and mesoscopic parameters /
cracks
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基金
国家自然科学基金项目(51508579,51674287);中南大学研究生科研创新项目(2018zzts729)
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