Posted in TAMWAVE

TAMWAVE 2021 Update

Getting ready for another semester of Foundations comes with a minor update to the TAMWAVE driven pile analyser, which includes axial and lateral settlement analysis and wave equation analysis of pile driving. The last major revision was in 2017 and details about that are here. The revisions this time are as follows:

  • Initial pile length reduced to 50′, and initial phreatic surface depth reduced to 25′.
  • H-Piles excluded from toe plugging.
  • Strain softening coefficient for soil shear modulus increased for more realistic values.
  • Toe quake for cohesive soils set to more conventional values, as Tomlinson’s method was used to compute Nq.
  • Added Davisson’s Method line for evaluation of virtual pile load test, and flipped the graph to more realistically simulate actual load-settlement curves. (See above for the new format.)
  • Marked the target SRD value differently to make it easier to see.

This will probably be the last update to the routine, which first went online in 2005. We hope that you find it useful.

Posted in TAMWAVE

TAMWAVE: Cavity Expansion Theory and Soil Set-Up

One of the things that was attempted in the TAMWAVE project is the use of cavity expansion theory to estimate soil set-up in cohesive soils.  Doing this, however, brought some complications that need some explanation.

Cavity expansion theory is basically the study of what happens when one body expands inside of another.  When this takes places, additional radial stresses (most analyses center around a cylinder or sphere) are generated.  In the case of driven piles, these additional stresses add to the pile’s resistance to load.  It can be argued that cavity expansion is one of the key advantages of driven piles.  In the case of drilled piles such as drilled shafts or auger-cast piles, this does not take place, as the soil is removed either before or during the actual pile installation.  The result of this is that driven piles, for the same length and diameter as a corresponding drilled pile, a driven pile will have a greater resistance to load (ultimate capacity.)

Applying cavity expansion theory to piles has a long history and is detailed in documents such as Randolph, Carter and Wroth (1979) and Yu and Houlsby (1991).  Our particular interest is with clays because, in addition to the changes in the soil from cavity expansion, the pore water pressure increases.  This is the primary (but not the only) reason why the SRD (soil resistance to driving) in cohesive soils is significantly less than the ultimate capacity; this fact inevitably complicates drivability studies.

The increase in pore water pressure is a dynamic phenomenon; it experiences a sudden increase during driving and then gradually dissipates after installation.  How gradually the latter takes place depends on many factors such as the permeability of the soil.  Study of this phenomenon is well represented in the literature; however, for the TAMWAVE project it is not really of interest.  The primary interest here is the value of SRD after the immediate increase of pore water pressures during driving.

Both cavity expansion theory and practice show that excess pore water pressures can easily exceed the effective stresses.  In principle, considering that we have established the beta (effective-stress dependent) method for both cohesionless and cohesive soils, this can mean a complete loss of SRD.  Although dramatic drops in SRD are not unknown, for most piles this is unrealistic.  The reason for this is that, like the dissipation, the build-up of pore water pressures is a dynamic phenomenon, albeit in a much smaller time frame.  Dissipation, hindered as it is by the low permeability of cohesive soils, begins immediately.  Pore water pressures (along with any other stresses induced by cavity expansion) also vary with the distance from the pile.

The result of all this is that prediction of both the increase of pore water pressure and its effect on the SRD of the pile during driving is a complicated phenomenon that is not completely represented by closed-form cavity expansion based solutions.  For a project such as this, what we need is something that will give a reasonable representation of soil set-up for cohesive soils.  To accomplish this, we stick with computing the excess pore water pressure, but with a different methodology.  We assume the following:

  1. The basic validity of our effective-stress based beta methods of shaft friction calculation.
  2. All of the decrease from static ultimate capacity to SRD takes place due to pore water pressure increase.
  3. The excess pore water pressure increases affect the effective stress used to compute the shaft friction.
  4. Only those pile segments under the water table are subject to this analysis.

Assuming all that, for a soil set-up factor (from this source, loosely adapted) S_r , the excess pore water pressures that affect the effective stress (which in turn determine the shaft friction) are computed by the equation

\Delta u = \sigma'_{vo}\left( 1 - \frac{1}{S_r} \right)

This gives identical results to those when the S_r are applied directly.

In practice this phenomenon is still subject to investigation.  Some of the research involves use of numerical methods (such as finite element methods) to simulate cavity expansion effects.  This is doubtless an advance over the closed-form solutions of the past, and a necessity given the complexity of the physics of the problem.  Empirical methods are also still being developed, such as are documented by Wang, Verma and Steward (2009).

Posted in TAMWAVE

New Version of TAMWAVE Online Wave Equation Program Now Available

The completely revised TAMWAVE program is now available.  The goal of this project is to produce a free, online set of routines which analyse driven piles for axial and lateral load-deflection characteristics and drivability by the wave equation. The program is not intended for commercial use but for educational purposes, to introduce students to both the wave equation and methods for estimating load-deflection characteristics of piles in both axial and lateral loading.

We have a series of posts which detail the theory behind and workings of the program:

This program replaces the original routine which was originally written in 2005 and updated in 2010. The documentation for that effort is here.

Posted in TAMWAVE

TAMWAVE 7: Analysis for a Cohesive Soil

With the analysis of the concrete pile in cohesionless soils complete, we turn to an example in cohesive soils.

The analysis procedure is exactly the same.  We will first discuss the differences between the two, then consider an example.

Differences with Piles in Cohesive Soils

  • The unit weight is in put as a saturated unit weight, and the specific gravity of the soil particles is different (but not by much.)
  • Once the simulated CPT data was abandoned, the “traditional” Tomlinson formula for the unit toe resistance, namely q_t = N_c c , where N_c = 9 , was chosen.
  • The ultimate resistance along the shaft is done using the formula of Kolk and van der Velde (1996).  This was used as a beta method, for compatibility with the method used for cohesionless soils.  Unless the ratio of the cohesion to the effective stress is constant, the whole concept of a constant lateral pressure due to cohesion needs to be discarded.
  • For saturated cohesive soils, an estimate of pile set-up is done using cavity expansion methods.  Originally excess pore pressure due to cavity expansion during driving was estimated using the method described by Randolph (2003); however, this ran into difficulties and a different method was substituted, which is described here.  This excess pore pressure is then added to the existing pore pressure and a new effective stress is computed at each point for the Kolk and van der Velde method.  The results are within reasonable ranges.

Test Case

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The only change in basic parameters from the other case was the change to a CH soil.  We opted not to perform a lateral load test this time, although the program is certainly capable of using the CLM 2 method with cohesive soils.

Pile Data
Pile Designation 12 In. Square
Pile Material Concrete
Penetration of Pile into the Soil, ft. 100
Basic “diameter” or size of the pile, ft. 1
Cross-sectional Area of the Pile, ft2 1.000
Pile Toe Area, ft2 1.000
Perimeter of the Pile, ft. 4.000
Soil Data
Type of Soil CH
Specific Gravity of Solids 2.7
Void Ratio 0.84
Dry Unit Weight, pcf 91.5
Saturated Unit Weight, pcf 120.0
Soil Internal Friction Angle phi, degrees
Cohesion c, psf 750
SPT N60, blows/foot 6
CPT qc, psf 12,696
Distance of Water Table from Soil Surface, ft. 50
Penetration of Pile into Water Table, ft. 50
Pile Toe Results
Effective Stress at Pile Toe, ksf 7.454
SPT (N1)60 at pile toe, blows/foot 3
Unit Toe Resistance qp, ksf 6.8
Shear Modulus at Pile Toe, ksf 474.8
Toe Spring Constant Depth Factor 1.366
Toe Spring Constant, kips/ft 2,358.0
Pile Toe Quake, in. 0.034
Poisson’s Ratio at Pile Toe 0.500
Toe Damping, kips-sec/ft 14.0
Toe Smith-Type Damping Constant, sec/ft 2.069
Total Static Toe Resistance Qp, kips 6.75
Pile Toe Plugged? Yes
Final Results
Total Shaft Friction Qs, kips 219.92
Ultimate Axial Capacity of Pile, kips 226.67
Pile Setup Factor 2.0
Total Pile Soil Resistance to Driving (SRD), kips 115.44

Shaft Segment Properties
Depth at Centre of Layer, feet Soil Shear Modulus, ksf Beta Quake,inches Maximum Load Transfer, ksf Spring Constant for Wall Shear, ksf/in Smith-Type Damping Constant, sec/ft Maximum Load Transfer During Driving (SRD), ksf
0.50 34.9 2.541 0.0400 0.116 2.91 2.709 0.116
1.50 60.4 1.180 0.0322 0.162 5.03 2.559 0.162
2.50 78.0 0.827 0.0291 0.189 6.50 2.489 0.189
3.50 92.2 0.655 0.0273 0.210 7.69 2.443 0.210
4.50 104.6 0.550 0.0260 0.227 8.72 2.407 0.227
5.50 115.6 0.479 0.0250 0.241 9.64 2.378 0.241
6.50 125.7 0.427 0.0243 0.254 10.48 2.353 0.254
7.50 135.0 0.387 0.0236 0.266 11.25 2.332 0.266
8.50 143.8 0.356 0.0231 0.277 11.98 2.312 0.277
9.50 152.0 0.330 0.0226 0.287 12.66 2.294 0.287
10.50 159.8 0.308 0.0222 0.296 13.31 2.278 0.296
11.50 167.2 0.290 0.0219 0.305 13.93 2.262 0.305
12.50 174.3 0.274 0.0216 0.313 14.53 2.248 0.313
13.50 181.2 0.260 0.0213 0.321 15.10 2.234 0.321
14.50 187.8 0.248 0.0210 0.329 15.65 2.221 0.329
15.50 194.1 0.237 0.0208 0.336 16.18 2.208 0.336
16.50 200.3 0.228 0.0206 0.344 16.69 2.196 0.344
17.50 206.3 0.219 0.0204 0.351 17.19 2.184 0.351
18.50 212.1 0.211 0.0202 0.357 17.67 2.173 0.357
19.50 217.7 0.204 0.0201 0.364 18.14 2.162 0.364
20.50 223.2 0.197 0.0199 0.370 18.60 2.151 0.370
21.50 228.6 0.191 0.0198 0.377 19.05 2.141 0.377
22.50 233.9 0.186 0.0196 0.383 19.49 2.130 0.383
23.50 239.0 0.181 0.0195 0.389 19.92 2.120 0.389
24.50 244.1 0.176 0.0194 0.395 20.34 2.110 0.395
25.50 249.0 0.172 0.0193 0.401 20.75 2.100 0.401
26.50 253.8 0.168 0.0192 0.406 21.15 2.091 0.406
27.50 258.6 0.164 0.0191 0.412 21.55 2.081 0.412
28.50 263.2 0.160 0.0190 0.418 21.94 2.072 0.418
29.50 267.8 0.157 0.0190 0.423 22.32 2.062 0.423
30.50 272.3 0.154 0.0189 0.429 22.69 2.053 0.429
31.50 276.7 0.151 0.0188 0.434 23.06 2.044 0.434
32.50 281.1 0.148 0.0188 0.439 23.42 2.034 0.439
33.50 285.4 0.145 0.0187 0.445 23.78 2.025 0.445
34.50 289.6 0.143 0.0186 0.450 24.13 2.016 0.450
35.50 293.8 0.140 0.0186 0.455 24.48 2.007 0.455
36.50 297.9 0.138 0.0186 0.461 24.82 1.998 0.461
37.50 301.9 0.136 0.0185 0.466 25.16 1.989 0.466
38.50 305.9 0.134 0.0185 0.471 25.49 1.980 0.471
39.50 309.9 0.132 0.0184 0.476 25.82 1.971 0.476
40.50 313.8 0.130 0.0184 0.481 26.15 1.962 0.481
41.50 317.6 0.128 0.0184 0.487 26.47 1.953 0.487
42.50 321.4 0.126 0.0184 0.492 26.79 1.944 0.492
43.50 325.2 0.125 0.0183 0.497 27.10 1.935 0.497
44.50 328.9 0.123 0.0183 0.502 27.41 1.926 0.502
45.50 332.6 0.122 0.0183 0.507 27.72 1.917 0.507
46.50 336.2 0.120 0.0183 0.513 28.02 1.908 0.513
47.50 339.8 0.119 0.0183 0.518 28.32 1.898 0.518
48.50 343.4 0.118 0.0183 0.523 28.61 1.889 0.523
49.50 346.9 0.117 0.0183 0.528 28.91 1.880 0.528
50.50 349.7 0.116 0.0183 0.533 29.15 1.871 0.000
51.50 351.9 0.115 0.0183 0.537 29.33 1.862 0.005
52.50 354.1 0.115 0.0184 0.541 29.51 1.853 0.011
53.50 356.2 0.114 0.0184 0.546 29.69 1.844 0.018
54.50 358.4 0.114 0.0184 0.550 29.87 1.835 0.023
55.50 360.5 0.113 0.0185 0.555 30.04 1.826 0.029
56.50 362.6 0.113 0.0185 0.559 30.22 1.816 0.035
57.50 364.7 0.113 0.0185 0.564 30.39 1.807 0.041
58.50 366.8 0.112 0.0186 0.568 30.57 1.797 0.047
59.50 368.9 0.112 0.0186 0.573 30.74 1.788 0.053
60.50 371.0 0.112 0.0187 0.578 30.92 1.778 0.059
61.50 373.0 0.111 0.0187 0.583 31.09 1.768 0.064
62.50 375.1 0.111 0.0188 0.588 31.26 1.757 0.070
63.50 377.1 0.111 0.0189 0.593 31.43 1.747 0.076
64.50 379.1 0.111 0.0189 0.598 31.60 1.736 0.082
65.50 381.2 0.110 0.0190 0.603 31.76 1.726 0.088
66.50 383.2 0.110 0.0191 0.609 31.93 1.715 0.093
67.50 385.2 0.110 0.0191 0.614 32.10 1.703 0.099
68.50 387.1 0.110 0.0192 0.620 32.26 1.692 0.105
69.50 389.1 0.110 0.0193 0.626 32.43 1.680 0.111
70.50 391.1 0.110 0.0194 0.632 32.59 1.668 0.117
71.50 393.0 0.110 0.0195 0.638 32.75 1.656 0.123
72.50 395.0 0.110 0.0196 0.645 32.91 1.643 0.129
73.50 396.9 0.110 0.0197 0.652 33.07 1.630 0.135
74.50 398.8 0.110 0.0198 0.659 33.23 1.617 0.141
75.50 400.7 0.110 0.0199 0.666 33.39 1.603 0.147
76.50 402.6 0.110 0.0201 0.673 33.55 1.589 0.153
77.50 404.5 0.111 0.0202 0.681 33.71 1.575 0.159
78.50 406.4 0.111 0.0203 0.689 33.87 1.560 0.166
79.50 408.3 0.111 0.0205 0.698 34.03 1.544 0.172
80.50 410.2 0.112 0.0207 0.707 34.18 1.528 0.179
81.50 412.0 0.112 0.0209 0.716 34.34 1.512 0.186
82.50 413.9 0.113 0.0211 0.726 34.49 1.494 0.193
83.50 415.7 0.113 0.0213 0.737 34.64 1.476 0.200
84.50 417.6 0.114 0.0215 0.748 34.80 1.457 0.207
85.50 419.4 0.115 0.0217 0.760 34.95 1.437 0.215
86.50 421.2 0.116 0.0220 0.773 35.10 1.416 0.223
87.50 423.0 0.117 0.0223 0.787 35.25 1.394 0.232
88.50 424.8 0.118 0.0227 0.802 35.40 1.370 0.241
89.50 426.6 0.120 0.0230 0.819 35.55 1.345 0.250
90.50 428.4 0.121 0.0235 0.838 35.70 1.318 0.260
91.50 430.2 0.123 0.0239 0.859 35.85 1.288 0.271
92.50 432.0 0.126 0.0245 0.882 36.00 1.256 0.283
93.50 433.8 0.129 0.0252 0.910 36.15 1.220 0.297
94.50 435.5 0.132 0.0260 0.944 36.29 1.179 0.313
95.50 437.3 0.137 0.0270 0.985 36.44 1.133 0.331
96.50 439.0 0.143 0.0284 1.038 36.58 1.077 0.354
97.50 440.8 0.152 0.0303 1.113 36.73 1.006 0.385
98.50 442.5 0.168 0.0335 1.235 36.87 0.908 0.433
99.50 444.2 0.181 0.0363 1.343 37.02 0.837 0.477

Data for Axial Load Analysis using ALP Method
Length of the pile, in. 1,200.0
Axial stiffness EA. lbs. 720,000,000
Circumference, in. 48.000
Point resistance, lbs. 6,750
Quake of the point, in. 0.034
Number of pile elements 100
Number of loading steps 20
Maximum pile load, lbs. 226,672.5
Load Increment, lbs. 22,667.3
Failure Load, lbs. 226,672.5
Results for Loading and Unloading Test
Load Step Force at Pile Head, kips Pile Head Deflection, in. Number of Plastic Shaft Springs
0 0.0 0.000 0
1 22.7 0.012 0
2 45.3 0.025 0
3 68.0 0.039 18
4 90.7 0.058 33
5 113.3 0.082 44
6 136.0 0.109 55
7 158.7 0.140 64
8 181.3 0.175 74
9 204.0 0.214 84
10 226.7 0.271 100
11 204.0 0.259 0
12 181.3 0.246 0
13 158.7 0.234 0
14 136.0 0.221 0
15 113.3 0.209 7
16 90.7 0.193 18
17 68.0 0.175 27
18 45.3 0.154 33
19 22.7 0.132 39
20 -0.0 0.108 44

alpimage
Plotted Results
x-axis = Pile Head Force
y-axis = Pile Head Deflection
Plot Limits:
x-axis from -0.000 to 226.673
y-axis from 0.000 to 0.271

Although the cohesive soils yield very different results from the cohesionless ones, the presentation is the same.  Note the significant difference between the element/segment SRD for the static resistance and with the pore pressure increase included.  The pile set-up factor is about 2, which is within an acceptable range.  This does not apply to the toe.

Screenshot_20180106_163425

The input for the wave equation is identical, except for the hammer selected, which is much smaller than for the cohesionless soils.  This is not due to set-up but to the lower capacity of the pile; the hammer selection does not account for set-up.  The user will have to select a smaller hammer size to take full advantage of this, depending upon the results.

General Output for Wave Equation Analysis
2018-01-06T15:59:49-05:00
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 65C
Hammer Rated Striking Energy, ft-lbs 19175
Hammer Efficiency, percent 50
Length of Hammer Cushion Stack, in. 18.5
Soil Resistance to Driving (SRD) for detailed results only, kips 115.4
Percent at Toe 5.85
Toe Quake, in. 0.009
Toe Damping, sec/ft 2.07

Initial Element Output
SRD = 115.44 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 6,500.0 1,880.5 99.40 0.0 0.80 9.74 0.0 1,000.000 0.00
Driving Accessory 1,100.0 711.5 144.00 0.0 0.51 0.00 0.0 1,000.000 0.00
Pile Head 150.0 60,000.0 144.00 0.5 1.00 0.00 11.6 0.040 2.71
4 150.0 60,000.0 144.00 0.6 1.00 0.00 20.1 0.032 2.56
5 150.0 60,000.0 144.00 0.8 1.00 0.00 26.0 0.029 2.49
6 150.0 60,000.0 144.00 0.8 1.00 0.00 30.7 0.027 2.44
7 150.0 60,000.0 144.00 0.9 1.00 0.00 34.9 0.026 2.41
8 150.0 60,000.0 144.00 1.0 1.00 0.00 38.5 0.025 2.38
9 150.0 60,000.0 144.00 1.0 1.00 0.00 41.9 0.024 2.35
10 150.0 60,000.0 144.00 1.1 1.00 0.00 45.0 0.024 2.33
11 150.0 60,000.0 144.00 1.1 1.00 0.00 47.9 0.023 2.31
12 150.0 60,000.0 144.00 1.1 1.00 0.00 50.7 0.023 2.29
13 150.0 60,000.0 144.00 1.2 1.00 0.00 53.3 0.022 2.28
14 150.0 60,000.0 144.00 1.2 1.00 0.00 55.7 0.022 2.26
15 150.0 60,000.0 144.00 1.3 1.00 0.00 58.1 0.022 2.25
16 150.0 60,000.0 144.00 1.3 1.00 0.00 60.4 0.021 2.23
17 150.0 60,000.0 144.00 1.3 1.00 0.00 62.6 0.021 2.22
18 150.0 60,000.0 144.00 1.3 1.00 0.00 64.7 0.021 2.21
19 150.0 60,000.0 144.00 1.4 1.00 0.00 66.8 0.021 2.20
20 150.0 60,000.0 144.00 1.4 1.00 0.00 68.8 0.020 2.18
21 150.0 60,000.0 144.00 1.4 1.00 0.00 70.7 0.020 2.17
22 150.0 60,000.0 144.00 1.5 1.00 0.00 72.6 0.020 2.16
23 150.0 60,000.0 144.00 1.5 1.00 0.00 74.4 0.020 2.15
24 150.0 60,000.0 144.00 1.5 1.00 0.00 76.2 0.020 2.14
25 150.0 60,000.0 144.00 1.5 1.00 0.00 78.0 0.020 2.13
26 150.0 60,000.0 144.00 1.6 1.00 0.00 79.7 0.020 2.12
27 150.0 60,000.0 144.00 1.6 1.00 0.00 81.4 0.019 2.11
28 150.0 60,000.0 144.00 1.6 1.00 0.00 83.0 0.019 2.10
29 150.0 60,000.0 144.00 1.6 1.00 0.00 84.6 0.019 2.09
30 150.0 60,000.0 144.00 1.6 1.00 0.00 86.2 0.019 2.08
31 150.0 60,000.0 144.00 1.7 1.00 0.00 87.7 0.019 2.07
32 150.0 60,000.0 144.00 1.7 1.00 0.00 89.3 0.019 2.06
33 150.0 60,000.0 144.00 1.7 1.00 0.00 90.8 0.019 2.05
34 150.0 60,000.0 144.00 1.7 1.00 0.00 92.2 0.019 2.04
35 150.0 60,000.0 144.00 1.8 1.00 0.00 93.7 0.019 2.03
36 150.0 60,000.0 144.00 1.8 1.00 0.00 95.1 0.019 2.03
37 150.0 60,000.0 144.00 1.8 1.00 0.00 96.5 0.019 2.02
38 150.0 60,000.0 144.00 1.8 1.00 0.00 97.9 0.019 2.01
39 150.0 60,000.0 144.00 1.8 1.00 0.00 99.3 0.019 2.00
40 150.0 60,000.0 144.00 1.9 1.00 0.00 100.6 0.019 1.99
41 150.0 60,000.0 144.00 1.9 1.00 0.00 102.0 0.018 1.98
42 150.0 60,000.0 144.00 1.9 1.00 0.00 103.3 0.018 1.97
43 150.0 60,000.0 144.00 1.9 1.00 0.00 104.6 0.018 1.96
44 150.0 60,000.0 144.00 1.9 1.00 0.00 105.9 0.018 1.95
45 150.0 60,000.0 144.00 2.0 1.00 0.00 107.1 0.018 1.94
46 150.0 60,000.0 144.00 2.0 1.00 0.00 108.4 0.018 1.93
47 150.0 60,000.0 144.00 2.0 1.00 0.00 109.6 0.018 1.93
48 150.0 60,000.0 144.00 2.0 1.00 0.00 110.9 0.018 1.92
49 150.0 60,000.0 144.00 2.1 1.00 0.00 112.1 0.018 1.91
50 150.0 60,000.0 144.00 2.1 1.00 0.00 113.3 0.018 1.90
51 150.0 60,000.0 144.00 2.1 1.00 0.00 114.5 0.018 1.89
52 150.0 60,000.0 144.00 2.1 1.00 0.00 115.6 0.018 1.88
53 150.0 60,000.0 144.00 0.0 1.00 0.00 0.0 0.018 1.87
54 150.0 60,000.0 144.00 0.0 1.00 0.00 1.2 0.018 1.86
55 150.0 60,000.0 144.00 0.0 1.00 0.00 2.5 0.018 1.85
56 150.0 60,000.0 144.00 0.1 1.00 0.00 3.8 0.018 1.84
57 150.0 60,000.0 144.00 0.1 1.00 0.00 5.1 0.018 1.84
58 150.0 60,000.0 144.00 0.1 1.00 0.00 6.4 0.018 1.83
59 150.0 60,000.0 144.00 0.1 1.00 0.00 7.6 0.018 1.82
60 150.0 60,000.0 144.00 0.2 1.00 0.00 8.9 0.019 1.81
61 150.0 60,000.0 144.00 0.2 1.00 0.00 10.1 0.019 1.80
62 150.0 60,000.0 144.00 0.2 1.00 0.00 11.3 0.019 1.79
63 150.0 60,000.0 144.00 0.2 1.00 0.00 12.6 0.019 1.78
64 150.0 60,000.0 144.00 0.3 1.00 0.00 13.8 0.019 1.77
65 150.0 60,000.0 144.00 0.3 1.00 0.00 14.9 0.019 1.76
66 150.0 60,000.0 144.00 0.3 1.00 0.00 16.1 0.019 1.75
67 150.0 60,000.0 144.00 0.3 1.00 0.00 17.3 0.019 1.74
68 150.0 60,000.0 144.00 0.4 1.00 0.00 18.4 0.019 1.73
69 150.0 60,000.0 144.00 0.4 1.00 0.00 19.6 0.019 1.71
70 150.0 60,000.0 144.00 0.4 1.00 0.00 20.7 0.019 1.70
71 150.0 60,000.0 144.00 0.4 1.00 0.00 21.8 0.019 1.69
72 150.0 60,000.0 144.00 0.4 1.00 0.00 23.0 0.019 1.68
73 150.0 60,000.0 144.00 0.5 1.00 0.00 24.1 0.019 1.67
74 150.0 60,000.0 144.00 0.5 1.00 0.00 25.2 0.019 1.66
75 150.0 60,000.0 144.00 0.5 1.00 0.00 26.2 0.020 1.64
76 150.0 60,000.0 144.00 0.5 1.00 0.00 27.3 0.020 1.63
77 150.0 60,000.0 144.00 0.6 1.00 0.00 28.4 0.020 1.62
78 150.0 60,000.0 144.00 0.6 1.00 0.00 29.4 0.020 1.60
79 150.0 60,000.0 144.00 0.6 1.00 0.00 30.5 0.020 1.59
80 150.0 60,000.0 144.00 0.6 1.00 0.00 31.5 0.020 1.57
81 150.0 60,000.0 144.00 0.7 1.00 0.00 32.6 0.020 1.56
82 150.0 60,000.0 144.00 0.7 1.00 0.00 33.6 0.021 1.54
83 150.0 60,000.0 144.00 0.7 1.00 0.00 34.6 0.021 1.53
84 150.0 60,000.0 144.00 0.7 1.00 0.00 35.6 0.021 1.51
85 150.0 60,000.0 144.00 0.8 1.00 0.00 36.6 0.021 1.49
86 150.0 60,000.0 144.00 0.8 1.00 0.00 37.6 0.021 1.48
87 150.0 60,000.0 144.00 0.8 1.00 0.00 38.6 0.021 1.46
88 150.0 60,000.0 144.00 0.9 1.00 0.00 39.6 0.022 1.44
89 150.0 60,000.0 144.00 0.9 1.00 0.00 40.6 0.022 1.42
90 150.0 60,000.0 144.00 0.9 1.00 0.00 41.5 0.022 1.39
91 150.0 60,000.0 144.00 1.0 1.00 0.00 42.5 0.023 1.37
92 150.0 60,000.0 144.00 1.0 1.00 0.00 43.4 0.023 1.34
93 150.0 60,000.0 144.00 1.0 1.00 0.00 44.4 0.023 1.32
94 150.0 60,000.0 144.00 1.1 1.00 0.00 45.3 0.024 1.29
95 150.0 60,000.0 144.00 1.1 1.00 0.00 46.2 0.025 1.26
96 150.0 60,000.0 144.00 1.2 1.00 0.00 47.2 0.025 1.22
97 150.0 60,000.0 144.00 1.3 1.00 0.00 48.1 0.026 1.18
98 150.0 60,000.0 144.00 1.3 1.00 0.00 49.0 0.027 1.13
99 150.0 60,000.0 144.00 1.4 1.00 0.00 49.9 0.028 1.08
100 150.0 60,000.0 144.00 1.5 1.00 0.00 50.8 0.030 1.01
101 150.0 60,000.0 144.00 1.7 1.00 0.00 51.7 0.034 0.91
102 150.0 786.0 144.00 1.9 1.00 0.00 52.6 0.036 0.84
Pile Toe 0.0 786.0 144.00 6.8 0.00 0.00 0.0 0.009 2.07

Final Element Output
SRD = 115.44 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
1 183 2.90 592 0.00 0.818 0.277 -9.74
2 119 1.55 538 0.00 0.696 0.681 0.12
3 121 1.56 2 0.00 0.270 0.265 -0.02
4 123 1.56 3 0.00 0.270 0.265 -0.03
5 125 1.55 465 0.01 0.270 0.265 -0.02
6 127 1.55 467 0.05 0.270 0.265 -0.02
7 128 1.55 469 0.10 0.269 0.265 -0.02
8 130 1.55 471 0.14 0.269 0.265 -0.02
9 132 1.55 471 0.18 0.268 0.265 -0.01
10 134 1.55 473 0.22 0.268 0.265 -0.00
11 136 1.54 475 0.26 0.268 0.265 0.00
12 138 1.54 477 0.30 0.267 0.265 0.01
13 140 1.54 476 0.34 0.267 0.265 0.02
14 142 1.54 477 0.37 0.267 0.266 0.03
15 144 1.53 478 0.40 0.267 0.266 0.05
16 146 1.53 477 0.43 0.267 0.266 0.08
17 148 1.53 477 0.46 0.267 0.267 0.11
18 150 1.52 476 0.48 0.267 0.267 0.14
19 152 1.52 477 0.50 0.268 0.268 0.17
20 154 1.52 478 0.51 0.269 0.269 0.20
21 156 1.51 476 0.53 0.269 0.269 0.23
22 158 1.51 476 0.54 0.270 0.270 0.26
23 160 1.50 475 0.55 0.271 0.271 0.30
24 162 1.50 476 0.55 0.271 0.271 0.34
25 164 1.49 476 0.55 0.272 0.272 0.37
26 166 1.49 476 0.54 0.273 0.273 0.41
27 168 1.48 475 0.53 0.274 0.274 0.45
28 170 1.48 475 0.51 0.274 0.274 0.48
29 172 1.47 476 0.48 0.275 0.275 0.53
30 174 1.47 475 0.45 0.276 0.276 0.58
31 176 1.46 474 0.41 0.276 0.276 0.63
32 178 1.46 472 0.37 0.277 0.277 0.68
33 180 1.45 471 0.32 0.278 0.278 0.71
34 182 1.44 472 0.28 0.278 0.278 0.72
35 184 1.43 466 0.23 0.278 0.278 0.72
36 185 1.42 516 0.24 0.279 0.279 0.70
37 186 1.41 524 0.26 0.279 0.279 0.65
38 188 1.40 529 0.28 0.279 0.279 0.58
39 190 1.38 532 0.31 0.279 0.279 0.51
40 192 1.37 533 0.34 0.279 0.279 0.44
41 194 1.36 542 0.38 0.279 0.279 0.38
42 196 1.35 541 0.42 0.279 0.279 0.33
43 198 1.33 544 0.45 0.279 0.279 0.28
44 200 1.32 543 0.49 0.279 0.279 0.23
45 203 1.31 542 0.52 0.279 0.279 0.18
46 205 1.30 545 0.55 0.278 0.278 0.12
47 207 1.28 544 0.58 0.278 0.278 0.08
48 209 1.27 542 0.60 0.277 0.277 0.03
49 211 1.26 544 0.63 0.277 0.277 -0.01
50 213 1.24 543 0.65 0.277 0.277 -0.05
51 216 1.23 542 0.67 0.276 0.276 -0.10
52 217 1.22 540 0.69 0.276 0.276 -0.14
53 218 1.22 539 0.69 0.277 0.275 -0.18
54 220 1.22 540 0.69 0.278 0.275 -0.22
55 222 1.22 539 0.69 0.279 0.274 -0.25
56 224 1.22 538 0.69 0.281 0.274 -0.28
57 226 1.22 538 0.68 0.282 0.274 -0.32
58 228 1.22 538 0.66 0.283 0.273 -0.36
59 230 1.22 537 0.65 0.285 0.273 -0.41
60 232 1.23 536 0.63 0.286 0.273 -0.46
61 235 1.23 534 0.60 0.287 0.273 -0.52
62 237 1.23 535 0.57 0.288 0.273 -0.56
63 239 1.23 533 0.54 0.290 0.273 -0.61
64 241 1.23 532 0.50 0.291 0.273 -0.63
65 244 1.23 530 0.46 0.292 0.273 -0.66
66 246 1.23 531 0.41 0.293 0.273 -0.69
67 248 1.23 531 0.35 0.294 0.273 -0.72
68 250 1.23 530 0.29 0.294 0.274 -0.74
69 253 1.23 532 0.23 0.295 0.274 -0.75
70 255 1.23 470 0.18 0.296 0.274 -0.75
71 253 1.23 474 0.21 0.296 0.275 -0.75
72 255 1.23 473 0.24 0.296 0.275 -0.75
73 257 1.23 476 0.27 0.296 0.276 -0.74
74 260 1.23 476 0.30 0.296 0.276 -0.74
75 262 1.23 478 0.33 0.296 0.277 -0.72
76 264 1.23 478 0.35 0.295 0.277 -0.71
77 266 1.23 480 0.38 0.295 0.278 -0.70
78 268 1.22 479 0.39 0.294 0.278 -0.68
79 271 1.22 478 0.41 0.294 0.279 -0.66
80 273 1.22 480 0.43 0.293 0.279 -0.65
81 275 1.21 478 0.44 0.292 0.280 -0.64
82 277 1.21 477 0.46 0.292 0.280 -0.62
83 279 1.20 479 0.47 0.291 0.281 -0.60
84 280 1.19 477 0.48 0.290 0.282 -0.58
85 279 1.18 474 0.49 0.290 0.282 -0.55
86 280 1.17 474 0.50 0.289 0.283 -0.53
87 281 1.15 476 0.50 0.289 0.284 -0.51
88 281 1.12 469 0.51 0.288 0.284 -0.48
89 280 1.10 471 0.51 0.288 0.285 -0.45
90 281 1.06 471 0.51 0.288 0.285 -0.42
91 281 1.02 472 0.50 0.288 0.286 -0.40
92 280 0.97 473 0.49 0.288 0.287 -0.37
93 281 0.92 474 0.46 0.288 0.287 -0.34
94 282 0.87 474 0.42 0.288 0.288 -0.30
95 283 0.81 475 0.37 0.289 0.288 -0.27
96 282 0.75 476 0.31 0.289 0.289 -0.25
97 283 0.68 478 0.25 0.289 0.289 -0.23
98 289 0.62 480 0.19 0.289 0.289 -0.21
99 294 0.56 482 0.12 0.290 0.290 -0.19
100 302 0.51 485 0.07 0.290 0.290 -0.17
101 307 0.47 489 0.02 0.290 0.290 -0.15
102 316 0.46 532 0.00 0.290 0.290 -0.12

forcetime
Force-Time History, SRD = 115.44 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 2.955
y-axis from -68,985.344 to 223,926.386

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
23.1 (45.3) 1.541 7.8 1.53 4 1.21 24 2000
46.2 (90.7) 0.744 16.1 1.54 4 1.05 54 1149
69.3 (136.0) 0.494 24.3 1.54 4 0.97 54 872
92.3 (181.3) 0.349 34.4 1.55 4 0.86 54 740
115.4 (226.7) 0.281 42.7 1.56 4 0.69 54 592
138.5 (272.0) 0.228 52.6 1.58 3 0.52 56 588
161.6 (317.3) 0.184 65.2 1.61 3 0.30 92 480
184.7 (362.7) 0.144 83.3 1.64 3 0.20 94 477
207.8 (408.0) 0.108 111.1 1.67 4 0.11 95 474
230.9 (453.3) 0.077 155.4 1.70 4 0.07 92 471

The bearing graph data is complete.  The only difference with the cohesionless soils is the way the soil resistance is reported; the values in parentheses are ultimate resistance without set-up and those outside are the SRD with set-up.  The blow count indicates that a smaller hammer may be in order.

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.