Soil density γ (kN/m³)
The unit weight of the material behind the wall (the backfill), not the ground under it. Heavier soil pushes harder — pressure is directly proportional to γ. Typical: 13–15 light fill or quarry waste, 18–20 compacted sand/gravel, 19–21 wet clay. If the wall retains normal compacted earth, use 18–19 rather than the light-fill default.
Friction angle φ (°)
How well the soil “stands up” on its own from grain-to-grain friction. Higher φ = soil supports itself = pushes less. It drives Ka = (1−sinφ)/(1+sinφ): at φ=40° only ~22% of the soil’s vertical weight becomes horizontal push; at φ=20° it is ~49% — more than double. Typical: 38–42° crushed rock, 30–35° sand/gravel, 25–30° silty soil, 18–25° clay. The single most influential soil input.
Cohesion c (kN/m²)
The “stickiness” of fine-grained soil, which lets it hold a vertical cut briefly without support. It reduces the push by 2c√Ka. Clean sand/gravel: c=0. Marls and clays: 10–25. Caution: cohesion is unreliable long-term — cracks fill with rainwater and the soil softens — so designs are often checked with c=0. Setting c=0 gives the safe-side answer.
µ concrete–soil friction
How much the wall base grips the foundation soil: sliding resistance Fr = µ×W. Typical: 0.55–0.6 blocks on gravel, 0.45–0.5 on sand, 0.3–0.35 on wet clay. If sliding governs, placing the first course on a compacted gravel bed raises µ cheaply.
Safety factor targets
Sliding ≥ 1.5 — the friction grip must beat the soil push with 50% reserve; standard for gravity walls. Overturning ≥ 2.0 — righting moment at least twice the tipping moment. The higher target reflects that overturning failure is sudden and unforgiving; some codes accept 1.5, but 2.0 is the conservative convention.
Total wall height H (m)
Top of the stack to the base, on the retained side. Modular: course count × block height — with 0.8 m modules, 6 courses = 4.8 m. Height matters brutally: the push force grows with H² and the overturning moment with H³, so adding one course to a 4.8 m wall raises the overturning moment by roughly 65%.
Concrete density (kN/m³)
Unit weight of the blocks themselves; solid conventional concrete is 23–24. Critical for a mass wall: weight is the only thing holding it in place. Blocks cast from foamed material at e.g. 800 kg/m³ (≈8 kN/m³) would cut stability to a third — mass lego blocks must be solid, dense concrete.
Base course height H1 / base width W1
H1 is the height of the bottom zone built with the wide blocks; one course laid flat = 0.8 m, two courses = 1.6 m. W1 is their front-to-back depth: 1.6 m = a standard 1600×800×800 block turned crosswise. Width fights overturning twice over — more weight and a longer lever arm (centroid at W1/2 from the toe) — so the resisting moment grows with W1².
Upper block width W2 (m)
Depth of the blocks above H1; 0.8 m = the same block placed normally. The model assumes front faces are flush (vertical face to the open side) with the step at the back, buried in the fill. That is conservative — in reality the soil sitting on the back step adds stabilising weight that is not counted.
Tie-back anchors (steel rod + deadman)
Horizontal steel rods through the wall at chosen heights, anchored to buried concrete deadman blocks behind the soil failure wedge. The tool auto-sizes the total force so every SF target is met, splits it equally between levels, then checks the rod steel (gross yield on the corrosion-reduced diameter), the deadman passive bearing (FS 2.0 on ultimate) and the minimum rod length so the deadman sits beyond the active wedge — extended ×(1+1.5·α·S) in the seismic case (EN 1998-5 §7.3.1). Anchors also restrain the block joints above their level.
Seismic action — EN 1998-5 / CYS NA
Cyprus NA zones: 1 = 0.15g (north), 2 = 0.20g (Nicosia / interior), 3 = 0.25g (SW–S coast). kh = α·S/r with S from the ground type and r from EN 1998-5 Table 7.1 (r=2 for a free wall that may slide slightly, r=1 rigid or anchored — set automatically when anchors are on); kv = ±0.5·kh, both signs checked. Soil thrust by Mononobe–Okabe with δ=0 and c=0 (both conservative); the dynamic increment acts at 0.5·H and the wall inertia kh·W is added. Lower SF targets than static are normal — the quake is a rare, short event.
Result boxes
Fa — total horizontal soil push per metre of wall, acting at H/3 above the base (red arrow in the diagram). Ma — Fa × its lever arm: the tipping torque about the toe. W — total block weight per metre run. Fr = µ·W — the grip resisting sliding. Mr — the righting torque: each block zone’s weight × distance of its centre from the toe. SF sliding = Fr/Fa and SF overturning = Mr/Ma — green when they meet your targets.