#### M.R. Svinkin

*VibraConsult, Cleveland, Ohio, USA*

ABSTRACT: Elastic properties of cushion materials are used to determine elastic properties of composite hammer cushions. Equivalent stiffness of the composite hammer cushion depends mostly on the characteristics of soft cushion material and only the thickness of a soft material, not the total cushion thickness, should be taken for calculations. Equivalent modulus of elasticity of the composite hammer cushion depends on the modulus of elasticity of a soft material and a ratio of stiff to soft layers thicknesses. A change of soft and stiff layers thicknesses and their ratio may be used as a tool to increase force transmitted to the pile.

### 1 INTRODUCTION

Hammer cushion is installed in a well on a top of the drive cap (helmet) under the anvil which is struck by the hammer ram. The drive cap is employed to hold the pile head in position under hammer and to transfer impact energy to the pile.

The hammer cushion is used for two opposite purposes. On the one hand the hammer cushion must transfer the hammer energy to the pile without excessive energy losses, but on the other hand the hammer cushion has to prevent pile and hammer damage from driving.

Various materials such as wood, rope, polymers, fibers, aluminum and others are placed in the hammer cushion well. Combination of materials, like aluminium with Conbest or micarta, are frequently used for hammer cushions (Practical guidelines 1984; GRL Manual 1997; SPS 1999; Penn State Fabricators 1999).

Laminated materials such as aluminium and Conbest or aluminium and micarta have a relatively constant elasticity during relatively long life, consistent and predictable energy transfer and more uniform driving results.

The transfer of hammer energy to the pile and protection of pile and hammer from possible damage during pile driving depend on the moduli of elasticity and the stiffness of the materials used to composite hammer cushions.

The purpose of this paper is to show how moduli of elasticity and stiffness of different laminated cushion materials effect equivalent modulus of elasticity and equivalent stiffness of the composite hammer cushions.

### 2 TWO CUSHION MATERIALS

A composite hammer cushion has alternate layers of soft materials like Conbest or micarta and layers of stiff materials like aluminium or steel.

Stiffness of a soft layer, k_{soft}, and a stiff layer, k_{stf}, may be written

(1)

where

- E
_{soft}= modulus of elasticity of soft material; - E
_{stf}= modulus of elasticity of stiff material; - A = cross-section of cushion materials;
- t
_{soft}= thickness of soft material layer; - t
_{stf}= thickness of stiff material layer.

It is common that E_{stf} is considerably greater than E_{soft} and t_{stf} is equal or less than t_{soft}.

#### 2.1 *Equal number of layers*

Soft and stiff material layers are in series. Therefore equivalent stiffness of the composite hammer cushion, k_{eq}, is

(2)

where

- n = number of layers of each material;
- remaining parameters are the same as defined previously.

Equation (2) may be rewritten as

(3)

Relationship between equivalent stiffness and equivalent modulus of elasticity is

(4)

Equating the right pars of equations (3) and (4), we obtain

(5)

Equation (3) can be simplified to analyze a contribution of each cushion material to elastic properties of the composite hammer cushion. Since term t_{soft}E_{stf} in the denominator of equation (3) is 30-100 times greater than term t_{stf}E_{soft}, the latter term can be neglected. After simplification, equation (3) becomes

(6)

According to equation (6), equivalent stiffness of the composite hammer cushion depends on the modulus of elasticity, the layer thickness, and the cross-section of a soft material.

After analogous simplification, equation (5) takes the form

(7)

where

- a = t
_{stf}/t_{soft}

It can be seen that equivalent modulus of elasticity of the composite hammer cushion depends on the modulus of elasticity of a soft material and a ratio of stiff to soft layers thicknesses.

Calculation of the equivalent stiffness and the equivalent modulus of elasticity using simplified equations (6) and (7) has an error margin about 3 % in comparison with results of equations (3) and (5).

2.2 *Unequal numbers of layers*

A stiff material has usually one additional layer in a combination of Conbest or micarta with aluminium. Equivalent stiffness of the composite hammer cushion, k_{eq}, can be expressed

(8)

where all parameter are as defined previously.

After transformation and simplification, equation (8) becomes equal to equation (6).

### 3 THREE CUSHION MATERIALS

Composite cushions of three materials like aluminium, micarta and steel rope are sometimes used. Such cushions consist of two soft and one stiff materials connected in series. Assume that each cushion material has one layer and two soft layers have the same thickness, t_{soft}. Also, assume a ratio of the materials moduli of elasticity as E_{stf}>>E_{soft}>E_{softest}, where E_{softest} is modulus of elasticity of the softest material.

Equivalent stiffness of the composite hammer cushion, k_{eq}, may be written

After transformation and simplification, equation (9) takes the form

(10)

According to equation (10), equivalent stiffness of the composite hammer cushion filled with three materials depends on the modulus of elasticity of two soft materials, the thickness of a soft material layer and the cross-section of cushion materials.

Relationship between equivalent stiffness and equivalent modulus of elasticity is

(11)

Equating the right parts of equations (10) and (11), and, assume E_{soft}=2E_{softest} for simplicity, we obtain

(12)

For assumptions taken, equivalent modulus of elasticity depends on the modulus of elasticity of the softest material and the ratio of stiff to soft layers thicknesses.

### 4. DISCUSSION OF RESULTS

#### 4.1 *Two cushion materials*

Equivalent modulus of elasticity and equivalent stiffness of the composite hammer cushion are used in wave equation analysis of pile drivability and pile capacity. It is common that the total thickness of hammer cushion is taken for wave equation analysis.

Equation (6) shows that only the soft material effects the equivalent stiffness and only the thickness of a soft material should be used in calculations. Decreasing the total thickness of the composite hammer cushion to the actual thickness of a soft material increases force transmitted to the pile and provides more realistic consideration of hammer cushion properties in wave equation analysis of pile drivability and capacity.

According to equation (7), the ratio of stiff to soft layers thicknesses effects the equivalent modulus of elasticity. Values of E_{eq} are increased with increasing the aluminium or steel thickness and keeping the same Conbest or micarta thickness. For example, an enlargement of the aluminium layer thickness from 1 to 3 inches with the same Conbest thickness of 1 inch increases two times the value of E_{eq}.

Thus, equivalent stiffness depends on the thickness of soft cushion layers and equivalent modulus of elasticity depends on the ratio of stiff to soft layers thicknesses. Therefore a change of layers thicknesses provides certain flexibility to regulate elastic properties of the composite hammer cushions and, under certain drivability conditions, gives an opportunity to increase force transmitted to the pile for account of the layers thicknesses change instead of switching to more powerful hammer. Such a hammer will increase force transmitted down the pile in limits allowable by the pile impedance. It is reasonable to change the thickness of soft and stiff layers of the composite hammer cushion as the first step in increasing dynamic force applied to the pile.

#### 4.2 *Three cushion materials*

Equivalent stiffness of the composite hammer cushion in equation (10) depends on the moduli of elasticity, the thicknesses, and the cross-section of the softest and soft material layers. According to equation (12), equivalent modulus of elasticity depends to a lesser degree on the ratio of stiff to soft layers in comparison with two cushion materials.

### 5 CONCLUSIONS

Proper determination of elastic properties of composite hammer cushions is important for the application of the wave equation method to piles.

Equivalent stiffness of the composite hammer cushion depends mostly on elastic properties of a soft cushion material: the modulus of elasticity, the layer thickness and the cross-section.

The total thickness of composite hammer cushion is usually taken into account for wave equation analysis of pile drivability and pile capacity. Since a soft material mostly effects the equivalent stiffness, only the thickness of a soft material should be used in calculations.

Equivalent modulus of elasticity of the composite hammer cushion depends on the modulus of elasticity of soft material and the ratio of stiff to soft layers thicknesses.

A change of soft and stiff layers thicknesses and their ratio may be used as a tool to increase force transmitted to the pile. This may improve pile drivability without switching to more powerful hammer for certain driving conditions.

### REFERENCES

- GRL and Associates, Inc. 1997.
*GRLWEAP – Wave Equation Analysis of Pile Driving, Manual*, Cleveland, Ohio. - Penn State Fabricators. 1999.
*Conbest cushion blocks – Information*, New York. - Practical guidelines for the selection, design and installation of piles. 1984. Committee on Deep Foundations, ASCE.
- Specialty Piling Systems, Inc. 1999.
*Hammer cushion materials – Information*, Slidell, Louisiana.