In a series of studies, the seepage failure problem of a pice-wise homogeneous sand column caused by a vertically ascending seepage flow has been considered. In the preceding papers, the author studied the seepage failure problem in the one-, two-and three-layer cases. In this paper, based on the previous studyn, the seegage failure problem in a multi-layer case is considered.
As mentioned in the 6 th paper, the “critical state chart for seepage failure of a sand column” indicates almost all the information about seepage failure of the sand column. It is also very useful in considering the safety fatocr for seegage failure of the sand column, and in designing a loaded filter which is placed on the top of the sand column to avoid seepage failure. Thus it is considered that the critical state chart is the condensed chart which represents the analytical results of a sand column obtained from the treatment of the seepage failure problem of the sand column on the basis of internal effective stress.
As mentioned in the 7 th papern, the author's approach to the seepage failure problem (i. e., an approach based on the internal effective stress) has more advantages than the Kahn's approach (i. e., an approach based on the “critical equilibrium of forces”). On the other hand the author's approach is more troublesome as alyers of a sand column increase in number than the Kahn's approach. Combined with Kahn's approach, therefore, the author's apprnach may become very useful, in spite of the increased number of layers of a sand column.
In the present study, combining the author's approach with the Kahn's approach, and based on the concept of a “minimum criterion”, a new simple method of obtaining the “critical state chart for seepage failure of a multi-layered sand column” is shown.
Using the critical state chart for seepage failure of a multi-layered sand column, the pressure exerted on the “Yokushi Ban” which is placed on the top of the sand column, and the effective stress diagram within the sand column with the “Yokushi-Ban” after a critical time can be calculated.
Thus the critical state chart for seepage failure of a multi-layered sand column can be obtained very easily through the use of the method developed by the author, and can be widely utilized:
(i) to consider a seepage failure problem in the case of a multi-layered sand column from the standpoint of internal effective stress,
(ii) to judge the safety factor for seepage failure of a multi-layered sand column,
(iii) to design a loaded filter to prevent the seepage failure of a multi-layered sand column, and
(iv) to consider a seepage problem of a multi-layered sand column with the “Yokushi-Ban”.
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