A discussion contribution on Vertical pile resistance in Coulomb wedge, R. Lennon and P. Thurlow (GE December 2006), by Dickon Woods (retired).
One of Lennon and Thurlow's conclusions on the presence of vertical piles in the soil retained by a wall is 'the failure wedge can be forced to form at a steep angle where the wedge intersects either a small number or none of the piles'.
This may not always be true as there is an inherent assumption (although not always stated) in using the Coulomb wedge method.
This is that the soil is modelled by an intact wedge. As a cohesionless soil cannot normally sustain tension should any occur within a wedge it cannot remain intact.
In this situation any calculated values are invalid and an alternative failure pattern may be applicable.
In reported results of the example - a 10m high vertically backed retaining wall retaining a cohesionless submerged soil containing a grid of vertical piles - used by Lennon and Thurlow to illustrate their paper, it appears that for trial triangular wedges, where the shear surface intersects the piles, tension does develop.
This is because the majority of the wedge weight is between the wall and the piles so the effect of piles is to hold back the wedge and so cause tension within it.
Table 1 (in Lennon and Thurlow's paper) provides a clear example of this in the wedge with the shear plane inclined at q=74 from the horizontal.
In this case the effective active force would have been 96.5kN/m without the piles, but when their restraint is included this force is reported as reduced to 56.4kN/ m. Since the piles are less than 0.4m from the end of the wedge that is remote from the wall they must be holding back the wedge and producing tension within it, invalidating the calculated value of the effective active force.It appears that an alternative wedge shape should be considered when the shear plane intersects the piles (q less than 76). One possible model is to assume that the wedge is trapezoidal comprising the soil between the back of the wall and the first line of the pile grid, 2.5m away for all wedges with q less than 76. Using the Coulomb wedge method and the same values for the soil parameters as in Lennon and Thurlow's example (f'=32°;d'= 2-3f'; gbuoyant=9.41kN/m 3) but using a trapezoidal wedge gives the results in Table A. This shows a maximum effective active force of 99.3kN/m (q=70° ) compared with 88.3kN/m reported by Lennon and Thurlow for a triangular wedge.
Implicit in using a trapezoidal wedge is that the pile grid fully supports the soil between them to a height of 3.13m. When the vertical piles are insuf ciently closely spaced to achieve this there will be a force from the partially supported soil exerted on the vertical plane of the wedge adjacent to the piles.
The magnitude of this force is not easily assessed but will increase the effective active force.
To give some indication of this increase a very crude approximation is to assume the position of the vertical plane bounding the trapezoidal wedge within the pile grid and to ignore the retaining effects of the piles.
With the limiting vertical plane at 3m and 3.5m from the wall back the calculated effective active forces are 107.8kN/m (q=68) and 114.6 kN/m (q=66) respectively.
The added consequence of the piles fully or partially supporting the soil between them is that the adequacy of the bending capacity and the penetration of the piles may need to be considered.
Whereas the piles do not create tension in the trapezoidal wedge it may not be the only alternative failure pattern. Could the cohesionless soil between the wall and the piles behave as if in a two-dimensional silo?
Without piles the effective active force on the wall would be 129.3 kN/m so the reduction indicated by adopting a trapezoidal wedge (which does not have to support tension and so remains intact) is about half that reported by Lennon and Thurlow and (with the hydrostatic force on the wall being about 490kN/m) very small if the groundwater conditions require considering the total force acting on the wall.
Reference Lennon, R. & Thurlow, P. Vertical pile resistance in the Coulomb wedge. Ground Engineering.
vol. 39, no. 12, pp. 30-32.