Earth Pressure API

Lateral earth-pressure maths (Rankine theory) as an API, computed locally and deterministically for retaining-wall design. The active endpoint computes the active earth pressure that pushes a wall outward when the soil is allowed to yield: the coefficient Ka = (1−sinφ)/(1+sinφ) from the soil friction angle, the pressure at the base of the wall σ = Ka·γ·H, the total thrust per metre run ½·Ka·γ·H², plus the contributions of a surface surcharge and of soil cohesion (which reduces the pressure by 2c√Ka and forms a tension crack of depth 2c/(γ√Ka)). The passive endpoint computes the passive resistance Kp = (1+sinφ)/(1−sinφ) that the soil mobilises when a wall is pushed into it — the resisting pressure and thrust, with cohesion adding 2c√Kp. The atrest endpoint computes the at-rest pressure K0 = 1−sinφ (Jaky) for unyielding walls such as basements and braced excavations. Everything is computed locally and deterministically, so it is instant and private. Ideal for geotechnical and civil-engineering tools, retaining-wall, sheet-pile and basement-wall design, excavation-shoring and foundation apps, and engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is Rankine lateral earth pressure; for slope geometry use a slope API and for open-channel weir flow use a weir API.