Soil Bearing Capacity Calculator
ANA›Life Services Authority›National Calculator Authority›Soil Bearing Capacity Calculator
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Soil Bearing Capacity Calculator
Calculate the ultimate and allowable bearing capacity of shallow foundations using Terzaghi's General Bearing Capacity Equation. Supports strip, square, and circular footings.
### Foundation Geometry
Footing Type
Strip Footing Square Footing Circular Footing
Foundation Width, B (m)
Foundation Depth, Df (m)
### Soil Properties
Cohesion, c (kPa)
Friction Angle, φ (degrees)
Unit Weight of Soil, γ (kN/m³)
### Design Parameters
Factor of Safety (FOS)
Water Table Condition
Deep (no effect) At Foundation Base At Ground Surface
Saturated Unit Weight, γ_sat (kN/m³) (if water table applies)
Calculate Bearing Capacity Results will appear here.
function soiUpdateFields() { // No dynamic field changes needed currently, placeholder for future }
function soiCalc() { const resultDiv = document.getElementById('soi-result');
// --- Read Inputs --- const footingType = document.getElementById('soi-footing-type').value; const B = parseFloat(document.getElementById('soi-width').value); const Df = parseFloat(document.getElementById('soi-depth').value); const c = parseFloat(document.getElementById('soi-cohesion').value); const phiDeg = parseFloat(document.getElementById('soi-friction').value); const gamma = parseFloat(document.getElementById('soi-unit-weight').value); const FOS = parseFloat(document.getElementById('soi-fos').value); const waterTable = document.getElementById('soi-water-table').value; const gammaSat = parseFloat(document.getElementById('soi-sat-unit-weight').value);
// --- Validation --- const errors = []; if (isNaN(B) || B 0."); if (isNaN(Df) || Df 45) errors.push("Friction angle φ must be between 0° and 45°."); if (isNaN(gamma) || gamma 0."); if (isNaN(FOS) || FOS 0."); if (waterTable !== 'deep' && gammaSat 0) { resultDiv.innerHTML = 'Input Errors:' + errors.map(e => '').join('') + ''; return; }
// --- Terzaghi Bearing Capacity Factors --- // phi in radians const phi = phiDeg * Math.PI / 180.0;
let Nc, Nq, Ngamma;
if (phiDeg === 0) { // Special case: purely cohesive soil (phi = 0) Nq = 1.0; Nc = 5.14; // pi + 2 Ngamma = 0.0; } else { // Terzaghi's original bearing capacity factors // Nq = e^(pitan(phi)) * tan^2(45 + phi/2) Nq = Math.exp(Math.PI * Math.tan(phi)) * Math.pow(Math.tan(Math.PI / 4 + phi / 2), 2); // Nc = (Nq - 1) * cot(phi) Nc = (Nq - 1) / Math.tan(phi); // Ngamma = 2(Nq + 1)*tan(phi) [Meyerhof's approximation, widely used] Ngamma = 2.0 * (Nq + 1) * Math.tan(phi); }
// --- Shape Factors (Terzaghi's shape factors) --- let sc, sq, sgamma; if (footingType === 'strip') { sc = 1.0; sq = 1.0; sgamma = 1.0; } else if (footingType === 'square') { sc = 1.3; sq = 1.0; sgamma = 0.8; } else { // circular sc = 1.3; sq = 1.0; sgamma = 0.6; }
// --- Water Table Correction --- // gammaQ: effective unit weight for overburden (q = gamma * Df) // gammaB: effective unit weight for base term (gamma * B) const gammaW = 9.81; // unit weight of water kN/m³ let gammaQ, gammaB;
if (waterTable === 'deep') { gammaQ = gamma; gammaB = gamma; } else if (waterTable === 'at-base') { // Water table at foundation base: // Overburden uses full gamma, base term uses submerged unit weight gammaQ = gamma; gammaB = gammaSat - gammaW; } else { // at-surface // Water table at ground surface: // Both terms use submerged unit weight gammaQ = gammaSat - gammaW; gammaB = gammaSat - gammaW; }
// Ensure effective unit weights are positive gammaB = Math.max(gammaB, 0.1); gammaQ = Math.max(gammaQ, 0.1);
// --- Overburden Pressure --- const q = gammaQ * Df; // kPa
// --- Ultimate Bearing Capacity (Terzaghi's equation) --- // qu = c * Nc * sc + q * Nq * sq + 0.5 * gamma_B * B * Ngamma * sgamma const term1 = c * Nc * sc; const term2 = q * Nq * sq; const term3 = 0.5 * gammaB * B * Ngamma * sgamma; const qu = term1 + term2 + term3;
// --- Allowable Bearing Capacity --- const qa = qu / FOS;
// --- Net Ultimate Bearing Capacity --- const qu_net = qu - q; const qa_net = qu_net / FOS;
// --- Format Output --- const footingLabel = footingType.charAt(0).toUpperCase() + footingType.slice(1); const wtLabel = waterTable === 'deep' ? 'Deep (no effect)' : waterTable === 'at-base' ? 'At Foundation Base' : 'At Ground Surface';
resultDiv.innerHTML = ` ### ✓ Bearing Capacity Results
ParameterValue Footing Type${footingLabel} Friction Angle, φ${phiDeg.toFixed(1)}° Bearing Capacity Factors Nc${Nc.toFixed(3)} Nq${Nq.toFixed(3)} Nγ${Ngamma.toFixed(3)} Shape Factors sc${sc.toFixed(2)} sq${sq.toFixed(2)} sγ${sgamma.toFixed(2)} Effective Unit Weights γ (overburden), γQ${gammaQ.toFixed(2)} kN/m³ γ (base term), γB${gammaB.toFixed(2)} kN/m³ Overburden Pressure, q${q.toFixed(2)} kPa Bearing Capacity Components Cohesion Term (c·Nc·sc)${term1.toFixed(2)} kPa Surcharge Term (q·Nq·sq)${term2.toFixed(2)} kPa Self-Weight Term (0.5·γB·B·Nγ·sγ)${term3.toFixed(2)} kPa Final Results Ultimate Bearing Capacity, qu${qu.toFixed(2)} kPa Net Ultimate Bearing Capacity, qu,net${qu_net.toFixed(2)} kPa Allowable Bearing Capacity, qa (FOS=${FOS})${qa.toFixed(2)} kPa Net Allowable Bearing Capacity, qa,net${qa_net.toFixed(2)} kPa
Water Table: ${wtLabel} | Factor of Safety: ${FOS}
`; }
#### Formula — Terzaghi's General Bearing Capacity Equation
Ultimate Bearing Capacity:
qu = c · Nc · sc + q · Nq · sq + 0.5 · γ · B · Nγ · sγ
Where q = γ · Df (overburden pressure)
Bearing Capacity Factors (Meyerhof):
- Nq = eπ·tan φ · tan²(45° + φ/2)
- Nc = (Nq − 1) · cot φ [= 5.14 when φ = 0°]
- Nγ = 2(Nq + 1) · tan φ
Terzaghi Shape Factors:
Footingscsqsγ Strip1.001.001.00 Square1.301.000.80 Circular1.301.000.60
Water Table Corrections:
- Deep: No correction — use γ throughout.
- At foundation base: Overburden uses γ; base term uses γ' = γsat − γw.
- At ground surface: Both terms use γ' = γsat − γw.
Allowable Bearing Capacity:
qa = qu / FOS
qu,net = qu − q | qa,net = qu,net / FOS
#### Assumptions & References
- Based on Terzaghi's (1943) general bearing capacity theory for shallow foundations (Df ≤ B).
- Bearing capacity factors Nc, Nq, Nγ follow Meyerhof (1963) formulations, which are widely adopted in modern practice.
- Shape factors follow Terzaghi's original values for strip, square, and circular footings.
- Soil is assumed to be homogeneous, isotropic, and the failure mode is general shear failure.
- Water table correction uses the effective stress approach with γw = 9.81 kN/m³.
- A Factor of Safety of 3.0 is typical for permanent structures (Das, 2016).
- References: Das, B.M. (2016). Principles of Foundation Engineering, 8th Ed. Cengage Learning. | Terzaghi, K. (1943). Theoretical Soil Mechanics. Wiley.
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