Posted in Geotechnical Engineering

An Updated Version of Our Mohr’s Circle Routine Available, with Documentation

In 2016 we posted about two- and three-dimensional Mohr’s Circle problems and their solution using a strictly linear algebra solution.  We’ve done two things recently to update that: we’ve resolved some of the limitations of the original method (especially with the eigenvectors/direction cosines) and we’ve put the routine online for your use.  Both can be accessed here:

  1. Mohr’s Circle and Linear Algebra (the documentation)
  2. Online Routine

Image above from Verruijt, A., and van Bars, S. (2007). Soil Mechanics. VSSD, Delft, the Netherlands.

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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.

Posted in TAMWAVE

TAMWAVE 5: Wave Equation Analysis, Overview and Initial Entry

With the static analysis complete, we turn to the wave equation analysis.  TAMWAVE (as with the previous version) was based indirectly on the TTI wave equation program.  Although the numerical method was not changed, many other aspects of the program were, and so we need to consider these.

Shaft and Toe Resistance

Most wave equation programs in commercial use still use the Smith model for shaft and toe resistance during impact.  Referencing specifically their use in inverse methods, Randolph (2003) makes the following comment:

Dynamic pile tests are arguably the most cost-effective of all pile-testing methods, although they rely on relatively sophisticated numerical modelling for back-analysis. Theoretical advances in modelling the dynamic pile-soil interaction have been available since the mid-1980s, but have been slow to be implemented by commercial codes, most of which still use the empirical parameters of the Smith (1960) model. In order to allow an appropriate level of confidence in the interpretation of dynamic pile tests, and estimation of the static response, it is high time that appropriate scientific models were used for pile-soil interaction, including explicit modelling of the soil plug for open-ended piles.

And that was in 2003…and the use of the Smith model in inverse methods was proceeded by its use in forward methods such as this one.  The model he is referring to from the mid-1980’s is, of course, the Randolph and Simons (1986) model, which was used in the ZWAVE program in the late 1980’s.  The details of this model were discussed in Warrington (1997).

The Randolph and Simons model is the one which is being used for the wave equation portion of this routine, as the static component was used for the ALP static axial pile analysis.  In converting the code from the Smith model to this one, there are some things that need to be understood.  We have discussed some of these earlier but others are as follows:

  • Randolph and Simons (1985) used a visco-elastic-plastic model for both shaft and toe, the major difference being the location of the plastic slider for the shaft resistance (as is evident in the ZWAVE poster.)  Some contemporary “experimental” codes (such as Salgado, Loukidis, Abou-Jaoude and Zhang (2015)) add a series of springs and masses to replicate the soil mass that surrounds the piles.  While these doubtless enhance the performance of the models, we stuck with the simple visco-elastic-plastic model in TAMWAVE because these are better replicated in true 3D continuum models like STADYN.  1D code is good because of its simplicity, especially with an online routine like TAMWAVE.
  • The 1′ segment/element lengths are carried over to the wave equation.  This is shorter than is customarily used even in commercial work but it saves interpolation of the properties along the shaft.
  • The “Smith-type” damping constants are simply the damping of the element computed divided by its ultimate/plastic resistance.  Unlike the Smith model, however, the damping force does not vary with the instantaneous static resistance, but is simply the velocity multiplied by the damping constant and the ultimate resistance of that element, be it shaft or toe.  Thus different Smith type constants should be expected from the model being used.  Additionally, with the shaft resistance, the resistance of a shaft segment is limited to its ultimate static resistance.  This means that all additional damping forces must take place during elastic shearing of the soil surface.  Implicit in the Randolph and Simons model is that, once plasticity is achieved, the soil closest to the pile is effectively decoupled from the soil mass, and thus the pile movement can no longer radiate additional energy into the soil.  The result of this is that, as seen here, the Smith-type damping constants are much higher than one would normally assign.  Corte and Lepert (1985), in a direct comparison of the two models, note that the two give nearly the same result if the original Smith damping constants are multiplied by 7.5 for the new model.  Dividing the new result by this brings the damping constants much closer, especially in the lower reaches of the pile where most of the shaft resistance is found, although the ratio of 7.5 should be regarded as study-specific.  Bringing some rationality to the issue of damping constants would go a long way to improve the results of pile dynamics, forward and inverse, since variations of these have a significant impact on the results.
  • We mentioned earlier that the toe quakes that resulted seemed high for this size of pile.  This may be due to the fact that “significant residual pressures are locked in at the pile base during installation (equilibriated by negative shear stresses along the pile shaft, as if the pile were loaded in tension.)  This will lead to a stiffer overall pile response in compression, and significantly higher end-bearing stresses mobilised at small displacements.”  (Randolph, 2003)  He goes on to state that “(f)or driven closed ended-piles the residual stress will be lower, but may still be as high as 75% of the base capacity…”  There are two ways to deal with this.  The first is to run the ALP program first and preload the base and shaft before using the resulting prestressed deflections to run the wave equation analysis.  This would be in effect a residual stress analysis (RSA,) which has been used in this field for many years.  The second is to use a “quick and dirty” method, i.e., to reduce the toe quake and thus simulate the higher toe stiffness and lower quake.  The latter was adopted in TAMWAVE, although one motivation from switching from P4XC3 to ALP was to make an RSA easier.  This is a possible point of future modification of the code.
  • A change not related to the pile-soil interaction is the elimination of slack computation, as the pile is uniform and continuous (the hammer-cap and cap-pile interface is obviously inextensible.

Initial Wave Equation Input

For our example the initial input of the wave equation is shown below.

Screenshot_20180105_232257

Most of the data required has been carried over from the static analysis.  The hammer database was added in 2010; however, it was reordered in ascending rated striking energy order and a hammer was suggested using the “initial guess” criterion in the Soils and Foundations Handbook, which essentially suggests to set the initial hammer energy in ft-lbs at 8% of the ultimate capacity in pounds.  This is a “rule of thumb” designed to help students who, faced with a wave equation program for the first time, will have some idea of where to start, although there is no guarantee that the hammer will be either too large or small.  Since the energies are sorted, the user can move up or down the list to try another hammer.

The cushion material properties of the hammer, and the coefficient of restitution used to model cushion plasticity, are discussed (with sample properties) in the WEAP87 documentation.  No attempt was done to either convert coefficients of restitution to viscous damping or alter the rebound curve as was done in ZWAVE.  Pile cushion thickness is only input for concrete piles; the input is not shown for others.

References

In addition to those already cited, the following is included:

Corte, J.-F., and Lepert, P. (1986) “Lateral resistance during driving and dynamic pile testing.”  Proceedings of the Third International Conference on Numerical Methods in Offshore Piling, Nantes, France, 21-22 May.  Paris: Éditions Technip, pp. 19-34.