Elastic Modulus of Rock given Deflection due to Thrust on Arch Dam Calculator

Elastic Modulus Formula:

\[ E = \frac{F \times K2}{\delta} \]

Elastic Modulus of Rock (E): Pa

1. What is Elastic Modulus of Rock given Deflection due to Thrust?

Definition: This calculator determines the elastic modulus of rock based on the thrust force, constant K2, and deflection measurements in an arch dam.

Purpose: It helps civil engineers assess the deformation characteristics of rock foundations for arch dam projects.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ E = \frac{F \times K2}{\delta} \]

Where:

\( E \) — Elastic modulus of rock (Pa)
\( F \) — Thrust of abutments (N)
\( K2 \) — Constant depending on b/a ratio and Poisson ratio
\( \delta \) — Deflection due to moments (m)

Explanation: The thrust force multiplied by constant K2 is divided by the measured deflection to determine the rock's stiffness.

3. Importance of Elastic Modulus Calculation

Details: Accurate determination of rock elastic modulus is crucial for assessing dam stability, foundation behavior, and structural integrity.

4. Using the Calculator

Tips: Enter the thrust force in Newtons, constant K2, and deflection in meters. All values must be > 0. Results have ±5% tolerance.

5. Frequently Asked Questions (FAQ)

Q1: What is typical elastic modulus for dam foundation rock?
A: Values typically range from 10-70 GPa, depending on rock type and quality.

Q2: How is constant K2 determined?
A: K2 depends on the arch dam's geometry (b/a ratio) and the rock's Poisson ratio.

Q3: Why is deflection measurement important?
A: Deflection directly affects the calculated modulus - small errors can significantly impact results (±5% tolerance).

Q4: How does this relate to dam safety?
A: Proper rock modulus ensures the foundation can withstand thrust forces without excessive deformation.

Q5: Can this be used for other structures?
A: The principle applies to any structure where rock deformation under load is critical.