Several classical methods have been proposed for the assessment of bottom stability against seepage failure of the soil, and they may be broadly divided according to the basic concepts such as those based on the examination of moment equilibrium, bearing capacity formulae, critical gradient method and Terzaghi's method. Failure sometimes occurs even in deep excavation and in front of the sheet pile designed by these methods. Soil heterogenic permeability plays an important role in head loss and seepage force distributions. Accordingly, the use of classical methods which do not take into account the permeability variability is inadequate.

Numerical approaches offer the possibility to treat complex cases. Therefore, to investigate the effect of layered soil permeability on the stability of a soil mass in front of a retaining wall, we consider, in this paper, the frequent case of a cofferdam driven into a two-layered soil medium where the permeability coefficients of the upper and lower layers are respectively K₁ and K₂. The sheet pile depth is equal to D and is subject to hydraulic head H as shown in Figure 258.1. The upper layer is has a thickness limit whereas the lower layer is semi-infinite. The bottom of the sheet pile lies in the upper or lower layer. Numerical analysis has been carried out to analyse the seepage failure using the computer code FLAC_-2D which is a commercially available finite difference explicit program.

Seven relative thicknesses of the upper layer (e/D=1/4, 1/2, 3/4, 1, 5/4, 3/2, 7/4) and eight values of relative permeability (k₁/k₂= 1/200, 1/100, 1/10, 1/5, 5, 10, 100 and 200) are investigated.

It should be noted that for all ratios e/D, the comparison of the critical hydraulic head loss for the cases corresponding to k₁/k₂= 100 and k₁/k₂= 200 (upper layer highly permeable compared to the lower layer) show a negligible difference not exceeding 1.2%. Therefore, the computation of the effective permeability by contrast is limited to k₁/k₂= 200.

Figure 258.1: Case study

When k₁/k₂>= 1 and e/D>=1.75, one obtains the critical hydraulic head loss corresponding to the case of a homogeneous and isotropic single layer, since the lower layer can be considered as an impermeable substratum.

The analysis of the results shows a high sensitivity of the critical pressure loss to the layer permeability contrast. The risk increases with the decrease of the thickness of the upper layer as well as its permeability. Indeed, for e/D>=1/4 a weak ratio of permeability k₁/k₂= 1/5 reduces the critical hydraulic head loss by 60%, while a ratio of permeability of k₁/k₂= 1/200 reduces it by 80% compared to the value suggested by Terzaghi for homogeneous isotropic ground.

For cases where the bottom of the sheet pile lies in the lower layer and the lower layer has a greater permeability coefficient than the upper layer (k₁/k₂<= 1), most of the head loss takes place in the upper layer, resulting in a significant reduction of its resultant body force.

On the other hand, for the cases where the upper layer has a greater permeability coefficient than the lower layer (k₁/k₂> 1), the head loss takes place solely in the lower layer, and the upper layer can be considered as a filter increasing the global stability of the soil in front of the sheet pile as well as the critical head loss.

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