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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Subpressão na fundação de barragem
A subpressão (uplift) é um dos fatores mais perigosos — e historicamente mais subestimados — na segurança de barragens. É a pressão da água que percola pela fundação rochosa e pelas juntas do concreto e atua de baixo para cima na base da barragem, empurrando-a para cima e reduzindo a força normal efetiva que a prende ao terreno. A resultante de subpressão por metro, supondo distribuição triangular, é U = ½·γ_w·H·B, a partir do peso específico da água γ_w, da carga hidráulica de montante H e da largura da base B. Seu efeito é insidioso: ao reduzir o peso efetivo, ela diminui o atrito disponível na base e, portanto, a resistência ao deslizamento — além de adicionar momento de tombamento. A ruptura da barragem de St. Francis (Califórnia, 1928), que matou centenas de pessoas, é um marco trágico que ensinou os engenheiros a respeitar a subpressão. A distribuição real depende de cortinas de injeção (que vedam a fundação) e de drenos (que aliviam a pressão a jusante da cortina), que a reduzem substancialmente; a hipótese triangular (cheia em montante, nula em jusante) é conservadora e usada no pré-dimensionamento. Controlar a subpressão com uma boa fundação, injeções e um sistema de drenagem eficiente é absolutamente essencial à segurança de qualquer barragem de gravidade. Informe o peso específico da água, a carga hidráulica e a largura da base.
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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.
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.
Pile Skin Resistance
Calculate a pile's side (friction) resistance, Q_l = f_s·A_s, from the average unit skin friction f_s (kPa) and the pile lateral surface area A_s (m², = π·D·L for a cylindrical pile). Side resistance is the share of pile capacity from FRICTION and ADHESION between the pile's lateral surface and the surrounding soil, along its whole buried length. As the pile tends to settle under load, the soil 'grips' its sides and resists — as a nail driven in wood resists pulling by face friction. The unit skin friction f_s depends on soil type (in clays, on undrained cohesion via the α method; in sands, on effective stress and friction via the β method), pile type (driven piles mobilize more friction than bored, displacing and compacting the soil) and surface roughness. Side resistance dominates in FLOATING (friction) piles, driven in soils without a firm bearing layer — they hang by friction. It is also the share mobilized FIRST under load (with small settlement), before the tip. This share adds to the tip resistance for the total capacity. Enter the unit skin friction and the side area.
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