What is modelled. A landfill cell is filled in lifts. Each lift is compacted by a steel-wheel compactor to an in-place density rho0(n) = rho_loose + (rho_max - rho_loose)(1 - e^(-n/n*)) after n passes (an empirical saturation curve; rho_loose = 350, rho_max = 1000 kg/m3, n* = 2.5 passes are typical-order values, illustrative, not a site measurement). Its thickness after compaction is h0 = h_loose rho_loose / rho0, so more passes means thinner lifts and more tonnes in the same airspace.
Stress. The vertical stress at the middle of lift i is the weight of everything above it plus half its own: sigma_i = (g/1000) [ sum_(j above) rho0_j h0_j + rho0_i h0_i / 2 ] in kPa. Because the mass per unit plan area of each lift is fixed, the stress does not change as the waste settles (one-dimensional column, wide fill, slopes and wall friction ignored).
Settlement (Sowers-type). Waste is a compressible, degrading skeleton, not soil. Strain of a lift: primary eps_p = C'c log10(sigma_i / sigma_ref), where sigma_ref is the stress at which the lift was placed (at least 5 kPa), plus secondary creep and biodegradation eps_s = C'a log10(1 + (t - t_placed) / t1) with t1 = 30 days. C'c is the compression ratio (0.1 to 0.4 is the usual range), C'a the secondary compression ratio (about 0.01 for dry, 0.03 conventional, up to 0.07 for wet bioreactor waste). The sum is capped at 60 %. Thickness is h = h0 (1 - eps) and density rho = rho0 / (1 - eps).
Airspace. The cell is a trapezoidal trough (floor 40 m, side slopes 1 vertical : 2 horizontal, 34 m deep); the volume between two heights is V = D [40 (y2 - y1) + 2 (y2^2 - y1^2)]; mass of a lift is rho0 times its as-placed volume. Settlement gives back airspace that can be refilled, which is why operators track it.
Checks on this page. (1) The engine sum of primary strains for n identical lifts loaded together is compared with the closed form C'c h0 log10((2n-1)!!) using log-gamma; (2) the secondary settlement of one lift is compared with its closed form after 10 years; (3) the summed lift volumes are compared with the trapezoid-prism formula; (4) the base stress is compared with g rho0 H. The compaction sweep compares the capacity gain of each extra pass with the mid-pass derivative (rho_max - rho_loose)/n* e^(-(n-1/2)/n*) times the volume.
Honest simplifications. No leachate, gas, temperature, moisture, differential settlement, side slopes sliding, liner strain, or daily cover as a separate material (cover is drawn as a thin layer only). Parameter values are typical orders of magnitude from textbooks, not design values for a real site; this is an educational model, not geotechnical design software. Vehicle motion is illustrative.