You choose the quake (magnitude, focal depth, distance), the ground under the city and the type of the hero building. The program generates a ground-motion record, runs six structures through it (the hero building, a brick house, an office tower, an apartment block, a bridge, parked cars) and plays the result back in 3D. Waves leave the glowing focus at real crustal speeds: P about 6 km/s, S about 3.5 km/s; the picture is a cut-away diorama (1 m = 1.8 km).

Peak ground acceleration on hard rock follows an attenuation law of the Campbell type (typical coefficients, simplified):

ln PGA[g] = -3.512 + 0.904 M - 1.328 ln sqrt(R^2 + (0.149 e^(0.647 M))^2)

R is the distance from the focus: R = sqrt(epicentral distance^2 + depth^2), so a deeper focus lowers shaking right above it. Radiated energy: log10 E[J] = 4.8 + 1.5 M (one magnitude unit = 31.6 times more energy). Felt intensity uses MMI = 3.66 log10(PGA[cm/s^2]) - 1.66.

A soil layer of thickness H and shear-wave speed Vs resonates at Ts = 4H/Vs. The accelerogram is made by summing 96 random-phase sinusoids with a Brune omega-squared source spectrum, multiplied by a soil transfer function that peaks at 1/Ts (hard rock 1x, stiff soil 1.8x, soft soil 2.8x, wet sand 2.3x) and then scaled to PGA = PGA_rock x Fa, where Fa = 1 + (Fa0 - 1) / (1 + (PGA_rock/0.45)^2) falls as shaking gets stronger (soil nonlinearity).

Each building is a stack of N lumped floor masses joined by inter-storey springs. With u the floor displacements relative to the ground:

M u'' + C u' + f(u) = -M 1 a_g(t)

The spring of each storey is bilinear (elastic, then yielding with a small post-yield stiffness ratio alpha; brittle masonry has negative alpha). Stiffness comes from the period rule of thumb T1 = (0.06...0.11 s) x N through the exact modal formula w1 = 2 sqrt(k/m) sin(pi/(2(2N+1))). Damping is stiffness-proportional, zeta = 3...8%. Integration is explicit with a 2.5 ms step.

Damage uses the peak inter-storey drift ratio: Slight at 0.6 x yield drift, Moderate / Extensive at 25% / 60% of the way from yield to collapse drift, Complete at the collapse drift. Typical mean damage ratios (illustrative, HAZUS-style): 2%, 10%, 50%, 100% of replacement value. When a storey exceeds its collapse drift the floors above fall on the storey below; the collapse continues down only while the kinetic energy of the falling mass exceeds the crushing energy of the next storey:

M_f g h_fall > eta (M_f + m) g h_crush

with h_fall = 0.9 h, h_crush = 0.35 h and a column over-strength eta that is largest for steel (3.0) and smallest for wood (1.3). Cascade times use free-fall time sqrt(2 h_fall / g).

For loose saturated sand the simplified procedure compares cyclic stress ratio and resistance: CSR = 0.65 (PGA/g)(sigma_v/sigma'_v) r_d, CRR = 1/(34-N) + N/135 + 50/(10N+45)^2 - 1/200 (N = 10 blows, magnitude scaling factor MSF = 10^2.24 / M^2.56), FS = CRR x MSF / CSR. FS below 1 means liquefaction: the model then cuts the surface shaking and sinks and tilts the buildings. A base-isolated building has a long first period (2.6 s) so the ground shakes underneath it while the building itself barely deforms, at the price of a large isolator displacement.

• The buildings are 1-D shear models: no torsion, no vertical load path, no P-delta. Collapse is a energy-balance cartoon, not a finite-element crush.
• The attenuation law, soil factors, drift thresholds, damage ratios and over-strength factors are typical or illustrative numbers, not code values; this is a teaching tool, not a design or hazard tool.
• Soil layering is reduced to one transfer function per site class; liquefaction is a single-layer screening test.
• Visual shaking and drifts are exaggerated by the slider. Cities and structures are generic; no real place or company is shown.