一种修正的Drucker-Prager屈服准则

A study of modified Drucker-Prager yield criterion

Drucker-Prager(以下简称D-P)屈服准则因其形式简单、物理意义明确而得到广泛的应用,然而经过多年的应用和研究,其缺点逐渐显现出来,如拉剪区偏大、不具有应力角效应等,针对这些不足,提出了修正的D-P屈服准则。在拉剪区用圆球面和横截面的组合方式代替原来的圆锥面,从而不改变D-P屈服准则压剪区的形式,在考虑岩石实际的拉伸强度的同时,也满足该屈服准则经过单轴抗拉强度点的条件;为考虑岩石在三轴压缩和三轴拉伸状态下不同的强度特性,即应力角效应,引入了一种角隅模型;为保证屈服准则始终通过岩石的单轴抗压强度点,建议了一种材料参数k值的取值方法。为验证屈服准则修正后的适用性和正确性,将修正屈服准则与真三轴试验结果进行了拟合,同时与Mohr-Coulomb(以下简称M-C)准则进行对比,结果表明,修正屈服准则可以很好地描述试验现象,且比M-C准则更接近真实结果。

Drucker-Prager yield criterion is widely used in rock engineering with the benefits of its simple form and clear physical meaning. However, its drawbacks are gradually revealed after years of research and application, such as lacking the effect of stress angle and the oversized tensile-shear region. Therefore, we propose a modified Drucker-Prager yield criterion in this study. In compressive-shear region, the same form of Drucker-Prager yield criterion is reserved, but in tensile-shear region, the original conical surface is replaced by the combination of a spherical surface and a cross section. This method can not only consider the real tensile strength of rock, but also satisfy the condition that the yield criterion passes the point of uniaxial tensile strength. A corner model is introduced to describe different strength characteristics of rock under triaxial compression and triaxial tension. To satisfy the condition that the yield criterion goes through the point of uniaxial compressive strength, a new method for calculating the value of k is suggested. Then the calculated results of the yield criterion are further fitted with that of true triaxial tests to verify the applicability and accuracy of the modified yield criterion. By comparing the results of the modified criterion with that of Mohr-Coulomb criterion, it is shown that the modified yield criterion can describe experimental data well, which is more realistic than the later.