Hydrostatic Thrust on Dam
Calculate the horizontal hydrostatic thrust per metre of length on a dam face, E = ½·γ·H², from the unit weight of water γ (≈ 9.81 kN/m³) and the water depth H (m) at the upstream face. Since hydrostatic pressure grows linearly with depth (p = γ·h), its diagram is triangular and the resultant is its area, ½·γ·H², applied at one third of the height from the base. This thrust is the main action tending to overturn and slide the dam, and the starting point of gravity dam stability analysis: it generates the overturning moment (about the downstream toe) and the horizontal force resisted by base friction. Dam stability depends on its self-weight (providing the stabilizing moment and normal friction force) exceeding these with adequate margin, also accounting for foundation uplift. Enter the unit weight of water and the depth.
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Empuxo hidrostático sobre barragem
O empuxo hidrostático horizontal por metro de comprimento sobre o paramento de uma barragem é E = ½·γ·H², a partir do peso específico da água γ (≈ 9,81 kN/m³) e da profundidade da água represada H. Como a pressão hidrostática cresce linearmente com a profundidade (p = γ·h, zero na superfície e máxima no fundo), seu diagrama é triangular, e a força resultante é a área desse triângulo, ½·γ·H², aplicada a um terço da altura a partir da base (no centroide do diagrama de pressões). Esse empuxo é a principal solicitação que tende a tombar e a fazer deslizar a barragem, e é o ponto de partida de toda a análise de estabilidade de barragens de gravidade: ele gera o momento de tombamento em torno do pé de jusante e a força horizontal que precisa ser resistida pelo atrito na base de fundação. A barragem se mantém estável porque seu peso próprio — gerado pela enorme massa de concreto ou de aterro — produz um momento estabilizante e uma força normal que mobiliza o atrito necessário, superando com folga adequada esses esforços. Mas há um inimigo oculto: a subpressão na fundação, que alivia o peso efetivo e precisa ser combatida com drenagem. Informe o peso específico da água e a profundidade.
Related Tools
Dam Sliding Safety Factor
Calculate the sliding safety factor of a gravity dam, FS = (μ·W) ÷ F_h, from the base friction coefficient μ (tan of the concrete-foundation friction angle, typically 0.6-0.75), the effective self-weight W (dam weight minus uplift, kN/m) and the destabilizing horizontal force F_h (hydrostatic thrust, kN/m). This factor compares the forces resisting the dam sliding on its foundation (mobilized base friction, proportional to the effective normal force) with those pushing it downstream (the reservoir thrust). It is one of the two fundamental gravity dam stability checks — the other being overturning. Codes typically require sliding FS ≥ 1.5 for normal loading. The simplified form uses friction only; fuller analyses add interface cohesion (c·B). Note how decisive uplift is: it reduces W and thus the numerator — hence the importance of foundation drainage. Enter the friction coefficient, effective weight and horizontal force.
Spillway Discharge (Creager/Ogee)
Calculate the discharge over a Creager/ogee dam spillway, Q = C·L·H^1.5, from the discharge coefficient C (typically 2.0-2.2 in SI for well-designed ogee profiles), the crest length L (m) and the head over the crest H (m). The spillway is a dam's most critical safety structure: it releases floods safely, preventing overtopping — the leading cause of dam failure. The ogee profile follows the shape of the underside of a free nappe, maximizing discharge while keeping crest pressure near atmospheric (avoiding cavitation). The coefficient C absorbs gravity and approach effects, exceeding that of a sharp-crested weir. Spillway design starts from the design flood (often the 10,000-year flood or the PMF) and sets the required crest length. Enter the discharge coefficient, crest length and head.
Dam Foundation Uplift
Calculate the uplift resultant per metre of length at a gravity dam base, assuming triangular distribution, U = ½·γ_w·H·B, from the unit weight of water γ_w, the head H (upstream water height) and the base width B. Uplift is the water pressure that percolates through the foundation and concrete joints acting upward on the dam base, reducing the effective normal force and thus the sliding friction resistance — one of the most dangerous and historically underestimated factors in dam stability (the 1928 St. Francis Dam failure is a landmark). The real distribution depends on grout curtains and drains, which reduce it; the triangular hypothesis (full upstream, zero downstream) is conservative and common in preliminary design. Uplift subtracts from self-weight in the sliding check and adds overturning moment. Enter the unit weight of water, the head and the base width.
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