Effects of the Stratified Filter with Head Loss

Abstract

In a series of studies, a seepage failure problem of a piece-wise homogeneous sand column caused by a vertically ascending seepage flow is considered. In this paper, based on the previous papers, the effects of the stratified filter with head loss is clarified.
The stratified filter with head loes is referred to as a piece-wise homogeneous sand column which consists of the following sand strata: the upper stratum has a greater coefficient of permeability than the lower stratum. The one-, two-and three-layered sand columns shown in Fig. 2 are compared with one another to clarify the effects of the stratified filter. The stratified filter with head loss has the following effects, from the point of view of internal effective stress:
(1) Critical difference he in the total hydraulic head between the topmost position and the bottom position of the stratified filter is identical in the one-, two-and three-layer cases.
Considering, however, the frictional resistance (at a critical time) between the vertical acryl cylinder wall and sand particles in an experiment with the acryl cylinder model; as for h_c
(one-layer case) <(two-layer case) <(three-layer case), according to the residual effective stress (at a critical time).
(2) Taking an area of the internal effective stress diagram as the parameter of the stability of the stratified filter; as for the stability (see Table 1),
(one-layer case) <(two-layer case) <(three-layer case).
(3) As for the maximum hydraulic gradient which takes place in the bottom layer of the stratified filter (see Table2),
(one-layer case) <(two-layer case) <(three-layer case).
But, on the other hand, as for the minimum hydraulic gradient which takes place in the top layer of the stratified filter (see Table 2),
(one-layer case) >(two-layer case) >(three-layer case).
Considering (2) and (3), the following is obtained:
(4) The lower layer of the stratified filter spends, in upward seepage flow through it, the greater part of difference h in the total hydraulic head between the topmost position and the bottom position of the stratified filter, and the upper layer of the stratified filter contributes to the increase in internal effective stress (i. e., the increase in stability).
Judging from the way each layer of the stratified filter spends, in upward seepage flow through it, difference h in the total hydraulic head (see (4)); the stratified filter has the following characteristic:
(5) By appropriately increasing the number of layers of the stratified filter, the location of the layers where the grain-size distribution must be considered to prevent sand particles from being scoured are able to be limited to the lower portion of the stratified filter.
The design of the stratified filter is related to the three following factors:
(i) the stability of the stratified filter,
(ii) the condition that sand particles must not be scoured, and
(iii) the restriction of the amount of flowing water (i. e., the restriction of water leakage).
(In practice, however, a filter is mostly positioned to meet condition (ii) only.) Conditions (i), (ii) and (iii) are related to the hydraulic gradient within each layer of the stratified filter, and are related to the coefficient of permeability of each layer. It is, therefore, considered that the stratified filter with head loss should be designed from the viewpoint of internal effective stress, taking the coefficient of permeability of each layer of the stratified filter into consideration.