Double resonance ground/structure

In case of an earthquake there is a risk of amplification of its effects on a building, this risk is known as “double resonance” and occurs when the value of the fundamental resonance frequency of the ground of foundation is similar to the one of the building.

The effects of the double resonances

The effects by double resonance ground / structure are responsible of the damage in the event of an earthquake. Each structure has its own resonant frequency Fb, it is necessary to investigate if in the subsoil there are amplifications due to stratigraphic resonance around that frequency.

For the calculation of the resonance frequency of the building, consolidated formulations in technical literature and reported on European legislation are applied. The frequency with which the resonance occurs in the ground is described by the law:

f=Vs/4H

Where:

• H = Height from the base plane (or building height);
• V_s = Speed ​​of the shear waves.

EASY HVSR: Allows to obtain immediate results in the estimation of: resonance frequency, stratigraphic profile and velocity of shear waves equivalent Vs, eq. All according to the guidelines suggested by the SESAME project.

Estimation of the T₁ vibration period according to EC 8

The estimation of the period of the principal vibrating mode in the direction under consideration (T1) is made according to the methods reported in annex C of EC8 part 1-2, for buildings with a height up to 80 m, the value of the period T1 can be approximated by the following formula:

T₁ = C_t(H)^3/4  [C1]

Where:

• T₁ = basic period of the building, expressed in seconds;
• C_t = coefficient that varies according to the type of building:
  • 0.085 for rigid steel knots with steel frames;
  • 0.075 for concrete frames with rigid knots and eccentric bracing;
  • 0.050 for all other structure;
• H = building height.

Verification of double resonance of the building/soil

If the percentage difference in the resonant frequency building / soil is ≤ 50%, there will be seismic amplification effects due to double resonance.
If the percentage difference in the resonant frequency of the building / soil is > 50%, the effects of local seismic amplification can be reasonably excluded for double resonance.