# «PILE DRIVING ANALYSIS BY THE WAVE EQUATION For technical assistance, contact: Dr. Lee L. Lowery, Jr., P.E. Department of Civil Engineering Texas A&M ...»

Since a total resistance of 300 kips is desired, the new piles should be driven to a resistance of 300/2.74 = 110 kips, as before. Thus, as seen from Figure 13, the new piles driven with the Link Belt 312 hammer should be driven to a blow count of 27 blows per foot.

Similarly, if the piles were changed to an HP8x36, driven by an MKT-DE 30 diesel hammer (Case XVII), the pile should be driven to a blow count of 14 blows per foot (see Figure 14).

Basic Output The output for the computer program is composed of three Basic sections.

1. Summary of input data fed to the program.

2. Time dependent solution for forces and displacements of selected elements.

3. Summary of maximum compressive and tensile forces (or stresses), maximum observed displacements, and the permanent set per blow of the hammer plus miscellaneous information regarding the problem.

(a) Input Data Summary Pertinent information input to the program is printed out, as is an alphanumeric identification for each problem. Descriptions and detailed discussions of the input data are given later in this report, and are not repeated here.

(b) Time Dependent Quantities To assist the user in determining whether a problem solution is complete, and to assist in locating possible input data errors when they occur, the computer will output forces (or stresses, as desired) at six points along the pile. These forces, labeled "F", are output at constant time intervals, as specified by the user. It is normal to print every second or every fifth time interval so the travel of force down the pile can be followed.

The main purpose of this output is to assist the user in locating possible input data errors if they occur. For example, an improperly located decimal for a given spring rate in the pile will usually show up as a dramatic change in force transmitted past that point.

Displacements (labeled "D") vs. time for selected elements are also output. Their main purpose is to assist the user in determining whether a solution is indeed complete. For example, if a particular solution were run for a maximum of 200 iterations, and the displacement of the point at this iteration still has a large downward motion, the problem should be rerun with an increased number of iterations.

**c) Solution Summaries**

The final solution summaries include a listing of the maximum compressive and tensile forces (or stresses, as desired) induced in the pile during driving, and the maximum displacements observed for each element. Also listed is the time interval in which these maximums were observed.

It is important to compare the time interval in which the maximum point displacement occurred, with the total number of time intervals the problem ran to insure that the point of the pile has indeed stopped moving down and is "rebounding". If the point is still moving down, the problem solution has been shut down too early and should be rerun.

**Also listed are:**

1. The permanent set of the pile for a single blow of the hammer, i.e., how far into the ground has the pile been permanently advanced due to one hammer blow.

2. The number of hammer blows required to advance the pile 1 inch, assuming that the soil resistance remains constant over that additional inch of penetration, and the number of blows required to advance the pile 1 foot.

3. The pile weight.

4. The total static soil resistance to penetration at the time of driving.

Selection of Allowable Stresses for Pile Materials Although allowable stresses for comparison with maximums predicted by the wave equation are known only by inference and by the past experience of the authors, it is believed that the following values are applicable. Further, though work has been done on the strength of rapidly loaded concrete, this work has not been correlated with stresses induced in driven piles.

However, it is generally accepted that at high rates of loading, concrete exhibits an increase in strength. For this reason, the authors recommend the following allowable stresses for concrete.

Allowable tensile stress = 5*sqrt(fc') Allowable compressive stress = 0.7*fc' where fc' = the 28-day compressive strength as normally defined.

Past experience has shown that if stresses are held below these allowables, spalling and tensile cracking are unlikely to occur. Similarly, allowable stresses in steel should be held to within 70% of the yield stress. Values for wood are normally held below 100% of the static strengths.

Note that the above values for concrete exclude the effect of any prestress in the pile. For example, assume that a pile with fc' = 5000 psi is prestressed to 800 psi compression. The allowable driving stresses would then be Allowed tensile stress = 5*sqrt(5000 psi) + 800 psi = 1150 psi Allowed compressive stress = (0.7)(5000 psi) - 800 psi = 2700 psi

## CHAPTER 3. INFORMATION REQUIRED FOR ANALYSIS

Introduction The following was written to familiarize those engineers engaged in the design and analysis of foundation piling with the use, potential, and advantages of pile driving analysis by the wave equation, but who have no direct interest in the theory behind the program. It will also acquaint the engineer with the type of input information needed to obtain the solution.To facilitate the collection of this information, a series of forms are provided. The engineer may use these forms either to transmit the necessary information to the person in charge of setting up and solving the problem or to accumulate the information required to prepare his own input data.

**In general, information concerning the following variables is required:**

(a) Hammer (b) Driving Accessories (c) Pile (d) Soil (e) Problem Background It should be emphasized that the more complete and accurate information available, the more accurate will be the results. For this reason, the forms are set up to accept as much information as possible. However, even when much of the information requested is unknown and must be assumed, a relatively accurate and useful solution can still be obtained.

When the forms request information which is unknown by the engineer, he may leave the space blank, in which case the programmer must enter values based on previous experience. The user may also enter an assumed value followed by a question mark, in which case the programmer will check the value to insure it is reasonable. Should they agree, it will be used as entered but if the value seems questionable, they will probably want to discuss it with the user. Any information which the engineer knows is correct should be entered without a question mark. In this case, the value will be assumed correct and entered as given.

As will be noted, the required information is broken into several sections. In each succeeding section, more detailed information is requested. For example, under "Hammer Information", the minimum information desired is the hammer type. However, even if the particular hammer was unknown, this space could be left blank and several different normally used hammers would be studied and their relative effectiveness compared.

Figures 15 and 16 give cross-sectional views and definitions of terms for a steam hammer and diesel hammer, respectively.

Cross-sectional area* *Applicable only if pile is uniform. If pile is tapered or stepped, a sketch showing section lengths and corresponding cross-sectional areas should be included.

Sketch of soil profile (on additional sheet) Tabulation of soil strength tests (unconfined compression, remolded and undisturbed tests, miniature vane, confined tests, etc., on additional sheet) Total soil resistance from load-test

Distribution of soil resistance on side of pile (on additional sheet)

E) Problem Background - (Use additional sheet if necessary to describe nature of problem observations, special conditions, etc.) Example Problem The following problem is given to illustrate the type of information required to set up the solution.

In this case, a 36 inch pipe pile of varying wall thickness is to be driven by a Vulcan 020 hammer.

The solution is needed because there is some question as to whether or not the pile will be able to penetrate a sand lens lying some 60 feet above the required design penetration.

** Problem Information Forms**

A) Hammer Information

1) Hammer Type: Vulcan 020

2) Hammer Energy:

Total output 60,000 ft-lb Influencing factors Probable hammer efficiency = 80%

3) Ram Stroke:

Observed (single-acting hammers) 3.0 feet Equivalent (double-acting hammers)

4) Velocity of Ram at Impact: V=sqrt(2*g*h*0.8) = 12.4 ft/sec

**Operating Pressure:**

Steam hammer pressure 130 psi Diesel hammer explosive pressure force

C) Pile Properties Material Steel Unit weight 490 lb/ft^3 Total length 350 ft.

Cross-sectional area* See Figure 17 Modulus of elasticity 30 X 10^6 psi Other factors (Describe fully) 36" O.D. pipe pile with wall thickness variations as noted on attached sheet. Pile driven open-ended but would expect plug to form at tip of pile.

Area of steel reinforcement, if present -----Prestress force in pile, if present ------D) Soil Information

1) Soil Properties:

Depth of pile embedment 110' (Prob. 1) & 165' (Prob. 2) Type of soil See Figure 18

2) Soil Properties:

Sketch of soil profile (on additional sheet) See Figure 18 Total soil resistance from load test none made (From Figure 19, RUTotal - 1360 kips & 1560 kips)

3) Soil Properties: (For Problem 1 and Problem 2) Resistance at point of pile(From Figure 19, 1040&760 kips) Resistance on side of pile (From Figure 19, 320&800 kips) Distribution of soil resistance on side of pile (on additional sheet) See Figure 20

E) Problem Background - (Use additional sheet if necessary to describe nature of problem observations, special conditions, etc.)

1) It is not known whether or not the Vulcan 020 hammer will have sufficient capacity to penetrate the sand lens encountered at 100 foot penetration. How likely is it that jetting will be required?

2) Once the sand lens has been penetrated, will the 020 hammer drive the pile to the design penetration?

3) In order to study alternate possible pile configurations, is it possible to determine to what final penetration the pile could be driven?

** Discussion of Solution of Example Problem**

The results of the wave equation analysis are presented in Figure 21 in the form of curves which enable the user to determine the blow count corresponding to any given resistance encountered by the pile. For example, according to the soil information given in Figure 19, the resistance at a penetration of 110 feet will be 1360 kips. Entering this value in Figure 21 and projecting horizontally to curve 1 indicates a rate of penetration of around 96 blows per foot.

Therefore, the contractor should have no difficulty in penetrating the sand lens.

At a penetration of 165 feet, the soils information of Figure 19 indicates a resistance of around 1560 kips. Entering this value in Figure 21 and projecting horizontally to curve 2 also gives a blow count around 96 blows per foot, indicating no problems should arise in driving the pile to the required depth after penetrating the sand lens.

If a rate of penetration of around 360 blows per foot is assumed to be practical refusal, curve 2 of Figure 21 indicates that the Vulcan 020 hammer should be able to drive this pile to a final resistance to penetration of over 2200 kips. Thus, by using the soils information presented in Figure 19, it is seen that the pile could probably be driven to a final depth of penetration of over 175 feet. The slight change in penetration will affect the solution very little, and Figure 19 will be sufficiently accurate. However, should a major change in penetration be indicated, the problem should probably be re-run at the new penetration.

** Recommendations Based on Example Solution**

1. It is recommended that the Vulcan 020 hammer be used to install the foundation piles. Even though a larger hammer could develop a higher ultimate resistance to penetration, the Vulcan 020

**hammer is recommended for the following reasons:**

a. The 020 hammer has the ability to drive the pile to a final resistance of penetration of over 2200 kips, whereas a resistance of only 1560 kips is required.

b. The time required to install the piles should be nominal since only 36 blows per foot are required to develop the 1560 kips capacity.

2. Because of its ability to be driven easily, the pile of Figure 17 should be acceptable.

3. Because of the ability of the Vulcan 020 hammer to drive the pile to a resistance to penetration of over 2200 kips, it is unlikely that installation problems will arise, assuming that the soils information supplied is representative of the area in which the structure is to be installed.

Introduction The computer program discussed herein is based on idealizing the actual pile driving system as a series of concentrated weights and springs. A comparison of an actual pile driving system with the idealized model is shown in Figure 22.

The ram and helmet are assumed to be rigid concentrated masses between which a spring is inserted to represent the elasticity of the cushion. The pile is idealized as a similar series of concentrated weights and weightless springs.

General Figure 22 shows a typical pile system and the idealization for this system. The idealization includes a simulation of the soil medium as well as the pile driver and pile. The pile hammer and pile are idealized as a system of concentrated weights connected by weightless springs. The springs represent the stiffness of the pile, cushion, and in some cases, the pile driver's ram. The soil medium is assumed to be weightless, i.e., the pile moves through the soil and does not move the adjacent soil mass, and is simulated by a spring and damper (dashpot) on each pile segment whose real counterpart is embedded in the soil. Additions or deletions to the real system (for example, addition of an anvil between the ram and capblock) can be handled easily.