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 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.

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.