عنوان مقاله [English]
This study has introduced, described and compared the performance of two popular integration methods for implementing complicated equations of soil models. Generally speaking, all methods can be classified into two categories of Explicit and Implicit approaches. Two famous methods of the implicit approach, the Closest Point Projection Method (CPPM) and the Cutting Plane Method, (CPM), which are defined under the framework of the Return Mapping algorithm, are considered in this study. Both the Cutting Plane Method and the Closest Point Projection Method are employed in order to implement an advanced critical two-surface model, published by M.T. Manzari and Y.F. Dafalias, in 1997, for sand. Since the CPPM and CPM methods are implicit, it has a great advantage, as both sizes of steps remain stable. A common weakness of both methods can handle the complexity of numerical integration methods for other types of integration method (explicit) named. As a result, the current research confirms that, as complicated as the Closest Point Projection Method is, it remains strongly stable in order to integrate equations under conditions of large strain and displacement, such as the liquefaction phenomenon. On the other hand, compared with the Closest Point Projection Method, the Cutting Plane Method is not only more precise and accurate, but also much faster. Additionally, the Cutting Plane Method benefits from an undeniable simplicity against the Closest Point Projection Method. Somewhat importantly, this study aims, by presentation of both the strong and weak points of each method simultaneously, to aid researchers in selecting a reasonable method, with regard to special conditions and the limitations of each problem.