Abstract:

Based on the principle of "conservation of energy," the Hiley formula—a method for estimating the ultimate bearing capacity from the final penetration during dynamic pile driving—has been widely applied and recognized. However, determining the coefficients in the formula is a complex and difficult process. In fact, dynamic pile driving is the process of driving a pile by utilizing the enormous instantaneous force generated when the hammer core of the pile hammer collides with the pile top. During the collision, the force changes very sharply and is accompanied by intense losses of mechanical energy in the forms of sound, light, heat, etc. Based on the collision principles of fundamental physics and applying the law of "conservation of momentum," this paper treats the hammer and the pile as a single system, establishes the relationship between hammer blow displacement and motion velocity, and derives an estimation formula for the hammer blow force. This provides a new method for selecting hammers for dynamic pile driving and for estimating the ultimate bearing capacity of pile foundations.‍

I. Overview

For dynamic pile driving problems, several pile foundation bearing capacity analysis methods are widely used in engineering: the formula method, the wave equation analysis method, and the empirical comprehensive analysis method [1]. These are used as methods for selecting the hammer blow energy of the pile hammer and estimating the ultimate bearing capacity.

The Hiley formula in dynamic pile driving formulas, used to predict the ultimate bearing capacity from the final penetration during pile driving (Pu = 孜W rH浊 /(e+c/2), proposed by Hiley A in 1930), is based on the "conservation of energy" theorem during hammer blows and on the rebound value. Its derivation method is based on the characteristic that the hammer core is a free-falling hammer; the hammer blow process is divided into four stages: before impact, after impact, elastic recovery, and rebound, and the conservation and transfer of energy in each stage are analyzed. The Hiley formula has been widely applied and recognized both in the West and in China. However, determining parameters such as the reduction coefficient 孜, the hammer blow efficiency coefficient 浊, and the elastic deformation c of the pile-soil system in the Hiley formula is a complex and difficult problem. In recent years, the widespread application of PDA dynamic testing technology in hammer-driven pile installation and the measured data from its results have provided an effective way to determine the relevant parameters in the Hiley formula.

However, in the actual pile driving process, mechanical energy is released in the forms of sound, light, heat, etc. during the impact of the hammer core on the driving cap and pile top, and during the compression deformation of the hammer cushion, pile cushion, and pile body. In this series of intense and complex evolution processes, energy is dissipated. Therefore, although the dynamic pile driving analysis method based on conservation of energy has played a certain role in solving engineering problems, it is difficult for the physical quantities involved in the formula to explain characteristics manifested during pile driving, such as "heavy hammer, light blow" and the "hammer-to-pile weight ratio."

II. Brief Analysis of the Dynamic Pile Driving Process

The dynamic pile driving process is actually the use of the hammer core of a pile hammer to strike the pile top. The hammer core is lifted to a certain height by external power equipment or by the work done by the internal fuel explosion of the pile hammer, and then falls rapidly, converting potential energy into kinetic energy. It strikes the pile top rapidly at velocity V1, generating an enormous instantaneous force that forces the pile body to overcome the lateral friction resistance generated by the rock and soil, after which the pile tip punches and shears the rock and soil and embeds itself into the rock and soil. The following briefly analyzes each stage of the hammer blow process, taking a single-acting hydraulic hammer as an example.

2.1 Hammer Core Energy Storage Stage

The hydraulic cylinder lifts the hammer core to a predetermined height H; this process converts external mechanical energy into the gravitational potential energy of the hammer core. Let the gravitational potential energy be Eg, the mass of the hammer core be m, and the total mass of the pile body (including the driving cap) be M. Then the gravitational potential energy stored in the hammer core is: Eg = mgH. The schematic diagram of dynamic pile driving is shown in Figure 1.

Figure 1 Schematic Diagram of Dynamic Pile Driving

2.2 Before the Hammer Core Strikes the Pile Top

After the hammer core rises to the set height and obtains gravitational potential energy Eg, under the control of the operating valve it falls rapidly in a state approximating free fall, converting gravitational potential energy into kinetic energy Ed. At this moment, the velocity V1 of the hammer core reaches its maximum value.

2.3 After the Hammer Core Strikes the Pile Top

After the hammer core strikes the pile top, the hammer core and the pile body (driving cap, etc.) form a system, and the velocity of the hammer core suddenly changes from the previous V1 to V2. During this collision process, part of the mechanical energy is dissipated in the forms of sound, light, and heat. 

2.4 Displacement of the Hammer-Pile System

After the hammer core strikes the pile top, an enormous hammer blow force is generated, forcing the pile body to overcome the lateral friction and end resistance of the rock and soil and produce downward displacement. Part of the displacement consists of the compression of the hammer cushion, pile cushion, and pile body; the other part is the penetration e into the rock and soil. Part of the momentum of the hammer-pile system is converted into elastic potential energy and stored in the elastic elements; the other part overcomes the resistance of the rock and soil to the pile body and produces effective penetration work.

2.5 Rebound of the Hammer-Pile System

After the hammer-pile system completes the downward displacement, its velocity rapidly drops to zero. However, as the downward process ends, the "elastic potential energy" stored in the compressed hammer cushion, pile cushion, and pile body is released in the reverse direction, driving the hammer-pile system to once again overcome the lateral friction of the rock and soil and move upward in rebound. Its rebound value is the quantity mentioned in the Hiley formula. At this point, one complete cycle of dynamic pile driving ends.

2.6 Velocity Changes of the Hammer-Pile System

Now take the domestic YZ-25 hydraulic hammer [2] driving a steel pipe pile with a pile body mass (including driving cap) of 50 t as an example for analysis. The hammer core mass is 25 t, and the hammer stroke H = 1.5 m. Assume: elastic compression value c = 30 mm, penetration e = 20 mm, and hammer blow frequency approximately 30 blows/min. The schematic diagram of the velocity changes of the hammer core during the hammer blow process is shown in Figure 2.

Figure 2 Schematic Diagram of Velocity Changes of the Hammer-Pile System