王延宁, 张强, 李子仪, 等. 考虑弹塑性耦合效应的应变软化模型[J]. 煤炭学报, 2020, 45(12): 4037-4051.
引用本文: 王延宁, 张强, 李子仪, 等. 考虑弹塑性耦合效应的应变软化模型[J]. 煤炭学报, 2020, 45(12): 4037-4051.
WANG Yanning, ZHANG Qiang, LI Ziyi, et al. Strain softening model considering elastic-plastic coupling effect[J]. Journal of China Coal Society, 2020, 45(12): 4037-4051.
Citation: WANG Yanning, ZHANG Qiang, LI Ziyi, et al. Strain softening model considering elastic-plastic coupling effect[J]. Journal of China Coal Society, 2020, 45(12): 4037-4051.

考虑弹塑性耦合效应的应变软化模型

Strain softening model considering elastic-plastic coupling effect

  • 摘要: 深部岩体峰后呈现应变软化特征、弹塑性耦合特征和塑性变形破坏等非线性特征。充分探明开挖工作面的岩体力学特征有助于预测围岩变形或破坏区域的形状,为后期的合理支护设计提供科学依据。然而,当前广泛使用的一维模型(例如Mohr-Coulomb和应变软化模型)无法很好的反映深部地下工程在高围压下的岩石变形特征。对此,通过三轴循环加卸载试验,获得各级围压下不同塑性累积阶段的岩石力学参数,进而研究塑性变形与围压二者综合影响下的围岩受力变形特征。通过构建应力-塑性剪切应变二维函数针对性描述其上述特征,建立了考虑围压影响的黏聚力、内摩擦角、弹性模量和剪胀角随塑性变形变化的数学模型。研究表明:黏聚力和内摩擦角可用指数函数及线函数分别描述其塑性变形和围压的相互关系,由此构建的二维函数,拟合精度可达95%;弹性模量随着围压增大而增大,可用负指数函数来描述,随着塑性变形而衰减,可用线函数来描述;剪胀角随着围压线性衰减,随着塑性变形先增大后减小,可用差值型指数函数描述;通过FLAC3D的二次开发,将该应变软化模型用于模拟岩石三轴压缩试验,证实模型设置准确合理。针对深部圆形硐室开挖,所提出的本构模型与应变软化模型和摩尔库仑模型相比,随着塑性区扩展,对围岩应力分布影响主要体现在切向应力峰值进一步向深部围岩转移,且径向应力随之降低;对位移场分布而言,随着塑性区扩展,所提本构模型得到的位移解逐步增长,符合岩体破裂后位移随损伤范围而增大的特点。

     

    Abstract: There are some nonlinear characteristics presented for the post-peak deep rock mass,such as strain softening,elastoplastic coupling and plastic deformation failure.A better understanding of rock mass mechanical deformation characteristics around the excavation helps us to predict the displacements or the shape of failed zone,and subsequently assist the design of proper support systems.However,the use of one-dimensional model,such as Mohr-Coulomb Model or Strain-Softening Model could not simulate the rock deformation under high confining pressure in deep underground engineering.Therefore,through triaxial cyclic loading-unloading test,the mechanical parameters of rock at the different stages of plastic accumulation under different confining pressures are obtained,the rock characteristics deformation under the combined influence of plastic deformation and confining pressure are studied.By constructing the two-dimensional function of stress-plastic shear strain and confining stress to describe the above characteristics,a mathematical model of cohesion,friction angle,elastic modulus and dilatancy angle with plastic deformation considering the influence of confining pressure is established.The results show that the cohesive and friction angle can be described by the exponential function and the line function respectively with the plastic deformation and confining pressure.The two-dimensional function constructed by this method can achieve a fitting accuracy of ninety-five percent.The elastic modulus increases with confining pressure which can be described by negative exponential function,whereas decreases with plastic deformation which can be described by linear function.The dilation angle linearly decreases with confining pressure and decreases at first then increases with plastic deformation,which can be described by the difference between two exponential functions.Furthermore,the model is introduced to the simulation of the rock triaxial compression test by FLAC3D,the results confirm the accuracy and rationality of the proposed model.Compared with the strain softening model (S-S Model) and the Mole-Coulomb model (M-C Model),the proposed model has a remarkable impact on the stress distribution of surrounding rocks as the plastic zone expands in the deep circular cavern excavation,which is mainly reflected in that the tangential stress peak is further transferred to the deep surrounding rocks,and the radial stress decreases accordingly.For the displacement field distribution,with the expansion of plastic zone,the displacement obtained by the proposed model gradually increases,which is consistent with the characteristic that the displacement of rock mass increases with the increase of damage range after fracture.

     

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