Posted in TAMWAVE

TAMWAVE 6: Results of Wave Equation Analysis

With the data entered for the wave equation analysis, we can now see the results.  There’s a lot of tabular data here but you need to read the notes between it to understand what the program is putting out.  If you are not familiar at all with the wave equation for piles, you need to review this as well.

General Output for Wave Equation Analysis
2018-01-06T10:13:03-05:00
Time Step, msec 0.04024
Pile Weight, lbs. 15,000
Pile Stiffness, lb/ft 600,000
Pile Impedance, lb-sec/ft 57,937.5
L/c, msec 8.04688
Pile Toe Element Number 102
Length of Pile Segments, ft. 1
Hammer Manufacturer and Size VULCAN O16
Hammer Rated Striking Energy, ft-lbs 48750
Hammer Efficiency, percent 67
Length of Hammer Cushion Stack, in. 16.5
Soil Resistance to Driving (SRD) for detailed results only, kips 572.7
Percent at Toe 35.39
Toe Quake, in. 0.220
Toe Damping, sec/ft 0.07

For those familiar with the wave equation, there are few surprises.  Some explanation of the parameters can be found with the documentation for the TTI program.

Initial Element Output
SRD = 572.68 kips
Element Element Weight, lbs. Element Stiffness, kips/in Element Cross-Sectional Area, in2 Element Soil Resistance, kips Element Coefficient of Restitution Element Initial Velocity, ft/sec Element Soil Shaft Stiffness, kips/in Element Quake, in. Element Damping, sec/ft
Ram 16,250.0 4,957.5 233.71 0.0 0.80 11.37 0.0 1,000.000 0.00
Driving Accessory 3,800.0 711.5 144.00 0.0 0.51 0.00 0.0 1,000.000 0.00
Pile Head 150.0 60,000.0 144.00 0.0 1.00 0.00 16.1 0.002 45.39
4 150.0 60,000.0 144.00 0.1 1.00 0.00 28.0 0.004 19.91
5 150.0 60,000.0 144.00 0.2 1.00 0.00 36.1 0.005 13.57
6 150.0 60,000.0 144.00 0.3 1.00 0.00 42.7 0.006 10.54
7 150.0 60,000.0 144.00 0.3 1.00 0.00 48.4 0.007 8.73
8 150.0 60,000.0 144.00 0.4 1.00 0.00 53.5 0.007 7.51
9 150.0 60,000.0 144.00 0.5 1.00 0.00 58.2 0.008 6.62
10 150.0 60,000.0 144.00 0.5 1.00 0.00 62.5 0.009 5.95
11 150.0 60,000.0 144.00 0.6 1.00 0.00 66.6 0.009 5.41
12 150.0 60,000.0 144.00 0.7 1.00 0.00 70.4 0.010 4.98
13 150.0 60,000.0 144.00 0.8 1.00 0.00 74.0 0.010 4.62
14 150.0 60,000.0 144.00 0.8 1.00 0.00 77.4 0.011 4.31
15 150.0 60,000.0 144.00 0.9 1.00 0.00 80.7 0.011 4.05
16 150.0 60,000.0 144.00 1.0 1.00 0.00 83.9 0.012 3.82
17 150.0 60,000.0 144.00 1.0 1.00 0.00 87.0 0.012 3.62
18 150.0 60,000.0 144.00 1.1 1.00 0.00 89.9 0.012 3.44
19 150.0 60,000.0 144.00 1.2 1.00 0.00 92.8 0.013 3.28
20 150.0 60,000.0 144.00 1.3 1.00 0.00 95.6 0.013 3.14
21 150.0 60,000.0 144.00 1.3 1.00 0.00 98.3 0.014 3.01
22 150.0 60,000.0 144.00 1.4 1.00 0.00 100.9 0.014 2.89
23 150.0 60,000.0 144.00 1.5 1.00 0.00 103.5 0.014 2.79
24 150.0 60,000.0 144.00 1.5 1.00 0.00 106.0 0.015 2.69
25 150.0 60,000.0 144.00 1.6 1.00 0.00 108.4 0.015 2.60
26 150.0 60,000.0 144.00 1.7 1.00 0.00 110.8 0.015 2.51
27 150.0 60,000.0 144.00 1.8 1.00 0.00 113.1 0.016 2.43
28 150.0 60,000.0 144.00 1.8 1.00 0.00 115.4 0.016 2.36
29 150.0 60,000.0 144.00 1.9 1.00 0.00 117.7 0.016 2.29
30 150.0 60,000.0 144.00 2.0 1.00 0.00 119.9 0.017 2.23
31 150.0 60,000.0 144.00 2.1 1.00 0.00 122.1 0.017 2.17
32 150.0 60,000.0 144.00 2.1 1.00 0.00 124.2 0.017 2.11
33 150.0 60,000.0 144.00 2.2 1.00 0.00 126.3 0.017 2.06
34 150.0 60,000.0 144.00 2.3 1.00 0.00 128.4 0.018 2.01
35 150.0 60,000.0 144.00 2.4 1.00 0.00 130.4 0.018 1.96
36 150.0 60,000.0 144.00 2.4 1.00 0.00 132.5 0.018 1.91
37 150.0 60,000.0 144.00 2.5 1.00 0.00 134.4 0.019 1.87
38 150.0 60,000.0 144.00 2.6 1.00 0.00 136.4 0.019 1.83
39 150.0 60,000.0 144.00 2.7 1.00 0.00 138.3 0.019 1.79
40 150.0 60,000.0 144.00 2.7 1.00 0.00 140.2 0.019 1.75
41 150.0 60,000.0 144.00 2.8 1.00 0.00 142.1 0.020 1.72
42 150.0 60,000.0 144.00 2.9 1.00 0.00 144.0 0.020 1.68
43 150.0 60,000.0 144.00 3.0 1.00 0.00 145.8 0.020 1.65
44 150.0 60,000.0 144.00 3.0 1.00 0.00 147.7 0.021 1.62
45 150.0 60,000.0 144.00 3.1 1.00 0.00 149.5 0.021 1.59
46 150.0 60,000.0 144.00 3.2 1.00 0.00 151.3 0.021 1.56
47 150.0 60,000.0 144.00 3.3 1.00 0.00 153.0 0.021 1.53
48 150.0 60,000.0 144.00 3.3 1.00 0.00 154.8 0.022 1.50
49 150.0 60,000.0 144.00 3.4 1.00 0.00 156.5 0.022 1.48
50 150.0 60,000.0 144.00 3.5 1.00 0.00 158.3 0.022 1.45
51 150.0 60,000.0 144.00 3.6 1.00 0.00 160.0 0.022 1.43
52 150.0 60,000.0 144.00 3.7 1.00 0.00 161.7 0.023 1.40
53 150.0 60,000.0 144.00 3.7 1.00 0.00 163.0 0.023 1.38
54 150.0 60,000.0 144.00 3.8 1.00 0.00 164.1 0.023 1.37
55 150.0 60,000.0 144.00 3.8 1.00 0.00 165.2 0.023 1.35
56 150.0 60,000.0 144.00 3.9 1.00 0.00 166.2 0.023 1.34
57 150.0 60,000.0 144.00 4.0 1.00 0.00 167.3 0.024 1.32
58 150.0 60,000.0 144.00 4.0 1.00 0.00 168.4 0.024 1.31
59 150.0 60,000.0 144.00 4.1 1.00 0.00 169.4 0.024 1.29
60 150.0 60,000.0 144.00 4.1 1.00 0.00 170.5 0.024 1.28
61 150.0 60,000.0 144.00 4.2 1.00 0.00 171.6 0.024 1.27
62 150.0 60,000.0 144.00 4.2 1.00 0.00 172.6 0.025 1.25
63 150.0 60,000.0 144.00 4.3 1.00 0.00 173.7 0.025 1.24
64 150.0 60,000.0 144.00 4.4 1.00 0.00 174.8 0.025 1.22
65 150.0 60,000.0 144.00 4.4 1.00 0.00 175.8 0.025 1.21
66 150.0 60,000.0 144.00 4.5 1.00 0.00 176.9 0.025 1.20
67 150.0 60,000.0 144.00 4.6 1.00 0.00 178.0 0.026 1.18
68 150.0 60,000.0 144.00 4.6 1.00 0.00 179.0 0.026 1.17
69 150.0 60,000.0 144.00 4.7 1.00 0.00 180.1 0.026 1.16
70 150.0 60,000.0 144.00 4.8 1.00 0.00 181.2 0.026 1.14
71 150.0 60,000.0 144.00 4.8 1.00 0.00 182.3 0.026 1.13
72 150.0 60,000.0 144.00 4.9 1.00 0.00 183.4 0.027 1.12
73 150.0 60,000.0 144.00 5.0 1.00 0.00 184.5 0.027 1.10
74 150.0 60,000.0 144.00 5.0 1.00 0.00 185.6 0.027 1.09
75 150.0 60,000.0 144.00 5.1 1.00 0.00 186.7 0.027 1.08
76 150.0 60,000.0 144.00 5.2 1.00 0.00 187.8 0.028 1.06
77 150.0 60,000.0 144.00 5.3 1.00 0.00 189.0 0.028 1.05
78 150.0 60,000.0 144.00 5.4 1.00 0.00 190.1 0.028 1.04
79 150.0 60,000.0 144.00 5.5 1.00 0.00 191.2 0.029 1.03
80 150.0 60,000.0 144.00 5.5 1.00 0.00 192.4 0.029 1.01
81 150.0 60,000.0 144.00 5.6 1.00 0.00 193.6 0.029 1.00
82 150.0 60,000.0 144.00 5.7 1.00 0.00 194.8 0.029 0.99
83 150.0 60,000.0 144.00 5.8 1.00 0.00 196.0 0.030 0.97
84 150.0 60,000.0 144.00 5.9 1.00 0.00 197.2 0.030 0.96
85 150.0 60,000.0 144.00 6.0 1.00 0.00 198.4 0.030 0.95
86 150.0 60,000.0 144.00 6.1 1.00 0.00 199.6 0.031 0.93
87 150.0 60,000.0 144.00 6.2 1.00 0.00 200.9 0.031 0.92
88 150.0 60,000.0 144.00 6.3 1.00 0.00 202.2 0.031 0.90
89 150.0 60,000.0 144.00 6.5 1.00 0.00 203.5 0.032 0.89
90 150.0 60,000.0 144.00 6.6 1.00 0.00 204.8 0.032 0.88
91 150.0 60,000.0 144.00 6.7 1.00 0.00 206.1 0.033 0.86
92 150.0 60,000.0 144.00 6.8 1.00 0.00 207.5 0.033 0.85
93 150.0 60,000.0 144.00 7.0 1.00 0.00 208.9 0.033 0.84
94 150.0 60,000.0 144.00 7.1 1.00 0.00 210.3 0.034 0.82
95 150.0 60,000.0 144.00 7.3 1.00 0.00 211.7 0.034 0.81
96 150.0 60,000.0 144.00 7.4 1.00 0.00 213.2 0.035 0.79
97 150.0 60,000.0 144.00 7.6 1.00 0.00 214.7 0.035 0.78
98 150.0 60,000.0 144.00 7.7 1.00 0.00 216.3 0.036 0.77
99 150.0 60,000.0 144.00 7.9 1.00 0.00 217.8 0.036 0.75
100 150.0 60,000.0 144.00 8.1 1.00 0.00 219.4 0.037 0.74
101 150.0 60,000.0 144.00 8.3 1.00 0.00 221.1 0.038 0.72
102 150.0 922.6 144.00 8.5 1.00 0.00 222.8 0.038 0.71
Pile Toe 0.0 922.6 144.00 202.7 0.00 0.00 0.0 0.220 0.07

A detailed output of the parameters for each segment/element.  TAMWAVE no longer uses the simplifications used in the past for resistance distribution along the shaft, i.e., uniform, triangular, etc., but constructs one based on the soil properties.  Much of this data is repeated from the static analysis.

Final Element Output
SRD = 572.68 kips
Element Time Step for Maximum Compressive Stress Maximum Compressive Stress, ksi Time Step for Maximum Tensile Stress Maximum Tensile Stress, ksi Maximum Deflection, in. Final Deflection, in. Final Velocity, ft/sec
1 50 3.70 164 0.00 1.299 1.299 -0.11
2 176 2.64 1 0.00 1.300 1.261 -2.56
3 178 2.64 2 0.00 0.650 0.646 -1.01
4 180 2.65 3 0.00 0.646 0.643 -0.93
5 182 2.66 4 0.00 0.641 0.639 -0.85
6 184 2.66 5 0.00 0.637 0.635 -0.78
7 186 2.67 6 0.00 0.632 0.631 -0.70
8 187 2.67 7 0.00 0.628 0.627 -0.62
9 190 2.68 8 0.00 0.623 0.622 -0.53
10 192 2.69 9 0.00 0.619 0.618 -0.45
11 194 2.69 10 0.00 0.614 0.613 -0.37
12 196 2.69 11 0.00 0.609 0.609 -0.30
13 198 2.70 12 0.00 0.604 0.604 -0.22
14 359 2.71 13 0.00 0.599 0.599 -0.14
15 361 2.72 14 0.00 0.594 0.594 -0.06
16 363 2.73 15 0.00 0.588 0.588 0.01
17 365 2.74 16 0.00 0.583 0.583 0.07
18 367 2.75 17 0.00 0.578 0.578 0.13
19 369 2.75 18 0.00 0.572 0.572 0.19
20 372 2.76 19 0.00 0.567 0.567 0.24
21 374 2.77 20 0.00 0.561 0.561 0.27
22 376 2.78 21 0.00 0.556 0.556 0.29
23 378 2.79 22 0.00 0.550 0.550 0.30
24 379 2.80 23 0.00 0.544 0.544 0.29
25 381 2.80 24 0.00 0.539 0.539 0.28
26 384 2.81 25 0.00 0.533 0.533 0.26
27 386 2.82 26 0.00 0.527 0.527 0.23
28 388 2.82 27 0.00 0.522 0.522 0.19
29 390 2.83 28 0.00 0.516 0.516 0.15
30 392 2.83 29 0.00 0.511 0.511 0.11
31 393 2.84 30 0.00 0.505 0.505 0.07
32 395 2.84 31 0.00 0.500 0.500 0.03
33 397 2.84 32 0.00 0.496 0.494 -0.01
34 399 2.84 33 0.00 0.491 0.489 -0.05
35 399 2.84 34 0.00 0.487 0.483 -0.08
36 400 2.84 35 0.00 0.483 0.478 -0.11
37 401 2.83 36 0.00 0.479 0.473 -0.14
38 400 2.82 37 0.00 0.474 0.468 -0.17
39 401 2.81 38 0.00 0.470 0.463 -0.19
40 400 2.80 39 0.00 0.466 0.457 -0.21
41 401 2.78 40 0.00 0.462 0.452 -0.24
42 399 2.76 41 0.00 0.458 0.447 -0.26
43 400 2.74 42 0.00 0.454 0.442 -0.27
44 399 2.71 43 0.00 0.449 0.437 -0.29
45 398 2.68 44 0.00 0.445 0.432 -0.30
46 397 2.65 45 0.00 0.441 0.427 -0.31
47 267 2.64 46 0.00 0.437 0.422 -0.32
48 270 2.64 47 0.00 0.433 0.417 -0.33
49 272 2.63 48 0.00 0.429 0.412 -0.33
50 275 2.62 49 0.00 0.425 0.407 -0.34
51 277 2.61 50 0.00 0.420 0.402 -0.34
52 279 2.60 51 0.00 0.416 0.397 -0.35
53 282 2.59 52 0.00 0.412 0.393 -0.35
54 284 2.58 53 0.00 0.407 0.388 -0.36
55 283 2.57 54 0.00 0.403 0.383 -0.36
56 286 2.56 55 0.00 0.398 0.378 -0.36
57 288 2.55 56 0.00 0.393 0.373 -0.36
58 290 2.54 57 0.00 0.389 0.368 -0.36
59 293 2.53 58 0.00 0.384 0.363 -0.36
60 295 2.52 59 0.00 0.379 0.358 -0.35
61 298 2.51 60 0.00 0.374 0.353 -0.35
62 300 2.50 61 0.00 0.368 0.349 -0.35
63 303 2.49 62 0.00 0.363 0.344 -0.35
64 301 2.47 63 0.00 0.358 0.339 -0.34
65 304 2.46 64 0.00 0.352 0.334 -0.34
66 306 2.45 65 0.00 0.347 0.329 -0.33
67 309 2.44 66 0.00 0.341 0.324 -0.32
68 311 2.43 67 0.00 0.336 0.319 -0.32
69 478 2.42 68 0.00 0.330 0.315 -0.31
70 480 2.43 69 0.00 0.324 0.310 -0.31
71 479 2.44 70 0.00 0.319 0.305 -0.30
72 481 2.44 71 0.00 0.313 0.300 -0.29
73 482 2.44 72 0.00 0.307 0.296 -0.29
74 481 2.43 73 0.00 0.302 0.291 -0.28
75 482 2.42 74 0.00 0.296 0.286 -0.28
76 480 2.40 75 0.00 0.290 0.282 -0.27
77 482 2.38 76 0.00 0.285 0.277 -0.26
78 479 2.35 77 0.00 0.280 0.273 -0.26
79 482 2.32 78 0.00 0.274 0.269 -0.25
80 483 2.28 79 0.00 0.269 0.264 -0.25
81 481 2.25 80 0.00 0.264 0.260 -0.24
82 483 2.21 81 0.00 0.259 0.256 -0.24
83 485 2.17 82 0.00 0.255 0.252 -0.23
84 483 2.13 83 0.00 0.250 0.248 -0.22
85 485 2.09 84 0.00 0.246 0.244 -0.21
86 487 2.05 85 0.00 0.241 0.240 -0.20
87 490 2.00 86 0.00 0.237 0.236 -0.19
88 487 1.95 87 0.00 0.233 0.232 -0.18
89 489 1.91 88 0.00 0.229 0.229 -0.18
90 492 1.86 89 0.00 0.226 0.225 -0.17
91 489 1.80 90 0.00 0.222 0.221 -0.16
92 492 1.75 91 0.00 0.218 0.218 -0.15
93 495 1.69 92 0.00 0.215 0.215 -0.15
94 497 1.63 93 0.00 0.212 0.211 -0.14
95 494 1.57 94 0.00 0.208 0.208 -0.15
96 497 1.51 95 0.00 0.205 0.205 -0.14
97 506 1.45 96 0.00 0.202 0.202 -0.15
98 508 1.39 97 0.00 0.199 0.199 -0.13
99 517 1.33 98 0.00 0.196 0.196 -0.16
100 521 1.28 99 0.00 0.193 0.193 -0.14
101 529 1.23 100 0.00 0.190 0.190 -0.15
102 532 1.24 101 0.00 0.188 0.187 -0.12

This table shows the end results of the run for the “target” SRD of the pile.  “SRD” is “soil resistance to driving,” and in TAMWAVE for cohesionless soils, SRD and the ultimate capacity are the same.  That’s not the case with cohesive soils, as we will see.  In any case TAMWAVE always does a “bearing graph” analysis, which proportionally varies the SRD and obtains different results for the blow count, maximum tensile and compressive stresses.  The bearing graph method isn’t perfect but it’s probably the best way we have to account for varying site conditions and to make judgments about the effect of those on our hammer selection.

The adoption of “Smith-type” damping was originally done for comparison purposes but for bearing graph analysis has one important advantages: it varies the soil radiation damping with the SRD, which is more realistic than just assuming fixed damping.

The table above only appears if the target SRD is actually achieved during bearing graph analysis.  If it doesn’t come up, the bearing graph analysis could not achieve net pile penetration at the target SRD, which means you need to revisit your hammer selection.

forcetime
Force-Time History, SRD = 572.68 kips
Blue Line = Pile Head Force
Red Line = Pile Head Impedance*Velocity
Vertical grid spacing from left to right is L/c, may not be complete for last spacing.
Plot Limits:
x-axis from 0.000 to 2.740
y-axis from -58,477.768 to 380,602.674

Here we see the second graphical output: the force-time history at the target SRD.  There are actually two histories: the actual pile head force (blue) and the pile head velocity multiplied by the impedance (red.)  For semi-infinite piles, the two should be the same; they will differ for actual finite piles, as is easily seen.  Although a “semi-infinite pile” may seem a very theoretical concept, the relationship of the two plots is very important in the field application of pile dynamics.

Summary of Results and Bearing Graph Data
Soil Resistance, kips Permanent Set of Pile Toe, inches Blows per Foot of Penetration Maximum Compressive Stress, ksi Element of Maximum Compressive Stress Maximum Tensile Stress, ksi Element of Maximum Tensile Stress Number of Iterations
114.5 1.707 7.0 2.61 30 0.67 43 1590
229.1 0.754 15.9 2.64 29 0.20 25 1124
343.6 0.355 33.8 2.67 28 0.00 102 719
458.1 0.111 108.2 2.71 32 0.00 102 567
572.7 0.000 0.0 2.84 34 0.00 102 549

The final results are shown here.  In this case, at the target SRD, no permanent set of the pile is recorded.  It will be necessary to vary the size of the hammer, being mindful of the stresses (whose allowable values are described here.)

At this point the analysis of this pile is complete.  The program gives you the choice of simply trying another hammer or starting over.  The latter is what we will do next with a sample case for cohesive soils.

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