基于摩尔-库伦准则的岩石材料加(卸)载分区破坏特征

Partition failure characteristics of rock material loading and unloading based on Mohr-Coulomb criterion

  • 摘要: 材料内一点的应力状态可以用摩尔圆来表示,而同一点的不同的应力状态可以用坐标系内应力圆的不断变化来表示,应力圆的变换主要可以分为“平移”、“翻转”、“半径扩大”“半径缩小”4种方式,这4种方式几乎包含了岩石材料的所有加(卸)载过程;加(卸)载速率可以用来表征不同应力状态间的转化的快慢程度,加(卸)载速率并不是单纯的单位时间的变化快慢,可以是单位空间尺度的变化,如单位长度、单位深度等;基于摩尔-库伦准则对岩石材料“双向受压”、“双向受拉”和“一拉一压”3种状态下的加卸载过程进行了分析,并获得了与之对应的临界破坏方程,在此基础上,通过引入时间加权平均加(卸)载速率,进一步分析了岩石材料破坏与时间加权平均加(卸)载速率之间的关系,并以时间加权平均加(卸)载速率为基础对岩石材料破坏与否进行了分区;采用FLAC3D对7种不同加载路径下常规三轴数值模拟实验,模拟所获得材料发生破坏时最大主应力峰值与理论计算结果吻合度高达98%;同时又进行7种轴向与径向加载速率之比、4种加载速率条件下常规三轴数值模拟试验。结果表明,只有当轴向和径向加载速率之比处于一定范围时,材料才会发生破坏,加载速率与材料破坏时最大主应力峰值正相关,与最大主应力和最小主应力之比负相关。

     

    Abstract: The stress state of a point in the material can be indicated by a Mohr circle and the different stress states of a point can be determined by charging stress circle under the coordinate system. The transformation of stress circle can be mainly divided into translation,flipping,radius expand and radius diminution. For rock material,these transforma- tions almost include all the processes of loading and unloading. Loading and unloading rate can be used to indicate the speed of transformation between different stress states,and it is not only the change of unit time,but also the change of unit space scale,such as unit length,unit depth,etc. Based on the Mohr-Coulomb criterion,this paper analyzed the rock materials loading and unloading processes under the states of compression-compression,tension-tension and ten- sion-compression,and found out the corresponding critical failure equation. On this basis, the relationship between time-weighted average loading and unloading rate of rock materials and the destruction level of rock materials were fur- ther obtained. According to the different time-weighted average loading and unloading rates,this paper also distinguish- ed whether the rock materials is destroyed. This research adopted the FLAC3D conventional three-axis numerical simu- lation experiments of seven different loading paths. The result showed when the material is damaged,the coincidence degree of the principle stress peak and the theoretical calculation result is as high as 98% . At the same time,this pa- per also conducted some simulation experiments under the conditions of seven kinds of axial and radial loading rates ratio and four types of loading rates. The test results indicated that the material is able to be destroyed when the ratio of the axial and radial loading rates reach within a certain range. The loading rate is positively correlated with the max- imum principal stress peak,which occurs at the state of material failure,and negatively correlated with the ratio of the maximum to the minimum principal stress.

     

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