# «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 ...»

Case I - Vulcan 08 Hammer

** Case II - Vulcan 010 Hammer Case III - Delmag D-15 Hammer**

The cases studied in this comparison utilized two steam hammers and one diesel hammer.

The two steam hammers studied were the Vulcan 08 and 010 hammers. The diesel hammer was a Delmag D-15. Properties of these and other typical hammers for use in the wave equation are listed in Appendix C. The pile used for this comparison was a 12-inch square prestressed concrete pile 60 feet long, driven 30 feet in clay. Detailed information regarding the set up for these example cases may be found in Appendix D. The pile is to be driven to an ultimate static soil resistance of 900 kips in clay having a "sensitivity" or "set up" factor of 2.0.

As previously mentioned, the wave equation can be used to predict the permanent set per blow of a given hammers which can then be used to plot curves similar to those in Figure 1. These curves relate the ultimate static soil resistance at the time of driving to the number of blows required to advance the pile one foot. Since a resistance of 900 kips desired, and since the soil is expected to "set up" by 2.0, the desired resistance during driving will be 900 kips/2.0 = 450 kips.

In other words, if a resistance to penetration at the time of driving equal to 450 kips can be attained, the soil will set up to the desired value of 900 kips. The sensitivity of any given soil must be determined by soils test, unless the pile is driven in a sand, which normally has a set up factor of 1.0. A comparison of unremolded vs. remolded tests is commonly used as a basis for determining a soil's sensitivity.

From Figure 1, it is seen that either the Vulcan 010 or Delmag D-15 hammers will drive the pile to the required level of resistance, with the D-15 hammer driving the pile faster at final penetration. However, as seen from Table 1, which lists the maximum stresses determined by the wave equation, the maximum stresses induced during driving are relatively high and problems with pile breakage may occur. For the D-15 hammer, maximum stresses of 5131 psi compression and 2143 psi tension were experienced.

A comparison of maximum compressive and tension stresses, for a 12-inch by 12-inch prestressed concrete pile using two steam hammers and one diesel hammer: Case I-Vulcan 08, Case II- Vulcan 010, Case III-Delmag D-15 hammer.

50 4358.4 -1704.8 4461.3 -1469.8 5130.6 -2143.4 100 4358.4 - 809.4 4461.3 -1161.7 5130.6 -1538.5 150 4358.4 - 574.0 4461.3 - 306.9 5130.6 -1083.3 200 4358.4 - 448.9 4561.4 - 266.2 5130.6 - 764.3 300 4384.6 - 923.2 4678.1 - 894.2 5130.6 -1129.0 400 4424.2 -1185.6 4741.8 -1246.5 5130.6 -1678.9 500 4477.6 -1249.8 4833.6 -1518.7 5130.6 -2075.6 Obviously, any number of additional hammers could be studied to determine the relative merit of each one. For example, at final penetration (450 kips) the expected blow count will be around 157 blows per foot if the D-15 hammer is used. It is possible that a larger hammer, perhaps a Vulcan 014, although more expensive, might be more economical in the long run if the pile could be installed faster. This could be determined by simply adding the 014 hammer to the previous study.

**Selection of Driving Accessories**

(a) Cushion Selection As noted in the previous section, high driving stresses can sometimes become a problem. This is normally corrected by choosing a different driving hammer, or by increasing the capblock or cushion thickness. Assuming that the D-15 hammer is selected to drive the 60-foot concrete pile of the previous example, the effect of varying the cushion thickness from 1-inch (Case III), to 6 and 12-inches will now be investigated (Case IV = 6-inch cushion, Case V = 12-inch cushion).

The maximum stresses determined by the wave equation for Cases III through V are listed in Table 2. If the allowable tensile stress is given as 2000 psi and a maximum compressive stress of 5000 psi is specified, it is seen that the 6-inch thick oak cushion would be required to prevent overstressing of the pile. Note that changing the cushion thickness also influences the ability to drive the pile, as seen in Figure 2. In this case, the increase in cushion thickness from 1-inch to 6-inches increased the blow count from 157 to 220 blows per foot at final penetration (450 kips resistance). Increasing the cushion thickness to 12-inches will make driving to 450 kips difficult as seen in Figure 2 (Case V).

(b) Helmet Selection A helmet or pile cap is used to adapt the driving hammer to the pile. The weight of the helmet is represented as a single rigid weight. Although increasing the weight of the helmet is sometimes attempted to reduce driving stresses, this is not normally done since it will, in some cases, decrease the ability to drive the pile to the desired penetration. Typical helmet properties for use in the wave equation vary widely from case to case and must be determined from the contractor.

For the following investigation, the 1.0 kip helmet of the D-15 hammer of Case V was increased to 5.0 kips (Case VI) and its effect determined.

Note from the summary of stresses in Table 3, that the maximum stresses are reduced, such that in this case the change in helmet weight was effective in reducing the driving stresses. Note also from Figure 3, that the drivability of the pile was relatively unchanged.

A comparison of maximum compressive and tension stresses for a 12-inch by 12-inch prestressed concrete pile using a Delmag D-15 hammer and varying the cushion thickness: Case III-l inch cushion, Case IV 6 inch cushion, Case V-12 inch cushion.

TABLE 3 - Stresses for Various Helmet Weights A comparison of maximum compressive and tensile stresses for a 12-inch by 12-inch prestressed concrete pile using a Delmag D-15 hammer and varying the helmet weight. Case V= 1 Kip helmet, Case VI= 5 Kip helmet.

Pile Size The size of the pile selected can also significantly affect the ability to reach a given resistance as well as the stresses induced during driving. The following cases were analyzed to demonstrate the influence of changing the pile size. Assume that a Vulcan 010 hammer is to be used to drive a 100-foot HP steel pile to a penetration of 80-feet.

**The pile selections are:**

The curves which compare the ability of the hammer to drive the piles for these cases are shown in Figure 4. These curves relate total soil resistance at the time of driving to the number of blows required to advance the pile 1-foot. Note from Figure 4 that the heavier piles have a dramatically increased ability to overcome resistance. Thus, if the only hammer available to drive the piles was the Vulcan 010, and the desired soil resistance immediately after driving is 400 kips, the HP8x36 pile could not be driven to the desired penetration, since the pile would refuse at 360 kips. For cases VII, VIII, and IX (see Appendix D), the soil parameters assumed that the piles were to be driven in sand. In this case, 90% of the total soil resistance was assumed to be distributed uniformly along the side of the pile, with 10% of the total placed in point bearing. Also the soil damping factors used were for sand. Since sand usually does not "set up" after driving stops, the soil resistance predicted by the wave equation (which would be the soil resistance immediately after driving) should equal the long-term capacity of the pile.

**Prediction of Pile Load Capacity**

The engineer is most interested in the static load carrying capacity of the piles being driven. In the past, he has had to rely on judgment based on empirical pile driving formulas or static load tests. However, use of the wave equation permits a much more realistic estimate to be made using results generated by the program. In the case of clays, or other soils in which "sensitivity" or "set up" of the soil is present, the soil resistance at the time of driving will be less than the long-term capacity of the pile. A typical example of this phenomena is shown in Figure 5, which relates the bearing capacity of a pile which was load-tested at various times after driving.

Note that the load test performed immediately after driving indicated a capacity of 76 kips, whereas the test after 1200 hours indicated a capacity of 160 kips. Thus, this particular soil had a set up factor of 160/76 = 2.11. This factor is usually determined by soils tests or during the driving of test piles before production driving begins.

In the case of sands, there is usually no observed set up, and the driving resistance immediately after driving (as predicted by the wave equation) will be the same as the long-term capacity of the pile. In the case where a pile is driven through clay and tipped in sand, only the soil capacity of the clay should be modified by a set up factor. For example, assume that a tapered pile is to be driven through clay having a long-term resistance of 400 kips and tipped in sand with a long-term bearing resistance of 50 kips (Case X). Further assume that the clay has a sensitivity of 2.0, i.e., that during driving, the clay will be remolded and its capacity during driving will be reduced to one-half of its long-term capacity. Then the resistance immediately after driving should be half of the clay capacity (due to remolding) plus the full sand capacity, or 400 kips/2.0 + 50 kips = 250 kips. Thus, from Figure 6, a rate of penetration of around 55 blows per foot should be expected at final penetration.

(a) Initial Driving As a second example, assume that a 40-foot tapered, mandrel driven pile (Case XI) will be installed to full embedment (40 feet) through a sand lens into a stiff clay as shown in Figure 7. The long-term capacity for each strata are to be divided by the corresponding set up factors to yield the resistances shown as "During Driving". Note that a set up factor is not applied to the point of the pile even though the soil is a clay, since the soil under the pile tip has not been remolded.

The soil resistance input data for use in the wave equation is thus listed under "During Driving" in Figure 7. Figure 8 relates the resistance to penetration vs. blow count observed while the pile is being driven, i.e., while the soil is in a "remolded" state. Since the required soil resistance at full penetration is 480 kips, Figure 8 indicates that a final blow count of 68 blows per foot is required.

(The 480 kips is determined by summing the "During Driving" resistances shown in Figure 7).

(b) Final Driving If the pile of Case XI above were to be re-driven several days later after the soil has set up to its full capacity, the input parameters for the soil resistance would change to those listed under "Long-Term Capacity" in Figure 7. The results of this change in resistance distribution is shown in Figure 9 for Case XII. Note that due to the set up in the clay, the resistance has now increased from 480 kips to 630 kips. Thus, as seen from Figure 9, it should take around 164 blows per foot to break the pile loose.

(c) Soil Set Up or Relaxation The same procedure as shown above can be used to determine how much a given soil will "set up" or "relax" after some period of time. For example, assume that a 60-foot long 12-inch diameter pipe pile with a 0.15-inch wall is to be driven to a penetration of 40-feet into a soft clay, using a Kobe 25 diesel hammer (Case XIII). The observed blow count in the field at the end of driving was 50 blows per foot, corresponding to a soil resistance of 360 kips (see Figure 10).

After 15 days, the pile was redriven with the same hammer, and required 150 blows per foot to advance the pile. Thus, from Figure 10, it is found that the soil resistance had set up to a value of 455 kips. Thus, the soil had a set up factor 455/360 = 1.26. If the pile were easier to drive after the 15-day delay, relaxation would obviously have occurred.

**Driving Stresses in Point Bearing Piles**

The determination of driving stresses in point bearing piles is performed in a manner similar to other soil types, i.e., the probable soil resistances to be encountered during driving are entered into the program, and a wave equation analysis performed. For example, assume that the steel pipe pile of Case XIV is to be driven through a soft clay to a point bearing in rock. The soil tests indicate that 100% of the soil resistance will be encountered under the point of the pile.

The results of this case are plotted in Figure 11, which shows total soil resistance at the time of driving vs. blows per foot required to advance the pile 1-foot. Resulting maximum stresses are listed in Table 4. Obviously the pile is greatly over stressed, and either a smaller hammer must be used, or the pile size will have to be increased.

100 58,047 0 200 72,061 5,338 300 80,113 8,369 400 91,518 11,372 500 106,750 14,647 600 116,686 14,427 700 119,006 4,310 Use of Wave Equation for Field Control One of the more important uses of the wave equation is its application toward field control and acceptance of piles during construction. For example, assume that the concrete pile of Case XV is to carry an ultimate load of 300 kips. The pile is to be driven by a Vulcan 30C hammer.

During driving of test piles which were to be load-tested, it was noted that at the specified penetration, the hammer was driving at 100 blows per foot. After 15 days, when the soil had set up to its full strength, the piles were load-tested to an ultimate load of 320 kips.

Thus, as seen in Figure 12, at the end of driving the resistance was 117 kips, and the soil set up was therefore 320/117 = 2.74. Since the desired ultimate resistance was only 300 kips, the desired resistance at the end of driving should be 300/2.74 = 110 kips, which corresponds to a blow count of 90 blows per foot (see Figure 12). Thus, the remaining piles in this area were driven to a blow count of 90 blows per foot. The slight change in depth of penetration will not affect the curve of Figure 12 and can thus be neglected. However, if the penetration was seriously changed, the curve of Figure 12 should probably be rerun.

As a further example, assume that later piles in this area were to be changed from the 10"x10" to 12"x12" piles which were to be driven by a Link Belt 312 diesel hammer (Case XVI).