OFFSHORE TECHNOLOGY CONFERENCE 6200 North Central Expressway
Dallas, Texas 75206
On the Appi ¡cation of MorisonTs Equation
to Fixed Offshore P'atforms
By
TECHNISCHE UNIVERSITEIT
Bruce G. Wade and Mike Dwyer, J. Ray McDermott & Co.
tabOFOrIumor
Arch lof
Mekelweg 2,2628 CD Detft rei-Q1578687'Fo15 181838
©Copyright 1976
Offshore Technology Conference on behalf of the American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. (Society of Iviining Engineers, The Metallurgical Society and Society of Petroleum Engineers), American Association of Petroleum Geologists, American Institute of Chemical Engineers, American Society of Civil Engineers, American Society of Mechanical Engineers, Institute of Electrical and Electronics En-gineers, Marine Technology Society, Society of Exploration Geophysicists, and Society of Naval Architects and Marine Engineers.
This paper was prepared for presentation at the Eighth Annual Offshore Technology Conference, Houston, Tex., May 3-6, 1976. Peimission to copy is restricted to ari abstract of not more than 300 words. li!ustrations may not be copied. Such use of an abstract should contain conspicuous acknowledgment of where and by whom the paper is presented.
THIS PAPER IS SUBJECT TO CORRECT/ON
PAPER
NUMBER 010 2723
ABSTRACT
Several methods are presented for calculating wave forces acting on
tubu-lar members of fixed offshore platforms. Each is within the guidelines set forth in American Petroleum Institute's RP 2A. The formulation of the methods considerec
are based upon several interpretations of the application of Morison's equation to randomly oriented tubular members. This paper presents a comparison of
these various methods with idcntical de-sign conditions and demonstrates de-
signif-icant differences between the methods. Horizontal and vertical water particle motions of a design wave were determined by Stokes Fifth Order Wave Theory. These kinematic vectors were used in calcula-tions with each of the wave force meth-ods on two deep water platforms, four-pile and eight-four-pile template structures,
to ompare the horizontal base shears and overturning moments. Comparisons between the methods are made using nuni-erous crest locations and several wave approach directions with respect to the global axes of the platforms. Variation of base shears and overturning moments between the methods considered were found to exceed 22% despite the fact that all the methods are within proced-ures generally accepted by industry.
Ex-ferences and illustrations at end of
paper.
elusion of vertical water particle velo-cities in any method resulted in small changes in base shear and overturning moment whereas the method of calcula-tion was found to produce significant differences in these quantities.
INTRODUCTION
Numerous technical papers, texts, and offshore design codes (Refs. i to 7) have referenced Morison's equation for determining hydrodynamic forces on small tubular structural elements. The
i1orison equation (8) includes terms for both drag and inertial forces. The drag term includes a drag coefficient, CD, and water particle velocity, while the inertia term involves an inertial co-efficient, Cm, and water particle acceleration. This equation is appli-cable to small objects (compared to the wave length) where wave kinematics do not change appreciably over a distance equal to the width of the structural e lenìent. Mor ison 's equa t ion is more
nearly correct when used to determine the hydrodynamic force on a small cylin-drical body that is in a vertical
at-titude. However, when a cylinder is
randomly orientated with respect to the mudline, there is considerable question
concerning the application of the Morison equation.
Borgman (9), Ippen (2), and Bursnall, et. al. (12), and more re-cently Chakarbrati, et. al. (lo) and Morgan, et. al. (11) have shown how Morison's equation for a vertical cylinder may be applied to a cylindri-cal member orientated in a random manner with respect to the mudline. A review of these papers reveal that there are a variety of methods for calculating wave forces acting on tubular members of fixed offshore platforms. Four differ-ent methods are presdiffer-ented in this paper, each of which is within procedures gen-erally used by industry (4), for compu-ting wave forces on a randomly oriented cylindrical member. The formulation of the methods considered are based upon various interpretations of the appli-cation of Morison's equation. Many of the wave force calculation methods pre-sented herein have been prepre-sented
prev-iously by other authors. This paper presents a comparison of these various methods with identical design condi-tions and demonstrates significant differences between the methods.
The wave force equations as in-troduced by Morison, et. al. (8) is:
+CmY1tDAx
(1) where U arnd x are the horizontal waterparticle velocity and acceleration vec-tors respectively acting on a cylinder of diameter D that is perpendicular to the mudline in water of mass density
It may be noted that both water particle kinematic vectors are normal to the cylinder and consequently the pressure vector, P, will be acting in a direction parallel to the mudline. Wave induced motion, however, includes both horizontal and vertical kinematic com-ponents. Furthermore, except for con-ductors, offshore platforms rarely have cylindrical members that are perfectly
vertical. In each of the wave force calculation methods presented, it is assumed that the total water particle velocity vector is:
U=Ux+y
(2)and similarly the total acceleration vector is:
(3)
'-.
where the subscripts x and y denote components parallel and perpendicular to the mudline respectively. An
appli-cable water surface wave theory (e.g. Stokes Fifth Order, Cnoidal, or Dean Wave Theories) may be used to determine the kinematic resultants U and A. The question remains, however, how to apply Equation (2) and (3) in Equation (1). This question is answered by consider-ing four different wave force calcu-lation methods, which are briefly summarized in Table I.
DEVELOPMENT OF WAVE FORCE CALCULATION METHODS
1. METHOD A
Method A assumes that the drag and inertial force resultants, FD
and Fi respectively, act on a projected area of a cylinder that is inclined about a normal to the mudline. Figure 1 illustrates the essential features of this method. The velocity and acceleration vectors flow past an elliptical cross section whose major axis is always parallel to the in-stantaneous direction of flow. It should be noted that the drag and in-ertial coefficients, CD' and Cm' re-spectively, change according to the shape of the elliptical section of the
inclined member and hence will vary from one end of a member to the other. Consequently, numerous drag and iner-tial coefficients must be specified in order Lo cover the wide ranges of
elliptical crôss sections encountered over a niember's length. Because the major axis of the elliptical cross section must always be parallel to the direction of flow, its drag coefficient, CD', will be less than the drag coeffi-cient for a circular cross section, CD, over all ranges of Reynolds Number (13). The differences between the drag co-efficients for circular and elliptical cross sections become negligible as the minor axis of the ellipse becomes equal to its major axis. Determining drag and inertial coefficients for all elliptical sections encountered is not
very practical and was simplified herein for purposes of comparison by assuming constant values of drag and
inertial coefficients. Particular attention should be made of Figure 1 where it is noted that the total
force, , has components acting
1182 ON THE APPLICATION OF MORISON'S EQUATION TO
TC 2723
ON TIlE APPLICATION OF MORISON'S EQUATION TO
FIXED OFFSHORE PLATFORMS 1183 in the direction of the resultant
ve-locity and acceleration vectors and that only one cosine is present for each component.
METHOD B
Method B assumes that only the components of pressure acting normal to an inclined cylinder produce loads. In Figure 2 the resultant drag and in-ertial pressures are shown resolved into normal and tangential components with respect to the longitudinal axis of the inclined cylinder. The normal components of pressure are retained while the tangentialpressures are
ig-nored. The justification for this can
be made when one considers that the coefficient of drag due to skin fric-tion is approximately 30 to 120 times smaller than the drag coefficient for transverse flow (14). Because only normal components for pressure are considered, the drag coefficient used with each method is that of a circular cross section. It should be noted that the total force
,F,
has drag and in-ertial forces that are not coplaner but both act normal to the longitudinal axis of the member. Also of note is that the final force equation for Method B contains only one cosine for each component as in Method A.METHOD C
Method C assumes that only the components of velocity and accelera-tion normal to an inclined cylinder produce loads. Figure 3 demonstrates the manner in which the drag and iner-tial pressures are developed. The nor-mal. components of water particle ve-locity and acceleration are retained while the tangential kinematic com-ponents are discarded. The
justifi-cation for this was discussed in the description of Method B. Since
nor-mal components of velocity and accel-eration are the only force producing components considered, the drag coeffi-cient used with this method is that for a circular cross section. Attention should be made of the total force F, which has drag and inertial forces that act normal to the longi-tudinal axis of the member. In general, the drag and inertial vectors will not be coplaner. Also of note is that the drag force has a cosine squared term.
Since the value of cosine will always be less than unity, it should be ex-pected that Method C would give Sig-nificantly less total horizontal base shears and overturning moments on a drag dominated jacket type platform than those predicted by Methods A and B.
Morgan, et. al. (11) recommended a method whereby the resultant drag pressure acts upon a projected area and whose force vector is in the di-rection of the normal to the inclined member. Method C as described herein corresponds to a wave force calculation method discussed by Morgan, et. al. It is interesting to note that in spite of completely different premises used to develop Method C and the wave force calculation procedure recommended by
Morgan, et. al., the final wave force equations for both methods are identi-cal except for the drag coefficients. The drag coefficient cited by Morgan, et. al., is for an elliptical cross section for the reasons cited previously and the drag coefficient for Method C is for a circular cross section.
Recently Chakrobarti, et. al. (10) has investigated wave forces on
ran-domly oriented tubes. In his devel-opment of a generalized wave force equation for inclined cylinders, he uses the same wave force calculation procedure as Method C.
METHOD D
Method D is the most conservative wave force calculation procedure con-sidered in this paper. This latter method assumes that resultant water particle velocities and accelerations always act perpendicular to the
longi-tudinal axis of an inclined member to a yaw angle of 60 degrees. Yaw angles, which in general will be unequal at each end of a member, are formed by the
included angle between the normal to the member's longitudinal axis and the resultant velocity or acceleration
vec-tors. The direction of the resultant
kinematic vectors, which are rarely normal to a member's longitudinal axis, are rotated up to 60 degrees without changing the magnitude of the vector and then applied to the entire length of an inclined member. A correction factor is applied to the resulting forces when yaw angles are greater
than 60 degrees. The yaw angle and appropriate equations are shown in Figure 4. Ippen (2) recommends that Method D, which is based upon limited
experimental evidence by Bursnall, et. al. (12), be used to compute wave
forces. It should be noted that the
equation for the total wave force, F, doe.s not contain any cosine factors as in all of the other methods considered herein.
ANALYSIS
Calculations using each of the four wave force methods were performed on two deep water platforms, a four-pile and an eight-four-pile template struc-ture, to compare the horizontal base shears and overturning moments pre-dicted by each of the four methods. A
general purpose wave load computer pro-gram was written whose input are or-bital wave velocities and accelerations, structural geometry, and various load-ing criterion constraints. A general description of each platform as well as the environmental loading criterion are summarized in Table II. The wave parameters, drag and inertial coeffi-cients, and wave theory were unchanged from the constraints given in Table II for each respective platform throughout the wave force calculation methods. Six different wava load calculations were performed on each structure, as described in Table I. It may he noted that the structural model of each plat-form is not over simplified and there-fore realistic wave loads should be expected. Boat landings, if any, as well as all of the conductors have been included for purposes of wave loading.
Comparisons between the methods were made using numerous crest lo-cations and several wave approach di-rections with respect to the global axis of the platform. Three wave approach angles were selected for each platform; a wave directed along the structure's longitudinal axis, trans-verse axis, as well as a wave perpen-dicular to a diagonal of the structure. These approach angles are denoted
herein as CO and 900 for the longitu-dinal and transverse axes for both structures. The diagonal wave approach angles aro shown schematically in
Figure 5 through 8 and are denoted
450 and 301.30 for the four-pile and eight-pile structures respectively. These angles were obtained by rotating a wave counterclockwise until its di-rection was perpenticular to the desired diagonal of the structure. The waves were stepped through the structure in five-foot increments in order to access the variation of overall horizontal base shear and overturning moment resulting from each wave loading calculation scheme.
DISCUSSION OF RESULTS
The results of the wave load analysis using each of the force calculation methods on the two
plat-forms are summarized in Tables III and IV. Typical graphical results are pre-sented in Figures 5 through 8 where the
variation of the diagonal wave induced base shear and overturning moment is presented as a function of crest
posi-tion relative to the global axis of each structure. For purposes of com-parison, all percent differences were referenced to A-1, the wave load case using the projected area calculation Method A with only horizontal wave kinematics included.
The results are surprising. The seemingly minor differences between Methods A through D result in a 22% (+10% to - 12%) variation of maximum base shear values for the four-pile structure and 17% variation of the eight-pile structure. The overturning moments are similarly spread over a 17%
and 16% range for the four-pile and eight-pile structures respectively. It was found that wave load case A-1 gave structure base shears and overturning moments that were approximately mid-way between the higher values predicted
by Method D and the lower values given by Method C. This may be explained when it is recalled that Method C
con-tained a cosine squared term in its drag component whereas Method D contained none and Method A contained only one
cosine. Jacket type offshore structures
which are predominantly drag rather than inertia dominated, would,of course, be quite sensitive to any changes in drag force calculations.
Only the variation of base shear and overturning moments induced by the diagonal wave are presented herein. The trend for the remaining wave
ap-proach angles, however, is very similar ON THE APPLICATiON OF MORISON'S EQUATION TO
to that presented in Figure 5 through
8. It becomes evident in these figures that the exclusion of vertical water particle kinematics have only a small effect, less than 2%, upon the struc-ture's base shear and overturning mo-nient. The authors included an eight-pile structure to study the effects of the vertical kinematics. It was
anticipated that the eight-pile struc-ture's long longitudinal axis would emphasize the vertical kinematic's contribution to the overturning moment. It was found that the exclusion of vertical water particle kinematics had approximately the same minimal effect upon the overturning moment in the longitudinìal direction of both the four-pile and eight-pile structures.
It is also interesting to note that the exclusion of vertical water par-ticle kinematics decreased the base shear and overturning moment in Method C and increased them in Method A.
CONCLUS IONS
Four methods are presented for calculating wave forces acting on tu-bular members of fixed offshore
plat-forms. Each method is within procedures
generally accepted by industry. Horizontal and vertical wave induced water particle kinematic vectors were used in each of the wave force methods on two deep water platforms to compare the horizontal base shear and over-turning moments. Comparisons between the wave force calculation methods were made using numerous crest loca-tions and several wave approach di-rections with respect to the global axis of the platform. Variation of base shears and overturning moments between the methods considered were found to exceed 22% despite the fact that all the methods are within
pro-cedures generally used by industry at present. The exclusion of vertical water particle velocities in any method resulted in very small changes in base shear and overturning moment, whereas the method of calculation was found to produce significant differences in these quantities. The recommendation reached by this paper is that addi-tional work is required in order to
es-tablish a uniform criteria for deter-mining wave loads for use by industry.
ACKNOWLEDGEMENTS
The authors are thankful to J. Ray McDermott & Company for giving permission to present the results of their investigation. The authors are especially indebted to Mr. Frank
Domi ngues for his helpful sugges t ions
and comments. NOMENCLATURE
A Resultant acceleration vector (ft/sec2), A = Ax + Ay
x Acceleration vector parallel to mud-line (ft/sec2)
Acceleration vector normal to mud-line (ft/sec2)
CD Morison drag coefficient for circu-lar cross section
Cj Morison drag coefficient for ellip-tical cross section
Cm Morison inertial coefficient for circular cross section
Cn Morison inertial coefficient for elliptical cross section
D Member diameter (ft)
Morison total force vector (lb/ft of member length)
FU Morison drag force vector (lb/ft of member length)
j Morison inertial force vector (lb/ft of member length)
Morison total pressure vector (lb/
ft2)
Morison inertial pressure vector
(lb/ft2)
in Normal component of i (lb/ft2) it Tangential component of j (lb/f t2)
D Morison drag pressure vector (lb/
ft2)
Normal component of D (lb/ft2) Dt Tangential compenent of D (lb/ft2)
U Resultant velocity vector (ft/see),
U = U, + Uy
i
ON THE APPLICATION OF MORISON'S EQUATION TO
fl86 FIXED OFFSHORE PLATFORMS OTC 2723
T,T,Ï
Unit vectors of local coordinate system defined by direction cosines of membern Normal velocity vector (ft/sec)
8. Morison, J. R. ,O'Brian, M.P., Johnson, J. W. and Schaaf, S. A., Tech, American Institute of Mining Engineering, Vol. 189, 1950, pp. 149-154.
ut Tangential velocity vector (ft/sec) 9. Borgman, L. E., "Computation of the Ocean-Wave Forces on I nd med
Q Yaw angle formed by resultant
ve-locity and/or acceleration vector Cylinders," J. of Geophysical Re-search, Trans., AGU, Vol. 39, No. 5
(or respective pressures in October, 1958, pp. 885-888. Method B) and normal to
longi-tudinal axis of member 10. Chakrabarti, S. K.Tam, W. A. and Woihert, A. L., "Wave Forces on a
p
Mass density of fluid (lb/ft2_sec2) Ramclomly Oriented Tube," OffshoreTechnology Conference, Paper No.
REFERENCES 2190, 1975.
1. Bretschneider, C. L., "Water Ldads
on Fixed, Rigid Marine Structures," li. Morgan, G. W. and Peret, J. W.,""Applied Mechanics of Marine Handbook of Ocean and Underwater Riser Systems, "Part IX, Petroleum
Engineering McGraw-Hill Book Co., Engineer, July, 1975, pp. 50-60.
1969.
2. Ippen, A. T., Estuary and Coastline 12. Bursnall, W."Experimental Investigation of theJ. and Loftin, L. K., Hydrodynamics, McGraw-Hill Book Pressure Distribution About a Co., 1966, pp. 341-375 Yawed Cylinder in the Critical
Reynolds Number Range, "NACA 3. Johnson E. R., "Horizontal Forces Technical Note 2463, 1951.
Due to Waves Acting on Large Ver-tical Cylinders in Deèp Water",
Naval Undersea Center, Publication 13. Delaney, N. K. and Sorensen, N. E.,"Low-Speed Drag of Cylinders of NUC TP322, October, 1972. Various Shapes," Ames Aeronautical
4. , "Design Procedures for
Laboratory, Muffett Field, Califor-nia, NACA, Technical Note 3038, Fixed, Offshore Platforms,"
Plan-ning, DesigPlan-ning, and Constructing Washington, November, 1953. Fixed Offshore Platforms, API RP 2A
American Petroleum Institute, January, 1976, pp. 9-10.
14. berner, S. F., "Pressure Drag" Fluid-Dynamic Drag, published by the author, 1965, page 3 - 5.
5. , Rules for Building and
Ux Velicity vector parallel to
mud-line (ft/sec)
Classing Offshore Mobile Drilling Units, American Bureau of Shipping.
Uy Velocity vector normal to mudline (f t/sec)
6. , Rules for the
Con-struction and Classification of Mobil Offshore Units, Det Norske
an Normal acceleration vector (ft/ sec2)
Ventas, Oslo, Norway, 1975.
7 Wiegel, R. L., "Wave Forces,"
t Tangential acceleration vector
(ft/sec2)
Oceanographical Engineering, Prentice-Hall, 1964, pp. 248-268.
TABLE i - SUMtkARY OF WAVE LOADING WETHODS
TABLE 2 - SUMMARY OF TEST STRUCTURE GEOMETRIES AND ENVIRONMENTAL LOADING Wave Load Name Method of Calculation Comments Mpthod Description A-1 A
Pressure resultant assumed to act on projected
area,
Vertical wave pressures are
excluded.
B-1 B
Resolution of resultant drag and inertial pressures into normal and tangential com'aonents. Tangential pressure components are ignored.
Horizontal and vertical wave pressures are
included.
C-1 C
Resolution of resultant velocity and acceleration into normal and tangential components.
Tangential kinematics are ignored,
Horizontal and vertical wave pressures are
included. A-2 A Pressure resultant assumed to act ori projected
area, Horizontal an-J vertical wave pressures are included. D-1 D
Resultant velocities and accelerations assumed to act normal to members. An area correction factor is applied to pressures when yaw angle is greater than 600. Horizontal and vertical wave pressures are included. C-2 C
Resolution of resultant velocity and acceleration into normal and tangential components,
Tangential kinematics are ignored,
Vertical wave pressures aro excluded. Test Structure No. 1 Test Structure No. 2 e ,..4.2 o-° n Platform Type No. of Piles Mudline Dimension. ft. x ft. No. of Conductors Conductor Size, in. Barge Bumpers
Boat Landings
Drilling & Production
4-Pile with 4 Skirt Piles
250 x 250
24 26 None Nono
Drilling & Production 8-Pile with 4 Skirt Piles
218 x 132
24 26 in.
2 double at opposite corners 6 single 2 B/3-4 & A/l-2 '
PCD
Wave Height, ft. Period, sec.Ref. Water Datum, ft.
Still Water I)epth, ft.
Current, f.p.s. Wave Theory Wind, p.s.f. 98.4 17.0 468,0 477.0 3.9&surfacctol.0@mudline 0.6 2.0 Stokes V 0.0 58.2 16.0 330.0 MLW 335.5
2.0, Const. with Depth
0.6
1.4
Stokes V
* All differences are referenced to A-1
TABLE 4 - SUMMARY OF RESULTS OF 330 MLW 8-PILE PLATFORM
*All differences are referenced to A-1
TABLE 3 * SUMMARY OF RESULTS OF 468 MLW 4-PILE PLATFORM Wave Load Name Wave Direction Degrees
Total Horizontal Base Shear Overturning
IDiff.I Ft.*. Moment Magnitude x l03ft-kips % * Diff. Location Ft. IDiff.I Ft. *KipsMagnitude % * Diff. Location Ft. 0.0 -60 0 10445 0.0 -50 0 3747 0.0 A-1 45.0 -50 0 l0..07 0.0 -35 0 3780 0.0 90.0 -60 0 9933 0.0 -50 0 3567 0.0 0.0 -60 0 10022 -4.0 -30 20 3581 -4.4 B-1 45.0 -60 0 9769 -7.0 -35 0 3485 -7.8 90.0 -65 5 9448 -4.9 -30 20 3369 -5.6 0.0 -70 10 9888 -5.3 -35 15 3509 -6.4 C-1 45.0 -70 10 9403 -10.5 -35 0 3339 -11.7 90.0 -65 5 9270 -6.7 -30 20 3291 -7.7 0.0 -60 0 10495 0.5 -30 20 3723 -0.6 A-2 45.0 -65 5 10447 -0.6 30 5 3710 -1.9 90.0 -65 5 10055 1.2 -30 20 3561 -0.2 0.0 -110 50 11487 10.0 -80 30 3931 4.9 D-1 45.0 -100 40 11516 9.6 -80 45 3939 4.2 90.0 -120 60 10965 10.4 -70 20 3746 5.0 0.0 -60 0 9735 -6.8 -30 20 3486 -7.0 C-2 45.0 -65 5 9245 -12.0 -35 0 3314 -12.3 90.0 -65 5 9099 -8.4 -30 20 3259 -8.6 Wave Load Name Wave Direction Degrees
Total Horizontal Baso Shear Overturning Moment
Loca tien Ft. Dii f .1 Ft. * Magnitude Kips * Diff. Location Ft. IDiff .1 Ft. * Magnitude xlO3ft-kips % * Diff. -0.0 -50 0 3398 0.0 -45 0 789 0.0 A-1 90.0 -30 0 3722 0.0 -30 0 895 0.0 301.3 -40 0 3749 0.0 -35 0 892 0.0 0.0 -50 0 3261 -4.0 -45 0 751 -4.8 B-1 90.0 -30 0 3614 -2.9 -30 0 867 -3.1 301.3 -40 0 3524 -6.0 -35 0 837 -6.2 0.0 -50 0 3187 -6.2 -45 0 731 -7.4 C-1 90.0 -30 0 3546 -4.7 -30 0 853 -4.7 301.3 -45 5 3386 -9.7 -40 5 804 -0.9 0.0 -45 5 3421 0.7 -45 0 779 -1.3 A-2 90.0 -30 0 3690 -0.9 -15 15 877 -2.0 301.3 -30 10 3711 -1.0 -25 10 871 -2.4 0.0 -85 35 3620 6.5 -85 40 829 5.1 D-1 90.0 -75 45 3994 7.3 -70 40 947 5.8 301.3 -80 40 3989 6.4 -75 40 938 5.2 0.0 -50 0 3172 -6.7 -45 0 735 -6.8 C-2 90.0 -30 0 3528 -5.2 -30 0 851 -4.9 301.3 -40 0 3369 -10.1 -35 0 804 -9.9
LIII 0F 1011 00U11 S a a
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Fig. 2
Fig. 3
Fig. 4
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Fig. 7 - Distance from crest, D, Ft.
0243441001 01 (01*1 640E 080*60 10018 04 I 004 FT 8196 -PItE P111(064 433*0804 *4013 001.3 0.0 9.0 8.0 7.0 40 3.8 36 3.0 o -LOO I
:.:
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re-I c-L c-0U *
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F I L-020 -000 -80 -60 -40 -20 Fig. 6 - Distance from crest, D, Ft.
Fig. 5 - Distance from crest, D, Ft. 009 84*1104 0F 030IL 3104101418 409(40 4CIINC
COIPAIISOI 03 101*0 3413 16(163 80114E 08 4 08 8 4(1F1. 9104 -PILE P080(311
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Fig. 8 - Distance from crest, D, Ft4
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