单轴压缩岩样轴向回跳及侧向回跳理论研究

Theoretical relation between snap-back of axial stress-strain curve and snap-back of axial stress-lateral strain curve for rock specimen in uniaxial compression

研究了单轴压缩条件下轴向回跳及侧向回跳之间的关系。在应变软化阶段,试样的弹性轴向应变及弹性侧向轴向应变由虎克定律确定;试样的轴向塑性应变及侧向塑性轴向应变由梯度塑性理论确定,它们与应力水平、剪切带倾角及宽度、软化模量及试样的尺寸有关。根据轴向应力-应变曲线及侧向应力-应变曲线软化段斜率的正负,得到了轴向回跳及侧向回跳的条件。轴向回跳的原因是轴向弹性应变的恢复快于轴向塑性应变的增加。侧向回跳的原因是侧向弹性应变的恢复快于侧向塑性应变的增加。当剪切带倾角的正切小于泊松比与试样宽高比之积时,若侧向变形发生回跳,则轴向变形就发生回跳;反之,若轴向变形发生回跳,则侧向变形就发生回跳。对于常规岩样,若侧向发生回跳,则轴向必定是回跳的。在应变软化阶段,根据轴向应变及侧向应变是否发生回跳,轴向应变与侧向应变曲线被划分为4种类型:即轴向回跳及侧向回跳情形、轴向回跳及侧向回跳情形、轴向不回跳及侧向回跳情形及轴向回跳及侧向不回跳情形,并得到了各种类型的条件。

Relation between the snap-back （Class Ⅱ behavior in rock mechanics） of axial stress-axial strain curve of rock specimen in uniaxial compression subjected to shear failure in the form of a single shear band and the snap-back of axial stress-lateral strain curve was investigated analytically. In strain-softening stage beyond the peak compressive stress, the axial and lateral elastic strains were determined by Hooke＇s law, while the axial and lateral plastic strains were derived by gradient-dependent plasticity where an characteristic length controls the thickness of shear band. The axial and lateral plastic strains are concerned with the compressive stress level, the inclination angle and the thickness of shear band, the softening modulus, and the geometrical size of rock specimen. According to the signs of the post-peak slopes of axial stress-axial strain curve and axial stress-lateral strain curve, the conditions of axial and lateral snap-backs were proposed. The reason for axial snap-back is that the recovery of axial elastic strain is faster than the increase of axial plastic strain. Similarly, the reason for lateral snap-back is that the recovery of lateral elastic strain is faster than the increase of lateral plastic strain. If the tangent of the inclination angle of shear band is less than Poisson＇s ratio multiplied by the ratio of width to height of the specimen, then the snap-back in axial direction occurs once the lateral snap-back takes place. Otherwise, the lateral snap-back occurs when the axial snap-back takes place. For the commonly used rock specimen （height/width is about 2） in laboratory, the lateral snap-back leads to the axial snap-back. In the strain-softening stage, the axial strain-lateral strain curve can be classified into four categories： axial snap-back and lateral snap-back, axial snap-through （Class I behavior） and lateral snap-through, axial snap-back and lateral snap-through, and axial snap-through and lateral snap-back. Conditions of these four kinds of cases were presented.