基于等效时间的双屈服面三维流变模型
Three-dimensional rheological model for double-yield surface based on equivalent time
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摘要: 为了同时描述土体剪缩剪胀及流变特性,运用Yin-Graham等效时间法建立了双屈服面三维流变模型。首先,以Yin-Graham三维流变方程作为反映剪缩机制的第一屈服面流变方程;其次,以Matsuoka-Nakai屈服准则作为反映剪胀机制的第二屈服面,以黏塑性功为硬化参数,采用非相关联流动法则,借鉴Mesri建模思路构建应力-黏塑性功-时间关系,利用等效时间法得到应力-黏塑性功-黏塑性功速率关系式,借助Perzyna过应力理论建立第二屈服面三维流变方程;再次,按照双屈服面模型理论将以上两个流变方程结合起来,提出一个基于等效时间的双屈服面三维流变模型,并利用经典的四阶Rung-Kutta方法编制差分计算程序,获得流变模型的数值解答;最后,利用加拿大膨润土及香港重塑海相沉积土三轴固结不排水流变试验将预测值与实测值进行对比,以验证该模型在流变试验中的适用性。结果表明:建立的流变模型可以较好地模拟不排水流变试验多级加载和单级加载发展过程以及土体剪缩剪胀特性。Abstract: In order to describe shear contractibility, dilatancy and rheological properties of soils, Yin-Graham’s equivalent time method is used to derive a three-dimensional rheological model for double-yield surface. Firstly, Yin-Graham’s three-dimensional rheological equation is used as the first yield surface rheological equation reflecting the shear-contraction mechanism. Secondly, Matsuoka-Nakai yield criterion is used as the second yield surface reflecting the dilatancy mechanism, viscoplastic work is used as hardening parameter and the non-associated flow rule is adopted, the stress-viscoplastic work-time relationship is proposed using Mesri’s modeling idea, stress-viscoplastic work-viscoplastic work rate relationship is obtained according to the equivalent time method, and the second yield surface three-dimensional rheological equation is established under Perzyna’s over-stress theory. Again, according to the theory of double-yield surface model, a three-dimensional rheological model of double-yield surface is proposed by combining the two rheological equations. The classical fourth-order Rung-Kutta method is used to compile the difference calculation program, and the numerical solution of the rheological model is obtained. Finally, the predictions are compared with the measured values by using triaxial consolidation undrained rheological test data of Canadian bentonite and remoulded Hong Kong marine deposits to verify the applicability of the model in rheological tests. The results show that the model can simulate the development process of multi-stage and single-stage loading in undrained rheological tests, and can reflect dilatancy and shear contractibility of soils.