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

Elastic Modulus Formula:

\[ E = \frac{F_s \times K_5}{\Phi \times T} \]

N
rad
m
Pa

1. What is Elastic Modulus of Rock?

Definition: Elastic Modulus of Rock is defined as the linear elastic deformation response of rock under deformation.

Purpose: It helps engineers understand how much a rock formation will deform under stress, which is crucial for dam construction.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ E = \frac{F_s \times K_5}{\Phi \times T} \]

Where:

  • \( E \) — Elastic Modulus of Rock (Pa)
  • \( F_s \) — Shear Force (N)
  • \( K_5 \) — Constant depending on b/a ratio and Poisson ratio (±5%)
  • \( \Phi \) — Angle of Rotation (rad)
  • \( T \) — Thickness of Circular Arch (m)

Explanation: The formula relates the elastic modulus to the shear force, arch geometry, and resulting rotation.

3. Importance of Elastic Modulus Calculation

Details: Accurate calculation ensures dam stability by predicting how much the foundation rock will deform under load.

4. Using the Calculator

Tips: Enter shear force in newtons, constant K5 (±5%), rotation angle in radians, and arch thickness in meters. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is typical K5 value range?
A: K5 typically ranges between 0.5-2.0 depending on arch geometry and Poisson's ratio (±5% variation).

Q2: How to measure angle of rotation?
A: Use precision inclinometers or tiltmeters installed at critical points on the dam.

Q3: Why is thickness important?
A: Thicker arches distribute shear forces over larger areas, reducing stress concentrations.

Q4: What affects elastic modulus most?
A: Rock type, jointing, weathering, and water content significantly impact modulus values.

Q5: How accurate is this calculation?
A: Results are theoretical estimates; field measurements and testing provide more accurate values.

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