# Articles and Monographs on Vibratory and Impact-Vibration Equipment Written by Vulcan Personnel

### Development of a Parameter Selection Method for Vibratory Pile Driver Design with Hammer Suspension

This paper details the mathematical modelling of vibratory pile driving systems using a linear model with the objective of obtaining a closed form solution to estimate either the power requirement of the machine, the torque requirement of the motor driving the eccentrics, or both. It begins by reviewing the system model for the system without a suspension, which is used to enable connection of the vibrating machine with a crane, a mast of a dedicated machine, or an excavator. It proceeds to solve the equations of motion for a system with a suspension, using Laplace transforms and solving the inverse transform using residues and complex integration. The model indicates that, under certain conditions, both the amplitude and the power consumption of the system increase with a suspension, but the results make the practical implications of the result uncertain. Finally a simple set of equations is developed for actual vibratory design which results in the suspension being ignored and the necessary torque of the driving motor computed.

## Inclusion of Rotational Inertial Effects in Power Consumption Calculations for Vibratory Pile Equipment

March 2022

Virtually all treatments of power consumption and modelled performance for vibratory pile driving equipment assume a constant rotational speed of the eccentrics. In reality this is not possible due to the inertial effects of the eccentrics themselves and the necessity that, without inertia, the power output of the motor for the eccentrics must follow the instantaneous power requirements, which continuously vary. In this paper the rotational inertial effects of the eccentrics are included in the calculations. Because of the non-linear nature of the equations, a numerical model was developed to estimate the dimensionless torque required to turn the eccentrics at a target rotational speed. The results track closely with those of the continuous torque model described by Warrington (2006) for a wide variety of inertia/eccentric moment ratios, although there are exceptional cases if the peak acceleration is increased and the frequency decreased. As an excursus, the method of computing the inertia/eccentric moment ratio and its corresponding pendulum frequency is described in detail for those who can apply this to other problems.

### Letter to Michael O’Neill re Wave Equation Analysis Program for Vibratory Hammers

Vulcan correspondence which gives important information for wave equation analysis of vibratory hammers, along with other important information on vibratory hammer theory. Note: Dr. Michael O’Neill was one of the greats of the geotechnical industry, both as an engineer and as a person. This is the “memorial book” collected after he passed away suddenly in 2003.

### Reconstructing a Soviet-Era Plastic Model to Predict Vibratory Pile Driving Performance

#### April 2021

The technique for driving piles by vibration (as opposed to impact) has been an important component of deep foundations and retaining wall installation since it was first demonstrated in the Soviet Union in the late 1940’s. The Soviets originally developed the technology and applied it to a wide variety of pile types. Nevertheless, the analytical methods they developed to estimate the performance of these machines have not been widely disseminated outside of the country, either before or after the breakup of the Soviet Union. In this paper one specific model, analysing longitudinal vibratory performance using a purely plastic/Coulombic model of soil resistance, is reconstructed and discussed. The model is compared with the most disseminated Soviet model for sizing vibratory pile drivers and predicting performance. Some discussion on Soviet vibratory modelling beyond the model presented is also included.

### Survey of Methods for Computing the Power Transmission of Vibratory Hammers

This paper is a survey of analytical methods used to calculate the power consumption and transmission of vibratory hammers used in the installation of piles. The paper discusses the parameters, derivation, and comparative usefulness of various methods of computing the power consumption of these machines. The paper also discusses the importance of torque calculations as well as power calculations. The power consumption of vibratory hammers is important because a) many of the existing methods for estimating the resistance and/or bearing capacity of the piles use power consumption as a parameter, and b) methods being developed to determine the bearing capacity and drivability of piles driven by vibration will probably use these methods. Suggestions for further research in this field, including factors to consider in modelling power transmission and consumption, are set forth.

### Vibratory and Impact-Vibration Pile Driving Equipment

This article is an overview of the application and vibratory and impact-vibration pile driving equipment. It includes the history of the development of the equipment, the types of piles that can be driven with this type of equipment, a description of the safe operation of the equipment, and an extensive treatment of methods of determining drivability and capacity of piles driven by vibratory and impact-vibration hammers.

Note: this has become something of a “hit” on ResearchGate, which attests to the abiding interest in this topic and to the lack of introductory monographs on the subject.