Keywords: earth dam, transient flow, unsaturated soil, transient analysis, three-dimensional model, permeability.

In the engineering design and monitoring of earth dams one of the main concerns is the evaluation of water flow rates, hydraulic gradients and poro-pressure build-ups in the estimation of the risks caused by water flowing through the dam, its foundation and abutments. This problem is usually investigated assuming three-dimensional flow conditions in the most representative cross section of the dam. Several arguments may be raised in favour of this approach, such as the higher speed of numerical processing, the ease of two-dimensional model construction, the great availability of computer programs for two-dimensional analysis, the use of the traditional hypothesis of plane flow throughout earth dams, etc. However, a bi-dimensional representation of an inherently three-dimensional problem can lead to incorrect answers, as in the case studied in this paper dealing with the hydraulic behaviour of the Macusani earth dam, planned to be built in a deep and narrow V-shaped valley in the Andes Mountains in Peru.

The numerical analyses were carried out with two and three-dimensional finite element models considered saturated and partially saturated flow in transient or steady state regimes. Three case studies were analyzed, dealing with the critical situations of first reservoir filling (cases I and II) and rapid drawdown of the upstream water level (case III). After comparing the flow patterns determined from the two and three-dimensional models, it has been observed that the wetting front advanced more rapidly in three-dimensional simulations due to the contribution of the flow velocity component outside the cross section of the dam, which cannot be taken into account by the two-dimensional analyses. For steady state flow conditions, when using the saturated coefficient of permeability recommended for use with the previous two-dimensional modelling, the final position of the phreatic surface resulted well above the drain, indicating that this structure was unable to transport all the volume of water generated by the out-of-plane flow. This situation is obviously not admissible in a good engineering project since the wetting of the downstream soil might cause problems related to the stability of the downstream slope. In the case II the same type of analysis has been repeated, but this time considering a saturated coefficient of permeability ten times higher than the value used previously. The numerical results show that, despite the three-dimensional effects, the drain now works well, without any potential risk to the dam. Finally in case III the effects of a rapid drawdown of the water reservoir were investigated. It has been observed that the upstream shell remained completely saturated and as a consequence, slope stability analyses are needed in order to assess the occurrence of potential soil slides just after the complete lowering of the reservoir.

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