Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculation HTML Code Included

Terzaghi Bearing Capacity Estimation in simple
terms with Calculation HTML Code
By Dr. C. Sachpazis
May 31, 2024
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in
geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory
provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per
unit area that the soil can support without undergoing shear failure.
Key Concepts
1. Ultimate Bearing Capacity (qu):
The ultimate bearing capacity is the maximum pressure that can be applied at the base of the
foundation before the soil fails in shear.
2. Net Ultimate Bearing Capacity(qnu):
This is the ultimate bearing capacity minus the overburden pressure at the foundation level.
3. Allowable Bearing Capacity {qa):
This is the ultimate bearing capacity divided by a factor of safety(FOS), to ensure the foundation's
safety and stability under load conditions.
Terzaghi's Bearing Capacity Equation
The ultimate bearing capacity for a strip footing can be expressed as:
Where:
• q,, = Ultimate bearing capacity
• c = Cohesion of the soil
• 1 = Unit weight of the soil
• DJ = Depth of the foundation
• B = Width of the foundation
• Ne, Nq, N1 = Bearing capacity factors, which depend on the internal friction angle(</>) of the soil
Bearing Capacity Factors

ThebearingcapacityfactorsNc,Nq,andNγaredimensionlesscoefficientsthatdependontheangleof
internal friction (¢) of thesoil. They can be derived from empirical formulas or charts based on
experimental data.
• Ne is related to the soil's cohesion.
• Nq accounts for the effect of the overburden pressure.
• N1 considers the effect of the soil weight.
The expressions for these factors are:
Assumptions in Terzaghi's Theory
1. Homogeneous and Isotropic Soil:
The soil is assumed to be homogeneous and isotropic, meaning its properties are consistent in all
directions.
2. Rigid Foundation:
The foundation is considered rigid and perfectly rough.
3. General Shear Failure:
The theory assumes that thesoil will fail in a general shear mode, characterized by well-defined
shear planes extending from the edges of the footing to the ground surface.
4. Semi-Infinite Soil Mass:
The soil mass is considered semi-infinite, meaning it extends infinitely in horizontal directions.
5. Shallow Foundation:
The depth of the foundation is assumed to be small compared to its width (shallow foundation).
Adjustments for Shape and Depth
For different foundation shapes (e.g., circular, square) and depths, Terzaghi's equation is modified by
introducing shape and depth factors:
Where sand dare shape and depth factors, respectively, which are determined based on the
foundation type and conditions.
Practical Considerations
When applying Terzaghi's theory in practice, geotechnical engineers must:
1. Conduct Soil Testing:
Perform site-specific soil tests to determine soil properties such as cohesion, internal friction angle,
and unit weight.
2. Factor of Safety:

Apply an appropriate factor of safety to account for uncertainties in soil properties and loading
conditions.
3. Settlement Analysis:
Consider the settlement behavior of the soil to ensure that the foundation will perform
satisfactorily under the expected loads.
4. Local Adjustments:
Adjust the theoretical values based on local experience and empirical correlations, if necessary.
Conclusion
Terzaghi's soil bearing capacity theory provides a robust framework for evaluating the load-carrying
capacity of shallow foundations. By understanding and applying this theory, geotechnical engineers can
design safe and efficient foundation systems that meet the demands of various construction projects.
By Dr. Costas Sachpazis
HTML code to calculate the bearing capacity of soil using Terzaghi's bearing capacity
theory
Now, based on the provided document, we can develop an HTML code to calculate the bearing
capacity of soil using Terzaghi's bearing capacity theory. The following code includes user inputs for
cohesion (c), unit weight of soil (y), depth of foundation (Df), width of foundation (B), and the internal
angle of friction (cp). It also considers the depth of the water table (Dw).
Here's the HTML code to create the form and perform the calculation:
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Bearing Capacity Calculator</title>
<style>
body {
font-family: Arial, sans-serif;
margin: 20px;
}
label, input {
display:
block;
margin:
10px 0;
}
input[type="text"], input[type="number"] {
width: 100%;
padding: 8px;
box-sizing: border-box;
}

button {
padding: 10px 20px;
background-color: #4CAF50;
color: white;
border: none;
cursor: pointer;
}
button:hover {
background-color: #45a049;
}
.result {
margin-top: 20px;
padding: 10px;
border: 1px solid #ccc;
}
.footer {
margin-top: 30px;
font-size: 0.9em;
color: #666;
}
</style>
</head>
<body>
<h1>Bearing Capacity Calculator</h1>
<form id="bearingCapacityForm">
<label for="c">Cohesion (c) [kN/m²]:</label>
<input type="number" id="c" name="c" required>
<label for="gamma">Unit Weight of Soil (γ) [kN/m³]:</label>
<input type="number" id="gamma" name="gamma" required>
<label for="Df">Depth of Foundation (Df) [m]:</label>
<input type="number" id="Df" name="Df" required>
<label for="B">Width of Foundation (B) [m]:</label>
<input type="number" id="B" name="B" required>
<label for="phi">Internal Angle of Friction (φ) [degrees]:</label>
<input type="number" id="phi" name="phi" required>
<label for="Dw">Depth of Water Table (Dw) [m]:</label>
<input type="number" id="Dw" name="Dw" required>
<button type="button" onclick="calculateBearingCapacity()">Calculate Bearing
Capacity</button>
</form>

<div class="result" id="result"></div>
<div class="footer">
Program written by Dr. Costas Sachpazis.
</div>
<script>
function calculateBearingCapacity() {
// Get the values from the form
const c = parseFloat(document.getElementById('c').value);
const gamma = parseFloat(document.getElementById('gamma').value);
const Df = parseFloat(document.getElementById('Df').value);
const B = parseFloat(document.getElementById('B').value);
const phi = parseFloat(document.getElementById('phi').value);
const Dw = parseFloat(document.getElementById('Dw').value);
// Convert phi from degrees to radians
const phiRad = phi * Math.PI / 180;
// Calculate Nq, Nc, and Ny using Terzaghi's bearing capacity factors
const Nq = Math.exp(Math.PI * Math.tan(phiRad)) * Math.tan(Math.PI / 4 +
phiRad / 2) ** 2;
const Nc = (Nq - 1) / Math.tan(phiRad);
const Ny = 2 * (Nq + 1) * Math.tan(phiRad);
// Calculate the correction factor for the water table
const DwB = Dw / B;
const DwDf = Dw / Df;
let gammaEffective = gamma;
if (DwDf < 1) {
gammaEffective = gamma * (1 - 0.5 * DwDf);
} else if (DwB < 1) {
gammaEffective = gamma * (1 - 0.5 * DwB);
}
// Calculate the ultimate bearing capacity
const qu = 1 / 2 * gammaEffective * B * Ny + gammaEffective * Df * Nq + c *
Nc;

// Calculate the allowable bearing capacity
const qa = qu / 3;
// Display the result
document.getElementById('result').innerHTML = `
<strong>Ultimate Bearing Capacity (qu):</strong> ${qu.toFixed(2)} kN/
m²<br>
`;
}
<strong>Allowable Bearing Capacity (qa):</strong> ${qa.toFixed(2)} kN/m²
</script>
</body>
</html>
This code provides a simple interface for users to input the required parameters and
calculates the ultimate and allowable bearing capacity based on Terzaghi's bearing
capacity theory. The form includes inputs for cohesion, unit weight of soil, depth of
foundation, width of foundation, internal angle of friction, and the depth of the water
table. The calculation considers the presence of the water table and adjusts the
effective unit weight accordingly.
By Dr. Costas Sachpazis

Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculation HTML Code Included

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