The following figure visualizes the value Δf frequency, distance between two peaks that leads to the calculation of the lengths of the tested elements, also appear the admittance and the dynamic stiffness at the origin of the curve (Fig. 4.1).

Fig. 4.1
figure 1

Curve V/F function of frequency

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The example that is presented comes from tests carried out on tie rods made 30 years ago to stabilize road retaining walls in a state in southern Brazil.

All the 664 tie rods on 6 retaining walls were tested. Our example is a retaining wall of 28 tie rods (Figs. 4.2 and 4.3).

Fig. 4.2
figure 2

Nondestructive test

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Fig. 4.3
figure 3

Front view of the retaining wall

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Tie rods P1 Panel 1 Tie rod 2—P1 7—P2 2—P2 4—P3 4—P3 5 were not tested for several reasons, for example: plate partly in contact with the wall or deterioration of the tie rod head.

The results presented in the following table gather the total length of the ground anchor the free-length and the calculated sealed length (Fig. 4.4).

Fig. 4.4
figure 4

Results table

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These results are compared to the design (Fig. 4.5).

Fig. 4.5
figure 5

Tie-rod execution drawing

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Here after the curves obtained during the tests used to calculate total lengths and free lengths, see the curves in the following figures test P1 2C panel 1 tie rod 2 test C.

On each tie rod 8 tests are performed (Figs. 4.6 and 4.7).

Fig. 4.6
figure 6

Total length 18,1 m

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Fig. 4.7
figure 7

Free-length 10 m

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The results obtained show that the tie rods produced correspond with the plans in terms of length.

It is necessary to draw attention to the fact that when calculating the length of the tie rods, the velocity of wave propagation in the tie rods is very often greater than 4000 m/s.

For example, the table below, taken from a test report, shows that the hypothesized retained velocities are 4500m/s and 5100m/s taking into account the site information (Fig. 4.8).

Fig. 4.8
figure 8

Table for calculating the lengths

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