# «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 ...»

Cards 0001 and 0002 for problem identification.

**Card 0102:**

AREA = 1000.0 EEM2 = 1.0, since there is no cushion used for this case Card 0103: RUT = 100, RUP = 20 MO = 3, pile is driven to full embedment (see Figure 31) POINTJ = 0.15, sand at the point DR1-DR2 = 2.5, 3.0

**Card 0201 and 0202:**

WAM(3) =.342 WAM(4) =.313 WAM(5) =.283 WAM(6) =.253 WAM(7) =.223 WAM(8) =.194

**Card 0301:**

XKAM(2) = 2520 XKAM(3) = 2303 XKAM(4) = 2083 XKAM(5) = 1863 XKAM(6) = 1645 XKAM(7) = 1425

Case XI Assume that a Raymond Step-Tapered mandrel driven pile 40 feet long is to be driven to full embedment with sand and clay at the side and clay at the point of the pile, using a standard Vulcan 010 steam hammer. (See Figure 32). This case is for initial driving of the pile, when the soil is completely remolded. See Case XII for re-driving the pile after the soil has set up.

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

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

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

Cushion: None, thus the spring rate of the pile segments will be placed above their corresponding weights.

Pile The pile to be driven is a Raymond Step-Tapered mandrel driven pile, 40 feet long.

Cross-sectional areas and weights were determined from the manufacturer, as listed by Chellis (30). The pile is divided into 8-foot segments since the mandrel lengths are manufactured 8 feet long. Note that the cross-sectional area of the core is listed by the manufacturer, as is the weight of the 8-foot core section. This core fits into an 8-foot corrugated shell section, whose weight is also listed. For example, for segment 5, the cross-sectional area of the core is 31 inches^2. It thus has a spring rate of XKAM(4) = AE/L = (31.0in^2)(30000 ksi)/(8ft x 12in/ft) = 9688 kips/inch and a weight of WAM(5) = (31.0 in2)(8 ft x 12 in/ft)(0.490 kips/ft3)/(1728 in3/ft3) = 0.84 kips (agrees with manufacturer) This weight is increased by 0.080 kips due to the weight of the shell. Thus, WAM(5) = 0.84 + 0.08 = 0.92 kips.

However, because the shell is corrugated it has practically no stiffness, thus the XKAM(4) value is not increased.

The core sections are pin-connected at each end, with a loose-fitting pin, such that there is a

1.125 inch space of 'SLACK' between each section. Thus, these sections can open up 1.125 inches before tension will be transmitted between adjacent sections. Thus, values for SLACK(3) through SLACK(6) will be input as 1.125 inches. Since the values for GAMMA(1) and (2) have been input 0.0, indicating that tension can never be transmitted through these springs, the values of SLACK(1) and (2) are meaningless, and are input as 100.0.

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 6 can transmit tension, GAMMA(3) through GAMMA(6) = -1.0.

Card Input: Case XI

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

Cards 0001 and 0002 for problem identification are modified.

Card 0101: NS1 = 1, NS2 = 2, NS3 = 3, NS4 = 4, NS5 = 6, NS6 = 7 NOP(4) = 1, read RUM(1) for each element from card series 400 (long form) NOP(7) = 1, run only until permanent set of pile is found NOP(10) = 2, read SJ(I) from card series 1100 (long form) NOP(12) = 1, read in joint slacks from card series 1200

**Card 0102:**

MP = 7, AREA = 1000.0, EEM2 = 1.0

**Card 0103:**

WAM(3) = 1.096, WAM(4) = 1.048, WAM(5) = 0.920, WAM(6) = 0.792 WAM(7) = 0.668

**Card 0301:**

XKAM(2) = 11563, XKAM(3) = 10938, XKAM(4) = 9688 XKAM(5) = 8125, XKAM(6) = 6875 Card 0401: soil resistance (see Figure 7 for soil resistance distribution) RUM(2) = 0.0, RUM(4) = 70.0, RUM(7) = 100.0, RUM(8) = 40.0 The value of RUM(4) = 70.0 because the 140 kips resistance is spread equally over 2 elements of the pile. (See Figure 7). The total resistance on the two upper elements equals 140 kips, thus RUM (3) and RUM(4) = 140.0 kips/2 = 70.0 kips each. Also, RUM(5)through RUM(7) = 300 kips/3 = 100.0 kips each since the resistance equals a total of 300 kips which is equally distributed over those 3 segments of the pile.

**Card 1101:**

SJ(2) = 0.0 SJ(4) = 0.05 SJ(7) = 0.20 SJ(8) = 0.01 Note that the first two soil damping values, for the ram and helmet are set to zero, although any value would do since there is no RU on them. The next two SJ values are for side friction in sand, the next 3 are for side friction in clay, and finally the point value is for point bearing damping in clay.

**Card 1201:**

SLACK(2) = 100.0 SLACK(6) = 1.125 The values of SLACK in the pile springs are input long form to the program when NOP(12) = 2 for each internal spring in the pile. Last spring slack is MP-1.

Case XII Assume that the Raymond Step-Taper pile of Case XI is to be driven to full embedment with sand and clay at the side and clay at the point of the pile, using a standard Vulcan 010 steam hammer.

This case is for FINAL driving of the pile in case XI, i.e., the pile is to be redriven several days after the pile was originally installed, after the soil is allowed to set up. (See Figure 7 for soil resistances and distribution).

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

Capblock The same values that were used in Case XI are used in Case XII. The values for GAMMA1 through GAMMA3 are the same as used in Case XI.

Cushion None used.

Pile The pile to be driven is the same mandrel pile, 40 feet long, as driven in Case XI.

The computed weights and spring rates for the pile were shown on Figure 32.

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 6 can transmit tension, GAMMA(3) through GAMMA(6) = -1.0, and SLACK values are the same as for Case XI.

Card Input: Case XII

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

Cards 0001 and 0002 for problem identification.

Card 0401: RUM(2)=0.0, RUM(4)=70.0, RUM(7)=150.0, RUM(8)=40.0 Note from Figure 7, "Long-Term Capacity", that there is no soil resistance on elements 1 or 2, thus RUM(2) = 0.0. On the next two segments, there is 140 kips/2, thus RUM(4) = 70.0, etc.

Case XIII Assume that a 12-inch O.D. pipe pile with a 0.25-inch wall, 60 feet long is to be driven to 40 feet below the mudline with clay at the side and at the point of the pile, using a standard KOBE K-25 diesel hammer.

Hammer

**From Appendix C, the properties of a KOBE K-25 hammer are found to be:**

Hammer Energy = 50,700 ft-lb Ram Weight (WAM(1)) = 5.51 kips Efficiency = 100% Observed Total Stroke of Ram (h) = 8.0 ft Distance from the Anvil to the Exhaust Ports = 1.46 ft Anvil Weight (WAM(2)) = 1.6 kips Helmet Weight (WAM(3)) = 1.5 kips (assumed) VELMI (Velocity of Ram at Impact)= sqrt[(64.4)(8.0 - 1.46)(1.00)] = 20.53 ft/sec XKAM(1) = 13464 kips/inch (See Appendix C) Cushion Not used for this case.

Capblock

**From Appendix C, the properties for this capblock are found to be:**

Capblock: ASBESTOS Size = 21 inches diameter(assumed) Thickness = 2 inches (assumed) Modulus of Elasticity = 40 ksi Coefficient of Restitution = 0.5 GAMMA2 = 0.0 Spring Rate (XKAM(2)) = pi(21in)^2(40ksi)/(4*2") = 6927 kips/inch Pile The pile to be driven is a 12-inch O.D. pipe pile, with a 0.25-inch wall, 60 feet long.

**The computed weights and spring rates for the pile segments are as follows:**

WAM(I) = (9.23in^2)(10ftx12in/ft)(490lb/ft^3)/1728in^3/ft^3 = 0.314 kips WAM(4) through WAM(9) = 0.314 kips XKAM(I) = (9.23in^2)(30000ksi)/(10ftx12in/ft) = 2312 kips/inch So XKAM(3) through XKAM(8) = 2312 kips/inch Soil The soil is assumed to act uniformly along the side of the pile only, with no point bearing beneath the pile tip.

**Card Input: Case XIII**

Using the values from Case XIII, the following information is input. The input for this case will be input "long form" throughout, even if not required, to demonstrate use of these options.

Cards 0001 and 0002: problem identification.

**Card 0101:**

1/Deltee = (Left Blank) NSTOP = 200, IPRINT = 5, NS1 = 1, NS2 = 2, NS3 = 3, NS4 = 4, NS5 = 6, NS6 = 9, NOP(1) = 1, standard printout NOP(2) = 1, read WAM(I) from card series 200 NOP(3) = 1, read XKAM(I) from card series 300 NOP(4) = 1, read resistance from card series 400 NOP(5) = 2, read GAMMAs from card series 500 NOP(6) = 2, read EEM(I) from card series 600 NOP(7) = 1, run program until permanent set of pile is found NOP(8) = 2, read VEL(I) from card series 800 NOP(9) = 2, read Q(I) from card series 900 NOP(10) = 2, read SJ(I) from card series 1000 NOP(11) = 2, read A(I) from card series 1100 NOP(12) = 1, no slack is present in any of the joints Note that long form input is being checked out here. The short form would have obviously been okay, also.

**Card 0102:**

MP = 9, last pile segment MH = 4, first pile segment

**Card 0103:**

MO = 6, segment of pile at the mudline DRI = 2.5, DR2 = 3.0, DR3 = 3.5, DR4 = 4.0 DR5 = 5.0, DR6 = 6.0

**Card 0201:**

WAM(1) = 5.51, ram weight WAM(2) = 1.6, anvil weight, WAM(3) = 1.5, helmet weight, WAM(9) = 0.314, weight of pile segment

**Card 0301:**

XKAM(1) = 13464, ram spring rate, XKAM(2) = 6927, capblock spring rate, XKAM(8) = 2312, pile spring rate

**Card 0401:**

RUM(5) = 0.0, no resistance on ram, anvil, or helmet RUM(9) = 30.0, resistance along the side of the pile for each pile segment 4 through 9.

RUM(10) = 0.0, no resistance under the point of the pile

**Card 0501:**

GAMMA1 = 238.1, explosive force of the ram GAMMA3 = 0.0 GAMMA8 = -1.0

**Card 0601:**

EEM(1) = 0.5 EEM(8) = 1.0

**Card 0801:**

VEL(1) = 20.53, velocity of the ram at impact VEL(9) = 0.0, velocity of remaining elements

**Card 0901:**

Q(10) = 0.1

**Card 1001:**

SJ(5) = 0.0 SJ(9) = 0.2 (side, clay, see Appendix C) SJ(10) = 0.01 (point, clay, see Appendix C) Card 1101: A(1) = 1000.0 (convert force in lbs to kips), A(8) = 9.25, area of each pile segment

Case XIV Assume that a pipe pile 60 feet long is to be driven to 40 feet below the mudline with rock at the point of the pile (all point bearing), using a standard Delmag D-44 diesel hammer.

Hammer

**From Appendix C, the properties of a Delmag D-44 hammer are found to be:**

Ram Weight (WAM(1)) = 9.5 kips Efficiency = 100% Observed Total Stroke of Ram = 8.0 ft Distance from the Anvil to the Exhaust Ports (c)= 1.19 ft Anvil Weight (WAM(2)) = 2.42 kips Helmet Weight (WAM(3)) = 1.6 kips (assumed) VELMI (Velocity of the Ram at Impact) = sqrt[(64.4)(8 - 1.19)(1.0)] = 20.94 ft/sec XKAM(1) = 10,600 kips/inch (Spring rate of hammer) Capblock The same values that were used in Case XIII are used in Case XIV.

Cushion Not used for this case.

Pile The same values that were used in Case XIII are used in Case XIV.

Soil The soil is assumed to act at the point of the pile only, with no resistance at the side.

Card Input: Case XIV

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

Cards 0001 and 0002 are modified.

**Card 0101:**

NOP(7) = 2, run problem full NSTOP iterations

**Card 0103:**

DRl = 2.O, DR2 = 3.0, DR3 = 4.0, DR4 = 5.0, DR5 = 6.O, DR6 = 7.0, DR7 = 8.0

**Card 0201:**

WAM(1) = 9.5 WAM(2) = 2.42 WAM(3) = 1.6

**Card 0301:**

XKAM(1) = 10,600

**Card 0401:**

RUM(9) = 0.0, no resistance on the side of the pile RUM(10) = 100.0, all point bearing pile Card 0501: GAMMA1 = 200, explosive force of the ram Card 0801: VEL(1) = 20.94, velocity of the ram at impact

**Card 1001:**

SJ(9) = 0.0, no soil on side of pile SJ(10) =.15, rock at the point of the pile

Case XV Assume that a l0"xl0" 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 Vulcan 30c hammer.

Hammer From Appendix C, the properties of a Vulcan 30c hammer are found to be: Hammer Stroke =

2.42 ft Ram Weight (WAM(1)) = 3.0 kips Efficiency = 66% Helmet Weight (WAM(2)) = 1.0 kips (assumed) Note that helmet weights and cushion dimensions are not listed in Appendix C, since they vary from job to job, and with each contractor.

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

VELMI = sqrt[(64.4)(2.42)(0.66)] = 10.14 ft/sec Capblock and Cushion From Appendix C, the properties for the capblock and cushion are found to be the same as used in Case I. The dimensions are also assumed to be the same. Thus, the spring rate and all other input parameters for this case are the same as in Case I.

Pile The pile to be driven is a l0"xl0" prestressed concrete pile, 60 feet long. Given information is as

**follows:**

Area = 100 in^2 Length = 60 feet Modulus of Elasticity = 3000 kips/in

**The pile segment weights are computed from:**

WAM(I) = AL(density) = WAM(3) = (100in^2)(10ftx12in/ft)(0.150kips/ft3)/1728in^3/ft^3 WAM(3) = 1.04 kips Thus, WAM(3) through WAM(8) = 1.04 kips

**To compute the spring rate of the 10-foot pile segments:**

XKAM(3) through XKAM(7) = AE/L = (10"x10")(3000ksi)/(10ftx12in/ft) = 2500 kips/inch Coefficients of restitution for the concrete pile should be 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 Identical to Case I.

Card Input: Case XV The same input for Case I is used except for the following: 0001 and 0002 cards for problem identification are changed. Card 0101: NS4 = 7, NS5 = 10, NS6 = 13

**NOP(7) = 1 Card 0102:**

VELMI = 10.14 AREA = 100

**Card 0103:**

RUP = 0.0, no resistance beneath the point of the pile DR1 = 2.0, DR2 = 2.5, DR3 = 3.0, DR4 = 3.25

**Card 0201:**