Experimental data and experience in industrial application revealed the high efficiency of the two-impact mode in driving various elements into the ground, which is due to the possibility of driving with different vibration parameters (including at high frequencies) without the danger of perturbing the operating stability of the impact-vibration mechanism.

The calculation scheme of driving in a two-impact mode is presented in Fig. 32. The difference in this scheme from the calculation scheme of a single-impact vibratory hammer consists in the introduction of the upper limiter of the movement of the vibration exciter, installed with a clearance w.

With the assumptions in Section 7, a piecewise linear system with the movement stages given below is examined.

Stage I – raising the impact part up to striking a blow on the upper limiter. The differential equation of motion for the stage and its initial conditions have the form (38). Completion of the stage occurs at the time of applying the impact on the upper limiter, i.e.,

with *t = t _{1} x = w, x = x_{1}*. (49)

Stage II – impact upward and joint movement of the hammer and pile after the impact up to the time of stoppage of the system:

(50)

After completion of the joint movement of the pile and hammer with *t = t _{2}*, stoppage of the hammer in the upper position is possible in this case, when the following inequality will occur

(51)

Stoppage of the hammer ends at the point of time *t’ _{2}*, at which

(52)

Stage III – flight of the impact part (dropping) down to application of the blow on the lower limiter. The movement in this stage is also described by Eq. (39) with the following initial and final conditions:

(53)

Stage IV – the impact downward and the subsequent driving of the pile, overcoming the lateral resistance of the ground up to the time of contact of the end of the pile with the ground:

(54)

Stage V – Driving of the tube, overcoming the lateral and frontal resistance of the ground prior to stoppage of the system. This is the basic working stage, during which the driving also takes place. The differential equation of motion of the system in this stage has the form (39) with the same final conditions and initial conditions with *t* = *t _{4}* (54). For the two-impact vibrating hammer the initial phase angle is determined with expression (40).

The differential equations of motion were solved on a computer,using dimensionless variables and parameters (42) and the additional parameter *u = m _{1} ω /P w*.

In analyzing the results obtained, it was found that the driving efficiency in the two-impact mode is substantially dependent on the size of the gap between the impact part and the upper limiter.

Graphs of the dependence of the optimal clearances u on the dimensionless resistance of the ground *f + γ* with different values of *sin α* are plotted in Fig. 33 (a clearance or gap at which the greatest sinkings per one impact are assured in stable operation of the vibrating hammer is understood to be optimal). An analysis of these graphs reveals that the magnitudes of the dimensionless optimal gaps are essentially dependent on the dimensionless resistances of the ground with small values of the parameter *sin α*, in which case large gaps correspond to high soil resistances. With the values *sin α* > 0.4 the magnitudes of the optimal gaps are practically independent of the soil resistance. In the following, all the driving parameters are given for the optimal gaps.

The graphs of the sinkings per one impact for the two-impact vibrating hammer are plotted in Fig. 34 in coordinates of *y* and *sin α*. The analogous graphs for the single-impact driving mode are given for comparison in the same Figure.

An analysis of these data reveals that the range of existence of the modes *n* = 1 for two-impact hammers is substantially broadened in comparison with single-impact hammers. Although modes with *n* = 1 are absent for single-impact hammers at the values *sin α* ≤ 0.3 and the *ξ _{1}* ≤ 0.5 values used in practice, these modes occur with all parameters of

*sin α*for the two-impact hammer.

This means in practice that by using the two-impact modes it is possible to employ light high-frequency vibrating hammers with a substantial compelling force with no adverse effect on the stability of their operation and at the same time increasing the driving rate of tubular or other elements.

It also follows from the data given in Fig. 34 that the maximum sinkings from the vibrating hammer impacts take place at *ξ _{1}* = 0.5, in which case the maximum sinkings occur at various values of

*sin α*as a function of the dimensionless resistance of the soil

*f + γ*.

Analysis reveals that if the driving parameters in the two-impact mode correspond to the optimal values of *u*, *sin α*, and *ξ _{1}*, the rate of driving in this mode exceeds the analogous rate in the single impact mode by 10-12%.

An experimental verification of the efficiency of the two-impact modes was carried out in the driving of tubes 83-274 mm in diameter into plastic loams with the aid of a special driver.

A comparison of the efficiency of the various modes was made with regard to the driving rate, extraction effort, stability of the working mode, maximum height of the ground plug that fills the tube, which is open at the bottom, during its driving, and the energy required. The typical graphs of driving a tube 103 mm in diameter and the filling of its cavity with the soil core with various vibrational and impact-vibrational modes are plotted in Fig. 35. The two-impact mode assured the maximum rate of tube driving and height of the ground plug.

The efficiency of two-impact driving of a tube under industrial conditions was verified with the aid of a vibrogripper, which was equipped with an impact attachment that assures its operation in the mode of an ordinary spring vibrating hammer, fastened with the driving element. The work was carried out in loams with a semihard consistency. In the driving of a soil collecting tube 1000 mm in diameter and 500 mm in height the operation of the vibrogripper (frequency 18 Hz, *sin α* = 0.3 – 0.35) was not efficient in the impact mode. The maximum driving depth attained during the various depressions of the springs *Q _{V,P}* did not exceed 10 – 15 cm. With an increase in the frequency above 18 Hz the stable operation of the vibrogripper in the impact mode was perturbed. Upper limiters were subsequently installed and the vibrogripper was adapted to the two-impact mode at a frequency of 25 Hz and

*sin α*= 0.18. Driving of the soil collecting tube in the two-impact mode was done with a speed of 0.5 m/min to the full height of the soil collector.

The results of these experiments revealed that, in contrast to the single-impact mode, the two-impact mode assures the possibility of an effective driving of a tube with a high frequency and a low value of *sin α*. For a light drivable construction (mass of the vibrogripper with impact attachment: 400 kg) the possibility of increasing the amplitude of the compelling force by increasing the frequency in the two-impact mode (without perturbing the operating stability) was the only means of assuring an effective driving of a tube in compact clay soils.

The efficiency of the two-impact mode was also confirmed under industrial conditions during extraction of the metal pile with the aid of the VSh-1 vibrating apparatus, adapted to the two-impact mode with a frequency of 13.3 Hz (Section 16).

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