given that the maximum depth of water is 77 m and the lake area around 18 ha. The bed rock is sandstone rock. The average rainfall over the catchment is about 250 mm/year during winter months only.
I think it depends on what type and length of other hydrometeorological data that you have for the area. In general, a common approach would be to establish a water balance for the lake.
This is a new dam under design and we have to estimate the annual infiltration rate.
Using the Green Ampt and Horton Approach does not account for the vertical head of 77 m of the lake height, that water table will reach the ground surface when the dam is full and that sediment will block all pores. In these conditions, I guess Darcy's equation is not practical.
If you still have access to bedrock, you may consider some geology study of substrate materials relative to fractures and hydraulic conductivity (saturated, and pressurized). 77m is substantial head pressure, and if bedrock was too thin or layered, the pressure may be enough for adjustments. If geology coring has not been considered, it might help estimate, and considering if there are any faults or underground fractures may be important in your estimates.
If the dam already existed, the water balance approach as suggested by measuring rainfall and stream inflow, stream outflow, estimating evaporation, any water used by others or bank vegetation, and what cannot be estimated is deep seepage loss as unexplained.
In a project as this, I would require a licensed civil engineer with high bond of insurance to review the results and suggest inventory and study needs to meet engineering requirements. Doing this would help protect you and move liability away from you or University.
If you base your calculations on steady-state boundary conditions, a first simple approximation would be to use Darcy. You would need to know sorrounding geologic material and hydraulic capacity. You would also need to know approximate groundwater levels surrounding the dam. Don´t you have similar dams in the nearby that you could compare with?
Thanks to all for their insight thoughts and ideas. The average value of K can be taken the order of 10^-6 m/s. Current water table is vet close to ground surface due to existing baseflow.