Posted in TAMWAVE

TAMWAVE 4: Shaft Resistance Profile, ALP and CLM2

With the basic parameters established, we can turn to the static analysis of the pile, both axial and lateral.

Shaft Resistance Profile

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 48.4 0.163 0.0022 0.009 4.03 45.394 0.009
1.50 83.9 0.163 0.0038 0.027 6.99 19.911 0.027
2.50 108.3 0.163 0.0050 0.045 9.02 13.572 0.045
3.50 128.1 0.163 0.0059 0.063 10.68 10.543 0.063
4.50 145.3 0.163 0.0067 0.081 12.11 8.730 0.081
5.50 160.6 0.164 0.0074 0.098 13.38 7.509 0.098
6.50 174.6 0.164 0.0080 0.116 14.55 6.623 0.116
7.50 187.6 0.164 0.0086 0.134 15.63 5.948 0.134
8.50 199.7 0.164 0.0091 0.152 16.64 5.414 0.152
9.50 211.1 0.164 0.0097 0.170 17.59 4.980 0.170
10.50 222.0 0.164 0.0102 0.188 18.50 4.618 0.188
11.50 232.3 0.164 0.0106 0.206 19.36 4.313 0.206
12.50 242.2 0.164 0.0111 0.224 20.18 4.050 0.224
13.50 251.7 0.164 0.0115 0.242 20.98 3.822 0.242
14.50 260.9 0.164 0.0120 0.260 21.74 3.621 0.260
15.50 269.8 0.164 0.0124 0.278 22.48 3.444 0.278
16.50 278.4 0.164 0.0128 0.296 23.20 3.285 0.296
17.50 286.7 0.164 0.0132 0.314 23.89 3.142 0.314
18.50 294.8 0.164 0.0135 0.332 24.57 3.013 0.332
19.50 302.7 0.164 0.0139 0.351 25.22 2.895 0.351
20.50 310.4 0.164 0.0143 0.369 25.86 2.787 0.369
21.50 317.9 0.164 0.0146 0.387 26.49 2.688 0.387
22.50 325.2 0.164 0.0149 0.405 27.10 2.597 0.405
23.50 332.4 0.165 0.0153 0.423 27.70 2.512 0.423
24.50 339.4 0.165 0.0156 0.441 28.29 2.434 0.441
25.50 346.3 0.165 0.0159 0.460 28.86 2.361 0.460
26.50 353.1 0.165 0.0162 0.478 29.42 2.292 0.478
27.50 359.7 0.165 0.0166 0.496 29.98 2.228 0.496
28.50 366.3 0.165 0.0169 0.515 30.52 2.168 0.515
29.50 372.7 0.165 0.0172 0.533 31.06 2.112 0.533
30.50 379.0 0.165 0.0175 0.552 31.58 2.058 0.552
31.50 385.2 0.165 0.0178 0.570 32.10 2.007 0.570
32.50 391.3 0.166 0.0181 0.589 32.61 1.960 0.589
33.50 397.4 0.166 0.0183 0.607 33.11 1.914 0.607
34.50 403.3 0.166 0.0186 0.626 33.61 1.871 0.626
35.50 409.2 0.166 0.0189 0.645 34.10 1.830 0.645
36.50 415.0 0.166 0.0192 0.664 34.58 1.790 0.664
37.50 420.7 0.166 0.0195 0.683 35.06 1.753 0.683
38.50 426.4 0.166 0.0197 0.702 35.53 1.717 0.702
39.50 432.0 0.167 0.0200 0.721 36.00 1.682 0.721
40.50 437.5 0.167 0.0203 0.740 36.46 1.649 0.740
41.50 443.0 0.167 0.0206 0.759 36.92 1.618 0.759
42.50 448.4 0.167 0.0208 0.778 37.37 1.587 0.778
43.50 453.8 0.168 0.0211 0.798 37.82 1.558 0.798
44.50 459.1 0.168 0.0214 0.817 38.26 1.530 0.817
45.50 464.4 0.168 0.0216 0.837 38.70 1.502 0.837
46.50 469.6 0.168 0.0219 0.856 39.13 1.476 0.856
47.50 474.8 0.169 0.0221 0.876 39.56 1.450 0.876
48.50 479.9 0.169 0.0224 0.896 39.99 1.426 0.896
49.50 485.0 0.169 0.0227 0.916 40.42 1.402 0.916
50.50 489.1 0.169 0.0229 0.933 40.76 1.382 0.933
51.50 492.3 0.170 0.0231 0.947 41.03 1.367 0.947
52.50 495.5 0.170 0.0233 0.960 41.30 1.352 0.960
53.50 498.7 0.171 0.0234 0.974 41.56 1.337 0.974
54.50 501.9 0.171 0.0236 0.988 41.83 1.323 0.988
55.50 505.1 0.171 0.0238 1.002 42.09 1.308 1.002
56.50 508.3 0.172 0.0240 1.016 42.36 1.294 1.016
57.50 511.5 0.172 0.0242 1.031 42.63 1.280 1.031
58.50 514.7 0.173 0.0244 1.045 42.89 1.266 1.045
59.50 517.9 0.173 0.0246 1.060 43.16 1.252 1.060
60.50 521.1 0.174 0.0248 1.075 43.42 1.238 1.075
61.50 524.3 0.174 0.0250 1.091 43.69 1.224 1.091
62.50 527.5 0.175 0.0252 1.106 43.96 1.211 1.106
63.50 530.7 0.176 0.0254 1.122 44.22 1.197 1.122
64.50 533.9 0.176 0.0256 1.139 44.49 1.184 1.139
65.50 537.1 0.177 0.0258 1.155 44.76 1.170 1.155
66.50 540.4 0.178 0.0260 1.172 45.03 1.157 1.172
67.50 543.6 0.178 0.0262 1.189 45.30 1.144 1.189
68.50 546.9 0.179 0.0265 1.207 45.57 1.130 1.207
69.50 550.2 0.180 0.0267 1.224 45.85 1.117 1.224
70.50 553.5 0.181 0.0269 1.243 46.12 1.104 1.243
71.50 556.8 0.182 0.0272 1.262 46.40 1.091 1.262
72.50 560.1 0.183 0.0274 1.281 46.68 1.078 1.281
73.50 563.5 0.184 0.0277 1.300 46.96 1.065 1.300
74.50 566.9 0.185 0.0280 1.321 47.24 1.051 1.321
75.50 570.3 0.186 0.0282 1.341 47.52 1.038 1.341
76.50 573.7 0.187 0.0285 1.363 47.81 1.025 1.363
77.50 577.2 0.188 0.0288 1.385 48.10 1.012 1.385
78.50 580.7 0.190 0.0291 1.407 48.39 0.999 1.407
79.50 584.3 0.191 0.0294 1.431 48.69 0.985 1.431
80.50 587.9 0.193 0.0297 1.455 48.99 0.972 1.455
81.50 591.5 0.194 0.0300 1.479 49.29 0.959 1.479
82.50 595.2 0.196 0.0303 1.505 49.60 0.945 1.505
83.50 598.9 0.197 0.0307 1.532 49.91 0.932 1.532
84.50 602.7 0.199 0.0310 1.559 50.22 0.919 1.559
85.50 606.5 0.201 0.0314 1.587 50.54 0.905 1.587
86.50 610.4 0.203 0.0318 1.617 50.87 0.891 1.617
87.50 614.4 0.205 0.0322 1.647 51.20 0.878 1.647
88.50 618.4 0.207 0.0326 1.678 51.53 0.864 1.678
89.50 622.5 0.210 0.0330 1.711 51.87 0.850 1.711
90.50 626.7 0.212 0.0334 1.745 52.22 0.837 1.745
91.50 630.9 0.215 0.0339 1.781 52.58 0.823 1.781
92.50 635.2 0.217 0.0343 1.817 52.94 0.809 1.817
93.50 639.7 0.220 0.0348 1.856 53.30 0.795 1.856
94.50 644.2 0.223 0.0353 1.896 53.68 0.781 1.896
95.50 648.8 0.226 0.0358 1.937 54.07 0.767 1.937
96.50 653.5 0.229 0.0364 1.981 54.46 0.753 1.981
97.50 658.3 0.233 0.0369 2.026 54.86 0.739 2.026
98.50 663.3 0.236 0.0375 2.073 55.27 0.725 2.073
99.50 668.3 0.240 0.0381 2.122 55.69 0.710 2.122

The results should be self explanatory; however, some observations are in order.

  • A 1′ increment was used for the analysis.  This will be carried over to both the static and dynamic axial analyses.  For this routine it’s probably overkill, but for a real system with multiple soil layers this eliminates a great deal of interpolation and adjustment.
  • Both the shear modulus and the maximum shear stress on the shaft surface vary with effective stress.  This tends to homogenise the quake to some degree.  The increase of shear modulus with depth also increases the shaft element stiffness as well.
  • Beta values are about 50% higher at the pile toe than at the pile head.  This is mostly due to the depth effect of the K value computed by the method used.
  • The resulting quakes are lower than the “traditional values.”  This varies from run to run.
  • The Smith-type damping constants are considerably higher than is usually expected.  This will be discussed with the wave equation analysis itself.
  • There is no difference between ultimate capacity and SRD with this run because of the cohesionless soils.  This will change with cohesive ones.

ALP Program

The original routine used the PX4C3 routine to construct the axial load-deflection curve.  For this routine it was replaced by the ALP program, which is described in Verruijt.  The Turbo Pascal code in the text was converted to php and modified for the online application.  The ALP99 program, which allows for layered soils, has been used in a classroom setting, is a good program but has three serious weaknesses:

  1. There is no guidance on what values of quake to use for either shaft or toe, and for beginners this is very confusing.
  2. The guidance on entering shaft resistance properties is primitive, to say the least.
  3. The program simply crashes if a resistance in excess of the ultimate resistance is entered, even though the latter is easily computed.

This online version of ALP addresses all of these by limiting the highest resistance during the “load test” and furnishing quake and resistance values all along the shaft and toe.

The basic parameters of ALP returned by TAMWAVE are shown below.

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. 202,673
Quake of the point, in. 0.879
Number of pile elements 100
Number of loading steps 20
Maximum pile load, lbs. 572,676.9
Load Increment, lbs. 57,267.7
Failure Load, lbs. 572,676.9

Some of these are repetitious from earlier data output.  The results of the actual “load test” are shown below.

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 57.3 0.033 22
2 114.5 0.082 39
3 171.8 0.144 52
4 229.1 0.216 64
5 286.3 0.300 74
6 343.6 0.395 85
7 400.9 0.601 100
8 343.6 0.571 10
9 286.3 0.534 22
10 229.1 0.489 31
11 171.8 0.437 39
12 114.5 0.378 45
13 57.3 0.314 52
14 0.0 0.244 58

The program ceases to load the pile and begins to unload when all of the shaft friction is mobilised or the ultimate load is achieved, whichever comes first.  This is intended to prevent the routine from going unstable with the applied load too near the maximum capacity of the pile, thus violating static equilibrium.

ALP solves the system by constructing a tridiagonal matrix and then solving the non-linear problem.  In some cases it will achieve a result before coming to actual convergence according to the convergence criterion.  In such cases ALP will report that no convergence was achieved.

alpimage
Plotted Results
x-axis = Pile Head Force
y-axis = Pile Head Deflection
Plot Limits:
x-axis from 0.000 to 400.874
y-axis from 0.000 to 0.601

One new feature with the current version of TAMWAVE is the inclusion of two basic graphs of the results.  This is one of them.  Contrary to American practice, the deflection (y) axis is upward even though the actual deflection is downward.  For serious plotting purposes it is probably best for the student to copy and paste the results into a spreadsheet or other plotting program and then make the results look more presentable.

CLM 2 Routine for Lateral Loads

To analyse lateral pile loading, the CLM2 Method is employed. Details on this method can be found with the CLM 2 spreadsheet here. Some notes about this are as follows:

  • The analyser is for single piles only, no group or bent analysis.
  • The following cases can be considered:
    • Free (Pinned) Head, Lateral Force Only
    • Free Head, Moment Only
    • Free Head, Combined Force and Moment
    • Fixed Head, Lateral Force Only
  • Any lateral load or pile head moment is entered when the soil properties are confirmed. If zero load or moment is entered, the results are expanded or truncated accordingly.

For this example the results of the CLM 2 analysis are here.

Data for Lateral Load Analysis using CLM2 Method
Nominal Soil Unit Weight, lb/in3 0.06944
Pile Moment of Inertia, in4 1,728.00
Pile Section Modulus, in3 288.00
Pile Solid Circle Moment of Inertia, in4 1,017.88
Moment of Inertia Ratio Ri 1.698
Pile Moment of Inertia Ratio Product, ksi 8,488.3
Pile-Soil Interaction Variable 97,803
Pile L/D Ratio 100.0
Characteristic Load, lbs. 2,745,232.8
Characteristic Moment, in-lbs. 196,821,533.6
Pile Head Fixity Free
Pile Head Lateral Load, lbs. 5,000.0
Pt/Pc 0.00182
Yt/D 0.00800
Pile Head Deflection due to Load, inches 0.096
Maximum Moment Due to Pile Head Lateral Load, in-lbs 136,112.3
Maximum Bending Stress Due to Pile Head Lateral Load, in-lbs 472.6

The results are explained in the CLM 2 documentation.  The bending stresses are not really meaningful in concrete piles, as flexure is generally transmitted through the reinforcement.  Parametric studies must be run manually, i.e., one load at a time.

CLM 2 is a quick way to obtain estimates of lateral loads, shears and moments for groundline piles and simple soil profiles, and both of these are present in TAMWAVE.  Since all of the soil input is already done, this source of error is eliminated.

Once these results are complete, the user can proceed to run a wave equation analysis.

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