Closure to “Prediction of Pile Capacity by the Wave Equation”

This paper will show on the basis of hindcast wave equation analysis that soil-pile set-up for large diameter driven pipe piles in clay is faster than what the current state-of-practice utilizes for design. Results of hindcast wave equation analyses utilizing observed blowcounts and hammer energy records from two deepwater sites, one in West Africa and the other one in the Gulf of Mexico, are presented to support this conclusion. For offshore structures, this increase in the rate of soil-pile set-up reduces foundation/anchor costs or reduces the waiting time until topsides can be set on the structure or mooring lines can be hooked up to anchors. Hindcast wave equation analyses were performed utilizing the observed blowcount and hammer energy information from two deepwater West Africa and Gulf of Mexico locations where pile driving was stopped and then restarted after a few days. This is a trial and error method of analysis where the soil resistance to driving (SRD) was varied until a good match was obtained between the observed blowcount at the startup of driving and the reported hammer energy using the GRLWEAP wave equation program. The set-up time for the piles ranged from about one to twelve (12) days and the piles ranged from 2134 mm to 2743 mm diameter open-ended pipe piles. The soils generally consisted of normally to slightly overconsolidated highly plastic clays. For the purpose of computing pile set-up, the ultimate pile capacity was computed using the API RP 2A (2000) guidelines. Results show that 60 to 80 percent of the ultimate pile capacity is mobilized in about 7 days, and the extrapolation of the set-up model suggests that the set-up is almost complete in about 60 days.

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Discussion of “Prediction of Pile Capacity by the Wave Equation”

Journal of the Soil Mechanics and Foundations Division ◽

10.1061/jsfeaq.0000674 ◽

1964 ◽

Vol 90 (6) ◽

pp. 207-209

Author(s):

Teddy J. Hirsch ◽

Charles H. Samson ◽

E. A. L. Smith

Keyword(s):

Wave Equation ◽

Pile Capacity

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The Three-Dimensional Wave Equation

Fundamentals of Geophysics ◽

10.1017/9781108685917.014 ◽

2020 ◽

pp. 394-396

Keyword(s):

Wave Equation ◽

Three Dimensional ◽

Dimensional Wave

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The wave equation in spherical coordinates

Theory of Reflectance and Emittance Spectroscopy ◽

10.1017/cbo9780511524998.017 ◽

1993 ◽

pp. 420-427

Keyword(s):

Wave Equation ◽

Spherical Coordinates

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Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

Al-Jabar Jurnal Pendidikan Matematika ◽

10.24042/ajpm.v11i1.5153 ◽

2020 ◽

Vol 11 (1) ◽

pp. 93-100

Author(s):

Vina Apriliani ◽

Ikhsan Maulidi ◽

Budi Azhari

Keyword(s):

Wave Equation ◽

Exact Solutions ◽

Internal Waves ◽

Water Waves ◽

Wave Equations ◽

Elliptic Functions ◽

Expansion Method ◽

Mkdv Equation ◽

Innovative Methods ◽

De Vries

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations.

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