Wave Loads on piers/piles 1

[WARose]

The situation: I have been asked to review a design for seismic and wave loading criteria by a engineering firm.

Job description: A steel structure supported on a heavy reinforced concrete mat, that is supported by reinforced concrete piles (about 4' in diameter), that cantilever up from the MWL (Mud Water Line) at heights varying from 25' to 50'. The piles are spaced at about 24' on centers. According to a outside consultant (who was asked about max. wave case, scour, max water height, etc.), the water height will never reach the mat. (Even in a worse case storm.) The "outside consultant" gave us worse case wave crest height and period. (Based on fetch, worse case storm wind velocity, etc.)

My concern: The FEA model (as it stands now) only has the static/breaking wave load (as per ASCE 7-10) inputted. It's like this thing is sitting in air: there is no accounting for the fact it is sitting in water. I think we need to go a bit deeper in separate cases. For the seismic case, since the SDC is forcing a modal analysis (should have mentioned that before), I think we need to be as accurate as possible to capture the behavior of it being in water. For the wave load case, the fact that a dynamic analysis shows that the structure has natural periods (with the majority of the mass participating) at just about the same period as the wave loading given by the "outside consultant"....makes me think a time-history analysis is in order here.

My Questions (in bold):

1. The forcing functions for most wave loading applications I have found are just to complicated to input (as is) into the FEA software I have. Therefore, I was thinking of working up the force applied as a function of time, and inputting that as a (simplified) sinusoidal function. Or perhaps just putting in the raw force vs. time that the equations yield. (Which I can do with my software.) Does this seem like a reasonable approach to you?

2. I am uncertain as to how to represent this thing sitting in the water. (I.e. the drag as it is setting into motion.) I was thinking about a multi-linear spring support. Any ideas as to the best way to represent this?

3. I usually specify damping by mode. In the modes that include the water drag (as it is set into motion).....what damping to consider? It will be a composite of the concrete pile stiffness (i.e. concrete damping) and the water dragging. But I don't have a clue on the water part. What would you specify for damping for the water drag?

 

[msquared48]

There is a NAFAC design manual for wave force determination.

I used it in 1984 to design a floating wharf and pier system on Tinea in the Pacific.

Don't remember the number.

Mike McCann, PE, SE (WA)

 

[Ussuri]

Is this any different to the design of an offshore platform? Would referring to something like API RP 2A be any use?

A simple method.

You would assess your wave motion criteria for your given design seastate (whether that's a 100, 1000, 10000 year storm), depending on your wave heights and water depth you would pick one of the wave theories that fit best (airy, stokes nth order, stream function etc). For a given phase (say 0 degree) calculate your horizontal and vertical wave velocities and accelerations, these will vary with depth. Calculate your current profile, again varying with depth. Then using this data and Morisons Equation you can calculate the force on each member, again depth varying.

Next step your wave through the structure, say now a phase of 15 degrees, and repeat. Then 30 degrees, repeat etc.

This will give you an idea of the total load on the structure, base shear, overturning and individual load on each element.

Doesn't consider any of the more complicated effects like shielding or diffraction, but it is a good start.

I would model the pile/soil interaction as s series of springs, but the spring constant will vary with soil depth. Again API RP 2GEO has methods for assessing the spring stiffnesses.

The simple models I have run in the past, using this approach the hydrodynamic load is applied as series of UDL's, varying with respect to wave phase, and analysed as a non-linear (non-dynamic) analysis, in which case do you need damping?

 

[WARose]

Is this any different to the design of an offshore platform?

I've never done one of those so I couldn't say.

You would assess your wave motion criteria for your given design seastate (whether that's a 100, 1000, 10000 year storm), depending on your wave heights and water depth you would pick one of the wave theories that fit best (airy, stokes nth order, stream function etc). For a given phase (say 0 degree) calculate your horizontal and vertical wave velocities and accelerations, these will vary with depth. Calculate your current profile, again varying with depth. Then using this data and Morisons Equation you can calculate the force on each member, again depth varying.

Next step your wave through the structure, say now a phase of 15 degrees, and repeat. Then 30 degrees, repeat etc.

This will give you an idea of the total load on the structure, base shear, overturning and individual load on each element.

Interesting approach. I had kind of envisioned doing something similar......but since the wavelength is similar to the pile spacing....it may not be necessary.

....in which case do you need damping?

In any case that involves the structure's movement in water. The piles resist later movement and their damping will be included.....the water does the same thing (via drag). But I am unsure what to specify for that aspect of it.

 

[Ussuri]

I'm not sure what you mean about the wavelength versus the pile spacing?

Working in the funny SI system, you are in about 15m of water so very shallow. I'm not sure what range of wave heights and periods you have, but you could be on or past the breaking limit. I have assumed max wave height of 10m and associated period of 8s which is about the breaking limit.

4 inch piles (100mm diameter). Say Drag on the pile is 0.5 x rho x Cd x A x V^2. If I assume an average horizontal velocity of 3m/s, Cd = 1.05, rho = 1025kg/m^3, A = 0.1m x 15m then I get 7.3kN drag due to wave alone (need to add in current effect and inertia as well). Cantilevered from seabed 7.3kN x 15m/2 = 55kNm. Based on soooo many assumptions and simplifications.

Below is wave component velocities and accelerations based on a regular wave. You can get much more complicated and go for full irregular wave/wave spectra if you wanted.

Water Depth 15 Wave Height 10 Wave period 8
9 Order Stream Function
d/gT**2 = 0.02389 H/gT**2 = 0.01593
Wavelength = 93.95
Max Surface Elevation = 7.473

Phase Angle (Deg) = 0.000

Depth Vh Vv Ah Av Pressure
0.000 4.476 0.000 0.000 -2.849 0.4469
m m/s m/s m/s2 m/s2 Bar


7.473 10.823 0.000 0.000 -1.662 -0.0392
5.226 7.784 0.000 0.000 -4.001 0.1110
2.979 5.974 0.000 0.000 -3.700 0.2470
0.731 4.780 0.000 0.000 -3.058 0.3954
-1.516 3.945 0.000 0.000 -2.440 0.5585
-3.763 3.344 0.000 0.000 -1.899 0.7350
-6.011 2.912 0.000 0.000 -1.432 0.9231
-8.258 2.605 0.000 0.000 -1.024 1.1212
-10.505 2.401 0.000 0.000 -0.660 1.3283
-12.753 2.284 0.000 0.000 -0.323 1.5434
-15.000 2.246 0.000 0.000 0.000 1.7661

Motions at Elevation 0.000

Phase SurfaceEl Vh Vv Ah Av Pressure
Deg m m/s m/s m/s2 m/s2 Bar

0.000 7.473 4.476 0.000 0.000 -2.849 0.4469
6.000 6.507 4.404 0.607 0.902 -2.721 0.4395
12.000 5.461 4.195 1.172 1.695 -2.370 0.4184
18.000 4.566 3.876 1.665 2.310 -1.873 0.3860
24.000 3.780 3.477 2.069 2.735 -1.320 0.3452
30.000 3.075 3.028 2.380 3.000 -0.774 0.2989
36.000 2.436 2.551 2.604 3.144 -0.263 0.2494
42.000 1.855 2.065 2.746 3.192 0.209 0.1983
48.000 1.328 1.582 2.815 3.153 0.636 0.1472
54.000 0.852 1.116 2.817 3.033 1.003 0.0973
60.000 0.423 0.677 2.764 2.851 1.292 0.0500
66.000 0.038 0.272 2.667 2.636 1.499 0.0058
72.000 -0.308
78.000 -0.618
84.000 -0.895
90.000 -1.140
96.000 -1.357
102.000 -1.548
108.000 -1.716
114.000 -1.864
120.000 -1.992
126.000 -2.103
132.000 -2.198
138.000 -2.279
144.000 -2.347
150.000 -2.403
156.000 -2.448
162.000 -2.482
168.000 -2.507
174.000 -2.522
180.000 -2.527

 

[WARose]

Thanks for the feedback Ussuri. I think I’ve resigned myself to the fact I’m probably going to have to use max. amplitude everywhere and use the worst frequency (for the dynamics of the structure). There are just so many piles (i.e. hundreds)....I can’t make a swiss watch here.

What is your opinion on the damping situation (question #3 in my OP)? Sounds like this isn’t your first trip to the rodeo so I’d be interested in hearing your opinion.

 

[Ussuri]

I'm not sure if I have an answer for you. In my experience damping is usually included for dynamic/frequency types of analysis (eg structures applied subjected to accelerations). For the simple structures I have done the hydrodynamic load is applied as a static load representing one point in time during the wave cycle. There are then multiple static load cases representing the different phases as the wave passes through.

The analysis is non-linear but primarily due to the soil/structure interaction. The water surrounding the structure is not usually explicitly modelled. At least, not in anything I have done.

The effect of the pile movement through the water is included in the added mass (mass x acceleration terms) in Morison's equation. Apologies if this is a bit simplistic, in order to move the pile through the water you must also displace the water surrounding it (i.e the force needed to move the pile is the force required to move the mass of the pile plus the force required to move the water out of the way). This extra force is accounted for by 'adding mass' to the pile buy use of added mass coefficients. Although I'm not sure that helps you.

 

[Settingsun]

Just pointing out the trap of switching between units. The piles are 4' not 4": 1220mm not 100mm

Warose, what are the wave parameters? If the wavelength is around 24' (7.3m) then the wave height would be low and the period 2-2.5 seconds. Or did you mean the wavelength is a multiple of the pile centres?

 

[Ussuri]

Good catch, I did think it seemed small.

WARose, I have had a look in API RP 2A. Lots of stuff about how to address damping. Our structures are small and subsea so we don't consider it.

 

[WARose]

Correct. The "outside consultant" called late yesterday and said that wavelength is wrong. (Actually much larger.)

Thanks for the damping info Ussuri.