基于广义位势理论的土的数值弹塑性模型及其初步应用研究

A numerical elastoplastic model based on generalized potential theory and its preliminary application

广义位势理论从数学角度出发建立土的本构模型,可克服传统本构理论的不足,而又同时包含了传统理论作为其特例,从而为土的本构模型研究提供新的和适用性更广的理论。以广义虎克定律为基础的邓肯-张模型以其简单方便、参数确定容易且有明确的物理意义而得到广泛的应用,而其最大缺点则是不能反映土的剪胀性;此外,邓肯-张模型采用双曲线函数拟合试验曲线也有一定的局限性。为保留其参数确定简便的优点,并弥补其不足,基于广义位势理论建立了数值弹塑性模型。该模型保留了邓肯-张模型在参数确定方面的简单性,同时由于采用了广义位势理论来建模,不再受广义虎克定律的限制,因而可弥补邓肯-张模型在反映土体剪胀性方面的缺陷。此外,该模型采用数值手段来表示试验曲线的建模方法,可以克服邓肯-张模型采用双曲线函数表示试验曲线方法的局限性,具有更为广泛的适应性。通过对一碎石桩复合土体三轴试验结果的数值模拟表明:基于广义位势理论的数值弹塑性模型计算与试验结果吻合良好,且在反映碎石的剪胀特性方面优于邓肯-张模型,从而初步证明了该模型的合理性及优越性。

A constitutive model of soil based on the generalized potential theory is rigorously developed, so that the deficiencies of traditional constitutive theories can be overcome, while the traditional theories can be regarded as its special cases. Hence the generalized potential theory provides an alternative approach to developing the constitutive model of soils. Duncan-Chang model based on the generalized Hooke＇s law is one of the most widely used models at present, in which the constitutive parameters can be determined conveniently and have clear physical meanings. However, this model cannot describe well the soil dilatancy, which is the most undesirable feature of Duncan-Chang model. In addition, the hyperbolic hypothesis is adopted to fit the experimental results using Duncan-Chang model, which is also one of the disadvantages of the model. To utilize the advantages of Duncan-Chang model and avoid its disadvantages, a numerical elastoplastic model based on the generalized potential theory is developed, in which the parameters can be determined as conveniently as those of Duncan-Chang model. Meanwhile, the proposed model is not subjected to the limitation of the generalized Hooke＇s law, and the soil dilatancy of soils can be well described. In addition, because the proposed model adopt a numerical method to fit the experimental results, it excludes the disadvantage of hyperbola hypothesis in Duncan-Chang model, resulting in a more adaptability of the proposed model. The performance of the proposed model is illustrated through simulating the triaxial testing results, showing that the proposed model yields good results, which describes well the soil dilatancy.