Pile Group Efficiency (Converse-Labarre)
Calculate a pile group's efficiency by the Converse-Labarre formula, η = 1 − (θ/90)·[(m−1)·n + (n−1)·m] ÷ (m·n), from the pile diameter D and spacing s (with θ = arctan(D/s), in degrees), and the number of piles per row m and per column n. When several piles are driven close together (forming a group under a cap), the group capacity is NOT simply the sum of individual capacities — there is INTERFERENCE between the stress bulbs of neighboring piles in the soil, which overlap. The efficiency η (less than 1) measures this loss: the CLOSER the piles (smaller spacing s relative to diameter D), the greater the overlap and the lower the efficiency. The Converse-Labarre formula, empirical and widely used, quantifies this reduction as a function of group geometry (pile count and spacing). So codes require a minimum pile spacing (typically 2.5-3 diameters) to limit efficiency loss. Efficiency times pile count times individual capacity gives the group capacity. This effect is more pronounced in friction piles in clay; in end-bearing piles in sand, the group may even have efficiency above 1 (driving densifies the sand). Enter the diameter, spacing and pile count per row and column.
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Eficiência de grupo de estacas (Converse-Labarre)
A eficiência de um grupo de estacas pela fórmula de Converse-Labarre é η = 1 − (θ/90)·[(m−1)·n + (n−1)·m] ÷ (m·n), a partir do diâmetro da estaca D e do espaçamento s (com θ = arctan(D/s), em graus), e do número de estacas em linha m e em coluna n. Quando várias estacas são cravadas próximas (formando um grupo sob um bloco de coroamento), a capacidade do grupo não é simplesmente a soma das capacidades individuais — há uma interferência entre os bulbos de tensão das estacas vizinhas no solo, que se sobrepõem. A eficiência η (menor que 1) mede essa perda: quanto mais próximas as estacas (menor espaçamento s em relação ao diâmetro D), maior a sobreposição e menor a eficiência. A fórmula de Converse-Labarre, empírica e muito usada, quantifica essa redução em função da geometria do grupo. Por isso as normas exigem um espaçamento mínimo entre estacas (tipicamente 2,5 a 3 diâmetros) para limitar a perda de eficiência. A eficiência multiplicada pelo número de estacas e pela capacidade individual dá a capacidade do grupo. Esse efeito é mais pronunciado em estacas de atrito em argila; em estacas de ponta em areia, o grupo pode até ter eficiência maior que 1 (a cravação adensa a areia). Informe o diâmetro, o espaçamento e o número de estacas em linha e coluna.
Related Tools
Pile Group Capacity
Calculate a pile group's bearing capacity, Q_g = η·N·Q_pile, from the group efficiency η, the number of piles N and the single isolated pile capacity Q_pile (kN). A pile group's capacity (piles driven close under a cap that distributes the column load among them) is each pile's individual capacity, times the pile count, adjusted by the group EFFICIENCY (η ≤ 1, discounting the interference between neighbors, computed by Converse-Labarre or other formulas). In clayey soils and friction piles, efficiency is below 1 (piles 'compete' for the same soil, and the group may even fail as a solid block — 'block failure', checked separately). In sands and driven piles, driving densifies the soil and efficiency can approach or exceed 1. The group capacity is what actually supports the column load above the cap, and must exceed it with the proper safety factor. This calculation, with the group settlement check (which can exceed a single pile's, since the group stress bulb is deeper), defines the design of a pile-group foundation. Enter the efficiency, the pile count and the individual capacity.
Soil Group Index (HRB/AASHTO)
Computes the group index of the HRB/AASHTO M 145 classification, the number in parentheses that follows the soil symbol in a soil report: GI = 0.2a + 0.005ac + 0.01bd, where a and b come from the percentage passing the No. 200 sieve and c and d come from the liquid limit and the plasticity index. Each term is truncated — a and b from 0 to 40, c and d from 0 to 20 — and the result is rounded to an integer and never negative, which makes the index range from 0 to 20. The higher the group index, the worse the soil as a subgrade: 0 points to clean, well behaved granular material, values above 12 point to plastic clay that only works once replaced or stabilised, and this is the number that feeds the pavement thickness charts. The complete formula with both terms was adopted; for subgroups A-2-6 and A-2-7 the standard calls for the 0.01bd term alone, and the result is the same: every A-2 soil has at most 35% passing the No. 200 sieve, which is exactly where the a term goes to zero, so the first two terms drop out on their own. Enter the percentage passing the No. 200 sieve, the liquid limit and the plasticity index.
Bearing Power Loss
Calculate the power dissipated by friction in a bearing, P = T × ω, multiplying the friction torque T by the angular velocity ω (rad/s). The result, in watts, is the mechanical energy converted to heat per unit time by friction — a loss that reduces efficiency and heats the lubricant and components. This heat must be dissipated (by convection or oil circulation) to keep a safe operating temperature, since overheating degrades the lubricant and can cause seizure. Estimating the dissipated power is essential to size the cooling and the oil flow. Enter the friction torque and the angular velocity.
Wave Group Velocity
Calculate the group velocity of an ocean wave in deep water, c_g = g·T ÷ (4π), from the period T (s). The result, in m/s, is the speed at which the wave energy (and the 'envelope' of a wave group) propagates — exactly half the celerity (phase velocity) in deep water. This difference explains a curious phenomenon: within a wave group, individual crests appear at the rear, advance through the group (faster than it) and disappear at the front. The group velocity is what matters for energy transport and predicting swell arrival at the coast. Enter the wave period.
Tunnel Face Pressure (EPB/Slurry)
Estimate the face support pressure needed to stabilize the excavation front of a mechanized tunnel, p = K·γ·H, from the earth pressure coefficient K (at rest K₀ ≈ 1−sinφ, or active), the soil unit weight γ (kN/m³) and the axis depth H (m). In closed-face TBMs (EPB or slurry), the pressurized chamber must balance the earth and water pressure at the front, avoiding both collapse (insufficient pressure) and blow-out (excessive pressure). Face pressure is the most critical operational parameter of a TBM, adjusted in real time per cover, water table and soil type. This gives the earth component; total pressure adds hydrostatic water pressure and a safety margin. Enter the earth pressure coefficient, unit weight and depth.
Faradaic Efficiency
Calculate the faradaic efficiency (current efficiency), η = (m_actual ÷ m_theoretical) × 100%, comparing the mass of product actually deposited or consumed with the theoretical mass predicted by Faraday's law for the charge that passed. The result, in %, measures what fraction of the current was actually used in the desired reaction; the rest is lost to side reactions (such as hydrogen or oxygen evolution) or short circuits. It is a key indicator in electrodeposition, industrial electrolysis, electroplating and batteries. Enter the actual mass obtained and the theoretical mass.
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