Page 1 of 21

Transactions on Engineering and Computing Sciences - Vol. 11, No. 2

Publication Date: April 25, 2023

DOI:10.14738/tecs.112.14452.

Toma, S., Seto, K., & Chen, W. F. (2023). Dynamic Analysis for Overturning of Pile Driving Machine, etc., on Soft Ground.

Transactions on Engineering and Computing Sciences, 11(2). 61-81.

Services for Science and Education – United Kingdom

Dynamic Analysis for Overturning of Pile Driving Machine, etc.,

on Soft Ground

Shouji Toma

Hokkai-Gakuen University, Sapporo, Japan

Kenji Seto

Hokkai-Gakuen University, Sapporo, Japan

Wai Fah Chen

University of Hawaii, Hawaii, USA

ABSTRACT

There were quite a few overturning accidents of heavy machinery which have a high

center of gravity such as pile driving machines, cranes, jacks, or working vehicles

with aerial platform. Researches to study the background of the accidents have

taken place from the structural stability point of view by the authors. The structural

instability, as can be seen typically in the elastic buckling of columns, may be a blind

spot because the structures deflect in different directions to that of the load, which

makes it difficult to predict. According to the past investigations, the overturning

mechanisms can be categorized into the three: (1) Type of overturning moment, (2)

Type of structural instability and (3) Type of equilibrium transition, in which Type

of equilibrium transition plays important role on the overturning on soft ground.

The past investigations were based on the static analysis. Dynamic analysis is

essential to include the effect of inertial forces which will significantly affect the

overturning accidents on the soft ground. In the static analysis, the displacement

inclination is considered to stop at the equilibrium position, but in the dynamic

analysis it will continue increasing due to the inertial force. Then, it is possible the

displacement may go beyond the equilibrium and even the stability limit to

overturn. In this paper, the equations of motion will be first introduced, then

behaviors of the machinery from time to time, i.e., the inclination-time curves, will

be obtained by solving the equations. It is shown that the dynamic analysis can

explain more precisely the overturning behaviors of the machinery on the soft

foundation than the static analysis.

Keywords: Overturning Accident, Overturning Mechanism, Pile Driving Machine, Crane,

Structural Stability, Soft Foundation, Initial Imperfections

INTRODUCTION

Overturning accidents of cranes, pile driving machines, Jacks, working vehicles with aerial

platform, etc., on soft ground have occurred frequently in Japan [1~3]. In the United States, the

Pile Driving Contractors Association (PDCA) also has a great concern on the accidents by

providing the information for the safe working platforms at the construction site [4, 5]. In

Page 2 of 21

62

Transactions on Engineering and Computing Sciences (TECS) Vol 11, Issue 2, April - 2023

Services for Science and Education – United Kingdom

general, the investigation of the causes is focused on comparing the ground strength to the

working pressure induced by the overturning moment [6]. On the other hand, in the early

studies it is pointed out that the theory of structural stability which can be seen typically in the

column buckling should be considered to investigate the causes of the overturning accidents,

and that a high center of gravity which may lead to the structural instability exists commonly

as the background of these accidents [7~9]. In the past, the fall accidents of bridge girders by

the overturning jacks were first studied [10], then the overturning behaviors of heavy

machinery such as pile driving machines or cranes which have a high center of gravity were

investigated [11, 12]. They are published in the international engineering journals as well [13,

14].

However, those researches are based only on the static analysis and the dynamic effect due to

the inertia force is not included. The dynamic analysis is essential to understand the

overturning mechanism more in detail. In this paper, the past static analyses are outlined at the

beginning, in which the overturning mechanism can be categorized into the three: (1) Type of

overturning moment, (2) Type of structural instability and (3) Type of equilibrium transition.

It is found that the type of equilibrium transition plays an important role on the overturning on

soft ground. Then, the equations of motion are derived for the dynamic analysis and solved to

obtain the displacement inclination change against time by oscillation. By the dynamic analysis

the mechanism will be explained how the initial inclination amplifies the inclination of the

machinery, thus increasing the possibility of the overturning.

This paper aims to understand generally the overturning mechanisms of the heavy machinery

from the stability point of view. Therefore, only the transverse direction of overturning is

discussed without any other directions and the attenuating force is disregarded.

OVERTURNING MECHANISMS BY STATIC ANALYSIS

Structural Model and Equilibrium Equations

Since details of the relationship of the load and the displacement inclination are described in

the previous papers [10~14], only the outline will be given in this paper. The structural model

in the static analysis assumes that, as shown in Fig. 1, the whole machine is rigid with

sufficiently large stiffness and connected to the ground with the rotational spring stiffness.

Whole weight of the machine is considered to concentrate at the center of gravity which is

calculated by applying the first degree of moment.

The equilibrium of moment in Fig. 1 leads to the following equation [15]:

Ks(θ − θo) − P(Lsinθ + ecosθ) = 0 (1)

in which Ks = rotational spring stiffness (assumed as linear), P = load (whole weight of

machine), L = height of load, θ= displacement inclination, θo= initial inclination, e = eccentricity

of load

Page 3 of 21

63

Toma, S., Seto, K., & Chen, W. F. (2023). Dynamic Analysis for Overturning of Pile Driving Machine, etc., on Soft Ground. Transactions on Engineering

and Computing Sciences, 11(2). 61-81.

URL: http://dx.doi.org/10.14738/tecs.112.14452

The first term of Eq. (1) is the righting moment and the second is the overturning moment. It

should be noted that Ks in Eq. (1) is assumed as linear, therefore the righting moment in Eq. (1)

will be increased unlimitedly as θ increases. From Eq. (1) the load-displacement relationship is

derived as follows:

P =

Ks( θ−θo)

Lsinθ+ecosθ

(2)

Figure 1. Structural Model in Static Analysis.

Assuming in Eq. (2) that the initial imperfections are zero, i.e., θo= 0 and e = 0, and that the

displacement inclination is infinitesimal, the eigenvalue load for overturning Pcr will be derived

as follows:

Pcr =Ks / L (3)

The load in Eq. (3) corresponds to the Euler load in the elastic column buckling. Non- dimensioning P of Eq. (2) by Pcr of Eq. (3) gives

P

Pcr

=

θ−θo

sinθ+ecosθ/L

(4)

Using Eq. (4), a relationship between the load and displacement inclination is plotted in Fig. 2.

It can be found that the displacement is increased significantly by the effect of the initial

inclination.