Elastic Modulus of Rock given Rotation due to Moment on Arch Dam Calculator

Elastic Modulus of Rock Formula:

\[ E = \frac{M_t \times K_1}{\Phi \times T \times t} \]

Moment acting on Arch Dam:

Joule

Constant K1:

Angle of Rotation:

radian

Thickness of Circular Arch:

meter

Horizontal Thickness of an Arch:

meter

Elastic Modulus of Rock (Pascal):

1. What is Elastic Modulus of Rock given Rotation due to Moment on Arch Dam?

Definition: This calculator determines the elastic modulus of rock based on the rotation caused by moment acting on an arch dam.

Purpose: It helps civil engineers assess the rock foundation's stiffness for arch dam design and stability analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ E = \frac{M_t \times K_1}{\Phi \times T \times t} \]

Where:

\( E \) — Elastic Modulus of Rock (Pascal)
\( M_t \) — Moment acting on Arch Dam (Joule)
\( K_1 \) — Constant depending on b/a ratio and Poisson ratio (±5%)
\( \Phi \) — Angle of Rotation (radian)
\( T \) — Thickness of Circular Arch (meter)
\( t \) — Horizontal Thickness of an Arch (meter)

Explanation: The formula relates the rock's elastic modulus to the dam's rotational response under applied moment.

3. Importance of Elastic Modulus Calculation

Details: Accurate estimation ensures proper dam design, foundation stability assessment, and safety against deformation.

4. Using the Calculator

Tips: Enter all required parameters. The constant K1 typically has ±5% variability. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What affects the constant K1 value?
A: K1 depends on the arch dam's geometry (b/a ratio) and the rock's Poisson ratio (±5% variability).

Q2: How is angle of rotation measured?
A: It's typically measured in radians using precise surveying instruments monitoring dam deformation.

Q3: What's a typical elastic modulus for dam foundations?
A: It varies widely (10-100 GPa) depending on rock type, from soft shales to hard granite.

Q4: Why is horizontal thickness important?
A: It represents the arch's cross-section dimension that resists the moment-induced rotation.

Q5: How accurate is this calculation?
A: Results are estimates (±5-10%) as rock properties can vary spatially in foundations.