Posted in Soil Mechanics

Computing Pore Water Pressure and Effective Stress in Upward (and Downward) Flow in Soil

Water flow through soil–and the whole subject of permeability–is one of those topics that tends to mystify students in undergraduate soil mechanics courses.  This article will deal with one type of flow–flow that is purely vertical, downward or upward–and show how it is possible to compute the pore water pressure and effective stress in soils with vertical water flow.

Hydrostatic Case

We’ll start with the hydrostatic case, classic in the determination of effective stresses in many soil strata.  The pore water pressure is computed by the equation usually written in this way:

u=\gamma_w z

where u is the pore water pressure, \gamma_w is the unit weight of the water, and z is the distance from the phreatic surface/water table, where by definition z = 0 .

Let us write this equation more generally, thus

\Delta u=\gamma_w \Delta z

where \Delta u is the change in the pore water pressure from some elevation 1 in the soil to some other elevation 2 in the soil, and \Delta z is the change in elevation from point 1 to point 2.  As a condition, since z is positive in the downward direction, \Delta z is likewise positive in the downward direction.

With soil layers and total stress, we routinely “pile on” the stresses from layer to layer, because the unit weight of the soil changes.  For hydrostatic water, we usually don’t because the unit weight of the water is considered a constant.

Vertically Flowing Water

With flowing water, although the unit weight of the water is a constant, the effect it has on effective stress changes.  For this case we can expand the previous equation to read as follows (from Verruijt, A., and van Bars, S. (2007). Soil Mechanics. VSSD, Delft, the Netherlands.):

\Delta u=\gamma_w \Delta z\left( i + 1 \right)

38

Note that we have added the hydraulic gradient into the mix, defined in the figure to the right.

This drawing shows a classic case of vertical, downward flow.  The coefficient of permeability k can be computed using methods described in Department of the Army (1986) — Laboratory Soils Testing for granular soils.  However, we can also use this test–or problems based on this test–to consider the effect of the flowing water on the effective stress, which in turn leads us to consider the topic of soil boiling when the flow is upward.  The best way to see how this works is to consider an example.

Upward Flow Example

Consider the permeameter setup below.  We will concentrate on the constant head permeameter on the left.  The soil sample is in grey, with a length L and an area A.

EM-1110-2-1906-163

There is a distance H1 from the top of the soil sample to the surface of the water above it.  There is an additional distance H2 from that water surface to the water surface of the constant head tank.

Now consider an example with the following parameters:

  • H1 = 0.5 m
  • H2 = 2.5 m
  • L = 2 m
  • \gamma_{sat} = 19 \frac{kN}{m^3}

Compute the effective stress at a point halfway between the upper and lower surfaces of the soil sample.

First, we compute the total stress at the top of the soil, thus

\sigma_t\mid_{z=0.5} = 0.5 m \times 9.8 \frac{kN}{m^3} = 4.9 kPa

Because the total stress at this point is due to free water, the pore water pressure u\mid_{z=0.5} = 4.9 kPa , and thus \sigma'_{vo} = 0 .

On the lower surface of the soil sample, the total stress is

\sigma_t\mid_{z=3} = 0.5 m \times 9.8 \frac{kN}{m^3} + 2.5\times 19\frac{kN}{m^3} = 52.4 kPa

The pore water pressure, however, is due to the free water that begins in the constant head tank and ends at the bottom surface of the soil, thus

u\mid_{z=3} = \left( 2.5 + 0.5 + 2 \right)\times 9.8 \frac{kN}{m^3} = 49 kPa

The effective stress at this point is 52.4 – 49 = 3.4 kPa.

So how do we compute the effective stress at the midpoint in the soil sample?  Let us revisit the equation

\Delta u=\gamma_w \Delta z\left( i + 1 \right)

And determine the pore water pressure at the midpoint.  We first want to compute the hydraulic gradient of the entire specimen, substituting yields

\Delta u\mid_{z=3} = 49 - 4.9 = 44.1 kPa = 9.8 \times 2.5 \left( 1+i \right)

Solving for the hydraulic gradient yields i = 0.8 .

Now we substitute this result back into the equation, changing the distance \Delta z = 1.25 m .  Keeping in mind that positive z is downwards, we start from the top of the soil sample.  The change in pore water pressure from the surface is

\Delta u\mid_{z=1.75} = 9.8 \times 1.25 \left( 1 + 0.8 \right) = 22.25 kPa

Adding the pore water pressure at the soil’s upper surface yields u = 4.9 + 22.25 = 26.95 kPa.  The total stress at this point is

\sigma_t\mid_{z=1.75} = 0.5 m \times 9.8 \frac{kN}{m^3} + 1.25\times 19\frac{kN}{m^3} = 28.65 kPa

The effective stress is simply 28.65 – 26.95 = 1.7 kPa.  Since this is the middle of the layer, we would expect this stress to be the average of the effective stress at the top of the soil and the bottom, which in fact is the case.  But we can use this technique to compute the pore water pressure at any point in the soil.

Comments

  • The hydraulic gradient is very high; in fact, the critical hydraulic gradient for this soil is 0.94, leaving us with a factor of safety of 1.17.  This is reflected in the very low effective stresses that result.  Had the critical hydraulic gradient been exceeded, the effective stresses would have been negative.  Many “textbook” problems of this nature actually exceed any sensible range of hydraulic gradients because they don’t compute it as a part of the solution.  The soil in this case is about to “boil” (or at least put significant upward pressure on the filter material.)
  • Many students wonder why the formula for the hydraulic gradient i=\frac{\Delta h}{\Delta l} cannot be applied directly.  The reason is simple: even with moving water, the direct hydrostatic effect due to gravity does not go away, and has to be considered.  Thus we have the term \left( i + 1 \right) rather than just i .
  • Had the flow been downward, the hydraulic gradient would have been negative, and the effective stresses would have increased relative to hydrostatic stresses rather than decreased.
  • As long as the flow is vertical, this equation can be used with flow net type problems as well.
  • The critical hydraulic gradient equation can be derived using this equation.  As mentioned above, the critical hydraulic gradient is reached when the effective stresses in the soil are zero.  Assuming that we’re starting at the upper surface where the effective stress is zero, at the lower surface of the soil sample (or soil element in a flow net) the effective stress is zero when the total stress and pore water pressure is zero, or

\gamma_{sat} \Delta z = \gamma_w \Delta z\left( i + 1 \right)

Solving for i_{crit} yields

i_{crit} = \frac{\gamma_{sat}}{\gamma_w} - 1

which is in fact the case.

  • We can also solve the problem to determine the hydraulic head at a point in the soil.  We start by modifying our equation as follows:

\Delta h=\Delta z\left( i + 1 \right)

For this problem, at the centre of the layer, we would start by solving for the hydraulic gradient, or

5 - 0.5=2.5\left( i + 1 \right)

where the left hand side represents the total change in hydraulic head from the upper to the lower surface of the soil.  As before i = 0.8 .

Now we use the equation directly to solve for the hydraulic head at the centre of the layer, thus

\Delta h=1.25\left( 0.8 + 1 \right) = 2.25 m

This must be added to the hydraulic head already at the surface, or 2.25 + 0.5 = 2.75 m.  By changing the value of \Delta z we can compute this change at any point and add it to the head at the upper surface.

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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.

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.  Excess pore pressure due to cavity expansion during driving is estimated using the method described by Randolph (2003).  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, preventing negative values when the total elevated pore water pressure exceeds the total pressure of the soil.  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.