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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。
The theory of generalized potential establishes the constitutive model of soil from the perspective of mathematics, which can overcome the shortcomings of the traditional constitutive theory and at the same time include the traditional theory as its special case, so as to provide a new and applicable method for the study of soil constitutive model Broad theory. The Duncan-Chang model based on generalized Hooke’s law is widely used for its simple and convenient, easy to determine parameters and clear physical meaning, and its biggest drawback is that it can not reflect the dilatancy of soil. In addition, Duncan- Zhang model hyperbolic function fitting test curve also has some limitations. In order to retain its parameters to determine the advantages of simplicity and to make up for the shortcomings, a numerical elastic-plastic model was established based on the generalized potential theory. The model retains the simplicity of the Duncan-Chang model in parameter determination. At the same time, because of the generalized potential theory, it is no longer limited by the generalized Hooke’s law, so it can make up for the Duncan- Defective flaws. In addition, the numerical method is used to represent the modeling method of the test curve, which can overcome the limitations of the Duncan-Chang model using the hyperbolic function to represent the test curve method, and has more extensive adaptability. The numerical simulation of the triaxial test results of composite soil with a gravel pile shows that the numerical elasto-plastic model based on the generalized potential theory is in good agreement with the experimental results and is superior to Duncan-Zhang in reflecting the dilatancy characteristics of the gravel Model, which proves the rationality and superiority of this model.