The figure below shows the St Johns landfill, a 225-acre landfill located in North Portland, Oregon, near the confluence of the Columbia and Willamette Rivers.  The landfill sits on a thick layer of silt (average thickness ~50ft), which in turn overlies a fairly transmissive gravel aquifer.  The aquifer covers the entire area between the Columbia and Willamette rivers and extends east past North Portland Road.  It is known the aquifer is well connected (hydraulically) with the two rivers.

Field data suggest that water level in the landfill is well above the water level in the surrounding surface water bodies due to infiltration of precipitation. This provides a driving force for leachate loading into the surface waters as well as the deep aquifer below the landfill. Metro recently capped the landfill to prevent further infiltration of precipitation (see below). 

You are asked to evaluate to evaluate the effectiveness of landfill capping by developing an analysis which describes the dissipation of the leachate mound inside the landfill.  For the parameters listed below, find the steady state mean water level inside the landfill. Also determine the hydraulic response time, or how long it will take for the mean water level to approach within approximately 40% of that of steady state.

• Conductivity of the floodplain sediments K_fp = 0.01 ft/d
• Average thickness of the floodplain sediments b_fp = 50 ft
• Transmissivity of the perimeter dike wall  T_d ≈ K_dh_s
• Perimeter dike thickness b_d = 3 ft
• Specific Yield = 0.05
• Water level in the landfill immediately following capping h₀ = 50 ft
• Long-term mean water level in the surrounding surface water bodies h_s = 10.5 ft
• Long-term mean head in the confined aquifer h_c = 9 ft
• Perimeter length L = 20,000 ft
• Landfill Area = 5000 ft²