# «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 ...»

Hammer From the contractor and Appendix C, the properties of a D-15 hammer, which is an open-end

**diesel hammer, are found to be:**

Ram Weight (WAM(1))= 3.3 kips Total Stroke of Ram (h)= 95 inches (observed in field) Distance from the Anvil to the Exhaust Ports c = 13.15 in.

Efficiency= 100% Anvil Weight (WAM(2))= 0.81 kips Helmet Weight (WAM(3))= 1.0 kips (from contractor)

**The ram velocity at impact (VELMI) is computed by:**

VELMI = sqrt[2g(h-c)efficiency] VELMI = sqrt[64.4(95-13.15)(1.0)/(12in/ft) VELMI = 21 ft/sec The spring rate for the ram XKAM(1), can be found in Appendix C. It was calculated by AE/L using the dimensions of the solid steel round hammer.

XKAM(1) = 2646 kips/inch The coefficient of restitution between the ram and the anvil will be 0.9. Thus, EEM1 = 0.9.

Capblock From Appendix C, the properties for the capblock are found to be: Capblock: OAK Diameter= 12.0 in.

Thickness= 1.0 in.^2 Modulus of Elasticity (E)= 45 ksi

**Thus, the spring rate of the capblock is:**

XKAM(2) = AE/L = pi(12^2)(45)/(4*1.0")

The GAMMA1 value for a D-15 is found in Appendix C to be 129.2 kips, since this is the explosive pressure force for this hammer.

GAMMA2 and GAMMA3 are 0.0 since these two springs cannot transmit tension. The remaining GAMMA values will be set to -1.0 automatically since tension can be transmitted in the pile.

Pile The pile used in this case is the same pile driven in Cases I and II, except the last pile segment (MP) is 9 because the diesel hammer system has a ram, anvil and a helmet as WAM(1) through WAM(3), whereas the previous stem hammer did not have an anvil.

Thus, WAM(4) through WAM(9) = 1.5 kips.

Soil Identical to Case 1.

Card Input: Case III

**Card 0201:**

WAM(1) = 3.3, ram weight WAM(2) = 0.81, anvil weight WAM(3) = 1.0, helmet weight WAM(9) = 1.5, pile segment weights for segments 4 through 9 Card 0301: XKAM(1) = 2646, ram spring rate XKAM(2) = 5089, capblock spring rate XKAM(3) = 6480, cushion spring rate XKAM(8) = 3600, pile segment spring rate for segment 8. The same input for Cases I and II is

**used, except for the following:**

0001 and 0002 cards for problem identification are changed.

Card 0101: NS6 = 9 Card 0102: MP = 9, MH = 4 VELMI = 21.0 ft/sec, EEM1 = 0.9, EEM2 = 0.5, EEM3 = 0.5, GAMMA1 = 129.2 kips Card 0103: MO = 7

**Card 0201:**

WAM(1) = 3.3 kips - ram weight WAM(2) = 0.81 kips - anvil weight WAM(3) = 1.0 kips - helmet weight WAM(9) = 1.5 kips, pile segment weights for segments 4 thru 9

**Card 0301:**

XKAM(1) = 2646 kips/inch, ram spring rate XKAM(2) = 5089 kips/inch, capblock spring rate XKAM(3) = 6840 kips/inch, cushion spring rate XKAM(8) = 3600 kips/inch, pile segment rate (segments 4-9)

Case IV Assume that a 12"x12" prestressed concrete pile 60 feet long is to be driven to a penetration of 30 feet below the mudline with clay at the side and at the point of the pile, using a standard Delmag D-15 open-end diesel hammer. This case is identical to Case III except that a thicker cushion is to be utilized.

Hammer The input parameters for the hammer are the same as those used in Case III.

Capblock The same capblock values that were used in Case III are used in Case IV.

Cushion The same type of cushion is used in this case as in Case III, except the thickness is increased from 1" to 6".

Thus, the spring rate for the cushion (XKAM(3)) for this case is XKAM(3) = (12in^2)(45 ksi)/6" = 1080 kips/inch The values of GAMMA1 through GAMMA3 are the same as used in Case III.

Pile The pile used in this case is the same pile driven in Case III.

Soil Identical to Case III.

Card Input: Case IV The same input for Case III is used, except for the following: 0001 and 0002 cards for problem

**identification are changed. Card 0301:**

XKAM(3) = 1080, cushion spring rate

Case V Assume that a 12"x12" prestressed concrete pile 60 feet long is to be driven to a penetration of 30 feet below the mudline with clay at the side and at the point of the pile, using a standard Delmag D-15 open end diesel hammer. This case is identical to Case IV except the cushion thickness is again increased.

Hammer The input parameters for the hammer are the same as those used in Case IV.

Capblock The same capblock values that were used in Case IV are used in Case V.

Cushion The same type of cushion is used in this case as in Case IV, except the thickness is increased from 6" to 12". Thus, the spring rate for the cushion (XKAM(3)) for this case is XKAM(3) = (12in^2)(45 ksi)/12" = 540 kips/inch The values for GAMMA1 through GAMMA3 are the same as used in Case IV.

Pile The pile used in this case is the same pile as driven in Case IV.

Soil Identical to Case IV.

Card Input: Case V The same input as for Case IV is used, except for the following: 0001 and 0002 cards for problem identification are modified. Card 0301: XKAM(3) = 540, cushion spring rate

Case VI Assume that a 12"x12" prestressed concrete pile 60 feet long is to be driven to a penetration of 30 feet below the mudline with clay at the side and at the point of the pile using a standard Delmag D-15 open-end diesel hammer.

Hammer The input parameters for the hammer are the same as those used in Case V except the helmet weight is increased from 1 kip to 5 kips.

Thus, WAM(3) = 5.0 kips, helmet weight Capblock The same capblock values that were used in Case V are used in Case VI.

Cushion The same values that were used in Case V are used in Case VI.

The values for GAMMA1 through GAMMA3 are the same.

Pile The pile used in this case is the same pile driven in Case V.

Soil identical to Case V.

Card Input: Case VI The same input for Case V is used, except for the following: Cards 0001 and 0002 for problem identification are modified. Card 0201: WAM(3) = 5.0, helmet weight

Case VII Assume that an HP8x36 steel pile 100 feet long is to be driven to a penetration of 80 feet below the mudline with sand at the side and at the point of the pile, using a standard Vulcan 010 steam hammer.

Hammer The input parameters for the hammer are the same as those used in Case II.

Capblock The same values that were used in Case II are used in Case VII.

The values for GAMMA 1 through GAMMA 3 are the same as used in Case II.

Cushion No cushion is used for this case. The helmet sits directly on the pile. Thus the pile spring rates will be brought up above their corresponding weights to supply the necessary spring between the helmet weight and the top pile weight.

Pile

**The pile to be driven is an HP8x36 steel pile, 200 feet long. Given information as follows:**

Area = 10.6 in^2 Length = 100 feet Modulus of Elasticity = 30000 ksi The pile will be divided in 10-foot segments. To compute the element weights, since the pile is known to weigh 36 lbs per foot, WAM(I) = (0.036 kips/ft)(10 ft/segment). Thus, WAM(3) through WAM(12) = 0.36 kips.

**To compute the spring rates of the pile segments, which are 10-foot segments:**

XKAM(2) through XKAM(ll) = AE/L = (10.6 in2)(30000 ksi)/10 ft x 12"/ft = 2650 kips/inch. Note that on previous cases, the spring rate of the cushion was placed between the helmet and the first pile segment, and the pile springs were placed beneath their corresponding weights. However, in this case, there is no cushion as none was required to reduce the stresses induced in the steel pile. Thus, the spring rate of the first pile segment will be placed between the helmet and the first pile weight, and all remaining pile springs will be placed above their corresponding weights. Coefficients of restitution for the steel pile should be set to 1.0, as damping is negligible. Also, since each of the pile springs 3 through 11 can transmit tension, GAMMA(3) through GAMMA(11) = -1.0.

Soil Tests at the site revealed that the soil was sand to a depth of 150 feet. Further lab tests indicated that 90% of the resistance would be distributed uniformly along the side of the pile, with the remaining 10% of the resistance under the pile tip. The soil has no set up factor (set up = 1.0).

Card Input: Case VII The same input for Case II is used for Case VII except for the following: 0001 and 0002 cards for problem identification are modified.

Card 0101: NS4 = 8, NS5 = 10, NS6 = 12 NOP(7) = 1,(run problem to determine permanent set only)

**Card 0102:**

MP = 12, AREA = 10.6, EEM2 = 1.0,

**Card 0103:**

MO = 5 SIDEJ = 0.05, sand at side of pile (see Appendix C) POINTJ = 0.15, sand at point of pile (see Appendix C) DR1-DR4 = 2.5, 3.0, 3.5, 3.75

**Card 0201:**

WAM(12) = 0.36, weight of each pile segment

**Card 0301:**

XKAM(11) = 2650, spring rate of pile segment

Case VIII Assume that an HP12x53 steel pile 100 feet long is to be driven to a penetration of 80 feet below the mudline with sand at the side and at the point of the pile, using a standard Vulcan 010 steam hammer. This case is identical to Case VII, except the pile is changed from an HP8x36 to an HP 12x53.

Hammer The input parameters for the hammer are the same as used in Case VII.

Capblock The same values that were used in Case VII are used in Case VIII.

The values for GAMMA1 through GAMMA3 are the same as used in Case VII.

Cushion Not used for this case.

Pile The pile to be driven is an HP12x53 steel pile, 100 feet long.

**Given information is as follows:**

Area = 15.6 in Length = 100 feet 2 Modulus of Elasticity = 30000 kips/in

**Segment weights 3 through 12 are computed by:**

WAM(I) = (0.053 kips/ft)(10 ft segment length) = 0.53 kips Thus, WAM(3) through WAM(12) = 0.53 kips

**Spring rates are computed by:**

XKAM(I) = (15.6 in^2)(30000 ksi)/(10 ft x 12 in/ft) Thus, XKAM(2) through XKAM(11) = 3900 kips/inch.

Coefficients of restitution for the steel pile should be set to 1.0, as the damping is negligible. Also, since each of the pile springs 3 through 11 can transmit tension, GAMMA(3) through GAMMA(11) = -1.0.

Soil Identical to Case VII.

Card Input: Case VIII

**The same input as for Case VII is used except the following:**

Cards 0001 and 0002 are modified.

**Card 0102:**

AREA = 15.6

**Card 0103:**

DR1-DR4 = 3.0, 4.0, 4.25, 4.50

**Card 0201:**

WAM(12) = 0.53, weight of each pile segment

**Card 0301:**

XKAM(11) = 3900, spring rate of pile segment

Case IX Assume that an HP14x102 steel pile 100 feet long is to be driven to a penetration of 80 feet below the mudline with sand at the side and at the point of the pile, using a standard Vulcan 010 hammer. This case is identical to Case VIII except the pile size is increased to an HP14x102.

Hammer The input parameters for the hammer are the same as those used in Case VIII.

Capblock The same values that were used in Case VIII are used in Case IX.

The values for GAMMA1 through GAMMA3 are the same as used in Case VIII.

Cushion - Not used for this case.

Pile

**The pile to be driven is an HP14x102 steel pile, 100 feet long. Given information as follows:**

Area = 30.0 in Length = 100 feet Modulus of Elasticity = 30000 kips/in Segment Weights = (0.102 kips/ft)(10 ft) Thus, WAM(3) through WAM(12) = 1.02 kips AE Spring Rates = (30.0 in^2)(30000 ksi)/(10 ft x 12 in/ft) Thus, XKAM(2) through XKAM(11) = 7500 kips/inch Coefficients of restitution for the steel pile should be set to 1.0, as the damping is negligible.

Also, since each of the pile springs 3 through 11 can transmit tension, GAMMA(3) through GAMMA(11) = -1.0.

Soil - Identical to Case VIII.

Card Input: Case IX The same input for Case VII is used for Case IX except the following: 0001 and 0002 cards for problem identification are modified.

**Card 0102:**

AREA = 30.0 Card 0103: DR1-DR4 = 3.0, 5.5, 6.5, 7.0

**Card 0201:**

WAM(12) = 1.02, weight of each pile segment

**Card 0301:**

XKAM(11) = 7500, spring rate of pile segments

Case X Assume that a tapered steel pipe 60 feet long is to be driven to full embedment with clay on the side and sand at the point of the pile, using a standard Vulcan 010 steam hammer.

Hammer The input parameters for the hammer are the same as those used in Case II.

Capblock The same capblock values that were used in Case II are used in Case X.

Cushion Not used in this case since it is a steel pile.

Pile The pile to be driven is a tapered steel pile 60 feet long, as shown in Figure 31. Given information

**as follows:**

The diameters listed in Figure 31 were obtained by proportion. For example, the center of the number 5 element is 7/12 up from the point of the pile. Thus, it has a diameter of 8 inches + (7/12)(16" - 8") = 12.67 inches. Diameters at the centers of each element were similarly obtained and are listed on Figure 31. The average areas listed were computed by multiplying the diameter by pi*D*wall thickness. Thus, the average area of segment 5 is (pi)(l2.67 in)(0.2093 in) = 8.33

**in^2. The weight is then computed from:**

WAM(5) = AL(density) = (8.33 in^2)(10ft x 12in/ft)(0.490k/ft^3)/1728in^3/ft^3 = 0.283 kips and its corresponding spring rate, which will be placed above the weight, will be given by XKAM(4) = AE/L = (8.33in^2)(30000ksi)/(10ftx12in/ft) = 2083 kips/inch Other weights and spring rates were computed in a similar manner and are tabulated in Figure 31.

Coefficients of restitution for the steel pile were set to 1.0, as the damping is negligible. Also, since each of the pile springs 3 through 7 can transmit tension, GAMMA(3) through GAMMA(7) = -1.0.

Soil

**The soil properties, as determined from soil borings and tests are assumed as follows:**

Soil Types: 57 ft of clay on side of pile Pile tipped in sand Soil Resistance: 80% distributed uniformly along side of pile in friction, 20% point bearing Set up of soil = 2.0 Card Input: Case X

**The same input for Case II is used except the following:**